source,target
ichhicl can‘ only Ilbe iuterpreted;erpretedTaw as aat;on=3.107: we can exclude the alternative identification as aat 2=0.339. because in this case. we would have also detected the llinc.," which can only be interpreted as at $z=3.107$; we can exclude the alternative identification as at $z=0.339$, because in this case, we would have also detected the line."
 At:ie[Dcoutzibnte107. the lline may senificautlv to the A baud flux. but object cannot be a reflection nebula. as eudssion is also detected in the Ro baud.which is free ofstrong ciission lines.," At $z=3.107$, the line may contribute significantly to the $K-$ band flux, but object cannot be a reflection nebula, as emission is also detected in the $R-$ band,which is free ofstrong emission lines."
 Object therefore appears to be a companion, Object therefore appears to be a companion
and therefore the atmospheric circulation for this planet is unconstrained at this point in (ime.,and therefore the atmospheric circulation for this planet is unconstrained at this point in time.
 Clouds would further complicate the appearance of the planets Gansmission spectrum bv efficiently scattering starlight at short wavelengths., Clouds would further complicate the appearance of the planet's transmission spectrum by efficiently scattering starlight at short wavelengths.
 At longer wavelengths in the mid-IR. the spectrum of GJ 1214b should remain mostly unaffected by clouds.," At longer wavelengths in the mid-IR, the spectrum of GJ 1214b should remain mostly unaffected by clouds."
 Qualitativelv. in the optical and near-Lt. clouds can flatten the planets transmission spectrum by scattering lieht ab higher altitudes than where spectral features in transmission are expected (o originale.," Qualitatively, in the optical and near-IR, clouds can flatten the planet's transmission spectrum by scattering light at higher altitudes than where spectral features in transmission are expected to originate."
 For GJ 1214b. we have previously found Chat clouds at pressures greater (han 200 mbar can explain the observations of a flat. transmission spectrum [rom 780 ιο 1000 nm by ?..," For GJ 1214b, we have previously found that clouds at pressures greater than 200 mbar can explain the observations of a flat transmission spectrum from 780 to 1000 nm by \citet{bea10}."
 This value was determined by cutting olf transmission al different heights in the planets abmosphere (o simulate the effects of an optically thick grav. cloud. deck., This value was determined by cutting off transmission at different heights in the planet's atmosphere to simulate the effects of an optically thick gray cloud deck.
 Clouds. deeper in the atmosphere than 200 mbar would have only a minimal effect on the Uiransnission spectrum at the wavelengths of the ? observations., Clouds deeper in the atmosphere than 200 mbar would have only a minimal effect on the transmission spectrum at the wavelengths of the \citet{bea10} observations.
 Η clouds are present. the exact shape of (he transmission spectrum at short wavelengths is determined by whether the scattering is occurring within (he Ravleieh or Mie regime. which will produce different power law slopes for the scattering opacity.," If clouds are present, the exact shape of the transmission spectrum at short wavelengths is determined by whether the scattering is occurring within the Rayleigh or Mie regime, which will produce different power law slopes for the scattering opacity."
 Unfortunately. sell-consistentlv modeling the cloud opacity requires knowledge of the cloud particle size and heieht distributions. which are currently. unknown for GJ 1214b.," Unfortunately, self-consistently modeling the cloud opacity requires knowledge of the cloud particle size and height distributions, which are currently unknown for GJ 1214b."
 Here we offer up some suggestions For what the cloud composition could be., Here we offer up some suggestions for what the cloud composition could be.
 Clouds are formed by condensation processes. which will occur if the partial pressure of a species surpasses its vapor or condensation pressure.," Clouds are formed by condensation processes, which will occur if the partial pressure of a species surpasses its vapor or condensation pressure."
 To determine whether cloud formation will occur in the atmosphere of GJ 1214b. we compare the planets T-P profile against the condensation curves of various molecules that are predicted to condense in hot planet and cool star atmospheres from ?..," To determine whether cloud formation will occur in the atmosphere of GJ 1214b, we compare the planet's T-P profile against the condensation curves of various molecules that are predicted to condense in hot planet and cool star atmospheres from \citet{lod06}."
 The only molecules (hat we find whose condensation curves intersect the predicted T-P profile of GJ 1214b are ACT and Zn5. as shown in Figure 7.. although we caution that the T-P profile of GJ 1214b is unconstrained by observations. so ils exact shape is somewhat uncertain.," The only molecules that we find whose condensation curves intersect the predicted T-P profile of GJ 1214b are KCl and ZnS, as shown in Figure \ref{f7}, although we caution that the T-P profile of GJ 1214b is unconstrained by observations, so its exact shape is somewhat uncertain."
 If (he T-P profile from Figure 7 is correct. (hen both KC and Zus should condense at pressures of ~500 mbar in GJ 1214b's aüimosphere at solar composition.," If the T-P profile from Figure \ref{f7} is correct, then both KCl and ZnS should condense at pressures of $\sim$ 500 mbar in GJ 1214b's atmosphere at solar composition."
 For hieher metallicities a wmuber of effects come into play which can shift the condensation to either higher or lower pressure in GJ 1214b's atmosphere., For higher metallicities a number of effects come into play which can shift the condensation to either higher or lower pressure in GJ 1214b's atmosphere.
 These effects are (1) the abunelaces of condensate materials tend to be higher at higher Z. (2) (the condensation curves for condensate species tend to shift to hisher temperature Le. to the right on Figure due to the increased vapor pressure of (he heavy elements in (he eas phase. ancl (3) the T-P profile tends to shift up aud to risht on Figure 7 due to the increased opacities from higher," These effects are (1) the abundaces of condensate materials tend to be higher at higher Z, (2) the condensation curves for condensate species tend to shift to higher temperature i.e. to the right on Figure \ref{f7} due to the increased vapor pressure of the heavy elements in the gas phase, and (3) the T-P profile tends to shift up and to right on Figure \ref{f7} due to the increased opacities from higher"
The velocity pattern is evolved in time by introducing changes to the spectral cocficicuts based ou two processes - the advection by the axisviunuetric flows (cliffereutial rotation aud meridional flow) and raudoni processes that lead to the finite lifetimes of the cells.,The velocity pattern is evolved in time by introducing changes to the spectral coefficients based on two processes - the advection by the axisymmetric flows (differential rotation and meridional flow) and random processes that lead to the finite lifetimes of the cells.
 The advection is governed by an advection equation where wis a velocity component. C(0)=rsindQ) eives the differcutial rotation profile and (0) eives the meridional flow velocity profile.," The advection is governed by an advection equation where $w$ is a velocity component, $U(\theta) = r \sin \theta \Omega(\theta)$ gives the differential rotation profile and $V(\theta)$ gives the meridional flow velocity profile."
 Representing was a series of spherical harmonie componcuts (Eqs., Representing $w$ as a series of spherical harmonic components (Eqs.
 1-3) aud projecting this advection equation outo a single spherical harmonic gives a series of coupled equations for the evolution of the spectral coefficients. (Appendix Aj)., 1-3) and projecting this advection equation onto a single spherical harmonic gives a series of coupled equations for the evolution of the spectral coefficients (Appendix A).
 Solid. body. rotation siauplv introduces a constantly mereasing phase for cach coefficient., Solid body rotation simply introduces a constantly increasing phase for each coefficient.
 Differential rotation couples the phase chauge iu one spectral cocfiicicut to spectral coefficients with svaveuunbers (+2 aud (+| for differential rotation of the form while a simple but reasonable meridional flow profile with couples one spectral coefficient to spectral coefficieuts with wavemmubers (2. (, Differential rotation couples the phase change in one spectral coefficient to spectral coefficients with wavenumbers $\ell \pm 2$ and $\ell \pm 4$ for differential rotation of the form while a simple but reasonable meridional flow profile with couples one spectral coefficient to spectral coefficients with wavenumbers $\ell \pm 2$. (
Spherical harimonies have fixed latitudinal structure.,Spherical harmonics have fixed latitudinal structure.
 Spectral power niust pass frou one spherical harmonic component to another in order to move a feature in latitudo.), Spectral power must pass from one spherical harmonic component to another in order to move a feature in latitude.)
 These cellular flows are embedded iu the Suus surface shear laver., These cellular flows are embedded in the Sun's surface shear layer.
 We approximate the chauee in the rotation rate in the outermost of the Sun as reported by Ioweetal.(2007) with where and the latitude dependence is given by Asstuning that the cells extend to depths similar to their horizoutal dimeusious. aud that they are advected at flow rates represcutative of that depth. Eq.," We approximate the change in the rotation rate in the outermost of the Sun as reported by \citet{Howe07} with where and the latitude dependence is given by Assuming that the cells extend to depths similar to their horizontal dimensions, and that they are advected at flow rates representative of that depth, Eq."
 9 is transformed into a fiction of ( with This shear laver profile is illustrated in Fig., 9 is transformed into a function of $\ell$ with This shear layer profile is illustrated in Fig.
 2 along with the eradieuts expected from theoretical argueimoeuts for flows that conserve augular momenta., 2 along with the gradients expected from theoretical arguements for flows that conserve angular momentum.
 We assunie a meridional flow which is coustaut with depth across this laver aud has a latitude dependence characterized by which eives a peak iieridional How velocity of Ίδης Lat 15? latitude., We assume a meridional flow which is constant with depth across this layer and has a latitude dependence characterized by which gives a peak meridional flow velocity of $15 \ \rm m \ s^{-1}$ at $45\degr$ latitude.
 The finite lifetimes for the cells are simulated bv introducing raudom perturbations to the spectral coefficient phases., The finite lifetimes for the cells are simulated by introducing random perturbations to the spectral coefficient phases.
 The size of these perturbations increaseswith wavenumber to give shorter lifetimes to smaller cells with where δρ) is the chauge in phase for a complex spectral cocficient of deeree 6 auc order i. Af is the time interval between simulated Doppler nuages. aud r(() is proportional to the lifetime or a spectral component of degree f.," The size of these perturbations increaseswith wavenumber to give shorter lifetimes to smaller cells with where $\delta\Phi_\ell^m$ is the change in phase for a complex spectral coefficient of degree $\ell$ and order $m$, $\Delta t$ is the time interval between simulated Doppler images, and $\tau(\ell)$ is proportional to the lifetime for a spectral component of degree $\ell$."
 Lifetimes are well approximated by a tfuur-over time for urbulent convective flows., Lifetimes are well approximated by a turn-over time for turbulent convective flows.
 The cellular flow velocities are roughly proportional to ( while heir diameters are inversely proportional to f., The cellular flow velocities are roughly proportional to $\ell$ while their diameters are inversely proportional to $\ell$.
 The turn-over times should then be inversely . 2 qvo ≻↥⋅≺∏⋯↥⋅⊓∪∐⋜↧↕↑∪↙−∙↖, The turn-over times should then be inversely proportional to $\ell^2$ .
↖↸∖∏∐≼↧⋜↕↥⋅↸∖⋜↧↴∖↴∪∐⋜∏⋝↕↸∖∏↑↑∪p ⋅ he data using, We find a reasonable fit to the data using
"The data cube is obtained from the sky brightness temperature 3D map T4,(@,6,v) by applying the frequency or wavelength dependent instrument response R(u,v,2).","The data cube is obtained from the sky brightness temperature 3D map $T_{sky}(\alpha, \delta, \nu)$ by applying the frequency or wavelength dependent instrument response ${\cal R}(u,v,\lambda)$."
" We have considered the simple case where the instrument response is constant throughout the survey area, or independent of the sky direction."," We have considered the simple case where the instrument response is constant throughout the survey area, or independent of the sky direction."
" For each frequency v; or wavelength A,—c/v;: The LSS signal extraction depends indeed on the white noise level.", For each frequency $\nu_k$ or wavelength $\lambda_k=c/\nu_k$: The LSS signal extraction depends indeed on the white noise level.
" The results shown here correspond to the (a) instrument configuration, a packed array of 11x=121 dishes (5 meter diameter), with a white noise level corresponding to 0.25mK per 3x3arcmin?500 kHz cell."," The results shown here correspond to the (a) instrument configuration, a packed array of $11 \times 11 = 121$ dishes (5 meter diameter), with a white noise level corresponding to $\sigma_{noise} = 0.25 \mathrm{mK}$ per $3 \times 3 \mathrm{arcmin^2} \times 500$ kHz cell."
 A brief description of the simple component separation procedure that we have applied is given here:, A brief description of the simple component separation procedure that we have applied is given here:
There is a minor discrepancy at early times (t«8Gyr) in the cooled mass generated by the two modelling techniques.,There is a minor discrepancy at early times $t<8$ Gyr) in the cooled mass generated by the two modelling techniques.
 'This is unlikely to be due to differences in cooling from the hot halo: given the similar density distributions (Fig. [4)), This is unlikely to be due to differences in cooling from the hot halo: given the similar density distributions (Fig. \ref{halogas}) )
" and cooling function, the two models should yield similar amounts of cooled gas, all else being equal."," and cooling function, the two models should yield similar amounts of cooled gas, all else being equal."
 'The discrepancy is also not due to a difference in the time of development of a hot gas halo., The discrepancy is also not due to a difference in the time of development of a hot gas halo.
 The top panel of Fig., The top panel of Fig.
" 4 shows that accreted gas in the model transitions from unshocked, cold gas to shocked, hot gas at an age of about 2 Gyr, while the bottom panel shows that this time is also when the model begins to develop a hot gas halo."," 4 shows that accreted gas in the model transitions from unshocked, cold gas to shocked, hot gas at an age of about 2 Gyr, while the bottom panel shows that this time is also when the model begins to develop a hot gas halo."
 This demonstrates that the adopted analytic separation of unshocked and shocked gas (free fall limited regime versus cooling limited regime) is an excellent analog to the transition between cold gas accretion and shocked gas accretion seen in simulations as a galaxy crosses the threshold mass capable of developing a hot halo., This demonstrates that the adopted analytic separation of unshocked and shocked gas (free fall limited regime versus cooling limited regime) is an excellent analog to the transition between cold gas accretion and shocked gas accretion seen in simulations as a galaxy crosses the threshold mass capable of developing a hot halo.
" It is important to note that this transition has always been included in analytic models of galaxy formation, and thus cold gas accretion at low galaxy mass does not alter the standard picture of galaxy formation."," It is important to note that this transition has always been included in analytic models of galaxy formation, and thus cold gas accretion at low galaxy mass does not alter the standard picture of galaxy formation."
 The discrepancy in cooled mass arises after the development of this hot halo., The discrepancy in cooled mass arises after the development of this hot halo.
 The simulated galaxy continues to accrete cold gas via filaments that penetrate within the hot gas halo (see Fig., The simulated galaxy continues to accrete cold gas via filaments that penetrate within the hot gas halo (see Fig.
" here, figure 5 of and also OcvirketB|al.(2008),, Agertzetal. and Dekeletal. (2009))), while cold gas accretion ends in the analytic model."," \ref{accretion} here, figure 5 of \scite{Brooks09} and also \scite{Ocvirk08}, \scite{Agertz09} and \scite{Dekel09}) ), while cold gas accretion ends in the analytic model."
" Brooksetal.(2009) demonstrated that the inclusion of cold gas accretion along filaments leads to an earlier phase of star formation than predicted if all gas was initially shock heated, due to the shorter cooling times onto the central galaxy of the cold gas."," \scite{Brooks09} demonstrated that the inclusion of cold gas accretion along filaments leads to an earlier phase of star formation than predicted if all gas was initially shock heated, due to the shorter cooling times onto the central galaxy of the cold gas."
 Fig., Fig.
" 12 shows that the simulated galaxy does indeed form stars earlier than the analytic model, though the overall discrepancy is never more than a factor of two."," 12 shows that the simulated galaxy does indeed form stars earlier than the analytic model, though the overall discrepancy is never more than a factor of two."
 In an attempt to adapt the simulations to include similar physics as theanalytic," In an attempt to adapt the to include similar physics as the model, Fig."
" model, Fig. ?? shows the effect on the stellar growth in the simulations if all of the cold gas had instead been shocked.", \ref{DelayedGrowth} shows the effect on the stellar growth in the simulations if all of the cold gas had instead been shocked.
 The hot gas has cooling times several Gyr longer than the cold gas., The hot gas has cooling times several Gyr longer than the cold gas.
" This is quantified, and a delay has been added to the formation time of the stars spawned from the cold accreted gas (Brooksetal.2009)."," This is quantified, and a delay has been added to the formation time of the stars spawned from the cold accreted gas \cite{Brooks09}."
". As seen in Fig. ??,,"," As seen in Fig. \ref{DelayedGrowth},"
 this delay leads to a slower build of up stellar mass in the simulations., this delay leads to a slower build of up stellar mass in the simulations.
" Comparison with shows this to be in even better agreement with the stellar growth of the analytic model, which neglects this cold gas accretion along filaments."," Comparison with \ref{baryons} shows this to be in even better agreement with the stellar growth of the analytic model, which neglects this cold gas accretion along filaments."
" In order to represent the same physical assumptions as this particular simulation, the semi-analytic code had to be significantly modified from the version which has been used most recently to study the collective properties of galaxy samples (Boweretal.2006;Stringer2009)."," In order to represent the same physical assumptions as this particular simulation, the semi-analytic code had to be significantly modified from the version which has been used most recently to study the collective properties of galaxy samples \cite{Bower06,Stringer09}."
". There are three very significant differences between this version of and the simulation studied here, all of which are manifest in the comparison of the history of the simulation and the Boweretal.(2006) model (Fig. ??))."," There are three very significant differences between this version of and the simulation studied here, all of which are manifest in the comparison of the history of the simulation and the \scite{Bower06} model (Fig. \ref{Bower}) )."
" When there are instabilities refDiskStability)) or merger events in this model which trigger disk collapse, of the available disk gas is assumed to accrete onto a central black hole."," When there are instabilities \\ref{DiskStability}) ) or merger events in this model which trigger disk collapse, of the available disk gas is assumed to accrete onto a central black hole."
" If the following criteria are satisfied, it is assumed that no hot halo gas will be able to cool onto the disk."," If the following criteria are satisfied, it is assumed that no hot halo gas will be able to cool onto the disk."
 This effect is visible in Fig., This effect is visible in Fig.
 ?? as a period of rapidly decreasing cold gas mass; during such phases it is no longer being replenished by gas cooling in from the halo., \ref{Bower} as a period of rapidly decreasing cold gas mass; during such phases it is no longer being replenished by gas cooling in from the halo.
" This is assumed to be extremely strong in the Boweretal.(2006) model, the justification being that a moremodest conversion of supernova energy to gas outflow would allow the formation of too many low-mass galaxies. ("," This is assumed to be extremely strong in the \scite{Bower06} model, the justification being that a moremodest conversion of supernova energy to gas outflow would allow the formation of too many low-mass galaxies. ("
"Indeed, it","Indeed, it"
programs. such as that at the UMRAO (Alleretal.1985.1999) which has tracked the integrated flux and polarization evolution of scores of AGN for decades at weekly or bi-weekly intervals.,"programs, such as that at the UMRAO \citep{AALH85,AAHL99} which has tracked the integrated flux and polarization evolution of scores of AGN for decades at weekly or bi-weekly intervals."
 With the VLBA it is now possible to monitor a large number of parsec scale jets at closely spaced. regular intervals. and here we present the first analysis of data of this type for flux and polarization variability.," With the VLBA it is now possible to monitor a large number of parsec scale jets at closely spaced, regular intervals, and here we present the first analysis of data of this type for flux and polarization variability."
 In this paper we focus on the overall variability properties of our sample to find common trends in the flux and polarization evolution of core regions and jet features., In this paper we focus on the overall variability properties of our sample to find common trends in the flux and polarization evolution of core regions and jet features.
 Section describes our sample. data reduction. and model-fitting procedures.," Section describes our sample, data reduction, and model-fitting procedures."
 Statistical methods used in analyzing the variability properties of our VLBI observations are discussed in$3., Statistical methods used in analyzing the variability properties of our VLBI observations are discussed in.
. We present and discuss our results in and summarize them in35., We present and discuss our results in and summarize them in.
. The Appendix explores a by-produet of our variability analysis — specifically. empirical estimates of the uncertainties in. the measurement of VLBI component properties.," The Appendix explores a by-product of our variability analysis -- specifically, empirical estimates of the uncertainties in the measurement of VLBI component properties."
 In all calculations presented here. we assume a universe with Oy20.3. Q420.7 and Hy=70 km s! Mpe!.," In all calculations presented here, we assume a universe with $\Omega_M=0.3$, $\Omega_\Lambda=0.7$ and $H_{0}=70$ km $^{-1}$ $^{-1}$ ."
" For spectral index we follow the convention. S,,«vt""."," For spectral index we follow the convention, $S_\nu \propto \nu^{+\alpha}$."
 We used the VLBA to conduct a series of six observations. each of 24 hour duration. at close to two month intervals during the year 1996.," We used the VLBA to conduct a series of six observations, each of 24 hour duration, at close to two month intervals during the year 1996."
 The observations were made at 15 GHz (42.0 em. U-band) and 22 GHz (A1.3 em. K-band).," The observations were made at 15 GHz $\lambda$ 2.0 cm, U-band) and 22 GHz $\lambda$ 1.3 cm, K-band)."
 We observed 11 target sources for six epochs and one (J12244-21) for only the last five epochs., We observed 11 target sources for six epochs and one (J1224+21) for only the last five epochs.
 These sources are listed in table 1.., These sources are listed in table \ref{t:Sources}.
 The epochs of observation during 1996 were the following: January 19th (1996.05). March 22nd (1996.23). May 27th (1996.41). July 27th (1996.57). September 27th (1996.74). and December 6th (1996.93).," The epochs of observation during 1996 were the following: January 19th (1996.05), March 22nd (1996.23), May 27th (1996.41), July 27th (1996.57), September 27th (1996.74), and December 6th (1996.93)."
 The sources were chosen from those regularly monitored by the University of Michigan Radio Astronomy Observatory (UMRAO) in total intensity and polarization at 4.8. 8.0. and 14.5 GHz.," The sources were chosen from those regularly monitored by the University of Michigan Radio Astronomy Observatory (UMRAO) in total intensity and polarization at $4.8$, $8.0$, and $14.5$ GHz."
 They were selected according to the following criteria. (, They were selected according to the following criteria. (
1) High total intensity: The weakest sources are about I Jy. the most powerful as much as 22 Jy. (,"1) High total intensity: The weakest sources are about 1 Jy, the most powerful as much as 22 Jy. ("
2) High polarized flux: Typically over 50 mJy. (,2) High polarized flux: Typically over 50 mJy. (
3) Violently variable: In both total and polarized intensity.,3) Violently variable: In both total and polarized intensity.
 Such sources are likely to be under-sampled by annual VLBI. (, Such sources are likely to be under-sampled by annual VLBI. (
4) Well distributed in right ascension: This allowed us to make an optimal observing schedule.,4) Well distributed in right ascension: This allowed us to make an optimal observing schedule.
 Most of the UMRAO sources meet the first three of the above criteria., Most of the UMRAO sources meet the first three of the above criteria.
 The 12 actually selected were the strongest. most violently variable sources. subject to the fourth eriteria.," The 12 actually selected were the strongest, most violently variable sources, subject to the fourth criteria."
" Clearly these sources do not comprise a “complete sample"" in any sense.", Clearly these sources do not comprise a “complete sample” in any sense.
 The frequency agility and high slew speeds of the VLBA antennas were used to schedule our observations to generate maximal (u.v)-coverage.," The frequency agility and high slew speeds of the VLBA antennas were used to schedule our observations to generate maximal (u,v)-coverage."
 Scan lengths were kept short (13 minutes for the first two epochs and 5.5 minutes for the last four). with à switch in frequency at the end of each scan.," Scan lengths were kept short (13 minutes for the first two epochs and 5.5 minutes for the last four), with a switch in frequency at the end of each scan."
 In addition. scans of neighboring sources were heavily interleaved at the cost of some additional slew time.," In addition, scans of neighboring sources were heavily interleaved at the cost of some additional slew time."
 Each source. was observed for approximately 45 minutes per frequency at each epoch., Each source was observed for approximately 45 minutes per frequency at each epoch.
 The data were correlated on the VLBA correlator in Socorro. NM.," The data were correlated on the VLBA correlator in Socorro, NM."
 After correlation. the data were distributed on DAT tape to Brandeis University where they were loaded into NRAO'sAstronomical Imaging Processing System (AIPS) (Bridle&Greisen1994;1988) and calibrated using standard techniques for VLBI polarization observations. e.g.. (Cotton1993;Roberts.Wardle&Brown1994).," After correlation, the data were distributed on DAT tape to Brandeis University where they were loaded into NRAO'sAstronomical Imaging Processing System (AIPS) \citep{BG94,G88} and calibrated using standard techniques for VLBI polarization observations, e.g., \citep{C93,RWB94}."
. For a detailed description of our calibration steps see Paper IIL., For a detailed description of our calibration steps see Paper III.
 One point that bears mentioning here is our calibration of the polarization position angle (also called the Electric Vector Position Angle or EVPA)., One point that bears mentioning here is our calibration of the polarization position angle (also called the Electric Vector Position Angle or EVPA).
 Our EVPAs were set at each epoch and at both 15 and 22 GHz by aligning the strong jet component. Ul (ΚΙ. in 2279 to an angle of 67.," Our EVPAs were set at each epoch and at both 15 and 22 GHz by aligning the strong jet component, U1 (K1), in 279 to an angle of $67^\circ$."
 This orientation is roughly parallel with the structural position angle for this component and is within 5° of the independently calibrated observations of Leppiinnen.Zensus&Diamond(1995).. Taylor(1998).. and Homan&Wardle(2000) whose epochs of observation bracket our own.," This orientation is roughly parallel with the structural position angle for this component and is within $5^\circ$ of the independently calibrated observations of \citet{LZD95}, \citet{T98}, and \citet{HW00} whose epochs of observation bracket our own."
 By examining the other sources in our sample. we see no evidence that this component in 2279 has significant Faraday rotation at these frequencies or varies in EVPA during our observations.," By examining the other sources in our sample, we see no evidence that this component in 279 has significant Faraday rotation at these frequencies or varies in EVPA during our observations."
 As a result of this EVPA calibration procedure. our internal consistency between epochs is very good with uncertainties z2—3 degrees on the most robust jet features (see the Appendix).," As a result of this EVPA calibration procedure, our internal consistency between epochs is very good with uncertainties $\approx 2-3$ degrees on the most robust jet features (see the Appendix)."
 Figure 1. compares our 15 GHz VLBA observations of JOS30+13 (PKS 0528+134) and J1751+09 (OT O81) to the single dish monitoring done by the UMRAO at 14.5 GHz., Figure \ref{f:compare} compares our 15 GHz VLBA observations of $+$ 13 (PKS $+$ 134) and $+$ 09 (OT 081) to the single dish monitoring done by the UMRAO at 14.5 GHz.
 The total fluxes and polarizations from our CLEAN maps agree quite well with the independent UMRAO results in all six of the VLBI epochs., The total fluxes and polarizations from our CLEAN maps agree quite well with the independent UMRAO results in all six of the VLBI epochs.
 The two sources plotted in figure 1. are quite compact. and the VLBA observations account for nearly all of the single dish flux.," The two sources plotted in figure \ref{f:compare} are quite compact, and the VLBA observations account for nearly all of the single dish flux."
 Although a detailed comparison ts difficult. on the more extended sources. such as 1120 and 2273. we see a nearly constant offset between the VLBA and single dish monitoring. and the VLBI core and jet seem to account for essentially all of the observed variability in the single dish monitoring.," Although a detailed comparison is difficult, on the more extended sources, such as 120 and 273, we see a nearly constant offset between the VLBA and single dish monitoring, and the VLBI core and jet seem to account for essentially all of the observed variability in the single dish monitoring."
 Given this. it may be possible to use frequent single dish monitoring to help interpolate between the more widely spaced VLBI epochs to follow the evolution of parsec-scale core and jet features.," Given this, it may be possible to use frequent single dish monitoring to help interpolate between the more widely spaced VLBI epochs to follow the evolution of parsec-scale core and jet features."
 To parameterize our data for quantitative analysis. we used the model fitting capabilities of the DIFMAP software package (Shepherd.Pearson&Taylor1994.1995). to fit the sources with a number of discrete Gaussian components.," To parameterize our data for quantitative analysis, we used the model fitting capabilities of the DIFMAP software package \citep{SPT94,SPT95} to fit the sources with a number of discrete Gaussian components."
 The fitting was done directly on the final. self-calibrated visibility data (1.e.. i1 the (u.v)-plane).," The fitting was done directly on the final, self-calibrated visibility data (i.e., in the (u,v)-plane)."
 Our procedures for fitting in total intensity (Stokes /) were described in Paper I. We fit the polarization in Stokes Q anc U by fixing the locations (and sizes) of the / components and allowing the fluxes to vary., Our procedures for fitting in total intensity (Stokes $I$ ) were described in Paper I. We fit the polarization in Stokes $Q$ and $U$ by fixing the locations (and sizes) of the $I$ components and allowing the fluxes to vary.
 This procedure for fitting the polarization forces coincidence with the 7 components anc does not account for cases where the polarization may be displaced from the total intensity., This procedure for fitting the polarization forces coincidence with the $I$ components and does not account for cases where the polarization may be displaced from the total intensity.
 While a close inspectior of the CLEAN images showed a number of cases with small displacements between total intensity and polarization peaks. our fitting procedure seemed insensitive to these and. in general. produced good agreement with the polarized fluxes andposition angles observed in our CLEAN images.," While a close inspection of the CLEAN images showed a number of cases with small displacements between total intensity and polarization peaks, our fitting procedure seemed insensitive to these and, in general, produced good agreement with the polarized fluxes andposition angles observed in our CLEAN images."
 Our full model-fits for each source will appear in Paper III., Our full model-fits for each source will appear in Paper III.
" As discussed in 83.. obtaining good estimates of the real ""1"," As discussed in , obtaining good estimates of the real “1"
"Now, assuming that the sum of gas mass and star mass is constant in the typical galaxy, the gas-mass fraction is simply given by Thus, given the cosmic history of the star-formation-rate density, one could compute j4(z) by backwards de-evolving the present-day Milky-Way gas mass fraction, µΜνν.","Now, assuming that the sum of gas mass and star mass is constant in the typical galaxy, the gas-mass fraction is simply given by Thus, given the cosmic history of the star-formation-rate density, one could compute $\mu(z)$ by backwards de-evolving the present-day Milky-Way gas mass fraction, $\mu_{\rm MW}$."
" The assumption of a total baryonic mass of galaxies staying constant in time is not necessarily realistic, as star formation ispartly fueled by newly accreted gas (Prodanovié&Fields 2008)."," The assumption of a total baryonic mass of galaxies staying constant in time is not necessarily realistic, as star formation ispartly fueled by newly accreted gas \citep{Prodanovic2008}."
". However, the overall effect of the details of the gas fraction evolution is relatively small (~factor of two, PF02)."," However, the overall effect of the details of the gas fraction evolution is relatively small $\sim$ factor of two, PF02)."
" A more realistic modeling of the evolving gas fraction, including the effects of infall, will be addressed in an upcoming publication."," A more realistic modeling of the evolving gas fraction, including the effects of infall, will be addressed in an upcoming publication."
" For the present study, we adopt a model given by Hopkins&Beacom(2006) for the global star-formation-rate density as a function of redshift, p.(z)."," For the present study, we adopt a model given by \citet{Hopkins2006}
 for the global star-formation-rate density as a function of redshift, $\dot \rho_\ast (z)$ ."
" For the Milky-Way parameters, following PF02 and references therein, we use ww= yr! and umw=0.14."," For the Milky-Way parameters, following PF02 and references therein, we use $\psi_{\rm MW} = 3.2 M_{\sun}$ $^{-1}$ and $\mu_{\rm MW} = 0.14$."
" Lastly, we parametrize the 3.2MoeMilky-Way y-ray luminosity as Lymw(E)=1.36x10°°(E/600MeV)"" s! MeV, where κ.=1.5 for E<600 MeV and κ=2.7 for E>600 MeV. This parametrization comes from a broken power-law fit to the ""GALPROP conventional"" (Strongetal.2004) model of the energy spectrum of the diffuse Milky-Way 4-ray emission (which is compatible with no GeV We set the normalization by requiring that the energy integral of L+,mw above 100 MeV is 2.85x1045photonss~ (see PF02 and references therein)."," Lastly, we parametrize the Milky-Way $\gamma$ -ray luminosity as $L_{\gamma, {\rm MW}}(E) = 1.36 \times 10^{39}
(E/600~\mathrm{MeV})^{-\kappa}$ $^{-1}$ $^{-1}$, where $\kappa =
1.5$ for $E \le 600$ MeV and $\kappa = 2.7$ for $E > 600$ MeV. This parametrization comes from a broken power-law fit to the “GALPROP conventional” \citep{Strong2004} model of the energy spectrum of the diffuse Milky-Way $\gamma$ -ray emission (which is compatible with no GeV We set the normalization by requiring that the energy integral of $L_{\gamma,\rm MW}$ above 100 MeV is $2.85\times 10^{42} {\rm \,
photons \,\, s^{-1}}$ (see PF02 and references therein)."
" In Fig. 1,,"," In Fig. \ref{fig:spectrum},"
" we plot, with the solid line, the y-ray intensity E?I(E) from normal galaxies, compared with the Sreekumar et ((1998) determination of the CGB from EGRET data."," we plot, with the solid line, the $\gamma$ -ray intensity $E^2
I(E)$ from normal galaxies, compared with the Sreekumar et (1998) determination of the CGB from EGRET data."
" The galaxy contribution appears to be important in particular for energies between 50 MeV and 1 GeV. We point out that due to the shift of the spectral break in the Milky- diffuse emission spectrum from 850 MeV (which was the location of the break in EGRET data which suffered from the GeV excess) to 600 MeV (the location of the break in GALPROP conventional), the peak of the normal galaxy contribution correspondingly shifted from ~500 MeV in PF02 to ~250 MeV in Fig."," The galaxy contribution appears to be important in particular for energies between 50 MeV and 1 GeV. We point out that due to the shift of the spectral break in the Milky-Way diffuse emission spectrum from 850 MeV (which was the location of the break in EGRET data which suffered from the GeV excess) to 600 MeV (the location of the break in GALPROP conventional), the peak of the normal galaxy contribution correspondingly shifted from $\sim$ 500 MeV in PF02 to $\sim$ 250 MeV in Fig."
 1 in this work., \ref{fig:spectrum} in this work.
" Additionally, the contribution of normal galaxies to the CGB declines with energy above 1 GeV faster than it did in PF02, as the high-energy slope of the Milky Way spectrum adopted here (2.7) is steeper than the value implied by EGRET data (2.4) and adopted by ΡΕΟΖ."," Additionally, the contribution of normal galaxies to the CGB declines with energy above 1 GeV faster than it did in PF02, as the high-energy slope of the Milky Way spectrum adopted here (2.7) is steeper than the value implied by EGRET data (2.4) and adopted by PF02."
" It is worth noting that a preliminary analysis ofFermi data indicates that the slope of the CGB spectrum at high energies may be substantially steeper (consistent with ~E~?4°, see M.Ackermann for the LAT Colaboration*)) than the EGRET measurement."," It is worth noting that a preliminary analysis of data indicates that the slope of the CGB spectrum at high energies may be substantially steeper (consistent with $\sim E^{-2.45}$, see M.Ackermann for the LAT ) than the EGRET measurement."
" 'To illustrate this point, in Fig. 1,,"," To illustrate this point, in Fig. \ref{fig:spectrum},"
 we also plot the preliminaryFermi CGB results., we also plot the preliminary CGB results.
" In Fig. 2,,"," In Fig. \ref{fig:z_dist},"
" we plot, with the solid line, the integrand of Eq. (1))"," we plot, with the solid line, the integrand of Eq. \ref{iofe}) )"
 in units of the integral as a function of redshift at E=300 MeV; this quantity represents the contribution to the mean CGB intensity at a given energy from galaxies in a specific redshift range., in units of the integral as a function of redshift at $E = 300$ MeV; this quantity represents the contribution to the mean CGB intensity at a given energy from galaxies in a specific redshift range.
" Following the evolution of the cosmic star-formation rate, it peaks at z~1 and declines for higher redshifts."," Following the evolution of the cosmic star-formation rate, it peaks at $z \simeq 1$ and declines for higher redshifts."
" The angular auto-power spectrum of the CGB map dueto normal galaxies is given by where r is the comoving distance and Pyai(k,z) is the galaxy power spectrum at comoving wave number k and redshift z (e.g.,Andoetal. 2007b)."," The angular auto-power spectrum of the CGB map dueto normal galaxies is given by where $r$ is the comoving distance and $P_{\rm gal} (k, z)$ is the galaxy power spectrum at comoving wave number $k$ and redshift $z$ \citep[e.g.,][]{Ando2007b}."
. The multipole £ corresponds roughly to the angular scale of 0=180? /£., The multipole $\ell$ corresponds roughly to the angular scale of $\theta = 180\degr / \ell$ .
 Note, Note
mass of 0.35A4..,mass of $\sim 0.35M_{\odot}$.
 Ehe rates are lower where the trajectory is aligned. with the A-B axis., The rates are lower where the trajectory is aligned with the A-B axis.
 This elfect is larger than the lowering of the event rate that is produced. by. the introduction of smooth matter., This effect is larger than the lowering of the event rate that is produced by the introduction of smooth matter.
 In addition. the predicted event rate is dependent on the photometric error assumed.," In addition, the predicted event rate is dependent on the photometric error assumed."
 This dependence comes from the svstematic uncertainty that the assumption introduces into the determination of the ellective transverse velocity., This dependence comes from the systematic uncertainty that the assumption introduces into the determination of the effective transverse velocity.
 The microlensing parameter distributions were calculated from an ensemble of 5000. simulations of the observed. data for cach image. ancl for cach assumption of trajectory direction. photometric error. and smooth matter content.," The microlensing parameter distributions were calculated from an ensemble of 5000 simulations of the observed data for each image, and for each assumption of trajectory direction, photometric error, and smooth matter content."
 The 5000 simulations were spread over 100075. of simulated. light curves., The 5000 simulations were spread over $\eta_{o}$ of simulated light curves.
 If the error in the average rate is assumed to be due to Poison noise then it is less than 1%., If the error in the average rate is assumed to be due to Poison noise then it is less than $\sim 1\%$.
 The errors in the modelling statistics are therefore not important in determining the probability. distributions for the average HIEMIS rate., The errors in the modelling statistics are therefore not important in determining the probability distributions for the average HME rate.
" Fiewes L. 2..3 and d display the. functions Pn. py,Gua). hxCN) and fy,(Nor) obtained. for the microlensing models. considered."," Figures \ref{0smooth_images}, \ref{0smooth_tot}, , \ref{50smooth_images} and \ref{50smooth_tot} display the functions $p_{\bar{R}}(\bar{R})$, $p_{\bar{R}_{tot}}(\bar{R}_{tot})$, $h_{N}\left(N\right)$ and $h_{N_{tot}}\left(N_{tot}\right)$ obtained for the microlensing models considered."
 Both the rates. for the individual imagesas well as the combined rates are, Both the rates for the individual imagesas well as the combined rates are
Consider small disturbances to uniform shear flow with shear sy.,Consider small disturbances to uniform shear flow with shear $s_K$.
 The dispersion relation for disturbances of the form exp(57+{μέ} is mτα2Blyn|ESug)D 1 where yy=(a/c)?sy.," The dispersion relation for disturbances of the form $\exp(\gamma\tau+i\kappa\xi)$ is ^2(1+2B|y_K|+3y_K^2) - ^4, where $y_K\equiv (a/c)^{1/2}s_K$."
 There is instability if 5>0 for some . which occurs if," There is instability if $\gamma>0$ for some $\kappa$, which occurs if."
 If (his instability is present. (he stress as à function of shear g(s) is triple-valued: (here are (three roots s.«sy<s tothe equation g(s)=g(sy).," If this instability is present, the stress as a function of shear $g(s)$ is triple-valued: there are three roots $s_-<s_K<s_+$ to the equation $g(s)=g(s_K)$."
 The root sy has ο(δι)<0 and hence is unstable. while g/(s_)>0 so the roots s— are stable.," The root $s_K$ has $g'(s_K)<0$ and hence is unstable, while $g'(s_\pm)>0$ so the roots $s_\pm$ are stable."
 Almost all of the steady-state solutions of equation (38)) are bounded and periodic. and can be expressed analvtically in terms of Jacobian elliptic functions (1984).," Almost all of the steady-state solutions of equation \ref{eq:chb}) ) are bounded and periodic, and can be expressed analytically in terms of Jacobian elliptic functions \citet{ncs84}."
. ILowever. these are the final state of the svstem: it turns out that all of the periodic solutions are unstable (CarrGurtin&Slemrod1984).," However, these are the final state of the system: it turns out that all of the periodic solutions are unstable \citep{car84}."
. The only stable. stationary solution is the “kink” solution. 25). where the two + signs are independent and we require that Bκ—3/V2.," The only stable, stationary solution is the “kink” solution, ], where the two $\pm$ signs are independent and we require that $B<-3/\sqrt{2}$."
 Of course. this solution does not satisfv our periodic boundary conditions.," Of course, this solution does not satisfy our periodic boundary conditions."
 Numerical integration of the partial differential equation (38)) for a unstable initial state shows that the svstem evolves to a state in which the shear is almost always nearly equal to either s. or s. just like the solutions of the simpler equation (20)).," Numerical integration of the partial differential equation \ref{eq:chb}) ) for a unstable initial state shows that the system evolves to a state in which the shear is almost always nearly equal to either $s_-$ or $s_+$, just like the solutions of the simpler equation \ref{eq:ch}) )."
 Moreover. the interfaces between high- and low-shear domains gradually drift. so that high-shear and domains eventually coalesce.," Moreover, the interfaces between high- and low-shear domains gradually drift, so that high-shear and low-shear domains eventually coalesce."
 Once the distance between interfaces is large compared, Once the distance between interfaces is large compared
that most of the ambiguities are removed.,that most of the ambiguities are removed.
 In ? and ? I investigated the influence of the spectral lines on the parameters retrieved by the inversion., In \citet{beckthesis2006} and \citet{beck+etal2006d} I investigated the influence of the spectral lines on the parameters retrieved by the inversion.
 | found that e.g. field strength is restricted by the splitting of the 1564.8 nm line within a limit of around +100 G. Most average quantities of the field topology (field strength. field orientation) are more or less uniquely restricted by the spectra: the main source of error are actually the spectra themselves: spatial resolution. signal-to-noise ratio. polarimetric sensitivity. and the polarimetric calibration.," I found that e.g. field strength is restricted by the splitting of the 1564.8 nm line within a limit of around $\pm 100$ G. Most average quantities of the field topology (field strength, field orientation) are more or less uniquely restricted by the spectra; the main source of error are actually the spectra themselves: spatial resolution, signal-to-noise ratio, polarimetric sensitivity, and the polarimetric calibration."
 The question that however remains open ts the 3-D organization of the magnetic fields., The question that however remains open is the 3-D organization of the magnetic fields.
 The present inversion yields field strength and orientation inside the formation height of the spectral lines. but is not able to differentiate between a vertical or horizontal interweavement of field lines.," The present inversion yields field strength and orientation inside the formation height of the spectral lines, but is not able to differentiate between a vertical or horizontal interweavement of field lines."
 The approach of the integration of the field inclination assumes coherent structures from one pixel to the next in the radial direction. which ts in my opinion highly probable. but need not be the case.," The approach of the integration of the field inclination assumes coherent structures from one pixel to the next in the radial direction, which is in my opinion highly probable, but need not be the case."
 The most prominent spectral feature inside the penumbra. the Evershed effect. is not present in the gappy model.," The most prominent spectral feature inside the penumbra, the Evershed effect, is not present in the gappy model."
 | remark that all velocities derived here (besides the line core velocity of Til) always refer to velocities magnetic fields., I remark that all velocities derived here (besides the line core velocity of ) always refer to velocities magnetic fields.
 To create the multi-lobed profiles in the neutral line of Stokes V. two components of magnetic fields with different orientation and bulk velocities are needed.," To create the multi-lobed profiles in the neutral line of Stokes V, two components of magnetic fields with different orientation and bulk velocities are needed."
 Η the gappy model solves the penumbral heat transport problems. still an explanation for the Evershed flow is needed.," If the gappy model solves the penumbral heat transport problems, still an explanation for the Evershed flow is needed."
" The inclination of the bg fielc shows an azimuthal variation that leads to a ""gappy"" structure (cf.", The inclination of the bg field shows an azimuthal variation that leads to a “gappy” structure (cf.
 Figs., Figs.
 11. and B2))., \ref{penumbralgrains} and \ref{integ2}) ).
 However. the spatial scale of the variation is larger than that predicted by ?..," However, the spatial scale of the variation is larger than that predicted by \citet{scharmer+spruit2006}."
 If the integratec curves are taken at face value. this also happens in layers far below the surface layer of 7 = 1.," If the integrated curves are taken at face value, this also happens in layers far below the surface layer of $\tau$ = 1."
 Another argument in favor of the gappy model is that the spatial resolution of the observations | used may not be sufficient to detect the signatures of the structuring suggestec by Scharmer Spruit., Another argument in favor of the gappy model is that the spatial resolution of the observations I used may not be sufficient to detect the signatures of the structuring suggested by Scharmer Spruit.
" In the other direction. it shoulc be possible to construct a sunspot model based on their suggestions. calculate the resulting spectra in the 1.5 pm and 630 nm lines. reduce the spatial resolution to. arounc 1"". and then invert the spectra with two depth-independent magnetic components."," In the other direction, it should be possible to construct a sunspot model based on their suggestions, calculate the resulting spectra in the 1.5 $\mu$ m and 630 nm lines, reduce the spatial resolution to around $^{\prime\prime}$, and then invert the spectra with two depth-independent magnetic components."
 The results for the be component coulc be compared with the present inversion results., The results for the bg component could be compared with the present inversion results.
" Contrary to the regrettable sentence of ? that significance"". [think it necessary to show that their model successfully reproduces spectroscopic or spectropolarimetric observations to support its validity."," Contrary to the regrettable sentence of \citet{scharmer+spruit2006} that ”, I think it necessary to show that their model successfully reproduces spectroscopic or spectropolarimetric observations to support its validity."
" The long lifetimes (on the order of ] hr) for filaments (e.g.?). and the lack of submerging flow channels led ? to the conclusion that interchange convection by rising hot flow channels is mechanism"" for the penumbra."," The long lifetimes (on the order of 1 hr) for filaments \citep[e.g.][]{langhans+etal2005}, and the lack of submerging flow channels led \citet{schliche+solanki2003} to the conclusion that interchange convection by rising hot flow channels is ” for the penumbra."
" This claim has been renewed recently by ? and ?.. who criticize the ""paradigm"" of embedded flow channels and suggest that the penumbral fine-structure can be explained by a model of field-free gaps reaching almost up to the solar surface."," This claim has been renewed recently by \citet{spruit+scharmer2006} and \citet{scharmer+spruit2006}, who criticize the ” of embedded flow channels and suggest that the penumbral fine-structure can be explained by a model of field-free gaps reaching almost up to the solar surface."
 The energy transport in their model is then effected by convection in the field-free plasma below the sunspot., The energy transport in their model is then effected by convection in the field-free plasma below the sunspot.
 On the one hand. the findings of Sect.," On the one hand, the findings of Sect."
 6 support the static behavior of the sunspot fields: the shape of the umbral-penumbral boundary and some especially dark patches inside the penumbra stay the same during around | hour., \ref{tempevol} support the static behavior of the sunspot fields: the shape of the umbral-penumbral boundary and some especially dark patches inside the penumbra stay the same during around 1 hour.
 On the other hand. the intensity pattern of. e.g.. the penumbral grains ts completely changed after less than half an hour (cf.," On the other hand, the intensity pattern of, e.g., the penumbral grains is completely changed after less than half an hour (cf."
 Appendix AppendixC:))., Appendix \ref{appb}) ).
 The time scales in the MTM model are of a comparable order., The time scales in the MTM model are of a comparable order.
 The snapshot shown in Fig., The snapshot shown in Fig.
 14 was taken at 1 1/2 hour after the start of the simulation. but reflects the final steady-state solution.," \ref{geomcomp} was taken at 1 1/2 hour after the start of the simulation, but reflects the final steady-state solution."
 The flow channel in the MTM evolves rapidly in the beginning. and spans around half of the penumbra after 30 min (?)..," The flow channel in the MTM evolves rapidly in the beginning, and spans around half of the penumbra after 30 min \citep{schliche+jahn+schmidt1998}."
 ? used LOS magnetograms of the center side penumbra., \citet{langhans+etal2005} used LOS magnetograms of the center side penumbra.
 These LOS magnetograms are not suitable to trace the dynamic evolution of the penumbra., These LOS magnetograms are not suitable to trace the dynamic evolution of the penumbra.
 On the center side. the field of the background component is parallel to the line-of-sight. whereas the dynamic flow channels are strongly inclined to it.," On the center side, the field of the background component is parallel to the line-of-sight, whereas the dynamic flow channels are strongly inclined to it."
 Thus. the life times measured there reflect the slow evolution of the background component.," Thus, the life times measured there reflect the slow evolution of the background component."
 The same applies to the findings of Sect. 6: , The same applies to the findings of Sect. \ref{tempevol}: :
the stronger field component will dominate the topology. and thus. the small amount of change in the geometry seen in Fig.," the stronger field component will dominate the topology, and thus, the small amount of change in the geometry seen in Fig."
 12. implies that the does evolve only slowly., \ref{teempevol} implies that the does evolve only slowly.
 The conclusion on the impossibility of interchange convection due to the lack of submerging flow channels needs some more explanations., The conclusion on the impossibility of interchange convection due to the lack of submerging flow channels needs some more explanations.
 To be convinced by the argumentation. one would have to agree on the fact that the penumbra is deep (some Mm). that flow channels originate from flux located initially on the boundary layer between the sunspot and its surroundings. and that this flux can become buoyant by heat input from the fully convective surroundings outside thespot.," To be convinced by the argumentation, one would have to agree on the fact that the penumbra is deep (some Mm), that flow channels originate from flux located initially on the boundary layer between the sunspot and its surroundings, and that this flux can become buoyant by heat input from the fully convective surroundings outside the."
. The first point is suggested by the observations. while the latter two are mainly based on the MTM.," The first point is suggested by the observations, while the latter two are mainly based on the MTM."
 If one can agree on the ingredients above. I believe the penumbral heat transport can be effected by hot rising flux tubes in full agreement with the observations.," If one can agree on the ingredients above, I believe the penumbral heat transport can be effected by hot rising flux tubes in full agreement with the observations."
 If flux becomes buoyant at the outer sunspot boundary due to heating. this necessarily is a process.," If flux becomes buoyant at the outer sunspot boundary due to heating, this necessarily is a process."
 As soon as the hot flux bundle has risen from the boundary layer. new different flux will form the boundary layer.," As soon as the hot flux bundle has risen from the boundary layer, new different flux will form the boundary layer."
 This new flux would come from -- in the terminology used throughout this paper — the background component., This new flux would come from – in the terminology used throughout this paper – the background component.
 After a time span on the order of 30 min it would also have to become buoyant. and follow the previously risen flux upwards.," After a time span on the order of 30 min it would also have to become buoyant, and follow the previously risen flux upwards."
 Due to the depth of the penumbra. several flow channels could be stacked on top of each other at the same time.," Due to the depth of the penumbra, several flow channels could be stacked on top of each other at the same time."
 The inversion results along a single column (cf., The inversion results along a single column (cf.
 Sect., Sect.
 4.4 and Appendix B.1.)) suggest exactly this configuration: two flow channels are seen along a radial cut at the same time at different locations in the penumbra., \ref{hotupfl} and Appendix \ref{appa1}) ) suggest exactly this configuration: two flow channels are seen along a radial cut at the same time at different locations in the penumbra.
 The question of penumbralheating then changes to the question if the penumbral energy losses can be replenished by, The question of penumbralheating then changes to the question if the penumbral energy losses can be replenished by
It has been suggested that the difference stems from the fact that full relativistic calculations shift the bounce spectrum to lower frequencies in comparison to the ones using an effective gravitational potential (Dimmelmeier (2007))),It has been suggested that the difference stems from the fact that full relativistic calculations shift the bounce spectrum to lower frequencies in comparison to the ones using an effective gravitational potential \citet{Dimmelmeier:2007}) ).
 After this first and predominantly axisymmetric stage of GW-emission. the occurrence of a low 7/|W|-instability revives the gravitational wave signal again around = 20ms post-bounce (Saijoetal.(2003):Watts(2005):Ottetal. (2007))).," After this first and predominantly axisymmetric stage of GW-emission, the occurrence of a low $T/|W|$ -instability revives the gravitational wave signal again around $\approx 20$ ms post-bounce \citet{ 2003ApJ...595..352S,2005ApJ...618L..37W,2005ApJ...625L.119O,2006AIPC..861..728S,2006ApJ...651.1068O,2007CQGra..24..139O}) )."
" Low 7/|W| dynamical instabilities are triggered in differentially rotating systems such as neutron stars in situations where the patten speed c,=«c/m of an unstable mode #7 matches the local angular velocity at a point in the star (see Fig. 7))."," Low $T/|W|$ dynamical instabilities are triggered in differentially rotating systems such as neutron stars in situations where the patten speed $\sigma_{p}=\sigma/m$ of an unstable mode $m$ matches the local angular velocity at a point in the star (see Fig. \ref{fig7.eps}) ),"
 commonly called (the modes are. as in. Wattsetal.(2005).. assumed to behave harmonically as exp[—i(ot—mó)]. where c 1s the mode's eigenfrequency).," commonly called (the modes are, as in \citet{2005ApJ...618L..37W}, assumed to behave harmonically as $\exp[-i(\sigma t -m\phi)]$, where $\sigma$ is the mode's eigenfrequency)."
 It permits the azimuthal fluid modes to amplify., It permits the azimuthal fluid modes to amplify.
 This non-axisymmetric process yields a quasi-periodic GW signal with à rather constant time-variation. leading to a narrow-band emission at 905 Hz which lasts until the end of our simulation. as one can see particularly in the upper panels of Fig.," This non-axisymmetric process yields a quasi-periodic GW signal with a rather constant time-variation, leading to a narrow-band emission at $905$ Hz which lasts until the end of our simulation, as one can see particularly in the upper panels of Fig."
 3. for times t >20 ms., \ref{fig3.eps} for times t $>20$ ms.
 The analysis method we use to observe the growth of nonaxisymmetric structures decomposes the density at a fixed radius and constant z--component into its azimuthal Fourier components as done before e.g. in ref. (Ou&Tohline2006:Ottetal. 2007)))," The analysis method we use to observe the growth of nonaxisymmetric structures decomposes the density at a fixed radius and constant -component into its azimuthal Fourier components as done before e.g. in ref. \citep{2006ApJ...651.1068O,2007CQGra..24..139O}) ):"
 where the Hi—L—e2complex Fourier. amplitudes. are defined by In Fig., where the complex Fourier amplitudes are defined by In Fig.
" 6. the normalized mode amplitudes A,,=|C,|/Co are monitored to measure the growth of unstable modes.", \ref{fig6.eps} the normalized mode amplitudes $A_{m}=|C_{m}|/C_{0}$ are monitored to measure the growth of unstable modes.
 In our model s15g we find i= {1.2.3}-modes being triggered. with the so-called η=2 bar-mode growing fastest.," In our model s15g we find $m=\{1,2,3\}$ -modes being triggered, with the so-called $m=2$ bar-mode growing fastest."
 Further. we state that the 7;=11.2.3] modes all possess the same pattern speed.," Further, we state that the $m=\{1,2,3\}$ modes all possess the same pattern speed."
 The close relation between the m=2 bar-mode instability and the emission of gravitational waves can be seen in the following features: First. the sudden onset of GW emission along the pole. which must be completely due to nonaxisymmetric dynamics. coincides with the amplitude of the ;=3 mode reaching approximately the absolute amplitude of the η=4 mode caused by the grid.," The close relation between the $m=2$ bar-mode instability and the emission of gravitational waves can be seen in the following features: First, the sudden onset of GW emission along the pole, which must be completely due to nonaxisymmetric dynamics, coincides with the amplitude of the $m=2$ mode reaching approximately the absolute amplitude of the $m=4$ mode caused by the grid."
 Secondly. the dominant frequency of emission corresponds perfectly to the eigenfrequency of the #= 2-mode.," Secondly, the dominant frequency of emission corresponds perfectly to the eigenfrequency of the $m=2$ -mode."
 Finally. the two GW-polarisations + and x are phase shifted by 7/2. as one would expect of a perfect. monochromatic GW-source such as a rotating bar.," Finally, the two GW-polarisations $+$ and $\times$ are phase shifted by $\pi/2$, as one would expect of a perfect, monochromatic GW-source such as a rotating bar."
 These findings in the context of the low T/\|W| instability and supernova dynamics stand in remarkable agreement with the recent ones of Ottetal.(2007).., These findings in the context of the low $T/|W|$ instability and supernova dynamics stand in remarkable agreement with the recent ones of \citet{2007CQGra..24..139O}.
 For low p-unstable models similar to 155. they found narrow-band GW emission at =920-930 Hz.," For low $\beta$ -unstable models similar to s15g, they found narrow-band GW emission at $\approx 920-930$ Hz."
 The main difference to our calculations is the point that the dominant mode which was found in those computations was the #7= ]-mode., The main difference to our calculations is the point that the dominant mode which was found in those computations was the $m=1$ -mode.
 As a closing remark to model s15g we state that the time evolution of the energy emitted by gravitational radiation (see Fig.5)) fits the behaviour of the waves., As a closing remark to model s15g we state that the time evolution of the energy emitted by gravitational radiation (see \ref{fig5.eps}) ) fits the behaviour of the waves.
 It demonstrates a large peak around bounce at 1.3x10°! erg/s followed by a ringdown and an oscillating renaissance at about 1011—10? erg/s for times t>20 ms., It demonstrates a large peak around bounce at $1.3\times10^{51}$ erg/s followed by a ringdown and an oscillating renaissance at about $10^{47}-10^{48}$ erg/s for times $t>20$ ms.
 The slow-rotating model sI5h undergoes a quasi-spherically symmetric. core collapse. consequently showing fairly weak," The slow-rotating model s15h undergoes a quasi-spherically symmetric core collapse, consequently showing fairly weak"
 Ha emission. (e.g.. Rutledgeetal.2000:West2004:Berger 2006)). Zeeman broadening of FeH molecular lines in Stokes / (Reiners&Basri 2007).. and. time-resolved spectropolarimetry in Stokes V. (Zeeman-Doppler imaging: Donatietal.2008:Morin 2008)).," $\alpha$ emission (e.g., \citealt{rbm+00,whw+04,ber06}) ), Zeeman broadening of FeH molecular lines in Stokes $I$ \citep{rb07}, , and time-resolved spectropolarimetry in Stokes $V$ (Zeeman-Doppler imaging; \citealt{dmp+08,mdp+08}) )."
 Each of these techniques Is sensitive to specific properties of the magnetic field., Each of these techniques is sensitive to specific properties of the magnetic field.
 Zeeman broadening provides a measure of thefntegrated surface magnetic flux. Bf (Reiners& 2006).. where B is the magnetic field strength and f£ is the field covering fraction.," Zeeman broadening provides a measure of the surface magnetic flux, $Bf$ \citep{rb06}, where $B$ is the magnetic field strength and $f$ is the field covering fraction."
 Zeeman-Doppler imaging (ZDD. on the other hand. only allows for a reconstruction of the large- (multipole number of (= few) surface field. but it also provides information on the field (Donatietal.Morinetal. 2008).," Zeeman-Doppler imaging (ZDI), on the other hand, only allows for a reconstruction of the large-scale (multipole number of $\ell\lesssim
{\rm few}$ ) surface field, but it also provides information on the field \citep{dmp+08,mdp+08}."
. The ZDI technique has led to à characterization of surface fields in several M dwarfs. revealing a transition from mainly toroidal and non-axisymmetric fields in MO-M3 objects to predominantly poloidal axisymmetric fields in mid-M dwarfs (Donatietal.2008:Morin2008).," The ZDI technique has led to a characterization of surface fields in several M dwarfs, revealing a transition from mainly toroidal and non-axisymmetric fields in M0-M3 objects to predominantly poloidal axisymmetric fields in mid-M dwarfs \citep{dmp+08,mdp+08}."
. The apparent shift in field geometrycoincides with the transition to full convection. and may reflect a change in dynamo mechanism.," The apparent shift in field geometrycoincides with the transition to full convection, and may reflect a change in dynamo mechanism."
 The field, The field
In the last 30 vears. many studies have been devoted to the evolution of the CNO isotopic ratios (c.g.. Aucouze. Lequeux Vigroux 1975: Vieroux. Audouze Lequeux 1976: Dearborn. ‘Vinsley Schramm: LOTS: Tosi 1982: D'Antona Matteucci 1991: Matteucci D'Xntona 1991: Prantzos. Aubert Xudouze 1996: see also ‘Losi 2000 for a recent reappraisal of the problem).,"In the last 30 years, many studies have been devoted to the evolution of the CNO isotopic ratios (e.g., Audouze, Lequeux Vigroux 1975; Vigroux, Audouze Lequeux 1976; Dearborn, Tinsley Schramm 1978; Tosi 1982; D'Antona Matteucci 1991; Matteucci D'Antona 1991; Prantzos, Aubert Audouze 1996; see also Tosi 2000 for a recent reappraisal of the problem)."
 Isotopic ratios are generally not lected by physicochemical fractionation elfects. (but. see. e.g.. Sheller. Lamrer beeorman 2002).," Isotopic ratios are generally not affected by physicochemical fractionation effects (but see, e.g., Sheffer, Lambert Federman 2002)."
 Therefore. they rellee rather Laitiullv. the relevan6 production. processes which occurred in stars of «cilleren masses and Liletines.," Therefore, they reflect rather faithfully the relevant production processes which occurred in stars of different masses and lifetimes."
 Llowever. despite he considerable. |orogress in the theories of stelar evolution and nucleosvnthesis. important (tlestions relate cto the vielis and the xocducion sites of some of the CNO isotopes stil remain open.," However, despite the considerable progress in the theories of stellar evolution and nucleosynthesis, important questions related to the yields and the production sites of some of the CNO isotopes still remain open."
 In this context. chemical evoluion models can be regarded as a powerful tool in order to discriminate among cdillerent ses of stellar vields and," In this context, chemical evolution models can be regarded as a powerful tool in order to discriminate among different sets of stellar yields and"
A somewhat cdillerent. treatment of. hydrodynamics and magnetic fields is realised within the MPL parallel -body/SPIL code (δυο (?.. 27.0 7)).,"A somewhat different treatment of hydrodynamics and magnetic fields is realised within the MPI parallel -body/SPH code $\textsc{Gadget}$ \citealp{SpringelGadget1}, , \citealp{SpringelGadget}, \citealp{GadgetMHD}) )."
 Phere are. two significant dillerences in the implementation relevant. even for non-radiative simulations: First. VINE follows a classical implementation which is integrating the internal energy. whereas GADGET utilises what is generally called the entropy conserving formulation.," There are two significant differences in the implementation relevant even for non-radiative simulations: First, $\textsc{Vine}$ follows a classical implementation which is integrating the internal energy, whereas $\textsc{Gadget}$ utilises what is generally called the entropy conserving formulation."
 The important cillerence thereby. is not. the fact that GADGET integrates the entropy. instead of the internal energy., The important difference thereby is not the fact that $\textsc{Gadget}$ integrates the entropy instead of the internal energy.
 The crucial dillerences are rather the wav in which he smoothing length h; is defined (in CADGET. h; is defined xwsed on the mass within the kernel instead of the number of xuticles) and the inclusion of correction terms arising from he varving smoothing length.," The crucial differences are rather the way in which the smoothing length $h_i$ is defined (in $\textsc{Gadget}$, $h_i$ is defined based on the mass within the kernel instead of the number of particles) and the inclusion of correction terms arising from the varying smoothing length."
 Also. the entropy conserving ormulation uses à way of svmmetrizing the kernel given hy he derivation of the SPILL equations. which in sum leads to conservation of energy and entropy at the same time (?)).," Also, the entropy conserving formulation uses a way of symmetrizing the kernel given by the derivation of the SPH equations, which in sum leads to conservation of energy and entropy at the same time \citealp{Springel&Hernquist2002}) )."
 The second. clillerence originates in an alternative ormulation of the artificial viscosity., The second difference originates in an alternative formulation of the artificial viscosity.
 In. GADGET. artificial viscosity is based on the signal velocity instead of sound speed (7)) and apt to incorporate magnetic waves in à natural wav (7)).," In $\textsc{Gadget}$, artificial viscosity is based on the signal velocity instead of sound speed \citealp{Monaghan1997}) ) and apt to incorporate magnetic waves in a natural way \citealp{Price&Monaghan2004SPMHDI}) )."
 This cillerent implementation was shown to bring measurable improvements specially for MILD applications (7)). but. should. not make too much of a clilference for passive magnetic fields.," This different implementation was shown to bring measurable improvements specially for MHD applications \citealp{GadgetMHD}) ), but should not make too much of a difference for passive magnetic fields."
 Phe implementation of the induction equation and the Euler potentials formalism is the same in both codes., The implementation of the induction equation and the Euler potentials formalism is the same in both codes.
 The integration in GADGET is also performed. using the leaplroe integration. scheme. but CLADGET. utilises a kiek-clrift-kick-scheme whereas VINE uses a scheme.," The integration in $\textsc{Gadget}$ is also performed using the leapfrog integration scheme, but $\textsc{Gadget}$ utilises a kick-drift-kick-scheme whereas $\textsc{Vine}$ uses a drift-kick-drift-scheme."
 The timestep is given by where 5 translates to the accuracy parameter Tyce in eq., The timestep is given by where $\eta$ translates to the accuracy parameter $\tau_\mathrm{acc}$ in eq.
 26 via n=2g., \ref{ts1} via $\tau_\mathrm{acc}=\sqrt{2\eta}$.
 For SPIE particles. also a C'ourant-like condition in the form is applied. where f; is the SPL softening length for gas particle # and the signal velocity between particles 7 and j as defined (77in ? with the maximum taken over all neighboring particles j of particle ἐς," For SPH particles, also a Courant-like condition in the form is applied, where $h_i$ is the SPH softening length for gas particle $i$ and $v_{ij}^\mathrm{sig}$ the signal velocity between particles $i$ and $j$ as defined in \cite{Price&Monaghan2004SPMHDI} with the maximum taken over all neighboring particles $j$ of particle $i$."
" μμ is an accuracy parameter which does not translate one-to-one to τοι, in ed.", $C_\mathrm{cour}$ is an accuracy parameter which does not translate one-to-one to $\tau_\mathrm{CFL}$ in eq.
 29 due to the different definition of the Courant. criterion., \ref{ts4} due to the different definition of the Courant criterion.
 We commonly use values of η=0.02 and Cus=0.15 to ensure that the timestep Af in CLADGIET does not get too large compared to VINE., We commonly use values of $\eta=0.02$ and $C_\mathrm{cour}=0.15$ to ensure that the timestep $\Delta t$ in $\textsc{Gadget}$ does not get too large compared to $\textsc{Vine}$.
 However. changing the accuracy parameters by a factor of two does not allect the overall evolution and amplification of the magnetic field in the simulated svstems (not shown).," However, changing the accuracy parameters by a factor of two does not affect the overall evolution and amplification of the magnetic field in the simulated systems (not shown)."
 Beside that. the codes diller in details of the tree construction for calculating gravitational forces.," Beside that, the codes differ in details of the tree construction for calculating gravitational forces."
 For more details we refer the reader to the code papers for VINE (?.. 7)) and δυο (7.. 7))," For more details we refer the reader to the code papers for $\textsc{Vine}$ \citealp{VINEI}, \citealp{VINEII}) ) and $\textsc{Gadget}$ \citealp{SpringelGadget}, \citealp{GadgetMHD}) )."
 The initial conditions for our δν Way like galaxy are realised. using the method described by 2? which is based on ?. (see also 2))., The initial conditions for our Milky Way like galaxy are realised using the method described by \citet{Springel2005} which is based on \citet{Hernquist1993} (see also \citealp{Johansson2009}) ).
 The galaxy. consists of an exponential stellar clise and a Lat extended: gas disc. a stellar bulge and a dark matter halo of collisionless particles.," The galaxy consists of an exponential stellar disc and a flat extended gas disc, a stellar bulge and a dark matter halo of collisionless particles."
 The gas is represented: by SPIEL particles adopting an isothermal equation of state with a fixed sound speed of e;z15 km Ll. which. corresponds to a temperature of Z7z2-101 Ix for a molecular weight of 1.4/1.1*myroten.," The gas is represented by SPH particles adopting an isothermal equation of state with a fixed sound speed of $c_s\approx 15$ km $^{-1}$ , which corresponds to a temperature of $T\approx2\cdot10^4$ K for a molecular weight of $1.4/1.1\cdot m_\mathrm{proton}$."
 We brielly note that by using an isothermal equation of state only one component of the ISM is modeled. typically this is a reasonably good approximation for the warm. eas phase in disc galaxies (e.g. 7.. ?2.. 7)).," We briefly note that by using an isothermal equation of state only one component of the ISM is modeled, typically this is a reasonably good approximation for the warm gas phase in disc galaxies (e.g. \citealp{Barnes2002}, \citealp{Li2005}, \citealp{Naab&Jesseit2006}) )."
 Assuming an isothermal equation of state implies that additional heat. created in shocks by adiabatic compression. and feedback. processes (e.g. by SNIED is radiated away immediately., Assuming an isothermal equation of state implies that additional heat created in shocks by adiabatic compression and feedback processes (e.g. by SNII) is radiated away immediately.
 In. addition. substantial heating processes prevent the gas [rom cooling below its effective. temperature. predefined. by its sound speed.," In addition, substantial heating processes prevent the gas from cooling below its effective temperature predefined by its sound speed."
 The parameters describing the initial conditions can be found in ‘Table 1.., The parameters describing the initial conditions can be found in Table \ref{tab1}.
 The particle numbers and. the eravitational and SPILL softening lengths used in the cilferent runs can be found in Table 2.., The particle numbers and the gravitational and SPH softening lengths used in the different runs can be found in Table \ref{tab2}.
 AXofore we include magnetic fields we allow the galaxy to evolve for approximately three half mass rotation periods., Before we include magnetic fields we allow the galaxy to evolve for approximately three half mass rotation periods.
 For simplicity we choose an initial magnetic field in the .r direction., For simplicity we choose an initial magnetic field in the $x$ direction.
 Its value. By=LO? €. corresponds to the typical value of intergalactic magnetic fields (2)).," Its value, $B_0=10^{-9}$ G, corresponds to the typical value of intergalactic magnetic fields \citealp{KronbergLesch&Hopp1999}) )."
 To set up the corresponding I5uler potentials. we choose We have checked. the stability of our discs in independent. simulations without magnetic fields.," To set up the corresponding Euler potentials, we choose We have checked the stability of our discs in independent simulations without magnetic fields."
 Figs., Figs.
 2 and 3 show the surface densities Mua. of the extended gascous disces and “Moja. of the exponential stellar disces. respectively. as a function of radius for /=0.5 Gar (red). ic. the time at which the magnetic field. is switched. on. and /=2.0 vr (black).," \ref{sigma_gas} and \ref{sigma_disc} show the surface densities $\Sigma_\mathrm{gas}$ of the extended gaseous discs and $\Sigma_\mathrm{stars}$ of the exponential stellar discs, respectively, as a function of radius for $t=0.5$ Gyr (red), i.e. the time at which the magnetic field is switched on, and $t=2.0$ Gyr (black)."
 Fig., Fig.
 4 shows the circular velocitycurves of the simulated galaxies at the same times., \ref{vrot} shows the circular velocitycurves of the simulated galaxies at the same times.
 The disces simulated with VINE (dottedline) and CrAber (solid line), The discs simulated with $\textsc{Vine}$ (dottedline) and $\textsc{Gadget}$ (solid line)
where £? is the Ricci scalar associated with the metric ον.,where $R$ is the Ricci scalar associated with the metric $g_{\mu\nu}$.
 Variations of the action with respect to the metric (which involve not only variations of the total Lagrangian density but also variations of the space-time measure) leads to Einstein's equations (see for instance ?)), Variations of the action with respect to the metric (which involve not only variations of the total Lagrangian density but also variations of the space-time measure) leads to Einstein's equations (see for instance \citealt{anderssoncomer-07}) ).
 The relativistic momenta of the nucleons can be expressed in a form similar to Eq. (26)), The relativistic momenta of the nucleons can be expressed in a form similar to Eq. \ref{eq.3pi}) )
 as The non-diagonalS components of the svmametric relativistic mobility matrix AA. are equali to those of the non-relativistic matrix A. while the diagonal elements are given by The relativistic momenta of the leptons take a very simple form If the constituents are all co-moving with the 4-velocity a. the 4-momoenta reduce to With the momenta specified. we can obtain the generalized. pressure V. from. σα. (6)).," as The non-diagonal components of the symmetric relativistic mobility matrix $\widetilde{\cal K}^{q q^\prime}$, are equal to those of the non-relativistic matrix ${\cal K}^{qq^\prime}$, while the diagonal elements are given by The relativistic momenta of the leptons take a very simple form If the constituents are all co-moving with the 4-velocity $u^\mu$, the 4-momenta reduce to With the momenta specified, we can obtain the generalized pressure $\Psi$ from Eq. \ref{eq.general_pressure}) )."
 As for the non-relativistic case. V can be decomposed into an ordinary “static” part given by Eq. (31))," As for the non-relativistic case, $\Psi$ can be decomposed into an ordinary “static” part given by Eq. \ref{eq.psi.static}) )"
 and an extra contribution V due to entrainment which can be expressed as where the entraüinment energy density is now delined by AXofore concluding this section. let us remark that the relativistic Lagrangian density can be written in the very concise form where the coellicients Ay and Àj are given by and adopting the following notations Equationi (51)) is consistent with the expansion of the Lagrangian>o density in powers of Crtnp). suggestedoo bv ?..," and an extra contribution $\Psi_{\rm ent}$ due to entrainment which can be expressed as where the entrainment energy density is now defined by Before concluding this section, let us remark that the relativistic Lagrangian density can be written in the very concise form where the coefficients $\lambda_0$ and $\lambda_1$ are given by and adopting the following notations Equation \ref{eq.lambda.rel2}) ) is consistent with the expansion of the Lagrangian density in powers of $(x^2 - n p)$, suggested by \citet*{andersson-02}."
 Lt can be clearly seen on Eq. (51)).," It can be clearly seen on Eq. \ref{eq.lambda.rel2}) ),"
 that in the absence of entrainment (i.e. Ay= 0) or in the case of co-moving Huis. the Lagrangian density reduces to the opposite of the internal energy. density.," that in the absence of entrainment (i.e. $\lambda_1=0$ ) or in the case of co-moving fluids, the Lagrangian density reduces to the opposite of the internal energy density."
" Ifthe nucleons were not interacting with each other. the mobility matrix introduced in Section 3. would be diagonal and we would simply have AU""=mn, and APP=min,"," If the nucleons were not interacting with each other, the mobility matrix introduced in Section \ref{sect.non-rel.hydro} would be diagonal and we would simply have ${\cal K}^{nn}=m/n_n$ and ${\cal K}^{pp}=m/n_p$."
 OF course we know that nucleons are strongly interacting., Of course we know that nucleons are strongly interacting.
" This means that the matrix A"". does not have such a simple structure.", This means that the matrix ${\cal K}^{qq^\prime}$ does not have such a simple structure.
 I is convenient to define neutron and. proton dynamical elective masses: by respectively., It is convenient to define neutron and proton dynamical effective masses by respectively.
 The deviations of m7 from the bare barvon mass m therefore arise entirely from. the nucleon-nucleon interactions., The deviations of $m_\star^q$ from the bare baryon mass $m$ therefore arise entirely from the nucleon-nucleon interactions.
 Let us point out that these effective masses depend on the nucleon densities and therefore vary with depth inside the neutron star., Let us point out that these effective masses depend on the nucleon densities and therefore vary with depth inside the neutron star.
 As a result of I5q. (191). ," As a result of Eq. \ref{eq.gal.inv}) ),"
the non-diagonal coellicients of the mobility matrix can be expressed as, the non-diagonal coefficients of the mobility matrix can be expressed as
except oy and 7 are inscusitive to this width.,except $\sigma_8$ and $\tau$ are insensitive to this width.
 The results for the basic flat tilted ACDM . parameters are shown in Table 1L., The results for the basic flat tilted $\Lambda$ CDM parameters are shown in Table \ref{tab:basic}.
 The confidence limits are obtained * nnrginaliiug the unilti-dimensioual liselihoods down o one dimension., The confidence limits are obtained by marginalizing the multi-dimensional likelihoods down to one dimension.
 The median value is obtained by finding e πορτα] of the resulting likelihood function while 1e lower aud upper error liauits are obtained by fudiug 1ο and inteerals respectively., The median value is obtained by finding the integral of the resulting likelihood function while the lower and upper error limits are obtained by finding the and integrals respectively.
 The CA\IBall data olubination iucludes: the ACBAR results preseuted here: 1ο WMAP 3 year TT. TE. and EE spectra. with the EE rot included at higher ( as iu ?:: the CBI extended mosaic results (7) and polarization results (77).. combined iu 1ο manner described iu Ίο the DASI two year results (?): the DASI EE aud TE baudpowers (7): the VSÀ final results (?):: the ATANTATA 1998 füeht results (2): and the TT. TE. and EE results from the BOOMERANC: 2003 flight (?2?2?)..," The CMBall data combination includes: the ACBAR results presented here; the WMAP 3 year TT, TE, and EE spectra, with the EE not included at higher $\ell$ as in \citet{hinshaw06}; ; the CBI extended mosaic results \citep{readhead04} and polarization results \citep{Readhead04b,Sievers05}, combined in the manner described in \citet{Sievers05}; the DASI two year results \citep{halverson02}; the DASI EE and TE bandpowers \citep{Leitch04}; ; the VSA final results \citep{dickinson04}; the MAXIMA 1998 flight results \citep{hanany00}; ; and the TT, TE, and EE results from the BOOMERANG 2003 flight \citep{jones06, piacentini06, montroy06}."
 Only (>350baudpowers are included or BOOMERANG because of overlap with WALAP3 (although inclusion of the lower (6 results leaves the xumalneter results essentially uuchiaueced)., Only $\ell > 350$bandpowers are included for BOOMERANG because of overlap with WMAP3 (although inclusion of the lower $\ell$ results leaves the parameter results essentially unchanged).
 While ACDAR and BOOMERANG are both calibrated through WALAP. his is a snuadl contribution to the total wucertainty iu he ACBAR calibration. and we treat the calibration uucertaimtics as independent m our parameter analysis.," While ACBAR and BOOMERANG are both calibrated through WMAP, this is a small contribution to the total uncertainty in the ACBAR calibration and we treat the calibration uncertainties as independent in our parameter analysis."
 Although the DAS CBI and BOOMERANG 2003 EE and TE results for high ( polarization are included. they have little impact on the values of the parameters we 6tan.," Although the DASI, CBI and BOOMERANG 2003 EE and TE results for high $\ell$ polarization are included, they have little impact on the values of the parameters we obtain."
 Iu all our runs we have used the updated WALAP3 likehhoodσα code (http:/flambda.estc.uasa.ecovs) which includes an updated poiut-source correction 7 ancl foreground mareinalization on large aneular scales., In all our runs we have used the updated WMAP3 likelihood code (http://lambda.gsfc.nasa.gov/) which includes an updated point-source correction \citet{huffenberger06} and foreground marginalization on large angular scales.
" These updates resultin a smallincrease in the Q,, aud os values compared to those reported in 2..", These updates result in a small increase in the $\Omega_m$ and $\sigma_8$ values compared to those reported in \citet{spergel06}.
 The results for the basic model paramcter set with various conibiuationus of data are sununarzed in Fie. 5.., The results for the basic model parameter set with various combinations of data are summarized in Fig. \ref{fig:basic}.
 The most striking feature of the results is that the solutions determined from WALAP3 aloue are quite compatible with the extension by ACBAR (aud that of the other data) to higher (., The most striking feature of the results is that the solutions determined from WMAP3 alone are quite compatible with the extension by ACBAR (and that of the other data) to higher $\ell$.
 This consistency means that the additional CAIB data(includiug ACBAR) have little iupact on the cosmological parameters deterimuned by WMADP2S., This consistency means that the additional CMB data (including ACBAR) have little impact on the cosmological parameters determined by WMAP3.
 We have tested the effect of a sienificautl sinaller ACBAR calibration error. such as we auticipate for the final ACBAR release.," We have tested the effect of a significantly smaller ACBAR calibration error, such as we anticipate for the final ACBAR release."
 Wefind a much lareer impact ou the parameter values and errors: the values are simular to those fouud for CMDall|LSS., Wefind a much larger impact on the parameter values and errors; the values are similar to those found for CMBall+LSS.
" With the original ? WALAPS likelihood code. there was a shift ins and @,, to higher values when additional data was included."," With the original \citet{spergel06} WMAP3 likelihood code, there was a shift in $\sigma_8$ and $\Omega_m$ to higher values when additional data was included."
 However. with the updated WALAP3 likelihood code. the addition of the ACBAR and CMDall baudpowers leads to essentially uo shift m σς aud ο): however. includius the LSS data docs still result in a slight iucrease in these parameters.," However, with the updated WMAP3 likelihood code, the addition of the ACBAR and CMBall bandpowers leads to essentially no shift in $\sigma_8$ and $\Omega_m$; however, including the LSS data does still result in a slight increase in these parameters."
" The new likelihood code corrects the lower power in the third acoustic peak which was leading to low values for ox aud ©,,,h7 ", The new likelihood code corrects the lower power in the third acoustic peak which was leading to low values for $\sigma_8$ and $\Omega_m h^2$ .
The comoving damping scale. determined as a derived cosinological parameter using oulv the ACDAR and WMAP3 data is Rp=10.5+0.2\Mpe|.," The comoving damping scale, determined as a derived cosmological parameter using only the ACBAR and WMAP3 data is $R_D=
10.5 \pm 0.2 \, {\rm Mpc}^{-1}$ ."
 The corresponding angular scale is fp=1355/2., The corresponding angular scale is $\ell_D= 1355 ^{+5}_{-5}$.
 These values for Ry and (5 are in excellent aerecment with values obtained usine earlier datasets (7).., These values for $R_D$ and $\ell_D$ are in excellent agreement with values obtained using earlier datasets \citep{BCP03}.
 We also fud the comoving sound crossing distance is Re⋅B . with a corresponding augular scale ἐς--LOO0)=95.9!n in aerecment with the value for 0 in Table 1," We also find the comoving sound crossing distance is $R_s= 147.8^{+2.3}_{-2.3} \, {\rm
Mpc}^{-1}$ , with a corresponding angular scale $\ell_s= 100/\theta =
95.9^{+1.0}_{-0.2}$ , in agreement with the value for $\theta$ in Table \ref{tab:basic}."
 Tuchision of lensing iu our standard parameter runs increases the best-fit model likelihoods iu all cases., Inclusion of lensing in our standard parameter runs increases the best-fit model likelihoods in all cases.
 The difference between the log likelihoods of the lensed aud uonlensed models for the WMADP2 run is AluL=0.86, The difference between the log likelihoods of the lensed and non–lensed models for the WMAP3 run is $\Delta \ln L=0.86$.
 The log likelihood difference increases to 1.7 with ACBAR iucluded. 2.16 with CATBall. and 3.69 for the CMDall|LSS data combination.," The log likelihood difference increases to 1.7 with ACBAR included, 2.46 with CMBall, and 3.69 for the CMBall+LSS data combination."
 The mean values of the paraimecters do uot shift sienificautlv with the inclusion of leusine: for example. σς increases from 0.7758 to 0.788 for the CMDall data set and from 0.801 to 0.8125 for CMDall|LSS.," The mean values of the parameters do not shift significantly with the inclusion of lensing; for example, $\sigma_8$ increases from 0.778 to 0.788 for the CMBall data set and from 0.804 to 0.813 for CMBall+LSS."
 The best-fit D;'« for the lens aud no-leus cases look quite simular. but the subtle smoothing of the peaks aud troughs by lensing results iu a better fit to the the data for each combination of experiments.," The best-fit ${\cal D}_\ell$ 's for the lens and no-lens cases look quite similar, but the subtle smoothing of the peaks and troughs by lensing results in a better fit to the the data for each combination of experiments."
 The first release of WALAP data showed evidence for ruuniune of the CAIB power spectrum spectral iudex. utieubulw when combined with measurements of LSS (?)..," The first release of WMAP data showed evidence for running of the CMB power spectrum spectral index, particularly when combined with measurements of LSS \citep{spergel03}."
" Extending the basicmodel to allow for ruunius of he spectral index around the pivot point &,=(.05Mpe. ! vields ηναι)0.053toos for WMAP3 only."," Extending the basicmodel to allow for running of the spectral index around the pivot point $k_\star=0.05$ $^{-1}$ yields $dn_s/d\ln k
(k_\star)=-0.053^{+0.031}_{-0.029}$ for WMAP3 only."
 The tendeney for negative— ruuniug indices is due mostly o the low f£ eud. where the multipoles are lower than the standard ACDAL model.," The tendency for negative running indices is due mostly to the low $\ell$ end, where the multipoles are lower than the standard $\Lambda$ CDM model."
 The contribution from the hieh f cud is less significant., The contribution from the high $\ell$ end is less significant.
 Since the WALAPS results extend o reasonably high f. the addition of the ACBAR results shifts the constraints only marginally d»o./dluk(k.)=0.015nost .," Since the WMAP3 results extend to reasonably high $\ell$, the addition of the ACBAR results shifts the constraints only marginally $dn_s/d\ln k (k_\star)=
-0.045^{+0.026}_{-0.026}$ ."
 The effect of adding the ACDAR data ca- © SCCLL clearly in Fig., The effect of adding the ACBAR data can be seen most clearly in Fig.
 7 which shows the correlation vetween vy aud εςοἱια..., \ref{fig:nrun} which shows the correlation between $n_s$ and $dn_s/d\ln k$.
 The central value is simular. mt the errors are further reduced with the CNIDall | LSS conibiuation. «νεΠιο}=0017i. S," The central value is similar, but the errors are further reduced with the CMBall + LSS combination, $dn_s/d\ln k (k_\star)= -0.047^{+0.021}_{-0.021}$."
oStnular to tle results from WAITAPL and carlicr versions the CMDaLB data set (27).. à uceative running is still favored at about the 2-7 level by each of the data combinations considered.," Similar to the results from WMAP1 and earlier versions of the CMBall data set \citep{BCP03,mactavish05}, a negative running is still favored at about the $\sigma$ level by each of the data combinations considered."
 The models including running favor siguificautlv owe values of the scalar spectral index. nv.=0.903pointroe," The models including running favor significantly lower values of the scalar spectral index, $n_s=0.903^{+0.029}_{-0.028}$."
 However this result depends on the choice of pivot Ay: a sinallervalue would vield a higher result while a higher one would givean even lower result., However this result depends on the choice of pivot point $k_\star$ : a smallervalue would yield a higher result while a higher one would givean even lower result.
 As described in Section 6.2... fluctuations from the thermal Suuvaev-Zeldovich (SZ) effect are expected to dominate over the damped primordialcontributions to the CMD anisotropy atmultipolesbevoud (~ 2500.," As described in Section \ref{sec:excess}, , fluctuations from the thermal Sunyaev-Zel'dovich (SZ) effect are expected to dominate over the damped primordialcontributions to the CMB anisotropy atmultipolesbeyond $\ell \sim 2500$ ."
 The magnitude oftheSZ signal depends strongly on, The magnitude oftheSZ signal depends strongly on
"Circumstellar disks of gas and dust, a natural result of the conservation of angular momentum, are a common outcome of the star formation process.","Circumstellar disks of gas and dust, a natural result of the conservation of angular momentum, are a common outcome of the star formation process."
" find that over half the low mass (« 2 Mo) pre-main-sequence T Tauri stars in the Taurus-Auriga star formation region have more infrared emission than expected from a normal stellar photosphere, indicating the presence of a dusty circumstellar disk heated by the parent star as well as active accretion."," find that over half the low mass $<$ 2 $_{\odot}$ ) pre–main-sequence T Tauri stars in the Taurus-Auriga star formation region have more infrared emission than expected from a normal stellar photosphere, indicating the presence of a dusty circumstellar disk heated by the parent star as well as active accretion."
" T Tauri stars fall into two categories: Weak-Line T Tauri Stars (WTTSs), characterized by low Ha equivalent widths, and Classical T Tauri Stars (CTTSs), with higher Ho equivalent widths indicative of ongoing gas accretion."," T Tauri stars fall into two categories: Weak-Line T Tauri Stars (WTTSs), characterized by low $\alpha$ equivalent widths, and Classical T Tauri Stars (CTTSs), with higher $\alpha$ equivalent widths indicative of ongoing gas accretion."
" These circumstellar disks generally have the following properties al.|2009):: mass surface densities U(r)οςr°%19, surface temperatures T(r)οςr9*99-8 (depending ondisk flaring), and Keplerian rotational velocitiesV(r)ος r9."," These circumstellar disks generally have the following properties : mass surface densities $\Sigma(r)\propto r^{0\,\mathrm{to}\,-1.0}$, surface temperatures $T(r)\propto r^{0\,\mathrm{to}\,-0.6}$ (depending ondisk flaring), and Keplerian rotational velocities$V(r)\propto r^{0.5}$ ."
"result from this double Caussian fitting test should be taken seriously, We are presenting a result frou this test in order to see if we find the same kind of the dependency of fitted paraicters on the fitting method which we find int 16 Bahuer lues as a way to support our asstuuption that the Paschen line profiles are similar to the Bahuer line profiles.","result from this double Gaussian fitting test should be taken seriously, We are presenting a result from this test in order to see if we find the same kind of the dependency of fitted parameters on the fitting method which we find in the Balmer lines as a way to support our assumption that the Paschen line profiles are similar to the Balmer line profiles."
" lu iuost Case, he fitted values from the double componen fit agree with those frou the single componen fit (without the additional correction factor). where the FWIIA and flux values from the double componen fittines aro in average larger and sxnaller than he sinele component fitting results respectively."," In most case, the fitted values from the double component fit agree with those from the single component fit (without the additional correction factor), where the FWHM and flux values from the double component fittings are in average larger and smaller than the single component fitting results respectively."
 This agrees well with the treu we fiud from our analysis of the Bahuer lines using single. double. aud multiple component Gaussian fittings (see above).," This agrees well with the trend we find from our analysis of the Balmer lines using single, double, and multiple component Gaussian fittings (see above)."
 One exception is | 002310.5. whose FWIIM changed by about., One exception is $+$ 002340.8 whose FWHM changed by about.
 Distiuguishiug the narrow aud the broad compoucuts is difficult for this object. therefore the mean value between the parameters roni the two different methods was adopted as the best-fit value. with the half of the difference as its error.," Distinguishing the narrow and the broad components is difficult for this object, therefore the mean value between the parameters from the two different methods was adopted as the best-fit value, with the half of the difference as its error."
" We rote that the double compoucut fit improved thereduced. \? values VAienificantlv. >OF 3) for only three objects. where the oeuprovenient cane from fitting of xoad extended wines which did uot affect the derived fing parameter values rather than through the chanec ft the ΕΛΗΝ values (except for | 0023hay,"," We note that the double component fit improved thereduced $\chi^{2}$ values significantly $> 0.3$ ) for only three objects, where the improvement came from fitting of broad extended wings which did not affect the derived fitting parameter values rather than through the change of the FWHM values (except for $+$ 002340.8)."
" Finally. the aeasured FWIAIs were corrected for the instrumental resolution aud the fitting methodology (anultiple component fit versus singele conrponeut fit). are the fluxes were coiverted to the ununositv assunmiues a standard ACDAL cosinology of 7270 kan secI d. Q,,, 20.3 aud O4204 (ee. hu et al."," Finally, the measured FWHMs were corrected for the instrumental resolution and the fitting methodology (multiple component fit versus single component fit), and the fluxes were converted to the luminosity assuming a standard $\Lambda$ CDM cosmology of $H_{0}$ =70 km $^{-1}$ $^{-1}$, $\Omega_{m}$ =0.3 and $\Omega_{\Lambda}$ =0.7 (e.g., Im et al."
 1997)., 1997).
 The LLOASTILCC lue hunuinosities. fluxes. aud FWIIMSs are preseuted iu Table 1..," The measured line luminosities, fluxes, and FWHMs are presented in Table \ref{tbl1}."
 LOS preseut the results of their line analvsis. base ou the NIR specra that were taken with the Spex spectrograph (Ravueretal.2003) ou the Iufrar« Telescope Facility (RTF) at an average spectra resolutiou of 1 XusLl.," L08 present the results of their line analysis, based on the NIR spectra that were taken with the Spex spectrograph \citep{rayner03} on the Infrared Telescope Facility (IRTF) at an average spectral resolution of 400 $\mathrm{km~s^{-1}}$."
 For the LOS sample. we use the line fluxes iux FWIIMS derived by them aud preseutec in them Tahle 2. after correcting ΕΠΑΕvalues for the instimental resolution.," For the L08 sample, we use the line fluxes and FWHMs derived by them and presented in their Table \ref{tbl2}, after correcting FWHMvalues for the instrumental resolution."
 We also applied the correction facOr οf ue; Leiqrbroad 50.9 and Loau/L singiebroud=l.08 which corrects for the difference in the line-fitting methods (LOS versus Greene Πο 2005) Oo cevive the line. parameters which are simular to the correction factors we derived for the fitting xocess of the G6 spectra., We also applied the correction factor of $_{multi}$ $_{single broad}$ =0.9 and $L_{multi}$ $L_{single broad}$ =1.08 which corrects for the difference in the line-fitting methods (L08 versus Greene Ho 2005) to derive the line parameters which are similar to the correction factors we derived for the fitting process of the G06 spectra.
 As for the accuracy of the LOS measurements. LOX quote a typical error of of ess.," As for the accuracy of the L08 measurements, L08 quote a typical error of of less."
" Therefore. we adopt a couscrvative value of for he measurement error of the fiuxes and the EWIIMSs ILOSCILed in Los,"," Therefore, we adopt a conservative value of for the measurement error of the fluxes and the FWHMs presented in L08."
 We note that contamination from the jost galaxy light o these measurements is negligible., We note that contamination from the host galaxy light to these measurements is negligible.
 The contamination ofthe ine flux due to the host galaxy is )ossible. but the (06 data were taken with a narrow slit to niunuize the 1ost ealaxy light to less than8%.," The contamination of the line flux due to the host galaxy is possible, but the G06 data were taken with a narrow slit to minimize the host galaxy light to less than."
. We expect that the SOC sateineut holds true for the LOS sample whose data were taken with a narrow slit for AGNs at z«0.1 which are located much closer to us than the C06 sample., We expect that the same statement holds true for the L08 sample whose data were taken with a narrow slit for AGNs at $z < 0.1$ which are located much closer to us than the G06 sample.
 Before constructing mass estimators based on the Paschen lines. we show here that how well the propertics of the Paschen lines correlate with the Balmer lines.," Before constructing mass estimators based on the Paschen lines, we show here that how well the properties of the Paschen lines correlate with the Balmer lines."
 A ight correlation between the two lines would imply that he Paschen lines originate from the broad line regious siular to the Balmer lines. thus serving as a strong justification for the use of the Pascheu lines as a mass estimator.," A tight correlation between the two lines would imply that the Paschen lines originate from the broad line regions similar to the Balmer lines, thus serving as a strong justification for the use of the Paschen lines as a mass estimator."
 Good correlations between the FWIAL values of the broad Bahuer lues aud the broad. Paschen lines were shown in Lüs., Good correlations between the FWHM values of the broad Balmer lines and the broad Paschen lines were shown in L08.
 Here. we extend the analysis to the ine flux ratios. aud add quasars from the G06 sample to he LOS sample to strenethen the eooduess of the FWIAL correlation.," Here, we extend the analysis to the line flux ratios, and add quasars from the G06 sample to the L08 sample to strengthen the goodness of the FWHM correlation."
 Furthermore. we also derive equations that relate the properties of the Daliner aud the Paschenu lines.," Furthermore, we also derive equations that relate the properties of the Balmer and the Paschen lines."
 Figure 5 shows the correlation between EWIIM values of the Bahuer and the Paschen broad Ines. while Figure 6 shows a correlation of line Iuuinosities of the broad Imes.," Figure 5 shows the correlation between FWHM values of the Balmer and the Paschen broad lines, while Figure 6 shows a correlation of line luminosities of the broad lines."
 To derive the correlations between the two quantities. we performed a linear bisector fit using the equations below.," To derive the correlations between the two quantities, we performed a linear bisector fit using the equations below."
 lere. X aud Y are line ideutifiors. iud A aud D are the correlation cocficicuts iu the fit for FWHAL aud C and D are the coefiicients for the line ποστ ratio fit.," Here, X and Y are line identifiers, and A and B are the correlation coefficients in the fit for FWHM, and C and D are the coefficients for the line luminosity ratio fit."
 The results of the fitting are suuuarized in Table 2., The results of the fitting are summarized in Table 2.
 The table also lists the rius scatter of the data poiuts with respect to the best-fit lines., The table also lists the rms scatter of the data points with respect to the best-fit lines.
 These results show that the Pascheu line buuinosities and PWHAs correlate well with those of the Baluer lines., These results show that the Paschen line luminosities and FWHMs correlate well with those of the Balmer lines.
 The iis scatters iu the line Iuninositv correlation are ~O.12-0.11 dex against Ha. and ~0.16-0.19 dex against IL.," The rms scatters in the line luminosity correlation are $\sim$ 0.12-0.14 dex against $\alpha$, and $\sim$ 0.16-0.19 dex against $\beta$."
 For the FWOAL values. the rms scatters are 0.015-0.06 dex against Ta. aud 0.05-0.06 dex agaist IL.," For the FWHM values, the rms scatters are 0.045-0.06 dex against $\alpha$, and 0.05-0.06 dex against $\beta$."
 The slightly larger scatters aud a notable offset im FWIIM. values of I} against Pascheu lines suggest the conplexities in ACN spectra around I> line noted iu LOS. an excess. broad compoucut in the red part of the IT? ne caused bv an unclear origin (c.g.. Mevers Peterson 1985: Vórron et al.," The slightly larger scatters and a notable offset in FWHM values of $\beta$ against Paschen lines suggest the complexities in AGN spectra around $\beta$ line noted in L08, an excess, broad component in the red part of the $\beta$ line caused by an unclear origin (e.g., Meyers Peterson 1985; Vérron et al."
 2002)., 2002).
 We also poiut out that the line widths of Balmer lunes are systematically larecr than those of the Pascheu lines. aud that the trend is stronger as the wavelength decreases.," We also point out that the line widths of Balmer lines are systematically larger than those of the Paschen lines, and that the trend is stronger as the wavelength decreases."
 This suggests that the Paschen broad Hines and the Baluer broad lues originate from a simular BLR. but with Baluer lines originating from the iuner region of the BER thau Paschen limes.," This suggests that the Paschen broad lines and the Balmer broad lines originate from a similar BLR, but with Balmer lines originating from the inner region of the BLR than Paschen lines."
" Siuilarh. we also examine correlations between (Lo, J aud Lp,a."," Similarly, we also examine correlations between $L_{5100\mathrm{\AA{}}}$ ) and $L_{\mathrm{P\alpha,\beta}}$ ."
 Ποια values are derived frou. L(5100) using Equation (1) of (Caeene&Πο 2005).., $R_{\mathrm{BLR}}$ values are derived from $L(5100)$ using Equation (4) of \citep{greene05}. .
 Fiewe 7 shows the correlation between Πριν aud Paschen line huninositics. aud Equations (1) aud (5) are the best-fit results.," Figure 7 shows the correlation between $R_{BLR}$ and Paschen line luminosities, and Equations (4) and (5) are the best-fit results."
significant reddening. we make no reddening correction of the line ratios.,"significant reddening, we make no reddening correction of the line ratios."
 To investigate the physical conditions implied. by both the low jonisation and high ionisation species. the photoionisation model code (Ferlandetal.1998) was used to create single slab photoionisation models for the emission lines of Q1131|16.," To investigate the physical conditions implied by both the low ionisation and high ionisation species, the photoionisation model code \citep{ferland} was used to create single slab photoionisation models for the emission lines of Q1131+16."
 Phe ionisation parameter was varied over the range -3.0 x log x 0. in steps of logU]-0.5. and the hydrogen density U]was varied over the range 3.0 x log(ng em 7) S.0 in steps of log(ng 7) =0.5.," The ionisation parameter was varied over the range -3.0 $\leq$ log[U] $\leq$ 0, in steps of log[U]=0.5, and the hydrogen density was varied over the range 3.0 $\leq$ $n_H$ $^{-3}$ ) $\leq$ 8.0 in steps of $n_H$ $^{-3}$ ) =0.5."
 Phe rest of the properties of the model were, The rest of the properties of the model were
mass loss) become stronger with decreasing energy. a behavior similar to the (vpical (vpes of shock formation (e.g.. see Lu et al.,"mass loss) become stronger with decreasing energy, a behavior similar to the typical types of shock formation (e.g., see Lu et al."
 1997 for adiabatic shocks: Lu Yuan 1998. Fukumura Tsuruta 2004 for isothermal shocks).," 1997 for adiabatic shocks; Lu Yuan 1998, Fukumura Tsuruta 2004 for isothermal shocks)."
 To exclusively illustrate the black hole spin dependence α of the mass loss efficiency. {νι we fix all other parameters (£4.À. raj) except lor a.," To exclusively illustrate the black hole spin dependence $a$ of the mass loss efficiency $f_{\dot{M}}$ we fix all other parameters $E_1, \lambda, r_{\rm sh}$ ) except for $a$ ."
" Figure 7 shows Jy, against e and fr for A=3.45 and ryfr=30."," Figure \ref{fig:spin}
 shows $f_{\dot{M}}$ against $a$ and $f_E$ for $\lambda=3.45$ and $r_{\rm sh}/m=30$."
" As seen in the earlier results. black hole rotation alone can clearly enhance the efficiency of mass outflows fy, from ~3% (for a/m= 0) up to ~95% (Lor a/m= 0.35)."," As seen in the earlier results, black hole rotation alone can clearly enhance the efficiency of mass outflows $f_{\dot{M}}$ from $\sim 3\%$ (for $a/m=0$ ) up to $\sim 95\%$ (for $a/m=0.35$ )."
 On the other hand. the corresponding energy loss efficiency. fj remains as low as e0.02—0.1%.," On the other hand, the corresponding energy loss efficiency $f_E$ remains as low as $\sim 0.02 - 0.1\%$."
 Note here that A would have to be properly adjusted in order to obtain Cie solutions for higher black hole spin a., Note here that $\lambda$ would have to be properly adjusted in order to obtain the solutions for higher black hole spin $a$.
 We have chosen above some representative values for the flow energv lor parametric purpose., We have chosen above some representative values for the flow energy for parametric purpose.
 Weakly viscous/invisckl accretion in general is a good model for some limited specilic cases. like our Galactic center. for example.," Weakly viscous/inviscid accretion in general is a good model for some limited specific cases, like our Galactic center, for example."
 For such specific cases. the realistic ‘hoice of enerey should be very small.," For such specific cases, the realistic choice of energy should be very small."
 From (his perspective we examine {οsee whether low pFyergy flows can still produce shock-driven outflows., From this perspective we examine tosee whether low energy flows can still produce shock-driven outflows.
" Figure 8. shows mass loss efliciency {ή iS a function of ry, for em.=0.", Figure \ref{fig:low-E} shows mass loss efficiency $f_{\dot{M}}$ as a function of $r_{\rm sh}$ for $a/m=0$.
 We set νι=1.000001 and A=3.73., We set $E_1=1.000001$ and $\lambda=3.73$.
 Mass outflows can poendeed be produced with f; ranging from ~1'4 up to ~65%.," Mass outflows can indeed be produced with $f_{\dot{M}}$ ranging from $\sim 1\%$ up to $\sim
65\%$."
 Both unstable and stable 10cks are present as in (he earlier cases but not continuously connected (no shock regions between the (wo)., Both unstable and stable shocks are present as in the earlier cases but not continuously connected (no shock regions between the two).
 The range of shock location is much narrower in radius in (liis case. over which the mass loss efficiency can significantly change as mentioned above.," The range of shock location is much narrower in radius in this case, over which the mass loss efficiency can significantly change as mentioned above."
 We will discuss is more in (he Discussion section., We will discuss this more in the Discussion section.
 Themajor correlations we [find among (he primary parameters are summarized in Table 1.., Themajor correlations we find among the primary parameters are summarized in Table \ref{tab:tbl-1}. .
 Table 2. shows various correlations with shock strength., Table \ref{tab:tbl-2} shows various correlations with shock strength.
 Compression ratio ns/n4 , Compression ratio $n_2/n_1$ 
Can pre-enriched gas produce a good fit to the observations?,Can pre-enriched gas produce a good fit to the observations?
 We tried a model with2o delaved increase in SE. elliciency and gas inllow. but. which is mace from pre-enriched gas 17 Gyr ago. such as might be expected from à very top heavy IME from which there is a high level of feedback to enrich the ISM. and very little material is left. trapped: in. stars.," We tried a model with delayed increase in SF efficiency and gas inflow, but which is made from pre-enriched gas 17 Gyr ago, such as might be expected from a very top heavy IMF from which there is a high level of feedback to enrich the ISM and very little material is left trapped in stars."
 We assumed Co=0.7 (thought to be typical for ellipticals FOO. although mocels with carly galactic winds require much higher values of C).," We assumed $C=0.7$ (thought to be typical for ellipticals – FG94, although models with early galactic winds require much higher values of $C$ )."
 For those galaxies with very old starbursts (t:=2 or less). apre-enriched. single burst model can give comparable fits to the data (as those in table 5).," For those galaxies with very old starbursts $*=2$ or less), a, single burst model can give comparable fits to the data (as those in table 5)."
 The pre-enriched gas required for these fits starts olf with metallicity Z 0.5 to 0.75 solar., The pre-enriched gas required for these fits starts off with metallicity $Z\sim$ 0.5 to 0.75 solar.
 This confirms our earlier suggestion that the stars dominating the light at the current epoch have to be made from. enriched material., This confirms our earlier suggestion that the stars dominating the light at the current epoch have to be made from enriched material.
 Llowever. for other galaxies the observed strength of LL? rules out an entirely old stellar population.," However, for other galaxies the observed strength of $\beta$ rules out an entirely old stellar population."
 These are the galaxies which required an intermediate (NGC 5831. NGC 2329) or voung (NGC 221) starburst in our delaved burst models (table 5).," These are the galaxies which required an intermediate (NGC 5831, NGC 2329) or young (NGC 221) starburst in our delayed burst models (table 5)."
 Worthey (1996). suggested. that a model of. elliptical formation with several episodes of star formation corresponding to mergers and/or interactions can Lit some of the observational [acts (e.g. presence of kinematic sub-structures. evidence for voung stars).," Worthey (1996) suggested that a model of elliptical formation with several episodes of star formation corresponding to mergers and/or interactions can fit some of the observational facts (e.g. presence of kinematic sub-structures, evidence for young stars)."
" ""Therefore. a future extension to the current models is to try including more starbursts.", Therefore a future extension to the current models is to try including more starbursts.
 However this introduces many more free parameters and the latest burst. will remain important ini terms of iis relative luminosity., However this introduces many more free parameters and the latest burst will remain important in terms of its relative luminosity.
 Worthey (1996) suggested that more bursts at earlier times may explain the observations of earlv-twpe. galaxies., Worthey (1996) suggested that more bursts at earlier times may explain the observations of early-type galaxies.
 Since we can already produce strong enough. lines with a single delayed: burst. more bursts will still not get round the problem of non-solar ratios. which contributes to the poor fits of current models to observations of some ellipticals.," Since we can already produce strong enough lines with a single delayed burst, more bursts will still not get round the problem of non-solar ratios, which contributes to the poor fits of current models to observations of some ellipticals."
 V96 showed that no single IME. constant in time. can generate the observed. line-streneths in a closed box mocel with a single SER constant.," V96 showed that no single IMF, constant in time, can generate the observed line-strengths in a closed box model with a single SFR constant."
 The elfects of a changing LME with time are explored by V96., The effects of a changing IMF with time are explored by V96.
 They find that a shallow LM at early times (followed bv a normal IME like that inferred for local stars) can produce stellar populations with lines as strong as those seen in earlv-tvpe galaxies., They find that a shallow IMF at early times (followed by a normal IMF like that inferred for local stars) can produce stellar populations with lines as strong as those seen in early-type galaxies.
 So. primordial ellipticals with a single EME are still ruled out for clillerent assumptions about the slope of the IME. but changing the IME with time. from shallow to steep. can produce strong lines.," So 'primordial' ellipticals with a single IMF are still ruled out for different assumptions about the slope of the IMF, but changing the IMF with time, from shallow to steep, can produce strong lines."
 We showed above that an early LATIF of massive stars (pre-enriching the ISM prior to normal SE) can fit the data for some galaxies as well as our merger model., We showed above that an early IMF of massive stars (pre-enriching the ISM prior to normal SF) can fit the data for some galaxies as well as our merger model.
 However. we note that strong interactions and mergers. accompanied bv highly increased. SE and rapid gas inflow are.observced to occur and that both observations and simulations tell us that such events can produce earlv-tvpe galaxies.," However, we note that strong interactions and mergers, accompanied by highly increased SF and rapid gas inflow are to occur and that both observations and simulations tell us that such events can produce early-type galaxies."
 On the other hand evidence for a variable ΠΟ is not so definite ucher Fahlman 1996)., On the other hand evidence for a variable IMF is not so definite (Richer Fahlman 1996).
 In fact Pacloan. Nordlund Jones (1997) recently. argued. for a universal IME. arising [rom 1 statistics of random. supersonic [lows which simulate conditions during star formation.," In fact Padoan, Nordlund Jones (1997) recently argued for a universal IMF, arising from the statistics of random supersonic flows which simulate conditions during star formation."
 So there is no need for v variable LAL to. produce the observed. line-strengths in ellipticals., So there is no need for a variable IMF to produce the observed line-strengths in ellipticals.
 Non-solar light-to-heavy metal ratios seem. required by the data for most earlv-tvpe galaxies (e.g. Fig., Non-solar light-to-heavy metal ratios seem required by the data for most early-type galaxies (e.g. Fig.
 6)., 6).
 Fits to the observed Mg» index are improved for models withofd stars if the Ales calibrations for dillerent Mg/Ee ratios from Barbuy (1994) are used., Fits to the observed $_2$ index are improved for models with stars if the $_2$ calibrations for different Mg/Fe ratios from Barbuy (1994) are used.
 Fig., Fig.
 7 compares a fit to the data for NGC 4472. and shows how the Mg» index is better fitted when non-solar Alefle is accounted for in these old stars.," 7 compares a fit to the data for NGC 4472, and shows how the $_2$ index is better fitted when non-solar Mg/Fe is accounted for in these old stars."
 We also tried modelling Mg» and «Eez (mean of Fe5270 and. Le5335) features. using SSPs from Weiss. Peleticr Alatteucci (1995) (from the top half of their table 4).," We also tried modelling $_2$ and $<$ $>$ (mean of Fe5270 and Fe5335) features, using SSPs from Weiss, Peletier Matteucci (1995) (from the top half of their table 4)."
 Weiss et aallowed. for enhanced. a-element compositions and published values for Mg» and «LEFez indices for old (12 to Ls Gyr). metal rich (CZ> Z.) SSPs with Mg/Fez solar.," Weiss et allowed for enhanced $\alpha$ -element compositions and published values for $_2$ and $<$ $>$ indices for old (12 to 18 Gyr), metal rich $Z\ge$ $_{\odot}$ ) SSPs with $\ge$ solar."
 Fig., Fig.
 S shows the predictions of some of our models with delayed, 8 shows the predictions of some of our models with delayed
eiven by (Allen&Romano1999.equation3.75) llere ο) is the ‘overlap reduction funcüon. which accounts for the separation and relative orientation of the detectors (Flanagan1993).. and πι) and 2>(f) are the noise power spectral densities of the detectors. and 1 is the integration time.,"given by \citep[][equation 3.75]{SNR}
 Here $\gamma (f)$ is the `overlap reduction function', which accounts for the separation and relative orientation of the detectors \citep{gammaf}, , and $P_1(f)$ and $P_2(f)$ are the noise power spectral densities of the detectors, and $T$ is the integration time."
 As the optimal filter depends on GOcC/). a range of filler fanctious based. on theoretical expectations of this [function will need to be used.," As the optimal filter depends on $\Omega_{\rm{GW}}(f)$, a range of filter functions based on theoretical expectations of this function will need to be used."
 In this study we use data of relative positions ancl orientations for 10 independent pairs of the five advanced detectors given in Table 3 of Nishizawaetal.(2009). ancl emplov the tensor-imode functions described in their equations (33-35)., In this study we use data of relative positions and orientations for 10 independent pairs of the five advanced detectors given in Table 3 of \citet{gamma2} and employ the tensor-mode functions described in their equations (33-35).
 For ET we assume lwo detectors of triangular shape (GO° between (he (vo arms) and separated by an angle of 1207. for which the ο} has a constant value of —3/8 from 1 Iz to 1000 Hz (lowelletal.2011).," For ET we assume two detectors of triangular shape $60^{\circ}$ between the two arms) and separated by an angle of $120^{\circ}$, for which the $\gamma(f)$ has a constant value of $-3/8$ from 1 Hz to 1000 Hz \citep{Eric2010}."
. We adopt a value of SNR = 3 to indicate detection. corresponding with false alarm rate of and detection rate of (Allen&Romano1999).," We adopt a value of SNR = 3 to indicate detection, corresponding with false alarm rate of and detection rate of \citep{SNR}."
. We also assume an integration time of 3 vears lor advanced detectors and 1 vear for ET., We also assume an integration time of 3 years for advanced detectors and 1 year for ET.
 Calculating the SNRs for SGWD model (e) shown in Figure 3. we find a value of 0.14 through eross-correlation by two the Advanced LIGO detectors Il-L. For the other four models shown in Figure 3. we find variation in SNR of within 20%.," Calculating the SNRs for SGWB model (e) shown in Figure 3, we find a value of 0.14 through cross-correlation by two the Advanced LIGO detectors H-L. For the other four models shown in Figure 3, we find variation in SNR of within $20\%$."
 For ET we find SNRs of 59 and 112 assuming ET-B and ET-D sensitivities respectively for model (e). indicating that this signal will be easilv-detected by third generation detectors.," For ET we find SNRs of 59 and 112 assuming ET-B and ET-D sensitivities respectively for model (e), indicating that this signal will be easily-detected by third generation detectors."
" These results. based on average quantities. suggest that to detect the DBII background with two Advanced LIGO detectors will require a rate greater than even the higher rate estimate. ro.~0.43Mpe""Myr.|,"," These results, based on average quantities, suggest that to detect the BBH background with two Advanced LIGO detectors will require a rate greater than even the higher rate estimate, $r_{2}\,\sim 0.43\,\rm{Mpc}^{-3}\rm{Myr}^{-1}$."
 As there will exist variation in the sensitivities. locations and orientations of detectors within a worldwide detector network. it is useful to compare the performances of different detector pairs and investigate how combining the network could improve the detection prospects.," As there will exist variation in the sensitivities, locations and orientations of detectors within a worldwide detector network, it is useful to compare the performances of different detector pairs and investigate how combining the network could improve the detection prospects."
 Two approaches of combining 2N detectors to increase (he sensitivity of a stochastic background search have been proposed by Allen&Romano(1999)., Two approaches of combining 2N detectors to increase the sensitivity of a stochastic background search have been proposed by \citet{SNR}.
. We apply these two methods to a network of 4 second generation detectors., We apply these two methods to a network of 4 second generation detectors.
 In each case. (he optimal SNR can be expressed as follows. with individual detectors (1-4) indicated in parenthesis:(i) (FC) - can be performed by directly correlating the outputs of 4 detectors," In each case, the optimal SNR can be expressed as follows, with individual detectors (1-4) indicated in parenthesis:(i) (FC) - can be performed by directly correlating the outputs of 4 detectors"
ünages were compared with the i data obtained by Cotté (1995). and it appears that the emission peaks seen in our Ha image do uot have any counterparts in the / image.,"images were compared with the $i$ data obtained by Côtté (1995), and it appears that the emission peaks seen in our $\alpha $ image do not have any counterparts in the $i$ image."
 This uxdicates that they could be genuine ΠΠ regious. so they are listed as well in Table 2.," This indicates that they could be genuine HII regions, so they are listed as well in Table 2."
 None of the fIuxes given iu Table 2 have been corrected for [NIL] contamination: these dwarf galaxies have typically very low nitrogen abundances (see companion paper). so this introduces au additional ~6% {lus uncertainty.," None of the fluxes given in Table 2 have been corrected for [NII] contamination; these dwarf galaxies have typically very low nitrogen abundances (see companion paper), so this introduces an additional $\sim $ flux uncertainty."
 For derivingOm accurate positions for the HII reeious.e HST Guide Star Reference Frame scaus [rom the STScI1 Digitized.man Sky1 wwere usec. and were Compared with positious obtaiued similarly by deriving astrometric plate solutions using bright stars in the Automatic Plate Measuriug (APM) catalog vvau Zee 2000).," For deriving accurate positions for the HII regions, HST Guide Star Reference Frame scans from the STScI Digitized Sky were used, and were compared with positions obtained similarly by deriving astrometric plate solutions using bright stars in the Automatic Plate Measuring (APM) catalog van Zee 2000)."
" In each case these positions agreed to within less than2"".", In each case these positions agreed to within less than.
 The HII regions in the two faintest galaxies (SC Ls aud SC 21) were just at the limit of detectability., The HII regions in the two faintest galaxies (SC 18 and SC 24) were just at the limit of detectability.
 In both cases. coincidence with continuum sources cast doubt on whether these are true Ha sources or possible artifacts of au imperfect continuum subtraction.," In both cases, coincidence with continuum sources cast doubt on whether these are true $\alpha$ sources or possible artifacts of an imperfect continuum subtraction."
 Further inspection and experimentation led to confidence that tliese are incleecl real Ha sources., Further inspection and experimentation led to confidence that these are indeed real $\alpha$ sources.
 Nouetleless. spectroscopic observations are required for coufirination.," Nonetheless, spectroscopic observations are required for confirmation."
 For the preseut paper. we will treat these Ha sources as bona lide HII regious.," For the present paper, we will treat these $\alpha$ sources as bona fide HII regions."
 Note that iu the case of the Local Group dI DDO 210. vau Zee et ((1997) found a similar single Ha detection to show broad Baliner lines aud no forbidden lines. aud they speculate that this source may be a Iuminous blue variable star.," Note that in the case of the Local Group dI DDO 210, van Zee et (1997) found a similar single $\alpha$ detection to show broad Balmer lines and no forbidden lines, and they speculate that this source may be a luminous blue variable star."
 Miller (1996) observed. aud detected: HII regious in the Sculptor group dls UCCA [12 (= ESO 171-C06) and ESO 215-G05 (= A 113). but did not detect Ha emission from six other Sculptor group dis.," Miller (1996) observed and detected HII regions in the Sculptor group dIs UGCA 442 $=$ ESO 471-G06) and ESO 245-G05 $=$ A 143), but did not detect $\alpha$ emission from six other Sculptor group dIs."
 Note that we did re-observe any of the Sculptor group dls from Miller's sample., Note that we did re-observe any of the Sculptor group dIs from Miller's sample.
 Miller's nonu-detection of HII regious in the Sculptor Dwarf Irregular Galaxy (= SDIG. ESO 319-CG1) has been confiriued by Heisler et ((1997).," Miller's non-detection of HII regions in the Sculptor Dwarf Irregular Galaxy $=$ SDIG, ESO 349-G31) has been confirmed by Heisler et (1997)."
 van Zee (2000) lias observed DDO 6 (= UGCA 15) aud did not detect any HIE regions. but did detect a small amount of diffuse Ha emission.," van Zee (2000) has observed DDO 6 $=$ UGCA 15) and did not detect any HII regions, but did detect a small amount of diffuse $\alpha$ emission."
 van Zee (2000) also observed DDO 226 (= UGCA 9) and did detect the presence of faint HII regious., van Zee (2000) also observed DDO 226 $=$ UGCA 9) and did detect the presence of faint HII regions.
 Jerjen et ((1998) detected a [aint HID region in ESO 291-C010., Jerjen et (1998) detected a faint HII region in ESO 294-G010.
 ESO 110-C402 is au HI uou-detection. and. based ou HST imagine. Ixarachentsev et ((2000) have cletermined tliat this is a dSph galaxy.," ESO 410-G05 is an HI non-detection, and, based on HST imaging, Karachentsev et (2000) have determined that this is a dSph galaxy."
 In light of the results of the more recent deeper spectroscopy. it iniglit. be interesting to re-observe the other nou-detection by Miller (1996). Le.. LCCA [38 (= ESO ," In light of the results of the more recent deeper spectroscopy, it might be interesting to re-observe the other non-detection by Miller (1996), i.e., UGCA 438 $=$ ESO 407-G18)."
Nonetheless. tle claim by Miller (1996) that the average current star formation lor dls iu the Sculptor group is suppressed relative to other nearby groups appears to be coufirmed (see discussion iu 83).," Nonetheless, the claim by Miller (1996) that the average current star formation for dIs in the Sculptor group is suppressed relative to other nearby groups appears to be confirmed (see discussion in 3)."
a redshift shell centered on the galaxy. clusters redshift z+0.) are ideutifiecl as members.,a redshift shell centered on the galaxy cluster's redshift $z_c \pm \delta_z$ ) are identified as members.
 Because photometric redshifts have a large uncertainty. (generally a factor of teu to fifty. higher hau spectroscopic redshifts). a large recslift shell 0.0.05) is used to identify likely cluster jembers.," Because photometric redshifts have a large uncertainty (generally a factor of ten to fifty higher than spectroscopic redshifts), a large redshift shell $\delta_z
\approx 0.05$ ) is used to identify likely cluster members."
 While certainly. useful. this approach does uot provide a reliable meaus for identifviug ine-ol-sieht coutamiuatiug galaxies.," While certainly useful, this approach does not provide a reliable means for identifying line-of-sight contaminating galaxies."
 As a result. we have developed au alternative technique which relies on. the probabilistic interpretation of a photometric redshift to determine cluster membership.," As a result, we have developed an alternative technique which relies on the probabilistic interpretation of a photometric redshift to determine cluster membership."
 We define the probability ensity functiou. Pfs). for an individual galaxys redshift to be a Gaussian probability distribution uuction with mean (5) given by the estimated photometric redshift aud standard deviation (o) elined by the estimated error in the photometric recshift.," We define the probability density function, $\Phi(z)$, for an individual galaxy's redshift to be a Gaussian probability distribution function with mean $\mu$ ) given by the estimated photometric redshift and standard deviation $\sigma$ ) defined by the estimated error in the photometric redshift."
 Usine this interpretation. we can calculate the probability that a galaxy has au actual redshift within a eiven redshift interval.," Using this interpretation, we can calculate the probability that a galaxy has an actual redshift within a given redshift interval."
 where N is a suitable normalization factor. z« is the cluster redshift. Az is the width in recshift space which vou are saiupliug. the limits of integratiou are and 5 is the incomplete eamma function. (," where $N$ is a suitable normalization factor, $z_c$ is the cluster redshift, $\Delta z$ is the width in redshift space which you are sampling, the limits of integration are and $\gamma$ is the incomplete gamma function. ("
Of course. 5[2.2] is also known as the error function. erfiz)).,"Of course, $\gamma[\frac{1}{2},z]$ is also known as the error function, $erf(z)$ )."
 Within this formalism. the only. uudeclared quantity is o or. alternatively. the uncertainty iu he estimated redshilt for a given galaxy.," Within this formalism, the only undeclared quantity is $\sigma$ or, alternatively, the uncertainty in the estimated redshift for a given galaxy."
 In our framework. this value can either be determined rou the intrinsic error in our photometric redshilt relation or in a separately calculated extrinsic error.," In our framework, this value can either be determined from the intrinsic error in our photometric redshift relation or in a separately calculated extrinsic error."
 As a result. this approach is stronely depeudent on the actual technique used to estimate he photometric redshift error and corresponding redshift error.," As a result, this approach is strongly dependent on the actual technique used to estimate the photometric redshift error and corresponding redshift error."
 In this paper. we have applied this echuique using empirically derived photometric redshilis since we have a well-defined calibration dataset of spectroscopic redshifts.," In this paper, we have applied this technique using empirically derived photometric redshifts since we have a well-defined calibration dataset of spectroscopic redshifts."
 Eipirically defined photometric redshifts are much less seusitive o uncertainties in the shape aud the evolution with redshift of the spectralenergy distribution of ealaxies than competing techuiques such as template photometric redshifts (Brunner 1997).., Empirically defined photometric redshifts are much less sensitive to uncertainties in the shape and the evolution with redshift of the spectralenergy distribution of galaxies than competing techniques such as template photometric redshifts \citep{myThesis}. .
"as (he deviation of these discrepant points is larger (han would be expected Lor a transit. we reset the D(/,) value of (hat point to the mean of the data.","as the deviation of these discrepant points is larger than would be expected for a transit, we reset the $\it{D(t_i)}$ value of that point to the mean of the data."
 The consequences of this shall be discussed further when considering the application of these criteria to the 47 Tuc dataset., The consequences of this shall be discussed further when considering the application of these criteria to the 47 Tuc dataset.
 The detection process is complicated bv (the varying observational conditions tvpical ol long time series of photometric data., The detection process is complicated by the varying observational conditions typical of long time series of photometric data.
 These can produce pseudo periodic signals with an associated increase in photometric measurement errors., These can produce pseudo periodic signals with an associated increase in photometric measurement errors.
" In order to reduce these effects. the contribution of each datapoint before it was used in the ΟΕωςΤΗ) Calculation was weighted by the size of its photometric uncertainty. wilh the standard weighting scheme: where V; is the point weight and o; is the errorbar associated with the i"" point."," In order to reduce these effects, the contribution of each datapoint before it was used in the $C(P_{mod},\tau_{shift})$ calculation was weighted by the size of its photometric uncertainty, with the standard weighting scheme: where $W_{i}$ is the point weight and $\it{\sigma_i}$ is the errorbar associated with the $^{th}$ point."
" The result is that points with large errorbars are given a small weight and hence do not add significantly to the final CUP,o¢-του) lor that model."," The result is that points with large errorbars are given a small weight and hence do not add significantly to the final $\it{C(P_{mod},\tau_{shift})}$ for that model."
" By incorporating both of the (1ρω.Το) and AN, detection criteria. and incorporating the outlier removal and Ην weighting scheme. the real detections and [alse detections in the time-series were kept to acceptable levels."," By incorporating both of the $S(P_{mod},\tau_{shift})$ and $N_{p}$ detection criteria, and incorporating the outlier removal and $\it{W_{i}}$ weighting scheme, the real detections and false detections in the time-series were kept to acceptable levels."
 We now discuss the application of these criteria to the 47 Tuc dataset. and illustrate (heir effect on the final (transit candidate lists.," We now discuss the application of these criteria to the 47 Tuc dataset, and illustrate their effect on the final transit candidate lists."
 The data were split into (wo bins lor separate analvsis. distinguishing lightcurves with relatively low photometric scatter (0.02 mag). and (hose with somewhat higher scatter (0.02mssz0.04 mag).," The data were split into two bins for separate analysis, distinguishing lightcurves with relatively low photometric scatter $\le$ 0.02 mag), and those with somewhat higher scatter $\le$ $\le$ 0.04 mag)."
 We found that applying slightly different. values of the detection criteria to the two bins we could keep the detection levels high and false detection levels low., We found that applying slightly different values of the detection criteria to the two bins we could keep the detection levels high and false detection levels low.
" We perlormed Monte Carlo tests. adding model transits of various depthlis and curations Lo actual dataset lighteurves with differing photometric uncertainties to determine the maximum photonmetric scatter for which the aleorithm could reasonably detect. transits with depths as large as Dye,= 0.03 mag."," We performed Monte Carlo tests, adding model transits of various depths and durations to actual dataset lightcurves with differing photometric uncertainties to determine the maximum photometric scatter for which the algorithm could reasonably detect transits with depths as large as $\it{D_{tran}} =$ 0.03 mag."
 The expected depth of a transit is dependent. upon stellar magnitude and (his value is the expected transit depth lor stars at the lower limit of our search range. as described in Weldrakeetal.(2005).," The expected depth of a transit is dependent upon stellar magnitude and this value is the expected transit depth for stars at the lower limit of our search range, as described in \citet{Weld2005}."
. Stars with scatter greater than 0.04 mag were [found to suffer from Large false detection rates and an unacceptably low transit recoverability rate., Stars with scatter greater than 0.04 mag were found to suffer from large false detection rates and an unacceptably low transit recoverability rate.
 With this lower limit. the total number of lighteurves with rms. «0.04 mag in the 47 Tuc dataset is 21.950. allowing a statistically robust sample for analvsis.," With this lower limit, the total number of lightcurves with rms $\le$ 0.04 mag in the 47 Tuc dataset is 21,950, allowing a statistically robust sample for analysis."
"find that there exist correlations in the residuals of fits such as the Mgy—o and? relations; for example, at fixed o the residual SMBH mass scales approximately as ~Mp-™, and at fixed My the residuals scale as ~o14°,","find that there exist correlations in the residuals of fits such as the $M_{BH}-\sigma$ and relations; for example, at fixed $\sigma$ the residual SMBH mass scales approximately as $\sim M_{b}^{0.72}$, and at fixed $M_{b}$ the residuals scale as $\sim \sigma^{1.40}$."
" By marginalizing over two parameters — Μι and either σ or R, — they found a best-fit BHFP which minimized these residual correlations with the form Mpgg~ M?o1-4, both in simulations and for observed systems(??7)."," By marginalizing over two parameters – $M_{b}$ and either $\sigma$ or $R_e$ – they found a best–fit BHFP which minimized these residual correlations with the form $M_{BH}\sim M_b^{0.72}\sigma^{1.4}$ , both in simulations and for observed systems."
". This is statistically(?) indistinguishable from a correlation with the bulge binding energy proxy Myo? (Mpa~ and can be interpreted as reflecting the nature of (Myo?)97),feedback regulated SMBH growth: accretion accelerates until feedback is sufficient to unbind the local gas supply, abruptly terminating the inflow and cutting off further growth."," This is statistically indistinguishable from a correlation with the bulge binding energy proxy $M_b\sigma^2$ $M_{BH}\sim (M_b\sigma^2)^{0.7}$ ), and can be interpreted as reflecting the nature of feedback regulated SMBH growth: accretion accelerates until feedback is sufficient to unbind the local gas supply, abruptly terminating the inflow and cutting off further growth."
" Therefore it is more “fundamental” than its various projections, such as the Mepy—o and relations — a point we discuss in more detail in 5.1.."," Therefore it is more “fundamental"" than its various projections, such as the $M_{BH}-\sigma$ and relations – a point we discuss in more detail in \ref{sec:discussion_fundamental}."
" To systematically test this hypothesis, we examine the binding energy correlation — which is statistically equivalent to the BHFP - in three different modes of SMBH fueling: major mergers, minor mergers, and unstable disks (see 3 for details)."," To systematically test this hypothesis, we examine the binding energy correlation – which is statistically equivalent to the BHFP – in three different modes of SMBH fueling: major mergers, minor mergers, and unstable disks (see \ref{sec:sims} for details)."
" Figure 9 shows the binding energy correlation for major mergers (grey hexagons), the mass ratio series (left: colored points; right: black triangles), and unstable disks (right: colored points), along with the observations listed in?."," Figure \ref{fig:bhfp_all} shows the binding energy correlation for major mergers (grey hexagons), the mass ratio series (left: colored points; right: black triangles), and unstable disks (right: colored points), along with the observations listed in."
". We find that over a range of baryonic masses, gas fractions, and orbital parameters they all lie along the same relation to within the scatter, and that all reproduce the observed correlation."," We find that over a range of baryonic masses, gas fractions, and orbital parameters they all lie along the same relation to within the scatter, and that all reproduce the observed correlation."
" Inasmuch as their growth is terminated at a critical accretion rate, the final masses of SMBHs should not be determined by the available fuel supply so long as the gas reservoir is much more massive than the SMBH."," Inasmuch as their growth is terminated at a critical accretion rate, the final masses of SMBHs should not be determined by the available fuel supply so long as the gas reservoir is much more massive than the SMBH."
" While it is the case that the final SMBH mass is strongly correlated with the total gas mass of the system, this reflects the structural properties of bulges in gas-rich merger remnants: owing the effects of dissipation, a more gas rich progenitor will lead to a more compact bulge at fixed total mass, and consequently a deeper central potential φε and velocity dispersion o???).."," While it is the case that the final SMBH mass is strongly correlated with the total gas mass of the system, this reflects the structural properties of bulges in gas–rich merger remnants: owing the effects of dissipation, a more gas rich progenitor will lead to a more compact bulge at fixed total mass, and consequently a deeper central potential $\phi_c$ and velocity dispersion $\sigma$."
" As shown by for major mergers, at fixed potential the gas fraction has no effect on SMBH growth."," As shown by for major mergers, at fixed potential the gas fraction has no effect on SMBH growth."
" One method of illustrating this is presented in Figure 10,, which shows the BHFP and binding energy correlations for the mass ratio series (colored points) as compared to those derived from simulations of major mergers (grey hexagons; solid line with the dotted line indicating the scatter)."," One method of illustrating this is presented in Figure \ref{fig:bind_gas_move}, which shows the BHFP and binding energy correlations for the mass ratio series (colored points) as compared to those derived from simulations of major mergers (grey hexagons; solid line with the dotted line indicating the scatter)."
" Here we show that increasing the initial gas fraction from f,—0.4 to 0.8 for the identical interaction will drive the remnant along the BHFP and binding energy correlations, but not systematically away"," Here we show that increasing the initial gas fraction from $f_g=0.4$ to $0.8$ for the identical interaction will drive the remnant along the BHFP and binding energy correlations, but not systematically away"
right-hand side) is much larger thaw COPCτςp,right-hand side) is much larger than $\GTcore^2$.
 Asa result. changing Teoreg has only a small effect ou Typ9.," As a result, changing $\GTcore$ has only a small effect on $T_{\ND,9}$."
 Even if the direct. Urea process were to operate aud cool the core to νου«1. the temperature around neutron drip will remain high.," Even if the direct Urca process were to operate and cool the core to $\GTcore \ll 1$, the temperature around neutron drip will remain high."
 As the crust temperature increases. crust neutrino bremssrahlung and the plasina neutrino orocess become increasingly important.," As the crust temperature increases, crust neutrino bremsstrahlung and the plasma neutrino process become increasingly important."
" At the higher accretiot rate. the brighter crust neutrino uminosity balauces the nuclear heating ""on the spot.”"," At the higher accretion rate, the brighter crust neutrino luminosity balances the nuclear heating “on the spot.”"
 Figure 10 compares proper temperature panel)) aud scaled luminosity panel)). as measured yy au observer at infinite distance. or mocel aaccreting a hip (Ly=Ly242x109ergs+: and Sipe 10eres t: Une)).," Figure \ref{fig:compare-mdot}
 compares proper temperature ) and scaled luminosity ), as measured by an observer at infinite distance, for model accreting at $\dot{m}_E$ $L_A=\LAo=2.12\ee{38}\erg\second^{-1}$; ) and $5\dot{m}_E$ $L_A=5\LAo=1.06\ee{39}\erg\second^{-1}$ ; )."
 The conductivity in both cases is se by electron-ion scattering., The conductivity in both cases is set by electron-ion scattering.
 As the crust neutrio cooling increases. a sualler fraction of Ls flows outward from the op of the crust.," As the crust neutrino cooling increases, a smaller fraction of $L_N$ flows outward from the top of the crust."
 At lower accretion rates. the chauge in temperatufe over the itner crust becomes sinaller relative to tle core temperature.," At lower accretion rates, the change in temperature over the inner crust becomes smaller relative to the core temperature."
 The crust becomes 11010 1early isothermal auc len‘e Inore sensitive to tle temiperatures at its boundaries (cfMiraka-Esct«léοἱa.1990:Ztniketal. 1992). ," The crust becomes more nearly isothermal and hence more sensitive to the temperatures at its boundaries \citep[cf.~][]{miralda-escude90,zdunik92}. ."
From equation (23)). the teiiperature increase over the 1lner c‘ust ds ECOSTs ELa 0.06L4. assuiines tlat L;=La.," From equation \ref{eq:T-integrand-high}) ), the temperature increase over the inner crust is $<0.5 T_{\rm core}$ for $L_A<0.06\LAo$, assuming that $L_i=L_N$."
 Toceimonstrate this. Figure 11 «isplays. Kk al accretion uminosly £4=eres tf. the proper temperature aie ]uminosity.," To demonstrate this, Figure \ref{fig:low-mdot-sf} displays, for an accretion luminosity $L_A=0.01\LAo=2.12\ee{36}\erg\second^{-1}$ , the proper temperature and luminosity."
 The hydrostatic structure is1.1-18.. te same as in Fietre 9..," The hydrostatic structure is, the same as in Figure \ref{fig:outer-boundary}."
 The top panel is for a conductivity se by electron-ion scattering: e bottom pajel is for a coiductivity set by electron-plOIIOI) scaleriig., The top panel is for a conductivity set by electron-ion scattering; the bottom panel is for a conductivity set by electron-phonon scattering.
 Solutious for several T. ‘e shown: he range of values are reduced from those used in Figue ϱ by ο”.ο.” hich is roiely how the temperaure at the base of a hydrogen/teliuu burniug shell scaes with ‘cretion rate (Schatzetal.1999J.," Solutions for several $T_\circ$ are shown; the range of values are reduced from those used in Figure \ref{fig:outer-boundary} by $(\dot{m}/\dot{m}_E)^{2/7}=0.01^{2/7}$, which is roughly how the temperature at the base of a hydrogen/helium burning shell scales with accretion rate \citep{schatz99}."
. Of course. the hydrogeu ane 1eliunm ignition ls unsable in an envelope this cold (seeBildstetr1995.andreferences tliereiu).. a so 74 is determinec by the compressi1 of matter lu tle allic»pliere aud by the flux flowiug o he top of the crust.," Of course, the hydrogen and helium ignition is unstable in an envelope this cold \citep[see][and references
therein]{bildsten98:_nuclear}, , and so $T_\circ$ is determined by the compression of matter in the atmosphere and by the flux flowing out the top of the crust."
 As T. is reduced. LO‘e alid more of the leal geleratec in the crust flows ottwards rather than into the core.," As $T_\circ$ is reduced, more and more of the heat generated in the crust flows outwards rather than into the core."
 As fouud by Zdunikeal.(1992).. all enhlaiced Core neutriuo eulssivity will drasticaly lower the crust uperature for leWw accrellol raen.," As found by \citet{zdunik92}, an enhanced core neutrino emissivity will drastically lower the crust temperature for low accretion rates."
" To illustrate how the €""ust temperature chalges with tlie temperaure in the hydrogen,/helium Durning regiO1 (T5). E com»ute the derivaive Τομ/αΓον where Terust is the temperature at the centroid of the heat-producing reglon. p0.17MeVfin..."," To illustrate how the crust temperature changes with the temperature in the hydrogen/helium burning region $T_\circ$ ), I compute the derivative $dT_\mathrm{crust}/dT_\circ$, where $T_\mathrm{crust}$ is the temperature at the centroid of the heat-producing region, $p=0.017\MeV\fermi^{-3}$."
 Figure 12. displays doa/dI5 as a function of 1. for five cli[Terent accretio rrates: La/LA=0.01 briangles)). 0.03 friangles)). 0.1 squares)). 0.3 squares)). aud 1.0 (asterisks)).," Figure \ref{fig:sensitive} displays $dT_\mathrm{crust}/dT_\circ$ as a function of $T_\circ$ for five different accretion rates: $L_A/\LAo = 0.01$ ), 0.03 ), 0.1 ), 0.3 ), and 1.0 )."
 Whenthe coucductivity is low (electron-ion scattering:penel)). Terust Is generally less seusitive to Z7; than when scattering sets the heat trausport panel)).," Whenthe conductivity is low (electron-ion scattering;), $T_\mathrm{crust}$ is generally less sensitive to $T_\circ$ than when electron-phonon scattering sets the heat transport )."
 The derivative (at a given accretiou rate), The derivative (at a given accretion rate)
"Starting with the initial temperature profile, we can understand the evolution of the cooling layer and the resulting lightcurve by noting that at a given depth, the thermal evolution occurs on the characteristic thermal timescale associated with that depth.","Starting with the initial temperature profile, we can understand the evolution of the cooling layer and the resulting lightcurve by noting that at a given depth, the thermal evolution occurs on the characteristic thermal timescale associated with that depth."
" This is illustrated in the middle panel of Figure 5,, which shows snapshots of the profile of the crust as it cools during quiescence."," This is illustrated in the middle panel of Figure \ref{f.T-tau}, which shows snapshots of the temperature profile of the crust as it cools during quiescence."
"temperature At a given time, the temperature profile has two parts: the inner layers have not yet started to cool and still have the temperature corresponding to the initial condition (the steady state profile during outburst); the outer layers have relaxed thermally and the temperature profile there corresponds to a constant outwards flux."," At a given time, the temperature profile has two parts: the inner layers have not yet started to cool and still have the temperature profile corresponding to the initial condition (the steady state profile during outburst); the outer layers have relaxed thermally and the temperature profile there corresponds to a constant outwards flux."
 The transition occurs at a depth where the thermal time at that depth is equal to the current time., The transition occurs at a depth where the thermal time at that depth is equal to the current time.
" In the bottom panel of Figure 5,, we show the thermal time as a function of depth, where we calculate the thermal time from the surface following (1969)., where p is the density, Cp the heat, and K the thermal conductivity."," In the bottom panel of Figure \ref{f.T-tau}, we show the thermal time as a function of depth, where we calculate the thermal time from the surface following , where $\rho$ is the density, $C_{P}$ the specific heat, and $K$ the thermal conductivity."
 In the top panel of specificFigure 5 we show the temperature profiles as a function of the thermal time., In the top panel of Figure \ref{f.T-tau} we show the temperature profiles as a function of the thermal time.
 This shows directly that the deviation of each of the dashed temperature away from the initial profile occurs at a depth profileswhere the thermal time is temperatureapproximately equal to the time since cooling began., This shows directly that the deviation of each of the dashed temperature profiles away from the initial temperature profile occurs at a depth where the thermal time is approximately equal to the time since cooling began.
 The temperature of the inner crust is also affected by conduction of heat into the core., The temperature of the inner crust is also affected by conduction of heat into the core.
 We show the timescale for thermal diffusion into the core in Figure 5 line))., We show the timescale for thermal diffusion into the core in Figure \ref{f.T-tau} ).
 The two thermal times intersect at a depth (P/g~10/6 gcm) where the thermal diffusion time is x400d., The two thermal times intersect at a depth $P/g\sim 10^{16}\nsp\columnunit$ ) where the thermal diffusion time is $\approx 400\nsp\unitday$.
 After this point the temperature in the inner crust drops markedly panel))., After this point the temperature in the inner crust drops markedly ).
 This understanding suggests a simple model of the lightcurve., This understanding suggests a simple model of the lightcurve.
 We start with the initial temperature profile set by the steady-state profile at the outburst accretion rate., We start with the initial temperature profile set by the steady-state profile at the outburst accretion rate.
" Then, for each time {, we locate the depth at which τ=1."," Then, for each time $t$, we locate the depth at which $\tau=t$."
 We then find the outwards flux in a constant flux solution that has a temperature equal to the initial temperature at the depth where f=r., We then find the outwards flux in a constant flux solution that has a temperature equal to the initial temperature at the depth where $t=\tau$.
 This value of flux is the flux emerging from the surface at time f., This value of flux is the flux emerging from the surface at time $t$.
" The dotted curve in Figure 2 shows a lightcurve calculated in this way, using the same parameters Qimp, Tp, and T; as the numerical model."," The dotted curve in Figure \ref{f.mxb1659-model} shows a lightcurve calculated in this way, using the same parameters $\Qimp$, $T_b$, and $T_c$ as the numerical model."
 The simple model shows excellent agreement with the numerical model., The simple model shows excellent agreement with the numerical model.
 The origin of the broken power law nature of the lightcurve lies in the change in slope of the thermal time with depth that occurs close to neutron drip (see the lower panel of Fig. 5;;, The origin of the broken power law nature of the lightcurve lies in the change in slope of the thermal time with depth that occurs close to neutron drip (see the lower panel of Fig. \ref{f.T-tau};
 neutron drip occurs at P/g~5x10?gcm?)., neutron drip occurs at $P/g\approx 5\times 10^{15}\ {\rm g\ cm^{-2}}$ ).
" The decrease in slope is primarily due to the suppression of C, in the inner crust, shown in Figure 6.."," The decrease in slope is primarily due to the suppression of $C_{p}$ in the inner crust, shown in Figure \ref{f.k-cp}."
" The ion contribution to the specific heat line)) decreases on going to higher densities roughly as (T/Opy, where the Debye temperature Op«O0,=(h/kg) the plasma of the ions. We[4xZ2e%non/(Amu)]"," The ion contribution to the specific heat ) decreases on going to higher densities roughly as $(T/\Theta_{D})^{3}$, where the Debye temperature $\Theta_{D} \propto \Theta_p=(\hbar/\kB)\left[4\pi Z^{2}e^{2}n_{\mathrm{ion}}/(A\mb)\right]^{1/2}$, the plasma temperature of the ions."
" assume that the neutrons in the temperatureinner crust are superfluid, in which case they have a negligible contribution to the heat capacity (Fig. 6,, line))."," We assume that the neutrons in the inner crust are superfluid, in which case they have a negligible contribution to the heat capacity (Fig. \ref{f.k-cp}, )."
" The thermal time also depends on the thermal conductivity, which changes from being set by phonon scattering in the outer crust to impurity scattering in the inner crust line))."," The thermal time also depends on the thermal conductivity, which changes from being set by phonon scattering in the outer crust to impurity scattering in the inner crust )."
" Electron-electron scattering, although included in our calculations, is not a significant component of the total thermal conductivity2007),, and we do not show it in Fig. 6.."," Electron-electron scattering, although included in our calculations, is not a significant component of the total thermal conductivity, and we do not show it in Fig. \ref{f.k-cp}."
" The slight step in the ion specific heat at P/gx10?gcm""? (Fig. 6,, panel))"," The slight step in the ion specific heat at $P/g \lesssim 10^{13}\nsp\columnunit$ (Fig. \ref{f.k-cp}, )"
 is caused by the liquid-solid transition in the crust., is caused by the liquid-solid transition in the crust.
 Our code does not follow the crystallization front and hence does not include the latent heat., Our code does not follow the crystallization front and hence does not include the latent heat.
" The depth where crystallization occurs is so shallow, however, that this omission does not appreciably affect the lightcurve, unlike the case for the cooling of white dwarf starstherein)."," The depth where crystallization occurs is so shallow, however, that this omission does not appreciably affect the lightcurve, unlike the case for the cooling of white dwarf stars."
. We note that observations taken shortly (<10d) after the end of the outburst could potentially detect the effect of the latent heat; this would provide an independent constraint on the temperature in the crust and a check on the value of the plasma parameter I at which the ions crystallize (see Appendix ??))., We note that observations taken shortly $\lesssim 10\nsp\unitday$ ) after the end of the outburst could potentially detect the effect of the latent heat; this would provide an independent constraint on the temperature in the crust and a check on the value of the plasma parameter $\Gamma$ at which the ions crystallize (see Appendix \ref{s.eos}) ).
" With some approximations, the same arguments allow us to make an analytic approximation to the lightcurve."," With some approximations, the same arguments allow us to make an analytic approximation to the lightcurve."
" The slope of the cooling curve can be written The first factor on the right hand side is the slope of the Τεῃ-- T relation, dInT3,/dInT~0.45—0.63 1))."," The slope of the cooling curve can be written The first factor on the right hand side is the slope of the $T_\mathrm{eff}$ $T$ relation, $\dif\ln\Teffinf/\dif\ln T\approx 0.45\textrm{--}0.63$ (Fig. \ref{f.teff-tb}) )."
 The second factor is the temperature gradient in the (Fig.initial model., The second factor is the temperature gradient in the initial model.
 The third factor is the dependence of thermal time with column depth., The third factor is the dependence of thermal time with column depth.
" We can obtain this analytically by noting that during the early part of the lightcurve, when the cooling wave is in the outer crust, we can approximatethe heat capacity as Cpx3kg/(Am,) the classical heat capacity of lattice, and use an approximate expression for the phonon aconductivity (see eq. [A3]]-[A4]])."," We can obtain this analytically by noting that during the early part of the lightcurve, when the cooling wave is in the outer crust, we can approximatethe heat capacity as $C_{P} \approx 3\kB/(A\mb)$ the classical heat capacity of a lattice, and use an approximate expression for the phonon conductivity (see eq. \ref{e.Wiedemann}] \ref{e.phonon-freq}] ])."
" Inserting these expressions into the expression for 7 (eq. [7]]),"," Inserting these expressions into the expression for $\tau$ (eq. \ref{e.tau}] ]),"
 we, we
used by the algorithm.,used by the algorithm.
 For this reason this result is not surprising. ancl the reconstructed correlation function is very questionable since it is based on the pixels which should have been omitted.," For this reason this result is not surprising, and the reconstructed correlation function is very questionable since it is based on the pixels which should have been omitted."
 To avoid the problem of. information transfer by smoothing the correlation function of the LLC (7vr) map is also investigated without additional smoothing., To avoid the problem of information transfer by smoothing the correlation function of the ILC (7yr) map is also investigated without additional smoothing.
 In figure 15. the corresponding correlation functions are plotted.," In figure \ref{Fig:correlation_function_ilc_KQ85_FWHM_000arcmin_nside_16}
 the corresponding correlation functions are plotted."
 The error (10)) is significantly larger now., The error \ref{Eq:error_C_theta_rec}) ) is significantly larger now.
 Without additional smoothing the dillerences between the correlation function of the reconstructed and of the full ILC (TNT) map are larger. but both agrec within the 26 οτο».," Without additional smoothing the differences between the correlation function of the reconstructed and of the full ILC (7yr) map are larger, but both agree within the $2\sigma$ errors."
 ‘This could ead to the conclusion that the reconstruction works without additional smoothing anc without a corresponding information transfer. but for 44=10.12 the errors are large compared. to the case with additional smoothing as it is shown in ligure 17..," This could lead to the conclusion that the reconstruction works without additional smoothing and without a corresponding information transfer, but for $l_{\hbox{\scriptsize max}}=10-12$ the errors are large compared to the case with additional smoothing as it is shown in figure \ref{Fig:correlation_function_ilc_KQ85_FWHM_600arcmin_nside_16}."
 For Aux15 the errors of the reconstructed correlation function are too large to allow any conclusion., For $l_{\hbox{\scriptsize max}}\gtrsim 15$ the errors of the reconstructed correlation function are too large to allow any conclusion.
 Due to these large errors the correlation function of the reconstructed LLC map also agrees on the same level with the correlation function obtained solely from the data outside the mask., Due to these large errors the correlation function of the reconstructed ILC map also agrees on the same level with the correlation function obtained solely from the data outside the mask.
 Thus. one cannot dilferentiate. between these (wo cases.," Thus, one cannot differentiate between these two cases."
 The reconstructed: correlation function shows sometimes a better agreement with the correlation function resulting from the masked ILC map and sometimes with the correlation function. of the full LLC map., The reconstructed correlation function shows sometimes a better agreement with the correlation function resulting from the masked ILC map and sometimes with the correlation function of the full ILC map.
 The quality of his agreement depends on y and A445., The quality of this agreement depends on $\vartheta$ and $l_{\hbox{\scriptsize max}}$.
 Fhus. the reconstruced correlation function favours neither the one of the maskec nor the one of the full ILC map.," Thus, the reconstructed correlation function favours neither the one of the masked nor the one of the full ILC map."
 Due to the large errors the reconstructed correlation function is uncertain by at least 100/77. and thus unsuited for the comparison with cosmological moclels., Due to the large errors the reconstructed correlation function is uncertain by at least $\mu\hbox{K}^2$ and thus unsuited for the comparison with cosmological models.
 The above discussion. puts forward arguments against he reconstruction method and favours methods which use only the data outside a given mask., The above discussion puts forward arguments against the reconstruction method and favours methods which use only the data outside a given mask.
 To provide a firm footing or the latter. the influence of the WOSS and ΙΟτὸ masks onto the ensemble average and the cosmic variance of the correlation function C'(9) is now investigated with respect o the CDM model.," To provide a firm footing for the latter, the influence of the KQ85 and KQ75 masks onto the ensemble average and the cosmic variance of the correlation function $C(\vartheta)$ is now investigated with respect to the $\Lambda$ CDM model."
 Both quantities are shown in figure 19 or an ensemble of 0000 CAIB simulations of the ΑςΔΙ model.," Both quantities are shown in figure \ref{Fig:correlation_function_100000lcdm_modelle_full_KQ85_Kq75_nside_128_s0.5}
 for an ensemble of 000 CMB simulations of the $\Lambda$ CDM model."
 Phe ensemble average and the standard. deviation is computed. from the correlation functions (9) obtained rom the data of full maps. outside the KQS5 mask and outside the Οτο mask.," The ensemble average and the standard deviation is computed from the correlation functions $C(\vartheta)$ obtained from the data of full maps, outside the KQ85 mask and outside the KQ75 mask."
 A resolution of Ας=128 and a mask threshold ον=0.5 is used., A resolution of $N_{\hbox{\scriptsize side}} = 128$ and a mask threshold $x_{\hbox{\scriptsize th}}=0.5$ is used.
 The ensemble averages are identical in all three cases., The ensemble averages are identical in all three cases.
 The standard deviation slightly increases with the size of the mask., The standard deviation slightly increases with the size of the mask.
 The smallest leo standard deviation is obtained by using no mask at all. he next larger deviation belongs to the KQS5 mask whereas he largest deviation is due to the larger WQ75 mask.," The smallest $\sigma$ standard deviation is obtained by using no mask at all, the next larger deviation belongs to the KQ85 mask whereas the largest deviation is due to the larger KQ75 mask."
 The increase of the standard. deviation. for the masked. data is. however. small compared to the uncertainty resulting rom the reconstruction method for the same mask.," The increase of the standard deviation for the masked data is, however, small compared to the uncertainty resulting from the reconstruction method for the same mask."
 This is à further argument for having more confidence in the correlation Function C'(7) computed [rom the data outside he mask than in the one obtained from a reconstructed Pull map., This is a further argument for having more confidence in the correlation function $C(\vartheta)$ computed from the data outside the mask than in the one obtained from a reconstructed full map.
 The main difference between the LLC correlation functions, The main difference between the ILC correlation functions
00J— |... a +h = ου,J = a_+ + b_- = < 0.
 In the case of a single lens. α=—20. b.=0. and |VJ|=4 on the critical curve (r= 1).," In the case of a single lens, $a_+ = -20$ , $b_-=0$, and $|\nabla J|=4$ on the critical curve $r=1$ )."
 Away from a cusp. ὁ./22044.," Away from a cusp, $\delta J \approx \delta J_1$ ."
 Near a cusp (b=0). 07 dominantly depends linearly on α-—dz amd equadratically on e=dz," Near a cusp $b=0$ ), $\delta J$ dominantly depends linearly on $u= dz_+$ and quadratically on $v = dz_-$."
" iJ =aut (Q +=) Jo? Therefore. (he critical curve (0.=0:J, 0) is parabolic near a cusp."," J = a u + (b_- + ) v^2 Therefore, the critical curve $\delta J =0; \ J_\circ = 0$ ) is parabolic near a cusp."
 u=-l— 2a{(h =)u2(24) Now we choose the cusp under consideration as the origin of the lens plane. and the eigendirection as the real axis so thal E—1(&ο=0).," u = - (b_- + ) v^2 Now we choose the cusp under consideration as the origin of the lens plane, and the eigendirection $E_+$ as the real axis so that $E_+ = 1 ~(\Leftrightarrow \varphi = 0)$."
 Then. Ka=1. and the lens equation (4)) reads as follows.," Then, $\bar\kappa_\circ = 1$, and the lens equation \ref{eqDLens}) ) reads as follows."
 The coellicients are almost real., The coefficients are almost real.
 In fact. we can ignore the imaginary component of ay. Slay)=—«a/12. when we consider only the lowest order terms.," In fact, we can ignore the imaginary component of $\alpha_3$, $\Im(\alpha_3) = - a_-/12$, when we consider only the lowest order terms."
 When there is a reflection svmmetry in (he svstem. ¢@—5.0 al the cusps on the svinnilry axis.," When there is a reflection symmetry in the system, $a_- = b_+ = 0$ at the cusps on the symmtry axis."
 That is (he case for the cusps on the lens axis of the binary lenses. as we can directly calculate from the binary equation (2)).," That is the case for the cusps on the lens axis of the binary lenses, as we can directly calculate from the binary equation \ref{eqLeq}) )."
 Without loss of generality. the real axis has been chosen to be the lens axis. ancl c.c stands for complex conjugate as usual.," Without loss of generality, the real axis has been chosen to be the lens axis, and $c.c$ stands for complex conjugate as usual."
 Then. b =0 (ο E ec) Ld teappaelleappali com deappaté cse(27)," Then, b_+ = _+ (- E_- + c.c ) = - E_- _+ ) + c.c = - i + c.c = 0."
 The last equality holds because 5075=OF is real on the real axis., The last equality holds because $\bar\kappa \partial^2\kappa = \partial^2\kappa$ is real on the real axis.
 n= |l= 1(28)TLhus. thecusps on the lens axis of the binary lenses have strong reflection svmmetries.," = _j;= 1 Thus, thecusps on the lens axis of the binary lenses have strong reflection symmetries."
Similar to HD32778.. the confidence limits in mnass-separation space for HD91204 are poorly constrained (Fig.,"Similar to HD32778, the confidence limits in mass-separation space for HD91204 are poorly constrained (Fig."
 10 middle)., \ref{contrasts} middle).
 However. since HD91204 has a larger database of velocities than HD32778. we can say to a confidence level that the companion to this star is not a close by (<0.15”) sub- or stellar secondary.," However, since HD91204 has a larger database of velocities than HD32778, we can say to a confidence level that the companion to this star is not a close by $\le$ $''$ ) sub-stellar or stellar secondary."
 The middle panel in Fig., The middle panel in Fig.
 11. shows the mass-separation parameter space for this star. reaching down onto the stars surface.," \ref{detects} shows the mass-separation parameter space for this star, reaching down onto the stars surface."
 Clearly very close-by companions can be ruled out to high levels of confidence due to the larger number of data points and the faet that this radial-velocity curve is a liner., Clearly very close-by companions can be ruled out to high levels of confidence due to the larger number of data points and the fact that this radial-velocity curve is a liner.
 This ts further highlighted by the large light region shown in the gray scale and a lack of any large contrast gradient., This is further highlighted by the large light region shown in the gray scale and a lack of any large contrast gradient.
" Objects with separations below 0.06” and masses above around 30M, can be ruled out to ~90-95% confidence and moving out to separations of 0.08"" we can still rule out objects down to around the planetary mass limit at the level of cofidence.", Objects with separations below $''$ and masses above around $_{\rm{J}}$ can be ruled out to $\sim$ confidence and moving out to separations of $''$ we can still rule out objects down to around the planetary mass limit at the level of confidence.
 Therefore. we can say that the companion to this star likely has a fairly large separation and is a faint substellar companion or. as for almost all of the imaged objects. the companion has a longer orbital period. but the melination of the system was such that when we were observing the companiot it was hidden behind the star at on-sky angular separations below 0.17.," Therefore, we can say that the companion to this star likely has a fairly large separation and is a faint substellar companion or, as for almost all of the imaged objects, the companion has a longer orbital period, but the inclination of the system was such that when we were observing the companion it was hidden behind the star at on-sky angular separations below $''$."
 In comparison to these other two stars. HD145825 has enough data points and exhibits enough curvature in. the timeseries that fairly high levels of confidence from the velocities overlap with the confidence limits from the imaging work.," In comparison to these other two stars, HD145825 has enough data points and exhibits enough curvature in the timeseries that fairly high levels of confidence from the velocities overlap with the confidence limits from the imaging work."
 The bottom panel in Fig., The bottom panel in Fig.
 10. shows that below the SDI curve we still have over confidence in ruling out close by (x0.17) objects down to low brown dwarf masses., \ref{contrasts} shows that below the SDI curve we still have over confidence in ruling out close by $\le$ $''$ ) objects down to low brown dwarf masses.
 In addition. the (27) confidence limit can rule out a lot of possible brown dwarf/stellar companions below the 0.1” angular separation limit of the SDI technique (Fig.," In addition, the $\sigma$ ) confidence limit can rule out a lot of possible brown dwarf/stellar companions below the $''$ angular separation limit of the SDI technique (Fig."
 11. bottom)., \ref{detects} bottom).
 The gray scale reveals more structure than HD32778 and HD91204 due to the significant curvature in the velocities., The gray scale reveals more structure than HD32778 and HD91204 due to the significant curvature in the velocities.
" Particularly we can see that the region around 0.2” separation is less constrained than inside and outside this separation and due to the indication of secondary curvature in the velocities. we arrive at fairly high confidence levels beyond 0.3” separation,"," Particularly we can see that the region around $''$ separation is less constrained than inside and outside this separation and due to the indication of secondary curvature in the velocities, we arrive at fairly high confidence levels beyond $''$ separation."
 From these combined constraints we can rule out to really high levels of confidence any brown dwarf/stellar companions with small separations (short period orbits)., From these combined constraints we can rule out to really high levels of confidence any brown dwarf/stellar companions with small separations (short period orbits).
" Also. at the lo level we can say that there are no objects at all below a separation of around 0.34” with masses above 40M, anc also no companions down into the giant exoplanet regime within 0.20""."," Also, at the $\sigma$ level we can say that there are no objects at all below a separation of around $''$ with masses above $_{\rm{J}}$ and also no companions down into the giant exoplanet regime within $''$."
 These combined data sets argue for the companion to HD145825 to be an extremely faint sub-stellar companion with a moderate separatio, These combined data sets argue for the companion to HD145825 to be an extremely faint sub-stellar companion with a moderate separation.
 Out of the five stars that we searched around. two possible detections were made around the stars HD25874 and HD120780.," Out of the five stars that we searched around, two possible detections were made around the stars HD25874 and HD120780."
 Both of these candidates fulfilled the requirements to be considered as bona fide candidates as they were bright sources. that had counterparts at 33° in the rolled images.," Both of these candidates fulfilled the requirements to be considered as bona fide candidates as they were bright sources, that had counterparts at $^{\circ}$ in the rolled images."
 However. after careful analysis we believe these to be artifacts of the reduction procedure and not true companion objects.," However, after careful analysis we believe these to be artifacts of the reduction procedure and not true companion objects."
 Both will be discussed here., Both will be discussed here.
 Figure 12. shows the 33° roll angle of the camera and how it projects along the image through the T3 filter (FI1CI.5754mo- l.6254um)) for HD25874., Figure \ref{annotate_hd25874} shows the $^{\circ}$ roll angle of the camera and how it projects along the image through the T3 filter $\mu$ $\mu$ m)) for HD25874.
 The detections are found at the ends of the second are along the projection with a separation from the central pixel of 0.29+0.01 and a position angle of 240°., The detections are found at the ends of the second arc along the projection with a separation from the central pixel of $\pm$ $''$ and a position angle of $^{\circ}$.
 This enhanced image highlights more of the speckles across the images in both negative and positive formats e.g. bright spot to the extreme left middle of the left panel and its counterpart in the corresponding position of the right panel., This enhanced image highlights more of the speckles across the images in both negative and positive formats e.g. bright spot to the extreme left middle of the left panel and its counterpart in the corresponding position of the right panel.
 Along the projected angle there is also another bright and dark par that could be separated by the roll angle and these are found at the ends of the inner arc., Along the projected angle there is also another bright and dark pair that could be separated by the roll angle and these are found at the ends of the inner arc.
 As these are so close and connected to the central star we believe these to be an artifact of the PSF subtraction. however worryingly since they are found projected along the same axis as the potential candidate detection they may signify that the detection is an artifact as well e.g. uncorrected residual trefoil in the image.," As these are so close and connected to the central star we believe these to be an artifact of the PSF subtraction, however worryingly since they are found projected along the same axis as the potential candidate detection they may signify that the detection is an artifact as well e.g. uncorrected residual trefoil in the image."
 As mentioned. Fig.," As mentioned, Fig."
 13 (upper) shows the contrast limits that were determined for HD25874. highlighting both the conventional AO and the SDI reduced limits.," \ref{hd25874_contrast} (upper) shows the contrast limits that were determined for HD25874, highlighting both the conventional AO and the SDI reduced limits."
" For companion candidates such as the one here it is clear that the SDI reduction performs significantly better than conventional AO e.g. gain of ~2.5 magnitudes at 0.2"".", For companion candidates such as the one here it is clear that the SDI reduction performs significantly better than conventional AO e.g. gain of $\sim$ 2.5 magnitudes at $''$.
 The confidence limits m this figure show a lot of structure at separations reaching well into the imaging phase space., The confidence limits in this figure show a lot of structure at separations reaching well into the imaging phase space.
 This is due to the large baseline (>4 yrs) of observations. even though they describe a liner system.," This is due to the large baseline $>$ 4 yrs) of observations, even though they describe a liner system."
" confidence limits are seen to rule out objects down into the planetary mass regime with angular separations below 0.14"". depending on where we place the boundary between exoplanets and brown dwarfs. and we can rule out such objects up to separations of almost 0.18” at the confidence limit."," confidence limits are seen to rule out objects down into the planetary mass regime with angular separations below $''$, depending on where we place the boundary between exoplanets and brown dwarfs, and we can rule out such objects up to separations of almost $''$ at the confidence limit."
 The lower panel better highlights the structure in detectability for this star and shows clearly that we have high levels of confidence out to the timeseries of this data set., The lower panel better highlights the structure in detectability for this star and shows clearly that we have high levels of confidence out to the timeseries of this data set.
" The gray scale shows similar structure to that of HD145825 with a large inner region that is highly constrained. a dark unconstrained region around 0.2” separation from the star and then a growing lighter constrained region out to separations of 0.3""."," The gray scale shows similar structure to that of HD145825 with a large inner region that is highly constrained, a dark unconstrained region around $''$ separation from the star and then a growing lighter constrained region out to separations of $''$."
 This time the constrained region at larger separations arises not from any curvature in the velocities but due to the overall span of velocity across the data set. showing that it is unlikely that lower mass companions at these orbital separations could give rise to this data set.," This time the constrained region at larger separations arises not from any curvature in the velocities but due to the overall span of velocity across the data set, showing that it is unlikely that lower mass companions at these orbital separations could give rise to this data set."
 By combining the imaging data with the radial-velocity data. we can say that with confidence we can rule out almost all companions to this star with separations below 0.17” (4.40 AU).," By combining the imaging data with the radial-velocity data, we can say that with confidence we can rule out almost all companions to this star with separations below $''$ (4.40 AU)."
 Again we conclude that the companion to this star is probably a widely separated. low mass (<70M)) and therefore really faint sub-stellar object.," Again we conclude that the companion to this star is probably a widely separated, low mass $<$ $_{\rm{J}}$ ) and therefore really faint sub-stellar object."
 If such is the case then there is a fairly high possibility here that the object is a brown dwarf located in the brown dwarf desert (?))., If such is the case then there is a fairly high possibility here that the object is a brown dwarf located in the brown dwarf desert \citealp{grether06}) ).
 Note that there were no other objects detected around this star out to orbital distances of ~52 AU., Note that there were no other objects detected around this star out to orbital distances of $\sim$ 52 AU.
same wavelength intervals.,same wavelength intervals.
 The masks available in the HARPS DRS pipeline are proprietary and not available outside the DRS. so they can only be used for the reduction of HARPS spectra.," The masks available in the HARPS DRS pipeline are proprietary and not available outside the DRS, so they can only be used for the reduction of HARPS spectra."
 Hence. for these calculations. we decided to create new masks using line lists for the spectral regions under study.," Hence, for these calculations, we decided to create new masks using line lists for the spectral regions under study."
" For the sake of simplicity. we used the ""extract stellar function from to retrieve a list of lines with estimated central depths expressed as a fraction of continuum flux for two generic solar-metallicity stars belonging to the two spectral types."," For the sake of simplicity, we used the “extract stellar” function from to retrieve a list of lines with estimated central depths expressed as a fraction of continuum flux for two generic solar-metallicity stars belonging to the two spectral types."
 We constructed the masks by simply overlapping a series of impulse functions centered at the wavelength of each spectral line and with amplitude proportional to the spectral line’s depth., We constructed the masks by simply overlapping a series of impulse functions centered at the wavelength of each spectral line and with amplitude proportional to the spectral line's depth.
 We were then able to cross-correlate both our thetic and our observed spectra with the same masks., We were then able to cross-correlate both our synthetic and our observed spectra with the same masks.
 The Cross-correlation was done using [DL’s function., The cross-correlation was done using 's function.
 ally. we extracted the bisectors from the resultant CCFs of thetic and observed spectra and compared them with one other.," Finally, we extracted the bisectors from the resultant CCFs of synthetic and observed spectra and compared them with one another."
 Fig., Fig.
 17. shows the CCF bisectors extracted from. the sythetic (left panel) and observed (right panel) spectra in the 6215-6275 range., \ref{fig:compbis_6215_6275_G8} shows the CCF bisectors extracted from the synthetic (left panel) and observed (right panel) spectra in the $6215$ $6275$ range.
" The CCFs were computed using the ""(Qn ""mask. that is the more closely corresponding to the Sun's spectral type."," The CCFs were computed using the “G” mask, that is the more closely corresponding to the Sun's spectral type."
 The agreement between the CCF bisectors from synthetic and observed spectra is very good: the curvature and asymmetry of the observed bisector are well reproduced by the theoretical caleulations., The agreement between the CCF bisectors from synthetic and observed spectra is very good: the curvature and asymmetry of the observed bisector are well reproduced by the theoretical calculations.
 Fig., Fig.
" 18. shows the CCF bisectors from the synthetic and observed spectra for the same wavelength interval computed using the ""K"" mask instead.", \ref{fig:compbis_6215_6275_K9} shows the CCF bisectors from the synthetic and observed spectra for the same wavelength interval computed using the “K” mask instead.
 While the curvature of the CCF bisector is more pronounced in the case of the synthetic spectrum. the overall agreement with the observed case is still good.," While the curvature of the CCF bisector is more pronounced in the case of the synthetic spectrum, the overall agreement with the observed case is still good."
 Small differences of these kind are acceptable considering. e.g.. that lines may be missing from the list used for the synthetic spectrum calculations and that elemental abundances were not adjusted to reproduce all line strengths.," Small differences of these kind are acceptable considering, e.g., that lines may be missing from the list used for the synthetic spectrum calculations and that elemental abundances were not adjusted to reproduce all line strengths."
" The correspondingCCF bisectors for the 5150—5200 interval computed for the synthetic and observed spectra with the ""G and ""K masks are shown in Fig.", The correspondingCCF bisectors for the $5150-5200$ interval computed for the synthetic and observed spectra with the “G” and “K” masks are shown in Fig.
 19 and 20.. respectively.," \ref{fig:compbis_5150_5200_G8_mgincluded} and \ref{fig:compbis_5150_5200_K9_mgincluded}, respectively."
 This region is characterized by the presence of one moderately strong and two strong lines at 5183. 5172. and 5167 which carry a significant weight in determining the overall shape of CCF bisector in this region.," This region is characterized by the presence of one moderately strong and two strong lines at $5183$, $5172$, and $5167$ which carry a significant weight in determining the overall shape of CCF bisector in this region."
 The agreement between CCF bisectors derived from synthetic and observed spectra is actually excellent for this region. implying that the modelling of these strong lines in our theoretical calculations is robust and satisfactory.," The agreement between CCF bisectors derived from synthetic and observed spectra is actually excellent for this region, implying that the modelling of these strong lines in our theoretical calculations is robust and satisfactory."
 We have shown that the well known CCF bisector parameters BIS. voor. and cp correlate well with logg and e Των.," We have shown that the well known CCF bisector parameters BIS, $v_\mathrm{bot}$, and $c_b$ correlate well with $\log g$ and $T_\mathrm{eff}$ ."
 We have constructed à new CCF bisector measure. the CBS. based," We have constructed a new CCF bisector measure, the CBS, based"
detector. aud moreover to the oft-axis position of the source in the FOV.,"detector, and moreover to the off-axis position of the source in the FOV."
 Iu contrast. the more detailed IMRT image reveals a number of X-ray sources clistributed over he ealactic disk (Fie. D).," In contrast, the more detailed HRI image reveals a number of X-ray sources distributed over the galactic disk (Fig. \ref{hrioveropt}) )."
 Iun comparison to the utmibered sources in Fie., In comparison to the numbered sources in Fig.
 1 he closer view allows to distinguish iuore details., \ref{hrifov} the closer view allows to distinguish more details.
 For example. source no.," For example, source no."
 9 in Fie., 9 in Fig.
 1 splits 1ito three ταν 4nots (labeled Aο in Fie. 3)., \ref{hrifov} splits into three X-ray spots (labeled A–C in Fig. \ref{hrisrcareas}) ).
 T10 lost MLULOUS source Ciucides with the center of NCGC (303 andl dominates ji the soft N-ravs., The most luminous source coincides with the center of NGC 4303 and dominates in the soft X-rays.
 The count rates al fluxes derived fco sources from the TRI are isted in Table Ll..., The count rates and fluxes derived for sources from the HRI are listed in Table \ref{tabhrisources}.
 The corresponding areas are plotted in Fig. ?)3, The corresponding areas are plotted in Fig. \ref{hrisrcareas}.
 «To determine the fluxes we used the euergv couversio1 factor (ECF) from tιο ROSAT doa1nenutation., To determine the fluxes we used the energy conversion factor (ECF) from the ROSAT documentation.
" The EXC""F determines the ratio betwee1 COL rates and unabsorbed source fux in the ROSAT baud OY giveu spectral pariuneters.", The ECF determines the ratio between count rates and unabsorbed source flux in the ROSAT band for given spectral parameters.
 For the disk sources AF we asse a 0.3 keV Riwvinond-Suith model (Baviuonud Suith 1977)) with an absorption column density of a7., For the disk sources A–F we assume a 0.3 keV Raymond-Smith model (Raymond Smith \cite{ray77}) ) with an absorption column density of $^{-2}$.
 For the nucleus a power law with P=2.6 iu a coli1 deusitv ofDl 22? (see Sect., For the nucleus a power law with $\Gamma$ =2.6 and a column density of $^{-2}$ (see Sect.
] 3.2.Qa and Tab: e5)) is applied as spectra model., \ref{specfit} and Table \ref{fittab}) ) is applied as spectral model.
 The contours of sources D. C. D. and F i1 Fie.," The contours of sources B, C, D, and F in Fig."
 3 are all located within the optical arii strucnre and coincide with bright Πα eiuission regions within the spiral armis (Fie. 1)., \ref{hrisrcareas} are all located within the optical arm structure and coincide with bright $\alpha$ emission regions within the spiral arms (Fig. \ref{hrioveropt}) ).
 In addition. source E is emibedded in the faint outer part of the soutliwestern spiral arm.," In addition, source E is embedded in the faint outer part of the southwestern spiral arm."
 \IR92 distinguished 79, \cite{mar92} distinguished 79
could still give Similarly. for the 55 MlIS line to be mased we require the corresponding level populations be inverted: which implies Condition is satisfied if the populations in the levels corresponding to the 1667. MlIz ancl 1720 MlIz lines are inverted while those in the levels corresponding to the 1612 MlIz and 1665 MlIS lines are not.,"could still give Similarly, for the 55 MHz line to be mased we require the corresponding level populations be inverted: which implies Condition is satisfied if the populations in the levels corresponding to the 1667 MHz and 1720 MHz lines are inverted while those in the levels corresponding to the 1612 MHz and 1665 MHz lines are not."
 Observationalv if the 1667 AMllIz and 1720 Mllz lines are miased. while the 1612 MllIz and 1665 MllIz lines are not. we could expect the 55 Mllz line levels to be inverted.," Observationaly if the 1667 MHz and 1720 MHz lines are mased, while the 1612 MHz and 1665 MHz lines are not, we could expect the 55 MHz line levels to be inverted."
 1n summary. a region where the 1720 MlIé line is mased. but the 1612 MlIz line is not. would be a promising region to look for mased emission from the 53/55 MlIS lines.," In summary, a region where the 1720 MHz line is mased, but the 1612 MHz line is not, would be a promising region to look for mased emission from the 53/55 MHz lines."
 Which of these is likely to be mased depends on whether the 1665 ΔΗΙ or 1667 Mllz line is mased., Which of these is likely to be mased depends on whether the 1665 MHz or 1667 MHz line is mased.
 Lt is interesting to note in this context that there are regions in our (Clurner1979) and in external galaxies(vanLangeveldectal.1995:Ixanekar.Chengalur&Chosh2004) where the satellite lines are conjugate. viz.," It is interesting to note in this context that there are regions in our \citep{turner}
 and in external \citep*{langevelde95,chengkan} where the satellite lines are conjugate, viz."
 where their profiles are. mirror images of one another. i.e. when one is in emission the other is in absorption. and the sum of the two profiles is consistent with noise.," where their profiles are mirror images of one another, i.e. when one is in emission the other is in absorption, and the sum of the two profiles is consistent with noise."
 Regions such as these are promising ones to search for the 53 MlIZ and 55 MIEZz OL lines., Regions such as these are promising ones to search for the 53 MHz and 55 MHz OH lines.
 H£ the hvperfine OLL 53 MllIz or 55 MlIz lines are strongly amplified. then the lines may be detectable.," If the hyperfine OH 53 MHz or 55 MHz lines are strongly amplified, then the lines may be detectable."
 Llowever. the amplification factor is a matter of speculation.," However, the amplification factor is a matter of speculation."
 Menonctal.(2005). attempted to detect the 53 MlI line. but could only place an upper limit to the amplification factor.," \citet{roshi}
 attempted to detect the 53 MHz line, but could only place an upper limit to the amplification factor."
" bor our particular observations. we have chosen the target region. Ci84.3|0.1 (a(2000)=is""59""06.75: o(2000)=LOI24 397.40) where the 1720 MIIz line is masec. while the 1612 Alllz line is in absorption."," For our particular observations, we have chosen the target region G34.3+0.1 $\alpha(2000) = 18^{h}\ 59^{m}\ 06^{s}.75$; $\delta(2000) = 
+01\degr\ 24\arcmin\ 39\arcsec.40$ ) where the 1720 MHz line is mased, while the 1612 MHz line is in absorption."
 Phe main lines are both seen in emission. although it is not clear if they are mased or not.," The main lines are both seen in emission, although it is not clear if they are mased or not."
 Phe lines all occur within the LSR. range of 56-58 kin *(Purner1979)..., The lines all occur within the LSR range of 56-58 km $^{-1}$ \citep{turner}.
 Lhe supernova remnant. ΧΑΕΕ is only 48? away [rom (54.90.1 and lies well within the 107 GMACE primary beam., The supernova remnant W44 is only 48' away from G34.3+0.1 and lies well within the $\degr$ GMRT primary beam.
 In this region the 1720 MlIZ line is mased. while the 1612 MIIz line is seen in absorption.," In this region the 1720 MHz line is mased, while the 1612 MHz line is seen in absorption."
 The main lines are also seen in absorption over a velocity range of 10 km (προς1979)..., The main lines are also seen in absorption over a velocity range of 10 km $^{-1}$ \citep{turner}.
 These lines occur over the velocity range 43-46 km +., These lines occur over the velocity range 43-46 km $^{-1}$.
 Thus both G34.3|0.1 and. W44 could eive rise to mased 53/55 MIITz lines., Thus both G34.3+0.1 and W44 could give rise to mased 53/55 MHz lines.
 Strictly speaking. the conditions described above. viz.," Strictly speaking, the conditions described above, viz."
 that the 1720 MlIz line is mased but the 1612 Mllz line is not etc., that the 1720 MHz line is mased but the 1612 MHz line is not etc.
 should be satisfied along the same line of sight inorder for the 55/53 MlIZ lines to be mased., should be satisfied along the same line of sight inorder for the 55/53 MHz lines to be mased.
 VLBI observations show that the OLL maser emission generally. comes from extremely compact (~ LOO mas) hot spots(Llolfmanetal., VLBI observations show that the OH maser emission generally comes from extremely compact $\sim$ 100 mas) hot \citep{hoffman}.
2003).. It is rare to have VLBI observations of all the four OLL 15 em transitions: hence it is dillicult at the current time to unambiguously identify a, It is rare to have VLBI observations of all the four OH 18 cm transitions: hence it is difficult at the current time to unambiguously identify a
Disks where the angular momentum is transported outwards (&« 0) tend to develop a warmer core. while the opposite trend «scours for disks where the aneular 1noiucntuni ds CALTIC( inwards (£2 0).,"Disks where the angular momentum is transported outwards $\xi<0$ ) tend to develop a warmer core, while the opposite trend occurs for disks where the angular momentum is carried inwards $\xi>0$ )."
 This is shown in Fig., This is shown in Fig.
 2 (Fig., \ref{fig:termica} (Fig.
 2 aud the following Fig. 3..," \ref{fig:termica} and the following Fig. \ref{fig:massa},"
 Fie. LL.," Fig. \ref{fig:epsilon},"
 aud Fig., and Fig.
 5 are shown in ogarithinic scale to better bring out the behavior in the 1mer parts of the disk)., \ref{fig:spessore} are shown in logarithmic scale to better bring out the behavior in the inner parts of the disk).
 Note that in the case of mnward augular monieutuu fiux ($>0) the effective thermal speed need not vanish at the imuer edec of the disk (as it does in our models) where à boundary laver is expected to be generated (see discussion at the cucl of Section 2.3))., Note that in the case of inward angular momentum flux $\xi>0$ ) the effective thermal speed need not vanish at the inner edge of the disk (as it does in our models) where a boundary layer is expected to be generated (see discussion at the end of Section \ref{chiboundary}) ).
 There are several quantities directly related to the disk density distribution iu the disk that allow us to characterize the role of the disk selt-eravity., There are several quantities directly related to the disk density distribution in the disk that allow us to characterize the role of the disk self-gravity.
 The most natural quantity to consider is the ratio of the mass of the disk to that of the ceutral object., The most natural quantity to consider is the ratio of the mass of the disk to that of the central object.
 Obviously. for our non-truucated models this quantity is nmeanineful onlv when referred to a given radius.," Obviously, for our non-truncated models this quantity is meaningful only when referred to a given radius."
 Fie., Fig.
 5 shows how rapidly iun radius the svstem becomes doiiumnated by the mass of the disk.," \ref{fig:massa}
 shows how rapidly in radius the system becomes dominated by the mass of the disk."
" Note that. iu any case. Miia)(AL, »0forr»0."," Note that, in any case, $M_{disk}(r)/M_{\star}\rightarrow 0$ for $r\rightarrow 0$."
 Iun galactic dywnuanüces tie local disk sclferavity is usually micasured in. terms of. the parameter e=gzGoτα2 rk., In galactic dynamics the local disk self-gravity is usually measured in terms of the parameter $\epsilon=\pi G\sigma/r\kappa^2$ .
 The fully sclferaviating selt-sinilar disk (with flat rotation curve) is cliaracterizec by e=1/1., The fully self-gravitating self-similar disk (with flat rotation curve) is characterized by $\epsilon=1/4$.
 The profile of this parameter (sec| Fie. 0) , The profile of this parameter (see Fig. \ref{fig:epsilon}) )
confirms that indeed. close to the ceuter. the influence of he central mass becomes stronger and strouger.," confirms that indeed, close to the center, the influence of the central mass becomes stronger and stronger."
" Caven the behavior of the xofiles AvanifA, and e(r). one nuelt conclude that the innermost disk should be treated as a standard EKepkYan accretion disk."," Given the behavior of the profiles $M_{disk}(r)/M_{\star}$ and $\epsilon(r)$, one might conclude that the innermost disk should be treated as a standard Keplerian accretion disk."
 This couclusion is contradicted bv t1e following arguineut., This conclusion is contradicted by the following argument.
 Insetting up the equatious of otr models.we have taken," Insetting up the equations of our models,we have taken"
In this note we report resulis of our investigation of (he limitations of using SDSS photometry for bright stars. and give a prescription lor setting zero points in CCD images taken through.CBVRI filters.,"In this note we report results of our investigation of the limitations of using SDSS photometry for bright stars, and give a prescription for setting zero points in CCD images taken through filters."
 We obtainedwgriz magnitudes [rom SDSS data release (DR5) for the Landolt(1992). standard stars in SDSS fields.," We obtained magnitudes from SDSS data release (DR5) \citep{abazajian05} for the \cite{landolt92}
 standard stars in SDSS fields."
 We first removed very blue and red stars outside the ranges 0.08«(r—ij)0.5 and 0.2<(ο—r)«L4., We first removed very blue and red stars outside the ranges $0.08 < (r-i) < 0.5$ and $ 0.2 < (g-r) < 1.4$ .
 We then plotted the (r—£P) vs. (g—r) color-color diagram and removed oullving points more than 2.5 stancarel deviations from the linear least squares fil., We then plotted the $(r-i)$ vs. $(g-r)$ color-color diagram and removed outlying points more than 2.5 standard deviations from the linear least squares fit.
 We derived transformation equations only [or stars with r2Id., We derived transformation equations only for stars with $r > 14$.
 A few points lving more than 2.5 standard. deviations away [rom the least-squares fils were removed., A few points lying more than 2.5 standard deviations away from the least-squares fits were removed.
 We obtained the following Gransformations: As is well known. tranformations to C are particularly problematic.," We obtained the following transformations: As is well known, tranformations to $U$ are particularly problematic."
 Since our aim is only lo give a prescription for selling CDVRI zero points rather than (to obtain transformations valid for inclividual stars for astrophivsical purposes. we determined (he transformation Lor the U filter as follows.," Since our aim is only to give a prescription for setting $UBVRI$ zero points rather than to obtain transformations valid for individual stars for astrophysical purposes, we determined the transformation for the $U$ filter as follows."
 First we removed all stars thal were more than 2.5 standard deviations from a linear fit in f[our-dimensional (u—49).(g—r).(r—i).(7-2) color space.," First we removed all stars that were more than 2.5 standard deviations from a linear fit in four-dimensional $(u-g), (g-r), (r-i), (i-z)$ color space."
 For the remaining stars with no saturation warning flags. we restricted ourselves to stars wilh 1«(u—9g)<2 and u>16.," For the remaining stars with no saturation warning flags, we restricted ourselves to stars with $1 < (u-g) < 2$ and $u
> 16$."
 For these stars we found no statistically significant dependence on the (4—g) color., For these stars we found no statistically significant dependence on the $(u-g)$ color.
 This is not surprising since. of the SDSS ugriz fillers. the passhand of the« filter agrees most closely to the Johnson-Cousins passbands.," This is not surprising since, of the SDSS $ugriz$ filters, the passband of the$u$ filter agrees most closely to the Johnson-Cousins passbands."
 The transformation for C is thus, The transformation for $U$ is thus
"Notice-. that there is. no power-law growth in"" the perturbation. energy forJ Ri.""E1/17"" consistent with the classical Richardson criterion (??)).",Notice that there is no power-law growth in the perturbation energy for ${\rm{Ri}} > 1/4$ consistent with the classical Richardson criterion \ref{RICH}) ).
 Iu our analysis the euergy decays witli time for 2a—1<0. or Ri>3/16.," In our analysis the energy decays with time for $2\alpha-1<0$, or ${\rm{Ri}} > 3/16$."
 Thus the energy of an initial isotropic set of incompressive perturbations iu a radially-stratified shearing sheet-inodel grows asymptotically (for Ri<3/16). just like the compressive sliwaves aud the incompressive sliwaves in au uustratified shearing sheet. for which the euergy is constant in time.," Thus the energy of an initial isotropic set of incompressive perturbations in a radially-stratified shearing sheet-model grows asymptotically (for ${\rm{Ri}} < 3/16$ ), just like the compressive shwaves and the incompressive shwaves in an unstratified shearing sheet, for which the energy is constant in time."
 The growth of au eusemble of incompressive sliwaves in a stratified disk is πο toa or convective type instability., The growth of an ensemble of incompressive shwaves in a stratified disk is due to a Rayleigh-Taylor or convective type instability.
 There is asyinptotie growth for 0<Bi«3/16. aud convective instability requires Ri«0.," There is asymptotic growth for $0 < {\rm{Ri}} < 3/16$, and convective instability requires ${\rm{Ri}} < 0$."
" One cau also see this by examining the asyinptotic euergy [or small values of Ηλ, such as would be expected for a Ixeplerian disk with modest radial gradients: ο 1)) Ri (EQ = 0))."," One can also see this by examining the asymptotic energy for small values of $|{\rm{Ri}}|$, such as would be expected for a Keplerian disk with modest radial gradients: E_i t 1) + E_i(t = 0)."
.(96) Evideutly for small values of Ri the near-linear growth iu time of the euergy is indepencent of the sien of Ri and therefore V7.7! We have studied the uouaxisyiuuetric linear tleory of a thin. radially-stratified disk.," Evidently for small values of Ri the near-linear growth in time of the energy is independent of the sign of Ri and therefore $N_x^2$ We have studied the nonaxisymmetric linear theory of a thin, radially-stratified disk."
" Our findings are: (1) incompressive. short-wavelenetl peru‘batious in the unstratilied shea‘jue sheet exhibit trausieut. growth auc asyiuptotie decay. bu ile enerey of an eusemble of suc1 cslwaves is constant with time (consistent. with Afshordi.Àdopadhlyay.&Narayan200 1)): (ii) short-waveleneth compressive sliwaves grow. asviuptotically in the uustratified shearing sheet. as cloes the energy of au ensemble of such shiwaves. which i ie abseuce of any otler dissipative effects (e.g..ζ radiative camping) will result in a compressive sliwave steepening into a trail of weak shocks: (ii) incompressive sliwaves in the stratiliec slearing sheet have deusity and azimutal velocity perturbations X. de,~1FH (for [Ri]<| (iv) incompressive slaves iu the stratified shearing sheet are associated. with au augular momenum flux proportional to —&,/Kky. leadim sliwaves therefore have positive angular ruomentum flux aud trailing sliwaves Lave 1egalive angular momeutum flux: (v) the euergy of au eusemble of iucompressive sliwaves in the str'atified shearim sheet behaves asymptotically as /+HH [or |Ri|<Jn1,"," Our findings are: (i) incompressive, short-wavelength perturbations in the unstratified shearing sheet exhibit transient growth and asymptotic decay, but the energy of an ensemble of such shwaves is constant with time (consistent with \citealt
{amn04}) ); (ii) short-wavelength compressive shwaves grow asymptotically in the unstratified shearing sheet, as does the energy of an ensemble of such shwaves, which in the absence of any other dissipative effects (e.g., radiative damping) will result in a compressive shwave steepening into a train of weak shocks; (iii) incompressive shwaves in the stratified shearing sheet have density and azimuthal velocity perturbations $\delta \Sigma$, $\delta v_y \sim t^{-{\rm Ri}}$ (for $|{\rm Ri}| \ll 1$ ); (iv) incompressive shwaves in the stratified shearing sheet are associated with an angular momentum flux proportional to $-\tilde{k}_x/k_y$; leading shwaves therefore have positive angular momentum flux and trailing shwaves have negative angular momentum flux; (v) the energy of an ensemble of incompressive shwaves in the stratified shearing sheet behaves asymptotically as $t^{1-4{\rm Ri}}$ for $|{\rm
Ri}| \ll 1$."
 For Ivepleriau disks with modest racial eracients. [Lil is expected to be «I. aud there will therefore be weak growth in a single sliw:ive for Ri<0 and near-Iinear growth tn the euergy of an ensemble of slawaves. iucepetrdent of the sieu of Ri.," For Keplerian disks with modest radial gradients, $|{\rm
Ri}|$ is expected to be $\ll 1$, and there will therefore be weak growth in a single shwave for ${\rm Ri} < 0$ and near-linear growth in the energy of an ensemble of shwaves, independent of the sign of Ri."
during commissioning and the first 33 davs of science operations.,during commissioning and the first 33 days of science operations.
 1.996 of the 10.000 stars have been explicitly included as a result of the dwarl/eiant discriminator while 2.272 of the ~10.000 stars have been explicitly excluded.," 1,996 of the $\sim 10,000$ stars have been explicitly included as a result of the dwarf/giant discriminator while 2,272 of the $\sim 10,000$ stars have been explicitly excluded."
 The remaining ~6.000 remain on the unclassified target list pending additional data.," The remaining $\sim 6,000$ remain on the unclassified target list pending additional data."
 The unclassified stars that were determined to be giants comprise part of the Quarter 2 Dropped Target List., The unclassified stars that were determined to be giants comprise part of the Quarter 2 Dropped Target List.
 The light curves of dropped targets are made available to the public GO days after release (Haasetal.2010)., The light curves of dropped targets are made available to the public 60 days after release \citep{haas}.
.Kepler is observing more than 150.000 stars during the first vear of mission operations. more (han 90.000 of which are G-ivpe stars on or near (he Main Sequence.," is observing more than 150,000 stars during the first year of mission operations, more than 90,000 of which are G-type stars on or near the Main Sequence."
 10.575 are G-(vpe stars brighter (han 18th magnitude.," 10,575 are G-type stars brighter than 13th magnitude."
 28.519 are brighter than 14th magnitude.," 28,519 are brighter than 14th magnitude."
 Over 90% of the target stars are selected based on detectability metrics Chat suggest a lerrestvialsize planet (22< 2H.) is detectable in 3.5 vears., Over $90\%$ of the target stars are selected based on detectability metrics that suggest a terrestrial-size planet $R < 2R_{e}$ ) is detectable in 3.5 years.
 The detectability metrics are derived [rom stellar properties in (heCatalog., The detectability metrics are derived from stellar properties in the.
 Stellar classifications (surface eravitv. effective temperature. and the inferred. stellar radius) are complete at the 80% level. independent of magnitude.," Stellar classifications (surface gravity, effective temperature, and the inferred stellar radius) are complete at the $80\%$ level, independent of magnitude."
 A photometric luminosity class discriminator is applied to 1.000 Alain Sequence ancl 1.000 Giant light curves (as indicated by KIC classifications and confirmed. in some cases. by. Hipparcos parallaxes) [rom commissioning data.," A photometric luminosity class discriminator is applied to 1,000 Main Sequence and 1,000 Giant light curves (as indicated by KIC classifications and confirmed, in some cases, by Hipparcos parallaxes) from commissioning data."
 We report agreement between the KIC and photometric discriminators >9054 of the time for stars brighter than 13th magnitude., We report agreement between the KIC and photometric discriminators $>90\%$ of the time for stars brighter than 13th magnitude.
 Priority on the target list is given to stars that can be followed up with high-precision radial velocity measurements Ilrom current ground-based facilities., Priority on the target list is given to stars that can be followed up with high-precision radial velocity measurements from current ground-based facilities.
 High priority is also assigned to the fainter (14<Ap 16) Ix and M-t0vpe cwarls that will benelit from future IR. spectrometers., High priority is also assigned to the fainter $14 \leq Kp < 16$ ) K and M-type dwarfs that will benefit from future IR spectrometers.
 Ancillary target lists are generated for special purposes (e.g. to detect planets around EBs. to extend the age-rotation relation for Main sequence stars. and (to ensure that (he closest Main Sequence stars are included).," Ancillary target lists are generated for special purposes (e.g. to detect planets around EBs, to extend the age-rotation relation for Main Sequence stars, and to ensure that the closest Main Sequence stars are included)."
 Finally, Finally
"with /?., being the photospherie radius.",with $R_*$ being the photospheric radius.
" The thermal equilibrium condition 1s where L,,, is the total luminosity output from all energy sources as described below in Sec.??.", The thermal equilibrium condition is where $L_{tot}$ is the total luminosity output from all energy sources as described below in \ref{ensources}.
. Starting with a mass A/ and an estimate for the outer radius ες. the code integrates Eqns. (??))," Starting with a mass $M$ and an estimate for the outer radius $R_*$ , the code integrates Eqns. \ref{hydro}) )"
 and (??)) outward from the center., and \ref{eqstate}) ) outward from the center.
" The total luminosity output {ο is compared to the stellar radiated luminosity, as in Eq.(??)) and the radius is adjusted until the condition of thermal equilibrium is met (a convergence of 1 in 10! is reached)."," The total luminosity output $L_{tot}$ is compared to the stellar radiated luminosity, as in \ref{thermal}) ) and the radius is adjusted until the condition of thermal equilibrium is met (a convergence of $1$ in $10^4$ is reached)."
 The first stars form inside ~LO°A/. haloes., The first stars form inside $\sim 10^6 \msun$ haloes.
" Simulations imply that DM halos have a naturally cuspy profile, but there is still some uncertainty about the exact inner slope of a DM halo: ???.."," Simulations imply that DM halos have a naturally cuspy profile, but there is still some uncertainty about the exact inner slope of a DM halo: \citet{2007ApJ...667..859D,2008MNRAS.391.1685S,2010arXiv1002.3660K}."
" Luckily, a previous paper (2) showed that a dark star results regardless of the details of the initial density profile, even for the extreme case of a cored Burkert profile (such a Burkert profile is completely unrealistic)."," Luckily, a previous paper \citep{DS3}
 showed that a dark star results regardless of the details of the initial density profile, even for the extreme case of a cored Burkert profile (such a Burkert profile is completely unrealistic)."
" In this paper, we use a Navarro, Frenk, White (NEW) profile (2) for conercteness."," In this paper, we use a Navarro, Frenk, White (NFW) profile \citep{NFW} for concreteness."
" We assume that initially both the baryons of the mass) and the DM of the mass) can be deseribed with the same NFW profile where pi is the ""central"" density and x, is the scale radius."," We assume that initially both the baryons of the mass) and the DM of the mass) can be described with the same NFW profile where $\rho_0$ is the ""central"" density and $r_s$ is the scale radius."
" Clearly at any point of the profile, baryons will only make up of the mass."," Clearly at any point of the profile, baryons will only make up of the mass."
" The density scale, pi can be re-expressed in terms of the critical density of the universe ata given redshift, p,.(2) via"," The density scale, $\rho_0$ can be re-expressed in terms of the critical density of the universe ata given redshift, $\rho_c(z)$ via"
OJ 287 in 1980-2010.,OJ 287 in 1980-2010.
 In the upper panel three outburst seasons of OJ 287 can be seen: 1982-84. 1994-95 and 2005-08.," In the upper panel three outburst seasons of OJ 287 can be seen: 1982-84, 1994-95 and 2005-08."
 The high Ha flux appeared just after the strong outbursts in. 1982-83. 290 days after the second peak.," The high $\alpha$ flux appeared just after the strong outbursts in 1982-83, 290 days after the second peak."
 Unfortunately. the sampling is too poor to draw any conclusions on the possible connection between continuum and BLR luminosity in OJ 287.," Unfortunately, the sampling is too poor to draw any conclusions on the possible connection between continuum and BLR luminosity in OJ 287."
 Such a connectiol would not even be necessarily expected because in BL Lae objects the vast majority of the continuum arises from the jet and is highly beamed by relativistic effects due to the small angle between the line of sight and the Jet axis., Such a connection would not even be necessarily expected because in BL Lac objects the vast majority of the continuum arises from the jet and is highly beamed by relativistic effects due to the small angle between the line of sight and the jet axis.
 Thus the observed continuum variations are not necessarily connected to the changes of the continuum source illuminating the Ha emitting clouds. most likely the inner parts of the accretion disk.," Thus the observed continuum variations are not necessarily connected to the changes of the continuum source illuminating the $\alpha$ emitting clouds, most likely the inner parts of the accretion disk."
 It is nevertheless an intriguing observation that the high line luminosity in 1984 was observed right after a luminous continuum outburst., It is nevertheless an intriguing observation that the high line luminosity in 1984 was observed right after a luminous continuum outburst.
 Given the weakness of the broad Ha line we are unable to study a possible connection between BLR velocity field and the suggested periastron of the secondary black hole in 2005-07 (?).., Given the weakness of the broad $\alpha$ line we are unable to study a possible connection between BLR velocity field and the suggested periastron of the secondary black hole in 2005-07 \citep{2007ApJ...659.1074V}.
 The average ime luminosities in. 2005-05. were log(L/ergs!) = 41.8. 41.1. 41.2 and 40.8 for broad Ha. narrow Ha. 46583[NII] and /46548[NII]. respectively.," The average line luminosities in 2005-08 were $\log(L/{\rm erg\
s}^{-1})$ = 41.8, 41.1, 41.2 and 40.8 for broad $\alpha$ , narrow $\alpha$, $\lambda$ 6583[NII] and $\lambda$ 6548[NII], respectively."
 The He luminosities of Seyfert galaxies and quasars are generally much higher as shown by he comparisons in Table 4+ and Fig. 6.., The $\alpha$ luminosities of Seyfert galaxies and quasars are generally much higher as shown by he comparisons in Table \ref{llumtable} and Fig. \ref{lumvertailu}.
 The quasar data were obtained from ?.. who give data of 77 429 quasars from the Fifth Data Release of the Sloan Digital Sky Survey (?)..," The quasar data were obtained from \cite{2007AJ....134..102S}, who give data of 77 429 quasars from the Fifth Data Release of the Sloan Digital Sky Survey \citep{2007ApJS..172..634A}."
 We selected quasars at the redshift interval z = 0.30—0.31 (147 quasars) and obtained the Πα line fluxes and widths from the SpecLine tables in the SDSS archive., We selected quasars at the redshift interval z = $0.30 - 0.31$ (147 quasars) and obtained the $\alpha$ line fluxes and widths from the SpecLine tables in the SDSS archive.
 Figure 6 shows only quasars with FWHM > 1000 km s! (101 quasars)., Figure \ref{lumvertailu} shows only quasars with FWHM $>$ 1000 km $^{-1}$ (101 quasars).
 In addition we plot data for 17 z = 0.36 Seyfert galaxies in. 2.., In addition we plot data for 17 z = 0.36 Seyfert galaxies in \cite{2008ApJ...673..703M}.
 As can be seen from Fig., As can be seen from Fig.
 6. the He luminosity of OJ 287 was lower than in typical quasars and Seyfert galaxies by a factor of ~ 10 in 2005-08., \ref{lumvertailu} the $\alpha$ luminosity of OJ 287 was lower than in typical quasars and Seyfert galaxies by a factor of $\sim$ 10 in 2005-08.
 In December 1984. however. the Ha luminosity was comparable to that of quasars and Seyferts.," In December 1984, however, the $\alpha$ luminosity was comparable to that of quasars and Seyferts."
 We finally note that the luminosities of the two narrow lines 6548 and 26583 |NIIJ]. however. are comparable to the narrow-line luminosities of the quasars in 9," We finally note that the luminosities of the two narrow lines $\lambda$ 6548 and $\lambda$ 6583 [NII], however, are comparable to the narrow-line luminosities of the quasars in \cite{2007AJ....134..102S}."
 We have presented high S/N spectra of the BL Lac object OJ 287 during seven epochs in. 2005-08., We have presented high S/N spectra of the BL Lac object OJ 287 during seven epochs in 2005-08.
" Our results can be summarized as follows: 1) We were able to detect five narrow emission lines. A16548.6583,NI]. 26563Ha and ;L16716.6731 [SIT] during at least one of the epochs and a broad He feature during two epochs."," Our results can be summarized as follows: 1) We were able to detect five narrow emission lines, $\lambda\lambda$ 6548,6583[NII], $\lambda6563$ $\alpha$ and $\lambda\lambda$ 6716,6731 [SII] during at least one of the epochs and a broad $\alpha$ feature during two epochs."
 The luminosities of the [NII] lines are comparable to those in quasars at the same redshift. whereas the broad Hw line is a factor of ~ 10 less luminous than the Ha line in quasars and Seyfert galaxies.," The luminosities of the [NII] lines are comparable to those in quasars at the same redshift, whereas the broad $\alpha$ line is a factor of $\sim$ 10 less luminous than the $\alpha$ line in quasars and Seyfert galaxies."
 2) The luminosity of the broad Ha line was a factor of ~ 10 lower in 2005-08 than in 1984 when itwas reported to have been detected the last time., 2) The luminosity of the broad $\alpha$ line was a factor of $\sim$ 10 lower in 2005-08 than in 1984 when itwas reported to have been detected the last time.
 3) We do not see any significant change in luminosity. position or width if the broad Ha line between the two epochs," 3) We do not see any significant change in luminosity, position or width if the broad $\alpha$ line between the two epochs"
statistics are not good enough to obtain a reliable Xταν spectrum.,statistics are not good enough to obtain a reliable X–ray spectrum.
 Iu particular. he ERO S2F1.1113 (—35 net couuts in the 0.51.5 keV baud) is detected oulv in the AIOSI while the S2E1.1193 (—21 uct counts in the 0.52 keV) and ERO 7711 (~31 uet counts in the27.5. in particular —1] uct counts in the 215 keV. plus ~20 net counts in the L57.5 keV) are detected oulv in the pu.," In particular, the ERO 443 $\sim$ 35 net counts in the 0.5–4.5 keV band) is detected only in the MOS1 while the 493 $\sim$ 24 net counts in the 0.5–2 keV) and ERO 714 $\sim$ 31 net counts in the2–7.5, in particular $\sim$ 11 net counts in the 2–4.5 keV plus $\sim$ 20 net counts in the 4.5–7.5 keV) are detected only in the pn."
 By performing a visual inspection of all the 3 EPIC cameras. we find hat. while S2E1.1193 and S2FL_7711 are ouly visible iu the image where they have Όσσα detected. S2FI_LLL8 is also barely visible iu the MOS2 imaec.," By performing a visual inspection of all the 3 EPIC cameras, we find that, while 493 and 714 are only visible in the image where they have been detected, 443 is also barely visible in the MOS2 image."
 Iu order to increase the statistics of this source we have used MOS|MOS2 data thus accumulating 50 net counts in total., In order to increase the statistics of this source we have used MOS1+MOS2 data thus accumulating $\sim$ 50 net counts in total.
 Later. we will use these statistics to derive the basic Nταν properties of S2F1.1113.," Later, we will use these statistics to derive the basic X–ray properties of 443."
 Some indications about the origin of the Xrav chussion of these 3. EROs have been derived by calculating their hardness (hereafter IR)., Some indications about the origin of the X–ray emission of these 3 EROs have been derived by calculating their hardness (hereafter HR).
" While the value of the TR (~ 0.9) derived for S2E1.1195 is not a discriminant of the Xravemiüssiou origin. both ILLS i;~ 0.3) aud 7711 (IRs, ~1) have hardness ratios typical of obscured ACNs (see Della Ceca et al. 2001)."," While the value of the HR $\sim$ –0.9) derived for 493 is not a discriminant of the X–rayemission origin, both 443 $_{443}\sim$ –0.3) and 714 $_{714}\sim$ 1) have hardness ratios typical of obscured AGNs (see Della Ceca et al. \cite{Dellaceca04}) )."
" By using a simulated spectrum at the redshift of the source and by assuming an intrinsic photon index of 1.9. we have estimated hat the intriusic cohunn deusitv uceded to reproduce the harduess ratios of [113 aud S2PL7711 ave consistent with values larecr han 1072 ? and of about 10?! 2. respectively,"," By using a simulated spectrum at the redshift of the source and by assuming an intrinsic photon index of 1.9, we have estimated that the intrinsic column density needed to reproduce the hardness ratios of 443 and 714 are consistent with values larger than $^{22}$ $^{-2}$ and of about $^{24}$ $^{-2}$, respectively."
 Although the statistics of S2F1.1I3 are not good enough to perform a complete Xταν spectral analysis. it allows us to compare the model used to reproduce the hardness ratio with the X.ταν data.," Although the statistics of 443 are not good enough to perform a complete X–ray spectral analysis, it allows us to compare the model used to reproduce the hardness ratio with the X–ray data."
 The good agrecineut betweenmodel aud data is shown iu Figure 3 where a rest- absorbed )owerlaw model (T=1.9. Ng < 107? 7) js superiuposed on the backeroundsubtracted Xταν counts. binned in order to have at least 15 total counts per cucrey channel.," The good agreement betweenmodel and data is shown in Figure 3 where a rest-frame absorbed power–law model $\Gamma$ =1.9, $_H$ $\times$ $^{22}$ $^{-2}$ ) is superimposed on the background–subtracted X–ray counts, binned in order to have at least 15 total counts per energy channel."
" From this model we derive a Galactie corrected flux of Fioqug,76. 752.1410. P? erg D 1 and. by usingB dtsH spectroscopic- redshift (1.70.05, see Table 1 and Sect."," From this model we derive a Galactic corrected flux of $_{(2-10\rm keV)}$ $\pm$ $\times$ $^{-15}$ erg $^{-2}$ $^{-1}$ and, by using its spectroscopic redshift $\pm$ 0.05, see Table 1 and Sect."
" [) we estimate am intrinsic huuinosity of Lyρω 20.6 <1 yl Cres 1 (the huuiuosity errors take uto account also he redslüft ""ucertaities). iun good aereciment with its high radio numositv (see Sect."," 4) we estimate an intrinsic luminosity of $_{(2-10\rm keV)}$ $\pm$ $\times$ $^{44}$ erg $^{-1}$ (the luminosity errors take into account also the redshift uncertainties), in good agreement with its high radio luminosity (see Sect."
 Tn order to estimate the flux and the buninosity or ERO S2F1.7711. we have calculated the vignettingcorrected count rates in the 27.5 keV band (the ERO das been detected only iu the 21.5 and 157.5 SSC xad).," In order to estimate the flux and the luminosity for ERO 714, we have calculated the vignetting--corrected count rates in the 2–7.5 keV band (the ERO has been detected only in the 2–4.5 and 4.5–7.5 SSC band)."
 Usine the measured count rates and asstuuine a oowerlawmodel with DP-—1.4 (simular to that of the uuresolved Cosme Nrav background since the source seelus to be very hard} we obtain a Galactic corrected Bux of Froque HELD S10 P ere 2s 12, Using the measured count rates and assuming a power–lawmodel with $\Gamma\sim$ 1.4 (similar to that of the unresolved Cosmic X–ray background since the source seems to be very hard) we obtain a Galactic corrected flux of $_{(2-10\rm keV)}$ $\pm$ $\times$ $^{-15}$ erg $^{-2}$ $^{-1}$.
" Takius into account the photometric redshift (1.02:0.2) and the imiriusic cohunuu deusitv derived from the WR aualvsis (Ny consistent+ with. 1074P P7. see above) we estiiate an intrinsic huninosity L,5okey DIO ore sf,"," Taking into account the photometric redshift $\pm$ 0.2) and the intrinsic column density derived from the HR analysis $_H$ consistent with $^{24}$ $^{-2}$, see above) we estimate an intrinsic luminosity $_{(2-10\rm keV)}>$ $^{44}$ erg $^{-1}$."
 Iu stumary. we find evidence that both S2FL_L113 aud S2FL771L1 are probably Xταν obscured ACNs of high huuinosity (>10!! ere 1).," In summary, we find evidence that both 443 and 714 are probably X–ray obscured AGNs of high luminosity $>10^{44}$ erg $^{-1}$ )."
 This result is also supported by the (210 keV)tooptical flux ratios of these two EROs asa function of their (2LO keV) fluxes (see Figure £., This result is also supported by the (2–10 keV)–to–optical flux ratios of these two EROs as a function of their (2–10 keV) fluxes (see Figure 4).
 The two EROs discussed here are plottec with solid circles. while the : EROs for which he presence of an obscured aud Yeh luminosity ACUNS is already indicated by the X spectral analysis (see Sec.," The two EROs discussed here are plotted with solid circles, while the 3 EROs for which the presence of an obscured and high luminosity AGNs is already indicated by the X--ray spectral analysis (see Sec."
 3.1) have been plotted with solid circles encircled by larger open circle., 3.1) have been plotted with solid circles encircled by larger open circle.
 For comparison in Figure Lowe plot also other Xrav emitting EROs taken from the literature Ge. Hollas-2NMM. Mignoli et al. 2001:," For comparison in Figure 4 we plot also other X–ray emitting EROs taken from the literature (i.e. Hellas2XMM, Mignoli et al. \cite{Mignoli};"
 Lockiman ole. Mainieri et al. 2002.. ," Lockman Hole, Mainieri et al. \cite{Mainieri}, ,"
Stevens et al. 2003: , Stevens et al. \cite{Stevens}; ; –
CDEN. Vienali et al. 2002.. ,"CDFN, Vignali et al. \cite{Vignali}, ,"
Alexander et al. 2002.. 2003..," Alexander et al. \cite{Alexander02}, \cite{Alexander03},"
 Darger et al. 2003: , Barger et al. \cite{Barger03}; –
CDES. Roche ct al. 2003..,"CDFS, Roche et al. \cite{Roche},"
 Szokolv et al. 2001: , Szokoly et al. \cite{Szokoly}; ;
ELATS. Willott et al 2003)).," ELAIS, Willott et al \cite{Willott}) )."
 Different saubols have been used to mark the differeiut EROs on the basis of the iuforinatiou available in the, Different symbols have been used to mark the different EROs on the basis of the information available in the
Tablel for G338.3-0.0 CASE 2). the current spin-down power of the pulsar is 1.65«107 ere 1. and the resulting radius of the PWN is just 2.45 pe. which is even smaller than the extension of the X-rays (~3.5 pe) assuming a distance of 10 kpe (Lemiereetal..2009).,"\ref{para} for G338.3-0.0 CASE 2), the current spin-down power of the pulsar is $1.65\times10^{37}$ erg $^{-1}$, and the resulting radius of the PWN is just 2.45 pc, which is even smaller than the extension of the X-rays $\sim3.5$ pc) assuming a distance of 10 kpc \citep[][]{Lea09}."
. A smaller jp=0.3«10.7. and the maximum energy of the particles is set to 500 TeV to reproduce the observational fluxes in the X-rays and >-rays.," A smaller $\eta_{\rm
B}=0.3\times10^{-3}$, and the maximum energy of the particles is set to 500 TeV to reproduce the observational fluxes in the X-rays and $\gamma$ -rays."
 The resulting multiband nonthermal emission is indicated in Fig.9 with soft densities of 1.0eV  and 6.0eV ° for the infrared and the optical soft photons. respectively.," The resulting multiband nonthermal emission is indicated in \ref{Figj1640b} with soft densities of 1.0 eV $^{-3}$ and 6.0 eV $^{-3}$ for the infrared and the optical soft photons, respectively."
 In this scenario. the PWN has been compressed by the reverse shock. and the resulting flux with energies below | eV is about two orders of magnitude higher than that in the CASE I.," In this scenario, the PWN has been compressed by the reverse shock, and the resulting flux with energies below 1 eV is about two orders of magnitude higher than that in the CASE 1."
 Motivated by the finding that the spectrum of the particles downstream of a relativistic shock consists of two components: arelativistic Maxwellian and a power-law high-energy tail with an index of —2.1+0.1 (Spitkovsky.2008).. we investigate the possibility of particles with this new spectrum injected in PWNe from the TS based on the studies of multiband emission from PWNe.," Motivated by the finding that the spectrum of the particles downstream of a relativistic shock consists of two components: a relativistic Maxwellian and a power-law high-energy tail with an index of $-2.4\pm0.1$ \citep[][]{Sp08}, we investigate the possibility of particles with this new spectrum injected in PWNe from the TS based on the studies of multiband emission from PWNe."
 Following the dynamical method proposed in Gelfandetal.(2009). we study the dynamical and multi-band radiative properties of the three composite SNRs GO.940.1. MSH 15-52 and G338.3-0.0.," Following the dynamical method proposed in \citet[][]{GSZ09}, we study the dynamical and multi-band radiative properties of the three composite SNRs G0.9+0.1, MSH 15-52 and G338.3-0.0."
 With appropriate parameters. we find that a typical PWN is an important 5-ray emitter during its evolution although the non-thermal radiation from the radio to the X-ray band is insignificant sometimes.," With appropriate parameters, we find that a typical PWN is an important $\gamma$ -ray emitter during its evolution although the non-thermal radiation from the radio to the X-ray band is insignificant sometimes."
 The multiband observations of the three PWNe in the remnants can be well reproduced with the new spectrum of the injected particles., The multiband observations of the three PWNe in the remnants can be well reproduced with the new spectrum of the injected particles.
 Therefore. our studies on the dynamical and multiwavelength radiative properties of PWNe provide evidence of high-energy electrons/positrons can be injected into a PWN with a Maxwellian plus a power-law high-energy tail from the TS of the PWN.," Therefore, our studies on the dynamical and multiwavelength radiative properties of PWNe provide evidence of high-energy electrons/positrons can be injected into a PWN with a Maxwellian plus a power-law high-energy tail from the TS of the PWN."
 In modeling the multiband nonthermal emission from a PWN detected in the radio. X-ray and +-ray bands. particles injected with a spectrum of a broken power-law are widely used to reproduce the observed multiwavelength emission (e.g..Venter&deJager.2006:Slane.2008:Zhangetal.. 2008).," In modeling the multiband nonthermal emission from a PWN detected in the radio, X-ray and $\gamma$ -ray bands, particles injected with a spectrum of a broken power-law are widely used to reproduce the observed multiwavelength emission \citep[e.g.,][]{Vd06,S08,ZCF08}."
. Of course. for the three PWNe discussed in this paper. the multiband observed spectra of them can also be explained if the particles are injected with a broken power-law.," Of course, for the three PWNe discussed in this paper, the multiband observed spectra of them can also be explained if the particles are injected with a broken power-law."
 However. it is unclear why the broken power-law spectrum 1s valid when using it to reproduce the multiwavlength emission from a PWN.," However, it is unclear why the broken power-law spectrum is valid when using it to reproduce the multiwavlength emission from a PWN."
" From our calculations. we have found out that the energy distribution of the electrons/positrons in the nebula can be approximated as a broken power-law with an index ~1 in the lower-energy band and an index of ~2.5 in the higher-energy part before the PWN undergos significant compression. which is most likely the physical explanation of the broad usage ""Sff a broken power law in modeling the multi-band non-thermal emission from PWNe."," From our calculations, we have found out that the energy distribution of the electrons/positrons in the nebula can be approximated as a broken power-law with an index $\sim 1$ in the lower-energy band and an index of $\sim2.5$ in the higher-energy part before the PWN undergos significant compression, which is most likely the physical explanation of the broad usage of a broken power law in modeling the multi-band non-thermal emission from PWNe."
 In this paper. high-energy electrons/positrons are injected into the PWN from the TS. and the main energy of the nebula is contained in these particles.," In this paper, high-energy electrons/positrons are injected into the PWN from the TS, and the main energy of the nebula is contained in these particles."
 These particles undergo radiative and adiabatie losses when the nebula evolves 1n the host SNR., These particles undergo radiative and adiabatic losses when the nebula evolves in the host SNR.
 Our study indicates that. for atypical PWN with the parameters similar as GO.9+0.1. the adiabatic loss of the particles in the nebula is significant after an age of ~1000 yr (see Fig.3. and Fig.4).," Our study indicates that, for atypical PWN with the parameters similar as G0.9+0.1, the adiabatic loss of the particles in the nebula is significant after an age of $\sim1000$ yr (see \ref{Epwn} and \ref{Epower}) )."
 Multiwaveband nonthermal emission from a PWN has been investigated using a simplified time-dependent injection model. in which high-energy electrons/positrons are injected into the PWN (e.g..Venter&deJager.2006:Slane.2008:Zhangetal.. 2008).," Multiwaveband nonthermal emission from a PWN has been investigated using a simplified time-dependent injection model, in which high-energy electrons/positrons are injected into the PWN \citep[e.g.,][]{Vd06,S08,ZCF08}."
. The pulsar inside the PWN transfers a part of its spin-down power to the particles with a spectrum of a broken power-law., The pulsar inside the PWN transfers a part of its spin-down power to the particles with a spectrum of a broken power-law.
 In the simplified time-dependent injection model in Zhangetal.(2008).. synchrotron loss of the particles is taken into account. whereas the adiabatic one ts ignored.," In the simplified time-dependent injection model in \citet[][]{ZCF08}, synchrotron loss of the particles is taken into account, whereas the adiabatic one is ignored."
 As a result. either a relatively smaller initial spin-down power of the pulsar or a smaller efficiency of the power to the kinetic energy of the accelerated electrons/positrons is employed in the model.," As a result, either a relatively smaller initial spin-down power of the pulsar or a smaller efficiency of the power to the kinetic energy of the accelerated electrons/positrons is employed in the model."
 Moreover. note that in Zhangetal.(2008)... an initial spin-down power of 1«1075 ere + for MSH 15-52 was used to investigate the multiband emission from the PWN. which is a factor of 15 smaller than that used in this paper.," Moreover, note that in \citet[][]{ZCF08}, an initial spin-down power of $1\times10^{38}$ erg $^{-1}$ for MSH 15-52 was used to investigate the multiband emission from the PWN, which is a factor of 15 smaller than that used in this paper."
 Besides the above reasons. the another main one ts a relatively big spin-down time scale of ~5000 vr. whichis x»Ey in the paper. used by Zhangetal. (2008).. whereas in this paper it is adopted to be 500 vr.," Besides the above reasons, the another main one is a relatively big spin-down time scale of $\sim 5000$ yr, which is $\propto \dot{E_0}^{-1}$ in the paper, used by \citet[][]{ZCF08}, , whereas in this paper it is adopted to be $500$ yr."
 The energy released by the pulsa is mainly determined by Lyή{μαςτο}. and the value in this paper is not much bigger than that in Zhangetal. (2005). ," The energy released by the pulsar is mainly determined by $E_0
\min \{T_{\rm age}, \tau_0 \}$, and the value in this paper is not much bigger than that in \citet[][]{ZCF08}. ."
Therefore. the multiband observed spectra for MSH 15-52 caαυ] be reproduced within the two scenarios even theinitial power of the pulsar ts significantly different.," Therefore, the multiband observed spectra for MSH 15-52 can be reproduced within the two scenarios even theinitial spin-down power of the pulsar is significantly different."
degeneracies between the NS magnetic configuration. viewing geometry. and compactiness make it diflieult to extract physical parameters from observations.,"degeneracies between the NS magnetic configuration, viewing geometry, and compactness make it difficult to extract physical parameters from observations."
 As an alternative. several recent works discuss the evolution of photon polarization states in NS magnetospheres. showing that. in the magnetar case. significant. linear. polarization fractions are expected. possibly containing a unique signature of the strong magnetic field per," As an alternative, several recent works discuss the evolution of photon polarization states in NS magnetospheres, showing that, in the magnetar case, significant linear polarization fractions are expected, possibly containing a unique signature of the strong magnetic field \citep[][]{HeylShaviv00a,HeylShaviv02a,Heyletal03a,LaiHo03a,vanAdelsbergLai06a,WangLai09a}."
formed for (he Crab nebula using the OSO-8 satellite (2)..," Measurements of significant X-ray polarization, at 2.6 keV and 5.2 keV, were performed for the Crab nebula using the OSO-8 satellite \citep[][]{Weisskopfetal76a}."
 These measurements confirmed an earlier detection bv a sounding rocket experiment (?).., These measurements confirmed an earlier detection by a sounding rocket experiment \citep[][]{Novicketal72a}.
 ILowever. as of (his writing. no subsequent. polarization measurements have been made [or anv object al energies [7~ keV (relevant for thermal magnetar emission).," However, as of this writing, no subsequent polarization measurements have been made for any object at energies $E\sim 0.1-10$ keV (relevant for thermal magnetar emission)."
 Recent advances in instrumentation have stimulated interest in future missions (ο perform polarimetry in the soft. X-ray banc. leading to several projects which are in active development (see???)..," Recent advances in instrumentation have stimulated interest in future missions to perform polarimetry in the soft X-ray band, leading to several projects which are in active development \citep[see][]{Costaetal01a,Kallman04a,Costaetal06a}."
 In this paper. we explore the future role of X-ray polarimetry as a complement {ο spectroscopy in interpreting observational spectra.," In this paper, we explore the future role of X-ray polarimetry as a complement to spectroscopy in interpreting observational spectra."
 We will argue that the combination of polarimetry aid spectroscopy can constrain several eritical NS parameters. including the temperature. magnetic field strength ancl geometry. size of emission region. and ratio of highly magnetized NSs with B~107—10 G. We use the latest magnetar abmosphere models of2.. and expand on the work of ?.. ?.. νι and ?.. lo compute the phase-resolved. observed Stokes parameters from magnetars.," We will argue that the combination of polarimetry and spectroscopy can constrain several critical NS parameters, including the temperature, magnetic field strength and geometry, size of emission region, and mass-to-radius ratio of highly magnetized NSs with $B\sim 10^{12}-10^{15}$ G. We use the latest magnetar atmosphere models of\citet[][]{vanAdelsbergLai06a}, and expand on the work of \citet[][]{HeylShaviv02a}, \citet[][]{Heyletal03a}, \citet[][]{LaiHo03a}, and \citet[][]{vanAdelsbergLai06a}, to compute the phase-resolved, observed Stokes parameters from magnetars."
 We assume (hat. these NSs have dipole magnetic field strengths of B=4xLOM G5x10! G and emit [rom a region centered around (he star polar cap wilh modest opening angle., We assume that these NSs have dipole magnetic field strengths of $B = 4\times 10^{13}$ G – $5\times 10^{14}$ G and emit from a region centered around the star polar cap with modest opening angle.
 We confirm that the polarization sienal Iron a finite region on a magnetar surface retains important information about the streneth of the magnetic field. as reported in previous works.," We confirm that the polarization signal from a finite region on a magnetar surface retains important information about the strength of the magnetic field, as reported in previous works."
 We show (hat this signal has a strong dependence on (he magnetic field and viewing geometry. and a weaker dependence on (he NS EOS. emission region size. and atmosphere composition.," We show that this signal has a strong dependence on the magnetic field and viewing geometry, and a weaker dependence on the NS EOS, emission region size, and atmosphere composition."
 Finally. we argue (hat. polarization measurements can break (he degeneracy inherent in inlerring physical parameters [from spectroscopic measurements alone.," Finally, we argue that polarization measurements can break the degeneracy inherent in inferring physical parameters from spectroscopic measurements alone."
 Qur paper is organized as follows: in relsect:Physies Inputs... we discuss our assumptions and (the atmosphere models used to calculate the emitted polarization Iraction [rom the NS surface.," Our paper is organized as follows: in \\ref{sect:Physics Inputs}, we discuss our assumptions and the atmosphere models used to calculate the emitted polarization fraction from the NS surface."
 Iu refsect:Emission Model.. we describe our methods for calculating the observed polarization signal [rom an extended NS polar cap. including relativistic effects.," In \\ref{sect:Emission Model}, we describe our methods for calculating the observed polarization signal from an extended NS polar cap, including relativistic effects."
 In relsect:ltesulis.. we show the results of our calculations [or several representative cases.," In \\ref{sect:Results}, , we show the results of our calculations for several representative cases."
For at least four decades. searches have been conducted for stars with properties very similar to the Sun (see Hardorp 1978. Cayrel de Strobel et al.,"For at least four decades, searches have been conducted for stars with properties very similar to the Sun (see Hardorp 1978, Cayrel de Strobel et al."
 1981; see also the review by Cayrel de Strobel 1996. and for a recent short summary e.g. Melénndez Ramírrez 2007).," 1981; see also the review by Cayrel de Strobel 1996, and for a recent short summary e.g. Melénndez Ramírrez 2007)."
" It would be important to find a star with physical characteristies indistinguishable from those of the Sun. a ""perfect good solar twin"". as defined by Cayrel de Strobel (1996)."," It would be important to find a star with physical characteristics indistinguishable from those of the Sun, a “perfect good solar twin”, as defined by Cayrel de Strobel (1996)."
 The reasons for this importance are both physical and technical., The reasons for this importance are both physical and technical.
 Physically. the statistics of solar twins would certainly. contribute to our understanding of the uniqueness or normality of the Sun (ef.," Physically, the statistics of solar twins would certainly contribute to our understanding of the uniqueness or normality of the Sun (cf."
 Gustafssor 1998)., Gustafsson 1998).
 Technically. a solar twin would be useful in setting zero points in the calibration of effective-temperature scales. basec on stellar colours.," Technically, a solar twin would be useful in setting zero points in the calibration of effective-temperature scales, based on stellar colours."
 Another use would be in the calibration of night-time reflectance spectroscopy of solar-system bodies. where the spectral component of the Sun must be removed before an analysis of the spectroscopic features of the body itself can be performed.," Another use would be in the calibration of night-time reflectance spectroscopy of solar-system bodies, where the spectral component of the Sun must be removed before an analysis of the spectroscopic features of the body itself can be performed."
 Numerous searches and accurate analyses have resulted 11 a small sample of solar-twin candidates (Porto de Mello da Silva 1997. Melénndez et al.," Numerous searches and accurate analyses have resulted in a small sample of solar-twin candidates (Porto de Mello da Silva 1997, Melénndez et al."
 2006. Takeda et al.," 2006, Takeda et al."
 2007. Melénndez et al.," 2007, Melénndez et al."
 2009. Ramírrez et al.," 2009, Ramírrez et al."
 2009)., 2009).
 Although these stars in. general have fundamental parameters very close to solar. recent advances in high-accuracy differential abundance analyses have proven almost all of them to have chemical compositions slightly. but systematically. deviating from that of the Sun.," Although these stars in general have fundamental parameters very close to solar, recent advances in high-accuracy differential abundance analyses have proven almost all of them to have chemical compositions slightly, but systematically, deviating from that of the Sun."
 A special opportunity in the search for solar twins is offered by the old and rich open cluster M67., A special opportunity in the search for solar twins is offered by the old and rich open cluster M67.
 It has à chemical composition similar to the Sun with [Fe/H] in the range 0.04 to 0.03 on the customary logarithmic scale normalised to the Sun (Hobbs Thorburn 1991]. Tautvaisiene et al.," It has a chemical composition similar to the Sun with [Fe/H] in the range $-$ 0.04 to 0.03 on the customary logarithmic scale normalised to the Sun (Hobbs Thorburn 1991, $\check{\rm s}$ iene et al."
 2000. Yong et al.," 2000, Yong et al."
 2005. Randich et al.," 2005, Randich et al."
 2006. Pace et al.," 2006, Pace et al."
 2008. Pasquini et al.," 2008, Pasquini et al."
 2008)., 2008).
 Its age is also comparable to that of the Sun: 44.8 Gyr YYadav et al., Its age is also comparable to that of the Sun: 4.8 Gyr Yadav et al.
 2008)., 2008).
 M67 is relatively nearby (~ ppc) and is only little. affected by interstellar extinction. which allows detailed spectroscopic studies of its main-sequence stars.," M67 is relatively nearby $\sim$ pc) and is only little affected by interstellar extinction, which allows detailed spectroscopic studies of its main-sequence stars."
 The depleted Li abundance of the Sun seems rather representative of solar-twins in the Galaxtie field (Baumann et al., The depleted Li abundance of the Sun seems rather representative of solar-twins in the Galaxtic field (Baumann et al.
 2010)., 2010).
 M67 also seems to contain Li-depleted G stars (Pasquini et al., M67 also seems to contain Li-depleted G stars (Pasquini et al.
 1997)., 1997).
 M67 thus offers good possibilities of finding solar-twin candidates for further exploration., M67 thus offers good possibilities of finding solar-twin candidates for further exploration.
 Pasquini et al. (, Pasquini et al. (
2008) (followed by a paper of Biazzo et al.,2008) (followed by a paper of Biazzo et al.
 2009) recently searched the cluster for solar analogs. and listed ten promising candidates.," 2009) recently searched the cluster for solar analogs, and listed ten promising candidates."
 Here we present an analysis of (NGC 2682 YBP 1194. ES 4063. ES IV-63. FBC 2867. MMJ 5357. SAND 770. 2MASS JO8510080+41148527). a cluster. solar-twin candidate suggested by Pasquini et al. (," Here we present an analysis of (NGC 2682 YBP 1194, ES 4063, ES IV-63, FBC 2867, MMJ 5357, SAND 770, 2MASS J08510080+1148527), a cluster solar-twin candidate suggested by Pasquini et al. ("
2008).,2008).
 Our analysis is based on high-resolution observations with relatively high signal-to-noise (S/N) ratio., Our analysis is based on high-resolution observations with relatively high signal-to-noise (S/N) ratio.
 In Section 2.. we discuss the observations and some aspects of the data reduction.," In Section \ref{sec:obs}, we discuss the observations and some aspects of the data reduction."
" Section 3. deseribes the analysis method and the determination of fundamental parameters(ζωα. logg. [Fe/H] and £,)."," Section \ref{sec:analys} describes the analysis method and the determination of fundamental parameters, $\log g$ , [Fe/H] and $\xi_{t}$ )."
 In Section 4+. we present the results of a detailed analysis of a number of chemical elements. and these results are compared to those obtained for known twins in the Galactic field.," In Section \ref{sec:comp} we present the results of a detailed analysis of a number of chemical elements, and these results are compared to those obtained for known twins in the Galactic field."
 In Section 5.. we present a new age determination for M67. and in Section 6 we discuss the results.," In Section \ref{sec:age}, we present a new age determination for M67, and in Section \ref{sec:disc} we discuss the results."
 The observations of M67-1194 were carried out with the multi-object spectrometer FLAMES-UVES at ESO-VLT in Service Mode in the spring of 2009 during a period of three months (18th of January — 3rd of April)., The observations of M67-1194 were carried out with the multi-object spectrometer FLAMES-UVES at ESO-VLT in Service Mode in the spring of 2009 during a period of three months (18th of January – 3rd of April).
 The observations analysed here are part of a larger project with a main goal to study atomic diffusion m stars of M67 (082.D-0726(A))., The observations analysed here are part of a larger project with a main goal to study atomic diffusion in stars of M67 (082.D-0726(A)).
 In each observing block of the project. one fibre of the spectrograph system was positioned on M67-1194 in order to collect as many observations as possible of this faint G dwarf.," In each observing block of the project, one fibre of the spectrograph system was positioned on M67-1194 in order to collect as many observations as possible of this faint G dwarf."
 We obtained altogether I8hh in 13 observing nights (23 individual observations)., We obtained altogether h in 13 observing nights (23 individual observations).
" The spectrometer setting (RED580) was chosen to yield a resolution of R=A/AA— 447.000 (1"" fibre) and a wavelength coverage of nnm."," The spectrometer setting (RED580) was chosen to yield a resolution of $R = \lambda/\Delta\lambda =$ 47,000 $1''$ fibre) and a wavelength coverage of nm."
 The typical signal-to-noise ratio (S/N) per frame is !(as measured in theline-free region between aand, The typical signal-to-noise ratio (S/N) per frame is $^{-1}$ (as measured in theline-free region between and
4 shows the growth of fragments formed in both simulations at the overlapping times.,\ref{arepo} shows the growth of fragments formed in both simulations at the overlapping times.
 There is a similar interval in both cases between the first sink forming and the first burst of fragmentation., There is a similar interval in both cases between the first sink forming and the first burst of fragmentation.
" In both cases the same number of sinks form, although there are slight differences in the mass growth rates due to the different N- dynamics which occur in each simulation."," In both cases the same number of sinks form, although there are slight differences in the mass growth rates due to the different N-body dynamics which occur in each simulation."
" As our results are reproduced by two highly complementary numerical schemes, we are confident that we capture the true physical evolution and are not strongly influenced by numerical artefacts."," As our results are reproduced by two highly complementary numerical schemes, we are confident that we capture the true physical evolution and are not strongly influenced by numerical artefacts."
 The fact that larger sinks are used here compared to the original ? simulations mean that we are not resolving tight binaries and missing some young low-mass objects formed within this radius that may have been ejected., The fact that larger sinks are used here compared to the original \citet{Greif11} simulations mean that we are not resolving tight binaries and missing some young low-mass objects formed within this radius that may have been ejected.
 Therefore our 20 AU sinks are a conservative estimate of the level of fragmentation., Therefore our $20$ AU sinks are a conservative estimate of the level of fragmentation.
" However, at this radius we are avoiding many of the uncertainties associated with protostellar mergers."," However, at this radius we are avoiding many of the uncertainties associated with protostellar mergers."
" As our young protostars would actually be puffy extended objects with radii about 100 (?),, there will be strong tidal forces evoked during close interactions, leading to the possibility that fragments formed close to each other will merge when they interact."," As our young protostars would actually be puffy extended objects with radii about $100$ \citep{Stahler86a}, there will be strong tidal forces evoked during close interactions, leading to the possibility that fragments formed close to each other will merge when they interact."
 It is still unclear how best to treat this possibility., It is still unclear how best to treat this possibility.
" By not forming low-mass objects in close proximity to existing sinks, encounters that are close enough for the stellar radii to touch occur rarely compared to the original simulations (typically between 0-2 times in each halo) and we generally avoid this issue."," By not forming low-mass objects in close proximity to existing sinks, encounters that are close enough for the stellar radii to touch occur rarely compared to the original simulations (typically between 0-2 times in each halo) and we generally avoid this issue."
" However, despite these small differences, qualitatively the evolution of the halos is similar to that in ?,, with the main difference being that we follow the evolution for ten thousand years compared to the original thousand."," However, despite these small differences, qualitatively the evolution of the halos is similar to that in \citet{Greif11}, with the main difference being that we follow the evolution for ten thousand years compared to the original thousand."
" 5 shows the combined mass function of all the sinks formed in minihalos 1-5, one and two thousand years after the first sink formed."," \ref{mf} shows the combined mass function of all the sinks formed in minihalos 1-5, one and two thousand years after the first sink formed."
 At 2000 yr in the non-feedback case ionisation effects are becoming important within Halo 5., At 2000 yr in the non-feedback case ionisation effects are becoming important within Halo 5.
" However, for the sake of the mass function only, we run Halo 5 until this point despite the lack of ionisation in our model."," However, for the sake of the mass function only, we run Halo 5 until this point despite the lack of ionisation in our model."
 This is due to the difficulty in achieving a statistically significant number of sinks for the mass function., This is due to the difficulty in achieving a statistically significant number of sinks for the mass function.
" At these early stages the sinks represent protostars rather than finished stars, and so these masses will not be those of the final population III stars."," At these early stages the sinks represent protostars rather than finished stars, and so these masses will not be those of the final population III stars."
 Nonetheless it can already be seen that the resulting mass function will contain a range of masses rather than just being one characteristic mass., Nonetheless it can already be seen that the resulting mass function will contain a range of masses rather than just being one characteristic mass.
" The mass functions show no systemic variation between the case with feedback and the reference case, and both cases contain a similar total amount of mass in stars at each time."," The mass functions show no systemic variation between the case with feedback and the reference case, and both cases contain a similar total amount of mass in stars at each time."
 Hence the feedback has not significantly altered the fragmentation and mass growth when considering the five minihalos combined., Hence the feedback has not significantly altered the fragmentation and mass growth when considering the five minihalos combined.
 This suggests that the results of previous studies which neglected this effect (e.g.?) will still be broadly correct., This suggests that the results of previous studies which neglected this effect \citep[e.g.][]{Stacy10} will still be broadly correct.
" The mass functions appear to be flatter than the IMF’s seen in the present day universe (??),, although as yet we have only of order ~50 sinks, so this remains statistically uncertain."," The mass functions appear to be flatter than the IMF's seen in the present day universe \citep{Kroupa02,Chabrier03}, although as yet we have only of order $\sim 50$ sinks, so this remains statistically uncertain."
" Tables 2 and 3 show the number of fragments formed in each halo when the mass of the most massive protostar first reaches 10 or 15 solar masses, respectively."," Tables \ref{n10} and \ref{n15} show the number of fragments formed in each halo when the mass of the most massive protostar first reaches $10$ or $15$ solar masses, respectively."
 ? find that ionising feedback does not become effective until the star is older than its Kelvin-Helmholtz time and is contracting towards the main sequence., \citet{Tan04} find that ionising feedback does not become effective until the star is older than its Kelvin-Helmholtz time and is contracting towards the main sequence.
 For their fiducial model this equates to a mass of around for a rotating protostar., For their fiducial model this equates to a mass of around for a rotating protostar.
" However the accretion rate for the most massive object is typically only a few 107? when the protostar has reached in our minihalos, whereas in the fiducial ? models the accretion rate is 10? for a 10 protostar."," However the accretion rate for the most massive object is typically only a few $10^{-3}$ when the protostar has reached in our minihalos, whereas in the fiducial \citet{Tan04} models the accretion rate is $10^{-2}$ for a 10 protostar."
" Since the Kelvin-Helmholtz contraction stage commences earlier with a lower accretion rate, as shown in 1,, we estimate that ionisation feedback will become important for our minihalos when the most massive star is between 10—15.."," Since the Kelvin-Helmholtz contraction stage commences earlier with a lower accretion rate, as shown in \ref{radmodel}, we estimate that ionisation feedback will become important for our minihalos when the most massive star is between $10-15$."
 Hz photodissociation will also become important at this time., $_{2}$ photodissociation will also become important at this time.
" Beyond this point, the assumptions that we make for the luminosity heating model break down, so we chose to terminate the simulations here."," Beyond this point, the assumptions that we make for the luminosity heating model break down, so we chose to terminate the simulations here."
malches the energy that would be transported aud dissipatecl out of that depth by an asstuned effective viscosity: where primes denote derivatives with respect to 2 and p is the background density profile.,matches the energy that would be transported and dissipated out of that depth by an assumed effective viscosity: where primes denote derivatives with respect to $z$ and $\bar{\rho}$ is the background density profile.
" For the y dependent οὐ forcing. we would like to show that the work per unit mass done bv the forcing on the flow al each y plane: malches (he enerev (hat would be transported and dissipated out of that plane by an asstuned effective viscosity: where now primes denote derivativeswilh respect (oY. tj, and ρω are the minimal and maximal depth respectively that we want to include in the fit and .N2[7p(z)dz."," For the $y$ dependent $x$ forcing, we would like to show that the work per unit mass done by the forcing on the flow at each $y$ plane: matches the energy that would be transported and dissipated out of that plane by an assumed effective viscosity: where now primes denote derivativeswith respect to $y$, $z_{min}$ and $z_{max}$ are the minimal and maximal depth respectively that we want to include in the fit and $N\equiv\int_{z_{min}}^{z_{max}} \bar{\rho}(z)dz$."
 The reason we do not want to include the entire simulated domain is that near the boundaries the flow is stronelv. affected by the impenetrable top and bottom wallsand is (hus non-phlivsical., The reason we do not want to include the entire simulated domain is that near the boundaries the flow is strongly affected by the impenetrable top and bottom wallsand is thus non-physical.
" We find the values of AT,and AT5,5 by least squares fitting ο to WI"" in the » reise me""urbin the+ range —L,/2↽ <⋅y∕L,/2respectively.", We find the values of $K^0_{1313}$and $K^0_{1212}$ by least squares fitting of $W_{xz}^{visc}$ to $W_{xz}^{turb}$ in the range $z_{min}<z<z_{max}$ and $W_{xy}^{visc}$ to $W_{xy}^{turb}$ in the range $-L_y/2<y<L_y/2$ respectively.
" Clearly.↽∙ the presence of the turbulence will cause random (lnetuations in the velocity prolile which should average oul if we combine a large enough umimber of time steps in evaluating (he quantities C,.. C. ὃν. and 5,,."," Clearly, the presence of the turbulence will cause random fluctuations in the velocity profile which should average out if we combine a large enough number of time steps in evaluating the quantities $C_{xz}$ , $C_{xy}$ , $S_{xz}$ and $S_{xy}$ ."
 These fluctuations are highly amplified when we, These fluctuations are highly amplified when we
removed by fitting a low-order Legeudre polvinonial to the continu sections of each order «X an O-star spectrui. and then dividing the correspouding order of the spectra bv this polynomial.,"removed by fitting a low-order Legendre polynomial to the continuum sections of each order of an O-star spectrum, and then dividing the corresponding order of the spectra by this polynomial."
 The resultant. almost flat orders were then combined using he taskscomb.," The resultant, almost flat orders were then combined using the task."
 This procedure proved to be satisfactory. except when the overlapping regions fall in a specral domain with verv steep intensity eradients. as in the |ne wine of A 1686 (see Fie.2)).," This procedure proved to be satisfactory, except when the overlapping regions fall in a spectral domain with very steep intensity gradients, as in the blue wing of $\lambda$ 4686 (see \ref{f2}) )."
 The combined spectra were then subdivided iuto spectral reeious roughly corresnudius to those of the lone-slit spectra discussed above (82.2.1)., The combined spectra were then subdivided into spectral regions roughly corresponding to those of the long-slit spectra discussed above 2.2.1).
 For consistency purposes. these spectra lave been coutimmum normalized by fitting a low-order Leseudre poyhonual to the contimmun sections that selected for the loue-slit spectra.," For consistency purposes, these spectra have been continuum normalized by fitting a low-order Legendre polynomial to the continuum sections that selected for the long-slit spectra."
 The light curve of is plotted as a function of the helocentic Julian date of observation iu Figure 1.., The light curve of is plotted as a function of the heliocentric Julian date of observation in Figure \ref{f1}.
 The main feature of this light curve is the gradual increase of the stellar σοιαι flux amounting to Ac ~-- 0.09 mae beeimmne at ILJD 2.150.316. followed by its decline on about the same timescale after ILJD 2.150.350.," The main feature of this light curve is the gradual increase of the stellar continuum flux amounting to $\Delta v$ $\approx$ 0.09 mag beginning at HJD 2,450,346, followed by its decline on about the same timescale after HJD 2,450,350."
 During the last 11 nights (after ILJD. 2.150.353). only mareinal," During the last 11 nights (after HJD 2,450,353), only marginal"
"The IT, rotational lines could strouglv affect the 12 band and may explain why the 8(12)/8(25) ratio is a factor of 22.5 larecr ou the southern rim of IC03. ie. at ~ ϱ 405. 22723 (ef","The $_2$ rotational lines could strongly affect the 12 band and may explain why the S(12)/S(25) ratio is a factor of $\simeq$ 2.5 larger on the southern rim of IC443, i.e. at $\simeq$ $^h$ $^m$ $^s$ $^o$ 23' (cf."
 Fie. 1))., Fig. \ref{iras_map}) ).
 This region is a well known powerful source of IT) (1.005(1)A22.12 line cluission (Burton ct al. 1988)), This region is a well known powerful source of $_2$ 2.12 line emission (Burton et al. \cite{burton88}) )
 whose spatial distrition closely resembles the TRAS 12 contours., whose spatial distribution closely resembles the IRAS 12 contours.
 (ποια.based observations of the (0.008(2)A112.3. rotational transition were obtained w Richter et al. (1995)), Ground–based observations of the 12.3 rotational transition were obtained by Richter et al. \cite{richter}) )
 who measured a line flux z10 ines brighter than (1.0)8(1)A22.12., who measured a line flux $\simeq$ 10 times brighter than 2.12.
 Assiniue a coustaut /1(A22.12) ratio over the large area mapped iu he latter transition bv Burton et al. (1988)), Assuming a constant 2.12) ratio over the large area mapped in the latter transition by Burton et al. \cite{burton88}) )
 vields iu average line surface brightuess of aout J510* Wan? orl/3o0fthe IRAS 12 ypeak surface briehtuess.," yields an average line surface brightness of about $1.5\,10^{-7}$ W $^{-2}$ $^{-1}$ or 1/3 of the IRAS 12 peak surface brightness."
" Considering that the I, spectrum of ICLEA is remarkably similar to that of Orion oeakl (e.g. Richter et al. 1995))", Considering that the $_2$ spectrum of IC443 is remarkably similar to that of Orion peak1 (e.g. Richter et al. \cite{richter}) )
 one then expects similar fluxes in the (0.008(3)A99.66. aud (0.008(2)A112.3. lines (Pariar et al. 1991)), one then expects similar fluxes in the 9.66 and 12.3 lines (Parmar et al. \cite{parmar}) )
 or. equivalently. that the two lines should account for about 2/3 of the TRAS 12 flux.," or, equivalently, that the two lines should account for about 2/3 of the IRAS 12 flux."
 Finally. it should be noted that IRAS was virtually diu to the To(O.0jS(1jAL17.0 line (c£.," Finally, it should be noted that IRAS was virtually blind to the $_2$ 17.0 line (cf."
 Fie. 3)), Fig. \ref{iras_filt}) )
 while the Helly forbidden eround state transition (0.0)8(0)A228.2 is most probably too weak to significantly contaminate the 25 IRAS baud (cf., while the highly forbidden ground state transition 28.2 is most probably too weak to significantly contaminate the 25 IRAS band (cf.
 e.g. Fig., e.g. Fig.
 2 of Oliva ct al. 1998))., 2 of Oliva et al. \cite{rcw103_iso}) ).
 Au ISOSWS spectiuu of ICLIS has revealed promincut ΟΠ and [Fell line cussion which. together with {STI and [OTV]. account for most of the observed IRAS fux in he 12. 25 xuids.," An ISO–SWS spectrum of IC443 has revealed prominent [NeII] and [FeII] line emission which, together with [SIII] and [OIV], account for most of the observed IRAS flux in the 12, 25 bands."
" Simple arguments indicate that this is probably he case in other radiative SNRs and this result suggests hat the unusually blue IRAS colours of radiative SNRs siuplv reflect line contamination. rather than a large »pulatiou of sinall eraius which are otherwise required o explain the warmer ""continu endssiou."," Simple arguments indicate that this is probably the case in other radiative SNRs and this result suggests that the unusually blue IRAS colours of radiative SNRs simply reflect line contamination, rather than a large population of small grains which are otherwise required to explain the warmer “continuum” emission."
 Available eround based data also indicate that S(2). ος} rotational ines of II» contribute to a large fraction of the IRAS 12 chussion from the southern ria of The relaive fluxes of the ionic lines detected by ISO vield a ~0.6 \ solar Fe gasphase relative abundance which is significantly lower than that found iu the much more poworul ROWL03 supernova remnant.," Available ground based data also indicate that S(2), S(3) rotational lines of $_2$ contribute to a large fraction of the IRAS 12 emission from the southern rim of The relative fluxes of the ionic lines detected by ISO yield a $\simeq$ 0.6 $\times$ solar Fe gas–phase relative abundance which is significantly lower than that found in the much more powerful RCW103 supernova remnant."
 This max inplv tha he shock in ICLL3 is slower aud thus less effective in cestroving the Febearing ooerains., This may imply that the shock in IC443 is slower and thus less effective in destroying the Fe–bearing grains.
 This scenario is also supported by the lower line surface brightuess aud [NGHE]/|NeII| ratio which both indicate a lower shock speed in ICE13., This scenario is also supported by the lower line surface brightness and [NeIII]/[NeII] ratio which both indicate a lower shock speed in IC443.
"model with average Z/H predicts line ratios about nearly the same as the Τειω--40000 K and log U=-3.67 model with an abundance enhancement of about 0.5 dex, would have the very different temperatures of 6530 K and 4680 K. The important conclusion of this section is that theoretically one can explain the low-ionization color-color diagram for the non-Barnard’s Loop samples by a range of values of U,Tstar, and Z/H. A simple ratio of nebular line intensities for two different ions cannot produce an unambiguous estimate ofΤο.","model with average Z/H predicts line ratios about nearly the same as the =40000 K and log U=-3.67 model with an abundance enhancement of about 0.5 dex, would have the very different temperatures of 6530 K and 4680 K. The important conclusion of this section is that theoretically one can explain the low-ionization color-color diagram for the non-Barnard's Loop samples by a range of values of U, and Z/H. A simple ratio of nebular line intensities for two different ions cannot produce an unambiguous estimate of."
 The reason for the designation WIM (warm ionized medium) is the fact that tthere is higher than the cold gas in the ISM., The reason for the designation WIM (warm ionized medium) is the fact that there is higher than the cold gas in the ISM.
 The actual value for the WIM's temperature is much more uncertain than sometimes stated in the literature because there are few observations (summarized in this section) that allow a direct determination and the indirect methods (based on only the I([N II] 6583 A))/I(Ha)) ratio) commonly employed are uncertain as they assume a fixed nitrogen ionization ratio and abundance., The actual value for the WIM's temperature is much more uncertain than sometimes stated in the literature because there are few observations (summarized in this section) that allow a direct determination and the indirect methods (based on only the I([N II] 6583 ) ratio) commonly employed are uncertain as they assume a fixed nitrogen ionization ratio and abundance.
 In this section we summarize the results for dderived by direct means., In this section we summarize the results for derived by direct means.
" There are three direct methods of determiningT,.", There are three direct methods of determining.
. The first is from the measurement of forbidden line intensity ratios within a single ion., The first is from the measurement of forbidden line intensity ratios within a single ion.
 The second is from the width of emission lines from ions of very different mass., The second is from the width of emission lines from ions of very different mass.
 The third is from the ratio of continuum to recombination line emission., The third is from the ratio of continuum to recombination line emission.
" Observations of the low-ionizationization WIM cannot use the most widely used indicator, the [O III] auroral/nebular line ratios."," Observations of the low-ionizationization WIM cannot use the most widely used indicator, the [O III] auroral/nebular line ratios."
" However, Reynoldsetal.(2001) were"," However, \citet{rey01} were"
 , 
Black holes are the vacuum solutions of Einstein's field equations in general relativity.,Black holes are the vacuum solutions of Einstein's field equations in general relativity.
 Classically. a black hole is conceived as a singularity in space time. censored from the rest of the Universe by a mathematically detined one way surface. the event horizon.," Classically, a black hole is conceived as a singularity in space time, censored from the rest of the Universe by a mathematically defined one way surface, the event horizon."
 In astrophysics. black holes are the end points of the gravitational collapse of massive celestial objects.," In astrophysics, black holes are the end points of the gravitational collapse of massive celestial objects."
" ""Observed! astrophysical black holes may be broadly classified into three different categories. the stellar mass CVgg a few A. ). the intermediate mass (significantly more massive than the stellar mass black holes but far less massive than the super massive black holes) and super massive (Ade42:10""AZ. ) black 10les."," `Observed' astrophysical black holes may be broadly classified into three different categories, the stellar mass $M_{BH}{\sim}$ a few $M_{\odot}$ ), the intermediate mass (significantly more massive than the stellar mass black holes but far less massive than the super massive black holes) and super massive $M_{BH}{\ge}{10^6}M_{\odot}$ ) black holes."
 All of the above mentioned candidates accrete matter from the surroundings. provided that the sources for such infalling material do exist.," All of the above mentioned candidates accrete matter from the surroundings, provided that the sources for such infalling material do exist."
 Depending on the iiatrinsic angular momentum content of accreting material. either spherically symmetric (zero angular momentum flow of matter). or axisymmetric (matter flow with non-zero finite angular momentum) flow geometry may be invoked to study an accreting black hole system.," Depending on the intrinsic angular momentum content of accreting material, either spherically symmetric (zero angular momentum flow of matter), or axisymmetric (matter flow with non-zero finite angular momentum) flow geometry may be invoked to study an accreting black hole system."
 Since he black holes manifest their presence only gravitationaly. and no spectral information can directly be obtained or these candidates. one must rely on the accretion processes to understand teir observational signature 2002). ," Since the black holes manifest their presence only gravitationally, and no spectral information can directly be obtained for these candidates, one must rely on the accretion processes to understand their observational signature \citep{pri81,kato-book,fkr02}. ."
The local Mach number AZ of the accreting fluid can be detined as the ratio of he local dynamical flow velocity o the local velocity of ?ropagation of the acoustiο perturbation embedded inside the accreting matter., The local Mach number $M$ of the accreting fluid can be defined as the ratio of the local dynamical flow velocity to the local velocity of propagation of the acoustic perturbation embedded inside the accreting matter.
 The flow will be locally subsonic or supersonie according to Al(r) lorI., The flow will be locally subsonic or supersonic according to $M(r) < 1$ or $ >1$.
 Thefl(»w Is transonic if at any moment it crosses 1=1., The flow is transonic if at any moment it crosses $M=1$.
 At a distance far away from the black hole. accreting material almost always remains subsonic (except possibly for the supersonic stellar wind fed accretion) since it possesses neσigible dynamical flow velocity.," At a distance far away from the black hole, accreting material almost always remains subsonic (except possibly for the supersonic stellar wind fed accretion) since it possesses negligible dynamical flow velocity."
 On the other hand. the flow velocity will approach the velocity of light e while crossing the event horizon. whereas the maximum possible value of sound sneed (even for the steepest possible equation of state) would be ¢/\/3. resulting AZ>1 ckyse to the event horizon.," On the other hand, the flow velocity will approach the velocity of light $c$ while crossing the event horizon, whereas the maximum possible value of sound speed (even for the steepest possible equation of state) would be $c/\sqrt{3}$, resulting $M>1$ close to the event horizon."
 In order to satisfy such inner boundary concition imposed by the event horizon. accretion onto black holes exhibi ransonic properties in general.," In order to satisfy such inner boundary condition imposed by the event horizon, accretion onto black holes exhibit transonic properties in general."
 A sonic/transonie transition in black hole accretion occurs when a subsonic to supersonic or supersonic to subsonic transition takes place either continuously (usually from a subsonic to a supersonic transition) or discontinuously (usually from a supersonic oa subsonic transition)., A sonic/transonic transition in black hole accretion occurs when a subsonic to supersonic or supersonic to subsonic transition takes place either continuously (usually from a subsonic to a supersonic transition) or discontinuously (usually from a supersonic to a subsonic transition).
 The particular value of the spatial location where such transition takes place coninuously is called a transonie point or a sonic point. and where such crossing takes place discontinuously are called shocks or discontinuities.," The particular value of the spatial location where such transition takes place continuously is called a transonic point or a sonic point, and where such crossing takes place discontinuously are called shocks or discontinuities."
 In supersonic black hole accretion. perturbation of various Kinds may produce shocks. where some dynamical and thermodynamic accretion variables changes disconinuously as such shock surfaces are crossed.," In supersonic black hole accretion, perturbation of various kinds may produce shocks, where some dynamical and thermodynamic accretion variables changes discontinuously as such shock surfaces are crossed."
 Cert;ain boundary conditions are to be satistied across the sqywock. and according to those conditions. shocks in black hole accretion dises are classitied into various categories.," Certain boundary conditions are to be satisfied across the shock, and according to those conditions, shocks in black hole accretion discs are classified into various categories."
 Such shock waves are quite often generated in supersonic accretion flows having small amount o “intrinsic angular momentum. resulting the final subsonie state of tthe flow.," Such shock waves are quite often generated in supersonic accretion flows having small amount of intrinsic angular momentum, resulting the final subsonic state of the flow."
" This is because the repulsive centrifugal potential barrier experienced by such flows is sufficiently strong to brake the infalling nx""tion and a stationary solution could be introduced only through a shock.", This is because the repulsive centrifugal potential barrier experienced by such flows is sufficiently strong to brake the infalling motion and a stationary solution could be introduced only through a shock.
 Rotating. transonic astrophysical fluid flows are thus believed to be ‘prone’ to the shock formation phenomena.," Rotating, transonic astrophysical fluid flows are thus believed to be `prone' to the shock formation phenomena."
 The study of steady. standing. stationary shock waves produced in black hoe accretion and related phenomena thus acquired an important status in recent years (Fukue1983.1987.2004.2:Chakrabarti1989:KafatosCzerny 2000).," The study of steady, standing, stationary shock waves produced in black hole accretion and related phenomena thus acquired an important status in recent years \citep{fuk83,fuk87,fuk04,fuk04a,c89,ky94,yk95,caditz-tsuruta,
fukumara-suruta,takahashi,das02,dpm03,abd06,dbd07,lyyy97,lugu,nf89,nagyam08,
nakayama,nagakura,toth,das-czerny}."
 On the other hand. a physical transonic accretion solutions can mathemaically be realized as critical solution on the phase portrai (spanned by dynamical flow velocity/Mach number and the radial distance) of the black hole accretion.," On the other hand, a physical transonic accretion solutions can mathematically be realized as critical solution on the phase portrait (spanned by dynamical flow velocity/Mach number and the radial distance) of the black hole accretion."
 Tus is becuuse. from analytica erspective. problems in |black hole accretion fall under the general class of nonlinear dynamics (Ray&Bhattacharjee2002:Afshordi2007:Bhattacharjeeetal. 2009).. since accretion describes the dynamics of a conipressible astrophysica fluid. governed by a set of nonlinear differential equations.," This is because, from analytical perspective, problems in black hole accretion fall under the general class of nonlinear dynamics \citep{rb02,ap03,ray03a,ray03b,rbcqg05a,rbcqg05b,crd06,rbcqg06,rbcqg07a,br07,gkrd07,jkb09}, since accretion describes the dynamics of a compressible astrophysical fluid, governed by a set of nonlinear differential equations."
 Such non-linear equations describing the steady. inviscid axisymmetric flow can urther be tailored to construct a first order autonomous dynamical system.," Such non-linear equations describing the steady, inviscid axisymmetric flow can further be tailored to construct a first order autonomous dynamical system."
 Physical transonie solution in such flows can be represenec mathematically as critical solutions in the velocity (or Mach number) phase plane of the flow — they are associated with the critical points (alternatively known as the fixed points or the equilibrium points. see Jordan&Smith(1999). and Chicone(2006) for further details abcnu he fixed point analysis techniques).," Physical transonic solution in such flows can be represented mathematically as critical solutions in the velocity (or Mach number) phase plane of the flow – they are associated with the critical points (alternatively known as the fixed points or the equilibrium points, see \cite{js99} and \cite{diff-eqn-book} for further details about the fixed point analysis techniques)."
 To maintain the transonicity such critical points will perforce have to be saddle points. which will enaE a solution to pass through themselves.," To maintain the transonicity such critical points will perforce have to be saddle points, which will enable a solution to pass through themselves."
 Hereafter. ‘multi-critical’ flow refers to the category of the accretion flow configuration which can have multiple critical points accessiMis ο the accretion flow.," Hereafter, `multi-critical' flow refers to the category of the accretion flow configuration which can have multiple critical points accessible to the accretion flow."
 For low angular momentum axisymmetric black hole accretion. it may so happen that the critical features are exhibied more than once in the johase portrait of a stationary solution describing such flow (Liang&Thompson1980:AbramowiezZurek198etal.2006:Das2007:&Czerny 2009). and accretion becomes multi-critieal.," For low angular momentum axisymmetric black hole accretion, it may so happen that the critical features are exhibited more than once in the phase portrait of a stationary solution describing such flow \citep{lt80,az81,boz-pac,boz1,fuk83,fuk87,fuk04,fuk04a,lu85,lu86,bmc86,ak89,abram-chak,
ky94,yk95,caditz-tsuruta,das02,bdw04,abd06,dbd07,das-czerny}, and accretion becomes multi-critical."
 In reality. such weakly rotating sub-Keplerian flows are exhibited in various physical situations. such as detached binary systems fed by accretion from OB stellar winds Hllarionov&Sunvaevt1975):LiangNolan ¢1980))). semi-detached low-mass non-magnetic binaries €Bisikaloetal. (1998))). and black holes fed by accretion from slowly rotating central stellar clusters (IHlarionov(1988):Ho(1999) and references therein).," In reality, such weakly rotating sub-Keplerian flows are exhibited in various physical situations, such as detached binary systems fed by accretion from OB stellar winds \cite{ila-shu,liang-nolan}) ), semi-detached low-mass non-magnetic binaries (\cite{bisikalo}) ), and super-massive black holes fed by accretion from slowly rotating central stellar clusters \cite{ila,ho} and references therein)."
 Even, Even
"were grouped to require at least 20 counts per bin using the ftool ""erppha"" to ensure valid results using X statistical analysis.",were grouped to require at least 20 counts per bin using the ftool “grppha” to ensure valid results using $\chi^2$ statistical analysis.
 The spectra were analyzed using XSPEC version 11.3.2ag (Arnaud1996)., The spectra were analyzed using XSPEC version 11.3.2ag \citep{a96}.
. Fits were restricted to the 0.6-10 keV range due to calibration uncertainties at energies less than 0.6 keV. The uncertainties reported in this work are Io errors. obtained by allowing all fit parameters to vary simultaneously.," Fits were restricted to the 0.6-10 keV range due to calibration uncertainties at energies less than 0.6 keV. The uncertainties reported in this work are $1\sigma$ errors, obtained by allowing all fit parameters to vary simultaneously."
 The observations were affected by pile-up. as the observed count rate varied from 161—331cts! (0.6-10 keV).," The observations were affected by pile-up, as the observed count rate varied from $161 - 331\,\mathrm{ct}\,\mathrm{s}^{-1}$ (0.6-10 keV)."
 To correct for pile-up. we followed the spectral fitting method described in Romanoetal.(2006) and. Rykoffetal.(2007): using various exclusion regions centered on the source. we refit the continuum spectrum until the fit parameters did not vary significantly.," To correct for pile-up, we followed the spectral fitting method described in \citet{rcccc06}
 and \citet{rmst07}: using various exclusion regions centered on the source, we refit the continuum spectrum until the fit parameters did not vary significantly."
 We found that a 10 pixel exclusion region was sufficient to correct pile-up in the brightest epochs., We found that a 10 pixel exclusion region was sufficient to correct pile-up in the brightest epochs.
 For simplicity. we use the same exclusion region for all of the observations.," For simplicity, we use the same exclusion region for all of the observations."
 We then caleulate the conversion factor to determine the non-piled-up equivalent count rate., We then calculate the conversion factor to determine the non-piled-up equivalent count rate.
 This is obtained from the ratio of the arf (at 1.5 keV) calculated with and without PSF correction., This is obtained from the ratio of the arf (at 1.5 keV) calculated with and without PSF correction.
 We note that this correction is only applied when estimating the source intensity. and Is not necessary when calculating colors. which are count rate ratios.," We note that this correction is only applied when estimating the source intensity, and is not necessary when calculating colors, which are count rate ratios."
"This trend can also be found in the work of ?,, where the MRI turbulent transport in presence of a toroidal field is investigated with more emphasis on the Pm>| regime.","This trend can also be found in the work of \cite{SH09}, where the MRI turbulent transport in presence of a toroidal field is investigated with more emphasis on the $Pm > 1$ regime."
 Their Figs., Their Figs.
" 6 and 7 show that, for Pm=2 and 4 at least (the only ones with enough data in the Pm>1 regime), the transport increases steadily with the Reynolds number for Re<1000 and much more weakly for Re=1000."," 6 and 7 show that, for $Pm=2$ and $4$ at least (the only ones with enough data in the $Pm > 1$ regime), the transport increases steadily with the Reynolds number for $Re \lesssim 1000$ and much more weakly for $Re \gtrsim 1000$."
" On the contrary, the spread in Reynolds number for Pm<1 is substantial, and systematic."," On the contrary, the spread in Reynolds number for $Pm \le 1$ is substantial, and systematic."
" Such a spread was not detected in our earlier investigation, due to the larger fluctuations in transport related to the box aspect ratio, as discussed earlier."," Such a spread was not detected in our earlier investigation, due to the larger fluctuations in transport related to the box aspect ratio, as discussed earlier."
" In fact, this dispersion seems to be an effect of the magnetic Reynolds number."," In fact, this dispersion seems to be an effect of the magnetic Reynolds number."
" To illustrate this point, the transport is represented on Fig."," To illustrate this point, the transport is represented on Fig."
" 6 as a function of Rm (left panel) and Re (right panel), for Pm<1; the colors describe different field strengths (8=10? to 104 from top to bottom)."," \ref{transpReRm} as a function of $Rm$ (left panel) and $Re$ (right panel), for $Pm \le 1$; the colors describe different field strengths $\beta=10^2$ to $10^4$ from top to bottom)."
" The statistics in the number of points at any given Re or Rm is rather low; however, it appears quite clearly that the dispersion of the points at any given Reynolds number is substantially larger in Re (with varying Rm) than in Rm (with varying Re)."," The statistics in the number of points at any given $Re$ or $Rm$ is rather low; however, it appears quite clearly that the dispersion of the points at any given Reynolds number is substantially larger in $Re$ (with varying $Rm$ ) than in $Rm$ (with varying$Re$ )."
 The largest Reynolds number data strongly support this conclusion., The largest Reynolds number data strongly support this conclusion.
" Furthermore, the of the transport as a function of Rm indicate the Rm dependence of the transport for Pm<1 is very similar to its Pm dependence as shown on Fig. 5.."," Furthermore, the of the transport as a function of $Rm$ indicate the $Rm$ dependence of the transport for $Pm \le 1$ is very similar to its $Pm$ dependence as shown on Fig. \ref{transp-pm}."
 This strongly suggests that the Pm dependence observed on this figure is in fact mostly a Rm dependence for Pm<1., This strongly suggests that the $Pm$ dependence observed on this figure is in fact mostly a $Rm$ dependence for $Pm \le 1$.
" Including the Pm=4 data destroys this correlation, which strengthens the idea that there are two regimes, depending on the Prandtl number (a feature that may be related to the existence of a transition around Pm=2 in zero net flux shearing box simulations)."," Including the $Pm=4$ data destroys this correlation, which strengthens the idea that there are two regimes, depending on the Prandtl number (a feature that may be related to the existence of a transition around $Pm=2$ in zero net flux shearing box simulations)."
" The relevant results of ?;; although less detailed, are consistent with these findings (see their Fig."," The relevant results of \cite{SH09}; ; although less detailed, are consistent with these findings (see their Fig."
 7)., 7).
the circular velocity from the mass of the host halo and its redshift.,the circular velocity from the mass of the host halo and its redshift.
" The rate at which mass is accreted scales with the Eddington rate for the SMBH, and we set either a fixed Eddington ratio of fgaa=1 (for Pop III seeds), fgaa=0.3 (for massive seeds), or an accretion rate derived from the distribution derived by Merloni&Heinz(2008) (we apply this model to massive seeds only)."," The rate at which mass is accreted scales with the Eddington rate for the SMBH, and we set either a fixed Eddington ratio of $f_{\rm Edd}=1$ (for Pop III seeds), $f_{\rm Edd}=0.3$ (for massive seeds), or an accretion rate derived from the distribution derived by \cite{Merloni08} (we apply this model to massive seeds only)."
" The empirical distribution of Eddington ratios derived by Merloni Heinz (2008, MHO08 thereafter) is fit by a function in log(Lsa/Lgaa)."," The empirical distribution of Eddington ratios derived by Merloni Heinz (2008, MH08 thereafter) is fit by a function in $\log(L_{\rm bol}/L_{\rm Edd})$."
" The fitting function of the Eddington ratio distribution as a function of SMBH mass and redshift, is computed in 10 redshift intervals (from z=0 to z= 5) for 4different mass bins (6<log(Mpu/Mo) <77<log(Mpu/Mo)<8 8«log(Msu/Mc)<9; 9«log(Mau/Mc)< 10), and then fit with an analytic function which is the sum of a Schechter function and a log-normal (A. Merloni, private communication)."," The fitting function of the Eddington ratio distribution as a function of SMBH mass and redshift, is computed in 10 redshift intervals (from $z=0$ to $z=5$ ) for 4different mass bins $6 < \log(M_{\rm BH}/\msun)< 7$; $7 < \log(M_{\rm BH}/\msun) < 8$; $8 < \log(M_{\rm BH}/\msun) < 9$; $9 < \log(M_{\rm BH}/\msun) < 10$ ), and then fit with an analytic function which is the sum of a Schechter function and a log-normal (A. Merloni, private communication)."
 The Eddington ratio distributions are then normalized to unity at every given mass and redshift., The Eddington ratio distributions are then normalized to unity at every given mass and redshift.
" We dub the three modelsPopIII-Edd, and respectively."," We dub the three models, and respectively."
 Note that in the model names the first part refers to the type of seed and the second part refers to the kind of accretion history assumed., Note that in the model names the first part refers to the type of seed and the second part refers to the kind of accretion history assumed.
 Therefore the modelPopIII-Edd refers to: initial sees from Pop III remnants always accreting at the Eddington rate; model refers to initial massive seeds accreting with Eddington ratios drawn from the MHOS8 distribution and the modelMassive-subEdd: initial massive seeds accreting 0.3.X Eddington at all times., Therefore the model refers to: initial sees from Pop III remnants always accreting at the Eddington rate; model refers to initial massive seeds accreting with Eddington ratios drawn from the MH08 distribution and the model: initial massive seeds accreting $0.3X$ Eddington at all times.
 In the model the accretion rate is not limited to the Eddington rate and mildly super-Eddington accretion rates (up to faa~ 10) are possible and allowed as per MHO8., In the model the accretion rate is not limited to the Eddington rate and mildly super-Eddington accretion rates (up to $f_{\rm Edd}\sim 10$ ) are possible and allowed as per MH08.
" For all three scenarios considered here, accretion starts after a dynamical timescale at the virial radius, tay,—108yr(Rvir/100kpc) (vvir/100kms~')~+, and lasts until the SMBH, of initial mass Min, has accreted AM."," For all three scenarios considered here, accretion starts after a dynamical timescale at the virial radius, $t_{\rm dyn}=10^8 {\rm yr}\; (R_{\rm vir}/100\, {\rm kpc})(v_{\rm vir}/100 \kms)^{-1}$ , and lasts until the SMBH, of initial mass $M_{\rm in}$, has accreted $\Delta M$."
" The lifetime of an AGN therefore depends on how much mass it accretes during each episode: where c is the radiative efficiency (c~ 0.1), traa=0.45 Gyr and Mg,=min[(My,+AM),1.3x108(σ/200 kms~')*?4Mo)."," The lifetime of an AGN therefore depends on how much mass it accretes during each episode: where $\epsilon$ is the radiative efficiency $\epsilon \simeq 0.1$ ), $t_{\rm Edd}=0.45$ Gyr and $M_{\rm fin}=\min[(M_{\rm in}+\Delta M),1.3\times10^8\,(\sigma/200 \kms)^{4.24}\msun]$ ."
" We further assume that, when two galaxies hosting SMBHs merge, the SMBHs themselves merge within the merger timescale of the host halos, which is a plausible assumption for SMBH binaries formed after gas-rich galaxy mergers Dottietal.(2007)."," We further assume that, when two galaxies hosting SMBHs merge, the SMBHs themselves merge within the merger timescale of the host halos, which is a plausible assumption for SMBH binaries formed after gas-rich galaxy mergers \cite{Dotti2007}."
. We adopt the relations suggested by Taffonietal.(2003) for the merger timescale., We adopt the relations suggested by \cite{Taffoni2003} for the merger timescale.
" Black holes are allowed to accrete during the merging process if the timescale for accretion, corresponding to the sum of the dynamical timescale and tacn, is longer than the merger timescale."," Black holes are allowed to accrete during the merging process if the timescale for accretion, corresponding to the sum of the dynamical timescale and $t_{\rm AGN}$, is longer than the merger timescale."
" As outlined earlier, in propagating the seeds it is assumed that accretion episodes and therefore growth spurts are triggered only by major mergers."," As outlined earlier, in propagating the seeds it is assumed that accretion episodes and therefore growth spurts are triggered only by major mergers."
 We find that in a merger-driven scenario for SMBH growth the most biased galaxies at every epoch host the most massive SMBHs that are most likely already sitting on the Mang— relation., We find that in a merger-driven scenario for SMBH growth the most biased galaxies at every epoch host the most massive SMBHs that are most likely already sitting on the $M_{\rm BH} -\sigma$ relation.
 Lower mass SMBHs (below 109 Ma) are insteadoc off the relation at z=4 and even at z=2.," Lower mass SMBHs (below $10^6\,\msun$ ) are instead off the relation at $z = 4$ and even at $z = 2$."
 These baseline results aremechanism., These baseline results are.
" In the initial massive seeds scenario, most of the SMBH seeds start out the z=0 Mgu—c relation, that is, they are ‘over massive’ compared to the local relation."," In the initial massive seeds scenario, most of the SMBH seeds start out the $z=0$ $\msigma$ relation, that is, they are `over massive' compared to the local relation."
" Seeds form only in haloes within a narrow range of velocity dispersion (c~15kms! at the earliest epochs, see eqns."," Seeds form only in haloes within a narrow range of velocity dispersion $\sigma \simeq 15\,{\rm
km\,s}^{-1}$ at the earliest epochs, see eqns."
 1 and 3., 1 and 3.
" The SMBH mass corresponding to e~15kms~"", according to the local Mgu—c relation, would be ~3x10?Mc."," The SMBH mass corresponding to $\sigma \simeq 15\,{\rm km\,s}^{-1}$, according to the local $M_{\rm BH} -\sigma$ relation, would be $\sim 3\times 10^3
\msun$."
 The MF instead peaks at 10?Mc (Lodato Natarajan 2007)., The MF instead peaks at $10^5\msun$ (Lodato Natarajan 2007).
" As time elapses, all haloes are bound to grow in mass by mergers."," As time elapses, all haloes are bound to grow in mass by mergers."
" The lowest mass haloes, though, experience mostly minor mergers, that do not trigger accretion episodes, and hence do not grow the SMBH."," The lowest mass haloes, though, experience mostly minor mergers, that do not trigger accretion episodes, and hence do not grow the SMBH."
" The evolution of these systems can be described by a shift towards the right of the Mau—o relation: o increases, but Msz stays roughly constant."," The evolution of these systems can be described by a shift towards the right of the $\msigma$ relation: $\sigma$ increases, but $M_{\rm BH}$ stays roughly constant."
" In what follows, we present a detailed comparison of the data with our three models, namely thePopIII-Edd: initial seeds from Pop III remnants with accretion assumed at all times at the Eddington rate;Massive-MH: wherein the initial massive seeds have accretion rates drawn from the distribution determined by MH08; Edd: initial massive seeds with accretion assumed at all Massive-subtimes to be at 0.3x the Eddington rate."," In what follows, we present a detailed comparison of the data with our three models, namely the: initial seeds from Pop III remnants with accretion assumed at all times at the Eddington rate;: wherein the initial massive seeds have accretion rates drawn from the distribution determined by MH08; : initial massive seeds with accretion assumed at all times to be at $0.3 \times$ the Eddington rate."
" For all three models, we compare our derived MF of BLQSOs with that estimated"," For all three models, we compare our derived MF of BLQSOs with that estimated"
with which Mechanisms L1 and Lb occur. was. specifically chosen in order to reproduce the observed numbers of short- and long-period BS binaries.,with which Mechanisms I and II occur was specifically chosen in order to reproduce the observed numbers of short- and long-period BS binaries.
 The important. point to take away is that the observed. BS binary period-eccentricity distribution olfers a potential constraint on the fraction of encounters that result in different merger scenarios., The important point to take away is that the observed BS binary period-eccentricity distribution offers a potential constraint on the fraction of encounters that result in different merger scenarios.
 Based on our results. Mechanism. LL must occur 4 times more often than Mechanism LE in order to reproduce the observed. BS period. distribution from 113 encounters (or. equivalently. 2|3 encounters involving à very wide binary and 2]|2 encounters between a short-period. binary and a lone-period binary).," Based on our results, Mechanism II must occur $\sim 4$ times more often than Mechanism I in order to reproduce the observed BS period distribution from 1+3 encounters (or, equivalently, 2+3 encounters involving a very wide binary and 2+2 encounters between a short-period binary and a long-period binary)."
 This can be tested. by performing numerical scattering experiments of encounters involving triples., This can be tested by performing numerical scattering experiments of encounters involving triples.
 Therefore. our results highlight the need for simulations of 113. 213 and 313 encounters to. be performed. in order to better. understand. their. expected contributions to. BS populations in open and globular clusters.," Therefore, our results highlight the need for simulations of 1+3, 2+3 and 3+3 encounters to be performed in order to better understand their expected contributions to BS populations in open and globular clusters."
 Once a preferred. encounter. scenario has been identified for an observed. binary or triple containing one or more Bss. numerical scattering experiments can be used. to further constrain the conditions under which that scenario will occur (or to show that it cannot occur)," Once a preferred encounter scenario has been identified for an observed binary or triple containing one or more BSs, numerical scattering experiments can be used to further constrain the conditions under which that scenario will occur (or to show that it cannot occur)."
 We have demonstrated. that a combination of observational and analytic constraints can be usec to isolate the parameter space relevant to the dynamical. formation of an observed. multiple star system (or population of star systems) containing one or more merger products., We have demonstrated that a combination of observational and analytic constraints can be used to isolate the parameter space relevant to the dynamical formation of an observed multiple star system (or population of star systems) containing one or more merger products.
" ""This will drastically narrow the relevant. parameter space for numerical scattering experiments.", This will drastically narrow the relevant parameter space for numerical scattering experiments.
 We have improved. upon the results of Perets&Fab-rvcky(2009). ancl Mathieu&Geller(2009) since. we have shown that dynamical encounters involving triples could not only be contributing to the lone-period DS binaries in NGC Iss. but they could also be an important formation mechanism. for short-periock BS binarics and triples containing Bss.," We have improved upon the results of \citet{perets09} and \citet{mathieu09} since we have shown that dynamical encounters involving triples could not only be contributing to the long-period BS binaries in NGC 188, but they could also be an important formation mechanism for short-period BS binaries and triples containing BSs."
 We have not ruled. out mass transfer or Ixozai-induced: mergers in. triples (primordial or otherwise) (Mathieu&Geller2009:PeretsLFab-rvcky 2009).. or even various combinations of cillerent mechanisms. as contributing formation channels to the BS binary population in NGC 188.," We have not ruled out mass transfer or Kozai-induced mergers in triples (primordial or otherwise) \citep{mathieu09,
 perets09}, or even various combinations of different mechanisms, as contributing formation channels to the BS binary population in NGC 188."
 For instance. à 113 exchange interaction could. stimulate a merger. indirectly if the resulting angle of inclination between the inner and outer orbits of the triple exceeds ~39. ultimately allowing the triple to evolve via the Ixozai. mechanism so that the eccentricitv of the inner binary increases while its period remains roughly constant (Eeeleton2006).," For instance, a 1+3 exchange interaction could stimulate a merger indirectly if the resulting angle of inclination between the inner and outer orbits of the triple exceeds $\sim 39^{\circ}$, ultimately allowing the triple to evolve via the Kozai mechanism so that the eccentricity of the inner binary increases while its period remains roughly constant \citep{eggleton06}."
. There is evidence to suggest that mass transfer. via toche lobe over Low could play a role in the formation of at least some Bss., There is evidence to suggest that mass transfer via Roche lobe over flow could play a role in the formation of at least some BSs.
 Ht is dillicult to account for. the near zero cecentricities of some of the long-period DS rinaries without at. least one episode of mass transfer laving occurred., It is difficult to account for the near zero eccentricities of some of the long-period BS binaries without at least one episode of mass transfer having occurred.
 This is because none of the normal MS-MS rinaries with similar periods have such small eccentricities (Mathieu&Geller2009)., This is because none of the normal MS-MS binaries with similar periods have such small eccentricities \citep{mathieu09}.
. On the other hand. it may not » Unreasonable to expect that some collision products Left in binaries undergo mass transfer since they are expected o expand aclabatically post-collision. ancl will sooner or ater evolve to ascend the giant branch.," On the other hand, it may not be unreasonable to expect that some collision products left in binaries undergo mass transfer since they are expected to expand adiabatically post-collision, and will sooner or later evolve to ascend the giant branch."
 As a result. of conservation of energv and angular momentum. the mass ransfer process will usually act to increase the orbital »eriods of these binaries provided it is conservativeLO91).," As a result of conservation of energy and angular momentum, the mass transfer process will usually act to increase the orbital periods of these binaries provided it is conservative."
. Interestinglv. the cut-olf period for. Roche lobe overllow is 1000 cays for low-mass stars (Egeleton2006).. which is in rough agreement with the lone-periocd peak in the observed: period-eccentricity: distribution of the DS binary population in NGC 188.," Interestingly, the cut-off period for Roche lobe overflow is $\sim 1000$ days for low-mass stars \citep{eggleton06}, which is in rough agreement with the long-period peak in the observed period-eccentricity distribution of the BS binary population in NGC 188."
 Therefore. mass transfer could also be contributing to the period gap observed. for the BS binaries.," Therefore, mass transfer could also be contributing to the period gap observed for the BS binaries."
 According to the results of Gelleratal.(2009).. the number of eiant-\IS binaries with P?1000 cdavs is comparable to the number of DS binaries CX. Geller. private communication).," According to the results of \citet{geller09}, the number of giant-MS binaries with $P \lesssim
1000$ days is comparable to the number of BS binaries (A. Geller, private communication)."
 It is unlikely that every giant-MS binary will form a BS from mass transfer. however. suggesting that at most a few of the long-period DS binaries in NGC ISS were formed via this mechanism.," It is unlikely that every giant-MS binary will form a BS from mass transfer, however, suggesting that at most a few of the long-period BS binaries in NGC 188 were formed via this mechanism."
 Finally. if the outer companion of a triple svstem evolves to over-fill its Roche lobe it. could. transfer mass to both of the components of the close inner binary.," Finally, if the outer companion of a triple system evolves to over-fill its Roche lobe it could transfer mass to both of the components of the close inner binary."
 This mechanism could therefore also produce two BSs in a close binary. although it predicts the presence of an orbiting triple companion.," This mechanism could therefore also produce two BSs in a close binary, although it predicts the presence of an orbiting triple companion."
 For these reasons. a better understanding of triple evolution. as well as binary evolution in binaries containing merger products. is needed.," For these reasons, a better understanding of triple evolution, as well as binary evolution in binaries containing merger products, is needed."
 The clissipational cllects of tides tend to convert stars bulk translational kinetic energies into internal or thermal energv within the stars. leading to an increase in the total eravitational binding energy of the stellar configuration (e.g.AleMillan.Wut&Making 1990).," The dissipational effects of tides tend to convert stars' bulk translational kinetic energies into internal or thermal energy within the stars, leading to an increase in the total gravitational binding energy of the stellar configuration \citep[e.g.][]{mcmillan90}."
. ὃν increasing the ternis U;; in Equation 1.. the initial orbital energies of any. binarics &oing into an encounter can increase accordingly in order to conserve energy.," By increasing the terms $_{ii}$ in Equation \ref{eqn:energy-conserv}, the initial orbital energies of any binaries going into an encounter can increase accordingly in order to conserve energy."
 A higher orbital energy. corresponds to a larger semi-major axis and hence cross section for collision., A higher orbital energy corresponds to a larger semi-major axis and hence cross section for collision.
 ‘This suggests that the derived encounter time-scales can be taken as upper limits in the limit that tidal dissipation is negligible., This suggests that the derived encounter time-scales can be taken as upper limits in the limit that tidal dissipation is negligible.
 We expect tides to be particularly elfective during encounters for which the total energy is very negative as à result of one or more very hard binarics being involved., We expect tides to be particularly effective during encounters for which the total energy is very negative as a result of one or more very hard binaries being involved.
 We have argued in Section 2.2 that the average stellar miss is expected to be comparable to (but slightly less than) the mass of the MAISTO in old OCs and low-mass GC's., We have argued in Section \ref{general} that the average stellar mass is expected to be comparable to (but slightly less than) the mass of the MSTO in old OCs and low-mass GCs.
 Me have also arguedὃν that most encounters will involve stars having masses slightly larger than the average stellar mass., We have also argued that most encounters will involve stars having masses slightly larger than the average stellar mass.
 We might therefore expect to find that a high proportion of merger products have masses that exceed that of the AIS'TO in very clyvnamically-evolvect clusters that have lost a aree [fraction of their low-mass stars., We might therefore expect to find that a high proportion of merger products have masses that exceed that of the MSTO in very dynamically-evolved clusters that have lost a large fraction of their low-mass stars.
 Consequently. a larger number of merger products could appear sullicienthy bright o end up in the DS region of the cluster CMD in these clusters than in their less cvnamicallv-evolved counterparts.," Consequently, a larger number of merger products could appear sufficiently bright to end up in the BS region of the cluster CMD in these clusters than in their less dynamically-evolved counterparts."
 This is consistent with the results of Ixnigge.Leigh&Sills(2009) and Leigh.Sills&Ixnigge(2009) who found that the number of DSs in the cores of GC's scales sub-linearly with he core mass., This is consistent with the results of \citet{knigge09} and \citet{leigh09} who found that the number of BSs in the cores of GCs scales sub-linearly with the core mass.
 In particular. since the cluster relaxation time increases with increasing cluster mass. it is the lowest mass GC's that should have lost the largest fraction of their low-mass stars.," In particular, since the cluster relaxation time increases with increasing cluster mass, it is the lowest mass GCs that should have lost the largest fraction of their low-mass stars."
 Therefore. if à larger fraction of merger products do indeed end up more massive than the MSTO in these clusters. this could be a contributing factor to the observed sub-linear dependence on core mass.," Therefore, if a larger fraction of merger products do indeed end up more massive than the MSTO in these clusters, this could be a contributing factor to the observed sub-linear dependence on core mass."
 It is also interesting to note that. since BSs are among the most massive cluster members and many are thought to have a binary companion. Bss should be preferentially retained in clusters as they evolve dynamically compared to low-mass ALS stars.," It is also interesting to note that, since BSs are among the most massive cluster members and many are thought to have a binary companion, BSs should be preferentially retained in clusters as they evolve dynamically compared to low-mass MS stars."
 “Phis, This
We have presented a new AICAIC aleorithiu for the hiel-L. low signal to noise limit of the joiut posterior Which solves the slow probabilistic couverecuce of the traditional Cübbs sampler iu this regiue.,"We have presented a new MCMC algorithm for the high-L, low signal to noise limit of the joint posterior which solves the slow probabilistic convergence of the traditional Gibbs sampler in this regime."
 This in principle allows sampling over the joint posterior pCi.sid) over the entire range of angular scales probed by current aud future CAIB experinenuts;," This in principle allows sampling over the joint posterior $p(C_{l}, \Bs | \Bd)$ over the entire range of angular scales probed by current and future CMB experiments."
 The Πιο coluputational burden is now cutirely in the map-malking step of Cübbs sampling. for which the cost per Cübbs iteration now scales with the expense of multiplication bv the inverse noise matrix INN[2," The limiting computational burden is now entirely in the map-making step of Gibbs sampling, for which the cost per Gibbs iteration now scales with the expense of multiplication by the inverse noise matrix $\BN^{-1}$."
 Asstnine pixel uncorrelated (but scan weighted) noise as a good approximation at small augular scales. the cost of au NP) anultipleation is that of a forward aud inverse," Assuming pixel uncorrelated (but scan weighted) noise as a good approximation at small angular scales, the cost of an $\BN^{-1}$ multiplcation is that of a forward and inverse"
is described in Sect.,is described in Sect.
 5 but it is important to note here that as the starburst radius increases the dust gets colder aud the spectrum shifts to lounger wavelenetls., 5 but it is important to note here that as the starburst radius increases the dust gets colder and the spectrum shifts to longer wavelengths.
 Starburst models with a radius of LOkpe come close to matching the coniplete spectral energv distribution but as we discuss in Sect., Starburst models with a radius of 10kpc come close to matching the complete spectral energy distribution but as we discuss in Sect.
 6 such extended starbursts are excluded by millimetre interferometry., 6 such extended starbursts are excluded by millimetre interferometry.
 Efstathiou. Rowan-Robinsou Siebenimoreeu (2000; rereatter ERRS) prescuted a starburst model tha conibined a simpe anodel for the evolution of eian nolecular clou stje stelay population svuthesis model of Druzual Charlot (1993) and detailed radiative trausfer hat included the effect of temperature fluctuating sinal erains with dust particle radius &<LOOA and PATIs o account for the detected infrared enmüssiou bands (Sichemmorecen Rrüesel 1992).," Efstathiou, Rowan-Robinson Siebenmorgen (2000; hereafter ERRS) presented a starburst model that combined a simple model for the evolution of giant molecular clouds, the stellar population synthesis model of Bruzual Charlot (1993) and detailed radiative transfer that included the effect of temperature fluctuating small grains with dust particle radius $a < 100$ and PAHs to account for the detected infrared emission bands (Siebenmorgen Krüggel 1992)."
 Au important feature of ιο ERRS model is that the expansion of the IIT region cads to the formation of a narrow shell of gas and dust., An important feature of the ERRS model is that the expansion of the HII region leads to the formation of a narrow shell of gas and dust.
 This naturally explains the fact that the near- aud micd-oeifared. spectra of starburst ealaxies are not dominated wv enmusson from hot laree (a> LOOA)) dust erains but w the PATs cussion., This naturally explains the fact that the near- and mid-infrared spectra of starburst galaxies are not dominated by emission from hot large $a>100$ ) dust grains but by the PAHs emission.
" As in ERRS we assiune that the oeutial ον of f1ο moleculu clouds that constitue the y.arburst is SOmae but we use the erai modcl described oe1 Sect,", As in ERRS we assume that the initial $A_V$ of the molecular clouds that constitute the starburst is $50$ mag but we use the grain model described in Sect.
 3., 3.
" We urther assume a constant star formation rate and an age of ολο,", We further assume a constant star formation rate and an age of 5Myr.
 The assumed starburst age is very poorly coustrained by our modeling but as we discuss oe1 section 6 a value of 5bMyr can explain the fact that the oeferred hunosities of the starburst aud cis components are coniparablo., The assumed starburst age is very poorly constrained by our modeling but as we discuss in section 6 a value of 5Myr can explain the fact that the inferred luinosities of the starburst and cirrus components are comparable.
 Tn Fig., In Fig.
 | we preseut fits to f1e galaxies in our sample with a colubination of starburst ando cirrus., \ref{ane.ps} we present fits to the galaxies in our sample with a combination of starburst and cirrus.
 Wo first normalize the cirrus nodel at 850750 and then scale the starburst model so that the comΠλ of starburst aux cunrus gives the best fit to the mid-infrared spectroscopy and is consistent with the far-infrared plotometry., We first normalize the cirrus model at $\mu m$ and then scale the starburst model so that the combination of starburst and cirrus gives the best fit to the mid-infrared spectroscopy and is consistent with the far-infrared photometry.
 As discussed in Sect., As discussed in Sect.
 3. for tiree ofthe objects we do not nee auv starburst contriution for explaining the SED.," 3, for three of the objects we do not need any starburst contribution for explaining the SED."
 For two of the objects we also find evidence for an ACN compoucut which we model with the tapered discs of Efstathiot Rowan-Robinson (1995)., For two of the objects we also find evidence for an AGN component which we model with the tapered discs of Efstathiou Rowan-Robinson (1995).
 The more hDuninous of f1e wo objects (SMM. 02399-0126). has been classified as a Sevtert 2 by Simail et al. (," The more luminous of the two objects (SMM J02399-0136), has been classified as a Seyfert 2 by Smail et al. ("
2002).,2002).
 SMIAL J02399-0136 is also he object that has been detected at 70 and 160455., SMM J02399-0136 is also the object that has been detected at 70 and $\mu m$.
 The uninosities o the tiree coniponenuts and the associated dust niasses are give rin Table 2., The luminosities of the three components and the associated dust masses are given in Table 2.
 Iu the ERRS mocel iu lucrease in the Iuniuositv trauslates into a Lincrease in the imiuber of molecular clouds that constitute the starburst and therefore the dust mass., In the ERRS model an increase in the luminosity translates into an increase in the number of molecular clouds that constitute the starburst and therefore the dust mass.
 Sicbenmorecn νήσος (2007) presented a starburst model which dis an evolution of an ewrlior ος described by νήσοςOO Tutukov (1978) aud E&zrüsecl85 Siebeninoreen (1991)., Siebenmorgen Krüggel (2007) presented a starburst model which is an evolution of an earlier model described by Krüggel Tutukov (1978) and Krüggel Siebenmorgen (1994).
 The model assumes that the stars are divided in two classes: OB stars that are surrounded by dense clouds aud constitute so-called hot spots aud other stars (old bilee stars or massive stars} that are dispersed in the diffuse medimm (see below)., The model assumes that the stars are divided in two classes: OB stars that are surrounded by dense clouds and constitute so-called hot spots and other stars (old bulge stars or massive stars) that are dispersed in the diffuse medium (see below).
 The hot spots determine the mid infrared part of he ciission spectrun., The hot spots determine the mid infrared part of the emission spectrum.
 The outer radius of the hot spots isi determiye by the condition of equal heating of the dust by f10 stars and the iaubieut iutersellar radiation field., The outer radius of the hot spots is determined by the condition of equal heating of the dust by the stars and the ambient interstellar radiation field.
 Both classes of stas are represented in the οςuation of radiativei transfer bv continuously distributed source teris., Both classes of stars are represented in the equation of radiative transfer by continuously distributed source terms.
 It is assumed that the uuuber deusitv of the hot spots aud othe other stars falls off with the radius othe starburs as wa), It is assumed that the number density of the hot spots and of the other stars falls off with the radius of the starburst as $r^{-1.5}$.
 Iu addition to the dist in the hot spots the mode asstumes that the volue of the starburst is Ἡed by dust which is uniformly distributed aud gives rise to a tota extinction Aj from the outer radius £7 of 1ο ealactic cleus to its center., In addition to the dust in the hot spots the model assumes that the volume of the starburst is filled by dust which is uniformly distributed and gives rise to a total extinction $A_V^{'}$ from the outer radius $R$ of the galactic nucleus to its center.
 lut Us homogeneous density mode he parameter A is (irectlv related to the dus mass Map and ouly oue of them is independent., In this homogeneous density model the parameter $A_V^{'}$ is directly related to the dust mass $M_{SB}^{'}$ and only one of them is independent.
" The other mode πο are the toalh iinuosity Loy, aud the starburst radius R.", The other model parameters are the total luminosity $L_{SB}^{'}$ and the starburst radius $R$.
 The OD sars are assumed to be confined to he central 350pc whereas the bulge stars fll the whole volue., The OB stars are assumed to be confined to the central 350pc whereas the bulge stars fill the whole volume.
 Iu Fig., In Fig.
 5 we combine starburst models computed with he method of Sicbcumoregen νήσος. (2007) with cirrus uodels and compare them with the data of he objects iu our suuple., \ref{rs.ps} we combine starburst models computed with the method of Siebenmorgen Krüggel (2007) with cirrus models and compare them with the data of the objects in our sample.
 As iu the case of he evolutiouarv mnodcls we first normalize the cirrus mode lat 8S5üjnn., As in the case of the evolutionary models we first normalize the cirrus model at $\mu m$.
 Tien we search in the SED library to fud asarburst mode] which. after scaling to the distance of the object but without further jormalization. best fit the 12k-iufrared specroscopy.," Then we search in the SED library to find a starburst model which, after scaling to the distance of the object but without further normalization, best fit the mid-infrared spectroscopy."
 The starburst radius is fixed at 3kpc to be coidstent with he sizes inferred from iterteyolmetry for these galaxies (Sect., The starburst radius is fixed at 3kpc to be consistent with the sizes inferred from interferometry for these galaxies (Sect.
 6)., 6).
 Unless otherwise iidicated the value of ¢ is asstunecd to be 5 as before., Unless otherwise indicated the value of $\psi $ is assumed to be 5 as before.
 Siace the original suggestionOO of ERRO3 aud Iia et al. (, Since the original suggestion of ERR03 and Kaviani et al. (
2x003) that SMCs are colder aud more extended than local ULIRGs a nuuber of studies have eiven support to this idea.,2003) that SMGs are colder and more extended than local ULIRGs a number of studies have given support to this idea.
 Rowan-Robinson et al. (, Rowan-Robinson et al. (
2001) discovered a nimiber of luuious cimus ealaxies in the ELAIS survey.,2004) discovered a number of luminous cirrus galaxies in the ELAIS survey.
 CΙΕ ot al. (, Chapman et al. (
2001) found hat the majority of SALGs in their σαuple are more extended iu the radio than local ULIRG:s.,2004) found that the majority of SMGs in their sample are more extended in the radio than local ULIRGs.
 This fiudiug was confirmed by Biges Ivison (20jS) who fouud a meclia resize of Skpc for the SMCs in their sample., This finding was confirmed by Biggs Ivison (2008) who found a median size of 5kpc for the SMGs in their sample.
 Iowever. Tacconi et al. (," However, Tacconi et al. ("
2006) showed that the SMCis iu their sample caunot )o 1uore extended than ~ Ikpc.,"2006) showed that the SMGs in their sample cannot be more extended than $\sim
4$ kpc."
 The evolutionary starburst model of ERRS «oes lot make a prediction ayout the size of the starburst but a, The evolutionary starburst model of ERRS does not make a prediction about the size of the starburst but a
In recent vears experiments on angular scales from several degrees to à few are minutes have started to delineate the CAIB power spectrum olfering a unique approach to the study of conditions in the early. history of the Universe.,In recent years experiments on angular scales from several degrees to a few arc minutes have started to delineate the CMB power spectrum offering a unique approach to the study of conditions in the early history of the Universe.
 Current. observations at. large. and intermediate. angular scales constrain the level of normalization of the SachsWolfe plateau (Bennett et al., Current observations at large and intermediate angular scales constrain the level of normalization of the Sachs--Wolfe plateau (Bennett et al.
 1996: Cutiérerez et al., 1996; Gutiérrrez et al.
 2000). and have shown the presence of the first. Doppler peak (de Bernarelis ct al.," 2000), and have shown the presence of the first Doppler peak (de Bernardis et al."
 2000: Llanany et al., 2000; Hanany et al.
 2000: Alauskopl et al., 2000; Mauskopf et al.
 2000: Llalverson et al., 2000; Halverson et al.
 2001)., 2001).
 A new generation of experiments is planned to cover angular scales ranging from. a lew arc minutes to several degrees. these. include. the and satellite missions.," A new generation of experiments is planned to cover angular scales ranging from a few arc minutes to several degrees, these include the and satellite missions."
 These experimental cHorts will potentially allow the determination of the main cosmological parameters at a level of a few per cent., These experimental efforts will potentially allow the determination of the main cosmological parameters at a level of a few per cent.
 To achieve this. a very. accurate subtraction of foregrounds is needed.," To achieve this, a very accurate subtraction of foregrounds is needed."
 These foregrounds include. svachrotron. free[ree and dust emission.," These foregrounds include synchrotron, free–free and dust emission."
 Itecently. a fourth component has been identified (Ixogut et al.," Recently, a fourth component has been identified (Kogut et al."
 1996a.b) in the analvsis of the DAIR data.," 1996a,b) in the analysis of the DMR data."
 Phe nature of this component is controversial and has been proposed to be freefree. (Müukherjee et. al., The nature of this component is controversial and has been proposed to be free–free (Mukherjee et al.
 101) or spinning cust. (cle Oliveira-C'osta ct al., 2001) or spinning dust (de Oliveira-Costa et al.
 1999. 2000).," 1999, 2000)."
 Progress in the study of this elusive component will require 10 existence of reliable maps at. frequencies in the range between LO and 20 Gllz where free.free emission is one of the ominating processes and spinning dust (Draine Lazarian 1998) may exhibit a turn-over in its spectrum., Progress in the study of this elusive component will require the existence of reliable maps at frequencies in the range between 10 and 20 GHz where free–free emission is one of the dominating processes and spinning dust (Draine Lazarian 1998) may exhibit a turn-over in its spectrum.
 The goal of the COSAIOSOALAS experiment. presented here is to map the cosmic microwave background. and Galactic dilfuse emission with mean sensitivities of 30. μὴν per beam (~ 17) in an area covering ~25% of the sky., The goal of the COSMOSOMAS experiment presented here is to map the cosmic microwave background and Galactic diffuse emission with mean sensitivities of 30 $\mu$ K per beam $\sim 1^{\circ}$ ) in an area covering $\sim 25$ of the sky.
 This will allow a measurement of CMD Óluctuations in the angular regions of the SachsWolfe plateau and the first) acoustic peaks., This will allow a measurement of CMB fluctuations in the angular regions of the Sachs–Wolfe plateau and the first acoustic peaks.
 The experiment is based on a circular scanning strateey and Consists of two ground-hasecl total power receivers working at, The experiment is based on a circular scanning strategy and consists of two ground-based total power receivers working at
sPhe recent. discovery.. of large numbers of. quasars at. racio. and X-ray. frequencies. with. very red optical.to.near-infrareduu continua. suggests that. existingLo optical. surveys may be severely incomplete. (eg.,The recent discovery of large numbers of quasars at radio and X-ray frequencies with very red optical–to–near-infrared continua suggests that existing optical surveys may be severely incomplete (eg.
 Webster⇁ et al., Webster et al.
 1995 and references⋅ herein)rerein)., 1995 and references therein).
 Webster et al. (, Webster et al. (
1995) ancl Alasci (1998). have argued that the anomalous colours are clue to extinction ον dust. although the location. of. the dust remains. a highly. controversial issue.,"1995) and Masci (1998) have argued that the anomalous colours are due to extinction by dust, although the location of the dust remains a highly controversial issue."
 Intervening dusty galaxies which happen lie along. the line-of-sight ofu⋅ otherwise normaldust. bluc quasars . expected to redden the observed optical continuum.. ors if edges. he optical depth is high enough. to remove quasars from an optical [ux-limited sample (eg.," Intervening dusty galaxies which happen to lie along the line-of-sight of otherwise normal blue quasars are expected to redden the observed optical continuum, or if the optical depth is high enough, to remove quasars from an optical flux-limited sample (eg."
 Wright 1990]., Wright 1990).
 As suggested ον existing obervational and theoretical studies of cosmic chemical evolution however (Pei Fall 1995 and references herein). one expects a reduction in the amount of dust to vigh redshift.," As suggested by existing obervational and theoretical studies of cosmic chemical evolution however (Pei Fall 1995 and references therein), one expects a reduction in the amount of dust to high redshift."
 Consequently. one then also expects that the srohability ofa background object being either reddened or obscured to be reduced.," Consequently, one then also expects that the probability of a background object being either reddened or obscured to be reduced."
" ""he etlects of foreground dust on observations of objects at cosmological distances has been discussed. by Ostriker Leister (1981): Heisler Ostriker (1988): Fall Pei (19080. 1993): Wright (1986. 1990) and Masci Webster (1995)."," The effects of foreground dust on observations of objects at cosmological distances has been discussed by Ostriker Heisler (1984); Heisler Ostriker (1988); Fall Pei (1989, 1993); Wright (1986, 1990) and Masci Webster (1995)."
" Using models of clusty galactic disks. these studies show that the line-of-sight.D. to a high. redshift."" quasar has a high. probability» of Ebeing intercepted.. by a galactie EMdisk. . M ≻⋜⊔⋅⇂⊔⇍⊔↓⋜⊔⋅↓∙∖⇁↓⇂↿↓∐⋅∠⇂⊔⊳∖∣∠⊔⊳∖↿↓⋅↓∣⋡⋯↓∩⊔↓≱∖↓⋜⊔⋅⋏∙≟∢⋅↓⋅↿↓↥⋜⋯⇂↓↥∢⊾∪↓≻↿⊔⇍⋜↧↓ 2.4. . . radius of the galaxy."," Using models of dusty galactic disks, these studies show that the line-of-sight to a high redshift quasar has a high probability of being intercepted by a galactic disk, particularly if the dust distribution is larger than the optical radius of the galaxy."
 Based on the dust. properties of local ealaxies. it is estimated that up to of bright. quasars ο 23 mav be obscured. by. clusty intervening systenis.," Based on the dust properties of local galaxies, it is estimated that up to of bright quasars to $z\sim3$ may be obscured by dusty intervening systems."
 sPhe principle2. issue. in. these caleulations. was that realisticD. distributions in⋠⊀⊀ galaxies. which. are. ‘soft’ around. the o will cause. many quasars to appear reddened without are. removing them from a Iux-limited sample.," The principle issue in these calculations was that realistic dust distributions in galaxies which are `soft' around the edges, will cause many quasars to appear reddened without removing them from a flux-limited sample."
 of Nonethe above studies however considered theeffects of evolution in dust. content., None of the above studies however considered the effects of evolution in dust content.
 Cosmic evolution in. dust is indirectly suggested by numerous claims of reduced chemical enrichment at 222., Cosmic evolution in dust is indirectly suggested by numerous claims of reduced chemical enrichment at $z\simgt2$.
 Evidence is provided. by observations of trace metals and their relative abundances in. 050 absorplion-line systems to 2~23 (Meyer Roth 1990: savaglio. D'Odorico Aolller L994: Pettini et al.," Evidence is provided by observations of trace metals and their relative abundances in QSO absorption-line systems to $z\sim 3$ (Meyer Roth 1990; Savaglio, D'Odorico Mölller 1994; Pettini et al."
 1994: Wolfe et al., 1994; Wolfe et al.
 1994: Pettini ct al., 1994; Pettini et al.
 1997: Songaila 1997). which are thought to arise [from intervening clouds or the haloes and disks of galaxies.," 1997; Songaila 1997), which are thought to arise from intervening clouds or the haloes and disks of galaxies."
 These studies indicate mean metallicities ~10:4 and <1% solar at z—2 and z~3 respectively. anc dust-to-gas ratios SSM of the galactic value al 2~2.," These studies indicate mean metallicities $\simeq 10\%$ and $\simlt1\%$ solar at $z\sim2$ and $z\sim3$ respectively, and dust-to-gas ratios $\simlt8\%$ of the galactic value at $z\sim2$."
 Dhese estimates are consistent with simple global evolution models of star. formation and gas consumption, These estimates are consistent with simple global evolution models of star formation and gas consumption
escape from an SNR (Aharonian Atovan 1996: Gabici et al.,escape from an SNR (Aharonian Atoyan 1996; Gabici et al.
 2009: Ohira et al., 2009; Ohira et al.
2010b)°.. However. these eanuniu-ravs are the secondary endssious of CRs from au SNR. and so these observations are ouly the indirect evidences of the CR escape scenario.," However, these gamma-rays are the secondary emissions of CRs from an SNR, and so these observations are only the indirect evidences of the CR escape scenario."
 Ou the other hand. the direct observations of CR electrons/positrous have been also ereath advanced.," On the other hand, the direct observations of CR electrons/positrons have been also greatly advanced."
 The PAMELA satellite discovered the excess of tle CR positron fraction (Adriani et al., The PAMELA satellite discovered the excess of the CR positron fraction (Adriani et al.
 2009) iud. as for the flux of CR clectrous plus positrons the experiments such as ATIC/PPB-BETS (Chane et al.," 2009) and, as for the flux of CR electrons plus positrons the experiments such as ATIC/PPB-BETS (Chang et al."
 2008: Torii ct al., 2008; Torii et al.
 20050). Fermi (Abdo ct al.," 2008b), Fermi (Abdo et al."
 2009a: Ackermamn ct al., 2009a; Ackermann et al.
 2010) and ILE.S.S. (Aharomian et al., 2010) and H.E.S.S. (Aharonian et al.
 2008. 2009) havc revealed an excess from the conventional model (sec also Alever et al.," 2008, 2009) have revealed an excess from the conventional model (see also Meyer et al."
 2010 for the energv calibration between Fermi aud ILE.S.S.)., 2010 for the energy calibration between Fermi and H.E.S.S.).
 These results sugeest that there are some additional electron/positron sources;, These results suggest that there are some additional electron/positron sources.
 Possible candidates include astroplivsical sources such as pulsars (Shen 1970: Atovan et al., Possible candidates include astrophysical sources such as pulsars (Shen 1970; Atoyan et al.
 1995: Chi et al., 1995; Chi et al.
 1996: Zhane Chene 2001: Cotman 2007: EKobavashi et al., 1996; Zhang Cheng 2001; Grimani 2007; Kobayashi et al.
 2001: Düeeschiug et al., 2004; Büeesching et al.
 2008: looper et al., 2008; Hooper et al.
 2009: Yuksel et al., 2009; Yuksel et al.
 2009: Profiuno 2008: Malvshev et al., 2009; Profumo 2008; Malyshev et al.
 2009: Crasso et al., 2009; Grasso et al.
 Auto2009: Ixzsvanalsa et al., 2009; Kawanaka et al.
 2010: ITexl et al., 2010; Heyl et al.
 2010: Blasi 2010). supernova remnantsP(Shaviv ct al.," 2010; Blasi Amato 2010), supernova remnants (Shaviv et al."
 2009: Blasi 2009: Blasi Serpico 2009: ita et al., 2009; Blasi 2009; Blasi Serpico 2009; Fujita et al.
 2009: IIu et al., 2009; Hu et al.
 2009: Dieriuaun et al., 2009; Biermann et al.
 2009: Moertscli Sarku 2009: Ahlers et al., 2009; Mertsch Sarkar 2009; Ahlers et al.
 2009). gamma-ray bursts (GRD: Ioka 2010: Iistler Yuksel 2009). microquasars(Weinzg Suuvaev 2002) and white dwarf pulsars(Nashivama et al.," 2009), gamma-ray bursts (GRB; Ioka 2010; Kistler Yuksel 2009), microquasars (Heinz Sunyaev 2002) and white dwarf pulsars (Kashiyama et al."
 2010)., 2010).
 Dark matter aunililatious/decays (c.g. Hooper 2009) and the propagation effect (Delaliave ct al., Dark matter annihilations/decays (e.g. Hooper 2009) and the propagation effect (Delahaye et al.
 2008: Cowsilk jureh 2000: Stawarg et al., 2008; Cowsik Burch 2009; Stawarz et al.
 2010) are also the possible processes for makiug the CR electron/positrou excess (for the comprehensive review. see Fan et al.," 2010) are also the possible processes for making the CR electron/positron excess (for the comprehensive review, see Fan et al."
 2010)., 2010).
 Iu the near future within a few vears. Alpha Magnetic Spectrometer - 02 CAMS-02) experiment will measure the positron fraction up to ITeV (Beischer et al.," In the near future within a few years, Alpha Magnetic Spectrometer - 02 (AMS-02) experiment will measure the positron fraction up to $\sim 1{\rm TeV}$ (Beischer et al."
 2009: Pato et al., 2009; Pato et al.
 2010: Pochou 2010) aud CALorimetric Electron Telescope (CALET) experiment will explore the clectrou up to ~LOTeV with an euergv resolution better than a few perceut (Tori et al., 2010; Pochon 2010) and CALorimetric Electron Telescope (CALET) experiment will explore the electron up to $\sim 10{\rm TeV}$ with an energy resolution better than a few percent (Torii et al.
 20082)., 2008a).
 Iu addition. the future Chereukov Telescope Array (CTA) will be able to measure the CR electron. spectra up to ~Το (CTA consortimu 2010).," In addition, the future Cherenkov Telescope Array (CTA) will be able to measure the CR electron spectrum up to $\sim 15{\rm TeV}$ (CTA consortium 2010)."
 These experiments will open the window to the CR astrophivsies with the TeV clectron and positrou colponcuts., These experiments will open the window to the CR astrophysics with the TeV electron and positron components.
 Especially. as I&obavashi ct al. (," Especially, as Kobayashi et al. ("
2001) have vointed out. iu the TeV euergy baud a few nearby sources uav leave spectral signatures and we will be able to sec a spectral shape of CR clectrous/positrous frou a single source. while in the lower enerey baud we can see only he superposed spectruui from multiple sources.,"2004) have pointed out, in the TeV energy band a few nearby sources may leave spectral signatures and we will be able to see a spectral shape of CR electrons/positrons from a single source, while in the lower energy band we can see only the superposed spectrum from multiple sources."
 Iu this paper. we suggest a possibilitv that the precise ucasurecineut of the CR electron spectimm in the very ügh euergy baud (21UTeV. expected with CALET and CTA) could directly prove the onere CR escapeif those clectrous/positrous are generated.dependeutby a pulsar embedded iu an SNR.," In this paper, we suggest a possibility that the precise measurement of the CR electron spectrum in the very high energy band $\gtrsim 1-10{\rm TeV}$, expected with CALET and CTA) could directly prove the energy-dependent CR escape if those electrons/positrons are generated by a pulsar embedded in an SNR."
 This is quite a natural situation to be realized because a pulsar should be eenerated in the center of a core-collapse supernova aud CR clectrous/positrons are considered to be generated in the pulsar wind nebula formed inside the SNR., This is quite a natural situation to be realized because a pulsar should be generated in the center of a core-collapse supernova and CR electrons/positrons are considered to be generated in the pulsar wind nebula formed inside the SNR.
 If the CR escape really occurs in a voung nearby pulsar/SNR syste. the electron spectrum from it will show a unique feature as explained in the followine aud. when it is observed. that will be the first direct evidence of the CR escape scenario.," If the CR escape really occurs in a young nearby pulsar/SNR system, the electron spectrum from it will show a unique feature as explained in the following and, when it is observed, that will be the first direct evidence of the CR escape scenario."
 To illustrate our main idea. we show a clear example of the effect of the enerey-depeudent CR escape iu the direct electron observatious.," To illustrate our main idea, we show a clear example of the effect of the energy-dependent CR escape in the direct electron observations."
" In the caleulatious of CR electrous/positrous. we usually assmune that they are injected iuto the interstellar matter (ISM) from a pulsar with a spectral form of where ο, is the energv of clectrous/positrous."," In the calculations of CR electrons/positrons, we usually assume that they are injected into the interstellar matter (ISM) from a pulsar with a spectral form of where $\varepsilon_e$ is the energy of electrons/positrons."
 The observed electron spectrum fle...f) cau be obtained by solving the diffusion “men where D(z.)=Doll|z./3€0V)? is the diffusion coefficient and P(2.) is the enerev loss rate.," The observed electron spectrum $f(\varepsilon_e,r,t)$ can be obtained by solving the diffusion equation where $D(\varepsilon_e)=D_0(1+\varepsilon_e/3{\rm GeV})^{\delta}$ is the diffusion coefficient and $P(\varepsilon_e)$ is the energy loss rate."
" Here we adopt Dy=5s«οαν|, à=1/3 that is consistent with the boron to carbon ratio according to the latest GALPROP code. and Pls.)=bz? with b=1019GeVts3 which includes the energy loss via svuchrotron ciission and inverse Conpton scatterings (with Thomson approximation)."," Here we adopt $D_0=5.8\times 10^{28}{\rm cm}^2{\rm s}^{-1}$, $\delta=1/3$ that is consistent with the boron to carbon ratio according to the latest GALPROP code, and $P(\varepsilon_e)=-b\varepsilon_e^2$ with $b=10^{-16}{\rm GeV}^{-1}{\rm s}^{-1}$ which includes the energy loss via synchrotron emission and inverse Compton scatterings (with Thomson approximation)."
" Then. if clectrous/positrous are injected from a poit-like source instantancously Gc. Q(Gocrf)xο(1)δ (1). the observed spectruni is simply written as where dap~vLe,yf as the diffusion leusth of CR clectrous/positrous."," Then, if electrons/positrons are injected from a point-like source instantaneously (i.e. $Q_e(\varepsilon_e,r,t)\propto \delta(t)\delta(r)$ ), the observed spectrum is simply written as where $d_{\rm diff}\sim \sqrt{4D(\varepsilon_e)t}$ is the diffusion length of CR electrons/positrons."
" This spectrum is roughly xoportional to 2,0?explΩςMH) up to the sharp cutoff at ορ~Ll/(bf). and exponentially camps vevond the diffusion leneth dag (Atovan et al."," This spectrum is roughly proportional to $\varepsilon_e^{-\alpha-3\delta/2}\exp(-r^2/(4D(\varepsilon_e)t))$ up to the sharp cutoff at $\varepsilon_e\sim 1/(bt)$, and exponentially damps beyond the diffusion length $d_{\rm diff}$ (Atoyan et al."
 1995: Ioka 2010)., 1995; Ioka 2010).
 Iowever. if the energv-«depeudeut escape of CR articles from the shock is taken iuto account. the electron spectrum would have a sharp cutoff in the ow energev side because lower cucrey CRs cannot escape into the ISAL," However, if the energy-dependent escape of CR particles from the shock is taken into account, the electron spectrum would have a sharp cutoff in the low energy side because lower energy CRs cannot escape into the ISM."
" The euergv of particles which are niuginallv capable of escapiug to the ISM τς is eoncrally determined by the confinement condition of CR particles. ie. the equality between the diffusion length of particles and the characteristic size of the svsteun: where Days vg, and Ry, are the diffusion coefiicicut around the supernova remnant shock. the shock velocity. and the size of the system. respectively."," The energy of particles which are marginally capable of escaping to the ISM $\varepsilon_{\rm esc}$ is generally determined by the confinement condition of CR particles, i.e. the equality between the diffusion length of particles and the characteristic size of the system: where $D_{\rm sh}$, $u_{\rm sh}$ and $R_{\rm sh}$ are the diffusion coefficient around the supernova remnant shock, the shock velocity, and the size of the system, respectively."
 Then the energy, Then the energy
"Because we simulate SNRs until they are several million years old, it is interesting to consider what effects galactic shear may have on the remnants.","Because we simulate SNRs until they are several million years old, it is interesting to consider what effects galactic shear may have on the remnants."
" Given the difference in Galactic rotation speed across the remnant, we calculated the maximum distance that galactic shear could stretch the SNR and compare it with the size of the SNR."," Given the difference in Galactic rotation speed across the remnant, we calculated the maximum distance that galactic shear could stretch the SNR and compare it with the size of the SNR."
 Let us first consider our simulation without a magnetic field., Let us first consider our simulation without a magnetic field.
" For this simulation, the maximum bubble diameter is about 230 pc, which occurs at 2 Myrs."," For this simulation, the maximum bubble diameter is about 230 pc, which occurs at 2 Myrs."
 From the galactic rotation curves of Maciel&Lago(2005) we see that the greatest possible difference in galactic rotation velocity (considering the scatter between observed data points) from one side of our remnant to the other would be 20 km/s (= 20 pc/Myr)., From the galactic rotation curves of \citet{Maciel_Lago} we see that the greatest possible difference in galactic rotation velocity (considering the scatter between observed data points) from one side of our remnant to the other would be 20 km/s $\approx$ 20 pc/Myr).
" Because our bubble consistently shrinks after 2 Myrs and is very small at late times, we will only consider the shear for the first 8 Myrs and approximate that the bubble stays the same size."," Because our bubble consistently shrinks after 2 Myrs and is very small at late times, we will only consider the shear for the first 8 Myrs and approximate that the bubble stays the same size."
" From this we find that, at most, galactic shear would stretch our bubble (20Myr)x8Myrs=160pc, which is much smaller than the diameter of our bubble."," From this we find that, at most, galactic shear would stretch our bubble $(20 {\frac{\rm{pc}}{\rm{Myr}}})\times 8 \rm{Myrs}= 160 \rm{pc}$, which is much smaller than the diameter of our bubble."
" Thus, the differential galactic rotation would not tear apart the bubble."," Thus, the differential galactic rotation would not tear apart the bubble."
" Of our simulated remnants, the one having the greatest width in the direction parallel to the plane is model B. Its maximum width is about 500 pc."," Of our simulated remnants, the one having the greatest width in the direction parallel to the plane is model B. Its maximum width is about 500 pc."
" Because of the flatness in the galactic rotation curve, over this distance a liberal"," Because of the flatness in the galactic rotation curve, over this distance a liberal"
aresee corresponds to 6.918 kpc in a Universe with 11 ΞΤΙ kms+ Alpe1 Ον =0.27. Οντὸ (Spergel et al.,"arcsec corresponds to 6.918 kpc in a Universe with $_\circ$ =71 km $^{-1}$ $^{-1}$, $\Omega_m$ =0.27, $\Omega_\Lambda$ =0.73 (Spergel et al."
 2003)., 2003).
" The published radio images show a double-Iobed. radio source which is hiehly asvmmetric in both Dux density and location of the outer components. and has two prominent hotspots at the outer edges (labelled as SW, and NI in Fie."," The published radio images show a double-lobed radio source which is highly asymmetric in both flux density and location of the outer components, and has two prominent hotspots at the outer edges (labelled as $_{\rm out}$ and $_{\rm inn}$ in Fig."
 1. left panel) with an overall angular separation of 47 aresec (325 kpc).," 1, left panel) with an overall angular separation of 47 arcsec (325 kpc)."
" The separations of the peaks of emission in NE;, and SW from the nucleus are 6.3 aresee (43.6 kpe) ancl 40.6 aresec (281 kpe) respectively (e.g. Hintzen. Ulvestach Owen 1983: Swarup. Sinha Πάνας 1984:vice et al."," The separations of the peaks of emission in $_{\rm inn}$ and $_{\rm out}$ from the nucleus are 6.3 arcsec (43.6 kpc) and 40.6 arcsec (281 kpc) respectively (e.g. Hintzen, Ulvestad Owen 1983; Swarup, Sinha Hilldrup 1984;Price et al."
 1993)., 1993).
 The corresponding arm-length ratio is —6. making it one of the very asvnimetric sources in terms of the location of the components.," The corresponding arm-length ratio is $\sim$ 6, making it one of the very asymmetric sources in terms of the location of the components."
 Phe lux density ratio of he two components at 1400 MllIz is 3.5. with SW. which is farther from the nucleus being also brighter.," The flux density ratio of the two components at 1400 MHz is 3.5, with $_{\rm out}$, which is farther from the nucleus being also brighter."
 In addition. here is weak component (SWiy4) with a flux density of 9 niv at. 12400. MIIz located: 73.5. aresee (24.2 kpc) south-west of the nucleus along the axis of the source.," In addition, there is weak component $_{\rm inn}$ ) with a flux density of 9 mJy at 1400 MHz located $\sim$ 3.5 arcsec (24.2 kpc) south-west of the nucleus along the axis of the source."
 There is no evidence of a distinct jet-like structure as defined by. Dricle Perley (1984)., There is no evidence of a distinct jet-like structure as defined by Bridle Perley (1984).
 From VLA C-array observations at 5 Cillz. Saikia et al. (," From VLA C-array observations at 5 GHz, Saikia et al. ("
1984) find the south-western component to be 15.4 per cent. polarised compared with 5.7 per cent for the north-castern one and 1.1 per cent for the core component.,1984) find the south-western component to be 15.4 per cent polarised compared with 5.7 per cent for the north-eastern one and 1.1 per cent for the core component.
 In an optical study of the host galaxies of intermecdiate-redshift’ quasars. Iónnnback et al. (," In an optical study of the host galaxies of intermediate-redshift quasars, Rönnnback et al. ("
1996). report an arm- structure resembling a tidal tail in 4€02.27 and show that the luminosity profile of the host. galaxy follows. an rb qaw.,1996) report an arm-like structure resembling a tidal tail in 4C02.27 and show that the luminosity profile of the host galaxy follows an $^{1/4}$ law.
" ""Their cllective radius is consistent with earlier measurements by Romanishin Lintzen (1989) although Ronnnback et al.", Their effective radius is consistent with earlier measurements by Romanishin Hintzen (1989) although Rönnnback et al.
 find the host galaxy magnitude to be 0 mag brighter., find the host galaxy magnitude to be $\sim$ 0.4 mag brighter.
 In the next Section we present GMT observations of the source at 619. MlIZz as well as the NVSS and FIRST images of the source., In the next Section we present GMRT observations of the source at 619 MHz as well as the NVSS and FIRST images of the source.
 In Section 3. we discuss the possibility that 4€02.27. (00035|0204). could. be a DDRQ exhibiting signs of episodic activity.," In Section 3, we discuss the possibility that 4C02.27 (J0935+0204) could be a DDRQ exhibiting signs of episodic activity."
 In this section we present the results of the CGALRT observations as well as the NVSS and FIRST images., In this section we present the results of the GMRT observations as well as the NVSS and FIRST images.
 The GAIRT and VLA images show the presence of a dilluse lobe bevond the north-eastern hotspot., The GMRT and VLA images show the presence of a diffuse lobe beyond the north-eastern hotspot.
 The source was observed with the CMIB on 2007 September 01 at 619. Mz for approximately 330 minutes on source., The source was observed with the GMRT on 2007 September 01 at 619 MHz for approximately 330 minutes on source.
 The observations were mace in the standard manner. with each observation of the target-source interspersed with observations of the phase calibrator. 083.," The observations were made in the standard manner, with each observation of the target-source interspersed with observations of the phase calibrator, $-$ 083."
 3€286 and 3C147 were both observed. for flux density. ancl bandpass calibration., 3C286 and 3C147 were both observed for flux density and bandpass calibration.
 The tux densities are on the Baars et al. (, The flux densities are on the Baars et al. (
1977) scale.,1977) scale.
 The data collected were calibrated and reduced. in the standard way using the NRAQO software package., The data collected were calibrated and reduced in the standard way using the NRAO software package.
 several rounds of self calibration were done to improve the, Several rounds of self calibration were done to improve the
 , 
C'ross-dispersed spectroscopy makes possible to acquire information of wide spectral regions iu a single exposure. by projecting several dispersiou axes on the detector simultaneously.,"Cross-dispersed spectroscopy makes possible to acquire information of wide spectral regions in a single exposure, by projecting several dispersion axes on the detector simultaneously."
 As a consequeuce. the reductiou process required to analyze this kind. of data is complicated. since different. cliffraction orders ueed to be selected. extracted. calibrated iudependently auc combined in the final step.," As a consequence, the reduction process required to analyze this kind of data is complicated, since different diffraction orders need to be selected, extracted, calibrated independently and combined in the final step."
 This difficulty led many authors to develop methods aud software packages [or the reduction of cross-cdispersed aud echelle spectra Piskunov&Valenti2002:Bochauskietal. 2009).," This difficulty led many authors to develop methods and software packages for the reduction of cross-dispersed and echelle spectra \citep[e.g.][]{moreno1982, rossi1985, piskunov2002, bochanski2009}."
. Iu the past decade the near infrared (NIB) µας also been explored by eross-dispersed spectrograplis. such as Spex (Raynerοἱal.2003) at the NASA Infrared Telescope Facility (RTE). with a resolving power of  2000 and reaching [rom 0.5 to 5.5jun. Other examples are TripleSpec (Ecelstetu aud the Folded-port Iufrared. Echellette (FIRE) (Simcoeetal.2008).. achieving R ~ 2600 aud Ro~ 6000 respectively. aud covering roughly tlie same wavelength domain (0.8 - [pun).," In the past decade the near infrared (NIR) has also been explored by cross-dispersed spectrographs, such as Spex \citep{rayner2003} at the NASA Infrared Telescope Facility (IRTF), with a resolving power of $\sim$ 2000 and reaching from 0.8 to $\upmu$ m. Other examples are TripleSpec \citep{edelstein2007} and the Folded-port Infrared Echellette (FIRE) \citep{simcoe2008}, achieving R $\sim$ 2600 and R $\sim$ 6000 respectively, and covering roughly the same wavelength domain (0.8 - $\upmu$ m)."
siuuples contain. e.g.. less than half of the photons from IC. 1329À. none of NGC 23516. and alinost noue from NGC 1915 (see Table 1).,"samples contain, e.g., less than half of the photons from IC 4329A, none of NGC 3516, and almost none from NGC 4945 (see Table 1)."
 Thus. if IC 1329À and NGC 1915 were substantially differeut from the average Sevtert 1 aud 2. respectively. we would expect significant ciffereuces in the spectral shape of the old and new averages.," Thus, if IC 4329A and NGC 4945 were substantially different from the average Seyfert 1 and 2, respectively, we would expect significant differences in the spectral shape of the old and new averages."
 However. the old and new average spectra can be fitted with ideutical models with hardlv anv increase of 47? with respect o iudependent fits. and the F-test eives the probability that their spectral shape differ of =50 for either Sevfert Ls or 2s.," However, the old and new average spectra can be fitted with identical models with hardly any increase of $\chi^2$ with respect to independent fits, and the F-test gives the probability that their spectral shape differ of $\la 50\%$ for either Seyfert 1s or 2s."
 Snnunanziug. we do fik that Sevfert 2s rave significantly harder spectra than Sevfert 1s Gvhereas them cutoff euergies or teniperatures are simular).," Summarizing, we do find that Seyfert 2s have significantly harder spectra than Seyfert 1s (whereas their cutoff energies or temperatures are similar)."
 This difference can be explained w the cependence of Compton reflection on orientation onlv for orientation close to ecec-ou (cos;SS3). 0.3)., This difference can be explained by the dependence of Compton reflection on orientation only for orientation close to edge-on $\cos i\la 0.3$ ).
 The aneular dependence of hermal-Comptonization spectra in slab geometry is of relatively münor nuportauce., The angular dependence of thermal-Comptonization spectra in slab geometry is of relatively minor importance.
 The effect of Thomsou-thick absorption in a torus sumounudiues he Ne source is nuüportaut in NGC 1915 aud. oossiblv. Mni 3.," The effect of Thomson-thick absorption in a torus surrounding the $\gamma$ source is important in NGC 4945 and, possibly, Mkn 3."
 We have obtained quantitative constraints ou the average electron temperature aud the Compton parameter (or. equivalently. the Thomson optical depth) in Sevtert Is aud 2s (approsximatcly AT~50 150 keV and y< ντο 1).," We have obtained quantitative constraints on the average electron temperature and the Compton parameter (or, equivalently, the Thomson optical depth) in Seyfert 1s and 2s (approximately $kT\sim 50$ –150 keV and $y<1$, $\tau\la 1$ )."
 These results put constraints on theoretical mocels of Sevterts as well as of tle cosmic Ny background., These results put constraints on theoretical models of Seyferts as well as of the cosmic $\gamma$ background.
 A detailed analysis of these constraimts is bevond the scope of this work aud we oulv outline the main relevant issues below., A detailed analysis of these constraints is beyond the scope of this work and we only outline the main relevant issues below.
 Physically. the value of teniperature iun a source is determined by enerev balance between heating and cooling.," Physically, the value of temperature in a source is determined by energy balance between heating and cooling."
 The balance depends. first of all. on the source geometry. which determines the fiux of seed photons incident ou the plasina.," The balance depends, first of all, on the source geometry, which determines the flux of seed photons incident on the plasma."
 Production of seed) photous appears to be donünated bv blackbody plirteums onitted by an optically-thick οςαι iu he vienütv of he hot plasma (Zdziarski ct 11999). with the flux. of thermal svuchrotron pliotous being neelieide da buuiuous ACUNS Wardzidsski Zdzimrski 203.," Production of seed photons appears to be dominated by blackbody photons emitted by an optically-thick medium in the vicinity of the hot plasma (Zdziarski et 1999), with the flux of thermal synchrotron photons being negligible in luminous AGNs (Wardzińsski Zdziarski 2000)."
 Thus. the values of AL puts constraints ou the geometry of the X-rav sources.," Thus, the values of $kT$ puts constraints on the geometry of the X-ray sources."
" Two seouetries appear possible: :| patchy corona above a cold. accretion disk. aud a hot accretion disk with au overlapping cold inediuu (either au outer cold disk. cold blobs or bot1, see. e.g... Poutanen 1998. Zdziarski et al."," Two geometries appear possible: a patchy corona above a cold accretion disk, and a hot accretion disk with an overlapping cold medium (either an outer cold disk, cold blobs or both, see, e.g., Poutanen 1998, Zdziarski et al."
" L998},", 1998).
 The patchy corona geometry has been discussed recently by. c.g. Hardt. Maraschi Cisellini (199D. Stern et ((1995). Poutanen Sveusson (1996). C96. and Deloborodov (19998).," The patchy corona geometry has been discussed recently by, e.g., Haardt, Maraschi Ghisellini (1994), Stern et (1995), Poutanen Svensson (1996), G96, and Beloborodov (1999a)."
" Iu the case of Sevterts which have ou average qtite soft spectra (Px~1.9) aud laree reflection (R.—0.75). the pacli""static corona still appears to be a viable model."," In the case of Seyferts which have on average quite soft spectra $\Gamma_{\rm X}\sim 1.9$ ) and large reflection $R\sim 0.75$ ), the patchy static corona still appears to be a viable model."
 The situation is ¢ifferent for those objects which have hard spectra and little reflection (see Zdzirski et 11999)., The situation is different for those objects which have hard spectra and little reflection (see Zdziarski et 1999).
" Th order to xoduce hard spectra. the cluittingi region should be well separated from the cold. accretion disk (οον, Svensson 1996). but iu that case the predicted reflection is close to nity."," In order to produce hard spectra, the emitting region should be well separated from the cold accretion disk (e.g., Svensson 1996), but in that case the predicted reflection is close to unity."
 Mildly relativistic motions of cunitting plasma away fro the disk. however. solve both problems producing lard Spectra aixd little reflection (Beloborodoy 19992. b)," Mildly relativistic motions of emitting plasma away from the disk, however, solve both problems producing hard spectra and little reflection (Beloborodov 1999a, b)."
 We naso note that this model can produce reflection arecr than unity when cuitting plasma Is MOVIE towards the disk., We also note that this model can produce reflection larger than unity when emitting plasma is moving towards the disk.
 Corona models either with or without ppair production are posside., Coronal models either with or without pair production are possible.
 We vote that stuclics of hermal pair plasmas in pair equilibrium predict no distinct pair annihilation even from a pair-donivated plasmas (Maciolek-Niedzwwiecki. Zdziarski Coppi 1995).," We note that studies of thermal pair plasmas in pair equilibrium predict no distinct pair annihilation even from a pair-dominated plasmas ek-Niedźwwiecki, Zdziarski Coppi 1995)."
 Thus. the lack of such a feature observe by OSSE (c.¢.. J97) does not rule out t1ο presence of thermal ppairs.," Thus, the lack of such a feature observed by OSSE (e.g., J97) does not rule out the presence of thermal pairs."
 The hot «isk. uodel has been developed ly Shapiro. Lightman Eardley (1976). whose solution brauch was cooling-domunated (aud thermally ustae).," The hot disk model has been developed by Shapiro, Lightman Eardley (1976), whose solution branch was cooling-dominated (and thermally unstable)."
 TucludingC» advection [m]gives rise to a stable. low-Iunünositv solution brauch. aud the intersection of the two branches lits the Iguuinositv aud t16 optical depth of an inner flow (Naravan ¥i 1995: Abramowicz ct 11995: see Zdziarski 1995 Or a model parainetrzing the flow bv 4).," Including advection gives rise to a stable, low-luminosity solution branch, and the intersection of the two branches limits the luminosity and the optical depth of an inner flow (Narayan Yi 1995; Abramowicz et 1995; see Zdziarski 1998 for a model parametrizing the flow by $y$ )."
 The role of ppair productlon Is In ecucra ucelieible (DBjórrussou et 11996)., The role of pair production is in general negligible (Björrnsson et 1996).
 The values of 4‘Too~LOO keV aud TOXOl ave predicted by this model close to the aNd possible huuiuositv of the hot flow. in an agreement with our results.," The values of $kT\sim 100$ keV and $\tau\la 1$ are predicted by this model close to the maximum possible luminosity of the hot flow, in an agreement with our results."
 In order to account for the observed range of Py aud. FR. an overlap," In order to account for the observed range of $\Gamma_{\rm X}$ and $R$ , an overlap"
"ffüuxes and τας, photometry.",fluxes and $z'$ -band photometry.
 Although the narrow-baud NB921 photometry consists of pure continu fis for objects at :«6.5. our galaxies are iostly very faiut in this band. preventing us from measuring reliable photometry.," Although the narrow-band NB921 photometry consists of pure continuum flux for objects at $z<6.5$, our galaxies are mostly very faint in this band, preventing us from measuring reliable photometry."
 The broad z/baud includes cussion from both coutiuuuu audLyra., The broad $z'$ band includes emission from both continuum and.
.. To decompose the z baud photometry we assume that the UV coutiuuun slopes (foxAM V are 22.2 (Bowensetal.2009)., To decompose the $z'$ -band photometry we assume that the UV continuum slopes $f_{\lambda} \propto \lambda^\beta$ ) are $\beta=-2$ \citep{bou09}.
. We further asstune that the coutimuun blaeward of lis entirely absorbed by IGAL, We further assume that the continuum blueward of is entirely absorbed by IGM.
 This is reasonable as seen from i~6 quasars (Fanetal.2006)., This is reasonable as seen from $z\sim6$ quasars \citep{fan06}.
. The only free parameter is then the continuum level when au observed spectrum )) is scaled to match the corresponding z baud photometry., The only free parameter is then the continuum level when an observed spectrum ) is scaled to match the corresponding $z'$ -band photometry.
 The results of the EEWs ave listed in Colum 8 of Table 1., The results of the EWs are listed in Column 8 of Table 1.
 Column 6 shows AMisoo. the absolute AB inaguitude of coutimmun at rest-rane 1300A.," Column 6 shows $M_{1300}$, the absolute AB magnitude of continuum at rest-frame 1300."
. The EW measurements are rough due to uncertainties frou the broad-band plotometiy. fluxes. and UV slopes.," The EW measurements are rough due to uncertainties from the broad-band photometry, fluxes, and UV slopes."
 We vary the assumed slope w 0.5 aud the typical change on the imieasured EWs is stnaller than15., We vary the assumed slope by 0.5 and the typical change on the measured EWs is smaller than.
. For a few galaxies with strong NB921 detections. we also derive their EWs based on he coutiuua from their ND921 photometry.," For a few galaxies with strong NB921 detections, we also derive their EWs based on the continua from their NB921 photometry."
 The results uostlv agree with the above measurements within., The results mostly agree with the above measurements within.
. Nevertheless. there is no doubt that most of the galaxies in our sample have large EWs.," Nevertheless, there is no doubt that most of the galaxies in our sample have large EWs."
 The median value of the EWs is 50A. with 1 galaxies having EWs higher thaw 100À.," The median value of the EWs is 50, with 4 galaxies having EWs higher than 100."
. They are ou average smaller than those in the bright sample of Nagaoctal.(2001.2005.2007).. whose EEWs are in the range of 90210À.," They are on average smaller than those in the bright sample of \citet{nag04,nag05,nag07}, whose EWs are in the range of 90–240."
. We know little about the EEW distribution of LDGs at 2—6., We know little about the EW distribution of LBGs at $z\sim6$.
 Current facilities can only ideutifv +—6 LBGs with prominent ]lines. but it is known that most LBCs at low redshift do uot have strong ecuussion.," Current facilities can only identify $z\sim6$ LBGs with prominent lines, but it is known that most LBGs at low redshift do not have strong emission."
 At 2=~3. the EEW distribution has been well determined based ou a spectroscopic suple of iore than 1000 LBGs (Shapleyetal.2003:Reddyct2008:&Steidel 2009).," At $z=2\sim3$, the EW distribution has been well determined based on a spectroscopic sample of more than 1000 LBGs \citep{sha03,red08,red09}."
. A half of the LBGs in this sample have aabsorption lines instead of emission lines. and ouly have EEWs ereater than 30 (with ~10 having EWs >50 ÀJ). while almost all the LBCs in our sample have EWs >30À.," A half of the LBGs in this sample have absorption lines instead of emission lines, and only have EWs greater than 30 (with $\sim10$ having EWs $>50$ ), while almost all the LBGs in our sample have EWs $>30$."
. Therefore. LBCs in our +>6 sample have much stronger eecnission on average.," Therefore, LBGs in our $z>6$ sample have much stronger emission on average."
 Statistics of EEWs for LBCs at 2>5 has been teutatively investigated (0.8.Starketal.2010. 2011)..," Statistics of EWs for LBGs at $z>5$ has been tentatively investigated \citep[e.g.][]{sta10,sta11}. ."
 For example. Starketal.(2011). found that at 21.75Mypyx20.25 the fractions of LBGs with EWs >25 aud >55 aare roughly and&%.. respectively. aud at 20.25««o1835 the two fractions iuerease rapidly to and ~254.," For example, \citet{sta11} found that at $-21.75<M_{\rm UV}<-20.25$ the fractions of LBGs with EWs $>25$ and $>55$ are roughly and, respectively, and at $-20.25<M_{\rm UV}<-18.75$ the two fractions increase rapidly to $\sim55$ and $\sim25$."
. Our suuple spius a UV luminosity range of 21.5€Aso)19.5. and the two fractions in our sample are (15/59) and (8/59). broach: consistent with the trend shown in their results.," Our sample spans a UV luminosity range of $-21.8\le M_{1300}\le -19.5$, and the two fractions in our sample are (15/59) and (8/59), broadly consistent with the trend shown in their results."
 The sstreneth may also vary with hlunünositv., The strength may also vary with luminosity.
 Some studies have reported the inverse relationship between EEW aud UV huninosity (e.g.Shapleyetal.2003:Andoetal.2006:Reddyct2008:Stark2010).. while others claimed that the relation is not obvious or there is no such relation (e.g.Nilssonetal.2009).," Some studies have reported the inverse relationship between EW and UV luminosity \citep[e.g.][]{sha03,and06,red08,sta10}, while others claimed that the relation is not obvious or there is no such relation \citep[e.g.][]{nil09}."
. Figure 3 shows the EEW as a function of the σοιπια. luninosity Mq300 for our sample., Figure 3 shows the EW as a function of the continuum luminosity $M_{1300}$ for our sample.
 The dashed line demonstrates the detection lunit for galaxies at 2=6.2., The dashed line demonstrates the detection limit for galaxies at $z=6.2$.
 The apparent strong correlation between EW aud AAsgy 1n our saniple is likely due to the nature of fiux-linüted sivevs., The apparent strong correlation between EW and $M_{1300}$ in our sample is likely due to the nature of flux-limited surveys.
 Nevertheless. our saniple has a similar Iuninositv range as the range of the +—3 LBC sample mentioned above.," Nevertheless, our sample has a similar luminosity range as the range of the $z\sim3$ LBG sample mentioned above."
 Tn the nest section we will use the EW? distribution at Do3 (Reddy&Steidel2009). to correct for sample incompleteness., In the next section we will use the EW distribution at $z\sim3$ \citep{red09} to correct for sample incompleteness.
 The galaxies preseuted in this paper provide a well-defined flux-limited ealaxv sample down to :/=27, The galaxies presented in this paper provide a well-defined flux-limited galaxy sample down to $z'=27$.
 The effective area is ~210 arcudu? (five DEIMOS mask coverage) and the redshift rauge is 6x:x6.1., The effective area is $\sim340$ $^2$ (five DEIMOS mask coverage) and the redshift range is $6\le z\le6.4$ .
" In the following subsections we will correct for salple incompleteness. calculate the spatial density of the galaxies. and derive the galaxy LF in this redshift range,"," In the following subsections we will correct for sample incompleteness, calculate the spatial density of the galaxies, and derive the galaxy LF in this redshift range."
 Due to various selection criteria that we applied. our sample is incomplete.," Due to various selection criteria that we applied, our sample is incomplete."
 The sample coupletcucss is complicated., The sample completeness is complicated.
 Tere we correct for inconleteuess which originates fπα three major steps. μ.ο... detection. galaxy caiidate selection. aud. spectroscopic identification.," Here we correct for incompleteness which originates from three major steps, source detection, galaxy candidate selection, and spectroscopic identification."
 The first major iuconipleteness comes from the detection of sources iu the SDF image., The first major incompleteness comes from the detection of sources in the SDF image.
 Because the SDF fie dois crowded. any Πο]του» ealaxies behind forceround objects are not detected.," Because the SDF field is crowded, any high-redshift galaxies behind foreground objects are not detected."
 It is straightforward to calculate this incorleteuess by nicasumriue the fraction of the area occupied by bright objects., It is straightforward to calculate this incompleteness by measuring the fraction of the area occupied by bright objects.
 There is another source of iucoimipleteuess due to the fact that fainter objects are more difficult to detect., There is another source of incompleteness due to the fact that fainter objects are more difficult to detect.
 We put a laree number of simulated galaxies (poiut sources) in the SDF z baud image and detect them using (Bertin&Arnouts1996) in the wav uxed for our galaxy candidate detection., We put a large number of simulated galaxies (point sources) in the SDF $z'$ -band image and detect them using \citep{ber96} in the way used for our galaxy candidate detection.
 We then measure the completeness as a fiction of magnitude z by couutius the fraction of detections., We then measure the completeness as a function of magnitude $z'$ by counting the fraction of detections.
 The combined completeness is ala Vox25 and drops to ~65 at ., The combined completeness is about at $z'<25$ and drops to $\sim65$ at $z'=27$.
 The second major incompleteness comes from the magnitude limit (z 27) aud color cut (.i 1.1) that we applied to the candidate selection., The second major incompleteness comes from the magnitude limit $z'<27$ ) and color cut $i'-z'>1.7$ ) that we applied to the candidate selection.
 The last major iuconipleteness is from the fact that our sample is biased towards LBGs with stroug eCluission. as discussed above.," The last major incompleteness is from the fact that our sample is biased towards LBGs with strong emission, as discussed above."
" We cannot identity LBCs with ffüuxes below our detection limit in the DEIMOSspectra,", We cannot identify LBGs with fluxes below our detection limit in the DEIMOSspectra.
 We use a selection function to correct these incompletcuesses., We use a selection function to correct these incompletenesses.
 The selection fiction is defined as the probability that a galaxy with a given magnitude. redshift. aud intrinsic spectral energy. distribution (SED) meets the criteria of our candidate selection aud," The selection function is defined as the probability that a galaxy with a given magnitude, redshift, and intrinsic spectral energy distribution (SED) meets the criteria of our candidate selection and"
the reported upper limits.,the reported upper limits.
 The non-Gaussian distribution of the SZE is very important on small patches of sky (??)..," The non-Gaussian distribution of the SZE is very important on small patches of sky \citep{cooray2001,zhang2006}."
 We incorporate the non-Gaussian statistics into our analysis by returning to the set of simulated SZ skys (?)., We incorporate the non-Gaussian statistics into our analysis by returning to the set of simulated SZ skys \citep{shaw2009}.
 We extract 7500 independent realizations of the APEX-SZ map and calculate the power in each realization under the two masks., We extract 7500 independent realizations of the APEX-SZ map and calculate the power in each realization under the two masks.
 The maps have been convolved by the experimental beam and do not include noise., The maps have been convolved by the experimental beam and do not include noise.
" This process maps out the full, non-Gaussian cosmic variance of the expected SZE power for og=0.77."," This process maps out the full, non-Gaussian cosmic variance of the expected SZE power for $\sigma_8 = 0.77$."
" We scale this to other cosmologies by assuming that the probability of measuring a power X will scale with og as Bayes’ theorem with a flat prior in og is applied to find a posterior probability density, P(og|X)."," We scale this to other cosmologies by assuming that the probability of measuring a power X will scale with $\sigma_8$ as Bayes' theorem with a flat prior in $\sigma_8$ is applied to find a posterior probability density, $P(\sigma_8| X)$."
 We determine the probability of a given SZE power from the data by marginalizing over a point source component as described in the last paragraph., We determine the probability of a given SZE power from the data by marginalizing over a point source component as described in the last paragraph.
" Finally, the likelihood function of og given the APEX-SZ data d is calculated by and integrated to find the CL upper limit on og."," Finally, the likelihood function of $\sigma_8$ given the APEX-SZ data ${\bf d}$ is calculated by and integrated to find the CL upper limit on $\sigma_8$."
" The limit rises to og<1.18, substantially weaker than the limit of og<0.94 derived under Gaussian assumptions (see the third row of Table 2,, labeled “Unconstrained og”)."," The limit rises to $\sigma_8 < 1.18$, substantially weaker than the limit of $\sigma_8 < 0.94$ derived under Gaussian assumptions (see the third row of Table \ref{tab:params}, labeled “Unconstrained $\sigma_8$ "")."
" The marginalized likelihood function for both og and are plotted in Figure 2,, while the 2d likelihood CP*surface for both parameters is shown in Figure 3.."," The marginalized likelihood function for both $\sigma_8$ and $C_\ell^{PS}$ are plotted in Figure \ref{FIG:like1d}, while the 2d likelihood surface for both parameters is shown in Figure \ref{FIG:like2d}."
 The upper limit is sensitive to the prior chosen since APEX-SZ does not make a detection of SZE power., The upper limit is sensitive to the prior chosen since APEX-SZ does not make a detection of SZE power.
" A flat prior on power, og, strongly prefers higher values of og than the flat prior on σε, and raises the upper limit from 1.18 to σε<1.50 at CL."," A flat prior on power, $\sigma_8^7$, strongly prefers higher values of $\sigma_8$ than the flat prior on $\sigma_8$, and raises the upper limit from 1.18 to $\sigma_8 < 1.50$ at CL."
 This is entirely due to the weighting by the prior as the prior probability for cg=2 is 240 times the probability of og=0.8., This is entirely due to the weighting by the prior as the prior probability for $\sigma_8 = 2$ is 240 times the probability of $\sigma_8=0.8$.
" Finally, we combine the four APEX-SZ band powers into a single band to facilitate the comparison to other data sets."," Finally, we combine the four APEX-SZ band powers into a single band to facilitate the comparison to other data sets."
" The resulting upper limit is ~100K? after including the APEX-SZ calibration and beam uncertainty as shown in the last row of Table 2,, “Flat Excess”."," The resulting upper limit is $\sim 100\, \mu$ $^2$ after including the APEX-SZ calibration and beam uncertainty as shown in the last row of Table \ref{tab:params}, “Flat Excess""."
" We have assumed that D, is constant across the four bands and subtracted the contribution due to the primary CMB anisotropies.", We have assumed that ${\it D}_\ell$ is constant across the four bands and subtracted the contribution due to the primary CMB anisotropies.
" However, this upper limit does not include a non-Gaussian contribution to cosmic variance."," However, this upper limit does not include a non-Gaussian contribution to cosmic variance."
 Submillimeter bright galaxies and radio sources are expected to dominate the primary temperature anisotropies for £22500 at 150 GHz., Submillimeter bright galaxies and radio sources are expected to dominate the primary temperature anisotropies for $\ell \gtrsim 2500$ at 150 GHz.
" The exact contribution from point sources, especially radio sources, will depend on our ability to detect and mask the brightest sources."," The exact contribution from point sources, especially radio sources, will depend on our ability to detect and mask the brightest sources."
" The exact 36 detection threshold in the APEX-SZ map depends on the map position due to the uneven coverage, but is approximately 2 mJy on average."," The exact $\,\sigma$ detection threshold in the APEX-SZ map depends on the map position due to the uneven coverage, but is approximately 2 mJy on average."
" As discussed below, the predicted band powers are fairly insensitive to the precise cut level unless it shifts by an order of magnitude."," As discussed below, the predicted band powers are fairly insensitive to the precise cut level unless it shifts by an order of magnitude."
 We assume both populations are drawn from Poisson distribution., We assume both populations are drawn from a Poisson distribution.
" The number acounts of dusty, submillimeter bright galaxies are modeled in ? based on surveys at higher frequencies."," The number counts of dusty, submillimeter bright galaxies are modeled in \citet{negrello2007} based on surveys at higher frequencies."
" Deep, high-resolution maps of the 150 GHz"," Deep, high-resolution maps of the 150 GHz"
(=HJD 22455224.94346) at V=7.8mmag (?)..,$=$ 2455224.94346) at $V=7.8$ mag \citep{iauc9111}.
" ? extrapolated the light curve to earlier times, indicating that the peak magnitude was V=7.5 on 2010 Jan 28.1 (=JD 22455224.605), and that the time of outburst was This time is used as the reference time to in this article."," \cite{usco_discovery} extrapolated the light curve to earlier times, indicating that the peak magnitude was $V=7.5$ on 2010 Jan 28.1 $=$ 2455224.605), and that the time of outburst was This time is used as the reference time $t_0$ in this article."
 The underlying system was identified as an eclipsing system by ? with an inclination angle of Z80° (?).., The underlying system was identified as an eclipsing system by \cite{schaefer_eclipse} with an inclination angle of $\stackrel{>}{_\sim}80^{\rm o}$ \citep{thoroughgood01}.
" Based on 29 accurate eclipse times from 2001-2009, we find a best fit linear ephemeris in units of days to be where E is an integer that counts the cycles."," Based on 29 accurate eclipse times from 2001-2009, we find a best fit linear ephemeris in units of days to be where $E$ is an integer that counts the cycles."
" The binary separation is 6.5+ 0.4RRo (?), and the component masses have been determined by ? to be >1.31 MM, for the white dwarf and 0.88+0.17 MM for the secondary."," The binary separation is $6.5\,\pm\,0.4$ $_\odot$ \citep{schaefer_eclipse}, and the component masses have been determined by \cite{thoroughgood01} to be $>1.31$ $_\odot$ for the white dwarf and $0.88\,\pm\,0.17$ $_\odot$ for the secondary."
" The radius of the companion is 0.2RRo, indicating that it is evolved (?)."," The radius of the companion is $2.1\,\pm\,0.2$ $_\odot$, indicating that it is evolved \citep{schaefer_eclipse}."
" The high mass of the white dwarf, close to the Chandrasekhar mass limit, is consistent with the short recurrence time scale and led to speculations that SSco may be a supernova Ia progenitor (?).."," The high mass of the white dwarf, close to the Chandrasekhar mass limit, is consistent with the short recurrence time scale and led to speculations that Sco may be a supernova Ia progenitor \citep{starrf88}."
" However, recent abundance measurements by ? indicate that the underlying white dwarf may of the ONeMg kind which does not contain enough nuclear binding energy for a IIa exposion."," However, recent abundance measurements by \cite{mason2011} indicate that the underlying white dwarf may of the ONeMg kind which does not contain enough nuclear binding energy for a Ia exposion."
" Consequently, even if the Chandrasekhar mass limit is reached, the white dwarf may turn into a neutron star via core collapse."," Consequently, even if the Chandrasekhar mass limit is reached, the white dwarf may turn into a neutron star via core collapse."
" XX-ray and UV monitoring started within a day after discovery (?,, but there was no X-ray detection until 2010 Jan 31 (day 4)."," X-ray and UV monitoring started within a day after discovery \citealt{atel2419}, but there was no X-ray detection until 2010 Jan 31 (day 4)."
 The XX-ray and UV light curves shown in Fig., The X-ray and UV light curves shown in Fig.
 1 will be discussed in more detail by Pagnotta et al. (, \ref{swlc} will be discussed in more detail by Pagnotta et al. (
in preparation).,in preparation).
" Until ~day 8, the X-ray light curve was essentially constant with weak, hard emission above kkeV (?).."," Until $\sim$ day 8, the X-ray light curve was essentially constant with weak, hard emission above keV \citep{atel2419}."
" On ~day 12, the ccount rate was found to be 100 times higher, exhibiting a supersoft spectrum (?) that resembles the class of supersoft sources "," On $\sim$ day 12, the count rate was found to be 100 times higher, exhibiting a supersoft spectrum \citep{atel2430} that resembles the class of supersoft sources (SSS, \citealt{kahab,heuvel}) )."
"At the same time, until ~day 12, the UV (SSS,flux ??)).dramatically decreased, supporting the picture of a shrinking photospheric radius, accompanied by a continuous increase in photospheric temperature."," At the same time, until $\sim$ day 12, the UV flux dramatically decreased, supporting the picture of a shrinking photospheric radius, accompanied by a continuous increase in photospheric temperature."
" Between days 12 and 25, no changes in X-ray and UV brightness were seen, while after day 25, another increase in X-rays with a simultaneous decrease in UV emission level occurred."," Between days 12 and 25, no changes in X-ray and UV brightness were seen, while after day 25, another increase in X-rays with a simultaneous decrease in UV emission level occurred."
" From day 14.25 - 17.54 after discovery, two well covered, and one partly covered, eclipses were seen in the UV light curve by ? who also reported that, in X-rays, no clear, sharp, deep or total eclipses were seen."," From day 14.25 - 17.54 after discovery, two well covered, and one partly covered, eclipses were seen in the UV light curve by \cite{ATel2442} who also reported that, in X-rays, no clear, sharp, deep or total eclipses were seen."
 The X-ray light curve was highly variable with typically lower flux around the time of eclipse., The X-ray light curve was highly variable with typically lower flux around the time of eclipse.
" Around 2010 Mar 8 (day to--~40ddays), the brightness ofSSco experienced a sharp drop in the X-ray/UV/Optical/IR bands (?),, indicating that nuclear burning had turned off."," Around 2010 Mar 8 (day $t_0\,+\sim 40$ days), the brightness ofSco experienced a sharp drop in the X-ray/UV/Optical/IR bands \citep{ATel2477}, indicating that nuclear burning had turned off."
" Reports of deeper and continuous aand oobservations taken on 2010 February 14 and 19 (t,=to+18.7 and tg=to+22.9 days), respectively were given by ? and ?.."," Reports of deeper and continuous and observations taken on 2010 February 14 and 19 $t_1=t_0+18.7$ and $t_2=t_0+22.9$ days), respectively were given by \cite{atel2451} and \cite{atel2469}."
" The times of these observations plus a second oobservation taken on £3=to+34.9 days are marked by gray shaded areas in Fig. 1,,"," The times of these observations plus a second observation taken on $t_3=t_0+34.9$ days are marked by gray shaded areas in Fig. \ref{swlc},"
 bracketing the respective start and stop times., bracketing the respective start and stop times.
" High-resolution X-ray grating spectra consist of photospheric continuum emission plus broad emission lines that varied greatly between the two observations (?),, yielding a systematic increase in flux in lines of higher ionization stage."," High-resolution X-ray grating spectra consist of photospheric continuum emission plus broad emission lines that varied greatly between the two observations \citep{atel2469}, yielding a systematic increase in flux in lines of higher ionization stage."
 Two 16-hour oobservations were carried out with start times 2010 February 19.65 =to+22.9 ddays) and 2010 March 3.7 (t3=to+34.9 ddays)., Two 16-hour observations were carried out with start times 2010 February 19.65 $t_2=t_0+22.9$ days) and 2010 March 3.7 $t_3=t_0+34.9$ days).
"(t9 Simultaneous X-ray light curves kkeV), X-ray spectra rrange, rresolution), and ultraviolet (UV) light curves and spectra rrange, rresolution) were extracted from the European Photon Imaging Camera (EPIC), the Reflection Grating Spectrometer (RGS), and the Optical Monitor (OM), respectively."," Simultaneous X-ray light curves keV), X-ray spectra range, resolution), and ultraviolet (UV) light curves and spectra range, resolution) were extracted from the European Photon Imaging Camera (EPIC), the Reflection Grating Spectrometer (RGS), and the Optical Monitor (OM), respectively."
" For day 22.9, 27 UV grism spectra (approximately 2000 seconds exposure time) were taken and were used to extract UV light curves by integrating over three different wavelength intervals: the full range,AA,, and the ranges aandAA."," For day 22.9, 27 UV grism spectra (approximately 2000 seconds exposure time) were taken and were used to extract UV light curves by integrating over three different wavelength intervals: the full range, and the ranges and."
". In addition, we extracted an uncalibrated zero-order light curve from the non-dispersed photons which represent the brightness over a broad wavelength band with central wavelength ~4000AA."," In addition, we extracted an uncalibrated zero-order light curve from the non-dispersed photons which represent the brightness over a broad wavelength band with central wavelength $\sim 4000$."
". Since the zero order is not flux calibrated, count rates are only presented as an indicator for relative brightness variations."," Since the zero order is not flux calibrated, count rates are only presented as an indicator for relative brightness variations."
" For day 34.9, only band-integrated fluxes are available but in high time resolution of the OM fast mode."," For day 34.9, only band-integrated fluxes are available but in high time resolution of the OM fast mode."
" Separate X-ray light curves were extracted in a soft kkeV) and a hard (0.5-1kkeV) band, $ and H, and were used to compute a spectral hardness light curve"," Separate X-ray light curves were extracted in a soft keV) and a hard keV) band, $S$ and $H$ , and were used to compute a spectral hardness light curve"
"Once mj, reaches the fragmentation barrier. growth bevond this stage would need to be treated in a different manner. lor example. by simple sweepup o£ small. less clisruplive parücles by large ones (Chizzietal.1993).","Once $m_L$ reaches the fragmentation barrier, growth beyond this stage would need to be treated in a different manner, for example, by simple sweepup of small, less disruptive particles by large ones \citep{cuz93}."
. Creation and disruption of these particles can be handled as part of the source and sink terms in which for example. disrupted particles are assumed (o be Iragmented back into a powerlaw distribution (which is suggested by experimental evidence and widelv assumed by other modelers) as opposed to monomers.," Creation and disruption of these particles can be handled as part of the source and sink terms in which for example, disrupted particles are assumed to be fragmented back into a powerlaw distribution (which is suggested by experimental evidence and widely assumed by other modelers) as opposed to monomers."
 The model as presented within this paper. however. should be useful lor the early stages of protoplanetary nebula particle erowth relevant to spectral energy distributions and MBI suppression.," The model as presented within this paper, however, should be useful for the early stages of protoplanetary nebula particle growth relevant to spectral energy distributions and MRI suppression."
 We leave (he incorporation of growth stages bevond the ellicient Iragmentation stage for a later paper., We leave the incorporation of growth stages beyond the efficient fragmentation stage for a later paper.
" Motivated by our ciseussion of the previous section. if we assume that the form οἱ the particle mass distribution function remains a powerlaw at all limes. we may express form)2em *. such that mm,(/) is the growing upper limit of the distribution. q is the slope which is assumed to be constant (although see below). and c(/) is a normalization coellicient."," Motivated by our discussion of the previous section, if we assume that the form of the particle mass distribution function remains a powerlaw at all times, we may express $f(m,t) = c(t)m^{-q}$ , such that $m_L(t)$ is the growing upper limit of the distribution, $q$ is the slope which is assumed to be constant (although see below), and $c(t)$ is a normalization coefficient."
 Taking the lower limit of the mass distribution to be img. then moments as expressed in Eq. (," Taking the lower limit of the mass distribution to be $m_0$, then moments as expressed in Eq. ("
2) are explicitly given for q—pz1 bv We then take (he time derivative of Eq. (,2) are explicitly given for $q-p\neq 1$ by We then take the time derivative of Eq. (
17) for the zeroth and second moments. ancl substitute these expressions on the LIIS of the corresponding moment equations in Eq. (,"17) for the zeroth and second moments, and substitute these expressions on the LHS of the corresponding moment equations in Eq. ("
5) lo gel whereEq. (,5) to get whereEq. (
18) is valid for ¢41. and Vy and E» are the integrals on the RIIS ofEq. (,"18) is valid for $q\neq 1$, and $\Gamma_0$ and $\Gamma_2$ are the integrals on the RHS ofEq. ("
5) for |—0 and &= 2. respectively.,"5) for $k=0$ and $k=2$ , respectively."
 That is, That is
radius rq which cau be estimated by equating the chauge in potential aud kinetic energies. leading to As there is flow still with positive radial moment behind this stalling front. a shell of stalled wind will form being supporte bv the riu pressure of the gas behiud it.,"radius $r_s$ which can be estimated by equating the change in potential and kinetic energies, leading to As there is flow still with positive radial momentum behind this stalling front, a shell of stalled wind will form being supported by the ram pressure of the gas behind it."
 Tf we assume that the shell be supported by the wind at some radius racy. then we can estimate the miaxiuun total mass in the shell.," If we assume that the shell be supported by the wind at some radius $r_{\rm shell}$, then we can estimate the maximum total mass in the shell."
" The supporting pressure P, of the stalling eas will je pe? where p is the density aud ο is the loca radial velocity.", The supporting ram-pressure $P_{\rm ram}$ of the stalling gas will be $\rho v^2$ where $\rho$ is the density and $v$ is the local radial velocity.
 Tle oppositely directec pressure generated by the shell is he due to the attractive eravitational force of the star CA.Mauirao where AL is the shel nass aud G is the gravitational constant., The oppositely directed pressure generated by the shell is the due to the attractive gravitational force of the star $G\mstar M_{\rm shell} /r_{\rm shell}^2$ where $M_{\rm shell}$ is the shell mass and $G$ is the gravitational constant.
 This force acts over the surface area of the shell Ira ," This force acts over the surface area of the shell $4\pi
r_{\rm shell}^2$."
Balancing the two oppositely directed pressures vields Uere we have used the mass-coutiuitv equation for spherical. flows A=lar>pe. where iis the mass-loss rate of the wind.," Balancing the two oppositely directed pressures yields Here we have used the mass-continuity equation for spherical flows $\mdot = 4\pi r^2 \rho v$, where is the mass-loss rate of the wind."
" If e=7/100kis+ and 0ΞAL/LOONL,yr|. then Note tha a distinction has been mace between the stalling radius c aud the radius of the shell r4."," If $v_2 = v / 100\kms$ and $_{-9} = \mdot / 10^{-9}\msunyr$, then Note that a distinction has been made between the stalling radius $r_s$ and the radius of the shell $r_{\rm shell}$."
 This is because the shell will only appear at the stalling radius if the wind firs expands out iuto a vacuui., This is because the shell will only appear at the stalling radius if the wind first expands out into a vacuum.
 If there is any auubieut deusity around the star pany. then this is swept up into the shell when the wind is “turned ou," If there is any ambient density around the star $\rho_{\rm amb}$, then this is swept up into the shell when the wind is “turned on”."
 The evolution of the wind will broadly be composed of several parts., The evolution of the wind will broadly be composed of several parts.
 Initially the wind will be driven into the surrounding medium aud will sweep up a shell of auubieut eas., Initially the wind will be driven into the surrounding medium and will sweep up a shell of ambient gas.
 This shell will stop expanding when the shell aud ram pressures balance., This shell will stop expanding when the shell and ram pressures balance.
 The shell then grows as it is receiving eas from the wind (at prestunably the same rate as the miass-loss rate from the star., The shell then grows as it is receiving gas from the wind (at presumably the same rate as the mass-loss rate from the star).
 Finally theshell becomes too massive to be supported and will fall back toward the star., Finally theshell becomes too massive to be supported and will fall back toward the star.
" Tf we assume that pays, is small then the shell radius the stalling radius.", If we assume that $\rho_{\rm amb}$ is small then the shell radius the stalling radius.
 Also the wind ram pressure in this. case is. the thermal pressure Dipa. where e isB the sound speed.," Also the wind's ram pressure in this case is the thermal pressure $\rho a^2$, where $a$ is the sound speed."
 For stalling radii of r;z5R=20. the shel lass for our standard star with a miass-loss rate of 10POAL twhich will be supported by the stalling wind is Af310TAL..., For stalling radii of $r_s \approx 5\rstar = 20\rsun$ the shell mass for our standard star with a mass-loss rate of $10^{-9.5}$ which will be supported by the stalling wind is $M_{\rm shell} \sim 3\times 10^{-14}\msun$.
 Given that the shell mass CYOWS a arate ofAL.. we find that it ix stable for a time which for the example above is txmlhr.," Given that the shell mass grows at a rate of, we find that it is stable for a time which for the example above is $t \approx 1$ hr."
 The timescales here are sinular to the flow timescale of the wind (approximately A.fe2:lhr for a wind speed of ij)., The timescales here are similar to the flow timescale of the wind (approximately $\rstar/v \approx 1$ hr for a wind speed of ).
 After this time the shells mass will have increased such that there is insufficient rani pressure to levitate the shell and so it will fall back to the star., After this time the shell's mass will have increased such that there is insufficient ram pressure to levitate the shell and so it will fall back to the star.
 As the shell falls inward. the wind rani pressure dnereases - both the wind deusitv aud the radial velocity ο increase (Mach iuubers in radiativelv driven flows can be ~100).," As the shell falls inward, the wind ram pressure increases - both the wind density and the radial velocity $v$ increase (Mach numbers in radiatively driven flows can be $\sim 100$ )."
 However. the increasing mass of the shell is now acting over a stnaller area.," However, the increasing mass of the shell is now acting over a smaller area."
 Heuce the effective pressure exerted by the shell inward due to the gravitational attraction by the ceutral star increases., Hence the effective pressure exerted by the shell inward due to the gravitational attraction by the central star increases.
" This pressure of the shell is the gravitational force divided by the area of the shell: Paci2κ|.‘whereas the ram pressure is+ Dua,X6/57.", This pressure of the shell is the gravitational force divided by the area of the shell: $P_{\rm shell} \propto r^{-4}$ whereas the ram pressure is $P_{\rm ram}\propto v/r^2$.
P The ratio of these two pressures is Note that iu the decoupled part of the wind e~r1/2 aud so as ALGaq dacreases and moves toward the star ή decreases) the ratio above grows.," The ratio of these two pressures is Note that in the decoupled part of the wind $v \sim r^{-1/2}$, and so as $M_{\rm shell}$ increases and moves toward the star $r$ decreases) the ratio above grows."
 This then implies that the shell can not be stable (halanced) at anv racius. aud must fall back to he star.," This then implies that the shell can not be stable (balanced) at any radius, and must fall back to the star."
 Once the shel has coutracted to the star. the wind is free again to expand to its stalling poiut aud the cvele restarts.," Once the shell has contracted to the star, the wind is free again to expand to its stalling point and the cycle restarts."
 This analvsis predicts that stars with botid decoupled winds will inevitably produce »oiodic structures associated with the wiud., This analysis predicts that stars with bound decoupled winds will inevitably produce periodic structures associated with the wind.
 However. a word of caution is wiarrauted here: this scenario predicts that a shell of eas should forma aud collapse onto the star with timescales of hoursdavs.," However, a word of caution is warranted here: this scenario predicts that a shell of gas should form and collapse onto the star with timescales of hours–days."
 There is a possibility that the oppositely directed eravity aud pressure gradieuts as the shell contracts may. break up the shell due to Ravleigh-Tavlor iustabilitics., There is a possibility that the oppositely directed gravity and pressure gradients as the shell contracts may break up the shell due to Rayleigh-Taylor instabilities.
 To illustrate the preceeding sectiow’s scenario. a 1D munerical hydrodynamic simulation has been complete.," To illustrate the preceeding section's scenario, a 1D numerical hydrodynamic simulation has been completed."
 The computer code utilises the second order CGodonuv scheme due to Falle (1991) to solve the lvdrodvuamiuc equations., The computer code utilises the second order Godonuv scheme due to Falle (1991) to solve the hydrodynamic equations.
" The line force is calculated using the standard Castor. Abbott Kleiu (1976) formalism, of the force uultiplicr. suppleimeutec with the finite-dise correction (Friend Abbott 1986) and the deusity weighting factor yon Abbott (1982)."," The line force is calculated using the standard Castor, Abbott Klein (1976) formalism of the force multiplier, supplemented with the finite-disc correction (Friend Abbott 1986) and the density weighting factor from Abbott (1982)."
 The erid has a spacing of at r=R increasing by to a maxinun spacing of at the outer radius of (there are 200 eid poiuts).," The grid has a spacing of at $r =$, increasing by to a maximum spacing of at the outer radius of (there are 200 grid points)."
" The outer boundary allows ooOas to flow through it freely whereas the inner ποπασ has the density ⋅⋅fixed at :10.5 te a Ὁ, aud the velocity extrapolated from the ucighbouring zones."," The outer boundary allows gas to flow through it freely, whereas the inner boundary has the density fixed at $10^{-12}$ g $^{-3}$ , and the velocity extrapolated from the neighbouring zones."
 We cau expect that after a time the radial velocity at the outer, We can expect that after a time the radial velocity at the outer
This difference in the optical spectra is due to the fact that the huuimositv of a M-tvpe giant is ~10°° cre 1 (iiost of which is euütted iu the optical aud neariufrared ranges). thus only iu case of laree Xraw huuinosities can spectral features produced by accretion enmieree iu the optical spectrmu.,"This difference in the optical spectra is due to the fact that the luminosity of a M-type giant is $\sim$ $^{36}$ erg $^{-1}$ (most of which is emitted in the optical and near-infrared ranges), thus only in case of large X–ray luminosities can spectral features produced by accretion emerge in the optical spectrum."
 It is thought that this cdiffereuce steuis from the mass accretion rate and therefore from the evolution of the svstem. CN L1tl being likely tighter aud more evolved according to Caudenzi Polcaro (1999).," It is thought that this difference stems from the mass accretion rate and therefore from the evolution of the system, GX 1+4 being likely tighter and more evolved according to Gaudenzi Polcaro (1999)."
 All of these systems are suspected to host a neutron star (NS)., All of these systems are suspected to host a neutron star (NS).
 Towever. oulv for sources CX 11 Laud Sct N-1. aud possibly for IU 19511231. is the nature of the accretor known: their Xrav enission is pulsed. indicating that the accreting object is indeed a NS (Lewin et al.," However, only for sources GX 1+4 and Sct X-1, and possibly for 4U 1954+31, is the nature of the accretor known: their X–ray emission is pulsed, indicating that the accreting object is indeed a NS (Lewin et al."
 1971: Iovania ct al., 1971; Koyama et al.
 1991: Corhet et al., 1991; Corbet et al.
 2006. 2007).," 2006, 2007)."
 The system IU 17002 Louly cdisplavs random X.ray variability: however. this is more likely due to ecometric effects rather than to different type of accretor (Masoetti ct al.," The system 4U 1700+24 only displays random X–ray variability: however, this is more likely due to geometric effects rather than to a different type of accretor (Masetti et al."
 2002)., 2002).
 Here we present the discovery of the fifth member of the SvyNB subclass: source IGR 2810., Here we present the discovery of the fifth member of the SyXB subclass: source IGR $-$ 2810.
 This source was first detected in hard Xrays above 20 keV withINTEGRAL. in the 28! IBIS survey (Bird ct al.," This source was first detected in hard X–rays above 20 keV with, in the $^{\rm nd}$ IBIS survey (Bird et al."
 2006: see also the 3°! IBIS survey of Bird et al., 2006; see also the $^{\rm rd}$ IBIS survey of Bird et al.
 2007) aud in the IBIS extragalactic survey of Bassani et al. (, 2007) and in the IBIS extragalactic survey of Bassani et al. (
2006). at a 20100 keV flux of 3410. H erg 2st. ASSUME a Crab-like spectra.,"2006), at a 20–100 keV flux of $\sim$ $\times$ $^{-11}$ erg $^{-2}$ $^{-1}$, assuming a Crab-like spectrum."
 Through positional cross-correlation analvsis. Stephen et al (," Through positional cross-correlation analysis, Stephen et al. ("
2006) associated this ciission with theROSAT source 1RNS 280736 (Voges et al,2006) associated this emission with the source 1RXS $-$ 280736 (Voges et al.
 1999). which has a flux of L1«10 H ere 2 | in the L12.L keV band. again assuniue a Crab-like Spectruni.," 1999), which has a flux of $\times$ $^{-11}$ erg $^{-2}$ $^{-1}$ in the 0.1–2.4 keV band, again assuming a Crab-like spectrum."
 Ou statistical grounds. Stephen et al. (," On statistical grounds, Stephen et al. ("
2006) pointed ou that this source is most likely the soft Nταν counterpart of IGR 2810.,2006) pointed out that this source is most likely the soft X–ray counterpart of IGR $-$ 2810.
" The S""-radiusROSAT XNταν eror OX enconipasses 2 relatively bright optical objects (sce Fig.", The $''$ -radius X–ray error box encompasses 3 relatively bright optical objects (see Fig.
 1)., 1).
 In order to better study this source in the soft Nrav band. aud to reduce its error circle to piupoiut its optical counterpart. we performed observatious with with the XBav Telescope (XRT. 0.3.10 keV: Durrows et al.," In order to better study this source in the soft X–ray band, and to reduce its error circle to pinpoint its optical counterpart, we performed observations with with the X–Ray Telescope (XRT, 0.3–10 keV; Burrows et al."
 2006) on board (Golirels et al., 2006) on board (Gehrels et al.
 2001)., 2004).
 These observations were part of our program of follow-up poiutiues of sources at soft Nravs with Susft/XRT., These observations were part of our program of follow-up pointings of sources at soft X–rays with /XRT.
" The capabilities of NRT allow the position of an X source to be determined with au uucertaüntv which can be better than 1"". aud can secure a nominal spectra coverage between 0.3 and LO keV. We also collected. Lave Nταν archival data of TIGR 2810 with the IBIS iustunent (Ubertini et al."," The capabilities of XRT allow the position of an X--ray source to be determined with an uncertainty which can be better than $''$, and can secure a nominal spectral coverage between 0.3 and 10 keV. We also collected hard X–ray archival data of IGR $-$ 2810 with the IBIS instument (Ubertini et al."
 2003) on board (Winkler et al., 2003) on board (Winkler et al.
 2003)., 2003).
 In parallel. we performed optica spectroscopic observations of the field of this source at the South African Astronomical Observatory (SAAO).," In parallel, we performed optical spectroscopic observations of the field of this source at the South African Astronomical Observatory (SAAO)."
 The paper is structured as follows: Sect., The paper is structured as follows: Sect.
 2 alc 3 will present Xrav ancl optical observations of ICR 2810. respectively: in Sect.," 2 and 3 will present X–ray and optical observations of IGR $-$ 2810, respectively; in Sect."
 the results of this multiwavelength campaign will be eiven. aud iu Sect.," 4 the results of this multiwavelength campaign will be given, and in Sect."
 5 a discussion ou them will be preseuted., 5 a discussion on them will be presented.
 Finally. Sect.," Finally, Sect."
 6 will draw the couclusious aud will outline possible future work. ou this source., 6 will draw the conclusions and will outline possible future work on this source.
 Throughout the paper. uncertainties are eiven at a confidence level.," Throughout the paper, uncertainties are given at a confidence level."
 We observed the field of IGR 2810 with ART onboardSwift twice: both poiutigs were performed iu Photon Counting mode (see Burrows et al., We observed the field of IGR $-$ 2810 with XRT onboard twice; both pointings were performed in Photon Counting mode (see Burrows et al.
 2006 for details ou this observing mode)., 2006 for details on this observing mode).
 The log of these observations 1s reported in Table 1., The log of these observations is reported in Table 1.
 The data reduction was performed using the NRTDAS v2.0.1 standard data pipeline package vO.10.6) in order to produce the final cleaned eveut fles., The data reduction was performed using the XRTDAS v2.0.1 standard data pipeline package v0.10.6) in order to produce the final cleaned event files.
 Asin both observations the NRT count rate of the source was high cuough to produce data pile-up. we extracted the eveuts in an annulus centered on the source aud 177 wide.," As in both observations the XRT count rate of the source was high enough to produce data pile-up, we extracted the events in an annulus centered on the source and $''$ wide."
 The size of the imner circle was determined following the procedure described in Romano et al. (, The size of the inner circle was determined following the procedure described in Romano et al. (
2006) and was it for the first observation aud 177 for the,2006) and was $''$ for the first observation and $\farcs$ 7 for the
Before prescuting the results from the WALAP analysis. we consider the question of convergence.,"Before presenting the results from the WMAP analysis, we consider the question of convergence."
 First. we compute the Gchuau-Rubin statistic (Gelman&Rubin1992) for cach σι using the eight chains computed with Connuauder and removing the first 20 samples for in.," First, we compute the Gelman-Rubin statistic \citep{gelman:1992} for each $\sigma_{\ell}$ using the eight chains computed with Commander and removing the first 20 samples for burn-in."
 We Bud that Ro Lis less than 0.01 for 6S300 and less than 1.1 for (=500. indicating very good convergence in terms of power spectra.," We find that $R-1$ is less than 0.01 for $\ell \lesssim 300$ and less than 1.1 for $\ell \lesssim 500$, indicating very good convergence in terms of power spectra."
 However. the fact that each o individually is well converged does uot automatically imply that the full likehhood is well converged. since the latter depends crucially ou the correlations between as. To assess the convergence in terms of cosmological parameters. we therefore analyse a tov model. bv fitting a simple amplitude aud tilt. 4 aud à». model. to the WMAPDP data between {=2 aud 250 with the GBR likelihood.," However, the fact that each $\sigma_{\ell}$ individually is well converged does not automatically imply that the full likelihood is well converged, since the latter depends crucially on the correlations between $\sigma_{\ell}$ 's. To assess the convergence in terms of cosmological parameters, we therefore analyse a toy model, by fitting a simple amplitude and tilt, $q$ and $n$, model, to the WMAP data between $\ell=2$ and 250 with the GBR likelihood."
 Mere Crd isa fiducial power spectrum. which is chosen to be the best-fit S-vear WMAP ACDM power spectra (Ποιατσetal.2008).. and (yivor=150.," Here $C_{\ell}^{\textrm{fid}}$ is a fiducial power spectrum, which is chosen to be the best-fit 5-year WMAP $\Lambda$ CDM power spectrum \citep{komatsu:2008}, and $\ell_{\textrm{pivot}}=150$."
 We then map out the likelihood in a erid over q aud ον, We then map out the likelihood in a grid over $q$ and $n$.
 This is repeated twice. first including samples from chains number 1 to land then from chains nuuber 5 to .," This is repeated twice, first including samples from chains number 1 to 4 and then from chains number 5 to 8."
 The results from this exercise are shown iu Figure 2 iu ternis of two sets of likelihood contours. corresponcdiug to each of the two chain sets; respectively.," The results from this exercise are shown in Figure \ref{fig:qn_model}
 in terms of two sets of likelihood contours, corresponding to each of the two chain sets, respectively."
 The agreement between the two is excellent. indicating that we also have good couvergence in terms of cosmological parameters with the existing sample set.," The agreement between the two is excellent, indicating that we also have good convergence in terms of cosmological parameters with the existing sample set."
 Note also that the poiut (q.n)=(1.0) lies well inside the la confidence region. indicating that the best-fit WALTAP model. which is obtained including Cs between (=2 aud 1021. also is a good fit to (=2 to 250 separately.," Note also that the point $(q,n) = (1,0)$ lies well inside the $1\sigma$ confidence region, indicating that the best-fit WMAP model, which is obtained including $\ell$ 's between $\ell=2$ and 1024, also is a good fit to $\ell=2$ to 250 separately."
" Third. as described in refsecinethod.. we construct the CBR covariance matrix frou N=O(10°) C, samples draw from the Ganaller) set of a samples."," Third, as described in \\ref{sec:method}, we construct the GBR covariance matrix from $N=\mathcal{O}(10^6)$ $C_{\ell}$ samples drawn from the (smaller) set of $\sigma_{\ell}$ samples."
 An outstanding question is how laree should be im order for this covariance matrix to reach convergence. as a function of fax.," An outstanding question is how large $N$ should be in order for this covariance matrix to reach convergence, as a function of $\ell_{\textrm{max}}$."
" To settle this question. we carry out the following simple exercise: First we produce two C, sample sets. each containing IN salples. and all drawn from a sinele 6; sample."," To settle this question, we carry out the following simple exercise: First we produce two $C_{\ell}$ sample sets, each containing $N$ samples, and all drawn from a single $\sigma_{\ell}$ sample."
 Secoud. we compute the two corresponding covariance matrices. invert these. then subtract them from cach other. and finally compute the standard deviation of all elemoeuts.," Second, we compute the two corresponding covariance matrices, invert these, then subtract them from each other, and finally compute the standard deviation of all elements."
 Third. we define the inverse covariance matrix to be converged if the RAIS MICAIC noise is less than 0.005. corresponding to of the diagonal eleiieuts. (," Third, we define the inverse covariance matrix to be converged if the RMS MCMC noise is less than 0.005, corresponding to of the diagonal elements. ("
We have checked that this produces robust parameter estimates.),We have checked that this produces robust parameter estimates.)
 We then fud the zinallest No such that this is satisfied. as a function of (ius," We then find the smallest $N$ such that this is satisfied, as a function of $\ell_{\textrm{max}}$."
 The results from this exercise are shown in Figure 3.., The results from this exercise are shown in Figure \ref{fig:covar_convergence}.
 Tere we see that the nuniber of samples required for convergence rises rapidly up to (~30. reaching a niudunun of ~8<101 samples. and then flattens to a plateau.," Here we see that the number of samples required for convergence rises rapidly up to $\ell\sim30$, reaching a maximum of $\sim8\times10^4$ samples, and then flattens to a plateau."
 To be ou the sate side. we therefore always use either 5«10? or 109 samples iu the WALAP analvsis.," To be on the safe side, we therefore always use either $5\times10^5$ or $10^6$ samples in the WMAP analysis."
 The reason for this behaviour becomes intuitive when considering the structure of the actual matrix., The reason for this behaviour becomes intuitive when considering the structure of the actual matrix.
 This is shown in Figure [. ou the form of a correlation matrix The nuu features of tlis matrix are negative correlations around the diagonal. with the largest auplitudes observed between ( aud (+2.," This is shown in Figure \ref{fig:covar}, on the form of a correlation matrix The main features of this matrix are negative correlations around the diagonal, with the largest amplitudes observed between $\ell$ and $\ell\pm2$."
 This is expected: First. two modes separated by Af=I have different parity. and can therefore not casily mimic cach other.," This is expected: First, two modes separated by $\Delta\ell=1$ have different parity, and can therefore not easily mimic each other."
 Ou the other laud. modes separated by Af=2 have both identical paritv and similar angular scale. id it is therefore possible to add power to oue mode id subtract it from the other. aud still maintain au essentially unchanged image.," On the other hand, modes separated by $\Delta\ell=2$ have both identical parity and similar angular scale, and it is therefore possible to add power to one mode and subtract it from the other, and still maintain an essentially unchanged image."
 The result is a noticeable iticorrelation between f£ aud (c 2., The result is a noticeable anti-correlation between $\ell$ and $\ell\pm2$ .
eravitational lens systems.,gravitational lens systems.
 These surveys have discovered. 18 lenses among a sample of ~ 12000 [lat-spectrum radio sources (Browne Myers 2000; Browne et 22001: Myers et 22001)., These surveys have discovered 18 lenses among a sample of $\simeq$ 12000 flat-spectrum radio sources (Browne Myers 2000; Browne et 2001; Myers et 2001).
 A robust statistical analvsis requires that careful ents be made to the above sample. and this will be discussed in detail by Browne et al.," A robust statistical analysis requires that careful cuts be made to the above sample, and this will be discussed in detail by Browne et al."
 ILowever. because preliminary estimates indicate that the lensing rate will not differ much from the 1/600 value derived here. we will assume a sample of 18 lenses and 12000 sources in the present analysis.," However, because preliminary estimates indicate that the lensing rate will not differ much from the $\simeq
1/600$ value derived here, we will assume a sample of 18 lenses and 12000 sources in the present analysis."
 Raw optical depths must be corrected to account for the magnification bias. which leads lo an over-representation of lensed sources in any Εικπο sample (e.$.. Turner et 11984: Maoz hix 1993).," Raw optical depths must be corrected to account for the magnification bias, which leads to an over-representation of lensed sources in any flux-limited sample (e.g., Turner et 1984; Maoz Rix 1993)."
 Magnilication bias enhances the lensing probability of sources in a bin of total flux density (5) by thefactor BGS)=o!(5)fdpPGQoCS/p). where OLS) is the source luminosity finetion and. P(gji)is the distribution of total magnifications (up=ulii. where the magnilication of the /th image is j/) produced by the lens.," Magnification bias enhances the lensing probability of sources in a bin of total flux density $S$ ) by thefactor $B(S) =
\phi^{-1}(S) \int d\mu\,\mu^{-1} P(\mu) \phi(S/\mu)$, where $\phi(S)$ is the source luminosity function and $P(\mu)$is the distribution of total magnifications $\mu = \sum_i |\mu_i|$, where the magnification of the $i$ th image is $\mu_i$ ) produced by the lens."
" The sources probed by CLASS are well-represented bv a power-law Iuminosity finetion. xS ""with ye2.1 (Rusin Tegmark 2001)."," The sources probed by CLASS are well-represented by a power-law luminosity function, $\phi(S) = dn/dS \propto S^{-\eta}$ , with $\eta \simeq 2.1$ (Rusin Tegmark 2001)."
" The bias thus reduces (o a simple form that is independent of flux densitv: B=<j""|>.", The bias thus reduces to a simple form that is independent of flux density: $B = <\mu^{\eta-1}>$.
 An SIS lens produces total magnilications described by the probability distribution P(gj)—8j νο ify =2.1. Bajs=4.76.," An SIS lens produces total magnifications described by the probability distribution $P(\mu) = 8 \mu^{-3}$; so if $\eta = 2.1$, $B_{SIS} =
4.76$."
 The cross sections of all SIS lenses are enhanced by this factor., The cross sections of all SIS lenses are enhanced by this factor.
 The situation is more complicated for the NEW profile as its lensing properties depend on Ay. which in turn depends on the halo mass aud the angular distances to the halo and the source.," The situation is more complicated for the NFW profile as its lensing properties depend on $\kappa_0$, which in turn depends on the halo mass and the angular distances to the halo and the source."
 We compute numerically the magnilications produced by NEW halos for 0.1«fy<10 and use this to tabulate Εν(η).," We compute numerically the magnifications produced by NFW halos for $0.1
< \kappa_0 < 10$ and use this to tabulate $B_{NFW}(\kappa_0)$."
 For the sources in the JVAS/CLASS survev. the redshift distribution is still poorly understood but the mean redshift is estimated to be <2.>=1.27 (Marlow et al.," For the sources in the JVAS/CLASS survey, the redshift distribution is still poorly understood but the mean redshift is estimated to be $<z_s>=1.27$ (Marlow et al."
 2000)., 2000).
 Since the lower flux source distribution of the JVAS/CLASS survey is inclistinenishable from the complete. brighter source distribution of the Caltech-Jodrell Bank VLBI sample (Ilenstock et al.," Since the lower flux source distribution of the JVAS/CLASS survey is indistinguishable from the complete, brighter source distribution of the Caltech-Jodrell Bank VLBI sample (Henstock et al."
 1997). we assume the latter quasar distribution for ές} in eq. (," 1997), we assume the latter quasar distribution for ${\cal P}(z_s)$ in eq. ("
1).,1).
 Fig., Fig.
 | compares the JVAS/CLASS data with the predicted lensing probabilities P(>8) calculated [rom eq. (, 1 compares the JVAS/CLASS data with the predicted lensing probabilities $P(>\theta)$ calculated from eq. (
1) for the ACDM. model] and models with «=—2/3.—1/2.-1/3.,"1) for the $\LCDM$ model and models with $\omega=-2/3, -1/2, -1/3$."
" The probability at @=4"" decreases rapidly as w increases towards 0.", The probability at $\theta\ga 4''$ decreases rapidly as $\omega$ increases towards 0.
 The most important systematics that affect. wide separation lensing are due to the halo concentration parameter c(M.z).," The most important systematics that affect wide separation lensing are due to the halo concentration parameter $c(M,z)$."
 In Fig., In Fig.
" 2a we quantify the dependence of P(>4"") on both w and the coellicient ol e(M.z). e,=e(M,.z 0)."," 2a we quantify the dependence of $P(>4'')$ on both $\omega$ and the coefficient of $c(M,z)$ , $c_* \equiv c(M_*,z=0)$ ."
 Il shows that models with larger w can tolerate a higher halo concentration due to the lower lensing rates in these models., It shows that models with larger $\omega$ can tolerate a higher halo concentration due to the lower lensing rates in these models.
 JVAS/CLASS thus far, JVAS/CLASS thus far
1999).,.
. The predominance in the ERG population of the latter would favor hierarchical ealaxy formation scenarios (White&Frenk1991).. while the former would support early formation of galaxies through. monolithic collapse (Larson1975).," The predominance in the ERG population of the latter would favor hierarchical galaxy formation scenarios \citep{Whi91}, while the former would support early formation of galaxies through monolithic collapse \citep{Lar75}."
. Therefore. (he study of ERGs can help constraining existing models for formation aud evolution of galaxies.," Therefore, the study of ERGs can help constraining existing models for formation and evolution of galaxies."
 The observed very red colors of those ERGs which are classified as elliptical galaxies are attributed predominantly to the large INX-correction arising Irom their high redshift., The observed very red colors of those ERGs which are classified as elliptical galaxies are attributed predominantly to the large K-correction arising from their high redshift.
 On the other hand. stzr-Iorming galaxies will owe their redness predominantly to dust extinction.," On the other hand, star-forming galaxies will owe their redness predominantly to dust extinction."
 This view implies that extremely red ellipticals will oceur only at high redshift (221) while extremely red galaxies at 2<1 will exhibit unusually heavy obscuration of either stellar or AGN emission. or both.," This view implies that extremely red ellipticals will occur only at high redshift $z \gtrsim\ 1$ ) while extremely red galaxies at $z \lesssim 1$ will exhibit unusually heavy obscuration of either stellar or AGN emission, or both."
 This is expected to be the reason for the small space densitv found for ERGs in the local Universe., This is expected to be the reason for the small space density found for ERGs in the local Universe.
 This letter reports the discovery of an ERG. PDFJOLI423. al 2=0.65.," This letter reports the discovery of an ERG, PDFJ011423, at $z = 0.65$."
 Multi-waveband photometric and spectroscopic observations reveal evidence of both star formation and AGN aclivily in (his ealaxy. which can be regarded as a “local” template for the study of this class of ERG at higher redshifts.," Multi-waveband photometric and spectroscopic observations reveal evidence of both star formation and AGN activity in this galaxy, which can be regarded as a “local” template for the study of this class of ERG at higher redshifts."
 Throughout this paper we adopt Lf)=65figs ! ! and qi=0.5., Throughout this paper we adopt $H_0 = 65~h_{65}$ $^{-1}$ $^{-1}$ and $q_0=0.5$.
" PDFJ0O11423 (a=ο23. 0=—45 3430"". J2000) was first noted as a faint GGIIz radio source (5,1644=1.07 nunJv) in the Phoenix Deep Survey 1999).."," PDFJ011423 $\alpha = 01^{h}14^{m}23^{s}$, $\delta =-45^{\circ}34'30''$ , J2000) was first noted as a faint GHz radio source $S_{1.4\,\rm{GHz}}=1.67$ mJy) in the Phoenix Deep Survey \citep{Hop98,Hop99}. ."
 Aperture photometry of the optical counterpart of the source gives R=21.1 and V —22.7 (Georgakakisefal. 1999).. locating PDEJO11423 close to the magnitude limit of the follow-up Two Degree Field multi-libre spectroscopic survey (Georgakakisefaf.1999).," Aperture photometry of the optical counterpart of the source gives $R$ =21.1 and $V$ =22.7 \citep{Geo99}, , locating PDFJ011423 close to the magnitude limit of the follow-up Two Degree Field multi-fibre spectroscopic survey \citep{Geo99}."
 Nevertheless. a strong emission line. identified as |OI1I]|3727 at a redshift 2=0.65. was detecte.," Nevertheless, a strong emission line, identified as [OII]3727 at a redshift $z=0.65$, was detected."
 In the light of the known strong correlation between the Fu-infrared (FIR) and GGIIZz luminosities for star-forming galaxies. these clues were sufficient to schedule PDEJOI1423 for observation by theObservatory (ISO). using ISOCAM (7 and jm) and ISOPHOT μυ).," In the light of the known strong correlation between the far-infrared (FIR) and GHz luminosities for star-forming galaxies, these clues were sufficient to schedule PDFJ011423 for observation by the ), using ISOCAM (7 and $\mu$ m) and ISOPHOT $\mu$ m)."
" The observations (J. AfonsoaL... in preparation) revealed the presence of a relatively bright source al 7 and 154a0n. with fluxes of 4.1 and. 1.6mmJy. respectively,"," The observations (J. Afonso, in preparation) revealed the presence of a relatively bright source at 7 and $\mu$ m, with fluxes of 4.1 and mJy, respectively."
 The object was also detected by750 al 90;0n (460 level). with a flux of 260mmJy.," The object was also detected by at $\mu$ m $\sigma$ level), with a flux of mJy."
 Subsequent near-IR. photometry. using the New Technology Telescope (NTT) and the CTIO 1.51 telescopes. showed this galaxy {οhave A —15.3 and J—18.4.," Subsequent near-IR photometry, using the New Technology Telescope (NTT) and the CTIO 1.5m telescopes, showed this galaxy tohave $K$ =15.3 and $J$ =18.4."
 PDEJOLT1423 is (hus classified as an ERG with 4$—A=5.8andJ—K 3.1., PDFJ011423 is thus classified as an ERG with $R-K=5.8$and$J-K=3.1$ .
ITD has a inoment of inertia ereater than the Πο oue.,$HD$ has a moment of inertia greater than the $H_{2}$ one.
 Furthermore. it has a finite dipolar moment which allows internal dipolu trasitious (transitions of the kind J)>J £1) aud internal transition rates ereater than in Jf. Aberalletal.(1982).," Furthermore, it has a finite dipolar moment which allows internal dipolar trasitions (transitions of the kind $J\rightarrow J\pm 1$ ) and internal transition rates greater than in $H_{2}$, \citet{Abgrall}."
 Due to its small moment of inertia. the differcuces between its energy states are snialler than the enerey cdiffercuces of the Z7» molecule.," Due to its small moment of inertia, the differences between its energy states are smaller than the energy differences of the $H_{2}$ molecule."
 All these properties make the Z/D molecule an efficient cooler at low temperatures. below ~100A. (see Nagakura&Omnuhu(2005): Ripamonti(2007):: AMeCweer&Bryan (2008): Palla(1999). and refercuces The Ziff molecule is formed mainly bw radiative association of Li aud JF aud associative detacluneut of Li aud LT (Stanciletal.1996): Moreover. this molecule have both a dipolarmoment and a monent of inertia larger than the ones of the IT wnolecule.," All these properties make the $HD$ molecule an efficient cooler at low temperatures, below $\sim 100K$ , (see \citet{NagakuraOmukai}; \citet{Ripamonti 2007}; \citet{McGreerBryan 2008}; \citet{Palla 1999} and references The $LiH$ molecule is formed mainly by radiative association of $Li$ and $H$ and associative detachment of $Li^{-}$ and $H$ \citep{Stancil 1996}: Moreover, this molecule have both a dipolarmoment and a moment of inertia larger than the ones of the $HD$ molecule."
 These characteristics could make the {111 moleculeD an efficient cooler at low temperatures. but the cooliug functions depend ou the uuuber density of the specie. so if the abundance of Liff is too low as expected in primordial enviroments (Stanciletal.1996) its cooling effect will be ueelieible.," These characteristics could make the $LiH$ molecule an efficient cooler at low temperatures, but the cooling functions depend on the number density of the specie, so if the abundance of $LiH$ is too low as expected in primordial environments \citep{Stancil 1996} its cooling effect will be negligible."
 For a review of L; chemestry see Bodo(2001) anc Bodoetal.(2003)., For a review of $Li$ chemestry see \citet{Bodo 2001} and \citet{Bodo 2003}.
. Iu the work of Calli&Palla(1998) the effect of LHD aud Lill was included ou the eas cooling., In the work of \citet{Galli 1998} the effect of $HD$ and $LiH$ was included on the gas cooling.
 To caleulate the ploto-destruction ratescoctiicicut. for photoionization. photodetachineut. and photodissociation. they assunued detailed balance with CAIB photous.," To calculate the photo-destruction ratescoefficient, for photoionization, photodetachment, and photodissociation, they assumed detailed balance with CMB photons."
 But. to study the effect of the first stars on the primordial gas we need the cross section for cach ploto-destruction process. im the spiri of Glover&Jappsen(2007).," But, to study the effect of the first stars on the primordial gas we need the cross section for each photo-destruction process, in the spirit of \citet{Glover}."
 These cross sections are described below., These cross sections are described below.
 Our current work inchides the photo-destructiou cross sections of both L/ aud £7 iux the photodisociation of LII Gn its rovibrational erouix state) in contrast to previous work., Our current work includes the photo-destruction cross sections of both $Li$ and $Li^{-}$ and the photodisociation of $LiH$ (in its rovibrational ground state) in contrast to previous work.
 We dmprove over recent works (Clover&Jappseu2007:Clover&Abel2008) that have studied primordia cooling by exploring the effect of the Z£D abundance iux the inclusion of a stellar radiation field.," We improve over recent works \citep{Glover,GA08} that have studied primordial cooling by exploring the effect of the $HD$ abundance and the inclusion of a stellar radiation field."
 This paper is organized as follow., This paper is organized as follow.
 In 822 we describe both the tlerma and chemical model required to follow the evolution of the eas temperature., In 2 we describe both the thermal and chemical model required to follow the evolution of the gas temperature.
 In §33 we present results ai discussion., In 3 we present results and discussion.
 It includes the gas temperature evolution as a function of eas density aud molecular coolers: the gas temperature evolution as a function of /Z7D abundance: the temperature evolution as a function of the ionization degree and finaly we show the effect of a star radiation field on the eas temperature., It includes the gas temperature evolution as a function of gas density and molecular coolers; the gas temperature evolution as a function of $HD$ abundance; the temperature evolution as a function of the ionization degree and finaly we show the effect of a star radiation field on the gas temperature.
 In §ll we preseut the conchisious., In 4 we present the conclusions.
 As areucd above. in a realistic cooling model of primordial gas. it is mandatory to include the molecular coolers.," As argued above, in a realistic cooling model of primordial gas, it is mandatory to include the molecular coolers."
" The main molecular coolers at low temperatures are Hy, HD aud Liff."," The main molecular coolers at low temperatures are $H_{2}$ , $HD$ and $LiH$ ."
 Iu addition to the previous molecules. the model should include the main species created in the primordial nuclesvuthesis.," In adition to the previous molecules, the model should include the main species created in the primordial nuclesynthesis."
 Our model includes 21 species: H7. ΠΠ. IP. Hy. IL). HJ. Ie. He. Πο. ΠΕΠΙ. D. D. IID. HD!. [oD!'. Li. Lil. Li. Lidl. Lill! aude .," Our model includes 21 species: $H$, $H^{+}$, $H^{-}$, $H_{2}$, $H_{2}^{+}$, $H_{3}^{+}$, $He$, $He^{+}$, $He^{++}$, $HeH^{+}$, $D$, $D^{+}$, $HD$, $HD^{+}$, $H_{2}D^{+}$, $Li$, $Li^{+}$, $Li^{-}$, $LiH$, $LiH^{+}$ and $e^{-}$."
 The reactions cousidercd for these species are described in table 1.. 2. aud 3..," The reactions considered for these species are described in table \ref{tbl-4}, \ref{tbl-4bis} and \ref{tbl-5}."
 This table docs not include the formation of 775 bv three bodyreaction because this reaction is not relevant at densities studied in this The cooling processes (see table 3)) considered in this work are: The molecular cooling functions are constructed as iu Calli&Palla(1998)., This table does not include the formation of $H_{2}$ by three bodyreaction because this reaction is not relevant at densities studied in this The cooling processes (see table \ref{tbl-5}) ) considered in this work are: The molecular cooling functions are constructed as in \citet{Galli 1998}.
. For both ff aud D moleculey. we adoptedthe approximate density dependent relation for the cooling functions., For both $H_{2}$ and $HD$ molecules we adoptedthe approximate density dependent relation for the cooling functions.
 For Lill we adopted the low density lait cooling function., For LiH we adopted the low density limit cooling function.
 The molecular cooling functions are trated as in Puyetal.(1993) at temperatures near Torayp. The first stars. by definition. formed in au ονοσα! without previous star.," The molecular cooling functions are trated as in \citet{Puy 1993} at temperatures near $T_{CMB}$ The first stars, by definition, formed in an environment without previous star."
 But. once population IIT stars are formed they cau plotoionize the halos where new stars will form.," But, once population III stars are formed they can photoionize the halos where new stars will form."
 This process is quantified bv the frequency dependent cross section. σαν). of the reaction A’|>>MIqoe where the specie A’ in- the { ionization state moves to /| Lionuizationstate due to the interaction witli photons.," This process is quantified by the frequency dependent cross section, $\sigma_{A}(\nu)$, of the reaction $A^{i}+\gamma\rightarrow A^{i+1}+e^{-}$ , where the specie $A^{i}$ in the $i$ ionization state moves to $i+1$ ionizationstate due to the interaction with photons."
 The presence of a radiation field triggers a rate: where na is the umber censity of specie 4: (77) is the specificintensity of radiation iu the ονολο! aud Ph is Plauck's constant., The presence of a radiation field triggers a photo-destruction rate: where $n_{A}$ is the number density of specie $A$; $i(\nu)$ is the specificintensity of radiation in the environment and $h$ is Planck's constant.
 The iutegral is calculated from thethreshold frequency of jonization. 1. to infinity.," The integral is calculated from thethreshold frequency of ionization, $\nu_{th}$ , to infinity."
" The heating of the eas due to photoionizations (leat in ο κ} is eiven by where fay, is the threshold cuerey of ionization.", The heating of the gas due to photoionizations (heat in $erg/cm^{3}s$ ) is given by where $h\nu_{th}$ is the threshold energy of ionization.
Stricth. im the lasttwo expressions /(7) should be uultiplicd by d.6 *. where 7=foaG)0 is the optvcal depth.,"Strictly, in the lasttwo expressions $i(\nu)$ should be multiplied by $1-e^{-\tau}$ , where $\tau=\int \sigma_{A}(\nu)n_{A}dl$ is the optycal depth."
 Hore we assume 727 1., Here we assume $\tau>>1$ .
 For example.4dl 77 was ↻∐∪↑∪↕∪↕∐∑⋜↧⊓∪∐↸⊳↥∪↴∖↴∖↴∖↸∖↸⊳↑↕∪∐↕↴∖∿↓∩↙⋅∣⊔∙∣↕↴∖∶↴∙∐∖⋜↧↑↸∖↥⊥∖⊐−⋅↴↜⋅ ⋅ ↑∐⋜⋯↕↕⋡∪↥⋅↙∕∣↕∐∣↓∣↗↙⋅∙↕↕⋟↖↖↽↸∖↑⋜∐↘↽↸∖∣∣∐↕∐↑∐↸∖↥⋅⋜⋯∶↴∙⊾↸∖ ↕↕∩↓↙⋅∣⊔⊽⋟∙⊺∐↕↴∖↴≼∐∖↴," For example, $H$ photoionization cross section is $\sim 10^{-18}cm^{2}$ , $\tau$ is greater than 1 for $dl>1-10^{-4}pc.$ If we take $n_{H}$ in the range $1-10^{4}cm^{-3}$ ."
↑⋜⋯↸⊳↸∖↕↴∖↴↖↖↽↸∖∐↴⋝↸∖↕∪↖↖↽↑∐↸∖∐⋜↧↕∪↴∖↴↸⊳⋜↧↕, This distance is well below the halo scale
↑⋜⋯↸⊳↸∖↕↴∖↴↖↖↽↸∖∐↴⋝↸∖↕∪↖↖↽↑∐↸∖∐⋜↧↕∪↴∖↴↸⊳⋜↧↕↸, This distance is well below the halo scale
↑⋜⋯↸⊳↸∖↕↴∖↴↖↖↽↸∖∐↴⋝↸∖↕∪↖↖↽↑∐↸∖∐⋜↧↕∪↴∖↴↸⊳⋜↧↕↸∖, This distance is well below the halo scale
HI maps of local spiral galaxies (Walter et al.,HI maps of local spiral galaxies (Walter et al.
 2008). many of which display disturbances in the outskirts (Bigiel et al.," 2008), many of which display disturbances in the outskirts (Bigiel et al."
 2010)., 2010).
 Attempting to constrain the dark matter halo in this way Is similar in spirit to earlier work on analysis of stellar tidal tails by Mihos. Dubinski Hernquist (1998).," Attempting to constrain the dark matter halo in this way is similar in spirit to earlier work on analysis of stellar tidal tails by Mihos, Dubinski Hernquist (1998)."
 If the satellite mass and pericentric distance of the satellites that produce these disturbances can be characterized. as for M51 (CBCB). then as we show below. the phase of the =| mode directly yields the scale radius of the dark matter halo.," If the satellite mass and pericentric distance of the satellites that produce these disturbances can be characterized, as for M51 (CBCB), then as we show below, the phase of the $m=1$ mode directly yields the scale radius of the dark matter halo."
 This method of probing the dark matter mass distribution is independent of the stellar light and is complementary to strong gravitational lensing. which primarily probes regions anterior to the Einstein radius. 10kpe in spirals (Wright Brainerd 2000; Treu Koopmans 2002).," This method of probing the dark matter mass distribution is independent of the stellar light and is complementary to strong gravitational lensing, which primarily probes regions interior to the Einstein radius, $\sim 10~\rm kpc$ in spirals (Wright Brainerd 2000; Treu Koopmans 2002)."
 The weak lensing signal has also been exploited by stacking the surface density contrast to produce mean density profiles for clusters (Sheldon et al., The weak lensing signal has also been exploited by stacking the surface density contrast to produce mean density profiles for clusters (Sheldon et al.
 2008) and total galaxy masses (Mandelbaum et al., 2008) and total galaxy masses (Mandelbaum et al.
 2006)., 2006).
 This paper is organized as follows: in $82. we demonstrate that the phase of the #7=1 mode can be used to quantitatively infer the scale radius of dark matter halos and apply the method to M51.," This paper is organized as follows: in 2, we demonstrate that the phase of the $m=1$ mode can be used to quantitatively infer the scale radius of dark matter halos and apply the method to M51."
 We discuss caveats and future work 1 $3.<2 and conclude in 84.," We discuss caveats and future work in 3, and conclude in 4."
 The simulations we discuss here have the same setup as in CBCB., The simulations we discuss here have the same setup as in CBCB.
 Since that paper discusses the simulation. setup in detail. we only briefly discuss it here.," Since that paper discusses the simulation setup in detail, we only briefly discuss it here."
 We carry out SPH simulations using the GADGET code (Springel 2005). of MSI interacting with its companion.," We carry out SPH simulations using the GADGET code (Springel 2005), of M51 interacting with its companion."
 CBCB carried out a simulation parameter survey and compared the resultant Fourier amplitudes of the low order modes of the gas surface density with the observed HI data of M51., CBCB carried out a simulation parameter survey and compared the resultant Fourier amplitudes of the low order modes of the gas surface density with the observed HI data of M51.
 They found that placing simulations on a variance vs variance plot (where the variance is with respect to the low order modes of the simulations and the data) made the best-fit simulations visually apparent., They found that placing simulations on a variance vs variance plot (where the variance is with respect to the low order modes of the simulations and the data) made the best-fit simulations visually apparent.
 Specifically. CBCB found that the fit to the HI data occurred for a 1:3 mass ratio satellite with a pericentric distance of 15kpe. parameters that are corroborated observationally and are in agreement with other simulation studies (Smith et al.," Specifically, CBCB found that the best-fit to the HI data occurred for a 1:3 mass ratio satellite with a pericentric distance of $15~\rm kpc$, parameters that are corroborated observationally and are in agreement with other simulation studies (Smith et al."
 1990; Dobbs et al., 1990; Dobbs et al.
 2010: Salo Laurikainen 2000)., 2010; Salo Laurikainen 2000).
 CBCB also found that the azimuthal location of the companion of the best-fit simulation agrees very closely with the observed location of M51°s companion. at the time when the Fourier amplitudes most closely match the data.," CBCB also found that the azimuthal location of the companion of the best-fit simulation agrees very closely with the observed location of M51's companion, at the time when the Fourier amplitudes most closely match the data."
 Thus. CBCB concluded that analysis of observed disturbances in the extended HI disks of galaxies can be used to infer the mass and current distance (in radius and azimuth) of galactic satellites.," Thus, CBCB concluded that analysis of observed disturbances in the extended HI disks of galaxies can be used to infer the mass and current distance (in radius and azimuth) of galactic satellites."
 Earlier work im this series of papers presented the basic reasoning as to why the mass-pericentric approach degeneracy in the tidal force can be broken when the time integrated response of the primary galaxy is considered (6800). and described the method to find the azimuth of galactic satellites from the phase of the modes (CBI1).," Earlier work in this series of papers presented the basic reasoning as to why the mass-pericentric approach degeneracy in the tidal force can be broken when the time integrated response of the primary galaxy is considered (CB09), and described the method to find the azimuth of galactic satellites from the phase of the modes (CB11)."
 Our main goal in this paper is to determine whether the scale radius of the dark matter halo in the primary galaxy can be inferred from analysis of observed disturbances in the extended HI disk of M51., Our main goal in this paper is to determine whether the scale radius of the dark matter halo in the primary galaxy can be inferred from analysis of observed disturbances in the extended HI disk of M51.
 Since we have earlier characterized the mass and pericentric approach distance of Μ515 companion. we take these quantities as inputs in our study here.," Since we have earlier characterized the mass and pericentric approach distance of M51's companion, we take these quantities as inputs in our study here."
 Here. we primarily vary the density profile (and hence the potential depth) of the dark matter halo of M51. which we take to follow an NFW profile.," Here, we primarily vary the density profile (and hence the potential depth) of the dark matter halo of M51, which we take to follow an NFW profile."
 We investigate whether varying the scale radius of the dark matter halo of M51 will be reflected in the disturbances of the extended HI disk cleanly enough to allow us to infer its value., We investigate whether varying the scale radius of the dark matter halo of M51 will be reflected in the disturbances of the extended HI disk cleanly enough to allow us to infer its value.
 We begin by studying the gas density response as M51 interacts with a 1:3 mass ratio satellite with a pericentric distance of 15kpe (parameters we derived in CBCB). while we vary the scale radius of the dark matter halo.," We begin by studying the gas density response as M51 interacts with a 1:3 mass ratio satellite with a pericentric distance of $15~\rm kpc$ (parameters we derived in CBCB), while we vary the scale radius of the dark matter halo."
" We vary the scale radius from low to high values (R,=11—32kpe) to investigate its effect on the resultant disturbances 1n the HI disk.", We vary the scale radius from low to high values $R_{s}=11-32~\rm kpc$ ) to investigate its effect on the resultant disturbances in the HI disk.
" The scale radius is related to the concentration parameter and the outer radius of the dark matter halo. 1.8.. R,=Rosoofc."," The scale radius is related to the concentration parameter and the outer radius of the dark matter halo, i.e., $R_{s}=R_{200}/c$."
 Therefore. we can either hold Ro; constant and vary the concentration parameter. or hold the concentration parameter constant and vary Rago.," Therefore, we can either hold $R_{200}$ constant and vary the concentration parameter, or hold the concentration parameter constant and vary $R_{200}$."
" The mass of the dark matter halo scales as R3, (M200=200p,.47S44). While the concentration parameter is related to the angular momentum of the halo as motivated by the Mo. Mao White (1998) formalism (Springel et al."," The mass of the dark matter halo scales as $R_{200}^{3}$ $M_{200}=200\rho_{c}\frac{4}{3}\pi R_{200}^{3}$ ), while the concentration parameter is related to the angular momentum of the halo as motivated by the Mo, Mao White (1998) formalism (Springel et al."
 2005). and affects the size of the baryonic disk.," 2005), and affects the size of the baryonic disk."
 Our earlier models (CBCB) were based on the Roy=160h!kpe case. which gives a galaxy mass consistent with observational estimates (Leroy et al.," Our earlier models (CBCB) were based on the $R_{200}=160~\rm h^{-1}~kpc$ case, which gives a galaxy mass consistent with observational estimates (Leroy et al."
 2008)., 2008).
 We first set Roy=160h!kpe and vary the concentration parameter. which is equivalent to varying the scale radius of the dark matter halo.," We first set $R_{200}=160~\rm h^{-1}~kpc$ and vary the concentration parameter, which is equivalent to varying the scale radius of the dark matter halo."
 Below we show that varying the concentration parameter and Roo such that the scale radius is constant gives nearly identical results for the phase of the ;/=1 mode in the outskirts. which demonstrates that the critical parameter that governs the formation of these disturbances (once we have an observational handle on the mass of the galaxy from the rotation curve) is the scale radius.," Below we show that varying the concentration parameter and $R_{200}$ such that the scale radius is constant gives nearly identical results for the phase of the $m=1$ mode in the outskirts, which demonstrates that the critical parameter that governs the formation of these disturbances (once we have an observational handle on the mass of the galaxy from the rotation curve) is the scale radius."
" Thus. the two cases we focus on here are: 1) holding Roo9 constant and varying c which corresponds to varying R,: this means we hold the mass of the dark halo constant while we vary the scale radius. where the density switches from r7! for rΆν tor for r>Ry. and 2) holding Κι constant and varying Rsoo (which will then also vary ο) and therefore the mass of the dark halo."," Thus, the two cases we focus on here are: 1) holding $R_{200}$ constant and varying $c$ which corresponds to varying $R_{s}$; this means we hold the mass of the dark halo constant while we vary the scale radius, where the density switches from $r^{-1}$ for $r \ll R_{s}$ to $r^{-3}$ for $r \gg R_{s}$, and 2) holding $R_{s}$ constant and varying $R_{200}$ (which will then also vary $c$ ) and therefore the mass of the dark halo."
" Figure 1. shows the resultant gas density response of M51 when we vary the scale radius (concentration) of the dark matter halo of M51 from a small (large) value 14). to the fiducial value used earlier by CBCB (R,=17.¢ 9.4). to a low (high) value (R,232.c= 5)."," Figure \ref{f:m51CVar} shows the resultant gas density response of M51 when we vary the scale radius (concentration) of the dark matter halo of M51 from a small (large) value $R_{s}=11,c=14$ ), to the fiducial value used earlier by CBCB $R_{s}=17,c=9.4$ ), to a low (high) value $R_{s}=32,c=5$ )."
 Varying the scale radius varies the potential depth of M51 and will therefore dramatically impact the formation of tidal features. as we see clearly from Figure |..," Varying the scale radius varies the potential depth of M51 and will therefore dramatically impact the formation of tidal features, as we see clearly from Figure \ref{f:m51CVar}."
 Steeper potential wells. which are produced by steeper density profiles. are more effective at holding on to the gas (Mihos. Dubinski Hernquist 1998).," Steeper potential wells, which are produced by steeper density profiles, are more effective at holding on to the gas (Mihos, Dubinski Hernquist 1998)."
" Therefore. the R,=1.c14 case yields more tightly wound structures relative to the fiducial value of the scale radius (R,=017.c 9.4). as well as of course the largest scale radius we consider here (R,=32.c2 5). where the density profile follows the shallow slope of ;7! nearly all the way out to where we can probe the extended HI disk of M51."," Therefore, the $R_{s}=11,c=14$ case yields more tightly wound structures relative to the fiducial value of the scale radius $R_{s}=17,c=9.4$ ), as well as of course the largest scale radius we consider here $R_{s}=32,c=5$ ), where the density profile follows the shallow slope of $r^{-1}$ nearly all the way out to where we can probe the extended HI disk of M51."
 Figure 2((a) shows how the phase of the #7=| mode varies as we vary the scale radius of the dark matter halo in the three cases shown in Figure 1.., Figure \ref{f:m51m1phaseCvar}( (a) shows how the phase of the $m=1$ mode varies as we vary the scale radius of the dark matter halo in the three cases shown in Figure \ref{f:m51CVar}.
" For projected gas surface density denoted X.ο). we calculate the phase of individual modes ""m"" by taking the FFT. where below we have set i=I: The phase of the modes contains information on the shape of the spiral planform. r.e.. tightly wrapped spirals will have à sharp gradient in the phase. while open spirals will have a flatter profile (Shu 1983; Chakrabarti Blitz 2011)."," For projected gas surface density denoted $\Sigma(r,\phi)$, we calculate the phase of individual modes “m” by taking the FFT, where below we have set $m=1$: The phase of the modes contains information on the shape of the spiral planform, i.e., tightly wrapped spirals will have a sharp gradient in the phase, while open spirals will have a flatter profile (Shu 1983; Chakrabarti Blitz 2011)."
" For the fiducial value of R,=17(c29.4) used by CBCB (shown in the solid green line). the phase of the ;/=1 mode in the simulation"," For the fiducial value of $R_{s}=17 (c=9.4)$ used by CBCB (shown in the solid green line), the phase of the $m=1$ mode in the simulation"
two planetary nebulae.,two planetary nebulae.
 Following Sarzi et al. (2005)..," Following Sarzi et al. \nocite{2006MNRAS.366.1151S},"
 their Equation Ll. we should be sensitive to emission lines with EW > 0.7AL.," their Equation 1, we should be sensitive to emission lines with EW $>$ 0.7."
 We carefully checked the individual spectra in cach cube. prior to co-adding. and found no evidence for such emission.," We carefully checked the individual spectra in each cube, prior to co-adding, and found no evidence for such emission."
 We also investigated the effect of sky subtraction on the determinations of line strength., We also investigated the effect of sky subtraction on the determinations of line strength.
 By varving the amount of sky that we subtracted from our spectra. we found that our measurements of aand Fes015 are quite robust against an error in sky subtraction. even if the skvlevels are varied by. LO per cent.," By varying the amount of sky that we subtracted from our spectra, we found that our measurements of and Fe5015 are quite robust against an error in sky subtraction, even if the skylevels are varied by 10 per cent."
 iis however already severely allected by a sky subtraction error of only two per cent (see Figure 7))., is however already severely affected by a sky subtraction error of only two per cent (see Figure \ref{fig:lick_sky}) ).
 This may be due to the proximity of the solar aabsorption feature present in the sky spectrum., This may be due to the proximity of the solar absorption feature present in the sky spectrum.
 Our Fe5015 and indices at 2 and 3 Ao in NGC 821 are unrealistically high. and therefore could be suffering from this problem. although variations in the continuum shape of the spectrum also play a role (sec next section).," Our Fe5015 and indices at 2 and 3 $R_e$ in NGC 821 are unrealistically high, and therefore could be suffering from this problem, although variations in the continuum shape of the spectrum also play a role (see next section)."
 The indices at 1 2. in this galaxy are less alfectec. and are in agreement with Proctor ct al. (2005)..," The indices at 1 $R_e$ in this galaxy are less affected, and are in agreement with Proctor et al. \nocite{2005MNRAS.362..857P}."
" They determined line strengths from long-slit data in this galaxy out to 1 42,.", They determined line strengths from long-slit data in this galaxy out to 1 $R_e$.
 We are not aware of studies in the literature where line strengths have been determined outside 1A. for these galaxies. to compare our results with.," We are not aware of studies in the literature where line strengths have been determined outside 1 $R_e$ for these galaxies, to compare our results with."
"eemission line is redshifted relatively to the systemic redshift of the galaxy, as is normally the case in galaxies driving large scale outflows (e.g.Pettinietal.2001;Steidel2010).","emission line is redshifted relatively to the systemic redshift of the galaxy, as is normally the case in galaxies driving large scale outflows \citep[e.g.][]{pe1,s10}."
". In any case, as we discuss below, this galaxy is sufficiently close to the QSO sight-line for an outflow at the canonical Vout=200 tto have travelled the projected distance of 79kkpc in 0.4 GGyr, less than half the age of the Universe at z=5.7."," In any case, as we discuss below, this galaxy is sufficiently close to the QSO sight-line for an outflow at the canonical $v_{\rm out} = 200$ to have travelled the projected distance of kpc in $\sim 0.4$ Gyr, less than half the age of the Universe at $z = 5.7$."
 In this section we derive the UV continuum fluxes of the galaxies from their 2450 magnitudes and use them to deduce values of the star formation rate SFRuv for comparison with the values of Riya measured above., In this section we derive the UV continuum fluxes of the galaxies from their $z_{850}$ magnitudes and use them to deduce values of the star formation rate $_{\rm UV}$ for comparison with the values of $_{\rm \Lya}$ measured above.
" At z= 5.7-6.0, the zg50 filter samples the far-UV spectrum where, according to Madau,Pozzetti&Dickinson(1998) for a Salpeter IMF."," At $z = 5.7$ –6.0, the $z_{850}$ filter samples the far-UV spectrum where, according to \citet{ma98}
 for a Salpeter IMF."
" As mentioned earlier, an IMF withfewer low-mass stars, such as that appropriate to the Milky Way (Chabrier 2003),, would lead to lower values of SFR by a factor of ~1.8."," As mentioned earlier, an IMF withfewer low-mass stars, such as that appropriate to the Milky Way \citep{ch3}, , would lead to lower values of SFR by a factor of $\sim 1.8$."
 The conversion in eq. (2)), The conversion in eq. \ref{eq:SFR_UV1}) )
" applies to the UV continuum atAA,, but the intrinsic (i.e. before reddening) UV slope of starburst galaxies is approximately flat in F, between 1500 andAA,, so that the above conversion should still apply."," applies to the UV continuum at, but the intrinsic (i.e. before reddening) UV slope of starburst galaxies is approximately flat in $F_\nu$ between 1500 and, so that the above conversion should still apply."
" On the other hand, the reddening correction is unknown for our galaxies; thus the values of SFRuv we derive are strictly lower limits."," On the other hand, the reddening correction is unknown for our galaxies; thus the values of $_{\rm UV}$ we derive are strictly lower limits."
" Furthermore, eq. (2))"," Furthermore, eq. \ref{eq:SFR_UV1}) )"
 is valid for the ideal case ofa continuous star formation episode lasting for more than MMyr; younger ages would lead to larger values SFRuv., is valid for the ideal case ofa continuous star formation episode lasting for more than Myr; younger ages would lead to larger values $_{\rm UV}$.
" Two corrections that we can apply, knowing the wavelengths of the eemission lines and the transmission curve of the ACS F850LP filter, are for absorption by the Lya forest and for the contribution to the zsso magnitudes by the eemission lineitself."," Two corrections that we can apply, knowing the wavelengths of the emission lines and the transmission curve of the ACS F850LP filter, are for absorption by the $\alpha$ forest and for the contribution to the $z_{850}$ magnitudes by the emission lineitself."
" For the latter, we simply subtracted the flux of the Lya line from the flux measured by SExtractor in the zeso band AAUTO)."," For the latter, we simply subtracted the flux of the $\alpha$ line from the flux measured by SExtractor in the $z_{850}$ band AUTO)."
 The correction for Lya forest absorption is a multiplicative factor accounting for the fact that not all the filter was illuminated in wavelength space., The correction for $\alpha$ forest absorption is a multiplicative factor accounting for the fact that not all the filter was illuminated in wavelength space.
" We applied the following correction to amend for this effect where [νο is the UV flux corrected for eemission, Ar is the total area under the throughput curve and Ar is the area under the same curve for wavelengths \>Aobs(Lya)) (thus assuming that, to a first approximation, there is negligible flux below the eemission line)."," We applied the following correction to amend for this effect where $f^{c}_{\nu_{0}}$ is the UV flux corrected for emission, $A_{T}$ is the total area under the throughput curve and $A_{F}$ is the area under the same curve for wavelengths $\lambda > \lambda_{\rm obs}$ ) (thus assuming that, to a first approximation, there is negligible flux below the emission line)."
" As can be seen from Table 1,, SFRov>SFRrya for all three galaxies."," As can be seen from Table \ref{mag}, $_{\rm UV} > {\rm SFR}_{\rm Ly\alpha}$ for all three galaxies."
" As mentioned above (Section 3.1), there are many possible reasons which can explain the common finding that the lline luminosity underestimates the true star formation rate in galaxies."," As mentioned above (Section 3.1), there are many possible reasons which can explain the common finding that the line luminosity underestimates the true star formation rate in galaxies."
" It is interesting that, out of the three galaxies observed, it is the one with the clearest evidence for a large- outflow (Target 3) that shows the largest difference between SFRuv and SFRrya."," It is interesting that, out of the three galaxies observed, it is the one with the clearest evidence for a large-scale outflow (Target 3) that shows the largest difference between $_{\rm UV}$ and $ {\rm SFR}_{\rm Ly\alpha}$."
" As discussed by Steideletal.(2011),, galaxy-scale outflows naturallylead to a diffuse, extended halo of eemission which is seldom captured in its entirety with slit Spectroscopy."," As discussed by \citet{s11}, galaxy-scale outflows naturallylead to a diffuse, extended halo of emission which is seldom captured in its entirety with slit spectroscopy."
" Having confirmed that all three targets are indeed at z= 5.5-6, we comment briefly on the colour selection for i-dropouts."," Having confirmed that all three targets are indeed at $z = 5.5$ –6, we comment briefly on the colour selection for $i$ -dropouts."
" According to Malhotraetal.(2005),, the colour Cut i775—Zaso>0.9 in sources with zaso<27.5 will include galaxies at z>5.4 with a completeness of ~80%."," According to \citet{mal5}, the colour cut $i_{775}-z_{850}>0.9$ in sources with $z_{850}\leq 27.5$ will include galaxies at $z>5.4$ with a completeness of $\sim 80$."
". However, galaxies at intermediate redshifts (z~ 1-2) also have i775—Za5o~1."," However, galaxies at intermediate redshifts $z \simeq 1$ –2) also have $i_{775}-z_{850} \sim 1$."
" Therefore, a color cut i775—25ο>1.3 may be a stronger criterion for eliminating lower redshift interlopers, but it was noticed by Malhotraetal.(2005) that it would lead to higher incompleteness (~20-30%)) for z~6 galaxies."," Therefore, a color cut $i_{775}-z_{850}>1.3$ may be a stronger criterion for eliminating lower redshift interlopers, but it was noticed by \citet{mal5} that it would lead to higher incompleteness $\sim 20$ ) for $z\sim 6$ galaxies."
"Concerning our three galaxies, we note that Target 1 has the reddest colour, i775—2450=2.25, but the lowest UV flux, once corrections have been applied for fforest absorption and eemission (see Table 1)).","Concerning our three galaxies, we note that Target 1 has the reddest colour, $i_{775}-z_{850}=2.25$, but the lowest UV flux, once corrections have been applied for forest absorption and emission (see Table \ref{mag}) )."
 The reason is that the eemission line makes a significant contribution to the flux measured in the 2g50 filter., The reason is that the emission line makes a significant contribution to the flux measured in the $z_{850}$ filter.
" With zg50=26.03+0.06 Target 2 is the faintest of the three in this band, even though its corrected UV flux is not the lowest."," With $z_{850}=26.03\pm 0.06$ Target 2 is the faintest of the three in this band, even though its corrected UV flux is not the lowest."
" Note that with 1775—zsso=1.23 this galaxy would be missed by a colour selection 1775—zaso>1.3, even though it is intrinsically bright: its UV luminosity, Luv— eergs! Hz!, corresponds to Luv= 1.25L26, adopting Li.&=5.44x1078 eerg s! Hz! from (2007).."," Note that with $i_{775}-z_{850}=1.23$ this galaxy would be missed by a colour selection $i_{775}-z_{850}>1.3$, even though it is intrinsically bright: its UV luminosity, $L_{\rm UV} = 6.8 \times 10^{28}$ erg$^{-1}$ $^{-1}$ , corresponds to $L_{\rm UV} =1.25 L^{\star}_{\rm z=6}$ , adopting $L^{\star}_{\rm z=6}=5.44 \times 10^{28}$ erg $^{-1}$ $^{-1}$ from \citet{bo7}. ."
" Target 3, which we associate with the aabsorber at z= 5.7238, has the brightest zsso magnitude of the three objects (zsso=25.34+0.05 mmag) and is also the most luminous with Luv=2.5 1..."," Target 3, which we associate with the absorber at $z = 5.7238$ , has the brightest $z_{850}$ magnitude of the three objects $z_{850}=25.34\pm 0.05$ mag) and is also the most luminous with $L_{\rm UV}=2.5\,L^{\star}_{\rm z=6}$ ."
" In this case, the weak line does not make a significant contribution to the"," In this case, the weak line does not make a significant contribution to the"
width of narrow component of ο HIJA5007 line. hereafter FWHAπο from two-component model. the typical error is about LO per cent.,"width of narrow component of [O $\lambda$ 5007 line [hereafter $FWHM^{n}([O III])$ ] from two-component model, the typical error is about 10 per cent."
 In the left panel of Fig., In the left panel of Fig.
" 2. we plotted the central black hole masses (Alas) versus £MAI"" COITLID."," 2, we plotted the central black hole masses $M_{H\beta}$ ) versus $FWHM^{n}([O III])$ ."
 Lhe mass versus AZ417COLLL]) is showed in fig., The mass versus $FWHM^{one}([O III])$ is showed in fig.
 1 in Bian Zhao (2004a)., 1 in Bian Zhao (2004a).
 We adopted the same range of x and y axes in order that we can compare the results with that in fig., We adopted the same range of x and y axes in order that we can compare the results with that in fig.
 1 in Dian Zhao (2004a)., 1 in Bian Zhao (2004a).
 The masses are calculated from the 112 linewidth using one-Gaussian fit. which are form Bian Zhao (2004a).," The masses are calculated from the $\beta$ linewidth using one-Gaussian fit, which are form Bian Zhao (2004a)."
" CGrupe Mathur (2004) also plot the Als,TOLL relation for a complete sample of τὸ soft. N-ravA’Cselected AGWNs: 43 broad-Iine ACGNs ancl 32 NLSIs.", Grupe Mathur (2004) also plot the $M_{bh} - \sigma_{[O III]}$ relation for a complete sample of 75 soft X-ray¨Cselected AGNs: 43 broad-line AGNs and 32 NLS1s.
 They found that the locus of NLSIs obviously deviates from the ωνor relation defined by “Tremaine ct al. (, They found that the locus of NLS1s obviously deviates from the $M_{bh}-\sigma_{[O III]}$ relation defined by Tremaine et al. (
2002).,2002).
 Considering the blue asymmetry of the © LL profile. they remeasured the width of the O LL line as two times half-width at half-maximum of the red. part of emission line ancl found. the deviation indeed exists.," Considering the blue asymmetry of the [O III] profile, they remeasured the width of the [O III] line as two times half-width at half-maximum of the red part of emission line and found the deviation indeed exists."
 In. the left-hand panel of Fig., In the left-hand panel of Fig.
 2. we still find this result. which is consistent with Cirupe Alathur (2004).," 2, we still find this result, which is consistent with Grupe Mathur (2004)."
 When we used the linewidth of 117 or lla to trace the virial velocity. around black bole. we should. subtract the contribution from NLRs.," When we used the linewidth of $\beta$ or $\alpha$ to trace the virial velocity around black hole, we should subtract the contribution from NLRs."
 The template built from Ο LI] or SLL] is used to model narrow Lo and (Grupe et al., The template built from [O III] or [S II] is used to model narrow $\alpha$ and $\beta$ (Grupe et al.
 1998: Grupo. Thomas Leighly 1999: Greene Lo. 2005a.b).," 1998; Grupe, Thomas Leighly 1999; Greene Ho, 2005a,b)."
 For seven NLS1s. IHtodriguez-Ardila et al. (," For seven NLS1s, Rodriguez-Ardila et al. ("
"2000) found that the narrow component of 1 is about. of the total line Llux and the © LL] A5007/11, ratio emitted in the narrow line regions (NLRs) varies from 1 to 5.r instead of the universally adopted value of 10.","2000) found that the narrow component of $\beta$ is about, of the total line flux and the [O III] $\lambda$ $\beta_{n}$ ratio emitted in the narrow line regions (NLRs) varies from 1 to 5, instead of the universally adopted value of 10."
 We also found the Ο LU] is not too weals in manv SDSS NLSIs., We also found the [O III] is not too weak in many SDSS NLSls.
 This is consistent with 10 results of a sample of 64 NLSIs presented by Veron-C'etty et al. (, This is consistent with the results of a sample of 64 NLSls presented by Veron-Cetty et al. (
2001).,2001).
" There are (33 SDSS NLSIs with O LI[AD007 /1E3, line ratio larger than one.", There are 63 SDSS NLSls with [O $\lambda$ $\beta_{n}$ line ratio larger than one.
 Lf we assume the narrow -- is emitted from NL~s for these objects. we should use the linewidth of the LL? broad. component to calculate the virial black hole masses. which are showed in the right panel of Fig.," If we assume the narrow $\beta$ is emitted from NLRs for these objects, we should use the linewidth of the $\beta$ broad component to calculate the virial black hole masses, which are showed in the right panel of Fig."
 2., 2.
" We also calculated the black hole mass. Mor. using EWHIAL of narrow component of O LI] line as the indicator οἱ σ. Le. mop=FMHM""COT]/2:35."," We also calculated the black hole mass, $M_{[O III]}$, using FWHM of narrow component of [O III] line as the indicator of $\sigma$, i.e. $\sigma_{[O III]} = FWHM^{n}([O III])/2.35$."
 The distributions of logCMg;/AM-o1167) for 149 SDSS NLSIs are shown in Table 1. where Aly. ds calculated from Ile ENIM. using one-Caussian fitting.," The distributions of $M_{H\beta}/M_{[O III]}$ ) for 149 SDSS NLSls are shown in Table 1, where $M_{H\beta}$ is calculated from $\beta$ FWHM using one-Gaussian fitting."
" These. 149 NLSIs statically cdeviatec the Ady,Torr relation defined by Tremaine et al. (", These 149 NLSls statically deviated the $M_{bh}-\sigma_{[O III]}$ relation defined by Tremaine et al. (
2002)(See Fig.,2002)(See Fig.
 2)., 2).
" Considering the spectrum resolution. the intrinsic 0 derived. from. FMWIUCGM""COII]) may be instrumentally broadened by about GO (hereafter tine) (Greene Ho 2005a)."," Considering the spectrum resolution, the intrinsic $\sigma$ derived from $FWHM^{n}([O
III])$ may be instrumentally broadened by about 60 (hereafter $\sigma_{inst}$ ) (Greene Ho 2005a)."
" he values of σ derived from FMAP""COLLL]) for all objects in Fig.", The values of $\sigma$ derived from $FWHM^{n}([O III])$ for all objects in Fig.
 l ave larger than 60+., 1 are larger than 60.
" To. first order. the intrinsic & can be approximated by 0=(σα02,4)NEN"," To first order, the intrinsic $\sigma$ can be approximated by $\sigma=(\sigma_{obs}^2-\sigma_{inst}^2)^{1/2}$."
 We found that the logarithm value of intrinsic σ would be lowered by 0.08 dex. which is small relative to the deviation in Fig.," We found that the logarithm value of intrinsic $\sigma$ would be lowered by 0.08 dex, which is small relative to the deviation in Fig."
 2 (also see. Table., 2 (also see Table.
 1)., 1).
" Subsample A consists of 63 objects with ο LI]A5007 /LL7, line ratio larger than 1.", Subsample A consists of 63 objects with [O $\lambda$ $\beta_{n}$ line ratio larger than 1.
 Subsample B consists of the rest S6 NLSIs., Subsample B consists of the rest 86 NLSls.
" H£ we used the width of the LL? broad. component to calculated the black hole masses. we found that these 63 objects in Subsample A follow the My,TOLL relation."," If we used the width of the $\beta$ broad component to calculated the black hole masses, we found that these 63 objects in Subsample A follow the $M_{bh} -
\sigma_{[O III]}$ relation."
 In these 63 objects. we found nine objects with the linewidth of the LE? broad component less than.," In these 63 objects, we found nine objects with the linewidth of the $\beta$ broad component less than."
 Lf we excluded these nineobjects from. sub-sample AL ie. Subsample €. the mean value. of Mg i/AM-o11:). would. be smaller. -0.0920.0% with a standard. deviation of 0.53.," If we excluded these nineobjects from sub-sample A, i.e. Subsample C, the mean value of $M_{H\beta}/M_{[O
III]}$ ) would be smaller, $\pm$ 0.07 with a standard deviation of 0.53."
 Therefore. it is possible that these 54 objects in Subsample Co are not. genuine," Therefore, it is possible that these 54 objects in Subsample C are not genuine"
is also shown.,is also shown.
 Svnthetie colors caleulatecl [or these models show that the Nitrogen-enriched atmosphere produces the closest matel to the (J—iv) and (11-- RA) photometry., Synthetic colors calculated for these models show that the Nitrogen-enriched atmosphere produces the closest match to the $J\!-\!K$ ) and $H\!-\!K$ ) photometry.
 We have nol attempted to modify our input chemistry further to optimize these fits. since such results would necessarily be of limited significance given the uncertainties in the available opacity data and (he limited wavelength coverage of our spectra.," We have not attempted to modify our input chemistry further to optimize these fits, since such results would necessarily be of limited significance given the uncertainties in the available opacity data and the limited wavelength coverage of our spectra."
 Clearly a direct detection of the waler absorption in the //-band. which we expect to occur at jam. andl J-band spectra. would help in resolving these uncertainties.," Clearly a direct detection of the water absorption in the $H$ -band, which we expect to occur at $\mu$ m, and $J$ -band spectra, would help in resolving these uncertainties."
 Such data would also allow for the study of irradiation. which is expected (to have the strongest impact at shorter wavelengths (Barman et al.," Such data would also allow for the study of irradiation, which is expected to have the strongest impact at shorter wavelengths (Barman et al."
 2000)., 2000).
 In conclusion. a brown dwarf with a considerable deficiency of Carbon. a lesser depletion of Oxvgen. and an enhancement of Nitrogen. reproduces much of the secondarys IR. SED. and the shape of the A-band at phase 0.0.," In conclusion, a brown dwarf with a considerable deficiency of Carbon, a lesser depletion of Oxygen, and an enhancement of Nitrogen, reproduces much of the secondary's IR SED, and the shape of the $K$ -band at phase 0.0."
 The additional absorption at jam cannot be accounted for in the current models., The additional absorption at $\mu$ m cannot be accounted for in the current models.
 If this band is indeed due to Fell. we expect it to become relatively stronger when the steam bands are reduced.," If this band is indeed due to FeH, we expect it to become relatively stronger when the steam bands are reduced."
 In that case the spectra could probably reproduce the “base” of the //-bancl emission., In that case the spectra could probably reproduce the “base” of the $H$ -band emission.
 The shape of the actual peak. however. does not correspond to any known stellar features. and also shows changes with phase that cannot be explained by inradiation effects.," The shape of the actual peak, however, does not correspond to any known stellar features, and also shows changes with phase that cannot be explained by irradiation effects."
 We conclude that evelotron emission al yam contaminates (he infrared spectrum for all orbital phases., We conclude that cyclotron emission at $\mu$ m contaminates the infrared spectrum for all orbital phases.
 It is clear (hat the /Eband spectra are inconsistent with Chat of a normal (or chemically altered) late-twpe or brown dwarf secondary. star., It is clear that the -band spectra are inconsistent with that of a normal (or chemically altered) late-type or brown dwarf secondary star.
 If the phase 0.0 dip near 1.6 jan is associated with Fell. then we estimate that of the L-band flux at this juncture is due to evelotvon emission.," If the phase 0.0 dip near 1.6 $\mu$ m is associated with FeH, then we estimate that $\approx$ of the $H$ -band flux at this juncture is due to cyclotron emission."
 Thus. to produce the observed. phase-dependent changes in the," Thus, to produce the observed, phase-dependent changes in the"
and au equation for the iiaguetie fux.,and an equation for the magnetic flux.
" Hore. T7, is tle stress enerev tensor of the matter aud the electromagnetic field. the primes denote quautitics in the frame of the frout. and verav. “svn. ete denote different forces or energv fluxes discussed by RL97."," Here, $T_{\alpha \beta}^\prime $ is the stress energy tensor of the matter and the electromagnetic field, the primes denote quantities in the frame of the front, and “grav,” “syn,” etc denote different forces or energy fluxes discussed by RL97."
" The equations were solved for different intrinsic xuaneters (RL97). but the example used below corresponds to a black hole mass Af=3&10M. uagnetie field at the base of the jet By=10°C. initial ion/lepton ratio f;=1. magnuoetic/particle energy at the ose of the jet po=15. viewing augle @=0.2 rad. the tmuunosity of background phnotous L,j,=10eyest, heir cuerey oem€,=10eV. and radius of their distribution Ryyον "," The equations were solved for different intrinsic parameters (RL97), but the example used below corresponds to a black hole mass $M = 3\times 10^8 M_{\odot}$, magnetic field at the base of the jet $B_0 = 10^3~{\rm G}$, initial ion/lepton ratio $f_{li}=1$, magnetic/particle energy at the base of the jet $\mu=15$, viewing angle $\theta=0.2~{\rm rad}$ , the luminosity of background photons $L_{ph}=10^{46} {\rm erg~s^{-1}}$, their energy $\epsilon_{ph}=10~ {\rm eV}$, and radius of their distribution $R_{ph}\approx 3\times 10^{17} {\rm cm}$."
"The deusity aud magnetic field ratios )etween the ""old"" aud “new matter are qnozz0.1 and By,fD,~ 0.4."," The density and magnetic field ratios between the “old"" and “new"" matter are $n_1/n_2 \approx 0.4$ and $B_1/B_2 \approx 0.4$ ."
 The velocities correspond to a bulk Loreutz actors Py=8 aud Do—18 (where P=|l(eje) H3, The velocities correspond to a bulk Lorentz factors $\Gamma_1=8$ and $\Gamma_2=18$ (where $\Gamma=[1-(v_j/c)^2]^{-1/2}$ ).
 The cases of a siugle aud reverse polarity of the maguetic field across the front were investigated aud compared., The cases of a single and reverse polarity of the magnetic field across the front were investigated and compared.
 After expulsion of new iatter. the frout accelerates up o Dz12. so that the Doppler boost factor is à=l/T] (ejfe)eos0]z 1.," After expulsion of new matter, the front accelerates up to $\Gamma\approx 12$, so that the Doppler boost factor is $\delta =
{1/{\Gamma[1-(v_j/c) {\rm cos} \theta]}} \approx 4$ ."
" Leptous are accelerated in the vont from 5=1 to c4c 10, οz105δν107. and 53%(6x10724 104)."," Leptons are accelerated in the front from $\gamma=1$ to $\gamma_1\approx 10^2$ , $\gamma_2\approx 10^3-5\times 10^3$, and $\gamma_3\approx (6\times 10^3-2\times 10^4)$ ."
 In the case of reversal olarity leptons are accelerated wp to higher energies: 259c10h10% aud 54zm10°)109.," In the case of reversal polarity leptons are accelerated up to higher energies: $\gamma_2\approx 10^4-10^5$, and $\gamma_3\approx 10^5-10^6$."
" These maxinunm values of ~ depend on the duration of expulsion of ""new? uatter with opposite polarity."," These maximum values of $\gamma$ depend on the duration of expulsion of “new"" matter with opposite polarity."
 Reconnection of the magnetic field may occur along the jet. in particular. in the frout. where matter is compressed.," Reconnection of the magnetic field may occur along the jet, in particular, in the front, where matter is compressed."
" The magnetic field at large distances is D,—Bolro/r;).", The magnetic field at large distances is $B_\phi = - B_0 (r_0/r_j)$.
" The maguetie eunerevdensity at some distance : along he jet is B2/s7 so that the total magnetic energy in the yout is E,=(B2/smjrr?). where we supposed that the region is a evliuder with a leugth equal to its radius."," The magnetic energy–density at some distance $z$ along the jet is $B_\phi^2/{8 \pi}$ so that the total magnetic energy in the front is $E_m=(B_\phi^2/{8\pi})(\pi r^3)$, where we supposed that the region is a cylinder with a length equal to its radius."
 Ifthe uaenetic field reverses polarity across the frout. then this uaenetie cherev nav be released entirelv iu the form of accelerated particles during au Alfveun time f£4=rjf. where the Alfvéóun velocity eqο|£zpe?DyE ," If the magnetic field reverses polarity across the front, then this magnetic energy may be released entirely in the form of accelerated particles during an Alfvénn time $t_A = r_j/v_A$, where the Alfvénn velocity $v_A = c/(1+ 4\pi \rho c^2/B_\phi^2)^{1/2} \sim c$."
"Thus. the ""Iuninositv owiug to the reconnection is The spectrmu of leptons resulting from collisiouless driven reconnection is a power law 57? for electron-diou plasma. aud 5.+? for olectrou-positron plasma (RL92)."," Thus, the “luminosity” owing to the reconnection is The spectrum of leptons resulting from collisionless driven reconnection is a power law $\gamma^{-2}$ for electron-ion plasma, and $\gamma^{-1.5}$ for electron-positron plasma (RL92)."
 In our analysis of the tine evolution ofthe front ina Povuting flux jet. we took into account the anmililation of magnetic field in the case where the field reverses polarity across the front.," In our analysis of the time evolution of the front in a Poynting flux jet, we took into account the annihilation of magnetic field in the case where the field reverses polarity across the front."
 We found larger particles cnereies in the case where the field reverses polarity., We found larger particles energies in the case where the field reverses polarity.
 The particle content of the jets is not kuown (Ixrolik. these Proceedings).," The particle content of the jets is not known (Krolik, these Proceedings)."
 In our model. the density of svuchrotron photons inside the front is typically wach lavgcr (10110° times) than the deusity of the backeround photons (see also RL97).," In our model, the density of synchrotron photons inside the front is typically much larger $10^4-10^5$ times) than the density of the background photons (see also RL97)."
 Interaction of the electrons with these photons produces a high density of highenergy SSC photons., Interaction of the electrons with these photons produces a high density of high–energy SSC photons.
" Analysis of different possible uechanisms of pair creation leads to the conclusion that interaction of SSC photons with svuchrotron photons is the most iurportaut process,", Analysis of different possible mechanisms of pair creation leads to the conclusion that interaction of SSC photons with synchrotron photons is the most important process.
" A pair forms when syn€ss27(n(1, where Cyn and e; are energies of svuchnrotron aud SSC photons."," A pair forms when $\epsilon_{syn} \epsilon_{ssc} > (m_e c^2)^2$, where $\epsilon_{syn}$ and $\epsilon_{ssc}$ are energies of synchrotron and SSC photons."
" For rough estuuates. we cau write eiy,(32)?hal. where w=οf£Gnie) is the cvclotron frequency in the frout frame. e;=esu. and |] is the 1nagnetie field streneth in the frout frame."," For rough estimates, we can write $\epsilon_{syn}=(3/2) \gamma^2 \hbar
\omega_o'$, where $\omega_o' = e| B'|/(m_ec)$ is the cyclotron frequency in the front frame, $\epsilon_{ssc} = \gamma^2 \epsilon_{syn}$, and $|B'|$ is the magnetic field strength in the front frame."
 An approximate condition for pair production is Electronpositron recombination is negligible for the conditions considered., An approximate condition for pair production is Electron–positron recombination is negligible for the conditions considered.
 We observed that the pairs form at a variety of parameters ofthe model., We observed that the pairs form at a variety of parameters ofthe model.
 Ina typical case. thetotal umber of pairs in the froutNy)erows proportionally to the total uumuber of 1015 N; accinulated by the front.," In a typical case, thetotal number of pairs in the front$N_l$grows proportionally to the total number of ions $N_i$ accumulated by the front."
 Thus. their ratio fj;=NYPN; is almost coustant duiug," Thus, their ratio $f_{li}\equiv N_l/N_i$ is almost constant during"
Moreover. we have have used (3.1)) for the second inequality.,"Moreover, we have where we have used \ref{sa5sD6}) ) for the second inequality."
 From (3.30)). (3.32)) aud (3.33)). we get: / np constant C' > 0.Step2.3. r X 1/2).Finally.putting together (3.30)) and (3.31)). we deduce tha / Ia the second line. we have used that r € (0.1).andthat r| log r|isbouucded. Step Putting (3.26)). (3.27)) aud (3.35)). we get (3.5)).," From \ref{Reg_eq3}) ), \ref{Reg_eq4}) ) and \ref{JM1}) ), we get: for some constant $C>0$ (Conclusion for $r\leq r_{2}/2$ Finally, putting together \ref{Reg_eq3}) ) and \ref{JM2}) ), we deduce that where in the second line, we have used that $r\in (0,1)$, and that $r|\log r|$ is (General Putting together \ref{misang}) ), \ref{result2}) ) and \ref{mwbasyd}) ), we get \ref{5s5_2}) )."
 ∎ ∖↾∖⊽≺↵⋜⋃⋅≺↵∐∩∖∖↽↓⋅≺↵⋜↕≺⇂⊽∖⊽↕∩⊳∖↕∩∖∖↽↕∐≺↵↥↽∐⋅∩∩↥⋅∩↥⋅↥↽⋝↕⋅∩↥↽≻∩↜∖∐↕∩∐∙⋅⋝⋅↕⋅⋅, $\hfill{\blacksquare}$ We are now ready to show the proof of Proposition \ref{prop1}.
 ⊉↕⋔⊖⊖↕↴⊖↕↴⊉↕⋔⊖↕⊃⊖⊟↕⊔⊖∐⇣⊰∙↕∙⇀−∖↥↽≻↥↽≻↥⊽∖⊽∎∐∑≟≺↵⊳∖∏∐⋯↕≺↵↸∫⊇⋅∶⋝⊤⊔⋅∖∖↽↥∐↕∣∣∣∶∣∣∶↕⋅↕∩↕∐≺↵↥∎⇂⇂∐∢∙∏∩∐∖↓∣∣⊽∈ — cofam cosa = Mes ∐≺↵↕⋅≺↵⋅∖∖↽≺↵∐⋜↕∖⇁≺↵⋜↕↥⊳∖∩⋃⊳∖≺↵≺⊔∐≺↵↥⋅⋜∥⋅↕↕∐⋜↕↕∖↓∣∶↕∩∖⇁≺↵↕⋅≤≥⊻⊽↸⋮↜∖≺↵≺↲≼⋮∶⋝⋅≺∪⊔," Applying estimate \ref{cara_eq1}) ), with $m=n=1$, to the function $\Psi\ti{u}\in W^{2,1}_{2}(\R^{2})\subseteq L^{\infty}(\R^{2})$ , we get: Here, we have also used the fact that $\Psi=1$ over $\Omega_T$ (see \ref{cut_off}) ))."
⋅↸⊽⊳∖↥∐∑∸⋜⋮∶⋝⋅⊤⊔−↸⋮∙⋅⋝⋅↖∖∎⊔⋜↕∐≺⊔∐≺↵ above inequality. we directly get. (3.1)).," Using \ref{5s5_1}) ), \ref{5s5_2}) ) andthe above inequality, we directly get \ref{prop1_eq}) )."
 a One of the main motivations for starting with the detailed proof of Proposition 3.1. (a simplified version of Theorem 1.2)) is that it was used to show [?.Theorem1.1].., $\hfill{\blacksquare}$ One of the main motivations for starting with the detailed proof of Proposition \ref{prop1} (a simplified version of Theorem \ref{theorem2}) ) is that it was used to show \cite[Theorem 1.1]{IJM_PI}.
 The other motivation is that the arguments of the proof of Theorem1.2. are all contained in the proof of Proposition 3.1..," The other motivation is that the arguments of the proof of Theorem\ref{theorem2}
 are all contained in the proof of Proposition \ref{prop1}."
 It sullices to make the following generalizations that we list, It suffices to make the following generalizations that we list.
"In order to extend the function «u⋅ €Ἡ""ul⇁⋅↽≻⋡∣“Orytothe function à⋅ ο€M""ulExtension""Onwith ο =(—1.2)""x(CT.27).we first make the extension separately aud successively with respect to the spatial variables πρ with ¢ =τετ, Thenwe make the extension with respect to the time variable that is treated somehow clillerently."," In order to extend the function $u \in W_{2}^{2m,m}(\Omega_{T})$ to the function $\ti{u}\in
W_{2}^{2m,m}(\widetilde{\Omega}_{T})$ with $\widetilde{\Omega}_{T}=(-1,2)^{n}\times (-T,2T)$, we first make the extension separately and successively with respect to the spatial variables $x_{i}$ , with $i=1\cdots n$ .Then we make the extension with respect to the time variable that is treated somehow differently."
 Fix (ro.....tyA)€(ο.1}Dx(0. T). the spatial exteusion of «t ," Fix $(x_{2},.\,.\,.\,,\,x_{n}, t)\in (0,1)^{n-1}\times
(0,T)$ , the spatial extension of $u$ "
is in the range of previousestimates*.,is in the range of previous.
. As discussed in Perrin et al. (, As discussed in Perrin et al. (
"2006), it is highly unlikely that the morphology arises from foreground extinction as suggested explanation to the morphology of the Padgett et al. (","2006), it is highly unlikely that the morphology arises from foreground extinction as suggested explanation to the morphology of the Padgett et al. ("
1999) sample.,1999) sample.
 Perrin et al. (, Perrin et al. (
2006) indeed discuss photoevaporation as a possible source for the extended emission.,2006) indeed discuss photoevaporation as a possible source for the extended emission.
" However, they oversimplify the photoevaporation model by just considering the radial scale rg, ignoring the fact that, as discussed in Section 2, dust grains can be carried to very large distances in the wind, and that at several flow scale heights from the disc the streamlines are spherical."," However, they oversimplify the photoevaporation model by just considering the radial scale $r_g$, ignoring the fact that, as discussed in Section 2, dust grains can be carried to very large distances in the wind, and that at several flow scale heights from the disc the streamlines are spherical."
" Our models show that the use of rg in discussing the characteristic scales of the flow in dust is a poor approximation, since, as shown in Figure 2,, dust entrained at ~1rg can be easily carried to radii and heights of »20r, producing a dust density that varies on scales different to rg as shown in Figure 3."," Our models show that the use of $r_g$ in discussing the characteristic scales of the flow in dust is a poor approximation, since, as shown in Figure \ref{fig:amax}, dust entrained at $\sim1r_g$ can be easily carried to radii and heights of $>20r_g$ producing a dust density that varies on scales different to $r_g$ as shown in Figure 3."
 Perrin et al. (, Perrin et al. (
2006) present models of the object in which they construct an in-falling envelope with a jet cavity surrounding an extended passive accretion disc.,2006) present models of the object in which they construct an in-falling envelope with a jet cavity surrounding an extended passive accretion disc.
 While their model (Figure 6 of Perrin et al., While their model (Figure 6 of Perrin et al.
" 2006) can also reproduce extended emission, it cannot reproduce the distinctive ‘wingnut’ morphology seen in the observations and in the model presented in this work (see the top panels of Figure 4))."," 2006) can also reproduce extended emission, it cannot reproduce the distinctive `wingnut' morphology seen in the observations and in the model presented in this work (see the top panels of Figure \ref{fig:images}) )."
 However both the model presented by Perrin et al. (, However both the model presented by Perrin et al. (
2006) and the ones presented in this work fail to reproduce one important aspect of the observations.,2006) and the ones presented in this work fail to reproduce one important aspect of the observations.
 The observed colour of PDS 144N is such that the extended regions of the emission become dominated by the redder scattered light., The observed colour of PDS 144N is such that the extended regions of the emission become dominated by the redder scattered light.
 T'his is opposite to what is predicted by the Perrin et al. (, This is opposite to what is predicted by the Perrin et al. (
2006) model which predicts a colour variation of red to blue with height and the blue band dominating the emission at large height.,2006) model which predicts a colour variation of red to blue with height and the blue band dominating the emission at large height.
" This is due to a dust population whose maximum grains size decreases with height, as you move from the disc population to the envelope (ISM like) population."," This is due to a dust population whose maximum grains size decreases with height, as you move from the disc population to the envelope (ISM like) population."
" On the contrary, our model reproduce the sign of the observed colour variation i.e that the relative strength of the red light increases with height."," On the contrary, our model reproduce the sign of the observed colour variation i.e that the relative strength of the red light increases with height."
" This is demonstrated in Figure 6 where we plot the change in H-K"" and H-L’ for the 6=107? s! model as a function of height above the mid-plane for the 6=107? s~!, where there is variations in the grain population at sizes of a few microns, which dominate the scattering opacity at NIR wavelengths."," This is demonstrated in Figure \ref{fig:colour} where we plot the change in H-K' and H-L' for the $\Phi=10^{43}$ $^{-1}$ model as a function of height above the mid-plane for the $\Phi=10^{43}$ $^{-1}$, where there is variations in the grain population at sizes of a few microns, which dominate the scattering opacity at NIR wavelengths."
" While our models predict that the colours become redder with height above the disc (due to the fact that larger grains are entrained at greater height, see Figure 2,, and these scatter red light more efficiently), our models predict scattered blue light to remain dominant at large heights (see Figure 4)."," While our models predict that the colours become redder with height above the disc (due to the fact that larger grains are entrained at greater height, see Figure \ref{fig:amax}, and these scatter red light more efficiently), our models predict scattered blue light to remain dominant at large heights (see Figure 4)."
" As discussed in Section ??,, in our model blue light dominates due to the spectral slope of the irradiating SED and the fact that small grains are present in the wind at all heights."," As discussed in Section \ref{sec:images}, in our model blue light dominates due to the spectral slope of the irradiating SED and the fact that small grains are present in the wind at all heights."
 We estimate using Figure 3 of Perrin et al. (, We estimate using Figure 3 of Perrin et al. (
"2006) a change in H-L’ (A(H-L)) of 21.5, at least three times larger than our simple model can predict.","2006) a change in H-L' $\Delta$ (H-L)) of $>$ 1.5, at least three times larger than our simple model can predict."
" However, in order to allow the redder bands to dominate over the bluer bands one needs to (i) increase the available disc emission at the redder wavelengths so there is more original flux to scatter and/or (ii) remove the smaller grains which are currently dominating the scattered light (iii) increase the optical depth to the star/disc so the extended region becomes optically thick, resulting in the reddening of photons as they pass through."," However, in order to allow the redder bands to dominate over the bluer bands one needs to (i) increase the available disc emission at the redder wavelengths so there is more original flux to scatter and/or (ii) remove the smaller grains which are currently dominating the scattered light (iii) increase the optical depth to the star/disc so the extended region becomes optically thick, resulting in the reddening of photons as they pass through."
 Grain growth in the disc provides a natural solution to both (i) and (ii)., Grain growth in the disc provides a natural solution to both (i) and (ii).
 Dullemond Dominik (2005) have shown that the dust grains in a disc easily grow to ~ lum reducing the opacity of the disc at shorter wavelengths and resulting in a disc spectrum that falls less steeply or even rises to longer wavelengths in the 1-5um range., Dullemond Dominik (2005) have shown that the dust grains in a disc easily grow to $\sim 1\mu$ m reducing the opacity of the disc at shorter wavelengths and resulting in a disc spectrum that falls less steeply or even rises to longer wavelengths in the $\mu$ m range.
" Furthermore, the removal of small grains from the disc will also result in the removal of small grains from the wind, reducing the scattering efficiency at the shorter bluer radiation."," Furthermore, the removal of small grains from the disc will also result in the removal of small grains from the wind, reducing the scattering efficiency at the shorter bluer radiation."
" Future observations of the Ίθμπι silicate feature may help disentangle the origin of the dust particles in the extended region around PDS 144N since an in-falling envelope would be entirely composed of amorphous ISM type grains, while, as shown by our models, a photoevaporative wind origin implies the presence of crystalline silicate grains in the extended regions."," Future observations of the $10\mu$ m silicate feature may help disentangle the origin of the dust particles in the extended region around PDS 144N since an in-falling envelope would be entirely composed of amorphous ISM type grains, while, as shown by our models, a photoevaporative wind origin implies the presence of crystalline silicate grains in the extended regions."
 We have considered the fate of dust grains that can be entrained in a photoevaporative wind from the surface of a disc surrounding a Herbig Ae/Be star., We have considered the fate of dust grains that can be entrained in a photoevaporative wind from the surface of a disc surrounding a Herbig Ae/Be star.
" For a median loss rate of ~107? Moyr-!, we find that grains up to radii of several microns can be entrained in the wind."," For a median mass-loss rate of $\sim10^{-9}$ $_\odot$ $^{-1}$, we find that grains up to radii of several microns can be entrained in the wind."
" We also show that, once entrained in the wind, the dust grains will remain entrained and be carried out to very large radius."," We also show that, once entrained in the wind, the dust grains will remain entrained and be carried out to very large radius."
" We have considered the observational imprint of this wind-entrained dust on edge-on discs, showing that the combination of a photoevaporative wind structure and a variable dust grain population resulting from the variable drag force at the base of the wind, can naturally reproduce a ‘wingnut’ morphology of the dust density distribution in the wind."," We have considered the observational imprint of this wind-entrained dust on edge-on discs, showing that the combination of a photoevaporative wind structure and a variable dust grain population resulting from the variable drag force at the base of the wind, can naturally reproduce a `wingnut' morphology of the dust density distribution in the wind."
 Using a combination of Monte-Carlo and ray, Using a combination of Monte-Carlo and ray
If we make the opposite assumption that when the thermatlizecl energy is adiabatically returued to the flow alone ος. the winds are completely mixed aud reach a siugle joint. characteristic velocity. then we get the maximal explosive support of the opening auele 0.,"If we make the opposite assumption that when the thermalized energy is adiabatically returned to the flow along $\thetas$, the winds are completely mixed and reach a single joint characteristic velocity, then we get the maximal explosive support of the opening angle $\thetas$."
 The additional support comes [rom the fact that uot only is the ram pressure perpeucicular to the shock therinalized. but even some of the ram pressure initallyalong the shock is thermalized. when the winds mix aud reach a common speed.," The additional support comes from the fact that not only is the ram pressure perpendicular to the shock thermalized, but even some of the ram pressure initally the shock is thermalized, when the winds mix and reach a common speed."
 This is essentially au increase in gas pressure clue to frictioual heating. and so we expect the smallest (0) in this case.," This is essentially an increase in gas pressure due to frictional heating, and so we expect the smallest $\momrat(\thetas)$ in this case."
 Here our global coustraint on 2s comes from the total scalar kinetic enerey flux and the total scalar mass flux that euter the shock zone. which iust iu turn flow out at a single characteristic speed. approximately aloug 0.. iu a imauuer consistent. with P.," Here our global constraint on $\ps$ comes from the total scalar kinetic energy flux and the total scalar mass flux that enter the shock zone, which must in turn flow out at a single characteristic speed, approximately along $\thetas$, in a manner consistent with $\ps$."
" Following this logie. the scalar mass [lux per wedge thickuess do. again in units where the total scalar momentum flux from star A is Sz. is AL, = Ihelas)) + (1+cos0.)).. auc the scalar kinetic energy flux in those units is Λι == (l-cos0.,))r4 c cos0i))eg which results in the coustraiut pDo—--— a2 .. where we have defined w=va/ep."," Following this logic, the scalar mass flux per wedge thickness $d\phi$, again in units where the total scalar momentum flux from star A is $8\pi$, is M_s = ) + ), and the scalar kinetic energy flux in those units is K_s = = (1 - ) + ) which results in the constraint = 2 , where we have defined $u = \va/\vb$."
 Applying eqs. (2.3)), Applying eqs. \ref{momrat}) )
 and (2.3)) then gives aud the expressions for P aud 2. may also be written in closed form but they are quite long and involved., and \ref{psfind}) ) then gives and the expressions for $\ps$ and $\pe$ may also be written in closed form but they are quite long and involved.
 Although it is not inunediately obvious. the result in eq. (17))," Although it is not immediately obvious, the result in eq. \ref{momratadmix}) )"
 doesindeed reduce, doesindeed reduce
results [rom the cosmological simulatious (Bahlcalletal.2000).. shown in Figures 1 - 3 [using GMfLA)esirieur=11000+20% for the simulation normalization (see Baheall et al.,"results from the cosmological simulations \citep{ba00}, shown in Figures 1 - 3 [using $(M/L_V)_{critical}=1400h \pm 20\%$ for the simulation normalization (see Bahcall et al."
" 2000)]. we find a global inass density. parameter of £2,=0.17£0.05."," 2000)], we find a global mass density parameter of $\Omega_m = 0.17 \pm 0.05$."
 The mean representative imass-to-light ratio for the universe is AL/Ly=210c50. comparable to that exhibited by groups aud poor clusters.," The mean representative mass-to-light ratio for the universe is $M/L_V = 240 \pm 50 h$, comparable to that exhibited by groups and poor clusters."
the extremes at cach period.,the extremes at each period.
" We adopt. a stellar radius.li-20851t..fora 19 Myr. 0.5 M. star (Baralle and a planet radius. It, 20.13 R.. which is consistent with a Jupiter mass planet of this age and roughly reprocluces the depth of the feature in the observed lighteurve."," We adopt a stellar radius,$_{s}=0.85$ $_{\odot}$, for a 12 Myr, 0.5 $_{\odot}$ star \citep{Baraffe98} and a planet radius, $_{p}$ =0.13 $_{\odot}$, which is consistent with a Jupiter mass planet of this age and roughly reproduces the depth of the feature in the observed lightcurve."
" A quadratic imb darkening law is used with parameters foundin Claret(2000) [or a star with T,ry=3500 Ix and loge=4.0.", A quadratic limb darkening law is used with parameters foundin \citet{Claret} for a star with $_{eff}=3500$ K and $=4.0$.
 The long period planet models (P =14.68 davs) shown iere are inconsistent. with the data due to their relatively ong ingress compared to the sharpness of the observed dip., The long period planet models (P $=14.68$ days) shown here are inconsistent with the data due to their relatively long ingress compared to the sharpness of the observed dip.
 Consequently. planets on longer. period orbits would also oe unable to explain the data.," Consequently, planets on longer period orbits would also be unable to explain the data."
 The short. period. planet (P =1.49 davs) on a circular orbit (6= 0.0) is also larecly inconsistent with the observed. sharpness of the dip., The short period planet (P $=1.49$ days) on a circular orbit $e=0.0$ ) is also largely inconsistent with the observed sharpness of the dip.
 The ingress of the short. period planet on the highly. eccentric orbit. provides the closest. match to the shape of the dip. however Lt still does not replicate the sharpness of the observed. feature.," The ingress of the short period planet on the highly eccentric orbit provides the closest match to the shape of the dip, however it still does not replicate the sharpness of the observed feature."
 In summary. we placed constraints on the properties of a potential orbiting planet that could have caused the drop in brightness of AU Mic that was observed on JD. 2453590.," In summary, we placed constraints on the properties of a potential orbiting planet that could have caused the drop in brightness of AU Mic that was observed on JD 2453590."
 The combination of the deep. sharp. non-repeated dip makes it unlikely that the observed feature. shown in Figure 5.. was caused by a transiting planet.," The combination of the deep, sharp, non-repeated dip makes it unlikely that the observed feature, shown in Figure \ref{fig:dip}, was caused by a transiting planet."
 In addition. there is no reason for us to believe the feature is caused by an instrumental problem.," In addition, there is no reason for us to believe the feature is caused by an instrumental problem."
" ""Therefore. we conclude this single event. which mümicks a planetary. transit is unexplained. and additional data is required to determine its true nature."," Therefore, we conclude this single event which mimicks a planetary transit is unexplained, and additional data is required to determine its true nature."
 In order to search for smaller. planets in the data. we first remove the dip in brightness discussed in 4.2. hy subtracting the average depth of the dip (26.4 mmag) from the data points between LLJD=2453590.884766 and 11D— 2453500.808682.," In order to search for smaller planets in the data, we first remove the dip in brightness discussed in \ref{sec:eventanal} by subtracting the average depth of the dip (26.4 mmag) from the data points between $=2453590.884766$ and $=2453590.898682$ ."
 We then re-run the box-fitting algorithm., We then re-run the box-fitting algorithm.
 In this trial. the highest. peak in the periodogram has a S/N=6-4. and thus is only consistent with noise.," In this trial, the highest peak in the periodogram has a $6.4$, and thus is only consistent with noise."
 Dherefore. we do not detect any significant. low-aniplitucle periodic box-shaped dips in brightness.," Therefore, we do not detect any significant, low-amplitude periodic box-shaped dips in brightness."
 The implications of this detection are discussed below., The implications of this non-detection are discussed below.
 ‘To set limits on the type of planet which could have been detected in our data. we generated: simulated lighteurves with fake transits accded to the observed. data and tried to recover the transit signal.," To set limits on the type of planet which could have been detected in our data, we generated simulated lightcurves with fake transits added to the observed data and tried to recover the transit signal."
 In the simulations. we placed a planet in orbit around AU Mic in the plane of the debris disk. (inclination angle equal to 17 from the linc-of-sight).," In the simulations, we placed a planet in orbit around AU Mic in the plane of the debris disk (inclination angle equal to $1^{\circ}$ from the line-of-sight)."
 We adopted a host star radius of 0.85 It. for a 12 Myr. 0.5 M. star.," We adopted a host star radius of 0.85 $_{\odot}$ for a 12 Myr, 0.5 $_{\odot}$ star."
 The orbital phase of the simualtecl planet. was chosen randomly from a uniform distribution. and the orbital period. of the planet was chosen randomlv from a uniform cistribution within our search range (0.515 days).," The orbital phase of the simualted planet was chosen randomly from a uniform distribution, and the orbital period of the planet was chosen randomly from a uniform distribution within our search range (0.5–15 days)."
 ALL simulated: planets are assumed to be on circular orbits., All simulated planets are assumed to be on circular orbits.
 We made no attempt to adopt the distribution of orbital properties of known planets since there are no observed data to constrain these values at the age of AU Mic., We made no attempt to adopt the distribution of orbital properties of known planets since there are no observed data to constrain these values at the age of AU Mic.
 Noise-free model lighteurves were created using the analytic eclipse models of which were then added to a version of the observed. data in which the detected dip in brightness described in 4.2 was subtracted olf., Noise-free model lightcurves were created using the analytic eclipse models of which were then added to a version of the observed data in which the detected dip in brightness described in \ref{sec:eventanal} was subtracted off.
 Vhus. the simulated lishteurves with fake transits acded have the same noise properties and sampling as the observed lighteurvoe.," Thus, the simulated lightcurves with fake transits added have the same noise properties and sampling as the observed lightcurve."
 The fake transit lighteurves were run through the box-fitting algorithm using the same search parameters as the observed. data (searching for periods between 0.515 days and durations of ~ 15 hours))., The fake transit lightcurves were run through the box-fitting algorithm using the same search parameters as the observed data (searching for periods between 0.5–15 days and durations of $\sim$ 1–5 hours).
 The fake transits were considered: recovered if the transit signature was detected with a S/N >8.8 and the derived: period was within of the input orbital period., The fake transits were considered recovered if the transit signature was detected with a S/N $\ge 8.8$ and the derived period was within of the input orbital period.
 Alias periods which are one half or twice the input period are also considered recoveries., Alias periods which are one half or twice the input period are also considered recoveries.
 We ran two sets of simulations (with 400 lighteurves each) using two different planet. radii., We ran two sets of simulations (with 400 lightcurves each) using two different planet radii.
" First. we simulated a lA; planet in orbit around AW Mic. adopting radius. 1t, 20.134 R. for a 12 Myr. 1 AL; planet from Baralleοἱ (2002)."," First, we simulated a $1 M_{J}$ planet in orbit around AU Mic adopting radius, $_{p}$ =0.134 $_{\odot}$ for a 12 Myr, 1 $_{J}$ planet from \citet{Baraffe02}."
. Such a planet produces an unmistakable signal in the simulated. lisghteurves with a depth of 230 mmag., Such a planet produces an unmistakable signal in the simulated lightcurves with a depth of $> 30$ mmag.
 The recovery fraction is a strong function of input. period. as ds shown in Figure 6 which plots the fraction of transiting Jupiter mass planets detected in the simulations as a function of input orbital period.," The recovery fraction is a strong function of input period, as is shown in Figure \ref{fig:addtrans1} which plots the fraction of transiting Jupiter mass planets detected in the simulations as a function of input orbital period."
 I£ we consider only short. period. planets with periods. P<5 days. of the sample are significant detections with a S/N SON (solid line in Figure 6)). and for9554.. he period is also correctly recovered. (dashed line).," If we consider only short period planets with periods, $\le 5$ days, of the sample are significant detections with a S/N $> 8.8$ (solid line in Figure \ref{fig:addtrans1}) ), and for, the period is also correctly recovered (dashed line)."
 We ran an additional set of simulations using a planet which represents a possible Neptune-like planet at the age of AU. Mic., We ran an additional set of simulations using a planet which represents a possible Neptune-like planet at the age of AU Mic.
 Since the theoretical models do not reach the mass of Neptune and no voung Neptune mass planets have been observed. we simply adopt à mass. M =0.05 M... and a radius. R=0.054 It... which is 2.5 times smaller. than the radius of the 12 Myr old. Jupiter.," Since the theoretical models do not reach the mass of Neptune and no young Neptune mass planets have been observed, we simply adopt a mass, M $=0.05$ $_{\odot}$ and a radius, $=0.054$ $_{\odot}$ , which is 2.5 times smaller than the radius of the 12 Myr old Jupiter."
 “Phis tvpe of. planet produces a transit depth of ~5 mmag which is smaller than the noise limit. of the data., This type of planet produces a transit depth of $\sim 5$ mmag which is smaller than the noise limit of the data.
 However. for orbital periods.," However, for orbital periods,"
"Gaussian distribution if theunderlying LF is a power-law, distorted by the error distribution and the completeness function.","Gaussian distribution if the LF is a power-law, distorted by the error distribution and the completeness function."
" In a Monte-Carlo approach we draw artificial observations from the best-fitting power-law, use our statistics tools to fit them again with Gaussian and power-law distribution, and determine the likelihood ratio for these artificial observations."," In a Monte-Carlo approach we draw artificial observations from the best-fitting power-law, use our statistics tools to fit them again with Gaussian and power-law distribution, and determine the likelihood ratio for these artificial observations."
 The likelihood ratio of the observed distribution compared to the distribution of likelihood ratios from our artificial tests then yields the probability that the determined superiority of the Gaussian fits is consistent with an underlying power-law distribution., The likelihood ratio of the observed distribution compared to the distribution of likelihood ratios from our artificial tests then yields the probability that the determined superiority of the Gaussian fits is consistent with an underlying power-law distribution.
 The uncertainties of the best-fitting model parameters are estimated by bootstrapping., The uncertainties of the best-fitting model parameters are estimated by bootstrapping.
" For additional details of the statistical model, see ?.."," For additional details of the statistical model, see \cite{Anders07}."
" As example, the LF in the V band for our YSC sample in the Antennae galaxies is shown in Fig. 3.."," As example, the LF in the V band for our YSC sample in the Antennae galaxies is shown in Fig. \ref{fig:fits}."
" From visual inspection, the best fit with an underlying Gaussian distribution appears to represent the data better than the best fit with an underlying power-law distribution."," From visual inspection, the best fit with an underlying Gaussian distribution appears to represent the data better than the best fit with an underlying power-law distribution."
" To quantify this, we perform our likelihood ratio test and the Monte-Carlo analysis."," To quantify this, we perform our likelihood ratio test and the Monte-Carlo analysis."
 For the observed distributions we find a likelihood ratio value of 23.1 (where larger values are equivalent to a stronger superiority of the Gaussian fit when compared to the power-law fit)., For the observed distributions we find a likelihood ratio value of 23.1 (where larger values are equivalent to a stronger superiority of the Gaussian fit when compared to the power-law fit).
" The Monte-Carlo analysis with 1000 test realisations drawn from the best-fitting power-law distribution results in a maximum likelihood ratio of 11.4, hence of the test distributions can reproduce a superiority of the Gaussian distribution as strong as observed."," The Monte-Carlo analysis with 1000 test realisations drawn from the best-fitting power-law distribution results in a maximum likelihood ratio of 11.4, hence of the test distributions can reproduce a superiority of the Gaussian distribution as strong as observed."
" Utilising the properties of Bernoulli-distributed variables, this corresponds to a probability « that the underlying distribution is still consistent with a power-law."," Utilising the properties of Bernoulli-distributed variables, this corresponds to a probability $<$ that the underlying distribution is still consistent with a power-law."
" This result is valid also for the other bands (except the I band, for which the observations are significantly shallower), and for several age and size subsamples."," This result is valid also for the other bands (except the I band, for which the observations are significantly shallower), and for several age and size subsamples."
" For more details, see ?.."," For more details, see \cite{Anders07}. ."
"B,=2~x10!5 G at maximum, similar to models used in previous studies and close to what one expects to be the final geometry after MHD equilibrium is reached in a hot, liquid, proto-NS (Ciolfietal.2009,2010;Lander&Jones2009).","$B_t=2 \times
10^{15}$ G at maximum, similar to models used in previous studies and close to what one expects to be the final geometry after MHD equilibrium is reached in a hot, liquid, proto-NS \citep{Ciolfi2009,Ciolfi2010,LJ2009}."
". In this particular model, at the age of 10 yrs the dipolar field has decreased to about of its initial value, while its internal toroidal field has been dissipated by more than a factor of 2."," In this particular model, at the age of $10^4$ yrs the dipolar field has decreased to about of its initial value, while its internal toroidal field has been dissipated by more than a factor of 2."
" Other initial conditions modify quantitatively the results, but the general trends remain nearly the same."," Other initial conditions modify quantitatively the results, but the general trends remain nearly the same."
 The evolution is followed for 10? years., The evolution is followed for $10^5$ years.
" During this time, we monitor the frequency, angular distribution, and energetics of the fractures."," During this time, we monitor the frequency, angular distribution, and energetics of the fractures."
 Fig., Fig.
 1 shows a snapshot of the deviation of stresses from the previous equilibrium in a typical 2000 yr old magnetar., 1 shows a snapshot of the deviation of stresses from the previous equilibrium in a typical 2000 yr old magnetar.
 The yellow regions are close to the breaking limit., The yellow regions are close to the breaking limit.
 Note that at this age the crust has already suffered hundreds of fractures., Note that at this age the crust has already suffered hundreds of fractures.
 That results in the patched appearance., That history results in the patched appearance.
 For this run we have fixed historye=0.9., For this run we have fixed $\epsilon = 0.9$.
 The results about frequency and energy distribution of events are contained in Fig., The results about frequency and energy distribution of events are contained in Fig.
 2., 2.
 We remind again that groups of bursts connected to the same fracture are classified as a single outburst in our simulations., We remind again that groups of bursts connected to the same fracture are classified as a single outburst in our simulations.
" We selected three representative periods in a magnetar life, each involving the same total number of events (1000)."," We selected three representative periods in a magnetar life, each involving the same total number of events (1000)."
" The first is labeled ""Young"" and spans the interval between 400 and 1600 yrs."," The first is labeled ""Young"" and spans the interval between 400 and 1600 yrs."
" The second is labeled ""Mid age"" and covers the period ©7—10 kyrs, and the third period is named ""Old"" and corresponds to the events recorded from 60 to 100 kyrs."," The second is labeled ""Mid age"" and covers the period $\approx 7-10$ kyrs, and the third period is named ""Old"" and corresponds to the events recorded from 60 to 100 kyrs."
" Note that this classification does not pretend to reflect an exact correspondence to SGRs and AXPs, which is just terminology based on historical reasons."," Note that this classification does not pretend to reflect an exact correspondence to SGRs and AXPs, which is just terminology based on historical reasons."
" Objects that could belong to the first category (young or ""SGR-like"") are SGR 1806-20, SGR 1900-14 and 1E 1547.0-5408; to the Mid Age or ""AXP-like"" list could belong SGR 1627-41, SGR 0526-66, SGR 0501+4516, 1E1048.1-5937, or 1E 22594586 among others; finally, examples of old objects could be SGR 041845729, SGR 1833-0832, XTE J1810-197, and PSR 71814-1744."," Objects that could belong to the first category (young or ""SGR-like"") are SGR 1806-20, SGR 1900+14 and 1E 1547.0-5408; to the Mid Age or ""AXP-like"" list could belong SGR 1627-41, SGR 0526-66, SGR 0501+4516, 1E1048.1-5937, or 1E 2259+586 among others; finally, examples of old objects could be SGR 0418+5729, SGR 1833-0832, XTE J1810-197, and PSR J1814-1744."
 The first important result is that there is a significant difference in the energetics and recurrence time as the star evolves., The first important result is that there is a significant difference in the energetics and recurrence time as the star evolves.
" This is because the initial evolution of the crustal magnetic field is faster due to the Hall drift, while at late times its has been rearranged into a more quasi-steady state and the evolution proceeds slower."," This is because the initial evolution of the crustal magnetic field is faster due to the Hall drift, while at late times its has been rearranged into a more quasi-steady state and the evolution proceeds slower."
" In young magnetars, the typical energies released after each starquake are of the order of 1044 erg and the typical event rate ~ I/yr."," In young magnetars, the typical energies released after each starquake are of the order of $10^{44}$ erg and the typical event rate $\sim$ 1/yr."
" This does not necessarily imply that a flare will be observed, since this is the energy released in the crust and the mechanism to transfer energy to the surface and magnetosphere may not work in many cases, especially when the fracture occurs in the inner crust."," This does not necessarily imply that a flare will be observed, since this is the energy released in the crust and the mechanism to transfer energy to the surface and magnetosphere may not work in many cases, especially when the fracture occurs in the inner crust."
" However, in our simulations we observed that more than of the fractures occur in the outer crust, simply because the crust is less strong there, so that we expect a relatively high efficiency of the process."," However, in our simulations we observed that more than of the fractures occur in the outer crust, simply because the crust is less strong there, so that we expect a relatively high efficiency of the process."
" For mid-age objects the energetics is shifted to lower values, a second peak appears at about 1041 erg, and the waiting time between outbursts increases to a few years."," For mid-age objects the energetics is shifted to lower values, a second peak appears at about $10^{41}$ erg, and the waiting time between outbursts increases to a few years."
 This trend is more pronounced as the object gets older: the recurrence time becomes of the order of tens of and half the events are events., This trend is more pronounced as the object gets older: the recurrence time becomes of the order of tens of years and nearly half the events are low-energy events.
 The yearsphysical nearlyreason behind the bimodal low-energydistribution is the directionality of stresses., The physical reason behind the bimodal distribution is the directionality of stresses.
" We found that fractures associated to the magnetic stress component Μορ are more frequent, but are associated to very low events X1031 theyerg."," We found that fractures associated to the magnetic stress component $M_{\theta,\phi}$ are more frequent, but they are mostly associated to very low energy events $\lsim
10^{41}$ erg."
" On the mostlyother hand, fractures caused by energythe M; component are responsible for most of the E>1044 erg events."," On the other hand, fractures caused by the $M_{r,\phi}$ component are responsible for most of the $E\gsim10^{44}$ erg events."
" The events associated to large values of M,.9 span the whole range of energies, but they become very rare after a few kyrs, so that the long-term energy distribution becomes more bimodal."," The events associated to large values of $M_{r,\theta}$ span the whole range of energies, but they become very rare after a few kyrs, so that the long-term energy distribution becomes more clearly bimodal."
" On average, we find that events related to stresses clearlycreated by the toroidal field are a hundred times more frequent."," On average, we find that events related to stresses created by the toroidal field are a hundred times more frequent."
 Our simulations hence predict that giant flares are expected to be less frequent than the less energetic bursts., Our simulations hence predict that giant flares are expected to be less frequent than the less energetic bursts.
Consider the evolution of p(/)=2xIFatDidi. the expectation value of µ.,"Consider the evolution of $\overline{\mu}(t)=2\pi\int_{-1}^{1}F(\mu',t)\mu' d\mu'$, the expectation value of $\mu$."
 We have Or HT) IIence fy is the Gime constant for relaxation to a uniform distribution of orientations. 0. given a fixed binary separation and unchanging stellar background.," We have or ) =_0 Hence $t_0$ is the time constant for relaxation to a uniform distribution of orientations, $\overline{\mu}=0$ , given a fixed binary separation and unchanging stellar background."
 It may be expressed in physical units as lo _¢:—RN \)(, It may be expressed in physical units as t_0 = ).
"20) Next consider the more interesting case where a. as well as the parameters py and o, that describe (he field stars. may be changing with time."," Next consider the more interesting case where $a$ , as well as the parameters $\rf$ and $\sf$ that describe the field stars, may be changing with time."
 This time dependence is not easily specilied but we can make progress by changing evolution variables from / to e=οσααμ)., This time dependence is not easily specified but we can make progress by changing evolution variables from $t$ to $x\equiv\log(a/a_0)$.
 First combining equations (7)) and (20a)). we find — iain.," First combining equations \ref{eq_evol1}) ) and \ref{eq_defdv}) ), we find = ]."
) Now changing variables. |Oradl |— (cL.," Now changing variables, = = (cf."
 equation (14))) and so Or|lLm;ATE —righl]]., equation \ref{eq_defH}) )) and so = ].
 This equation gives the evolution of the binarys orientation in terms of changes in ils semi-major axis a. with noexplicit dependence on the parameters that describe (he stellar," This equation gives the evolution of the binary's orientation in terms of changes in its semi-major axis $a$ , with noexplicit dependence on the parameters that describe the stellar"
in Figure 2 a ,in Figure \ref{fig:HR} a ).
Thus it is unlikely that the peaks B and C are associated). with background or foreground objects., Thus it is unlikely that the peaks B and C are associated with background or foreground objects.
" Though we cannot state any strong conclusions about the detailed merger process due to the limited angular resolution, from the position of the hot spot, the absence of luminous galaxies in the peak B and relative high metalicity in the hot spot, we suggest the following possible scenario: a substructure recently passed close to the BCG with mixing, from north to south, and the central part of the substructure became the brightest peak B by compression, like the bullet cluster etal.2002).. In the(Mar"," Though we cannot state any strong conclusions about the detailed merger process due to the limited angular resolution, from the position of the hot spot, the absence of luminous galaxies in the peak B and relative high metalicity in the hot spot, we suggest the following possible scenario: a substructure recently passed close to the BCG with mixing, from north to south, and the central part of the substructure became the brightest peak B by compression, like the bullet cluster \citep{2002ApJ...567L..27M}."
"kevitch above, the presence of the peak C is not necessary."," In the above, the presence of the peak C is not necessary."
 Such a faint peak aligned with two other peaks also has been found in other mergingclusters etal.2002;Maurogordato2010)..," Such a faint peak aligned with two other peaks also has been found in other mergingclusters \citep{2002ApJ...565..867S, 2010arXiv1009.1967M}."
" Sunetal.(Sun(2002) discussed the origin of the faint peak in A2256 and suggest an another previous merger origin or the scenario that a fainter peak is originated from the gas of a middle peak, which lagged behind when merger (in this scenario the peak B should move from south)."," \cite{2002ApJ...565..867S} discussed the origin of the faint peak in A2256 and suggest an another previous merger origin or the scenario that a fainter peak is originated from the gas of a middle peak, which lagged behind when merger (in this scenario the peak B should move from south)."
" The former scenarios is possible for our target, but the latter do not explain the hot spot."," The former scenarios is possible for our target, but the latter do not explain the hot spot."
" In addition, we propose an another possible scenario: the peaks B and C belonged to one clump before the merging and it fell and split in two."," In addition, we propose an another possible scenario: the peaks B and C belonged to one clump before the merging and it fell and split in two."
 One passed near the center decreasing its velocity by pressure of ambient dense gas (peak B) and the other passed through relatively far from the center or in less dense region (peak C)., One passed near the center decreasing its velocity by pressure of ambient dense gas (peak B) and the other passed through relatively far from the center or in less dense region (peak C).
" Thus the peak C went ahead of the peak B. For the last scenario, the merger should be so significant as to separate gas from dark matter subclump."," Thus the peak C went ahead of the peak B. For the last scenario, the merger should be so significant as to separate gas from dark matter subclump."
" If the galaxy on the peak B is associated with the peak, however, the merger is not so strong."," If the galaxy on the peak B is associated with the peak, however, the merger is not so strong."
" In either case, we suggest that the hotspot is originated from adiabatic compression and heating by the densest clump (peak B)."," In either case, we suggest that the hotspot is originated from adiabatic compression and heating by the densest clump (peak B)."
 Figure 4 shows the galaxy distribution of the SDSS spectroscopic data along the line of sight., Figure \ref{fig:galdi} shows the galaxy distribution of the SDSS spectroscopic data along the line of sight.
 We found the bimodal distribution around the group., We found the bimodal distribution around the group.
" As shown by triangles in Figure 2 a), the galaxies in the distant peak (z—0.09 0.092) are widely distributed in the group."," As shown by triangles in Figure \ref{fig:HR} a), the galaxies in the distant peak $z=0.09-0.092$ ) are widely distributed in the group."
" If we assume both peaks are associated with the group, the velocity dispersion oy=1197+191kms""!is unusually higher than the expected value from T-ovy and Lx-oy relations (e.g.Osmond&Ponman 2004).."," If we assume both peaks are associated with the group, the velocity dispersion $\sigma_\mathrm{V} = 1197 \pm 191 \, \mathrm{km \, s^{-1}}$is unusually higher than the expected value from $T$ $\sigma_\mathrm{V}$ and $L_\mathrm{X}$ $\sigma_\mathrm{V}$ relations \citep[e.g.][]{2004MNRAS.350.1511O}. ."
" Performing the Anderson-Darling test, we found that the distribution deviates from the Gaussian = 2.33 compared with the critical value of non Gaussian,(A?* A?*>1.93 2009)."," Performing the Anderson-Darling test, we found that the distribution deviates from the Gaussian \citep[$A^{2\ast} = 2.33 compared with the critical value of non Gaussian, $A^{2\ast}>$ ."
" If we take the single peak belongs to the target only,cy=471+ 88kms~!, which"," If we take the single peak belongs to the target only,$\sigma_V=471 \pm 88 \,\mathrm{km \, s^{-1}}$ , which"
ionization and heating is not uuderstood (e.g.. Reyuolds 1995: Rand 1998).,"ionization and heating is not understood (e.g., Reynolds 1995; Rand 1998)."
 Observed line intensities. yarticulaἽν the high values of [S Πα and [N H]/Ha compared to those in traditional. discrete H II regions surroundiug O and early B stars sugeest that photoionization by a dilute radiation field jays au important role (e.g.. Domgórrgeu Mathis 1991): both models aud observations iudicate hat these emission lines originate primarily [rom warm (~101 Is regions in whicithe hydrogeu is early fuly louized (e.g... Semmbach οἱ al 1999: Revuolds et al 1998y.," Observed line intensities, particularly the high values of [S $\alpha$ and [N $\alpha$ compared to those in traditional, discrete H II regions surrounding O and early B stars suggest that photoionization by a dilute radiation field plays an important role (e.g., Domgörrgen Mathis 1994); both models and observations indicate that these emission lines originate primarily from warm $\sim 10^4$ K) regions in which the hydrogen is nearly fully ionized (e.g., Sembach et al 1999; Reynolds et al 1998)."
 I heis been suMODecested by Miller Cox {1993) aud Dove Shull (1991). for example. that Lymer COLuijuun racliation originating rom Osars penetrates the H I cloud layer aud ionizes diffuse iuerstelar gas within the disk aud ower halo.," It has been suggested by Miller Cox (1993) and Dove Shull (1994), for example, that Lyman continuum radiation originating from O stars penetrates the H I cloud layer and ionizes diffuse interstellar gas within the disk and lower halo."
 While O stars are the ouly known source with sullicient powe‘to 1naiutain the WIM. the ugh opacity of the interstellar HI has led others to propose tlie exIntelice of more widely clistributect sources of ionization (e.g.. Slavin et al 1993: Mellott et al 1988 aud Sciauma 1990: Rayimoud 1992: Skibo Ramaty 1993).," While O stars are the only known source with sufficient power to maintain the WIM, the high opacity of the interstellar H I has led others to propose the existence of more widely distributed sources of ionization (e.g., Slavin et al 1993; Mellott et al 1988 and Sciama 1990; Raymond 1992; Skibo Ramaty 1993)."
 Photoionization iuodels incorporating a low iouization parameter U (the ratio of photon deusity to gas density) have been generally successful in accounting for the elevated [S II]/Ha aud [N II]/Ha aud low [ο III] A5007/Ha ratios observed iu the WIM (e.g.. Dorugórrgen Mathis 1901: Creenawalt. Walterbos. Braun 1997: Martin 1907: Wane. Heckman. Lehnert 1998).," Photoionization models incorporating a low ionization parameter U (the ratio of photon density to gas density) have been generally successful in accounting for the elevated [S $\alpha$ and [N $\alpha$ and low [O III] $\lambda$ $\alpha$ ratios observed in the WIM (e.g., Domgörrgen Mathis 1994; Greenawalt, Walterbos, Braun 1997; Martin 1997; Wang, Heckman, Lehnert 1998)."
 However. the models have faied to explain observed iu sotie of the ratios.," However, the models have failed to explain observed in some of the ratios."
 For example. Band (1998) observed that [S H]/Ho aud [N H]/Ha increase with incveasing distance |z| from the midplane of NGC 891. havinD>ο values of 0.2 aud 0.35. respectively. lear z = 0. and 0.6 aud. 1.0. respectively. uear |z| = 2000 pe.," For example, Rand (1998) observed that [S $\alpha$ and [N $\alpha$ increase with increasing distance $|$ $|$ from the midplane of NGC 891, having values of 0.2 and 0.35, respectively, near z = 0, and 0.6 and 1.0, respectively, near $|$ $|$ = 2000 pc."
 To account for such large rati atlügh |z|. Haud had to acOpt a lard stellar spectru1i (an upper IMF cutoll of 120 AL.) plus acditinal hardening as the radiation propagated away from the uidplane.," To account for such large ratios at high $|$ $|$ , Rand had to adopt a hard stellar spectrum (an upper IMF cutoff of 120 $_{\odot}$ ) plus additional hardening as the radiation propagated away from the midplane."
 However. a hard spectrt luz:p2years LO be inconsistent. with He I A5876 recombiration liie observatious (Raul 1905. 1997. ane referencestherein).," However, a hard spectrum appears to be inconsistent with He I $\lambda$ 5876 recombination line observations (Rand 1998, 1997, and referencestherein)."
 More significanly. the models fail to account for the fact tlat. wlile the variations in [5 H]/Ha and [N II]/Hao are kuge. [S ΗΝ II] realls weary constant.," More significantly, the models fail to account for the fact that, while the variations in [S $\alpha$ and [N $\alpha$ are large, [S II]/[N II] remains nearly constant."
 A siluilar behavior for [S HI]. [N II]. and Ha has bee1 JServed in other gaaxies (e.g. Colla. Det111). Domedrrgen 1996: Otte Dettina: 1999) as wel as in the Milky Way (Hallier. Revuolds. Tute 1999).," A similar behavior for [S II], [N II], and $\alpha$ has been observed in other galaxies (e.g., Golla, Dettmar, Domgörrgen 1996; Otte Dettmar 1999) as well as in the Milky Way (Haffner, Reynolds, Tufte 1999)."
 Colla et al (1996) aud Raxd QOS have pointed out that the coustajt value o [S H]/[N IH] cannot ve reproduced by photoiouUzajon nodes. because iu these models variations it [S a and [N H]/Ha are primarily the reslt o[ va'jatlois in the ionization paraimeer U. which always produce arger changes in [5 II]/Ha tl ani1 [N II]/Ho.," Golla et al (1996) and Rand (1998) have pointed out that the constant value of [S II]/[N II] cannot be reproduced by photoionization models, because in these models variations in [S $\alpha$ and [N $\alpha$ are primarily the result of variations in the ionization parameter U, which always produce larger changes in [S $\alpha$ than in [N $\alpha$."
 This is due to the ciferent lonization pxtentials of S ancl N. with the result t alsultu “Call ye primarily Or primarily . depeucding on the spectrum and streneth of the racliatio1 [iecl. wliereas nitrogen remains primarily wider ue:uly all WIN couditious (e.g.. Howk Savage 1999).," This is due to the different ionization potentials of S and N, with the result that sulfur can be primarily $^+$ or primarily $^{++}$, depending on the spectrum and strength of the radiation field, whereas nitrogen remains primarily $^+$ under nearly all WIM conditions (e.g., Howk Savage 1999)."
 Another observation that pure photoionization models fail to reproduce is the rise in [O /H;j with increasing [z|. or increasing [S II]/Ha and [N H]/Ho (Raud 1998. Greenawalt et al 1997).," Another observation that pure photoionization models fail to reproduce is the rise in [O $\beta$ with increasing $|$$|$ , or increasing [S $\alpha$ and [N $\alpha$ (Rand 1998, Greenawalt et al 1997)."
 In, In
where 4 is the imaginary part of the complex momentum.,where $k^I$ is the imaginary part of the complex momentum.
" The mean [ree path can also be defined. for a proton. as wilh p, and p, the neutron and proton densities in asymmetric matter. equal to LN3—2 and Ay.)—. respectively, ("," The mean free path can also be defined, for a proton, as with $\rho_n$ and $\rho_p$ the neutron and proton densities in asymmetric matter, equal to $\frac{(k_F^n)^3}{3\pi^2}$ and $\frac{(k_F^p)^3}{3\pi^2}$, respectively. ("
An analogous definition holds for the neutron.),An analogous definition holds for the neutron.)
 The above expression represents the leneth of (he unit volume in the phase space defined by the elfective scattering area and the number of particles/volume [7].., The above expression represents the length of the unit volume in the phase space defined by the effective scattering area and the number of particles/volume \cite{PP}.
 Notice that we sel (he appropriate cross section to zero if (he nucleon momentum is less than or equal to the Fermi momentum (of that particular nucleon (wpe). since final states (as well as intermediate ones) are Pauli-blocked when calculating the mean Iree path for the reasons mentioned above.," Notice that we set the appropriate cross section to zero if the nucleon momentum is less than or equal to the Fermi momentum (of that particular nucleon type), since final states (as well as intermediate ones) are Pauli-blocked when calculating the mean free path for the reasons mentioned above."
 Equivalent considerations in Ref., Equivalent considerations in Ref.
 [1] meant. that the angular integration in Eq. (, \cite{sk05} meant that the angular integration in Eq. (
"3) was restricted through a condition involving 17, as well.",3) was restricted through a condition involving $P_{tot}$ as well.
 First. we show the mean free path of nucleons in svnuuetric matter as a function of the nucleon kinetic energy (calculated as 7=vican?— m). see Fig.," First, we show the mean free path of nucleons in symmetric matter as a function of the nucleon kinetic energy (calculated as $T=\sqrt{q_0^2+m^2}-m$ ), see Fig."
 1., 1.
 The chosen densities correspond to Fermi momenta of fi| and Lf+ for the dashed and the solid curve. respectively.," The chosen densities correspond to Fermi momenta of $fm^{-1}$ and $fm^{-1}$ for the dashed and the solid curve, respectively."
 The density dependence is quite large., The density dependence is quite large.
 Again. in the present approximation. (he cross section goes sharply to zero. ancl (hus the mean," Again, in the present approximation, the cross section goes sharply to zero, and thus the mean"
which show smaller Api when compared to quasars.,which show smaller $M_{\rm BH}$ when compared to quasars.
 However. given the small number of NLRG (only 3 objects). this result can not be considered very meaningful.," However, given the small number of NLRG (only 3 objects), this result can not be considered very meaningful."
 For the accretion rates. the results are different.," For the accretion rates, the results are different."
 We found that the ρωμα ratio for FSRQ is alwavs significantly larger than lor BLRG (Py—3x10.7) and SSRO (Pes=0.01)., We found that the $L_{\rm Bol}/L_{\rm Edd}$ ratio for FSRQ is always significantly larger than for BLRG $P_{\rm KS}=3\times10^{-3}$ ) and SSRQ $P_{\rm KS}=0.01$ ).
 Moreover a strong correlation (ir=0.72) between i and His present (ay<0.01) as appears evident in Figure G (left panel)., Moreover a strong correlation $r=0.72$ ) between $\dot{m}$ and $R$ is present $\alpha_{\rm K}<0.01$ ) as appears evident in Figure \ref{EffvsR} (left panel).
 Llowever we individuate (wo possible effects inducing the (nol necessary real) correlations. (, However we individuate two possible effects inducing the (not necessary real) correlations. (
1) The Doppler enhanced. non-thermal. emission. expected {ο increase wilh A. could shift the points (in particular FSRQ) to the upper region of the plot. because of an overestimation of Lp.,"1) The Doppler enhanced, non-thermal, emission, expected to increase with $R$, could shift the points (in particular FSRQ) to the upper region of the plot, because of an overestimation of $L_{\rm Bol}$."
 In addition. (2) the accretion rate value of NLRG could be affected by. gas obscuring the nucleus.," In addition, (2) the accretion rate value of NLRG could be affected by gas obscuring the nucleus."
 The bolometric liminosity in Table 6. has been derived [from the optical luminosity using a conversion [actor inferred by the Quasar Spectral Energy. Distribution study by Elvis et al. (, The bolometric luminosity in Table \ref{tab:bhm} has been derived from the optical luminosity using a conversion factor inferred by the Quasar Spectral Energy Distribution study by Elvis et al. (
1994).,1994).
 The ratio between <Lp> and <Lsjokey> inclicates that the X-ray conversion [actor is very similar to the DLRG optical one. but much smaller in the case of NLRG.," The ratio between $<L_{\rm Bol}>$ and $<L_{\rm 2-10\;keV}>$ indicates that the X-ray conversion factor is very similar to the BLRG optical one, but much smaller in the case of NLRG."
 This could reflect uncertainties in the optical de-reddening., This could reflect uncertainties in the optical de-reddening.
 Indeed. if the X-ray. conversion [actor is applied to the average NLRG X-ray Dhuminositv. value. the deduced <Ly2 increases by more than a factor 10. and. as a consequence. (he accretion rate of NLRG aligns with the BLRG value. increasing from login=—2.92 to logi=—1.4.," Indeed, if the X-ray conversion factor is applied to the average NLRG X-ray luminosity value, the deduced $<L_{\rm Bol}>$ increases by more than a factor 10, and, as a consequence, the accretion rate of NLRG aligns with the BLRG value, increasing from $\log{\dot{m}}=-2.92$ to $\log{\dot{m}}=-1.4$."
 On the contrary. the statistical difference between Sevlert 1s and BLRG accretion rates appears (to be more genuine.," On the contrary, the statistical difference between Seyfert 1s and BLRG accretion rates appears to be more genuine."
 Sevfert 1s seem (o have more efficient accretion. as confined bv the Kolmogorov-Smirnov test (Ps=3x10 7).," Seyfert 1s seem to have more efficient accretion, as confirmed by the Kolmogorov-Smirnov test $P_{\rm KS}=3\times10^{-3}$ )."
" Note that. if the Ly, of radio galaxies is allected by beamed radiation. the discrepancy. becomes lareer."," Note that, if the $L_{\rm Bol}$ of radio galaxies is affected by beamed radiation, the discrepancy becomes larger."
 Figure 5. shows a clear anti-correlation between (he iron line EW and the 210 keV Iuninositv. the well known “A-rav Baldwin elfect.," Figure \ref{EWvsL} shows a clear anti-correlation between the iron line EW and the 2–10 keV luminosity, the well known “X-ray Baldwin effect”."
 As confirmed bv the generalized Ixendall's tau lest. a correlation is present. not only when both and objects are considered ανJARURV< 0.01). but also when Sevlert 1s are removed [rom the sample (oIN= 0.04).," As confirmed by the generalized Kendall's tau test, a correlation is present, not only when both and objects are considered $\alpha_{\rm K}^{\rm ASURV}<0.01$ ), but also when Seyfert 1s are removed from the sample $\alpha_{\rm K}^{\rm ASURV}=0.04$ )."
 The simplest and immediate interpretation is that a beamed. radiation dilutes the features in AGN., The simplest and immediate interpretation is that a beamed radiation dilutes the features in AGN.
 However. while lor Blazars the robustness of this interpretation is clearly attested by the case of 3C 273 (Grandi&Palumbo2004).. for the other AGN the question is not so certain (as shown in Section 5).," However, while for Blazars the robustness of this interpretation is clearly attested by the case of 3C 273 \citep{gra04}, for the other AGN the question is not so certain (as shown in Section 5)."
 Moreover. the observation of the Baldwin elfect also in radio quiet AGN (Pageetal.2004: indicates a possibly more complex picture.," Moreover, the observation of the Baldwin effect also in radio quiet AGN \citep{pag04,zho05} indicates a possibly more complex picture."
 We then investigated other possibilities., We then investigated other possibilities.
0.5cm 0.3cm 020111 12pt plus 2ptheadings: cosmology: distance scales | cosmology: large scale structure of (he universe cosmology: observation cosmology: theory galaxies: kinematics and dvnamies — galaxies: statistics 23pt plus 2pl Peculiar velocity survevs are an important (ool for probing the mass distribution of the universe on large scales.,0.5cm 0.3cm 0.3cm 12pt plus 2pt: cosmology: distance scales – cosmology: large scale structure of the universe – cosmology: observation – cosmology: theory – galaxies: kinematics and dynamics – galaxies: statistics 23pt plus 2pt Peculiar velocity surveys are an important tool for probing the mass distribution of the universe on large scales.
 In the analvsis of these surveys. galaxies or clusters of galaxies are asstuned to be tracers of the matter velocity field. which in linear theory is directly related to the density field.," In the analysis of these surveys, galaxies or clusters of galaxies are assumed to be tracers of the matter velocity field, which in linear theory is directly related to the density field."
 Thus peculiar velocity data can complement other measures of the mass distribution by placing constraints on (he properties of the density field. for example. the power spectrum of fluctuations.," Thus peculiar velocity data can complement other measures of the mass distribution by placing constraints on the properties of the density field, for example, the power spectrum of fluctuations."
 Peculiar velocities also provide a powerlul test of the gravitational instability theory of structure formation., Peculiar velocities also provide a powerful test of the gravitational instability theory of structure formation.
 In practice. the use of peculiar velocities to constrain properties of the density field is complicated. by several factors.," In practice, the use of peculiar velocities to constrain properties of the density field is complicated by several factors."
 First ancl foremost is the fact that a direct relationship between velocity and density fields holds only in linear theory: (his necessitates (hat we focus on large enough scales so that linearity can be reasonably assumed., First and foremost is the fact that a direct relationship between velocity and density fields holds only in linear theory; this necessitates that we focus on large enough scales so that linearity can be reasonably assumed.
 This also requires (hat we can adequately separate largescale contributions to the velocity field from smallscale. nonlinear contributions.," This also requires that we can adequately separate large–scale contributions to the velocity field from small–scale, nonlinear contributions."
 One of the most straightforward. methods of analvzing peculiar velocity data is to exanine (he statisties of loworder moments of the velocity field. for example. the bulk flow (Lauer&Postman1994:Riess.PressIxirshner1995).," One of the most straightforward methods of analyzing peculiar velocity data is to examine the statistics of low–order moments of the velocity field, for example, the bulk flow \citep{LP,RPK}."
. The idea here is that in ealeulating loworder moments the small scale modes will be averaged out. so that the values of these moments will reflect only largescale motion.," The idea here is that in calculating low–order moments the small scale modes will be averaged out, so that the values of these moments will reflect only large–scale motion."
 It has been shown. however. that (he sparseness of peculiar velocity data can lead (o smallscale modes making a significant contribution {ο," It has been shown, however, that the sparseness of peculiar velocity data can lead to small–scale modes making a significant contribution to"
Since its cliscovery in 1992. simultaneously with the SIGALX instrument on the satellite and the BATSE instrument on theCORO satellite (Castro-Tirado. ναι. Lund. 1992: Llarmon. Paciesas. Fishman. 1992). GRS 1915|105 has been one of the most extensively stucliccl sources of recent times.,"Since its discovery in 1992, simultaneously with the SIGMA instrument on the satellite and the BATSE instrument on the satellite (Castro-Tirado, Brandt, Lund, 1992; Harmon, Paciesas, Fishman, 1992), GRS 1915+105 has been one of the most extensively studied sources of recent times."
 The popularity of this source is due toits highly complex and variable nature at all wavelengths from gamma ravs to radio., The popularity of this source is due to its highly complex and variable nature at all wavelengths from gamma rays to radio.
 The many unusual features include relativistic jets (Alirabel Roclrigguez 1994: Fender et 11999). N-ray Quasi-periocic Oscillations (QPOs) (Morgan. Remillard L996) anc accretion instabilities resulting in jet formation (Pooley Fender 1997: Eikenberry et al.," The many unusual features include relativistic jets (Mirabel guez 1994; Fender et 1999), X-ray Quasi-periodic Oscillations (QPOs) (Morgan Remillard 1996) and accretion instabilities resulting in jet formation (Pooley Fender 1997; Eikenberry et al."
 1998: Mirabel et al., 1998; Mirabel et al.
 1998)., 1998).
 The svstem exhibits a wide variety of radio behaviour on timescales from minutes to weeks (Foster et al., The system exhibits a wide variety of radio behaviour on timescales from minutes to weeks (Foster et al.
 1996: Pooley Fender 1997)., 1996; Pooley Fender 1997).
 High time resolution observations using the Ile Telescope (RL) and more continuous coverage on hourly time-scales. revealed. new aspects of the radio emission (Pooley Fender 1997 hereafter PLOT).," High time resolution observations using the Ryle Telescope (RT) and more continuous coverage on hourly time-scales, revealed new aspects of the radio emission (Pooley Fender 1997 hereafter PF97)."
 3oth2040 min period. QPOs associated with soft X-ray variations (first reported. in the radio by Pooler (1995.1996)) ancl a change of ϱΡΟ period. were clearly visible during. some inclividual observations.," Both20--40 min period QPOs associated with soft X-ray variations (first reported in the radio by Pooley (1995,1996)) and a change of QPO period, were clearly visible during some individual observations."
 Vhe infrared. variability from. this source is. similar., The infrared variability from this source is similar.
 Following observed 1 and 2 mag variations in theJ.ff and dy-bancl [uxes (CCastro-Tirado et 14993: Mirabel οἱ 11994: Chaty et 11996). Fender et ((1997). reported rapid infrared. lares which had amplitudes. rise. decay. and recurrence time-scales strikinglv similar to those of the racio [ares observed with the RPS hours later. suggesting infrared. svnchrotron emission.," Following observed 1 and 2 mag variations in the, and -band fluxes (Castro-Tirado et 1993; Mirabel et 1994; Chaty et 1996), Fender et (1997) reported rapid infrared flares which had amplitudes, rise, decay and recurrence time-scales strikingly similar to those of the radio flares observed with the RT 8 hours later, suggesting infrared synchrotron emission."
 Further WP observations taken simultaneously with the William Llerschel Telescope (WILT) showed 26-min oscillations in. both the radio and infrared. emission. (Fender. Pooles 1998)., Further RT observations taken simultaneously with the William Herschel Telescope (WHT) showed 26-min oscillations in both the radio and infrared emission (Fender Pooley 1998).
 From these observations. the authors showed that the radio variations were delaved by 33 (or perhaps 59) minutes relative to the infrared.," From these observations, the authors showed that the radio variations were delayed by 33 (or perhaps 59) minutes relative to the infrared."
 Is there à correlation between the radio or infrared emission and the X-rays?, Is there a correlation between the radio or infrared emission and the X-rays?
 here is clearly some correlation between X-ray states and radio emission (CORO Burst, There is clearly some correlation between X-ray states and radio emission Burst
Free-floating planetarv-mnass objects have been purported in young clusters such as σ Orionis (ZapateroOsorioοἱal.2002) and the Trapezium (Lucasetal.2006).,Free-floating planetary-mass objects have been purported in young clusters such as $\sigma$ Orionis \citep{zap02} and the Trapezium \citep{lucas06}.
. These are brown clwarls whose masses are below the deuterium-burning limit of 13 Jupiter masses (μμ). and their existence imposes severe restrictions on brown dwarl formation models.," These are brown dwarfs whose masses are below the deuterium-burning limit of 13 Jupiter masses $M_{\rm Jup}$ ), and their existence imposes severe restrictions on brown dwarf formation models."
 The models must account both for the generation of low-mass cloud fragments and also for, The models must account both for the generation of low-mass cloud fragments and also for
the origin of the box at z=0 which requires us to add the comoving distance from z=0 to Z to the subhalo positions.,the origin of the box at $z=0$ which requires us to add the comoving distance from $z=0$ to $\tilde{z}$ to the subhalo positions.
 In Section 4 we discuss the selection. criterion for subhalo pairs in relation to the radius eos of the parent halo where the mean density is 200 times the critical value., In Section 4 we discuss the selection criterion for subhalo pairs in relation to the radius $R_{200}$ of the parent halo where the mean density is 200 times the critical value.
 From the N-body simulations we know which pairs of subhaloes are in the same FOR halo., From the N-body simulations we know which pairs of subhaloes are in the same FOF halo.
 However. this does not euarantee that these objects are eravitationally bound to the FOP halo.," However, this does not guarantee that these objects are gravitationally bound to the FOF halo."
 There are too many haloes in our simulations to check explicitly for binding. so we will use proxies instead.," There are too many haloes in our simulations to check explicitly for binding, so we will use proxies instead."
 This will allow us to make contact with the observational selection applied by Marinoni Buzzi and to see how their cuts translate into cuts in simulation quantities., This will allow us to make contact with the observational selection applied by Marinoni Buzzi and to see how their cuts translate into cuts in simulation quantities.
 We investigate these selection criteria and. provide robust selection cuts which are independent of cosmology and redshift., We investigate these selection criteria and provide robust selection cuts which are independent of cosmology and redshift.
 In particular we address the following question: how do we construct a sample of pairs that matehes the heoretical expectation for the AAP function. in the most avourable case in which we know the correct. cosmology?," In particular we address the following question: how do we construct a sample of pairs that matches the theoretical expectation for the AAP function, in the most favourable case in which we know the correct cosmology?"
 Using information output from the simulations about the subhaloes selected. and the properties of the parent. halo. (c.g. the POF algorithm returns Z/s99). we can quantify the definition of a close pair in a rigorous wav.," Using information output from the simulations about the subhaloes selected and the properties of the parent halo, (e.g. the FOF algorithm returns $R_{200}$ ), we can quantify the definition of a close pair in a rigorous way."
 LE we selected only round pairs we would expect &ood agreement with the AAP function. provided that we know the correct cosmological nmiocdel.," If we selected only bound pairs we would expect good agreement with the AAP function, provided that we know the correct cosmological model."
 As a first approach to identify suitable pairs. we shall select. subhaloes which are within og) of the main halo. be. APμμcPeng. with no other restrictions on velocity or distance to a nearest neighbour.," As a first approach to identify suitable pairs, we shall select subhaloes which are within $R_{200}$ of the main halo, i.e. $\Delta r_{\perp,\mbox{\tiny max}} = R_{200}$, with no other restrictions on velocity or distance to a nearest neighbour."
 As this information is not available to an observer. our second approach will be to translate these selection criteria into observable. quantities such as the angle ϐ between a pair of subhaloes.," As this information is not available to an observer, our second approach will be to translate these selection criteria into observable quantities such as the angle $\theta$ between a pair of subhaloes."
 Alarinoni Buzzi used the following selection criteria to pick their sample of pairs: (1) a maximum line of sight. velocity cillerence of the pair AV=700 kms to avoid projection of neighbouring systems. (2) a maximum comoving transverse separation of Aryiia.=0.7 Alpesh. (3) a minimum comoving transverse separation Aryμμ=20 kpc/h and (4) a minimum comoving distance from the centre of the galaxy. pair to another galaxy.," Marinoni Buzzi used the following selection criteria to pick their sample of pairs: (1) a maximum line of sight velocity difference of the pair $\Delta V = 700$ km/s to avoid projection of neighbouring systems, (2) a maximum comoving transverse separation of $\Delta r_{\perp,\mbox{\tiny max}} = 0.7$ $/h$, (3) a minimum comoving transverse separation $\Delta r_{\perp ,\mbox{\tiny min}} = 20$ $/h$ and (4) a minimum comoving distance from the centre of the galaxy pair to another galaxy."
 The latter two conditions avoid selecting pairs which may be in the process of merging or which ave interacting with another galaxy., The latter two conditions avoid selecting pairs which may be in the process of merging or which are interacting with another galaxy.
 The value for the maximum velocity dillerence was chosen such that the relative increase ANZN in the sample size was «1%vs when the velocity cut was increased by LOO km/s. while the niaximunm. comoving transverse separation was chosen to be equal to the distance from Andromeda to the Milkv. Was.," The value for the maximum velocity difference was chosen such that the relative increase $\Delta N/N $ in the sample size was $<1\%$ when the velocity cut was increased by 100 km/s, while the maximum comoving transverse separation was chosen to be equal to the distance from Andromeda to the Milky Way."
 L, Fig.
 3 shows the measured distributions of the orientation of subhalo pairs in real ancl redshift space in the low resolution οςΟΝΕ simulation at z=0., \ref{pdf} shows the measured distributions of the orientation of subhalo pairs in real and redshift space in the low resolution $\Lambda$ CDM simulation at $z=0$.
 The starting point is the sample of subhalo pairs within a common FOL halo. without any further selection.," The starting point is the sample of subhalo pairs within a common FOF halo, without any further selection."
 This is shown in real space by the black histogram in Fie. 3, This is shown in real space by the black histogram in Fig. \ref{pdf}.
 «Note that for the lower resolution ACDAL simulation there are approximately 65.000 subhalo pairs at z=0.," Note that for the lower resolution $\Lambda$ CDM simulation there are approximately 65,000 subhalo pairs at $z=0$."
 The real space distribution of the tilt. follows the expected random. distribution and is uniform in cos(z)., The real space distribution of the tilt follows the expected random distribution and is uniform in $\cos(\tau)$.
 The distribution of all subhalo pairs in redshift space is shown in red which is clearly skewed., The distribution of all subhalo pairs in redshift space is shown in red which is clearly skewed.
 The mean of this distribution cdilfers from the prediction of the AAP function by —40%.., The mean of this distribution differs from the prediction of the AAP function by $\sim 40$.
 Applying the final set of cuts to this overall sample as outlined below leaves approximately 19.000. pairs. ancl produces the blue hashed region which is skewed towards smaller angles ancl agrees with the predictions of the AAP function given in Iq.," Applying the final set of cuts to this overall sample as outlined below leaves approximately 19,000 pairs, and produces the blue hashed region which is skewed towards smaller angles and agrees with the predictions of the AAP function given in Eq."
 9 o within 0., \ref{aapfunction} to within .
54... We discuss the selection cuts that give rise to this blue hashed region below., We discuss the selection cuts that give rise to this blue hashed region below.
 comparison of the red and blue histograms in Fig., A comparison of the red and blue histograms in Fig.
 3. shows that in recdshift space if no selection cuts are made to isolate bound: pairs 1e distribution is clearly randomized by outliers., \ref{pdf} shows that in redshift space if no selection cuts are made to isolate bound pairs the distribution is clearly randomized by outliers.
 In an attempt to isolate. subhaloes that are gravitationally bound. to. their parent FOL halo and rence to test if their orientations in redshift space are distributed. according to the predictions. of the AAP unction. we first select. pairs of subhaloes within Moo and exclude all other pairs.," In an attempt to isolate subhaloes that are gravitationally bound to their parent FOF halo and hence to test if their orientations in redshift space are distributed according to the predictions of the AAP function, we first select pairs of subhaloes within $R_{200}$ and exclude all other pairs."
 We find that this sample of pairs ras a non-negligible correlation between Ae; and Ar such hat (Ae)fdr)=UO., We find that this sample of pairs has a non-negligible correlation between $\Delta v_{\parallel}$ and $\Delta r$ such that $\langle \Delta v_{\parallel}/ \Delta r \rangle \ne 0 $.
 As a result. we use the full expression in Eq.," As a result, we use the full expression in Eq."
 7 for the parameter o., \ref{sig} for the parameter $\sigma$.
 This gives an AAP function which is in remarkably good agreement with the measured mean of the clistribution. the ensemble average of Eq.," This gives an AAP function which is in remarkably good agreement with the measured mean of the distribution, the ensemble average of Eq."
 1. ab = Oina ACDAL simulation. to better than a percent.," 1, at $z=0$ in a $\Lambda$ CDM simulation, to better than a percent."
 This agreement diminishes at higher redshifts. with the AAP function ancl the measured mean dillering by over the redshift range 2=0.251.," This agreement diminishes at higher redshifts, with the AAP function and the measured mean differing by over the redshift range $z=0.25 - 1$."
 lt is possible to remove subhalo pairs which have Arfa)40 by selecting. pairs according to an upper imit in the line of sight peculiar velocity dillerence. Ati.," It is possible to remove subhalo pairs which have $\langle \Delta v_{\parallel}/ \Delta r \rangle \ne 0 $ by selecting pairs according to an upper limit in the line of sight peculiar velocity difference, $\Delta v_{\tiny \mbox{max}}$."
 The velocity cilferenee of pairs of galaxies is related to he common gravitational potential of the pair which. in most cases. is weaklv correlated. with their separation.," The velocity difference of pairs of galaxies is related to the common gravitational potential of the pair which, in most cases, is weakly correlated with their separation."
 Llowever. we find that pairs with large velocity. differences lve non-zero correlations. e.g. in the ACDAL simulation ab 2o=0. using all subhalo pairs with Ae 950km/s we ind (Ae)fAr)=85h km/s/Mpc.," However, we find that pairs with large velocity differences have non-zero correlations, e.g. in the $\Lambda$ CDM simulation at $z=0$, using all subhalo pairs with $\Delta v > 950$ km/s we find $\langle \Delta v_{\parallel}/ \Delta r \rangle =8.5h$ km/s/Mpc."
 Observationally these subhaloes would not be detected as the apparent tilt between he pair is approximately zero. due to their large peculiar velocity dillerence. and as a result the pair would lie along he same line of sight.," Observationally these subhaloes would not be detected as the apparent tilt between the pair is approximately zero, due to their large peculiar velocity difference, and as a result the pair would lie along the same line of sight."
 In Fig., In Fig.
 4 we plot the distribution of the line of sight. peculiar velocity. difference Ae in the eft panel. for all subhaloes in the lower resolution ACDAL simulation.," \ref{dvdr} we plot the distribution of the line of sight peculiar velocity difference $\Delta v$ in the left panel, for all subhaloes in the lower resolution $\Lambda$ CDM simulation."
 The grev shaded: region corresponds to. the selection cut in Ae., The grey shaded region corresponds to the selection cut in $ \Delta v$.
 Once we remove any correlated: pairs rom the sample. and impose the restriction that Arpuu= {οσους we find that the measured mean ancl the predicted AAD function agree extremely well in the redshift. range >=02.," Once we remove any correlated pairs from the sample, and impose the restriction that $\Delta r_{\perp,\mbox{\tiny max}} = R_{200}$ , we find that the measured mean and the predicted AAP function agree extremely well in the redshift range $z=0-2$."
 We present these results in more detail in the ollowing section., We present these results in more detail in the following section.
 Note the first term in the expression for a. Ίσα. Τι.," Note the first term in the expression for $\sigma$, Eq. \ref{sig},"
 is now negligible as we have removed any correlated ALLS., is now negligible as we have removed any correlated pairs.
 As Rooy is not an observable quantity. the next step is to see if this cut. can be translated into a cut in ϐ. he observed. angular separation of the pair.," As $R_{200}$ is not an observable quantity, the next step is to see if this cut can be translated into a cut in $\theta$ , the observed angular separation of the pair."
 In Fig., In Fig.
 4 we xot the distribution of the comoving transverse separation Ary asa fraction of Roos in the lower right panel. for all subhaloes in the lower resolution ACDAIL simulation.," \ref{dvdr} we plot the distribution of the comoving transverse separation $\Delta r_{\perp}$ as a fraction of $R_{200}$ in the lower right panel, for all subhaloes in the lower resolution $\Lambda$ CDM simulation."
" The comoving transverse separation Ary as a fraction of fous or the subhaloes that are selected by @<06,5, is shownas a redhashed region while the distribution of those not", The comoving transverse separation $\Delta r_{\perp}$ as a fraction of $R_{200}$ for the subhaloes that are selected by $\theta < \theta_{\mbox{\tiny max}}$ is shownas a redhashed region while the distribution of those not
A specifie optical path is defined by a starting location al the bottom of the model abmosphere and by a unit vector 7 which defines the path orientation.,A specific optical path is defined by a starting location at the bottom of the model atmosphere and by a unit vector $\bb{n}$ which defines the path orientation.
" We calculate the projected wind velocity along this path throughout the entire model atmosphere as where V4 is the wind horizontal velocity vector according to the circulation. moclel. my is the horizontal unit vector projected on the sphere (ie.. defining the north/south and east/west directions) and (he representative zenith angele 6,=53 des is uniformly adopted in all our caleulations."," We calculate the projected wind velocity along this path throughout the entire model atmosphere as where $\bb{V_{\rm h}}$ is the wind horizontal velocity vector according to the circulation model, $\bb{n_{\rm h}}$ is the horizontal unit vector projected on the sphere (i.e., defining the north/south and east/west directions) and the representative zenith angle $\theta_0 = 53$ deg is uniformly adopted in all our calculations."
 A detailed ealeulation would require us to take into account the three-dimensional geometry of the problem. wilh varving pressure levels in each of the model vertical columns crossed by the slanted optical path.," A detailed calculation would require us to take into account the three-dimensional geometry of the problem, with varying pressure levels in each of the model vertical columns crossed by the slanted optical path."
 Rather than performing delicate (hree-climensional interpolations between various model columns. we use the profile of wind velocities in a single vertical column.," Rather than performing delicate three-dimensional interpolations between various model columns, we use the profile of wind velocities in a single vertical column."
" That is. we use values of Vy as if the optical path were exactly vertical. even though the calculation assumes a zenith angle 4,=53 deg and various azimnuthal orientations for the projection."," That is, we use values of $\bb{V_{\rm h}}$ as if the optical path were exactly vertical, even though the calculation assumes a zenith angle $\theta_0 = 53$ deg and various azimuthal orientations for the projection."
 While this approximation clearly emphasizes vertical velocity gradients over horizontal ones. it still captures representative changes in Vy. both in magnitude and direction. along the selected optical path (with a specific azimuthal orientation).," While this approximation clearly emphasizes vertical velocity gradients over horizontal ones, it still captures representative changes in $\bb{V_{\rm h}}$, both in magnitude and direction, along the selected optical path (with a specific azimuthal orientation)."
 It should (lius be sufficient to evaluate the typical magnitude of projected velocity. eradients along representative optical paths in the model aümosphere., It should thus be sufficient to evaluate the typical magnitude of projected velocity gradients along representative optical paths in the model atmosphere.
 Figure 1. shows profiles of wind velocity projected along representative optical paths. as a Ffunetion of pressure. p (a proxy for height in the atmosphere).," Figure \ref{fig:one} shows profiles of wind velocity projected along representative optical paths, as a function of pressure, $p$ (a proxy for height in the atmosphere)."
 All velocities are expressed in units of the local value of the adiabatic sound speed. μωβ)ορ.T).," All velocities are expressed in units of the local value of the adiabatic sound speed, $V_{\rm proj}(p)/
c_s(p;T) $."
 The same Lfo- atmospheric gas parameters as in are used to calculate the sound speed: e;=MVRT. with an acliabatic index >=1/(1—&). &=0.321 and a gas constant R=4593 J kg! !.," The same $H_2$ -dominated atmospheric gas parameters as in are used to calculate the sound speed: $c_s \equiv
\sqrt{\gamma {\cal R} T}$, with an adiabatic index $\gamma =
1/(1-\kappa)$, $\kappa=0.321$ and a gas constant ${\cal R}=4593$ J $^{-1}$ $^{-1}$."
 The various panels show profiles at the model substellar point (a). antistellar point (b). west equatorial terminator (c) and north pole (d).," The various panels show profiles at the model substellar point (a), antistellar point (b), west equatorial terminator (c) and north pole (d)."
 In each panel. the various curves show projected. velocity profiles for optical paths oriented to the east (solid line). north-east (dotted). north (dashed) and north-west (dash-dotted) on the sphere.," In each panel, the various curves show projected velocity profiles for optical paths oriented to the east (solid line), north-east (dotted), north (dashed) and north-west (dash-dotted) on the sphere."
 Projected velocity proliles for other cardinal directions can be deduced by svimnmnetrx., Projected velocity profiles for other cardinal directions can be deduced by symmetry.
 Figure l reveals sienilicant gradients in projected wind velocity as one crosses (he almosphere along representative slanted optical paths for thermal radiation., Figure \ref{fig:one} reveals significant gradients in projected wind velocity as one crosses the atmosphere along representative slanted optical paths for thermal radiation.
 Velocity differentials over one pressure scale height easily amount (o ~ 0.2- 0.5ος and (they exceed e; im some cases. especially high up in the atmosphere.," Velocity differentials over one pressure scale height easily amount to $\sim 0.2$ - $0.5~c_s$ and they exceed $c_s$ in some cases, especially high up in the atmosphere."
" Velocity differentials Zc, are tvpical when crossing several pressure scale heights.", Velocity differentials $\ga c_s$ are typical when crossing several pressure scale heights.
 The different panels in Figure l1 illustrate the diverse character of projected. velocity, The different panels in Figure \ref{fig:one} illustrate the diverse character of projected velocity
was reported in Kukarkin et al. (1969)).,"was reported in Kukarkin et al. \cite{Kukarkin1969}) ),"
 which has a period of ~340 ddays., which has a period of $\sim340$ days.
 The remainder of this paper is structured as follows: In Sect. 2..," The remainder of this paper is structured as follows: In Sect. \ref{OBSERVATIONS},"
 we describe our AMBER observations and the strategy followed in the data calibration and reduction., we describe our AMBER observations and the strategy followed in the data calibration and reduction.
 In Sect. 3..," In Sect. \ref{RESULTS},"
 we report on the results obtained: Sect., we report on the results obtained: Sect.
 3.1. 1s centered on our estimate of the effective temperature and Sect., \ref{TEFF} is centered on our estimate of the effective temperature and Sect.
 3.2. on the size effects observed at the CO band heads., \ref{CObands} on the size effects observed at the CO band heads.
 In Sect. 4..," In Sect. \ref{MODELING},"
 we compare our results with synthetic data obtained from model stellar atmospheres., we compare our results with synthetic data obtained from model stellar atmospheres.
 In Sect. 5..," In Sect. \ref{CONCLUSIONS},"
 we summarize our conclusions., we summarize our conclusions.
 We observed RS Cap with the ESO Very Large Telescope Interferometer (VLTI) using the Astronomical Multi-BEam combineR. AMBER (see Petrov et al.," We observed RS Cap with the ESO Very Large Telescope Interferometer (VLTI) using the Astronomical Multi-BEam combineR, AMBER (see Petrov et al."
 2007. for details on this instrument). in medium-resolution mode CUAL~ 1500).," \cite{Petrov2007} for details on this instrument), in medium-resolution mode $\lambda/\Delta\lambda \sim 1500$ )."
 This instrument performs simultaneous observations of the interferometric fringes generated by three telescopes., This instrument performs simultaneous observations of the interferometric fringes generated by three telescopes.
 Therefore. it measuresphases. which are quantities independent of atmospheric or instrumental telescope-dependent contributions (e.g. Rogers et al. 1974)).," Therefore, it measures, which are quantities independent of atmospheric or instrumental telescope-dependent contributions (e.g. Rogers et al. \cite{Rogers1974}) )."
 AMBER also measures the so-called on each baseline. which roughly represents the phase of spectral features with respect to that in thecontinuum!.," AMBER also measures the so-called on each baseline, which roughly represents the phase of spectral features with respect to that in the."
. The observations were performed on 4 June 2009. from UUT to UUT. using the three VLTI Auxiliary Telescopes (AT) positioned on stations EO. GO. and HO.," The observations were performed on 4 June 2009, from UT to UT, using the three VLTI Auxiliary Telescopes (AT) positioned on stations E0, G0, and H0."
 These stations are distributed roughly in the east-west direction., These stations are distributed roughly in the east-west direction.
 In Table 1.. we give the projected baseline lengths and position. angles for our observations. together with a summary of the atmospheric observing conditions.," In Table \ref{OBSERVCONFIG}, we give the projected baseline lengths and position angles for our observations, together with a summary of the atmospheric observing conditions."
" 18 Cap (ΜΟΠΙ star located at 220h51m49.3s. ó=—26755’08.9"". J2000.0) was also observed as a calibrator. with the same observing configuration used to obtain the RS Cap visibilities."," 18 Cap (M0III star located at $\alpha = 20\textrm{h}\,51\textrm{m}\,49.3\textrm{s}$, $\delta = -26^{\circ}\,55'\,08.9''$, J2000.0) was also observed as a calibrator, with the same observing configuration used to obtain the RS Cap visibilities."
 The high flux densities of RS Cap and 18 Cap in the H band (magnitudes of 0.25 and 0.42. respectively). allowed us to use the fringe tracker FINITO (see Gai et al. 2004)).," The high flux densities of RS Cap and 18 Cap in the H band (magnitudes of 0.25 and 0.42, respectively), allowed us to use the fringe tracker FINITO (see Gai et al. \cite{Gai2004}) ),"
 which employs part of the H-band light to correct. in real time. the delay shifts of the fringes due to atmospheric turbulences. thus increasing the coherence of the signal.," which employs part of the H-band light to correct, in real time, the delay shifts of the fringes due to atmospheric turbulences, thus increasing the coherence of the signal."
 A larger coherence allows the use of a longer detector integration time (DIT)., A larger coherence allows the use of a longer detector integration time (DIT).
 Given the moderately good atmospheric conditions during our observations (see Table 1)). we achieved a DIT of mms with a negligible signal loss due to atmospheric jitter.," Given the moderately good atmospheric conditions during our observations (see Table \ref{OBSERVCONFIG}) ), we achieved a DIT of ms with a negligible signal loss due to atmospheric jitter."
 This allowed us to simultaneously observe a large spectral range of the K-band (between 2.13 and μπι) using medium-resolution mode., This allowed us to simultaneously observe a large spectral range of the K-band (between 2.13 and $\mu$ m) using medium-resolution mode.
" This wavelength range contains the '*CO (2-0). (3-1). and (4-2). as well as the CO (2-0) band heads. together with the continuum blueward of the ""CO (2-0) band head at um. The data acquisition was carried out in the following order: (1) observation of an artificial signal for calibration of the instrumental dispersive effects: (2) one exposure of dark frames (an exposure consisted on 200 frames of mms each): (3) five exposures of the target; and (4) one exposure of empty sky close to the target."," This wavelength range contains the $^{12}$ CO $-$ 0), $-$ 1), and $-$ 2), as well as the $^{13}$ CO $-$ 0) band heads, together with the continuum blueward of the $^{12}$ CO $-$ 0) band head at $\mu$ m. The data acquisition was carried out in the following order: (1) observation of an artificial signal for calibration of the instrumental dispersive effects; (2) one exposure of dark frames (an exposure consisted on 200 frames of ms each); (3) five exposures of the target; and (4) one exposure of empty sky close to the target."
 The observations of dark. target. and sky exposures were iterated once for CCap (spanning 10 minutes). three times for CCap (spanning 1 hour). and one more time for CCap (spanning 10 minutes).," The observations of dark, target, and sky exposures were iterated once for Cap (spanning 10 minutes), three times for Cap (spanning 1 hour), and one more time for Cap (spanning 10 minutes)."
 The dead time between iterations. when the sources were not observed. was dedicated to the setup of the instrument: preparation of the optical-delay lines. telescope pointing. etc.," The dead time between iterations, when the sources were not observed, was dedicated to the setup of the instrument: preparation of the optical-delay lines, telescope pointing, etc."
 The raw visibilities and differential closure phases for RS Cap and 18 Cap were obtained using the libraries (version. 2.2) and the interface provided by the Jean-Marie Mariotti. Center (J[MMC)., The raw visibilities and differential closure phases for RS Cap and 18 Cap were obtained using the libraries (version 2.2) and the interface provided by the Jean-Marie Mariotti Center (JMMC).
 First. we manually aligned the spectrally-dispersed photometry channels of the ATs to the interferometric channel. based on observations of the target and calibrator stars.," First, we manually aligned the spectrally-dispersed photometry channels of the ATs to the interferometric channel, based on observations of the target and calibrator stars."
 We removed the bad pixels and took into account the flat. dark. and sky contributions.," We removed the bad pixels and took into account the flat, dark, and sky contributions."
 Afterwards. we calibrated the instrumental dispersive effects and fringe-fitted each frame of RS Cap and 18 Cap (based on the P2VM algorithm. of Tatulli et al. 2007)).," Afterwards, we calibrated the instrumental dispersive effects and fringe-fitted each frame of RS Cap and 18 Cap (based on the P2VM algorithm of Tatulli et al. \cite{Tatulli2007}) )."
 The resulting. visibilities of individual frames were selected and averaged for each exposure in several ways. to test the robustness of our results on different averaging and selection schemes.," The resulting visibilities of individual frames were selected and averaged for each exposure in several ways, to test the robustness of our results on different averaging and selection schemes."
 The finally chosen selection scheme was based on an atmospheric piston criterion (keeping only frames with a piston smaller than jim. to select only well-detected and centered fringes in all three baselines) and keep of the remaining frames based on a noise ratio (SNR) criterion.," The finally chosen selection scheme was based on an atmospheric piston criterion (keeping only frames with a piston smaller than $\mu$ m, to select only well-detected and centered fringes in all three baselines) and keep of the remaining frames based on a signal-to-noise ratio (SNR) criterion."
 After the frame selection. we obtained a single frame-averaged visibility spectrum for each exposure.," After the frame selection, we obtained a single frame-averaged visibility spectrum for each exposure."
 The last step in the data reduction was to average the visibilities of all exposures of each star to increase the SNR., The last step in the data reduction was to average the visibilities of all exposures of each star to increase the SNR.
 This step was performed outsideamdlib. with an in-house developed python-based program that uses the PyFITS library (provided by the Space Telescope Science Institute. operated by AURA for NASA).," This step was performed outside, with an in-house developed python-based program that uses the PyFITS library (provided by the Space Telescope Science Institute, operated by AURA for NASA)."
 The averaged closure phases and differential phases (1.e.. those resulting from the averaged exposures) are zero within 3°. in absolute value. for both stars and for all the spectral channels.," The averaged closure phases and differential phases (i.e., those resulting from the averaged exposures) are zero within $3^{\circ}$, in absolute value, for both stars and for all the spectral channels."
 These small values of the closure phases indicate that the emission from both sources is symmetric. at least in the direction of the projected baselines of our observations and to the scale corresponding to our spatial resolution.," These small values of the closure phases indicate that the emission from both sources is symmetric, at least in the direction of the projected baselines of our observations and to the scale corresponding to our spatial resolution."
 This is unsuprising. given that we probe only the first lobe of the Fourier transform of the observed source structure. which is. therefore. only partially resolved.," This is unsuprising, given that we probe only the first lobe of the Fourier transform of the observed source structure, which is, therefore, only partially resolved."
 The uncertainties in the amplitude and phase for each spectral channel were computed from their standard deviations during the averaging of the exposures., The uncertainties in the amplitude and phase for each spectral channel were computed from their standard deviations during the averaging of the exposures.
 Fractional uncertainties of only |-2% in the observed visibilities were obtained for all channels and baselines., Fractional uncertainties of only $1-2$ in the observed visibilities were obtained for all channels and baselines.
to efficiently identify point sources and determine their contribution to the total cluster luminosity.,to efficiently identify point sources and determine their contribution to the total cluster luminosity.
 We find that this contribution is at the few per cent level - much smaller than the typical survey flux uncertainty — and conclude that point source contamination is not an issue for the current study., We find that this contribution is at the few per cent level – much smaller than the typical survey flux uncertainty – and conclude that point source contamination is not an issue for the current study.
" The bias in the measured masses of the mass—luminosity data is completely degenerate with the mass function normalization, A, which in turn affects inferences made on the other parameters."," The bias in the measured masses of the mass–luminosity data is completely degenerate with the mass function normalization, $A$, which in turn affects inferences made on the other parameters."
" Consequently, it is important to include in the analysis the mean correction to masses motivated by departures from hydrostatic equilibrium,ὖ,, and the scatter in this bias among clusters,s5,, as well as the uncertainty in both quantities."," Consequently, it is important to include in the analysis the mean correction to masses motivated by departures from hydrostatic equilibrium, and the scatter in this bias among clusters, as well as the uncertainty in both quantities."
" shows that the constraints obtained by fixing the mean[I4] bias and bias scatter at their nominal values (blue, dashed contours) are spuriously tighter than those of our standard analysis (black, solid contours) by ~50 per cent on and og and ~30 per cent on w."," shows that the constraints obtained by fixing the mean bias and bias scatter at their nominal values (blue, dashed contours) are spuriously tighter than those of our standard analysis (black, solid contours) by $\sim 50$ per cent on and $\sigma_8$ and $\sim 30$ per cent on $w$."
" Also shown is the result of neglecting the bias correction entirely (red, solid contours), which results in lower values of og compared with the nominal correction."," Also shown is the result of neglecting the bias correction entirely (red, solid contours), which results in lower values of $\sigma_8$ compared with the nominal correction."
" Comparing the results for priors and in with our standard-prior results, it is clear that the TableD]uncertainty in has a greater effect than the uncertainty inb."," Comparing the results for priors and in with our standard-prior results, it is clear that the uncertainty in has a greater effect than the uncertainty in."
". This is encouraging, since the former is due primarily to the very small number of simulations used to calibrate the observational mass bias."," This is encouraging, since the former is due primarily to the very small number of simulations used to calibrate the observational mass bias."
 Straightforwardly increasing the number of simulated clusters should result in significant improvement to our constraints., Straightforwardly increasing the number of simulated clusters should result in significant improvement to our constraints.
 The mass distribution of clusters available to a flux-limited survey is influenced by the degree of scatter in flux for a given mass., The mass distribution of clusters available to a flux-limited survey is influenced by the degree of scatter in flux for a given mass.
" As described in[2], this effect can be decomposed into convolutions due to intrinsic scatter in the mass-luminosity relation and measurement error in the survey flux determinations."," As described in, this effect can be decomposed into convolutions due to intrinsic scatter in the mass–luminosity relation and measurement error in the survey flux determinations."
 Failure to account for either of these sources of scatter when evaluating the number of detectable clusters predicted by a set of model, Failure to account for either of these sources of scatter when evaluating the number of detectable clusters predicted by a set of model
of M.,of $\dot M$.
" The X-ray observations (especially if undertaken at peak) tightly. constrain Me,Jw.", The X-ray observations (especially if undertaken at peak) tightly constrain $\dot M\epsilon_e/w$.
 The microphnvsical parameter. e. has [ar less dispersion as compared (o ej and as such the X-ray observations vield a robust estimate of AL (relative to that obtained [rom radio observations).," The microphysical parameter, $\epsilon_e$ has far less dispersion as compared to $\epsilon_B$ and as such the X-ray observations yield a robust estimate of $\dot M$ (relative to that obtained from radio observations)."
 We find Mz10SweAL.vyLC," We find $\dot M\simlt 10^{-8}w_7\,M_{\odot}\,{\rm yr}^{-1}$."
 The X-ray observations are quite sensitive and it is not likely that these limits will be easily surpassed in (his decade., The X-ray observations are quite sensitive and it is not likely that these limits will be easily surpassed in this decade.
 We thank the CARMA and EVLA stall for promptly seheduling this target of opportunity., We thank the CARMA and EVLA staff for promptly scheduling this target of opportunity.
 This work made use of data supplied bv the Ulx. Science Data Centre at the University of Leicester., This work made use of data supplied by the UK Science Data Centre at the University of Leicester.
 We thank the ASTRON Raclio Observatory for the generous and swift allocation of observing time., We thank the ASTRON Radio Observatory for the generous and swift allocation of observing time.
 PTF is a fullv-automated. wicle-field survey. aimed at a systematic exploration of explosions and variable phenomena in optical wavelengths.," PTF is a fully-automated, wide-field survey aimed at a systematic exploration of explosions and variable phenomena in optical wavelengths."
 The participating institutions are Caltech. Columbia University. Weizmann Institute of Science. Lawrence Berkeley Laboratory. Oxlord and University of California al Derkelev.," The participating institutions are Caltech, Columbia University, Weizmann Institute of Science, Lawrence Berkeley Laboratory, Oxford and University of California at Berkeley."
 The program is centered on a 12Ixx8lx.. 7.8 square degree CCD array (CEILII21x) re-engineered for the 1.2-m Oschin Telescope at the Palomar Observatory by Caltech Optical Observatories.," The program is centered on a 12Kx8K, 7.8 square degree CCD array (CFH12K) re-engineered for the 1.2-m Oschin Telescope at the Palomar Observatory by Caltech Optical Observatories."
 Photometric follow-up is unudertaken bv the automated Palomar 1.5-1 telescope., Photometric follow-up is undertaken by the automated Palomar 1.5-m telescope.
 Research al Caltech is supported by grants [rom NSF and NASA., Research at Caltech is supported by grants from NSF and NASA.
 The Weizmann PTF partnership is supported in part by the Israeli Science Foundation via grants to A.G. Weizmann-Caltech collaboration is supported by a grant. [rom the BSF to A.G. and S.R.IN.. ALG. further acknowledges the Lord Sielf of Drimpton Foundation., The Weizmann PTF partnership is supported in part by the Israeli Science Foundation via grants to A.G. Weizmann-Caltech collaboration is supported by a grant from the BSF to A.G. and S.R.K. A.G. further acknowledges the Lord Sieff of Brimpton Foundation.
 MAUS acknowledges support from the Hubble fellowship and Carnegie-Princeton Fellowship., MMK acknowledges support from the Hubble fellowship and Carnegie-Princeton Fellowship.
 We thank the ASTRON Radio Observatory for the generous and swift allocation of observing time., We thank the ASTRON Radio Observatory for the generous and swift allocation of observing time.
 The Westerbork Svnthesis Raclio Telescope is operated by ASTRON (Netherlands Foundation for Radio Astronomy) with support Irom the Netherlands Organization for Scientific Research (NWO)., The Westerbork Synthesis Radio Telescope is operated by ASTRON (Netherlands Foundation for Radio Astronomy) with support from the Netherlands Organization for Scientific Research (NWO).
 AJvdll was supported by NASA erant NNIOPZDAOOI-GLAST., AJvdH was supported by NASA grant NNH07ZDA001-GLAST.
 S.D.C. acknowledges generous financial assistance from Gary, S.B.C. acknowledges generous financial assistance from Gary
accordingly (5.—0.5 mae t. see also 2009¢)).,"accordingly $\gamma \simeq -0.5$ mag $^{-1}$, see also )."
 The results for MIOL and MIOG are larecr than that cited for NE3 (5c03 mae +)., The results for M101 and M106 are larger than that cited for M33 $\gamma \simeq -0.3$ mag $^{-1}$ ).
 The results differ in vet another manner. namely that the slope of he Wescuheit function imferred from classical Cepheids sapling the ner of regionMIOG differs roni the outer region. while the classical Cepheids of M33 Gunner outer) exhibit a comparable slope.," The results differ in yet another manner, namely that the slope of the Wesenheit function inferred from classical Cepheids sampling the inner region of M106 differs from the outer region, while the classical Cepheids of M33 (inner outer) exhibit a comparable slope."
 The discrepancies are manifold aud the proposed netallicity effect is nonetheless too large., The discrepancies are manifold and the proposed metallicity effect is nonetheless too large.
 The sizeable distance offset between the iuuer and outer reeious of the ealaxies arises frou photometric containimation and other source(s)., The sizeable distance offset between the inner and outer regions of the galaxies arises from photometric contamination and other source(s).
 Consider the following example. iu taudem with he results of Fie. 2..," Consider the following example, in tandem with the results of Fig. \ref{fig2},"
 which compares the distances ο. classical Cepheids aud RR Lyyae variables at a colunon zero-point (c.g.. LMC. SAIC. and IC 1613).," which compares the distances to classical Cepheids and RR Lyrae variables at a common zero-point (e.g., LMC, SMC, and IC 1613)."
 The Weseuheit functions inferred yon OGLE LMC classical Cepheids and RR Lyrae variables are adopted as the calibrating set2003)., The Wesenheit functions inferred from OGLE LMC classical Cepheids and RR Lyrae variables are adopted as the calibrating set.
. RR Lyrae variables likewise follow scatter reduced Wesenheit functions2010)., RR Lyrae variables likewise follow scatter reduced Wesenheit functions.
 The distance offset between classical Cepheids and RR. Lyrac variables in the SAIC as established via. the OGLE LAIC Wescnheit relations is: Agi&0.0 (Fie. D)., The distance offset between classical Cepheids and RR Lyrae variables in the SMC as established via the OGLE LMC Wesenheit relations is: $\Delta \mu_0\simeq-0.04$ (Fig. \ref{fig7}) ).
 The distance offset between classical Cepheids and RR Lyrae variables in IC 1613 as established via the OGLE LAIC Weseuhei relatious is: Ajig&|0.02 (Fig. 1))., The distance offset between classical Cepheids and RR Lyrae variables in IC 1613 as established via the OGLE LMC Wesenheit relations is: $\Delta \mu_0\simeq+0.02$ (Fig. \ref{fig7}) ).
" The distances inferred from the standard candles agree to within the uncertainfies. despite the neglect of metallicity correctious for variable types sampling different temperature. radius. and density regimes,"," The distances inferred from the standard candles agree to within the uncertainties, despite the neglect of metallicity corrections for variable types sampling different temperature, radius, and density regimes."
 Ilence the evidence does not support a sizeable metallicitv effect., Hence the evidence does not support a sizeable metallicity effect.
 The couparison between the variable types is indepeneut of zero-point and uucertaiuties tied to extiuctjon corrections., The comparison between the variable types is independent of zero-point and uncertainties tied to extinction corrections.
 Adiuuttedly. additional observations of extragalactic RR Lvrae variables are desrade aud the Wesenheit function characterizing tha population as interred. ποια pulsation models. f1ο Magellanic Clouds. and elobular clusters are mareinally discrepant," Admittedly, additional observations of extragalactic RR Lyrae variables are desirable and the Wesenheit function characterizing that population as inferred from pulsation models, the Magellanic Clouds, and globular clusters are marginally discrepant"
the progenitors of blue strageler stars (BSS). lound to exist in environments of high stellar density. such as globular clusters or the cores of open clusters.,"the progenitors of blue straggler stars (BSS), found to exist in environments of high stellar density, such as globular clusters or the cores of open clusters."
 As already mentioned. the main reason lor developing the evolution code presented here was the need for an efficient. and fast. tool that could. be integrated into the MODEST (MOdelling DEnse STellar svstems) collaboration. combining dynamical N-bocly calculations with hvdrodyvnamiecs(he colliding or merging of starsand stellar evolution. lor the simulating of dense stellar environments.," As already mentioned, the main reason for developing the evolution code presented here was the need for an efficient and fast tool that could be integrated into the MODEST (MOdelling DEnse STellar systems) collaboration, combining dynamical N-body calculations with hydrodynamics—the colliding or merging of stars—and stellar evolution, for the simulating of dense stellar environments."
 Whereas for normal stars. il is possible to construct aud tabulate pre-compulecd evolutionary (racks lor the use of MODEST calculations. merger products. having completely unpredictable configurations. must be evolvedsifu.," Whereas for normal stars, it is possible to construct and tabulate pre-computed evolutionary tracks for the use of MODEST calculations, merger products, having completely unpredictable configurations, must be evolved."
 A non-canonical initial model will be the product of a hydrodynamic merger ealeulation. usually by smoothed particle hydrocvnamics (SPII) methods.," A non-canonical initial model will be the product of a hydrodynamic merger calculation, usually by smoothed particle hydrodynamics (SPH) methods."
 The first step in adapting such a model to quasi-static stellar evolution caleulations is to obtain a hyvedrostatically relaxed configuration., The first step in adapting such a model to quasi-static stellar evolution calculations is to obtain a hydrostatically relaxed configuration.
 This is achieved by applying the quasi-dvnamic method of ?.., This is achieved by applying the quasi-dynamic method of \citet{1967ApJ...150..131R}.
 Instead of eqs.(," Instead of eqs.,"
2). consider (he equations where r(m.7) is regarded as a function of the mass coordinate mmand (he quasi-time τ. and p(p.s.Y) is determined bv the EOS.," consider the equations where $r(m,\tau)$ is regarded as a function of the mass coordinate $m$and the quasi-time $\tau\,$, and $p(\rho,s,Y)$ is determined by the EOS."
 The quasi-time has no physical meaning: its purpose is provide asviptotically (1e. for 7— x) a hydrostatic solution., The quasi-time has no physical meaning: its purpose is provide asymptotically (i.e. for $\tau\rightarrow\infty$ ) a hydrostatic solution.
 Equation is called quasi-dvnamic because the correct dynamic equation would have ο. / the irue limeon its left-hand. side., Equation is called quasi-dynamic because the correct dynamic equation would have $\partial^2 r/\partial t^2$ —with $t$ the true time—on its left-hand side.
 Let the boundary conditions be r=0 at the center. and p=0 at the surface.," Let the boundary conditions be $r=0$ at the center, and $p=0$ at the surface."
 For a eiven distribution of entropy s(2). and of the number fractions. collectively denoted. by Y(on). and an initial distribution of radii r(.0). the foregoing equations are to be solved for rn.7) (and p(m.7). and pin.7) ).," For a given distribution of entropy $s(m)\,$, and of the number fractions, collectively denoted by $Y(m)\,$, and an initial distribution of radii $r(m,0)\,$, the foregoing equations are to be solved for $r(m,\tau)$ (and $\rho(m,\tau)\,$, and $p(m,\tau)\,$ )."
 since (he entropy s and the composition Y are not varied. the (quasi) motion 15 adiabatic: du= —pd(l/p).," Since the entropy $s$ and the composition $Y$ are not varied, the (quasi) motion is adiabatic: $du=-pd(1/\rho)\,$ ."
 Multiplving by Or/Or and integrating over the mass of the star vields. aller an integration by parts.," Multiplying by $\partial r/\partial\tau$ and integrating over the mass of the star yields, after an integration by parts,"
"I. wilh »=3 representing a dipolar magnetic field. and 7=f/((0—1),). D, the birth period. and > the period's time-derivative at pulsar birth. (",", with $n = 3$ representing a dipolar magnetic field, and $\tau_0 = P_0/((n-1)\dot{P}_0)$, $P_0$ the birth period, and $\dot{P}_0$ the period's time-derivative at pulsar birth. ("
The subseript ‘O° denotes quantities at pulsar birth).,The subscript `0' denotes quantities at pulsar birth).
 These quantities are connected to the spindown huninosity αἱ birth via We assume that the particles are confined in (he PWN for a time TZ. alter which the PWN breaks up and releases (hem into the surrounding ISM.," These quantities are connected to the spindown luminosity at birth via We assume that the particles are confined in the PWN for a time $T$, after which the PWN breaks up and releases them into the surrounding ISM."
 The time evolution of the particle spectrum Q(E.1) inside the PWN is described bv VULN," The time evolution of the particle spectrum $Q(E,t)$ inside the PWN is described by - ),"
 The time evolution of the particle spectrum Q(E.1) inside the PWN is described bv VULNS," The time evolution of the particle spectrum $Q(E,t)$ inside the PWN is described by - ),"
 The time evolution of the particle spectrum Q(E.1) inside the PWN is described bv VULNSΠ," The time evolution of the particle spectrum $Q(E,t)$ inside the PWN is described by - ),"
 The time evolution of the particle spectrum Q(E.1) inside the PWN is described bv VULNSΠΟ," The time evolution of the particle spectrum $Q(E,t)$ inside the PWN is described by - ),"
 The time evolution of the particle spectrum Q(E.1) inside the PWN is described bv VULNSΠΟΠ," The time evolution of the particle spectrum $Q(E,t)$ inside the PWN is described by - ),"
for NGC 5077 is in good agreement (within a factor of 2.3) with the Mgy—Mp correlation between BH and host bulge mass.,for NGC 5077 is in good agreement (within a factor of 2.3) with the $M_{\rm BH}-M_{\rm bul}$ correlation between BH and host bulge mass.
 The black hole mass predicted by the Mgy—c correlation is à factor of 3.4 lower than our measure. adopting the relation found by Tremaineetal.(2002) and in excellent agreement using the parameterization by Ferrarese&Ford(2005).," The black hole mass predicted by the $M_{\rm BH}-\sigma$ correlation is a factor of 3.4 lower than our measure, adopting the relation found by \citet{tremaine02} and in excellent agreement using the parameterization by \citet{ferrarese05}."
. This result. in conjunction. with. the. previous. results. for NGC 3998 (Paper D. strengthens the possibility of a connection between the residuals from the Mgy—c relation and the bulge effective radius.," This result, in conjunction with the previous results for NGC 3998 (Paper I), strengthens the possibility of a connection between the residuals from the $M_{\rm BH}-\sigma$ relation and the bulge effective radius."
 While NGC 3998. indeed. has one of the lowest values of R. among galaxies with measured Mgy and shows a negative residual. NGC 5077 has a larger effective radius and shows a small positive residual.," While NGC 3998, indeed, has one of the lowest values of $R_{\rm e}$ among galaxies with measured $M_{\rm BH}$ and shows a negative residual, NGC 5077 has a larger effective radius and shows a small positive residual."
 We also recently showed that the same result was found for the Seyfert galaxy NGC 5252: a larger effective radius corresponds in this galaxy to a still larger positive residual., We also recently showed that the same result was found for the Seyfert galaxy NGC 5252: a larger effective radius corresponds in this galaxy to a still larger positive residual.
" Apparently. only with a combination of at least ~ and KR, is it possible to account for the correlations between Mpy and other bulge properties. indicating the presence of a black holes ""fundamental plane""."," Apparently, only with a combination of at least $\sigma$ and $R_{\rm e}$ is it possible to account for the correlations between $M_{\rm BH}$ and other bulge properties, indicating the presence of a black hole's “fundamental plane”."
 Clearly. the number of direct black-hole mass measurements must be further increased. together with precise determinations of c and R.. to test these conclusions on a stronger statistical basis.," Clearly, the number of direct black-hole mass measurements must be further increased, together with precise determinations of $\sigma$ and $R_{\rm e}$, to test these conclusions on a stronger statistical basis."
 In a forthcoming paper we will present new BH mass determinations and discuss the physical implications of our results., In a forthcoming paper we will present new BH mass determinations and discuss the physical implications of our results.
color offset of +0.009 uag to the NGC 6791 p10101jetry. as we did for M67 aud the Hyades.,color offset of +0.009 mag to the NGC 6791 photometry as we did for M67 and the Hyades.
 No acdjustinent will be wmide to V., No adjustment will be made to $V$.
 For the cluster CAD relation. we will use the fiducial relation compiledipi by Saucageeal.(2003) limited to aLadj ited B—V below 1.25 since our redest field star ls al (B-Ευ = 1.09 aud the reddening is E(B—V) = 0.125.," For the cluster CMD relation, we will use the fiducial relation compiled by \citet{slv03} limited to an adjusted $B-V$ below 1.25 since our reddest field star is at $(B-V)_0$ = 1.09 and the reddening is $(B-V)$ = 0.125."
 je results are illtstrated in Fig., The results are illustrated in Fig.
 8. which 1as tle same symbol definitions as Fig.," 8, which has the same symbol definitions as Fig."
 7. ising the | relation of NCC 6791 with (Gav—AL) = 13.15.," 7, using the fiducial relation of NGC 6791 with $(m-M)$ = 13.45."
 For tle samme 19 stars redder than 8—V le average residtal in Ady is 0.005.," For the same 19 stars redder than $B-V$ = 0.90, the average residual in $M_V$ is 0.005."
 Wha Is €ille‘ell compared to he Hyades coriparisou je removal of the :ippar'ent asyinmetry in reskuals for duer stars :uxl the weak evidence for a slope a recdder colors., What is different compared to the Hyades comparison is the removal of the apparent asymmetry in residuals for bluer stars and the weak evidence for a slope at redder colors.
 TIis change indicates that the fiducial relation foONG C 6191 is a better natch to the CMD position of the average fiek| star of hie metallicity 1ian the Hades. as one would ex»ect if tlie typical star in the sample is οder than the Hyacles clister but younger than (GC 6791.," This change indicates that the fiducial relation for NGC 6791 is a better match to the CMD position of the average field star of high metallicity than the Hyades, as one would expect if the typical star in the sample is older than the Hyades cluster but younger than NGC 6791."
 The possibility that the field stars inay be youeer than. NGC 6791 comes from the sharp tur1 toward negative residuals lor B—V buer thai 0.55., The possibility that the field stars may be younger than NGC 6791 comes from the sharp turn toward negative residuals for $B-V$ bluer than 0.85.
 With tle adopted cluste‘reddening ol E(B—V) = 0.125. this color marks the start of the rapic vertica rise iu the cluser turnoll. thereby leacling to anoualously bright absolute uaguitudes relative to less evolved stars.," With the adopted cluster reddening of $(B-V)$ = 0.125, this color marks the start of the rapid vertical rise in the cluster turnoff, thereby leading to anomalously bright absolute magnitudes relative to less evolved stars."
 For a fixed value o ‘the recdeuiug aud metalicity. taking iuto accoun the potential uicertalniv iu the color offset applied to the fidiClal relation for NGC 679)|. thea dpewent modulus is (n—AL) = 13.16 + 0.019.," For a fixed value of the reddening and metallicity, taking into account the potential uncertainty in the color offset applied to the fiducial relation for NGC 6791, the apparent modulus is $(m-M)$ = 13.46 $\pm$ 0.049."
 Saiageetal.(2003) suppvy uo estimate of the uicertaiuy in thei: [fiducial relations., \citet{slv03} supply no estimate of the uncertainty in their fiducial relations.
 We have doile an incdeperdent check on their relation by eriving the fiduclal curve over the color range o juterest μι& only stars in the core of NGC TOL., We have done an independent check on their relation by rederiving the fiducial curve over the color range of interest using only stars in the core of NGC 6791.
" Sta""S betwee1b- Vv = (0.96 and 1.26 were iclentified. ane retained if hey fell within +0.3 uag of he relation.", Stars between $B-V$ = 0.96 and 1.26 were identified and retained if they fell within $\pm$ 0.30 mag of the \citet{slv03} relation.
 Stars between B—V = 0.96 atd 1.02 were adjuste in V to the ceutra color of the bin using the slope of the main sequeuce reation as defiued by Saxlageeal.(2003) ancl coumecd iuto bius 0.06 uag wide in V., Stars between $B-V$ = 0.96 and 1.02 were adjusted in $V$ to the central color of the bin using the slope of the main sequence relation as defined by \citet{slv03} and counted into bins 0.06 mag wide in $V$.
 The resilting histogram was it with a gaussian »olile to eline the peak of the clistribution., The resulting histogram was fit with a gaussian profile to define the peak of the distribution.
 The bin was jen shifted recdward i1 B—V by 0.0L mag aud the process repeated., The bin was then shifted redward in $B-V$ by 0.04 mag and the process repeated.
 The |iducial points were compa'ed to those o .oaucdageetal.(2003):: the average difference for the 7 poitis. in the sense (SLV - 0is). is Q.000 + 0.020. indicating that the fictucial relation is not a significant source of uncertainty.," The fiducial points were compared to those of \citet{slv03}; the average difference for the 7 points, in the sense (SLV - ours), is 0.009 $\pm$ 0.020, indicating that the \citet{slv03} fiducial relation is not a significant source of uncertainty."
 I we alow for εί ).025 uucertaiuty in E(G8—V aud £0.06 uncertainty d [Fe/H]. the combined internal and exterual errors unply (i—AL) = 13.KK) cx 0.15. with the dominait source of error being the reccdeniig Uncertainty.," If we allow for $\pm$ 0.025 uncertainty in $(B-V)$ and $\pm$ 0.06 uncertainty in [Fe/H], the combined internal and external errors imply $(m-M)$ = 13.46 $\pm$ 0.15, with the dominant source of error being the reddening uncertainty."
" If the true modulus is caleulated. the error bars a'e reduced because the reddening elect is partially compensated by the cor'elated change in Ay: the true moclulus is (0—M), = 13.07 x 0.09. internal and external errors incl«lec."," If the true modulus is calculated, the error bars are reduced because the reddening effect is partially compensated by the correlated change in $A_V$ ; the true modulus is $(m-M)_0$ = 13.07 $\pm$ 0.09, internal and external errors included."
 How «does this result compare with current estimates?, How does this result compare with current estimates?
 The clefinitive value for NCC 6791 at present is that of Gruneahletal.(2008) based upou analysis of the cluster eclipsing binary. V20.," The definitive value for NGC 6791 at present is that of \citet{gru08}
 based upon analysis of the cluster eclipsing binary, V20."
 The beauty of the techique is that the masses aid radii cau be determinecl independent of the recldening aud metalliciy aud age estimation cau be carried out through comparison to isochroues in the mass-racius plane without requiring a transformation of the theoretical parameters to the observational plane., The beauty of the technique is that the masses and radii can be determined independent of the reddening and metallicity and age estimation can be carried out through comparison to isochrones in the mass-radius plane without requiring a transformation of the theoretical parameters to the observational plane.
 Conversiou of the stellar parameters to luminositiesauc distances still requires, Conversion of the stellar parameters to luminositiesand distances still requires
corresponding to linear combinations in. the May98 and Tay&JJune98 amplitude spectra.,corresponding to linear combinations in the May98 and June98 amplitude spectra.
 In Fig., In Fig.
 7 we plot the FT of he residuals of the May&JJune98 dataset after prewhitening withCone andwy.," \ref{fig:lincombs} we plot the FT of the residuals of the June98 dataset after prewhitening with, and."
.. The amplitudes of these linear combination modes are very low. only a factor of two above the noise level.," The amplitudes of these linear combination modes are very low, only a factor of two above the noise level."
 If hey are present in the 1997 and 2001 amplitude spectra. which lave greater noise levels. they would therefore not be detectable.," If they are present in the 1997 and 2001 amplitude spectra, which have greater noise levels, they would therefore not be detectable."
" Three of the four linear combination regions lie very close o the dominant signals: the combination (e5,,,— @y-,,) Is only 40 pn Hz from ως Goss, Yona) IS 30 pez from cu. and Goss,| Wao dis 40 Az from css."," Three of the four linear combination regions lie very close to the dominant signals: the combination ${\omega}_{_{230}}-{\omega}_{_{370}}$ ) is only 40 $\mu$ Hz from ${\omega}_{_{650}}$ , ${\omega}_{_{230}}-{\omega}_{_{650}}$ ) is 30 $\mu$ Hz from ${\omega}_{_{370}}$ , and ${\omega}_{_{650}}+{\omega}_{_{370}}$ ) is 40 $\mu$ Hz from ${\omega}_{_{250}}$."
" The proximity of the linear combinations to the dominant signals is unfortunate: at these small separations the window functions partially overlap. which almost certainly contributes to the confusion in οὐοι, and 2..."," The proximity of the linear combinations to the dominant signals is unfortunate; at these small separations the window functions partially overlap, which almost certainly contributes to the confusion in ${\omega}_{_{650}}$ and ${\omega}_{_{370}}$."
 Our choice of whether a signal is due to a real or combination mode is dictated by their relative amplitudes: the combination mode is defined to have a smaller amplitude than the constituent real modes., Our choice of whether a signal is due to a real or combination mode is dictated by their relative amplitudes: the combination mode is defined to have a smaller amplitude than the constituent real modes.
 Despite their low signal-to-noise. we discovered 24 signals in the linear combination regions that corresponded to better than | //;Hz (some to better than 0.1. // Hz) to the set of 43 combinations calculated from the highest-amplitude components ofBory and (Table 3).," Despite their low signal-to-noise, we discovered 24 signals in the linear combination regions that corresponded to better than 1 $\mu$ Hz (some to better than 0.1 $\mu$ Hz) to the set of 43 combinations calculated from the highest-amplitude components of, and (Table 3)."
 By calculating the fraction of the frequency axis that is filled by possible linear combinations. we estimate that only 6 coincidences would be expected by chance alignments.," By calculating the fraction of the frequency axis that is filled by possible linear combinations, we estimate that only 6 coincidences would be expected by chance alignments."
 Thus. we have confidence that the fine structure in and iis real: a signal is more likely to be real if it appearsin linear combinations aswell (Kleinman et al.," Thus, we have confidence that the fine structure in and is real: a signal is more likely to be real if it appearsin linear combinations aswell (Kleinman et al."
 1998)., 1998).
absorption (aud both Lya aud Lv obscure the Lv3).,absorption (and both $\alpha$ and $\beta$ obscure the $\gamma$ ).
 If the foreerouud Lye absorption is from +<2.8 (where TeteLya lL). this obscuration should not significantly weaken bounds& that ignore it.," If the foreground $\alpha$ absorption is from $z < 2.8$ (where $\tau_{\rm eff, Ly\alpha} \lesssim 1$ ), this obscuration should not significantly weaken bounds that ignore it."
 The focus of this Letter is on absorption iu uuderdeuse regions aud what this absorption implics about the ionization state of denser. ucighboring regions.," The focus of this Letter is on absorption in underdense regions and what this absorption implies about the ionization state of denser, neighboring regions."
" Approximately of the volume las A,<0.2 at z=3. «has A,x0.15 (Miralda-Esciudéetal.2000).. anda larger fraction iu redshift space."," Approximately of the volume has $\Delta_b < 0.2$ at $z=3$, has $\Delta_b < 0.15$ \citep{miralda00}, and a larger fraction in redshift space."
" Equation (1)). combined with the kuowledee that the least deuse regious iu the Do3 ICAL have A,~0.1. suggest that the ΠΟ Lyra forest is sensitive to ΠΟ fractions in such uudoerdeusities of the order 15€ (aud higher series lines to ~LOW Iu order to achieve such coustraiuts. the locations of uuderdense reeious inst be kuown."," Equation \ref{eqn:GP_HEII}) ), combined with the knowledge that the least dense regions in the $z\sim 3$ IGM have $\Delta_b \sim 0.1$, suggest that the HeII $\alpha$ forest is sensitive to HeII fractions in such underdensities of the order $1\%$ (and higher series lines to $\sim 10\%$ In order to achieve such constraints, the locations of underdense regions must be known."
 The HII Ίσα forest reveals this information., The HI $\alpha$ forest reveals this information.
 The HI Lye Comn-Peterson optical depth is where we have asstuned photoionization equilibrium with Ty. the HI photoionization rate in units of 10.ts ! and a power-law tenmiperature-densitv relation given wt =TyA;1 where ><1.6 (Cuedin&Thu1998).," The HI $\alpha$ Gunn-Peterson optical depth is where we have assumed photoionization equilibrium with $\Gamma_{12}$ – the HI photoionization rate in units of $10^{-12}$ $^{-1}$ –, and a power-law temperature-density relation given by $T = T_0 \, \Delta_b^{\gamma-1}$ where $\gamma < 1.6$ \citep{gnedin98}."
. The term ADU1) ij equation 2— arises frou the eniperature depeudence of the recombination rate., The term $\Delta_b^{0.7 (\gamma - 1)}$ in equation \ref{eqn:tauHI} arises from the temperature dependence of the recombination rate.
 We use the values 5=1.3. 7)=Ls.000Tk. aud Tyo5. consistent with observations (MeDonaldctal.2001:Faucher-Cuü," We use the values $\gamma = 1.3$, $T_0 = 18,000\,$ K, and $\Gamma_{12} = 0.8$ , consistent with observations \citep{mcdonald01b, faucher08}."
gueéreetal.2008a).. Dj» is expected to be rearly spatially invariant owing to the lounge mean free ith: Gutp) of hydrogeudoniziug photons aud the larec number of sources within a mf, $\Gamma_{12}$ is expected to be nearly spatially invariant owing to the long mean free path (mfp) of hydrogen-ionizing photons and the large number of sources within a mfp.
" The smaller the value of A, that can be reliably located in the III ἵνα forest. the better one cau coustrain the Well fraction from the ΠΟ Lsaüuan forest."," The smaller the value of $\Delta_b$ that can be reliably located in the HI $\alpha$ forest, the better one can constrain the HeII fraction from the HeII Lyman forest."
 However. contimmun fittingtends to artificially remove flux such that the flax in the lowest deusity pixels is set to zero. thereby preventing oue frou distiuguisliug between «μα. values of Αρ. Fauche," However, continuum fittingtends to artificially remove flux such that the flux in the lowest density pixels is set to zero, thereby preventing one from distinguishing between small values of $\Delta_b$."
r-Ciguereetal.(2008) estimated. that coutinuun fitting on average renioves 3% of the transmission at +=3., \citet{faucher08b} estimated that continuum fitting on average removes $3$ of the transmission at $z = 3$.
" Therefore. a value of A,=0.15. which vields hinzz0.03 or 3% absorption. is approximately the unin density coutrast over 0 that can be discriminated at 2~3."," Therefore, a value of $\Delta_b = 0.15$, which yields $\tau_{\rm HI}^{\rm GP} \approx 0.03$ or $3\%$ absorption, is approximately the minimum density contrast over $0$ that can be discriminated at $z\sim 3$."
" While a more rigorous derivation of the ται A, would be worthwhile. we cluploy A,=0.15 for this study."," While a more rigorous derivation of the minimum $\Delta_b$ would be worthwhile, we employ $\Delta_b = 0.15$ for this study."
" Figure d shows the HIE Ίσα spectrum (dotted curve. R=A\fAX= 1000) and HoII Ίνα spectrum (thick solid curve, R SOO) of the =3.29 quasar Q0302-003 (Worseck&Wisotzki2006).. one of the most-stuclied Πο Lye sieltlines."," Figure \ref{fig:spectra} shows the HI $\alpha$ spectrum (dotted curve, $R \equiv \lambda/ \Delta \lambda = 1000$ ) and HeII $\alpha$ spectrum (thick solid curve, $R=800$ ) of the $z=3.29$ quasar Q0302-003 \citep{worseck06}, one of the most-studied HeII $\alpha$ sightlines."
 Note that for 3.1<23.2 a region spanning ~100 comoving Mpe (cMpc) τςd (except perhaps near 2=3.1) such that there is uo siguificaut Well Ίνα transiission., Note that for $3.1< z < 3.2$ -- a region spanning $\approx 100$ comoving Mpc (cMpc) – $\tau < 4$ (except perhaps near $z = 3.1$ ) such that there is no significant HeII $\alpha$ transmission.
 The short-dashed horizoutal line iu Figure l| represcuts the transmission for 7=L., The short-dashed horizontal line in Figure \ref{fig:spectra} represents the transmission for $\tau = 4$.
 Many of the clemenuts with 7<1 in Hell Lyra absorption admit LOO% ITI Lye trausimission (see the cvan highlighted. regions in Figure 1))., Many of the elements with $\tau < 4$ in HeII $\alpha$ absorption admit $\sim 100\%$ HI $\alpha$ transmission (see the cyan highlighted regions in Figure \ref{fig:spectra}) ).
" These regions should have A,=0.15 from the above discussion.", These regions should have $\Delta_b \lesssim 0.15$ from the above discussion.
" Equation (1)) aud the limit 7<1 implies that the cloments with A,<0.15 have πο>0.008. underdeuseThroughout this Letter. we adopt this bound on πω for the most underdense. saturated elements in the ΠΟ Lye spectrum of Q0302-003. althoueh a more detailed analvsis could imiprove upou it."," Equation \ref{eqn:GP_HEII}) ) and the limit $\tau < 4$ implies that the underdense elements with $\Delta_b < 0.15$ have $x_{\rm HeII} > 0.008$ Throughout this Letter, we adopt this bound on $x_{\rm HeII}$ for the most underdense, saturated elements in the HeII $\alpha$ spectrum of Q0302-003, although a more detailed analysis could improve upon it."
 Another welbstudied Uell forest sishtlne. the +=2.89 quasar IIE2317-1312 (not shown). has a Camu-Petersou trough af zz2.85 with no detected Well Ίσα transmission aud provides a simular bound.," Another well-studied HeII forest sightline, the $z=2.89$ quasar HE2347-4342 (not shown), has a Gunn-Peterson trough at $z\approx 2.85$ with no detected HeII $\alpha$ transmission and provides a similar bound."
 Sometime before := 2.8. the second electron of iuterealactic πομ was reionized by a source of ultraviolet photous (uost probably quasars)./ aud afterward the helium was kept doubly ionized by the mctagalactic radiation background.," Sometime before $z \approx 2.8$ , the second electron of intergalactic helium was reionized by a source of ultraviolet photons (most probably quasars), and afterward the helium was kept doubly ionized by the metagalactic radiation background."
 If a eas parcel is expose fo a radiation background with ell photoionization rate Πω. the Well fraction as a function," If a gas parcel is exposed to a radiation background with HeII photoionization rate $\Gamma_{\rm HeII}$ , the HeII fraction as a function"
"Approximately 50 planetary nebulae (PNs) are presently known to have ""small scale” heterogeneities located inside or outside the main ionized nebulae (Goncalvesοἱal.9001).","Approximately 50 planetary nebulae (PNs) are presently known to have “small scale"" heterogeneities located inside or outside the main ionized nebulae \citep{goncalves01}."
. Cometary knots are a subcategory of small scale structures found. commonly in nearby. evolved PNsPNs (ODelletal.2002).," Cometary knots are a subcategory of small scale structures found commonly in nearby, evolved PNsPNs \citep{odell02}."
. Because of its closest proximity. (213 parsecs (1997))). the Helix Nebula (NGC. 7293) is the best case to study (he structure and excitation conditions of cometary knots.," Because of its closest proximity (213 parsecs \cite{harris97}) ), the Helix Nebula (NGC 7293) is the best case to study the structure and excitation conditions of cometary knots."
 The nature of the cometary knots in the [Helix was first established by Meaburnοἱal.(1992)., The nature of the cometary knots in the Helix was first established by \cite{meaburn92}.
. The detailed structure of the cometary knots has been resolved in ionized gas lines in the optical by ODell&Handron(1996) with further, The detailed structure of the cometary knots has been resolved in ionized gas lines in the optical by \cite{odell96} with further
xl we can trace the silhouette of DP15.513-0.029 i the structure of DP15.512-0.006.,and we can trace the silhouette of DP45.543-0.029 on the structure of DP45.542-0.006.
 These protrusions wiouslv beean as pre-existiug density eulhaucenmenuts in the original surrounding molecular cloud. aud they evolved iuto the forms seen wader the combined effect of photoionization and flows coming from the nearby Iu reeious.," These protrusions obviously began as pre-existing density enhancements in the original surrounding molecular cloud, and they evolved into the forms seen under the combined effect of photoionization and flows coming from the nearby H regions."
 These pillars are the result of the interaction of massive stars with their cuviroument. aud they are most likely places of star formation.," These pillars are the result of the interaction of massive stars with their environment, and they are most likely places of star formation."
 For our research we asstuue a distance to the molecular cloud GRSAIC|0.060 of 6.0 pc., For our research we assume a distance to the molecular cloud GRSMC45.453+0.060 of 6.0 kpc.
 This distance was cletermuned 15.kinematically153 by Simonetal.(2001)., This distance was determined kinematically by \citet{Simoetal01}.
 A simple measurement of the leugth aud width of the pillars is eiven in Table 1., A simple measurement of the length and width of the pillars is given in Table 1.
 The definition of these nuüeasurenaents is of course subjective because the base of the pillars mergses iuto larger dust structures., The definition of these measurements is of course subjective because the base of the pillars merges into larger dust structures.
 We waut to emphasize that we measure projected (quantities. since the inclination aneles are unknown.," We want to emphasize that we measure projected quantities, since the inclination angles are unknown."
 Our estimated values are in agreement with those that Walborn calculated for other dust pillars in the Calaxy., Our estimated values are in agreement with those that \citet{Walbetal02b} calculated for other dust pillars in the Galaxy.
" The heads of the two pillars that we discovered are dramatically different as seen frou, our point of view.", The heads of the two pillars that we discovered are dramatically different as seen from our point of view.
 Both of them show the presence of vouug stellar objects. but while the stars in the head of DP15.513-0.029 appear to remain enclosed iu the dusty cocoon. those of DP15.512-0.006 have already started to disrupt the interstellar medium.," Both of them show the presence of young stellar objects, but while the stars in the head of DP45.543-0.029 appear to remain enclosed in the dusty cocoon, those of DP45.542-0.006 have already started to disrupt the interstellar medium."
 This is a perfect idicator of οσοπιο stellar evolution. aud it may sueecst that the stars iu the atter pillar are older.," This is a perfect indicator of ongoing stellar evolution, and it may suggest that the stars in the latter pillar are older."
 However. it is possible that due to he ecometry of the region. the dust may be concealing he disruption of the ISAL produced. by the new born stars in DP15.513-0.029.," However, it is possible that due to the geometry of the region, the dust may be concealing the disruption of the ISM produced by the new born stars in DP45.543-0.029."
 From the 2\LASS point source catalogue of this region. aud at a resolution of 270 per πο we find three objects at the tip of DP15.512-0.006. and two in DP15.513-0029.," From the 2MASS point source catalogue of this region, and at a resolution of $2\farcs0$ per pixel we find three objects at the tip of DP45.542-0.006, and two in DP45.543-0.029."
 We mav speculate that the stars in these pillars represent a second generation of star formation in lis region., We may speculate that the stars in these pillars represent a second generation of star formation in this region.
 /Studies of bright-rinuned clouds containius infrared sources have been taken as evideuce of star ornation induced by radiatively driven implosion (Walboru2002:Hesteretal.1996:Sueitani&Ogura 1991).," Studies of bright-rimmed clouds containing infrared sources have been taken as evidence of star formation induced by radiatively driven implosion \citep{Walbetal02b,Hestetal96,SugiOgur94}."
 Trigeered second-generation star formation in he viciuitv of O-tvpe stars iud clusters is ubiquitous. and often the secoud. generation is associated with dust ανν.," Triggered second-generation star formation in the vicinity of O-type stars and clusters is ubiquitous, and often the second generation is associated with dust pillars."
 These processes nav play an important role in he self propagation of star formation in the Calasy., These processes may play an important role in the self propagation of star formation in the Galaxy.
 Recent Calactic surveys in radio and the infrared are providing us with exciting new tools to studv nearby star formation and the interaction of massive stars with thei environment., Recent Galactic surveys in radio and the infrared are providing us with exciting new tools to study nearby star formation and the interaction of massive stars with their environment.
 Tn this research we have used the Galactic Leeacy Infrared Alid-Plane Survey Extraordinaire (GLIMPSE) conducted using the aud the Calactic Ring Survey (CRS) performed at the Five College Radio Ástrouoiy Observatory., In this research we have used the Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE) conducted using the and the Galactic Ring Survey (GRS) performed at the Five College Radio Astronomy Observatory.
 GRS has the ability to ideutifv aud probe active star-fornuug eas. aud CGLIMPSE delineates the structure of molecular clouds aud their dust composition.," GRS has the ability to identify and probe active star-forming gas, and GLIMPSE delineates the structure of molecular clouds and their dust composition."
 We discovered two remarkable dust pillars near the nolecular cloud CRSAIC15.153|0.060., We discovered two remarkable dust pillars near the molecular cloud GRSMC45.453+0.060.
 Even though hey seem close to each other (in projection). oue of them shows a more evolved structure that the other. from our »omt of view.," Even though they seem close to each other (in projection), one of them shows a more evolved structure that the other, from our point of view."
 We intend to continue our research. of this whole star orniue region of the Galaxy., We intend to continue our research of this whole star forming region of the Galaxy.
 We will perform near infrared studies to gather information on their stellar opulatious by meaus of photometry and spectroscopy., We will perform near infrared studies to gather information on their stellar populations by means of photometry and spectroscopy.
 A future paper will investigate. the truth of the speculations proposed in this Letter iu more detail. but jew spectroscopic aud plotometiic observatious of this reeion are strongly encouraged im order to characterize he nature of these clouds and the stella: population associated with them.," A future paper will investigate the truth of the speculations proposed in this Letter in more detail, but new spectroscopic and photometric observations of this region are strongly encouraged in order to characterize the nature of these clouds and the stellar population associated with them."
 The space-mass-age distributions of the objects in these regious will tell us a ercat deal about the relationships between ligher- aud lowerauass star formation., The space-mass-age distributions of the objects in these regions will tell us a great deal about the relationships between higher- and lower-mass star formation.
 Iu particular we are interested in the distribution of stellar ages in order to corroborate our hypothesis of the two-stage star formation process., In particular we are interested in the distribution of stellar ages in order to corroborate our hypothesis of the two-stage star formation process.
 The early results of our research indicate the iuportauce of large field-ofview IR observatious like the ones provided by the GLIAIPSE survey., The early results of our research indicate the importance of large field-of-view IR observations like the ones provided by the GLIMPSE survey.
 We are coufideut that our detailed studies of star formune regions near the Calactic plane will play a crucial role in the overall nuderstauding of the Milkv. Wav., We are confident that our detailed studies of star forming regions near the Galactic plane will play a crucial role in the overall understanding of the Milky Way.
 Leonardo Uhbeda acknowledges funding from the Fouds québbéccois de la recherche sur la nature et les technologies., Leonardo Úbbeda acknowledges funding from the Fonds québbéccois de la recherche sur la nature et les technologies.
 This work was supported by UST eraut TIST-AR-1L09G68.02-A., This work was supported by HST grant HST-AR-10968.02-A.
accretion disc.,accretion disc.
 The energeties are again an issue as the reflection albedo of the dise should be quite high. however. with the soft component lux of 2.610 1% eres em> 1 . comparable to 13°° eres + of the hard Component it appears plausible that the soft component is mace via reprocessing.," The energetics are again an issue as the reflection albedo of the disc should be quite high, however, with the soft component flux of $\times$ $^{-13}$ ergs $^{-2}$ $^{-1}$ , comparable to $\times$ $^{-13}$ ergs $^{-2}$ $^{-1}$ of the hard component it appears plausible that the soft component is made via reprocessing."
 Fig 10 shows the covariance spectra at. the QDPO imeseale (0.2-0.4 mlz: black) compared to that of. the onger (0.01-0.2 mllz: red) and shorter (0.4-2 mllz: green) imescale variability., Fig 10 shows the covariance spectra at the QPO timescale (0.2-0.4 mHz: black) compared to that of the longer (0.01-0.2 mHz: red) and shorter (0.4-2 mHz: green) timescale variability.
 “Phe rapid variability is somewhat iarder than the QPO but still contains a similar but smaller i00. soft. component.," The rapid variability is somewhat harder than the QPO but still contains a similar but smaller hot, soft component."
 This subtle dillerence. between the QPO and rapid. variability is not at all evident. [rom the rms spectra alone (Middleton et al 2009)., This subtle difference between the QPO and rapid variability is not at all evident from the rms spectra alone (Middleton et al 2009).
 Lt is only revealed w these better signal-to-noise covariance spectra., It is only revealed by these better signal-to-noise covariance spectra.
 Lowever. he change in spectral shape between the QPO and. long imescale variability is so large that this is clear even in the rms spectra (Middleton et al 2009).," However, the change in spectral shape between the QPO and long timescale variability is so large that this is clear even in the rms spectra (Middleton et al 2009)."
 The remaining observations have insullicient variability power at the QPOὃν [frequency to make covariance spectra in the narrow QPO energy band. so we use only. two frequeney bands. covering long (0.02-0.2 mlz) and short (0.2-2 mllz) timescale variability. and compare these to the same frequency. bands in. Obs2. where short corresponds to the co-added: ΟΡΟ and rapid. variability spectrum.," The remaining observations have insufficient variability power at the QPO frequency to make covariance spectra in the narrow QPO energy band, so we use only two frequency bands, covering long (0.02-0.2 mHz) and short (0.2-2 mHz) timescale variability, and compare these to the same frequency bands in Obs2, where 'short' corresponds to the co-added QPO and rapid variability spectrum."
 The short timescale covariance spectra are shown in Fig 11a., The short timescale covariance spectra are shown in Fig 11a.
 Obsda and b are very similar to Obs2. showing the hotter soft excess component which is present in the ΟΡΟ however Obs3 (black) is slightly softer. appearing to peak at. lower temperatures consistent with the SX in the mean spectrum.," Obs4a and b are very similar to Obs2, showing the hotter soft excess component which is present in the QPO however Obs3 (black) is slightly softer, appearing to peak at lower temperatures consistent with the SX in the mean spectrum."
 Fie Lb shows the corresponding plot for the long timescale variability. showing clearly that this is dominated. by the soft excess in all observations with a shape similar to the SX component in the time-averaged spectrum.," Fig 11b shows the corresponding plot for the long timescale variability, showing clearly that this is dominated by the soft excess in all observations with a shape similar to the SX component in the time-averaged spectrum."
 Understanding the variability of IS J1034|396 is importan as the significant QPO (in Obs2) makes it unique amonegs AGN., Understanding the variability of RE J1034+396 is important as the significant QPO (in Obs2) makes it unique amongst AGN.
 “Phe QPO is plainly not present in Obs3. showing tha the QPO is transient rather than a long-livect feature of the lighteurve.," The QPO is plainly not present in Obs3, showing that the QPO is transient rather than a long-lived feature of the lightcurve."
 Comparing the spectral and timing properties of the average and frequency binned data allows us to compare and contrast the physics whilst the QPO was present. anc not present., Comparing the spectral and timing properties of the average and frequency binned data allows us to compare and contrast the physics whilst the QPO was present and not present.
 This also allows us to test some of the propose models for the QPO (e.g. Maitra Miller 2010: Das Czerny 2010)., This also allows us to test some of the proposed models for the QPO (e.g. Maitra Miller 2010; Das Czerny 2010).
 All of the observations are consistent with a two component continuum. with a strong soft excess ancl weak high energy tail.," All of the observations are consistent with a two component continuum, with a strong soft excess and weak high energy tail."
 Phe strength and shape of the soft excess clearly varies between observations. while the (much lower signal to noise) power law tail remains fairly constant.," The strength and shape of the soft excess clearly varies between observations, while the (much lower signal to noise) power law tail remains fairly constant."
 llowever. on much shorter timescales (within a single observation) this behaviour is reversed.," However, on much shorter timescales (within a single observation) this behaviour is reversed."
 The fractional r.ni.s as a [function of energy shows that the soft excess is always much less variable than the tail. especially on the most rapid timescales.," The fractional r.m.s as a function of energy shows that the soft excess is always much less variable than the tail, especially on the most rapid timescales."
 Lhe dominance of the soft excess in the energy spectrum means that this strongly οος the amount. of rapid variability at low energies as in Middleton et al (2009)., The dominance of the soft excess in the energy spectrum means that this strongly dilutes the amount of rapid variability at low energies as in Middleton et al (2009).
 Llowever. we now go bevond this and look in detail at the spectrum. of the variability using the much better signal-to-noise covariance spectra.," However, we now go beyond this and look in detail at the spectrum of the variability using the much better signal-to-noise covariance spectra."
 Εις reveals a new aspect of the QPO δω (0.2-0.4 mlz variability ie. 5000-2500s timescale). which is that. as well as the power law tail. it also," This reveals a new aspect of the QPO itself (0.2-0.4 mHz variability i.e. 5000-2500s timescale), which is that, as well as the power law tail, it also"
The ealaxy classification scheme of Hubble(1926) has proved durably useful.,The galaxy classification scheme of \citet{hu26} has proved durably useful.
 As moclified ancl extended by deVaucouleurs(1959).. it is still the standard method for classifving low-redshift galaxies with high surface brightness.," As modified and extended by \citet{de59}, it is still the standard method for classifying low-redshift galaxies with high surface brightness."
 The IIubble classification scheme was originally based on the appearance of galaxies on photographie plates., The Hubble classification scheme was originally based on the appearance of galaxies on photographic plates.
 Elliptical galaxies have smooth elliptical isophotes: spiral galaxies have spiral aris (hat wind outward from a central bulge or bar., Elliptical galaxies have smooth elliptical isophotes; spiral galaxies have spiral arms that wind outward from a central bulge or bar.
 It was later discovered that for huminous galaxies. (he surface brightness profile is strongly correlated with the IIubble tvpe.," It was later discovered that for luminous galaxies, the surface brightness profile is strongly correlated with the Hubble type."
" If the surface brightness J is measured along the major axis of a galaxys image. it 1s found that bright elliptical galaxies have surface brightness profiles (hat are well fit bv α de Vaucouleurs. or H11 Jaw, for which log7x—RE! (deVaucouleurs1943)."," If the surface brightness $I$ is measured along the major axis of a galaxy's image, it is found that bright elliptical galaxies have surface brightness profiles that are well fit by a de Vaucouleurs, or $R^{1/4}$ law, for which $\log I \propto
- R^{1/4}$ \citep{de48}."
. By contrast. the azimuthally averaged surface brightness profile of a spiral galaxy. outside its central bulge. is (wpically well fit bv an exponential law. logsx—H (Freeman1910).," By contrast, the azimuthally averaged surface brightness profile of a spiral galaxy, outside its central bulge, is typically well fit by an exponential law, $\log I \propto - R$ \citep{fr70}."
. It was also eventually realized that galaxies of different Hubble type have different. kinematic properties., It was also eventually realized that galaxies of different Hubble type have different kinematic properties.
 The disks of spiral galaxies are rotationallv. [lattened. with stars and eas on nearly circular orbits with litile random motion.," The disks of spiral galaxies are rotationally flattened, with stars and gas on nearly circular orbits with little random motion."
 Bright elliptical galaxies (MyS —20). bv contrast. are slowly rotating and are supported mainly by their anisotropic velocity dispersion.," Bright elliptical galaxies $M_B \la -20$ ), by contrast, are slowly rotating and are supported mainly by their anisotropic velocity dispersion."
 One shortcoming of the IIubble classification scheme. inposed by necessity. is that elliplical galaxies are classified bv (heir apparent. (wo-climensional shape. seen in projection on the sky. rather than their intrinsic three-dimensional shape.," One shortcoming of the Hubble classification scheme, imposed by necessity, is that elliptical galaxies are classified by their apparent two-dimensional shape, seen in projection on the sky, rather than their intrinsic three-dimensional shape."
 Consider an idealized galaxy whose surfaces of constant luminosity density are concentric. coaxial. similar ellipsoids. with principal axes of lengths a>5c: the shape of the galaxy can then be described by the two axis ratios 9=b/a and 4= cfe.," Consider an idealized galaxy whose surfaces of constant luminosity density are concentric, coaxial, similar ellipsoids, with principal axes of lengths $a \geq b \geq c$; the shape of the galaxy can then be described by the two axis ratios $\beta \equiv b/a$ and $\gamma \equiv c/a$ ."
 Equivalently. (he shape can be described by the (vo numbers > and T. where the triaxialitv parameter T is eiven by the relation T=(1—3B2)/(1—52).," Equivalently, the shape can be described by the two numbers $\gamma$ and $T$, where the triaxiality parameter $T$ is given by the relation $T \equiv (1-\beta^2) / (1-\gamma^2)$."
 If (he ellipsoidal galaxy is seen in projection. though. its isophotes will be concentric. coaxial. similar ellipses.," If the ellipsoidal galaxy is seen in projection, though, its isophotes will be concentric, coaxial, similar ellipses."
 The shape of the projected image can then be described bv the single axis ratio gq=B/A. where A and D are (he major and minor axis leneth of anv isophote.," The shape of the projected image can then be described by the single axis ratio $q \equiv B/A$, where $A$ and $B$ are the major and minor axis length of any isophote."
 Although knowing the apparent axis ratio q is not. bv itself. sufficient to determine (he intrinsic axis ratios 2 and 5. the thiree-dimensional shape of galaxies is not bevond all conjecture.," Although knowing the apparent axis ratio $q$ is not, by itself, sufficient to determine the intrinsic axis ratios $\beta$ and $\gamma$, the three-dimensional shape of galaxies is not beyond all conjecture."
 Two approaches to determining the three-dimensional shape of galaxies have been used., Two approaches to determining the three-dimensional shape of galaxies have been used.
 First. the intrinsic shape of an individual galaxy canbe modeled if kinematic data are available i addition to photometric data," First, the intrinsic shape of an individual galaxy canbe modeled if kinematic data are available in addition to photometric data"
to 15. show that this is not the case.,to \ref{fig:app_broadening_20090213} show that this is not the case.
 This indicates that all of the CBFs studied showed significant pulse broadening and may be interpreted as being dispersive., This indicates that all of the CBFs studied showed significant pulse broadening and may be interpreted as being dispersive.
 Although some previous studies have suggested a dispersive nature for “EIT waves”. the true extent of this dispersion may have been disguised by the nature of pomt-and-click analyses of running-difference images.," Although some previous studies have suggested a dispersive nature for “EIT waves”, the true extent of this dispersion may have been disguised by the nature of point-and-click analyses of running-difference images."
 The variation i PA-averaged integrated pulse intensity with distance was studied rather than the variation in. peak pulse intensity due to the presence of pulse broadening., The variation in PA-averaged integrated pulse intensity with distance was studied rather than the variation in peak pulse intensity due to the presence of pulse broadening.
 This was found by multiplying the FWHM by the peak pulse intensity at a given time. and produced inconclusive results.," This was found by multiplying the FWHM by the peak pulse intensity at a given time, and produced inconclusive results."
 While the peak intensity of the pulse was generally observed to decrease with distance and the FWHM was observed to increase with distance in both passbands. the PA-averaged integrated intensity typically showed no strong variation with distance in either passband. although a strong offset between the 171 aand 195 ddata was typically observed.," While the peak intensity of the pulse was generally observed to decrease with distance and the FWHM was observed to increase with distance in both passbands, the PA-averaged integrated intensity typically showed no strong variation with distance in either passband, although a strong offset between the 171 and 195 data was typically observed."
 Contrasting results were found for the 2009 February 12 and 2009 February 13 events respectively. suggesting that further investigation using simultaneous analysis of multiple passbands at very high cadence Is required. something that will be routinely available from the spacecraft.," Contrasting results were found for the 2009 February 12 and 2009 February 13 events respectively, suggesting that further investigation using simultaneous analysis of multiple passbands at very high cadence is required, something that will be routinely available from the spacecraft."
 The results of our analysis suggest that the studied CBFs may be interpreted as dispersive pulses exhibiting negative acceleration., The results of our analysis suggest that the studied CBFs may be interpreted as dispersive pulses exhibiting negative acceleration.
" This is consistent with the fast-mode magnetoacoustic wave interpretation for a freely-propagating “EIT wave"".", This is consistent with the fast-mode magnetoacoustic wave interpretation for a freely-propagating “EIT wave”.
 The variation in the integrated intensity of the pulse was inconclusive. implying that more analysis is required to definitively determine the physical nature of the disturbance.," The variation in the integrated intensity of the pulse was inconclusive, implying that more analysis is required to definitively determine the physical nature of the disturbance."
 The consistency of the results between the events studied suggests that the conclusions drawn here may be applicable to a larger sample of CBFs., The consistency of the results between the events studied suggests that the conclusions drawn here may be applicable to a larger sample of CBFs.
 The initial velocities of the CBFs are comparable to the lower range of estimated Alfvénn speeds, The initial velocities of the CBFs are comparable to the lower range of estimated Alfvénn speeds
in the minimization of (2)).,in the minimization of \ref{chisq}) ).
 In Fig., In Fig.
 9 we see that the age- degeneracy is much. smaller in diffusion A'-means bases. quantified by the slope of the linear trend in. ;logtZi)r versus Aflog/.o2.," \ref{wild:ageZ} we see that the age-Z degeneracy is much smaller in diffusion $K$ -means bases, quantified by the slope of the linear trend in $\Delta \log\langle Z_* \rangle_L$ versus $\Delta
\langle \log t_* \rangle_L$."
 Some clegeneracy in age-metallicity still exists for the dilfusion Av-means bases. but the magnitude of the slope of the trend is half.," Some degeneracy in age-metallicity still exists for the diffusion $K$ -means bases, but the magnitude of the slope of the trend is half."
" One may note that both loefZ.3, and ‘lowefad, are significantly biased for all 4 bases in Fig. 9.."," One may note that both $\log\langle Z_*
\rangle_L$ and $\langle \log t_* \rangle_L$ are significantly biased for all 4 bases in Fig. \ref{wild:ageZ}."
 Fhis probably occurs due to the simulation. prescription. which includes mostly old. SSPs from a large. fine grid of age and Z. One may be inclined to use these estimated. biases to. correct the estimates of real galaxy spectra.," This probably occurs due to the simulation prescription, which includes mostly old SSPs from a large, fine grid of age and Z. One may be inclined to use these estimated biases to correct the estimates of real galaxy spectra."
 However. the amount of bias is dependent on the particular prescription of SELL in the simulations.," However, the amount of bias is dependent on the particular prescription of SFH in the simulations."
 Since there is no general model that describes galaxy SELL for a wide range of galaxies. there is no straightforward wav to estimate the bias. if any. that will occur.," Since there is no general model that describes galaxy SFH for a wide range of galaxies, there is no straightforward way to estimate the bias, if any, that will occur."
 In this section. we apply the fitting techniques to a sample of SDSS spectra to compare the results using cdillerent. bases.," In this section, we apply the fitting techniques to a sample of SDSS spectra to compare the results using different bases."
 We compare the physical. parameters estimated. from each, We compare the physical parameters estimated from each
his discrepancy.,this discrepancy.
 Observationally it is also important to attack this problem by investigating the effect of age aud uctallicity ou the RC in other nearby galaxies where the xoperties of the RC can be studied iu detail., Observationally it is also important to attack this problem by investigating the effect of age and metallicity on the RC in other nearby galaxies where the properties of the RC can be studied in detail.
 Tn this paper we prCsent ano analysis desigιο to determine the distance to M33. using the TRGD aud he RC based on photonetry of stars in ten MEX) fields obtained from Z7ST/WFEPC2 images., In this paper we present an analysis designed to determine the distance to M33 using the TRGB and the RC based on photometry of stars in ten M33 fields obtained from $HST/WFPC2$ images.
 M33 is a1 ideal arect to apply both trw TROB and RC methods of distance determination usine ILST/WEPC? data., M33 is an ideal target to apply both the TRGB and RC methods of distance determination using $HST/WFPC2$ data.
 This paper is composed as follows., This paper is composed as follows.
 In 82 we o»yeseut he data and reduction echuique., In 2 we present the data and reduction technique.
 83Pa displavs the color-uaenitude diagrams oft1ο lneasured stars. aud esnuates he distance to ΑΟ using the TRGD and RC methods.," 3 displays the color-magnitude diagrams of the measured stars, and estimates the distance to M33 using the TRGB and RC methods."
 Primary results are discussect imi laud are μπαΊσσα m 85., Primary results are discussed in 4 and are summarized in 5.
" We have analyzed LESTAVFPC2 data for ten fields in AI33 obtained for Sarajedinietal. (1998)""s cvcle 5 program (60-5911).", We have analyzed $HST/WFPC2$ data for ten fields in M33 obtained for \citet{sar98}' 's cycle 5 program (GO-5914).
 Each field was observed for four orbits. viclding a total exposure time of [800 seconds for FOSS(V) and 5200 seconds for Psliy(7).," Each field was observed for four orbits, yielding a total exposure time of 4800 seconds for $F555W (V)$ and 5200 seconds for $F814W (I)$."
 These data were obtained originally for the study of globular clusters in M32. and a globular cluster is centered in each PC chip.," These data were obtained originally for the study of globular clusters in M33, and a globular cluster is centered in each PC chip."
 The data from the PC chip were preseuted by Sarajedinietal.(1998). and Sarajedinietal.(2000)., The data from the PC chip were presented by \citet{sar98} and \citet{sar00}.
. Tn this study we use all field stars in the WF2. WES. aud WEL chips as well as iu the PC chip.," In this study we use all field stars in the WF2, WF3, and WF4 chips as well as in the PC chip."
 Uereatter we refer to cach observed region using the elobulay clusters designation., Hereafter we refer to each observed region using the globular cluster's designation.
 Figure 1 illustrates the location of the regions in ΑΠΟ used in this study., Figure 1 illustrates the location of the regions in M33 used in this study.
 Considering the nuuuber of fields aud the deep exposures. these data are ideal for stucving the field stars as well as the globular clusters iu NE.," Considering the number of fields and the deep exposures, these data are ideal for studying the field stars as well as the globular clusters in M33."
 Table 1 lists the positions. ealactocentiic distances. deprojected radial distances. aud the reddening values of all the regions used iu this studs.," Table 1 lists the positions, galactocentric distances, deprojected radial distances, and the reddening values of all the regions used in this study."
 The position of the region iu Table 1 3s the center of the ΑΕΡΟΣ., The position of the region in Table 1 is the center of the WFPC2.
" The egalactoceutric distance is the distance from the ceuter of M33 (RA(2000) = OL! 33751902, Dec(2000) 30°39/36"".7) (Cotton.Condon.&Arbizzaui1999)."," The galactocentric distance is the distance from the center of M33 (RA(2000) = $^h$ $^m$ $^s$ .02, Dec(2000) $^\circ$ $^\prime$ $^{\prime\prime}$ .7) \citep{cot99}."
.. All the regions were assumed to be in the plane of MOX disk aud were deprojected to estimate the actual radial distance., All the regions were assumed to be in the plane of M33's disk and were deprojected to estimate the actual radial distance.
 Au inclination of 56° and a position angle of 237 for M3 were used for deprojection of the positions (Regan&Vogol199 1)., An inclination of $56^\circ$ and a position angle of $23^\circ$ for M33 were used for deprojection of the positions \citep{reg94}.
. For foreground reddening correction. the COBE/TIRAS extinction maps of Schlegel.Fiukbeiner.&Davis(1998) απο used.," For foreground reddening correction, the COBE/IRAS extinction maps of \citet{sch98} are used."
 The reddening values of all the reeious are as low as EVV2)=0.06 (E(BV)= 0.01)., The reddening values of all the regions are as low as $E(V-I)=0.06$ $E(B-V)=0.04$ ).
" The extinction laws for Ry =3.3. 4,=L95EQDVW) and ΓιLF)H=LB5L(BV) (Cardellietal.19859).. ave adopted in this study."," The extinction laws for $R_V=$ 3.3, $A_{I}=1.95E(B-V)$ and $E(V-I)=1.35E(B-V)$ \citep{car89}, are adopted in this study."
 The photometry of the stars in the CCD inages has been obtained using themiudltiphot routine of the ITSTphot package (Dolphiu2000a)., The photometry of the stars in the CCD images has been obtained using the routine of the HSTphot package \citep{dol00a}.
. The IISTphot package was designed for photometry of ΠΠFPC2 data aud cluplovs a Library of Tiny Tin poiut-spread-fuuctious (PSFs) for PSF fitting to account for variations m the PSF due to location on the chip aud the centering within a pixel., The HSTphot package was designed for photometry of $HST/WFPC2$ data and employs a library of Tiny Tim point-spread-functions (PSFs) for PSF fitting to account for variations in the PSF due to location on the chip and the centering within a pixel.
 After PSF-fittine. corrections are also mace for ecometric distortion. CTE effect. aud the 31/7 row effect. (Dolphin2000D).," After PSF-fitting, corrections are also made for geometric distortion, CTE effect, and the $^{th}$ row effect \citep{dol00b}."
. Themudtiphot routine eives the magnitudes transformed to the standard svsteni as well as dustrmuental maguitudes., The routine gives the magnitudes transformed to the standard system as well as instrumental magnitudes.
 The IISTphot plotometiv used zero poiuts from Dolphin(2000b) which provides corrections to the Uoltzmanetal.(1995). values., The HSTphot photometry used zero points from \citet{dol00b} which provides corrections to the \citet{hol95} values.
 The umuber of the measured stars in each region is nuanv tens of thousands (from 60000 to ~SO000 stars) which are too many to plot iu a color-magnitude diagram (CAID)., The number of the measured stars in each region is many tens of thousands (from $\sim 60000$ to $\sim80000$ stars) which are too many to plot in a color-magnitude diagram (CMD).
 Therefore. as au example. Fig.," Therefore, as an example, Fig."
 2 shows the color-magnitude diagram (CMD) for one field., 2 shows the color-magnitude diagram (CMD) for one field.
 In the case of the PC chip. at the center of which a globular cluster is located. the stars at ro<2.8 arcsec from the ceuter of the cluster are considered to be members while those at pc[L6 aresec are cousidered to be field stars.," In the case of the PC chip, at the center of which a globular cluster is located, the stars at $r<2.8$ arcsec from the center of the cluster are considered to be members while those at $r>4.6$ arcsec are considered to be field stars."
 Figure 2 shows a CMD for the measured stars in the C20-region. which happens to be our most clistant ficld from the center of M3.," Figure 2 shows a CMD for the measured stars in the C20-region, which happens to be our most distant field from the center of M33."
 Several features are seen in Figure 2. (, Several features are seen in Figure 2. (
a) There is a broad red giant brauch (ROB). the tip of which is seen at [zz21.0 nag.,"a) There is a broad red giant branch (RGB), the tip of which is seen at $I \approx 21.0$ mag."
 The mean color of the RGB of these field stars is redder than that of the elobular cluster C20 in the same region (represented by the solid line)., The mean color of the RGB of these field stars is redder than that of the globular cluster C20 in the same region (represented by the solid line).
 The locus of C20 was derived from the median color of the stars at reo2s aresce from the ceuter of C20. (, The locus of C20 was derived from the median color of the stars at $r<2.8$ arcsec from the center of C20. (
b) A red clump is distinctively seen at £2:21.5 mae and (WL)zz1.0: (c) Asvinptotic giant brauch. (ACB) stars are also seen along and above the RGB: and (d) There is a blue phune at (VWF)+00 extending up to Zzz20 mae. which consists of mniassive nian sequence stars and evolved supergiauts.,"b) A red clump is distinctively seen at $I \approx 24.5$ mag and $(V-I) \approx 1.0$; (c) Asymptotic giant branch (AGB) stars are also seen along and above the RGB; and (d) There is a blue plume at $(V-I)\approx 0.0$ extending up to $I\approx 20$ mag, which consists of massive main sequence stars and evolved supergiants."
 These features are also seen iu the CMDs of the other roeglous., These features are also seen in the CMDs of the other regions.
 Iu Figure 3. the CMDs of all the regions are showu in number deusitv coutour maps (less Diagrams).," In Figure 3, the CMDs of all the regions are shown in number density contour maps (Hess Diagrams)."
 The density contour maps are constructed on LOO100 erids iu the CAID domain (the size of each exit is A(VD)«AI=0.03.\ 0.1). and are smoothed using Gaussian filters of 2 erid width.," The density contour maps are constructed on $100 \times 100$ grids in the CMD domain (the size of each grid is $\Delta(V-I) \times \Delta I = 0.03 \times 0.1$ ), and are smoothed using Gaussian filters of $2$ grid width."
 Basic features secu in Figure 3 are simular to those in Figure 2., Basic features seen in Figure 3 are similar to those in Figure 2.
 Number deusity contour maps are useful for revealing the areas with the highest stellar density., Number density contour maps are useful for revealing the areas with the highest stellar density.
 All CNIDs in Figure 3 show a stroug peak at the position of the red champ (marked by the crosses)., All CMDs in Figure 3 show a strong peak at the position of the red clump (marked by the crosses).
 The plotometry of the stars in the RL and R12-acgionus is siguificautlv affected by crowding. because they are located close to the center of M33.," The photometry of the stars in the R14- and R12-regions is significantly affected by crowding, because they are located close to the center of M33."
 Therefore only the stars in the PC chip @vhich has lugher spatial resolution than the WF chips) are used to measure the maenitude of the red clamp in these reeious in the following., Therefore only the stars in the PC chip (which has higher spatial resolution than the WF chips) are used to measure the magnitude of the red clump in these regions in the following.
 We have determined the distance to ΑΟ using the 7-baud inagnitude of the TRGB. following the description eiven iu Lee.Freediuan.&Madore(1993).," We have determined the distance to M33 using the $I$ -band magnitude of the TRGB, following the description given in \citet{lee93}."
. Figure | displavs the Z-band πιοτν functions of red stars iucludiug the ROB and ACB stays., Figure 4 displays the $I$ -band luminosity functions of red stars including the RGB and AGB stars.
 In Figure. { there is a sudden increase at Zrpge;p220.9 in all the regious as marked by the arrow. which correspouds to the TRGB.," In Figure 4 there is a sudden increase at $I_{TRGB} \approx 20.9$ in all the regions as marked by the arrow, which corresponds to the TRGB."
 We have measured the Z-baud magnitude of the TRGD using this feature in the huuinositv fiction by eve detection (supplemented by using the edege-detection filters, We have measured the $I$ -band magnitude of the TRGB using this feature in the luminosity function by eye detection (supplemented by using the edge-detection filters
function of slape lu(0).,function of shape $\ln(\theta)$.
 So the resulting power spectruu is nearly flat., So the resulting power spectrum is nearly flat.
 A more accurate way to see the [latiess behavior is to adopt the Limber's equation., A more accurate way to see the flatness behavior is to adopt the Limber's equation.
 The 3D gas pressure power spectrum UN)xDIhk 7. where Ask) is the Fourier trausloqn of the gas pressure profile fj(r).," The 3D gas pressure power spectrum $P_p(k)\propto \delta^2_p(k)\propto k^{-2}$ , where $\delta_p(k)$ is the Fourier transform of the gas pressure profile $f_p(r)$ ."
" From Limber's eqtation. ChxfPNG).z)f7 us (1+1)C1/(28)xI""."," From Limber's equation, $C_l\propto \int P_p(l/\chi(z),z) f(z) d\chi \propto l^{-2}$, thus $l(l+1)C_l/(2\pi)\propto l^0$."
 Here. f(2) is the redshift depeidence of the SZ ellect.," Here, $f(z)$ is the redshift dependence of the SZ effect."
 The halo mass fuiiction also plays a role for the flat power spectrum., The halo mass function also plays a role for the flat power spectrum.
 5iice SIS profile does uot apply to the core o‘halos. a egiven cluster is 1o longer SIS at scales sinaler than its core size.," Since SIS profile does not apply to the core of halos, a given cluster is no longer SIS at scales smaller than its core size."
 Sinaller clusters take ove“and exeud the flat power spectrum., Smaller clusters take over and extend the flat power spectrum.
 The )OWOL spectrum ii our simulation clearly shows this flatuess aid suggests the roe οἱ these alos., The power spectrum in our simulation clearly shows this flatness and suggests the role of these sub-arcminute halos.
 These ialos also explain the cliscrepaucy between our simulation and analytical »edicetious., These halos also explain the discrepancy between our simulation and analytical predictions.
 1; COL'espolds to he comoving size <O.8E pe Or 2«1 where he dominant SZ contrirutLO comes [ron.," $1^{'}$ corresponds to the comoving size $\lesssim 0.8
h^{-1}$ Mpc for $z<1$ where the dominant SZ contribution comes from."
 This physical size corresponds to g‘oups of galaxies., This physical size corresponds to groups of galaxies.
 Cur‘et preclictious ron the P'ess-5clechtere picture assume a lower udass limit cuto[ correspouding o the mass scale of groips., Current predictions from the Press-Schechter picture assume a lower mass limit cutoff corresponding to the mass scale of groups.
 { ithe |jerarchical 1jethod. the gas wiudow fuuctjon is à [ree parameter. whic1 has an implici1 clepenclencο ol his lower mass cutoff (they can be related by the gas deity dis»ersion).," In the hierarchical method, the gas window function is a free parameter, which has an implicit dependence on this lower mass cutoff (they can be related by the gas density dispersion)."
 The cut off Or conijbutious from grou25 of galaxies in analyical models results ilasinal er y aud power spectra., The cut off for contributions from groups of galaxies in analytical models results in a smaller $\bar{y}$ and power spectrum.
 If only. gravitaional heatiug is iclucled. high nass halos and low mass halos shoid. have comparable gas fraclols.," If only gravitational heating is included, high mass halos and low mass halos should have comparable gas fractions."
 The Press-Seiechiter formalism predicts many more halos towards he low tnass end. so oue ex)ecs pure gravity simulations to lave lucreasing power s»ectra with inc'easlug high resolution.," The Press-Schechter formalism predicts many more halos towards the low mass end, so one expects pure gravity simulations to have increasing power spectra with increasing high resolution."
 Noi-eravitatioual heating avoids such a divergeuce., Non-gravitational heating avoids such a divergence.
 As described iu the halo moclel ol Pen(1999).. nou-eravitational leating has two ellects.," As described in the halo model of \citet{Pen99}, non-gravitational heating has two effects."
 Firstly. the energy injection makes the halo eas less clumpy.," Firstly, the energy injection makes the halo gas less clumpy."
 Then the coutriition to the power spectrum at smaller angular scales decreases relative to larger angular scales., Then the contribution to the power spectrum at smaller angular scales decreases relative to larger angular scales.
 This could explain the slightly differences between our simulation. CBI and BIMA results.," This could explain the slightly differences between our simulation, CBI and BIMA results."
 Seconelly. the uon-gravitational energy. injection increases the thermal euergy of the gas.," Secondly, the non-gravitational energy injection increases the thermal energy of the gas."
 For halos with ass lower than some threshold. the gravity cau not hold gas auc nost of the gas is ejected from tlese halos. as must Lave been tlie case lor ealactic size lialos.," For halos with mass lower than some threshold, the gravity can not hold gas and most of the gas is ejected from these halos, as must have been the case for galactic size halos."
 This srovide a reasonable lower mass limit cut off in the Press-Schechter picture., This provide a reasonable lower mass limit cut off in the Press-Schechter picture.
 Thus the amplituce aud shape of the SZ power specru is a sensitive measurement of the non-gravitational energy injection., Thus the amplitude and shape of the SZ power spectrum is a sensitive measurement of the non-gravitational energy injection.
 To obtain a better uucderstaucling of the SZ ellect. other pliysicical processes such as adiative cooling need to be considered.," To obtain a better understanding of the SZ effect, other physicical processes such as radiative cooling need to be considered."
 Since radiative cooling through thermal breiusstralilung .s a p> process. 1H jecomes. relevant ouly at scales <100 kpe. which corresponds to /c101.," Since radiative cooling through thermal bremsstrahlung is a $\rho^2$ process, it becomes relevant only at scales $\lesssim 100$ kpc, which corresponds to $l\gg 10^4$."
 ΤΙese augular scales are uot observable by any plaued experiments. so we neglect the discussion of iative cooling iu his paper.," These angular scales are not observable by any planed experiments, so we neglect the discussion of radiative cooling in this paper."
 Our current simulation has reached tlie resolution needed to see the COtribution from siiall halos aud the predicted SZ amplitude is already near the observed values., Our current simulation has reached the resolution needed to see the contribution from small halos and the predicted SZ amplitude is already near the observed values.
" We expected to be able to observe he effects o: uou-gravitationual heating fonm galaxy wixls aud oler sources in tlie upcoming expe""ó1neuts.", We expected to be able to observe the effects of non-gravitational heating from galaxy winds and other sources in the upcoming experiments.
 Iu order to solve the discrepancy probler1 completely. dillereuces between codes 1wist be COsidered.," In order to solve the discrepancy problem completely, differences between codes must be considered."
 Our group is currently riuineiffe‘ent codeswith identical initial coucition. identical cosmological parameters aud. variots resolutionκ from 6I? to 512? ," Our group is currently runningdifferent codeswith identical initial condition, identical cosmological parameters and various resolutions from $64^3$ to $512^3$ "
models then allowed us to define our limiting A magnitude as a function of J—A. which is shown in Figure 2..,"models then allowed us to define our limiting $K$ magnitude as a function of $J-K$, which is shown in Figure \ref{fig:2colorsmc}."
 Additionally. we excluded stars that had low 2MAÀSS color quality codes. along with possible galaxies. clusters and double stars as per the UCACS.," Additionally, we excluded stars that had low 2MASS color quality codes, along with possible galaxies, clusters and double stars as per the UCAC3."
 We ended up with 661 possible SAIC supergiants and an additional 16 stars in the NGC 602 field for a total of O77 stars., We ended up with 661 possible SMC supergiants and an additional 16 stars in the NGC 602 field for a total of 677 stars.
 Our observations were taken on (he Cerro Tololo 4-2neter telescope using Hydra. a spectrometer with 138 fibers aud a 2/327 field of view.," Our observations were taken on the Cerro Tololo 4-meter telescope using Hydra, a multi-object spectrometer with 138 fibers and a $^\circ$ field of view."
" Before observing. we created assignment [iles (hat matched our targets with specilic 2"" diameter fibers on the instrument."," Before observing, we created assignment files that matched our targets with specific $\arcsec$ diameter fibers on the instrument."
 More targets were assigned to higher priority fields so if bad weather struck. we would observe the highest priority fields first.," More targets were assigned to higher priority fields so if bad weather struck, we would observe the highest priority fields first."
 In the end. we were able to assign (592) of the stars in 26 SAIC fields and (14) of the stars in the NGC 602 field (alter being limited by the number of fields we were likely to be able to observe).," In the end, we were able to assign (592) of the stars in 26 SMC fields and (14) of the stars in the NGC 602 field (after being limited by the number of fields we were likely to be able to observe)."
 Additionally. 105 stars were assigned twice in different. fiber configurations.," Additionally, 105 stars were assigned twice in different fiber configurations."
 The locations of the fields ancl stars for which we eventually collected spectra are shown in Figure 3.., The locations of the fields and stars for which we eventually collected spectra are shown in Figure \ref{fig:SMCobserved}.
 As discussed in Section 1.. we plannecl on distinguishing SAIC supergiants [rom foreground stars by measuring the stars’ radial velocities.," As discussed in Section \ref{INTRO}, we planned on distinguishing SMC supergiants from foreground stars by measuring the stars' radial velocities."
 The Ca IL triplet (AA8498.8543. 8662) is ideal for such a measurement because its strong lines are measurable over a broad. temperature range.," The Ca II triplet $\lambda\lambda\ 8498, 8543, 8662$ ) is ideal for such a measurement because its strong lines are measurable over a broad temperature range."
 Qur highest priority goal was to obtain red spectra of our objects., Our highest priority goal was to obtain red spectra of our objects.
 Bul we also aimed to collect blue spectra For later classification purposes., But we also aimed to collect blue spectra for later classification purposes.
 All of our observations were taken over a cloudy five night span in 2009 October., All of our observations were taken over a cloudy five night span in 2009 October.
 Two niehis were completely overcast ancl during the other three nights we experienced heavy cirrus., Two nights were completely overcast and during the other three nights we experienced heavy cirrus.
" The seeing averaged around 1"". which was acceptable considering the ILvdra fibers are 2"" in diameter."," The seeing averaged around $\arcsec$, which was acceptable considering the Hydra fibers are $\arcsec$ in diameter."
 In the blue. our wavelength range was 3650 1525 wwilh a spectral resolution of 1.3 ((3 binned pixels).," In the blue, our wavelength range was 3650 – 4525 with a spectral resolution of 1.3 (3 binned pixels)."
 In the red. our wavelength range was 7300 9050 wwith a spectral resolution of 2.6 ((again 3 binned pixels).," In the red, our wavelength range was 7300 – 9050 with a spectral resolution of 2.6 (again 3 binned pixels)."
 For all of our observations we used (he same grating. the IARPGL-D. and simply changed the blocking filters between the blue (BG39) and the red (065515).," For all of our observations we used the same grating, the KPGL-D, and simply changed the blocking filters between the blue (BG39) and the red (OG515)."
 While we aimed al observing all 26 fields in both the red and the blue. after the first eight fields. we quickly realized (hat due to the first night being lost to weather ancl the never-endiug cirrus. our ambitions were (oo high.," While we aimed at observing all 26 fields in both the red and the blue, after the first eight fields, we quickly realized that due to the first night being lost to weather and the never-ending cirrus, our ambitions were too high."
 Additionally. we were observing during the Full Moon which impacted the quality of our blue spectra.," Additionally, we were observing during the Full Moon which impacted the quality of our blue spectra."
 So. we settled with observing only one control field and the remaining 18 fields in only the red.," So, we settled with observing only one control field and the remaining 18 fields in only the red."
 All of the fields were observed for three, All of the fields were observed for three
Using the definition of the lower velocity border as done by ? one finds With the above result one obtains the PUI distribution in the form The local PUL density can be derived from the interplanetary H-atom density η. 0). which depends on the radial distance 7 and the inclination àgle @ with respect to the upwind axis. and the effective (charge exchange + photoionization)- induced injection rate +].,"Using the definition of the lower velocity border as done by \citet{fahr07b} one finds With the above result one obtains the PUI distribution in the form The local PUI density can be derived from the interplanetary H-atom density $%
n_{\mathrm H}(r,\theta ), which depends on the radial distance $r$ and the inclination angle $\theta$ with respect to the upwind axis, and the effective (charge exchange + photoionization)- induced injection rate $\beta _{\mathrm{pui}}=n_{\mathrm H}(r,\theta )\left[n_{\mathrm s}(r)\sigma
_{\mathrm{ex}}U+\nu _{\mathrm i}\right]$ ."
 Here nG3. σος. U. v; denote the solar wind proton density. the charge exchange cross section. the solar wind bulk velocity and the photoionization frequency.," Here $n_{\mathrm s}(r)$, $\sigma _{\mathrm{ex}}$, $U$, $\nu _{\mathrm i}$ denote the solar wind proton density, the charge exchange cross section, the solar wind bulk velocity and the photoionization frequency."
 The H-atom density at distances 7.>SAU in the upwind hemisphere i$ satisfactorily well given by the following eXpression (see?) and thus leads to the following PUI density (alsosee?) From the above one derives the following radial space derivative which lateron in this paper will be needed To caleulate the PUI pressure. one morequantity in addition is needed. namely the upper velocity border τις.," The H-atom density at distances $r\geq 5\,\mathrm{AU}$ in the upwind hemisphere is satisfactorily well given by the following expression \citep[see][]{fahr71}
 and thus leads to the following PUI density \citep[also see][]{fahr99}
 From the above one derives the following radial space derivative which lateron in this paper will be needed To calculate the PUI pressure, one morequantity in addition is needed, namely the upper velocity border $v_{\infty }$."
" To determinev4, we follow the idea presented by ?? assuming that PUL power law distributions result from a specific quasi-equilibrium state self-establishing such that the wave field transfers per unit of time as much energy to PUIs by energy diffusion. as energy is expended in the solar wind frame for the work done by the pressure gradient of comoving PUIs against the magnetosonic fluctuations."," To determine $%
v_{\infty we follow the idea presented by \citet{fisk06,fisk07}
 assuming that PUI power law distributions result from a specific quasi-equilibrium state self-establishing such that the wave field transfers per unit of time as much energy to PUIs by energy diffusion, as energy is expended in the solar wind frame for the work done by the pressure gradient of comoving PUIs against the magnetosonic fluctuations."
 The important restriction to energy diffusion by nonlinear mteraction with the compressive fluctuations is that the typical diffusion period rq=3L;fva should be much larger than the convection period given by Teom=Ly/U (see ?).., The important restriction to energy diffusion by nonlinear interaction with the compressive fluctuations is that the typical diffusion period $\tau_{\mathrm{diff}}\simeq 3L_{\mathrm m}^2/v\lambda_{\parallel}$ should be much larger than the convection period given by $\tau_{\mathrm{conv}}\simeq L_{\mathrm m}/U$ \citep[see][]{chalov03}. .
 This leads to the requirement with 4j as the mean free path for particles parallel to the magnetic field., This leads to the requirement with $\lambda_{\parallel}$ as the mean free path for particles parallel to the magnetic field.
 The uppermost velocity v4 is the limit at which this condition is just fulfilled: We assume the interaction of the particles with a slab Alfennic turbulence field., The uppermost velocity $v_{\infty}$ is the limit at which this condition is just fulfilled: We assume the interaction of the particles with a slab Alfènnic turbulence field.
 The mean free path is given by with the pitch-angle diffusion coefficient from ? for cyclotron resonant wave-particle interaction with unpolarized. one-dimensional. and isotropic. turbulence. which leads to the velocity independent expression for the mean free path. with the reference value for the diffusion coefficient.," The mean free path is given by with the pitch-angle diffusion coefficient from \citet{chalov03} for cyclotron resonant wave-particle interaction with unpolarized, one-dimensional, and isotropic turbulence, which leads to the velocity independent expression for the mean free path, with the reference value for the diffusion coefficient."
" Therefore. the upper velocity border is given by which evaluates to by taking £,,=3AU and ty,=0.3AU (?).."," Therefore, the upper velocity border is given by which evaluates to by taking $L_{\mathrm m}=3\,\mathrm{AU}$ and $\lambda_{\parallel,\mathrm E}=0.3 \,\mathrm{AU}$ \citep{chalov_fahr99}."
" The ratio is needed in the later caleulation and should be compared with the result obtained by ? deriving the upper velocity border from the study of the upper-most resonance possibilities of ions with the largest prevailing correlation lengths L4, existing in the solar wind velocity structures. yielding the result which gives smaller values than those derived. for conditions when balanced pressure equilibrium in the sense of 9? is adopted."," The ratio is needed in the later calculation and should be compared with the result obtained by \citet{fahr07b} deriving the upper velocity border from the study of the upper-most resonance possibilities of ions with the largest prevailing correlation lengths $L_{\mathrm m}$ existing in the solar wind velocity structures, yielding the result which gives smaller values than those derived for conditions when balanced pressure equilibrium in the sense of \citet{fisk07}
 is adopted."
 Here below we shall demonstrate that this value for Ww... which is the direct consequence of the assumptions by Fisk. definitely leads to unreasonable consequences when we investigate the associated PUT pressure.," Here below we shall demonstrate that this value for $\psi _{\infty }$, which is the direct consequence of the assumptions by Fisk, definitely leads to unreasonable consequences when we investigate the associated PUI pressure."
 We calculate the PUI pressure resulting from power-law distributed PUIs upstream of the shock and find with Eqs. (9)). (10). CLE». ," We calculate the PUI pressure resulting from power-law distributed PUIs upstream of the shock and find with Eqs. \ref{puipress}) ), \ref{nunull}) ), \ref{fpuinull}) ),"
and (23)) where we have introduced x=r/rj., and \ref{psi}) ) where we have introduced $x=r/r_{\mathrm E}$.
 We obtain the pressure gradient by differentiation: which leads with Eq. (14)), We obtain the pressure gradient by differentiation: which leads with Eq. \ref{ngrad}) )
 to Ifnow we derive the effective upstream Mach number. neglecting thereby solar wind electron and proton pressures compared to the PUI pressure. i.e assuming Pi;Py« Py. and," to Ifnow we derive the effective upstream Mach number, neglecting thereby solar wind electron and proton pressures compared to the PUI pressure, i.e assuming $P_{e};P_{s}\ll P_{\mathrm{pui}}$ , and"
leads to strong cecentricity damping.,leads to strong eccentricity damping.
 Thus the observed eccentricities of apparently. isolated extrasolar planets are so far unexplained by this scenario., Thus the observed eccentricities of apparently isolated extrasolar planets are so far unexplained by this scenario.
 The other possible formation mechanism is through fragmentation or gravitationnal instability in a protostellar disc (e.g. Cameron 1978. Boss 2000).," The other possible formation mechanism is through fragmentation or gravitationnal instability in a protostellar disc (e.g. Cameron 1978, Boss 2000)."
 This may occur carly in the life of a protostcllar disc surrounding a class 0 protostar on a dynamical timescale., This may occur early in the life of a protostellar disc surrounding a class 0 protostar on a dynamical timescale.
 Such disces have been observed (sec. e.g.. Pudritz et al.," Such discs have been observed (see, e.g., Pudritz et al."
 1996) and the characteristic size is about 100 au., 1996) and the characteristic size is about 100 au.
 Ht is unlikely that such a process would operate at distances smaller than about 50 au from the central star as. in the optically thick parts of the disc. non aXisvMimMetric density waves redistibute mass and angular momentum before. fragmentation can proceed ( eg.," It is unlikely that such a process would operate at distances smaller than about 50 au from the central star as, in the optically thick parts of the disc, non axisymmetric density waves redistibute mass and angular momentum before fragmentation can proceed ( eg."
 Papaloizou Savonije 1991. Laughlin Bodenheimer 1994).," Papaloizou Savonije 1991, Laughlin Bodenheimer 1994)."
 Fragmentation is more likely when cooling is ellicient. as may occur in the optically thin parts of the disc. bevoncd about 50 au (Papaloizou ct al 1999).," Fragmentation is more likely when cooling is efficient, as may occur in the optically thin parts of the disc, beyond about 50 au (Papaloizou et al 1999)."
 Llowever. the detailed. conditions required for it to occur are unclear and may require constraining influences from the external environment ( Pickett et al 2000).," However, the detailed conditions required for it to occur are unclear and may require constraining influences from the external environment ( Pickett et al 2000)."
 Note that fragmentation may also occur before a disc is completely. formed. during the initial collapse of the protostellar envelope.," Note that fragmentation may also occur before a disc is completely formed, during the initial collapse of the protostellar envelope."
 Such opacity limited fragmentation has been estimated to produce objects with a lower mass limit of 7 Jupiter masses (Masunaga Inutsuka 1999). but there is no definitive argument to rule out somewhat smaller masses (Dodenheimer et al.," Such opacity limited fragmentation has been estimated to produce objects with a lower mass limit of 7 Jupiter masses (Masunaga Inutsuka 1999), but there is no definitive argument to rule out somewhat smaller masses (Bodenheimer et al."
 2000)., 2000).
 lt is possible that both a disc and fragments may form simultaneously out of the envelope. the relative importance of the two processes depending for instance on the angular momentum content of the envelope. on the strength of any magnetic field ( so far neglected in dise fragmentation calculations) and. possibly on the initial clumpiness.," It is possible that both a disc and fragments may form simultaneously out of the envelope, the relative importance of the two processes depending for instance on the angular momentum content of the envelope, on the strength of any magnetic field ( so far neglected in disc fragmentation calculations) and possibly on the initial clumpiness."
 Note that [large scale observations of class 0 envelopes so far clo not rule out the presence of clumps with masses smaller than about LO Jupiter masses (Motte André 2001)., Note that large scale observations of class 0 envelopes so far do not rule out the presence of clumps with masses smaller than about 10 Jupiter masses (Motte André 2001).
 li ds the purpose of this paper to investigate the evolution under gravitational interactions of a distribution of [NN massive. planets. which we assume to have been formed through a fragmentation process rapidly enough tha their orbits can undergo subsequent cvnamical relaxation on a time scale of hundreds. of orbits., It is the purpose of this paper to investigate the evolution under gravitational interactions of a distribution of $N$ massive planets which we assume to have been formed through a fragmentation process rapidly enough that their orbits can undergo subsequent dynamical relaxation on a time scale of hundreds of orbits.
 La common with related: work on orbital evolution ocuring alter assunmiuicc formation in a disc (eg., In common with related work on orbital evolution ocuring after assummed formation in a disc (eg.
 Weidenschilling Alazari 1996. ltasio Ford. 1996. Lin Ida 1997) we shall neglect. the ellects of any remnant disc gas so that apart [rom tica interactions with the central star there are only eravitationa interactions.," Weidenschilling Mazari 1996, Rasio Ford 1996, Lin Ida 1997) we shall neglect the effects of any remnant disc gas so that apart from tidal interactions with the central star there are only gravitational interactions."
 TFhus this work complements studies of the initial fragmentation process in a gaseous mecum., Thus this work complements studies of the initial fragmentation process in a gaseous medium.
 It turns out that the resulting evolution leads to similar end states independently of whether the initial configuration is assumed to be in the form ofa spherical shell or a disk.like structure., It turns out that the resulting evolution leads to similar end states independently of whether the initial configuration is assumed to be in the form of a spherical shell or a disk–like structure.
 The motivations for this work are firstly the suggestion bv Black (1997) ancl Stepinski Black (2000) that massive extrasolar planets on highly eccentric orbits could actually be the lowmass tail of the lowmass companion distribution to solarlike stars. produced. by fragmentation processes., The motivations for this work are firstly the suggestion by Black (1997) and Stepinski Black (2000) that massive extrasolar planets on highly eccentric orbits could actually be the low–mass tail of the low–mass companion distribution to solar–like stars produced by fragmentation processes.
 l]lere we wish to investigate to what extent. planets. with orbital elements similar to those observed can be produced and in particular whether hot Jupiters’ orbiting close to the star can be formed., Here we wish to investigate to what extent planets with orbital elements similar to those observed can be produced and in particular whether 'hot Jupiters' orbiting close to the star can be formed.
 Secondly we consider the recently detected population of frec-Doating planets and its relationship to that of planets orbiting solartwpe stars ( Lucas Roche 2000. Zapatero Osorio et al.," Secondly we consider the recently detected population of free-floating planets and its relationship to that of planets orbiting solar–type stars ( Lucas Roche 2000, Zapatero Osorio et al."
 2000)., 2000).
 It is of interest to know to what extent frec-Doating planets could be produced as a result of ejection from the neighbourhood of a star., It is of interest to know to what extent free-floating planets could be produced as a result of ejection from the neighbourhood of a star.
 We have considered the orbital evolution of IN. bodies with masses in the giant planet range. which are assumed to be formed. rapidly. using up the gas in a protostellar clise or envelope around a solar mass star. so that they can undergo subsequent dynamical relaxation on a timescale ~—100 orbits.," We have considered the orbital evolution of $N$ bodies with masses in the giant planet range, which are assumed to be formed rapidly, using up the gas in a protostellar disc or envelope around a solar mass star, so that they can undergo subsequent dynamical relaxation on a timescale $\sim 100$ orbits."
 We have performed calculations with 5xiN<100. In all the runs we performed. most of the planets where ected from the system. and. at most 3. planets remained x»und. to the central star.," We have performed calculations with $5
\le N \le 100.$ In all the runs we performed, most of the planets where ejected from the system and at most 3 planets remained bound to the central star."
 We found that close encounters with the central star occured. for about of the planets or all values of N considered., We found that close encounters with the central star occured for about of the planets for all values of $N$ considered.
 Such close encounters early in he evolution tended to result in collisions., Such close encounters early in the evolution tended to result in collisions.
 These tended to x avoided at later times so that tidal interaction nueht then result in orbital circularization at. fixed. pericentre distance cacing to the formation of a very closely orbiting giant rlanct., These tended to be avoided at later times so that tidal interaction might then result in orbital circularization at fixed pericentre distance leading to the formation of a very closely orbiting giant planet.
 Typically the runs ended. up with either. (i) one potential “hot Jupiter’ plus up to two external’ companions. ie. planets orbiting near the outer edge of the initial distribution: (ii) one or two external’ planets or even none at all: (iii) one planet on an orbit with a semimajor axis 10 to a 100 times smaller than the outer boundary radius of the inital distribution together with an external companion.," Typically the runs ended up with either (i) one potential 'hot Jupiter' plus up to two 'external' companions, i.e. planets orbiting near the outer edge of the initial distribution; (ii) one or two 'external' planets or even none at all; (iii) one planet on an orbit with a semi–major axis 10 to a 100 times smaller than the outer boundary radius of the inital distribution together with an 'external' companion."
 Apart [rom the potential “hot Jupiters’. all these objects are on highly eccentric orbits.," Apart from the potential 'hot Jupiters', all these objects are on highly eccentric orbits."
 We found that. apart from the close orbiters. the probability of ending up with a planet orbiting at a given distance from the central star increases with the distance.," We found that, apart from the close orbiters, the probability of ending up with a planet orbiting at a given distance from the central star increases with the distance."
 The objects that become unbound max contribute to a population of freely lloating planets ( Lucas Roche 2000. Zapatero Osorio et al.," The objects that become unbound may contribute to a population of freely floating planets ( Lucas Roche 2000, Zapatero Osorio et al."
 2000) whieh could be several times larger than that of giant planets found. close to the central star., 2000) which could be several times larger than that of giant planets found close to the central star.
 Thus the dynamical relaxation process considered here may operate in some cases to. produce giant planets with high orbital eccentricity at several astronomical units from their central star as well as closely orbiting planets., Thus the dynamical relaxation process considered here may operate in some cases to produce giant planets with high orbital eccentricity at several astronomical units from their central star as well as closely orbiting planets.
 Ln all cases a population of loosely bound planets is also expected., In all cases a population of loosely bound planets is also expected.
 The plan of this paper is as follows., The plan of this paper is as follows.
 In section 2. we describe the model and. basic equations used., In section \ref{mod} we describe the model and basic equations used.
 In section 3λ the initial conditions are formulated. and in section 4 the physics of the relaxation process Is discussed.," In section \ref{ini-bc}
 the initial conditions are formulated and in section \ref{relax2} the physics of the relaxation process is discussed."
 In section 5 we present our numerical results and in section 6 we summarize and discuss them., In section \ref{results} we present our numerical results and in section \ref{disc} we summarize and discuss them.
The apparent relative velocitv of the Sun in the direction of ealactic rotation (Vy. ) varies wilh distance of reference field stars from the Galactic plane.,The apparent relative velocity of the Sun in the direction of galactic rotation $V_{Y \sun}$ ) varies with distance of reference field stars from the Galactic plane.
 This remarkable [act was established by Hanson(1989) Irom proper motions of fairly distant stus. aud recently confirmed by Girardetal.(2006).. who used absolute proper motions of giant stars in the direction of south Galactic pole.," This remarkable fact was established by \citet{han89} from proper motions of fairly distant stars, and recently confirmed by \citet{gir}, who used absolute proper motions of giant stars in the direction of south Galactic pole."
 The thick disk dominates between z=1 and 3 kpc. where the rotational lag of Ποια stars is found to follow a nearly linear dependence on vertical heieht. accompanied. predictably. by a growth of velocity dispersion in the X direction.," The thick disk dominates between $z=1$ and $3$ kpc, where the rotational lag of field stars is found to follow a nearly linear dependence on vertical height, accompanied, predictably, by a growth of velocity dispersion in the $X$ direction."
 The slope of the lag. from both cited papers. is estimated at —30|.," The slope of the lag, from both cited papers, is estimated at $-30$."
.. Girard et. al., Girard et al.
 also offer a clvnamical interpretation of this phenomenon. finding it consistent will a general model of the Galactic potential.," also offer a dynamical interpretation of this phenomenon, finding it consistent with a general model of the Galactic potential."
 The sample of nearby Hipparcos stars considered in this paper is practically limited to 200 pe. and is dominated by thin disk stus.," The sample of nearby Hipparcos stars considered in this paper is practically limited to 200 pc, and is dominated by thin disk stars."
 Is there a similar vertical gradient of rotational velocity for the thin disk?, Is there a similar vertical gradient of rotational velocity for the thin disk?
 Evidently from Eq. À..," Evidently from Eq. \ref{exp.eq},"
" a vertical lag affects the determination of the centroid velocity Vy expressed by (he dipole vector harmonic E,. because D'(z) is negative evervwhere except z—0."," a vertical lag affects the determination of the centroid velocity $V_Y$ expressed by the dipole vector harmonic $\vec{E}_1^{-1}$, because $\Gamma(z)$ is negative everywhere except $z=0$."
 If thevelocity of rotation falls off with increasing z. the relative solar velocity Vy. should grow with distance due to the acdmixture of high-z stars.," If thevelocity of rotation falls off with increasing $z$, the relative solar velocity $V_{Y \sun}$ should grow with distance due to the admixture of $z$ stars."
 This is not what we find in Table 1.. where (he more distant stus (II«10 mas) appear (o rotate faster than the overall sample of stars.," This is not what we find in Table \ref{vsun.tab}, where the more distant stars $\Pi <
10$ mas) appear to rotate faster than the overall sample of stars."
" However. a more accurate consideration reveals (hat for a number ∪↓↶↕↽≻∪⋟∖⊽⋟∖⊽↕∣↽≻↥≼↲↓⋟∏∐≺∢∐∪∐≀↧↴↥↓⋟∪↕⋅∐↓⋟∖⊽∪↓≯∏⋡⊳∶⇄⋝≼⋡≼↲⋅≸↽↔↴⋅⋅↕⇁⋅ De >. −∣⋝⋅⊔∐↲∐⋯⊳∖⊽↥≺∢∐≀↧↴↕⋅≀↧↴≺∢∩↲↕⋅↕⋝∖⊽⊔≺∢↕⋅≼↲⋟∖⊽↕↽≻∪∐⋟∖⊽≼↲↕⋟∖⇁ ⋅⋅ − expected in the £4! harmonic. because the £,! harmonic is (oo sensitive to the choice of centroid solar motion."," However, a more accurate consideration reveals that for a number of possible functional forms of $\Gamma(z)$ (e.g., $\Gamma
\cdot |z|$, $\Gamma \cdot |z|^2$ ), the most characteristic response is expected in the $\vec{E}_3^{-1}$ harmonic, because the $\vec{E}_1^{-1}$ harmonic is too sensitive to the choice of centroid solar motion."
 Our choice of velocitv in Table 1.. consistent with the estimation lor (he more distant half of Hipparcos stars. is justified by the fact that the OMM parameters are determined in the distance-weighted (or proper motion) space where distant stars are more significant. and whatever kinematics anomalies the nearest stars mav have. has little bearing on the OMM estimation problem.," Our choice of velocity in Table \ref{vsun.tab}, consistent with the estimation for the more distant half of Hipparcos stars, is justified by the fact that the OMM parameters are determined in the distance-weighted (or proper motion) space where distant stars are more significant, and whatever kinematics anomalies the nearest stars may have, has little bearing on the OMM estimation problem."
" The rotation gradient dipole E! emerges with a robust positive⋅⋅ coellicient∙− e,!=11.254∙1.17-|. which. is. consistent. with. a negative gradient of E(z)."," The rotation gradient dipole $\vec{E}_1^{-1}$ emerges with a robust positive coefficient $e_1^{-1}=11.25\pm 1.17$, which is consistent with a negative gradient of $\Gamma(z)$."
 We performed direct simulations of the vector harmonic response (o a linear gradient T(z)=1-fz] for dilferent values of D and the height of the Sun above the plane z.., We performed direct simulations of the vector harmonic response to a linear gradient $\Gamma(z)=\Gamma \cdot |z|$ for different values of $\Gamma$ and the height of the Sun above the plane $z_{\sun}$.
 A eood mateh with observations was found for P——20 tand =.=15 pe. which vielded a set of coefficients e!=11.4141.17. hd=—2.04d047. and ¢'=0.75+0.22 ↳↽∐↓⋟∖⊽↳↽↕↽≻≺∢⋅⋅≀↕↴∐⊔∐↲↕⋅≼↲⋟∖⊽↥−≻↓∐≀↧↴↕⋅∐↓∪∐↕≺⋱∖⊽∣↽≻≼↲↕∐≸↽↔↴∐↥⋟∖⊽↕↖≺↽↔↴∐∐↓≺∢≀↧↴∐↥⋅∐∪⊔⊔↲," A good match with observations was found for $\Gamma=-20$ and $z_{\sun}=15$ pc, which yielded a set of coefficients $e_1^{-1}=11.41\pm 1.17$, $h_2^{1}=-2.04\pm 0.47$, and $e_3^{-1}=0.75\pm 0.22$, all the rest 21 harmonics being insignificant."
↥≼↲≺∢⊔⋅↕≺∢∐≀↧↴↕⋅∐↓∪∐↕≺⋱∖⊽≀↕↴↕⋅≼↲↕∐ −−−−∙ − − − good agreement with our fit [or all star. whereas the hd coellicient is fairly close to the fit (—1.09+ 0.47. not shown in Table 2)).," Both electric harmonics are in good agreement with our fit for all star, whereas the $h_2^{1}$ coefficient is fairly close to the fit $-1.09 \pm 0.47$ , not shown in Table \ref{om.tab}) )."
 Therefore. a linear gradient of rotational velocity οἱ the thin. disk. of: roughly. —20. 1-“is a plausible. explanation. to (he corresponding," Therefore, a linear gradient of rotational velocity of the thin disk of roughly $-20$ is a plausible explanation to the corresponding"
 Therefore. a linear gradient of rotational velocity οἱ the thin. disk. of: roughly. —20. 1-“is a plausible. explanation. to (he corresponding.," Therefore, a linear gradient of rotational velocity of the thin disk of roughly $-20$ is a plausible explanation to the corresponding"
of Massachusetts and the Infrared Processing and Analysis Center (JPL/ Caltech).,of Massachusetts and the Infrared Processing and Analysis Center (JPL/ Caltech).
 As the space-density of active SMDII derived in this work is significantly larger than that found in previous studies. in is section we attempt to validate our results by discussing possible limitations and. acelitional sources of error. which may exist in these analyses: 1) whilst the sensitivity of the ata used in this survey is high. the volume considered is relatively small compared. to that of the SDSS. thus our results may be subject to cosmic variance: 2) given 10 modest. errors associated with the Mpg estimates. the Ἱποριο Alga binning structure is likely to be subjective uel thus degenerate towards objects scattering between the clined bins.," As the space-density of active SMBHs derived in this work is significantly larger than that found in previous studies, in this section we attempt to validate our results by discussing possible limitations and additional sources of error which may exist in these analyses: 1) whilst the sensitivity of the data used in this survey is high, the volume considered is relatively small compared to that of the SDSS, thus our results may be subject to cosmic variance; 2) given the modest errors associated with the $\Mbh$ estimates, the adopted $\Mbh$ binning structure is likely to be subjective and thus degenerate towards objects scattering between the defined bins."
 Under these assumptions. in SAL we investigate whether the sample is indeed. representative of the local Universe and in &X2 we discuss the construction of a Monte Carlo simulation to assess the clleet of our adopted. Myg binning.," Under these assumptions, in A1 we investigate whether the sample is indeed representative of the local Universe and in A2 we discuss the construction of a Monte Carlo simulation to assess the effect of our adopted $\Mbh$ binning."
 Given the large. incidence of XCGNs within our sunple it is possible that. the volume considered. in our sample is over-dense compared to other regions in the local Universe., Given the large incidence of AGNs within our sample it is possible that the volume considered in our sample is over-dense compared to other regions in the local Universe.
 The construction of the original sample of 64 bolometrically luminous galaxies in GAO was designed to be complete down to the llux-limit of the Itevised Bright Galaxy Sample., The construction of the original sample of 64 bolometrically luminous galaxies in GA09 was designed to be complete down to the flux-limit of the Revised Bright Galaxy Sample.
 This imposed a distance constraint of D«15 Alpe (see Fig., This imposed a distance constraint of $D<15$ Mpc (see Fig.
 l of €LA09). and hence did not include the Virgo cluster ab {0z16 Alpe. and thus our sample does not incorporate known local over-densities: however. this volume mav not be representative ofthe Universe at large.," 1 of GA09), and hence did not include the Virgo cluster at $D \approx
16$ Mpc, and thus our sample does not incorporate known local over-densities; however, this volume may not be representative of the Universe at large."
 Yo robustly test our considered. volume (Yz1.3 Alpe?). we constructed. a total SMDBII space density function for all galaxies to 2«15 Alpe ancl compared this to the local total (active|inactive) SAIBIT mass function of Marconi et al. (," To robustly test our considered volume $V \approx 1.3 \times
10^4$ $^3$ ), we constructed a total SMBH space density function for all galaxies to $D<15$ Mpc and compared this to the local total (active+inactive) SMBH mass function of Marconi et al. ("
2004) derived. from the luminosity function of local galaxies.,2004) derived from the luminosity function of local galaxies.
" Given the large co-moving volume (Y,5ε1000 Gpe?) considered in Marconi et al. (", Given the large co-moving volume $V_c \approx 1000 {\rm \ Gpc}^3$ ) considered in Marconi et al. (
2004). their clerivect SMDLI mass function is unlikely to sulfer from. significant Cosmic variance.,"2004), their derived SMBH mass function is unlikely to suffer from significant cosmic variance."
" Our total SMDBLL mass function was formulated. using all galaxies. identified. in the NASA/IPAC. Extra-galactic Database (NED) to D.<15 Alpe with a total A-band uminositv of. Lisa1.510""L.."," Our total SMBH mass function was formulated using all galaxies identified in the NASA/IPAC Extra-galactic Database (NED) to $D<15$ Mpc with a total -band luminosity of $L_{\rm K,gal} \ga
1.5 \times 10^9 \Lsun$."
" The luminosity hreshold. is designed to include all galaxies which could x»entiallv host a SMDLIL with Albu10""M. using the Mag Long relation."," The luminosity threshold is designed to include all galaxies which could potentially host a SMBH with $\Mbh
\ga 10^6 \Msun$ using the $\Mbh$ $L_{\rm K,bul}$ relation."
 This conservative lower limit assumes hat Lisa=Lean (6. that all galaxies in the sample have an earlv-tvpe galaxy classification).," This conservative lower limit assumes that $L_{\rm K,gal}= L_{\rm K,bul}$ (i.e., that all galaxies in the sample have an early-type galaxy classification)."
" In reality. the majority of the sources identified in NED to D<15 Alpe are late-vpe galaxies (16. Lisa3 Lina). and therefore theMig imit is likely to be Alby10""M.."," In reality, the majority of the sources identified in NED to $D<15$ Mpc are late-type galaxies (i.e., $L_{\rm K,gal} \gg
L_{\rm K,bul}$ ), and therefore the$\Mbh$ limit is likely to be $\Mbh
\ll 10^6 \Msun$."
" To D«15 Alpe. we identify 105 galaxies which potentially host a SALBLI with Mibuz10""M.."," To $D<15$ Mpc, we identify 105 galaxies which potentially host a SMBH with $\Mbh \goa 10^6 \Msun$."
 To estimate Mig in each of these galaxies. we relate the associated: Llubble-type from. the Third Relerence Catalogue of Bright Galaxies (7) toa mean bulge/disce ratio (e.g. 2)) and establish an individual bulge luminosity based on galaxy-type and Lig nu.," To estimate $\Mbh$ in each of these galaxies, we relate the associated Hubble-type from the Third Reference Catalogue of Bright Galaxies \citep{rc3} to a mean bulge/disc ratio (e.g., \citealt{benson07}) ) and establish an individual bulge luminosity based on galaxy-type and $L_{\rm
 K,bul}$ ."
 We convert the estimated bulec luminosity to Mpg using the Alpa Zia ," We convert the estimated bulge luminosity to $\Mbh$ using the $\Mbh$ $L_{\rm K,bul}$ "
16 Applegate clleet (23).,the Applegate effect \citealt{applegate92}) ).
 This mechanism invokes magnetic activity evcles in the low-mass components of such binaries to redistribute angular momentum within the interior of the star. thereby changing the stellar quadrupole moment which leads to changes in the orbital period of the components.," This mechanism invokes magnetic activity cycles in the low-mass components of such binaries to redistribute angular momentum within the interior of the star, thereby changing the stellar quadrupole moment which leads to changes in the orbital period of the components."
 Later. ?.— proposed. that the Applegate mechanism. could also be driven by effectively converting rotational kinetic energv and magnetic οποιον back and forth.," Later, \cite*{lanza98} proposed that the Applegate mechanism could also be driven by effectively converting rotational kinetic energy and magnetic energy back and forth."
 Reearcless of the details of the exact. physical mechanism at work. he Applegate effect should. also operate in most exoplanet systems since the host stars are (bv selection) low-mass stars with a convective outer laver which should. exhibit. some orm of dvnamo activity.," Regardless of the details of the exact physical mechanism at work, the Applegate effect should also operate in most exoplanet systems since the host stars are (by selection) low-mass stars with a convective outer layer which should exhibit some form of dynamo activity."
 Ht will therefore be important. to know the magnitude of the Applegate clleet for exoplanet systems when interpreting any Εν., It will therefore be important to know the magnitude of the Applegate effect for exoplanet systems when interpreting any TTVs.
 In this paper we oiellv review the Applegate mechanism in the next section. xore applving the analysis of ? to estimate the effects on known transiting exoplanet svstems.," In this paper we briefly review the Applegate mechanism in the next section, before applying the analysis of \cite{applegate92} to estimate the effects on known transiting exoplanet systems."
 Finally. we look at the implications that the Applegate clleet has for PLY work in detecting additional planets as well as for the measurement of the level of tidal dissipation in verv-hot Jupiter's.," Finally, we look at the implications that the Applegate effect has for TTV work in detecting additional planets as well as for the measurement of the level of tidal dissipation in very-hot Jupiter's."
 Alany types of binary stars show evidence for changes in their orbital periods revealed: most. easily. through eclipse times., Many types of binary stars show evidence for changes in their orbital periods revealed most easily through eclipse times.
 If a star suddenly increases its orbital period. P? by an amount ολο. then the eclipses will arrive progressively later and later until. alter a time 7. they are clelavecl by an amount Af=PAP/P with respect to an ephemeris based upon the initial period.," If a star suddenly increases its orbital period $P$ by an amount $\Delta P$, then the eclipses will arrive progressively later and later until, after a time $T$, they are delayed by an amount $\Delta t = T\Delta P/P$ with respect to an ephemeris based upon the initial period."
 These. variations can be tracked. through comparison. of observed. times to. those calculated: assuming linear ephemericles via the so-called ο.€ diagrams., These variations can be tracked through comparison of observed times to those calculated assuming linear ephemerides via the so-called $O-C$ diagrams'.
 The period changes observed in close binary stars have typical magnitudes of AP/P~10 (which can take on either sign) and thus significant deviations can build. up over time.," The period changes observed in close binary stars have typical magnitudes of $\Delta P/P \sim 10^{-5}$ (which can take on either sign), and thus significant deviations can build up over time."
 One famous example is the 2.87 day-period binary Aleol which has exhibited. deviations [from linearity of the order of 3 hours over the 200 vears it has been. followed.," One famous example is the 2.87 day-period binary Algol, which has exhibited deviations from linearity of the order of 3 hours over the 200 years it has been followed."
 Cataclysmic variable stars. detached: white cbwarf/main-sequence binaries. RS CVn stars anc Wo UMa stars. all exhibit similar variations on timescales of vears to decades.," Cataclysmic variable stars, detached white dwarf/main-sequence binaries, RS CVn stars and W UMa stars all exhibit similar variations on timescales of years to decades."
 These variations. which are at best quasi-periodic. are more often than not too large to be explained by. long-term cllects such as nuclear evolution of the stars. mass. loss through winds or angular momentum loss from gravitational radiation or magnetic braking.," These variations, which are at best quasi-periodic, are more often than not too large to be explained by long-term effects such as nuclear evolution of the stars, mass loss through winds or angular momentum loss from gravitational radiation or magnetic braking."
 The latter in particular strugeles when confronted with orbital periods that as well as decrease., The latter in particular struggles when confronted with orbital periods that as well as decrease.
 7. realised. that. period. changes in binary systems without either mass or angular momentum loss could be driven by variations in the quacrupole moment of one or both stars., \cite{applegate87} realised that period changes in binary systems without either mass or angular momentum loss could be driven by variations in the quadrupole moment of one or both stars.
 Taking just one star to have a /cquadrupole moment Q (in the equatorial plane) and mass AJ then. as shown in equation 4 of ?.. its companion orbits in à eravitational potential of the form. where r is the distance from the star.," Taking just one star to have a quadrupole moment $Q$ (in the equatorial plane) and mass $M$ then, as shown in equation 4 of \cite{applegate92}, its companion orbits in a gravitational potential of the form, where $r$ is the distance from the star."
 The orbital speed is given by (e?=rdofdr and therefore. from equation. 1.. if GQ increases (the star becomes more oblate) then the gravitational field in the equatorial plane of the star also increases.," The orbital speed is given by $v^2 = rd\phi /dr$ and therefore, from equation \ref{eqn:phi}, if $Q$ increases (the star becomes more oblate) then the gravitational field in the equatorial plane of the star also increases."
 Ln order to balance for the increased. gravity. the companion then requires to increase its centrifugal acceleration (/r at constant angular momentum (re is constant).," In order to balance for the increased gravity, the companion then requires to increase its centrifugal acceleration $v^2/r$ at constant angular momentum $rv$ is constant)."
 Thus e must increase and à must. decrease. and hence the orbital period decreases., Thus $v$ must increase and $r$ must decrease and hence the orbital period decreases.
 Phe opposite is true if Q decreases., The opposite is true if $Q$ decreases.
 Under this scenario. ? showed that the resulting period changes are given by (their equation 7): where 2 is the radius of the star and. @ is the orbital separation of the components.," Under this scenario, \cite{applegate92} showed that the resulting period changes are given by (their equation 7): where $R$ is the radius of the star and $a$ is the orbital separation of the components."
 The common denominator in all the binaries that exhibit period variations of the tvpe described above is that at least one of the components is a low-mass star with a convective envelope capable of sustaining a magnetic field eenerating dvnamo., The common denominator in all the binaries that exhibit period variations of the type described above is that at least one of the components is a low-mass star with a convective envelope capable of sustaining a magnetic field generating dynamo.
 Given that the variation timescales are of the order of vears to decades. stellar activity eveles are the prime candidate for effecting the changes in the stellar cquacdrupole moment.," Given that the variation timescales are of the order of years to decades, stellar activity cycles are the prime candidate for effecting the changes in the stellar quadrupole moment."
 Models of the 1980s (7: 2)) supposed that dvnamo-gencrated magnetic fields. distorted. the star from its equilibrium shape., Models of the 1980's \citealt{applegate87}; \citealt{warner88}) ) supposed that dynamo-generated magnetic fields distorted the star from its equilibrium shape.
 These were criticised by 2. since such distortions leave the pressure and gravity &racients unbalanced (the star is driven from hyelrostatic equilibrium)., These were criticised by \cite{marsh90d} since such distortions leave the pressure and gravity gradients unbalanced (the star is driven from hydrostatic equilibrium).
 This unbalanced force needs to be balanced by the magnetic Ποια. and ? showed that the stars had insullicient luminosity to drive such changes on the observed. timescales.," This unbalanced force needs to be balanced by the magnetic field, and \cite{marsh90d} showed that the stars had insufficient luminosity to drive such changes on the observed timescales."
 This issue was quickly. resolved. by 2? where magnetic activity was still invoked. to drive the (9. variations but rather than forcing the star from hyelrostatic equilibrium. he magnetic fields are supposed to drive angular momentunm ransfer within the star.," This issue was quickly resolved by \cite{applegate92} where magnetic activity was still invoked to drive the $Q$ variations but rather than forcing the star from hydrostatic equilibrium, the magnetic fields are supposed to drive angular momentum transfer within the star."
 For instance. if angular momentum is transported from the core to the envelope of the star. the star will become more oblate overall.," For instance, if angular momentum is transported from the core to the envelope of the star, the star will become more oblate overall."
 Ες required much ess energy than the earlier models since the star performs a transition [rom one state of hydrostatie. equilibrium to another., This required much less energy than the earlier models since the star performs a transition from one state of hydrostatic equilibrium to another.
 With this model ?. was able to explain the observed »iod changes in binary stars. and the Applegate elfect jas continued to survive the test of time apart from a [ew refinements (e.g. 2)).," With this model \cite{applegate92} was able to explain the observed period changes in binary stars, and the Applegate effect has continued to survive the test of time apart from a few refinements (e.g. \citealt{lanza98}) )."
 ‘The same process that occurs in binary stars will also occur in exoplanet svstems in the case where the host star is magnetically active., The same process that occurs in binary stars will also occur in exoplanet systems in the case where the host star is magnetically active.
 Since the majority of exoplanet hosting stars known to date are lower main-sequence stars with convective outer lavers. these stars. should harbour some form of magnetic field generating stellar cvnamo.," Since the majority of exoplanet hosting stars known to date are lower main-sequence stars with convective outer layers, these stars should harbour some form of magnetic field generating stellar dynamo."
 For any given energy budget (AL). the equations of ? allow the magnitude of the period change. to be caleulated numerically which. for the sake of," For any given energy budget $\Delta E$ ), the equations of \cite{applegate92} allow the magnitude of the period change, to be calculated numerically which, for the sake of"
We haved caleulated light curves at the following four frequencies: 75 Mllz (radio. A). 1.43 GIIz (radio. VLA)). 4.56x10! Hz (R-band. VLT)) and 3.63xLOM Iz (1.5 KeV N-ravs. XRT)).,"We haved calculated light curves at the following four frequencies: 75 MHz (radio, ), 1.43 GHz (radio, ), $4.56 \times 10^{14}$ Hz (R-band, ) and $3.63 \times 10^{17}$ Hz $1.5$ KeV X-rays, )."
 In this letter we summarize and discuss the results in detail for the following cases: This wav we cover both small ancl large opening angles ancl the effect of increased jet enerev and cireumburst density., In this letter we summarize and discuss the results in detail for the following cases: This way we cover both small and large opening angles and the effect of increased jet energy and circumburst density.
 For all cases we have computed light curves for a range of observer angles: ων.=0. 0.1. 0.2. 0.4. 0.8 and 7/2 rad.," For all cases we have computed light curves for a range of observer angles: $\theta_{obs} = 0$, 0.1, 0.2, 0.4, 0.8 and $\pi / 2$ rad."
 The resulting light curves for case D have been plotted in Fig., The resulting light curves for case B have been plotted in Fig.
 1. For three observer limes we have calculated broadband spectra as well. aud these are plotted in Fig. 2..," \ref{lightcurves_figure} For three observer times we have calculated broadband spectra as well, and these are plotted in Fig. \ref{spectra_figure}."
 For the whole set of simulations (case A-D). we have summarized the shapes of the light eurves by fillinge smoothly connected power laws in lime. usinee for all observer angles except 7/2. when both jets are seen exactly on edge and is sufficient.," For the whole set of simulations (case A-D), we have summarized the shapes of the light curves by fitting smoothly connected power laws in time, using for all observer angles except $\pi / 2$, when both jets are seen exactly on edge and is sufficient."
 Using multiple smoothly. connected. power laws to describe the data is common both in theoretical ancl observational studies (e.g. &Sari 2002)).," Using multiple smoothly connected power laws to describe the data is common both in theoretical and observational studies (e.g. \citealt{, Beuermann1999, Granot2002}) )."
 Fit parameter Fy sets the scale of the light curve (here. we have set reclshilt zc0 and observer luminosity distance d;=1075x em).," Fit parameter $F_0$ sets the scale of the light curve (here, we have set redshift $z=0$ and observer luminosity distance $d_L = 10^{28}$ cm)."
 Different power law regimes meet al, Different power law regimes meet at
for our physical model encouraged us to first extrapolate measurements obtained in the most reliable regime.,for our physical model encouraged us to first extrapolate measurements obtained in the most reliable regime.
 Removing the final few percent of CTI trails might require detailed investigation of such disagreements., Removing the final few percent of CTI trails might require detailed investigation of such disagreements.
" In particular, there is mounting evidence that trails behind sources of different flux may change in as well as amplitude."," In particular, there is mounting evidence that trails behind sources of different flux may change in as well as amplitude."
" A slight steepening of faint trail was also present in Masseyetal.(2010),, but ascribed to uncertain background level and read noise."," A slight steepening of faint trail was also present in \citet{m10}, but ascribed to uncertain background level and read noise."
" Read noise is added to an imageafter CTI, so creates spurious faint peaks that are not trailed, and act to spuriously steepen the true mean trail when they are accidentally included in the average."," Read noise is added to an image CTI, so creates spurious faint peaks that are not trailed, and act to spuriously steepen the true mean trail when they are accidentally included in the average."
" A physical effect that we do not model, but which might also affect faint trails, is the breakdown of the volume-driven charge packet model at very low flux levels discussed by Shortetal.(2010)."," A physical effect that we do not model, but which might also affect faint trails, is the breakdown of the volume-driven charge packet model at very low flux levels discussed by \cite{short10}."
". However, while this is important in Time-Delay Integration (TDI) mode observations (and potentially dark exposures), it is not so in science imaging where a large zodiacal sky background is always present."," However, while this is important in Time-Delay Integration (TDI) mode observations (and potentially dark exposures), it is not so in science imaging where a large zodiacal sky background is always present."
" If anything, the effect would also predict shallower trails behind faint sources, from high-7 traps."," If anything, the effect would also predict shallower trails behind faint sources, from $\tau$ traps."
 A second physical mecahnism by which the trail could change shape could be the onset of surface full well traps above a certain flux., A second physical mecahnism by which the trail could change shape could be the onset of surface full well traps above a certain flux.
" However, this explanation seems unlikely at a value of 20,000 electrons >80,000 full well depth), and because such traps would have been present since manufacture, while almost all appear to have accumulated over time at the same rate."," However, this explanation seems unlikely at a value of 20,000 electrons $>80,000$ full well depth), and because such traps would have been present since manufacture, while almost all appear to have accumulated over time at the same rate."
" We shall therefore continue to use a single trail profile, but recommend further testing of this apparent shape change, for example in combination with mean-variance measurements at a range of flux levels to determine whether the shape change is gradual or discreet and, if discreet, whether it coincides with other discontinuities."," We shall therefore continue to use a single trail profile, but recommend further testing of this apparent shape change, for example in combination with mean-variance measurements at a range of flux levels to determine whether the shape change is gradual or discreet and, if discreet, whether it coincides with other discontinuities."
" 'The 4C decrease in the operating temperature of the ACS/WPFC detectors in July 2006 did not affect the density of charge traps, or the amount of flux lost from a source."," The 4C decrease in the operating temperature of the ACS/WFC detectors in July 2006 did not affect the density of charge traps, or the amount of flux lost from a source."
" Howver, it lengthened their release times and the amount of spurious flux in the first 9 pixels behind a source fell by22%,, which benefits some astronomical measurements."," Howver, it lengthened their release times and the amount of spurious flux in the first 9 pixels behind a source fell by, which benefits some astronomical measurements."
 Weak lensing measurements suffer by way of a spurious shear signal induced the readout direction., Weak lensing measurements suffer by way of a spurious shear signal induced the readout direction.
" Extrapolating from the trap characterisation of Rhodesetal.(2010),, we estimate in mid-2010 a mean shear of ~5% in galaxies detected at a S/N of 10."," Extrapolating from the trap characterisation of \citet{rhodes10}, we estimate in mid-2010 a mean shear of $\sim$ in galaxies detected at a S/N of $10$."
" Similarly, we expect a value twice as bad for a galaxy at the chip gap (but zero at the edge), and about half as bad in a galaxy one magnitude brighter."," Similarly, we expect a value twice as bad for a galaxy at the chip gap (but zero at the edge), and about half as bad in a galaxy one magnitude brighter."
 Verifying this in practice would require a new survey similar in size to COSMOS (Scovilleetal.2007).., Verifying this in practice would require a new survey similar in size to COSMOS \citep{scoville07}.
methocls. including fitting the data using a q(z) parameterization. principal components. and a non-parametric “slicing window method.,"methods, including fitting the data using a $q(z)$ parameterization, principal components, and a non-parametric “sliding window"" method."
 We find. consistent results between all these methods that provides evidence for an accelerating universe based solely on the first-vear SDSS-IL SN data., We find consistent results between all these methods that provides evidence for an accelerating universe based solely on the first-year SDSS-II SN data.
 The strongest evidence we find comes when we make the strongest assumptions. that qo is constant and the universe is Lat which gives probability for acceleration of OTA.," The strongest evidence we find comes when we make the strongest assumptions, that $q_0$ is constant and the universe is flat which gives probability for acceleration of $>97\%$."
 We also compare our SDSS-LLSN data with the local BAO measurements. and. find they are in good agreement.," We also compare our SDSS-II SN data with the local BAO measurements, and find they are in good agreement."
 This is in contrast with the findings of Percivalοἱal.(2007) whieh found tension between the two distance measures. but confirms the new BAO analvsis of Percival et al. (," This is in contrast with the findings of \citet{2007MNRAS.381.1053P} which found tension between the two distance measures, but confirms the new BAO analysis of Percival et al. ("
2009) who note that this tension has now lessenect.,2009) who note that this tension has now lessened.
 ‘Taking this observation further. we test the distance duality relation. Le. for any metric theory of gravity. we expect αι(αν|z)7)=L.," Taking this observation further, we test the distance duality relation, i.e., for any metric theory of gravity, we expect $d_L/(d_A (1+z)^2) = 1$."
 We see no evidence for a discrepancy from this relation (at the one sigma level) in contrast to previous claims [for a potential violation on the 2c level as seen in (Bassett&kung2004:Lazkoz.Nesseris&Perivolaropoulos 2008)..," We see no evidence for a discrepancy from this relation (at the one sigma level) in contrast to previous claims for a potential violation on the $2\sigma$ level as seen in \citep{2004PhRvD..69j1305B, 2008JCAP...07..012L}."
 Finally. we present a new measurement of the cquation-ol-state parameter of dark enerev using a combination of geometrical distances in the universe and estimates for the growth rate of structure.," Finally, we present a new measurement of the equation-of-state parameter of dark energy using a combination of geometrical distances in the universe and estimates for the growth rate of structure."
" Our strongest constraint comes from the combination of all four cata-sets discussed herein (SDSS-LLSN. BAO. redshift-space distortions. ISW) with «e=OSLMNEETE and Oy,=0.22MIMEITTE (assuming a Ilat universe)."," Our strongest constraint comes from the combination of all four data-sets discussed herein (SDSS-II SN, BAO, redshift-space distortions, ISW) with $w=-0.81^{+0.16}_{-0.18}(stat)$ and $\Omega_M=0.22^{+0.09}_{-0.08}(stat)$ (assuming a flat universe)."
 However. the combination of just the SDSS-LL SNe and. the I5W measurements alone is almost as powerful in constraining these parameters (Table E).," However, the combination of just the SDSS-II SNe and the ISW measurements alone is almost as powerful in constraining these parameters (Table 1)."
 Our results only change slightly io we allow curvature to vary. consistent with the CMD measurements (see Appendix (X)).," Our results only change slightly if we allow curvature to vary, consistent with the CMB measurements (see Appendix \ref{appendix_curvature}) )."
 We quote a systematic uncertainty of Awe=£0.15 based on the details of the AMILCS2k2 lisht.curve Litter (see Ixesslerctal.2000. for a Fuller discussion), We quote a systematic uncertainty of $\Delta w =\pm0.15$ based on the details of the MLCS2k2 light–curve fitter (see \citealt{kessler} for a fuller discussion).
 Thus we have shown that low-redshift! cosmological probes give a self-consistent picture of the clistanec-redshift relation., Thus we have shown that low-redshift cosmological probes give a self-consistent picture of the distance-redshift relation.
 When combined with growth of structure and ISW at the same epoch that picture is consistent with ACDAL and re-enforces the complementarity amongst other data and analyses in the literature., When combined with growth of structure and ISW at the same epoch that picture is consistent with $\Lambda$ CDM and re-enforces the complementarity amongst other data and analyses in the literature.
 We thank an anonymous referee for helpful commoents on this xiper Which ercathy improved the content of the paper., We thank an anonymous referee for helpful comments on this paper which greatly improved the content of the paper.
 RCN on behalfof the authors would like to thank Mike Turner for yelpful cliscussions on the go fit and Eric Aubourg for useful discussions on the distance duality relation., RCN on behalf of the authors would like to thank Mike Turner for helpful discussions on the $q_0$ fit and Eric Aubourg for useful discussions on the distance duality relation.
 We also thank tick Iessler ancl Mark Sullivan for extensive. discussions about their work and. papers., We also thank Rick Kessler and Mark Sullivan for extensive discussions about their work and papers.
 PC thanks Jussi Valliviita for 1elpful suggestions., TG thanks Jussi Välliviita for helpful suggestions.
 LIL. CS and RCN are grateful to SPEC or funding this research with rolling grants ST/F002335/1 and ST/11002774/1.," HL, CS and RCN are grateful to STFC for funding this research with rolling grants ST/F002335/1 and ST/H002774/1."
 L.-J. S is supported by the D.O.IZ at Fermilab., H.-J. S is supported by the D.O.E at Fermilab.
 ονιν is grateful for the support of US NSE erant AST0607485., A.V.F. is grateful for the support of US NSF grant AST–0607485.
 Funding for the creation and distribution of the SDSS and SDSS-LL has been provided by the Alfred. P. Sloan Foundation. the Participating Institutions. the National Science. Foundation. the U.S. Department of. Energy. the National Xeronauties ancl Space Administration. the Japanese Monbukagakusho. the Max. Planck Society. anc the Higher Education. Funding Council for Eneland.," Funding for the creation and distribution of the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."
 The SDSS Web site The SDSS is managed. by the Astrophysical Research Consortium for the Participating Institutions., The SDSS Web site The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions.
 “Lhe 'articipating Institutions are the American Museum of Natural History. Astrophysical Institute Potsclam. University of Basel. Cambridge University. Case. Western teserve University. University of Chicago. Drexel University. Fermilab. the Institute. for Aclvanececk Study. he Japan Participation Group. Johns Hopkins University. he Joint Institute for Nuclear Astrophysics. the Wavli Institute for Particle Astrophysics ancl Cosmology. the korean Scientist Croup. the Chinese Academy of Sciences (LAXAMOST). Los Alamos National Laboratory. the anck-Institute for Astronomy (AIPA). the Max-Planck-Institute for Astrophysics (ALPLA). New Mexico. State University. Ohio State University. University of Pittsburgh. University of. Portsmouth. Princeton University. the United States Naval Observatory. and the University of Washington.," The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, Cambridge University, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPA), the Max-Planck-Institute for Astrophysics (MPiA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington."
 This work is based in part on observations made at the following telescopes., This work is based in part on observations made at the following telescopes.
 “Phe Hobby-IEberlv Telescope (LLETE) is a joint project of the University of Texas at Austin. the Pennsylvania State University. Stanford University. Luchwig-AMaximillians-Universitàtt Münnchen.. and Cieorg-Xugust-Universititt. Ciótttingen.," The Hobby-Eberly Telescope (HET) is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximillians-Universit\""att Münnchen, and Georg-August-Universit\""att Götttingen."
 The WET is named in honor of its principal benefacetors.. William DP. Lobby and. Robert I5. Eberly.," The HET is named in honor of its principal benefactors, William P. Hobby and Robert E. Eberly."
 The Alarcario Low-Resolution Spectrograph is named for Alike Marcario of High. Lonesome Optics. who [abricated: several optical elements for the instrument but died. before its completion: it is a joint project of the Lobby-Eberly ‘Telescope partnership and the Instituto cde Astronomíaa de la Universidad. Nacional Xutónnoma cde Aléxxico.," The Marcario Low-Resolution Spectrograph is named for Mike Marcario of High Lonesome Optics, who fabricated several optical elements for the instrument but died before its completion; it is a joint project of the Hobby-Eberly Telescope partnership and the Instituto de a de la Universidad Nacional Autónnoma de Méxxico."
 The Apache Point Observatory 3.5 m telescope is owned. and operated. by the Astrophysical Research Consortium., The Apache Point Observatory 3.5 m telescope is owned and operated by the Astrophysical Research Consortium.
 We thank the observatory director. Suzanne Lawley. and site manager. Bruce Gillespie. for their support of this project.," We thank the observatory director, Suzanne Hawley, and site manager, Bruce Gillespie, for their support of this project."
 The Subaru Telescope is operated hy the National Astronomical Observatory of Japan., The Subaru Telescope is operated by the National Astronomical Observatory of Japan.
 Phe Willian Lerschel Telescope is operated by the Isaac Newton Group on the island of La Palma in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias., The William Herschel Telescope is operated by the Isaac Newton Group on the island of La Palma in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.
 The W. M. Weck Observatory is operated as a scientific partnership among the California Institute of ‘Technology. the University of California. ancl the National Acronautics and Space Administration: the observatory was mace possible by the generous financial support of the W. M. Ixeck Foundation.," The W. M. Keck Observatory is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration; the observatory was made possible by the generous financial support of the W. M. Keck Foundation."
The first galaxies. by definition. are expected to contain very young stellar populations of very low metallicity.,"The first galaxies, by definition, are expected to contain very young stellar populations of very low metallicity."
 However. the possibility of detecting unambiguous observable signatures of such primordial stellar populations with current or indeed planned future instrumentation is currently a matter of considerable debate.," However, the possibility of detecting unambiguous observable signatures of such primordial stellar populations with current or indeed planned future instrumentation is currently a matter of considerable debate."
 For example. one long-sought distinctive spectral signature of the first generation of galaxies is relatively strong Hell emission at Arent=1640À ," For example, one long-sought distinctive spectral signature of the first generation of galaxies is relatively strong HeII emission at $\lambda_{rest} = 1640$ "
In (his paper. the faint end of the dillerential galaxy iunber counts. n(Ó). has been studied by means of SBF measurements.,"In this paper, the faint end of the differential galaxy number counts, $n(m)$, has been studied by means of SBF measurements."
 Once the contribution from cosmic ravs has been evaluated. ancl eliminated. [rom the SBF signal. the background. PSF-convolved variance originating [rom [aint objects has been carefully analvzed.," Once the contribution from cosmic rays has been evaluated and eliminated from the SBF signal, the background PSF-convolved variance originating from faint objects has been carefully analyzed."
 Our conclusions ean be summarized as follows: This work is based on observations with the NASA/ESATelescope. obtained in the Space Telescope Science Institute. which is operated by the Association of Universities for Research in Astronomy. Ine. (AURA). under NASA contract NÀS5-26555.," Our conclusions can be summarized as follows: This work is based on observations with the NASA/ESA, obtained in the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. (AURA), under NASA contract NAS5-26555."
 This research has been supported by the Instituto de, This research has been supported by the Instituto de
As the accretion capability (rp/rp) inc‘eases [or a inarginally supersonic orbital Mach number CVs). the thermal pressure can be saturated at the junction of high deusity boundaries appearing as a tip in the linear aualysis. so that tle inner boundary extends beyoud the outer boundary of the pattern.,"As the accretion capability $r_B/r_p$ ) increases for a marginally supersonic orbital Mach number $\mach$ ), the thermal pressure can be saturated at the junction of high density boundaries appearing as a tip in the linear analysis, so that the inner boundary extends beyond the outer boundary of the pattern."
 The induced wake reveals tle ollowiug nonlinear behaviors: Usiug these theo'etical diagnostics. we can derive tle object mass. velocity. aid distance from the orbital center wih a given sound speed of the ineium.," The induced wake reveals the following nonlinear behaviors: Using these theoretical diagnostics, we can derive the object mass, velocity, and distance from the orbital center with a given sound speed of the medium."
 Lu the case that conceutrie arcs are obseved. the perturing object is expected to be at tie center of the circular ares. potentially ον& rp.," In the case that concentric arcs are observed, the perturbing object is expected to be at the center of the circular arcs, potentially giving $r_p$."
 The angular size of the ares corresponding o 2tal1M—1)? probes the orbital Mac| number fy o ‘the object of interest. or the correspondiug velocity |p with the aid of an estiiate of the sounc speed c.," The angular size of the arcs corresponding to $2\tan^{-1}(\mach^2-1)^{1/2}$ probes the orbital Mach number $\mach$ of the object of interest, or the corresponding velocity $V_p$ with the aid of an estimate of the sound speed $\cs$."
" The object mass AL, (or he ace'etion radius rj= GMj/c) ca rhe rouglly estimated (ror1 the density contrast rp/r at a distatce r from the center.", The object mass $M_p$ (or the accretion radius $r_B=GM_p/\cs^2$ ) can be roughly estimated from the density contrast $\sim r_B/r$ at a distance $r$ from the center.
 High augular Jesoution observations are required to identify the broadeniug of arm edges ( 2r.) so as to estilate thie «)bject size re., High angular resolution observations are required to identify the broadening of arm edges $\sim2r_s$ ) so as to estimate the object size $r_s$.
" On he other haud. au observation of a spira structure can provide information OL ry and M, by measurement of arm spacing and arm width."," On the other hand, an observation of a spiral structure can provide information on $r_p$ and $\mach$ by measurement of arm spacing and arm width."
" Au observation of smooth dersity distritution without sarp discontinuity provides au upper limit of the object speed (1,uw 1).", An observation of smooth density distribution without sharp discontinuity provides an upper limit of the object speed $\mach<1$ ).
 Finalv.au observation oL the arm structure with a inissiug iuner boundary suggests the uoulilear wake condition. rg/ry(M—1)!= 0.1.," Finally,an observation of the arm structure with a missing inner boundary suggests the nonlinear wake condition, $r_B/r_p\,(\mach^2-1)^{-1}\gtrsim0.1$ ."
"single cosmic rav interaction is given bv (e.g. Dermoer 1986a: Strong Moskalenko 1998): where EP20.0575 (ev is the width of the Breit)Wigner distribution. myerz1.232 GeV is the average rest energy of the A isobar. and s=2myc(E,|myer) is the square of the energy in the center of mass frame. where 47= lor535z2(1lS33)€5.mL]gil) and 44/7=0 otherwise. with the Lorentz Factor of the A isobar in the center of mass frame. and is the Lorentz factor of the center of mass.","single cosmic ray interaction is given by (e.g., Dermer 1986a; Strong Moskalenko 1998): where $\Gamma \simeq 0.0575$ GeV is the width of the Breit–Wigner distribution, $m_{\Delta}^oc^2 \simeq 1.232$ GeV is the average rest energy of the $\Delta$ –isobar, and $s = 2 m_pc^2 (E_p + m_pc^2)$ is the square of the energy in the center of mass frame, where $H^{\pm}=1$ for $ \gamma_{\Delta}^{\pm}
\gamma_{\pi}^{\prime}
(1 - 
\beta_{\Delta}^{\pm}
\beta_{\pi}^{\prime}) \leq \gamma_{\pi} \leq
\gamma_{\pi}^{\prime}
(1 +
\beta_{\Delta}^{\pm}
\beta_{\pi}^{\prime})$ and $H^{\pm}=0$ otherwise, with the Lorentz factor of the $\Delta$ –isobar in the center of mass frame, and is the Lorentz factor of the center of mass."
 Finally. is the Lorentz factor of the pion in the A isobar svstem.," Finally, is the Lorentz factor of the pion in the $\Delta$ –isobar system."
 At high. energies the spectrum of pions can. be approximated by the simple formula proposed by Berezinsky Ixudrvavtsev (1990): where e;=1.22 and e»=0.92., At high energies the spectrum of pions can be approximated by the simple formula proposed by Berezinsky Kudryavtsev (1990): where $c_1=1.22$ and $c_2=0.92$.
 Thus the injection rate of pions is given hy: and the injection rate of relativistic electrons/positrons is given by: where. following Moskalenko Strong (1998). in the calculation of the pion injection rate we combine the isobaric model (I5qs.23-. 24)) with the sealing mocel (eq. 29))," Thus the injection rate of pions is given by: and the injection rate of relativistic electrons/positrons is given by: where, following Moskalenko Strong (1998), in the calculation of the pion injection rate we combine the isobaric model \ref{Fpi_steck}- \ref{f_steck}) ) with the scaling model (Eq. \ref{Fpi_bere}) )"
" and adopt a linear interpolation between the two regimes. in the enerev range 3-7 GeV. [n our calculations we adopt the fits to the inclusive cross section a*(4),) given in Dernier (1050) whieh allow to describe separately the rates of eencration of 7 and π"," and adopt a linear interpolation between the two regimes, in the energy range 3-7 GeV. In our calculations we adopt the fits to the inclusive cross section $\sigma^{\pm}(E_p)$ given in Dermer (1986b) which allow to describe separately the rates of generation of $\pi^+$ and $\pi^-$."
 The pion decay is well known to gencrate a muon spectrum in the following form: Aluons are produced in a relatively narrow range of energies. between a kinematic minimum and maximum eiven by and In order to speed up the computation. we assume that the spectrum of muons is a deltafunction at the energy Ly=12ania|μις).," The pion decay is well known to generate a muon spectrum in the following form: Muons are produced in a relatively narrow range of energies, between a kinematic mimimum and maximum given by and In order to speed up the computation, we assume that the spectrum of muons is a delta–function at the energy $E_{\mu}=1/2(E_{\mu,{\rm min}} + E_{\mu,{\rm max}})$."
 Therefore: The spectrum of electrons. and positrons from. the muon decay. £5(LLbo). was calculated by Blasi Colafranceseo (1999).," Therefore: The spectrum of electrons and positrons from the muon decay, $F_{e^{\pm}}(E_{\pi},E_{\mu},E_e)$, was calculated by Blasi Colafrancesco (1999)."
 Combining their results with σας. (31)), Combining their results with Eqs. \ref{qepm1}) )
" ancl (35)) we obtain the rate of production of secondary clectrons/positrons: where Eu=DLE,m(n|m) and and llereAz=2mzzBE,αςnm;HE. and we put ]5qs.36- 37)) are then combined with Eq."," and \ref{fmupi_delta}) ), we obtain the rate of production of secondary electrons/positrons: where $E_{\rm min}=2 E_e m_{\pi}^2/(m_{\pi}^2 + m_{\mu}^2)$, and and Here $\lambda_{\pi}= 2 m_{\pi}^2 E_e/(m_{\pi}^2 + 
m_{\mu}^2) E_{\pi}$, and we put \ref{qepm2}- \ref{ppi}) ) are then combined with Eq."
 10 to calculate. the time evolution of the spectrum. of the accelerated. secondary leptons.," \ref{elettroni}
 to calculate the time evolution of the spectrum of the accelerated secondary leptons."
 Finally. it ds useful to derive the injection rate of secondary cleetrons/positrons at high energies (in. the scaling approximation) and for a simple power law spectrum," Finally, it is useful to derive the injection rate of secondary electrons/positrons at high energies (in the scaling approximation) and for a simple power law spectrum"
tost galaxy and of moderate ecceutricity.,host galaxy and of moderate eccentricity.
 The second mast (the third period of star formation) is expected ο be two to four times weaker than the first burst hat follows initial star formation for most dwarfs., The second burst (the third period of star formation) is expected to be two to four times weaker than the first burst that follows initial star formation for most dwarfs.
 This second burst nav not have vet occurred ii some cwarfs which. with a higher perigalacticon. may be expected o undergo another burst at a future poiut.," This second burst may not have yet occurred in some dwarfs which, with a higher perigalacticon, may be expected to undergo another burst at a future point."
 For dwarts lear apogalacticon and on the verge of expericucing hei first or second burst of star formation we predict hat low columns of diffuse ionized gas will be prescut in the vicinity of the dwarfs., For dwarfs near apogalacticon and on the verge of experiencing their first or second burst of star formation we predict that low columns of diffuse ionized gas will be present in the vicinity of the dwarfs.
 Such gas although much oo faint to be secu in cussion should have sufücie colum to be detectable in absorption aloug QSO sie ines., Such gas although much too faint to be seen in emission should have sufficient column to be detectable in absorption along QSO sight lines.
 In particular this iufalliug eas should appear iu recently infalhug Z5 Car) chwarfs that are now near apogalacticon., In particular this infalling gas should appear in recently infalling $\lta5$ Gyr) dwarfs that are now near apogalacticon.
 Leo II is possibly the best candidate for lis search., Leo II is possibly the best candidate for this search.
 Lépineetal.(2011) iu calculating the xoper motion suggest it is near either porigalacticon 6x apogalacticon. we would take the stronger view that 6lue to its deficiency in gas (Snappctal.1978) and he diticulty of stripping at such laree radi (Nichols&Bland-Tawthoru2011) as well as the longer time speut at larger radii that it is near apogalacticon.," \citet{Lepine2011} in calculating the proper motion suggest it is near either perigalacticon or apogalacticon, we would take the stronger view that due to its deficiency in gas \citep{Knapp1978} and the difficulty of stripping at such large radii \citep{Nichols2011} as well as the longer time spent at larger radii that it is near apogalacticon."
 Whe conibined with a recent iufall (Rochaetal.2011) aud th abuudance of extragalactic sources nearby (Lépineotal.2011) Leo II becomes a good candidate for QSO sight hues picking wp any wari eas infalhug outo the dwiut., When combined with a recent infall \citep{Rocha2011} and the abundance of extragalactic sources nearby \citep{Lepine2011} Leo II becomes a good candidate for QSO sight lines picking up any warm gas infalling onto the dwarf.
 Although Fornax is not near its expected apogalactico1 (Luxetal.2010). the offset lydrogen feature althoug1 possibly Galactic gas (Greevich&πα2009) απl uunmerous QSO sieht lines (Tinney1999) would be wort1 investigating, Although Fornax is not near its expected apogalacticon \citep{Lux2010} the offset hydrogen feature although possibly Galactic gas \citep{Grcevich2009} and numerous QSO sight lines \citep{Tinney1999} would be worth investigating.
 Dwarts that have experienced no burst vet iu this model. may |)o isolated enough to allow eas expelled frou initial star formation to fall back iuto the dwarf tri¢eeecring another burst (Dougetal.2003) and may have multiple bursts already. this process is unlikely to have happened in dwarts tha have already. experienced one orbit of the Calaxy.," Dwarfs that have experienced no burst yet in this model, may be isolated enough to allow gas expelled from initial star formation to fall back into the dwarf triggering another burst \citep{Dong2003} and may have multiple bursts already, this process is unlikely to have happened in dwarfs that have already experienced one orbit of the Galaxy."
 This mide‘Las able to place limits on the orbits of Carina arc E»nax based upon the timing of their bursts after iufall., This model is able to place limits on the orbits of Carina and Fornax based upon the timing of their bursts after infall.
 Ii particular. Carina is likely to have just passed. apeosdlacticou. with a high perigaacticon and low apogaacicon.," In particular, Carina is likely to have just passed apogalacticon, with a high perigalacticon and low apogalacticon."
 For Carina to be explained bv this model. the| Second. apogalacticon will not have had a Durst of star formation. with the dwiurf still uudergomg star formaki froin its first burst.," For Carina to be explained by this model, the second apogalacticon will not have had a burst of star formation, with the dwarf still undergoing star formation from its first burst."
 This extended period of star foriμαion would have preveuted a burst until the third apogaletcticon., This extended period of star formation would have prevented a burst until the third apogalacticon.
 As clwarst hat lose gas are likely to «O 8O às eas clouds of not iusieuificaut mass (Maveretal.2OG) there will )be a large amount of variation as to how nanny clouds have nianaged to all iu by the beginniug «M star formation. and could result iu a second burst beiug larger than tic first unlike tlje results inplied by this model.," As dwarfs that lose gas are likely to do so as gas clouds of not insignificant mass \citep{Mayer2006} there will be a large amount of variation as to how many clouds have managed to fall in by the beginning of star formation, and could result in a second burst being larger than the first unlike the results implied by this model."
 D.C.L. is erateful to the University of Svdnuev for hosting him during the preparation of this paper. J.D.-IL, D.C.L. is grateful to the University of Sydney for hosting him during the preparation of this paper. J.B.-H.
 is supported by a Federation Fellowship from the Australian Research Council., is supported by a Federation Fellowship from the Australian Research Council.
 The expulsion of gas from a dwarf is not automatic. aid is helped ereatv by internal heating assisted rau pressure stripping (Nichols&Blaud-Tawtlor2011).," The expulsion of gas from a dwarf is not automatic, and is helped greatly by internal heating assisted ram pressure stripping \citep{Nichols2011}."
. 0“ader instantaneous rau pressure stripping this eas. once lost. eventually ends up in the host.," Under instantaneous ram pressure stripping this gas, once lost, eventually ends up in the host."
 However. gas once remove’ from the 1nain body will experieuce less drag (arising from rai pressure) as the free sream velocity is reduced both bv the cwiut ealaxies shock aid by the turbulent wake behind.," However, gas once removed from the main body will experience less drag (arising from ram pressure) as the free stream velocity is reduced both by the dwarf galaxies shock and by the turbulent wake behind."
 Even gas which is uubound at perigalacticou but sufficicΠΤΙ) close aay Inaintain euouel momentum to later be reaccreted when far from the Cialaxies ceuter., Even gas which is unbound at perigalacticon but sufficiently close may maintain enough momentum to later be reaccreted when far from the Galaxies center.
 This gas cau be nodelled 1 ithe Nichols&Dand-Hawthorn(2011) case by the addition of cold eas ator an apogalacticon (over a suitade period of time. depeudenu upon the οσα time) with the magnitude dictated by he above model.," This gas can be modelled in the \citet{Nichols2011} case by the addition of cold gas after an apogalacticon (over a suitable period of time, dependent upon the freefall time) with the magnitude dictated by the above model."
 A simple case o this is a Carina like orbit modelled from +=5 is shown in Figure As.., A simple case of this is a Carina like orbit modelled from $z=5$ is shown in Figure \ref{fig:app}.
" Iu this case, eas was added at the appropriate apogalacticons to simulate a Carina like burst."," In this case, gas was added at the appropriate apogalacticons to simulate a Carina like burst."
 The additioial amount of eas adde at the second period of star formation (the first burst) was quickly lost. this ix due to the srort period of time over which gas is added (300 Myr) and the stronger external radiation field preseut.," The additional amount of gas added at the second period of star formation (the first burst) was quickly lost, this is due to the short period of time over which gas is added $300$ Myr) and the stronger external radiation field present."
 Although the first aud second burst initially beein losing gas at the same rate. ouce mass ds lost. the external radiation feldcnhanuced by he increased star formation of the Galaxyhas a larger effect ou the first burst. resulting iu à ΠΙΟ more rapid gas oss than the second. burst.," Although the first and second burst initially begin losing gas at the same rate, once mass is lost, the external radiation field—enhanced by the increased star formation of the Galaxy—has a larger effect on the first burst, resulting in a much more rapid gas loss than the second burst."
"paper in connection with this problem. we also adopt here the metallicity derived from the ""iraditional"" approach: Γον=—1.18.","paper in connection with this problem, we also adopt here the metallicity derived from the “traditional” approach: $_{avg} = -1.18$."
 Model parameters. values of [Fe/II] taken from CTG. and. values of [Cu/Fe| derived here for individual cluster stars in M71. MA. M5. NGC 362. NGC 288. M3. MIO. NGC 10006. M13 and M15 are given in Table 1..," Model parameters, values of [Fe/H] taken from CTG, and values of [Cu/Fe] derived here for individual cluster stars in M71, M4, M5, NGC 362, NGC 288, M3, M10, NGC 7006, M13 and M15 are given in Table \ref{tbl-1}."
 Cu abundances are normalized to the mean of |Fe/1l) derived from Fe I and Fe II., Cu abundances are normalized to the mean of [Fe/H] derived from Fe I and Fe II.
 Some clusters give rise to specific concerns. and we address those in the following section.," Some clusters give rise to specific concerns, and we address those in the following section."
 AA was one of the few clusters in our sample for which both Cu lines were available for analvsis., 	M4 was one of the few clusters in our sample for which both Cu lines were available for analysis.
 However. the 5782 feature falls close to the end of the spectral orders in this cluster. and so ~ of the spectrum used for fitting in the other clusters is unavailable.," However, the 5782 feature falls close to the end of the spectral orders in this cluster, and so $\sim$ of the spectrum used for fitting in the other clusters is unavailable."
 This is not likely to be a source of significant error since the spectrum in these stars is very clean (high S/N and relatively weak features)., This is not likely to be a source of significant error since the spectrum in these stars is very clean (high S/N and relatively weak features).
 A potentially more serious problem in MA is the presence of a diffuse interstellar band (DIB) at (e.g. Herbig1975:INrelowski&Sneden 1993)).," 	A potentially more serious problem in M4 is the presence of a diffuse interstellar band (DIB) at (e.g. \citealt{Herbig1975, Krelowski1993}) )."
 Fortunately. the Cu feature is shifted enough bv Ms radial velocity that the DIB does not directly affect it (see Figure 3)).," Fortunately, the Cu feature is shifted enough by M4's radial velocity that the DIB does not directly affect it (see Figure \ref{m4m5}) )."
 To improve the fit of the synthetic spectrum. the DID was divided out manually using SPECTRE (Fitzpatrick&Snecden1937).. effectively. treating the feature as continuum.," To improve the fit of the synthetic spectrum, the DIB was divided out manually using SPECTRE \citep{Fitzpatrick1987}, effectively treating the feature as continuum."
propose that electrons can be accelerated to sufficiently high energies at the termination shock of the sub-relativistic wind from the central part of the advection dominated accretion flow onto the GC black hole. in analogy to the pulsar wind nebulae.,"propose that electrons can be accelerated to sufficiently high energies at the termination shock of the sub-relativistic wind from the central part of the advection dominated accretion flow onto the GC black hole, in analogy to the pulsar wind nebulae."
 The authors explain the broad band emission from Ser (from radio to TeV >-rays) and suggest that the GeV source observed by EGRET has another origin., The authors explain the broad band emission from Sgr $^*$ (from radio to TeV $\gamma$ -rays) and suggest that the GeV source observed by EGRET has another origin.
 This is consistent with the recent determination of the position of the EGRET source 3EG J1746-2851 by Hooper&Dingus(2002) and Pohl(2005).., This is consistent with the recent determination of the position of the EGRET source 3EG J1746-2851 by \citet{Hooper2002} and \citet{Pohl2005}. .
 Other scenarios for the >-ray production in the vicinity of Ser A. both leptonic and hadronic. have also been found to be consistent with the TeV observations (for reasonable sets of parameters) but not with the GeV observations (Aharonian&Neronov2005).," Other scenarios for the $\gamma$ -ray production in the vicinity of Sgr $^*$, both leptonic and hadronic, have also been found to be consistent with the TeV observations (for reasonable sets of parameters) but not with the GeV observations \citep{Aharonian2005}."
. It is generally expected that ~-rays produced in such compact source models should show relatively fast variability., It is generally expected that $\gamma$ -rays produced in such compact source models should show relatively fast variability.
 The same level of TeV flux reported by HESS in 2004 and by MAGIC in 2005. and also during their own observation periods extending over a few months. rather suggest a stable source on a year time scale.," The same level of TeV flux reported by HESS in 2004 and by MAGIC in 2005, and also during their own observation periods extending over a few months, rather suggest a stable source on a year time scale."
 However. the x-ray flux above 2.8 TeV (3.76 significance) reported by Whipple during the extended period from 1995 through 2003 is a factor ~2 larger (Kosack2004 )..," However, the $\gamma$ -ray flux above 2.8 TeV $3.7 \sigma$ significance) reported by Whipple during the extended period from 1995 through 2003 is a factor $\sim 2$ larger \citep{GC_whipple}."
 The origin of 5-ray emission in other types of sources is also. possible as demonstrated by the detection of the second TeV --ray source in the direction of the GC consistent with the location of the composite supernova remnant SNR G 0.90.1 CAharonianetal. , The origin of $\gamma$ -ray emission in other types of sources is also possible as demonstrated by the detection of the second TeV $\gamma$ -ray source in the direction of the GC consistent with the location of the composite supernova remnant SNR G 0.9+0.1 \citep{Aharonian2005a}. .
2005).. Pohl(1997) proposed that the GeV emission can be related to the GC radio arc. Crockeral. (2005).," \citet{Pohl1997} proposed that the GeV emission can be related to the GC radio arc. \citet{Crocker2005},"
. see also Fatuzzo&Melia(2003).. argue for the GeV and TeV emission coming from different sites of the shell of the very powerful supernova remnant Ser A East.," see also \citet{Fatuzzo2003}, argue for the GeV and TeV emission coming from different sites of the shell of the very powerful supernova remnant Sgr A East."
 More extended ~-ray emission might also originate in the interaction of relativistic particles with the soft radiation and matter of the central stellar cluster around the GC., More extended $\gamma$ -ray emission might also originate in the interaction of relativistic particles with the soft radiation and matter of the central stellar cluster around the GC.
 These particles can be accelerated by e.g. a very energetic pulsar. à 5-ray burst source. shocks in the winds of the massive stars. or a shell type supernova remnant (Bednarek2002;2005:Grasso&Maccione 2005)..," These particles can be accelerated by e.g. a very energetic pulsar, a $\gamma$ -ray burst source, shocks in the winds of the massive stars, or a shell type supernova remnant \citep{Bednarek2002,Biermann2004,Quataert2005,Crocker2005,Grasso2005}."
 If the TeV >-rays are produced by leptons scattering off the infrared photons from the dust heated by the UV stellar radiation (as discussed by Quataert&Loeb (2005))). then the >-ray power at ~100 GeV should be almost an order of magnitude higher due to scattering of UV radiation.," If the TeV $\gamma$ -rays are produced by leptons scattering off the infrared photons from the dust heated by the UV stellar radiation (as discussed by \citet{Quataert2005}) ), then the $\gamma$ -ray power at $\sim 100$ GeV should be almost an order of magnitude higher due to scattering of UV radiation."
 The ~-ray energy spectrum should steepen between ~(0.11 TeV. Instead. the HESS collaboration reports à simple power— law spectrum between ~0.2.10 TeV (Aharonianetal.2004)..," The $\gamma$ -ray energy spectrum should steepen between $\sim 0.1-1$ TeV. Instead, the HESS collaboration reports a simple power law spectrum between $\sim 0.2-10$ TeV \citep{GC_hess}."
 In order to produce a gamma-ray spectrum well deseribed by a single power law up to ~20 TeV. hadrons should have energies of about 10° TeV. Such hadrons diffuse through the region of the TeV source (7 pe. Aharonianetal.(2004))) on a time scale of the order of 104 years. assuming the average magnetic field strength in this region of LO+ G and the Bohm diffusion coefficient.," In order to produce a gamma-ray spectrum well described by a single power law up to $\sim 20$ TeV, hadrons should have energies of about $10^{3}$ TeV. Such hadrons diffuse through the region of the TeV source $<7$ pc, \citet{GC_hess}) ) on a time scale of the order of $10^4$ years, assuming the average magnetic field strength in this region of $10^{-4}$ G and the Bohm diffusion coefficient."
 Therefore. the natural source of relativistic hadrons seems to be the supernova remnant Ser A East or the energetic pulsar created in the supernova explosion (Crockeretal.2005;LaRosaetal.2005;Bednarek2002).," Therefore, the natural source of relativistic hadrons seems to be the supernova remnant Sgr A East or the energetic pulsar created in the supernova explosion \citep{Crocker2005,LaRosa2005,Bednarek2002}."
. However. this relatively young source of relativistic hadrons cannot be identified with the last 7-ray burst in the center of our Galaxy if it appeared ~10° years ago (Biermannetal.2004).," However, this relatively young source of relativistic hadrons cannot be identified with the last $\gamma$ -ray burst in the center of our Galaxy if it appeared $\sim 10^6$ years ago \citep{Biermann2004}."
. The GC can also be the brightest source of VHE ~-rays from particle dark matter annihilation (Pradaetal.2004;Hooperetal.2004:Flix2005).," The GC can also be the brightest source of VHE $\gamma$ -rays from particle dark matter annihilation \citep{Prada2004,Hooper2004,DM_MAGIC}."
. Most SUSY dark matter scenarios lead to a cut-off in the >-ray energy spectrum below 10 TeV. The observed ~-ray energy spectrum extends up to 20 TeV. Thus most probably the maim part of the observed --radiation is not due to dark matter annihilation (Horns2004).., Most SUSY dark matter scenarios lead to a cut-off in the $\gamma$ -ray energy spectrum below 10 TeV. The observed $\gamma$ -ray energy spectrum extends up to 20 TeV. Thus most probably the main part of the observed $\gamma$ -radiation is not due to dark matter annihilation \citep{Horns2004}. .
 However. an extended 5-ray source due to dark matter annihilation peaking in the region 10 GeV to 100 GeV (Elsiisser&Mannheim2005) cannot be ruled out yet.," However, an extended $\gamma$ -ray source due to dark matter annihilation peaking in the region 10 GeV to 100 GeV \citep{Elsaesser2005} cannot be ruled out yet."
 The MAGIC observations confirm the VHE -ray source at the Galactic Center., The MAGIC observations confirm the VHE $\gamma$ -ray source at the Galactic Center.
 The measured flux is compatible with the measurement of HESS (Aharonianetal.2004) within errors., The measured flux is compatible with the measurement of HESS \citep{GC_hess} within errors.
 The VHE -ray emission does not show any significant time variability; our measurements rather affirm a steady emission of ~-rays from the GC region., The VHE $\gamma$ -ray emission does not show any significant time variability; our measurements rather affirm a steady emission of $\gamma$ -rays from the GC region.
 The excess is point like. it’s location is spatially consistent with as well as SgrA East.," The excess is point like, it's location is spatially consistent with $^*$ as well as SgrA East."
 The nature of the source of the VHE -rays has not yet been identified., The nature of the source of the VHE $\gamma$ -rays has not yet been identified.
 Future simultaneous observations with the present Cherenkov telescopes. the GLAST telescope and in the lower energies will provide much better information on the source localization and. variability of emission.," Future simultaneous observations with the present Cherenkov telescopes, the GLAST telescope and in the lower energies will provide much better information on the source localization and variability of emission."
 This will shed new light on the nature of the high energy processes inthe GC., This will shed new light on the nature of the high energy processes inthe GC.
 We would like to thank the [AC for the excellent working conditions at the Observatory de los Muchachos in La Palma., We would like to thank the IAC for the excellent working conditions at the Observatory de los Muchachos in La Palma.
 The support of the German BMBFand MPG. the Italian INFN and the SpanishCICYT ts gratefully acknowledged.," The support of the German BMBFand MPG, the Italian INFN and the SpanishCICYT is gratefully acknowledged."
 This work was also supported by ETH Research Grant and the Polish MNil Grant 1P03D01028., This work was also supported by ETH Research Grant TH-34/04-3 and the Polish MNiI Grant 1P03D01028.
sspectra.,spectra.
 The /ACIS spectrum has only. one biu. containing 19 counts.," The /ACIS spectrum has only one bin, containing 19 counts."
 The fit is statistically acceptable (using κ statisfies) and the best-fit parameters are cousistent with those published clsewhere (C)., The fit is statistically acceptable (using $\chi^2$ statistics) and the best-fit parameters are consistent with those published elsewhere (G09).
 Using the same method as described in Section 3.1.. the simultaneous fitting with a multiplication factor suggests that the flux has chauged between the oobservation and the Ας observation.," Using the same method as described in Section \ref{sec:core}, the simultaneous fitting with a multiplication factor suggests that the flux has changed between the observation and the /ACIS observation."
 Tudeed. as the factor ineutioued is fixed to 1 for the pu spectruii the best-fit factor is 0.51VOUS) for the ACTS spectiiuu.," Indeed, as the factor mentioned is fixed to 1 for the pn spectrum, the best-fit factor is $0.54\ud{0.30}{0.24}$ ) for the ACIS spectrum."
 Higher signal-to-noise data will permit confirmation of the apparent variability iu the fiux of this candidate GLAINB., Higher signal-to-noise data will permit confirmation of the apparent variability in the flux of this candidate qLMXB.
 We have performice the spectral analysis of two candidate— qLMNDs. —ino NGC 6301 aud detected on a Chnaudra//ACIS observation., We have performed the spectral analysis of two candidate qLMXBs in NGC 6304 – and – detected on a /ACIS observation.
 The third reported candidate qLAINB was outside of the feld of view of telescope., The third reported candidate qLMXB was outside of the field of view of telescope.
 As suggested previously. the candidate Ds resolved iuto two ssources: 292T718.0.. a bright (LxEο7ergs +) thermal source aud15.5.. a second fainter harder— source of unknown classification.," As suggested previously, the candidate is resolved into two sources: , a bright $L_{\rm X}=0.5\tee{33}\cgslum$ ) thermal source and, a second fainter harder source of unknown classification."
 The spectra of the wwas fitted with a NS atinosphere model at the distauce of NCC 6001 aud the best-fit parameters are consistent with the parameters obtained from the fit of the data (610991., The spectrum of the was fitted with a NS atmosphere model at the distance of NGC 6304 and the best-fit parameters are consistent with the parameters obtained from the fit of the data (G09).
 The spectrum of wwas fitted with a simple absorbed power-law aud the photon index is consistent with the best-fit iudex of the power-law component from the fat (C09)., The spectrum of was fitted with a simple absorbed power-law and the photon index is consistent with the best-fit index of the power-law component from the fit (G09).
 The low count statistics did not permit for a thorough verification of the models using the vz-xtatisties but a simmitancous fit of the candidate qLMXD spectra aand Chandra) showed that the observed flux aud spectral parameters of aand ccolmbined are consisteut with those of the previously observed17..," The low count statistics did not permit for a thorough verification of the models using the -statistic, but a simultaneous fit of the candidate qLMXB spectrum and ) showed that the observed flux and spectral parameters of and combined are consistent with those of the previously observed."
 The photon iudex of lis consistent with typical photon iudices of cataclvsiiic variables (CVs:?).., The photon index of is consistent with typical photon indices of cataclysmic variables \citep[CVs;][]{richman96}.
 A deeper exposure will be required to attempt a more precise spectral fitting. using thermal brenisstrahlunse ος. for example. aud confrm the possible CV classification of this faint source.," A deeper exposure will be required to attempt a more precise spectral fitting, using thermal bremsstrahlung model for example, and confirm the possible CV classification of this faint source."
 Another caudidate (LAINB.292017.. was also observed in the field of view and was named 292916.," Another candidate qLMXB, was also observed in the field of view and was named."
1.. The Cash-statistic fit of the source spectra provided best-fit parameters that were consistent with the values previously reported., The Cash-statistic fit of the source spectra provided best-fit parameters that were consistent with the values previously reported.
 The unabsorbed flux (0.5-10 keV) caving the more recent oobservation.: however. was a factor: 0.5LU0.30 confidence) lower.," The unabsorbed flux (0.5-10 keV) during the more recent observation, however, was a factor $0.54\ud{0.30}{0.24}$ confidence) lower."
 This is significantly lower than the previously observed flux. aud calls iuto question the classification of this X-ray source as an U-atimosphere qLMXD. since such stroug variability is not expected On Years thucscales. uuless a protracted (~years) long οπας (e... Ly2 19) ended veceutly (1 vr) C?) there is no evidence supporting this scenario in the preseut case.," This is significantly lower than the previously observed flux, and calls into question the classification of this X-ray source as an H-atmosphere qLMXB, since such strong variability is not expected on $\sim$ years timescales, unless a protracted $\sim$ years) long outburst (e.g., $L_{X}\approxgt$ ) ended recently 1 yr) \citep{rutledge02c,brown09}; there is no evidence supporting this scenario in the present case."
 Finally. the improved aastroletry permitted us to verity the association of the SSOTIECO with its possible counterpart wwith a probability of association of.," Finally, the improved astrometry permitted us to verify the association of the source with its possible counterpart with a probability of association of."
. Overall. the oobservatorv allowed το. resolve. both spatially and spectrally. the sinele source in the core.292717.. iuto two sources. one of them being the caudidate qLMXD.," Overall, the observatory allowed to resolve, both spatially and spectrally, the single source in the core, into two sources, one of them being the candidate qLMXB."
 The secoud observed candidate qLMXD..292917... showed consistent best-fit IL-atinosphere paraimecters. but also exhibit a significant decrease in its flux. which is not expected for qLAINBs.," The second observed candidate qLMXB, showed consistent best-fit H-atmosphere parameters, but also exhibit a significant decrease in its flux, which is not expected for qLMXBs."
 A lougery exposure will permit us to assert with better certitude the spectral classification of the sources in the core ofNGC 6301 aud the other candidate qELMXD., A longer exposure will permit us to assert with better certitude the spectral classification of the sources in the core ofNGC 6304 and the other candidate qLMXB.
 where n.(2) denotes the normalised redshift clistribution of ealaxies in the survey., where $n_{\rm g}(z)$ denotes the normalised redshift distribution of galaxies in the survey.
 We use C1.(4) as our weak lensing observable anc evaluate it for 100 angular frequency. bins. logarithmically spaced between Guin=LO and fis=107.," We use $C_\kappa(\ell)$ as our weak lensing observable and evaluate it for 100 angular frequency bins, logarithmically spaced between $\ell_{\rm min}=10$ and $\ell_{\rm max}=10^4$."
" ""Phe fiducia cosmology used. in our calculations is set to £24,=0.25. ax=0.9. the barvon density Q)=0.05. the power-law exponent of the initial matter power spectrum. generate by inflation ης=1.0. and the LIubble parameter =0.7. where {fy=fh100km/s/Mpce."," The fiducial cosmology used in our calculations is set to $\Omega_{\rm m}=0.25$ , $\sigma_8=0.9$, the baryon density $\Omega_{\rm b}=0.05$, the power-law exponent of the initial matter power spectrum generated by inflation $n_{\rm s}=1.0$, and the Hubble parameter $h=0.7$, where $H_0 = h\, 100\,{\rm km/s/Mpc}$."
 Moreover the geometry. of the Universe is assumed Lat by default., Moreover the geometry of the Universe is assumed flat by default.
 To compute P5. we employ the transfer function by aux apply the corrections due to non-linear evolution hy(1996).," To compute $P_\delta$, we employ the transfer function by and apply the corrections due to non-linear evolution by."
 The projected. surface mass density is assumed. to be Gaussian distributed. which implies that the covariance is eiven by i.c. different angular frequencies are u," The projected surface mass density is assumed to be Gaussian distributed, which implies that the covariance is given by i.e. different angular frequencies are ."
"ncorrelated? Here. Af is the width of the angular frequeney bin. and 1,=.100deg? the survey size."," Here, $\Delta \ell$ is the width of the angular frequency bin, and $A_{\rm s}=100\,{\rm deg}^2$ the survey size."
" The rancom orientations of the intrinsic shapes of source galaxies vield a shape noise contribution to equation. (18). determined. by the intrinsic. ellipticity dispersion σι=0.35 and the total number density of galaxies on the sky n»,=20arcmin"," The random orientations of the intrinsic shapes of source galaxies yield a shape noise contribution to equation ), determined by the intrinsic ellipticity dispersion $\sigma_\epsilon=0.35$ and the total number density of galaxies on the sky $\bar{n}_{\rm g}=20\,{\rm arcmin}^{-2}$."
 We have implemented. a redshift cistribution of the form where the characteristic redshift scale zy is related to the median redshift via to2μα1., We have implemented a redshift distribution of the form where the characteristic redshift scale $z_0$ is related to the median redshift via $z_0 \approx z_{\rm med}/1.4$.
 The survey is assumed to have a median redshift) μα=0.9., The survey is assumed to have a median redshift $z_{\rm med}=0.9$.
 Following widespread. practice. we make use of a Gaussian likelihood for ἐς). where the power spectra obtained for the fiducial cosmology Ῥιμ serve as our mock datavector.," Following widespread practice, we make use of a Gaussian likelihood for $C_\kappa(\ell)$, where the power spectra obtained for the fiducial cosmology $\vek{p}_{\rm fid}$ serve as our mock datavector."
 We assume Lat priors and make sure that the likelihood. peaks well inside the region of parameter space considered. so that the posterior is reaclily obtained from L by renormalisation in parameter space.," We assume flat priors and make sure that the likelihood peaks well inside the region of parameter space considered, so that the posterior is readily obtained from $L$ by renormalisation in parameter space."
 Again assuming Ciaussianity. the corresponding Fisher matrix reacs where both the derivatives and the covariance are evaluated al py.," Again assuming Gaussianity, the corresponding Fisher matrix reads where both the derivatives and the covariance are evaluated at $\vek{p}_{\rm fid}$."
 In writing equation (21) we have assumed that the covariance does not depend on cosmology: for the. same reason we keep the covariance in equation (20) fixed at its value for the fiducial set of cosmological parameters., In writing equation ) we have assumed that the covariance does not depend on cosmology; for the same reason we keep the covariance in equation ) fixed at its value for the fiducial set of cosmological parameters.
 For most of the analysis we will only vary μι and σε and keep all other cosmological parameters at. their iducial values., For most of the analysis we will only vary $\Omega_{\rm m}$ and $\sigma_8$ and keep all other cosmological parameters at their fiducial values.
 We compute the posterior on a grid in the Quax plane according to equation (20) and also derive he marginal distributions for the two parameters., We compute the posterior on a grid in the $\Omega_{\rm m}-\sigma_8$ plane according to equation ) and also derive the marginal distributions for the two parameters.
 In big.1 we show confidence levels anc marginal distributions for he likelihood. analysis as well as for the standard. Fisher matrix analvsis using equation (21).," In $\,$ we show confidence levels and marginal distributions for the likelihood analysis as well as for the standard Fisher matrix analysis using equation )."
" While the marginal Fisher matrix errors on Qy, and ox are still relatively close o the actual results. neither the tails in the marginal distributions. nor the banana-shaped form. of the. two-dimensional posterior and the extent of the confidence contours along the degeneracy can be reproduced. by the standard Fisher matrix."," While the marginal Fisher matrix errors on $\Omega_{\rm m}$ and $\sigma_8$ are still relatively close to the actual results, neither the tails in the marginal distributions, nor the banana-shaped form of the two-dimensional posterior and the extent of the confidence contours along the degeneracy can be reproduced by the standard Fisher matrix."
 As a first step in the. Dox-C'ox-Fisher. formalism: we determine the Box-Cox parameters from the full likelihood. using either the concentrated. maximum Likelihood from equation (6) or the QQ-plot correlation coefficient from. equation (S).," As a first step in the Box-Cox-Fisher formalism we determine the Box-Cox parameters from the full likelihood, using either the concentrated maximum likelihood from equation ) or the QQ-plot correlation coefficient from equation )."
" The latter is restricted. to. one-dimensional distributions. Lc. in this case the marginal distributions of both Oy, and ex. whereas μας iscalculated. for. the individual marginal distributions as well as for the two-dimensional posterior."," The latter is restricted to one-dimensional distributions, i.e. in this case the marginal distributions of both $\Omega_{\rm m}$ and $\sigma_8$, whereas $L_{\rm max}$ iscalculated for the individual marginal distributions as well as for the two-dimensional posterior."
" To obtain Linas. a random. sample ol size 10"" is created. [rom the respective distribution."," To obtain $L_{\rm max}$, a random sample of size $10^6$ is created from the respective distribution."
 The optimal values for (λα) for which Lis or roo attain a maximum are listed in Table 1.," The optimal values for $(\vek{\lambda},\vek{a})$ for which $L_{\rm max}$ or $r_{\rm QQ}$ attain a maximum are listed in Table ."
 Working on one- or two-dimensional distributions. with Lus OF ro) as statistic. results in largely. cüllerent optimal valuesfor the Box-Cox parameters.," Working on one- or two-dimensional distributions, with $L_{\rm max}$ or $r_{\rm QQ}$ as statistic, results in largely different optimal valuesfor the Box-Cox parameters."
 To gain further insight. we plot both statistics in the plane spannecl by A and e for the marginal distribution of ex in Fig.2. left panel.," To gain further insight, we plot both statistics in the plane spanned by $\lambda$ and $a$ for the marginal distribution of $\sigma_8$ in $\,$, left panel."
 Both Lus OF rec) agree well in the region where they maximise., Both $L_{\rm max}$ or $r_{\rm QQ}$ agree well in the region where they maximise.
 For à wide range in (A.e)-espace this maximum lies on a nearly perfect and almost linear degeneracy line.," For a wide range in $(\lambda,a)$ -space this maximum lies on a nearly perfect and almost linear degeneracy line."
 This degeneracy is mirrored in the shape of the Box- transformed. clistribution. as can be seen in the right απο of Fig.2. where we show the skewness and excess kurtosis of the transformed distribution.," This degeneracy is mirrored in the shape of the Box-Cox transformed distribution, as can be seen in the right panel of $\,$, where we show the skewness and excess kurtosis of the transformed distribution."
 The degeneracy in maximum Zi or roo is closely matched by the minimum skewness with values close to zero., The degeneracy in maximum $L_{\rm max}$ or $r_{\rm QQ}$ is closely matched by the minimum skewness with values close to zero.
 Phe kurtosis also features his degeneracy: however. it does not. vanish. but. instead obtains à shallow minimum at small negative values along he degeneracy line.," The kurtosis also features this degeneracy; however, it does not vanish, but instead obtains a shallow minimum at small negative values along the degeneracy line."
 Note that the skewness ancl kurtosis of he original distribution can be read. olf at A., Note that the skewness and kurtosis of the original distribution can be read off at $\lambda=1$.
 In this case contour lines are horizontal., In this case contour lines are horizontal.
 The mean and variance of the transformed distributions increase along the degeneracy line for larger νιues of A and e. so that the degeneracy can be broken by fixing either of the two lowest-orcler moments of the transformed distributions.," The mean and variance of the transformed distributions increase along the degeneracy line for larger values of $\lambda$ and $a$, so that the degeneracy can be broken by fixing either of the two lowest-order moments of the transformed distributions."
 llowever. since mean ancl variance are uncritical for our purposes. we leave them as free parameters and simply use the (λα) combinations on the degeneracy line that. ο codes. produce. theexact values hence determined. by numericalοσον and the maximisation algorithm used.," However, since mean and variance are uncritical for our purposes, we leave them as free parameters and simply use the $(\lambda,a)$ combinations on the degeneracy line that our codes produce, theexact values hence determined by numericaleffects and the maximisation algorithm used."
 See c.g. the values for A and e in the third and fourth row of Table which lic in the regionof maximum danas. Pog and minimum skewness.," See e.g. the values for $\lambda$ and $a$ in the third and fourth row of Table which lie in the regionof maximum $L_{\rm max}$ , $r_{\rm QQ}$ and minimum skewness."
 In the appendix we provide a tov model that illustrates basic properties of, In the appendix we provide a toy model that illustrates basic properties of
for the distribution of mass and velocities for isolated galaxies and those predictions match the observational data.,for the distribution of mass and velocities for isolated galaxies and those predictions match the observational data.
 There are uo theoretical predictions for MOND., There are no theoretical predictions for MOND.
" What we conveniently called ""MOND predictions” were actuallyrequirements.", What we conveniently called “MOND predictions” were actually.
 For example. MOND ast produce the radial velocities of satellites or shallow slope of tlic muuber-density in the ceutral region.," For example, MOND must produce the radial velocities of satellites or shallow slope of the number-density in the central region."
 We thank S. MeCGaugh for challenging us to do MONDian analysis of the satellite notion., We thank S. McGaugh for challenging us to do MONDian analysis of the satellite motion.
 We are erateful to J. Woltziman for numerous comments and sugeestious and thank J. Detaucort-Rijo for conuueunts, We are grateful to J. Holtzman for numerous comments and suggestions and thank J. Betancort-Rijo for comments.
 We are especially grateful to Aneus et al for providing us with the draft of their paper and for extensive discussions., We are especially grateful to Angus et al for providing us with the draft of their paper and for extensive discussions.
 We still have different wavs of looking at the situation with MOND., We still have different ways of looking at the situation with MOND.
 Still. these productive discussions resulted in improveients in their and our papers.," Still, these productive discussions resulted in improvements in their and our papers."
 We acknowledge support bv the NSF eraut. AST-0107072 to NMSU and thank the Spanish MEC uuder eraut PNAYA 2005-07789 for their support., We acknowledge support by the NSF grant AST-0407072 to NMSU and thank the Spanish MEC under grant PNAYA 2005-07789 for their support.
 Computer simulations used iu this research were conducted on the Columbia superconiputer at the NASA Advanced Supercomputing Division and ou Seaborg at the National Encrey Research Scientific Computing Center (NERSC)., Computer simulations used in this research were conducted on the Columbia supercomputer at the NASA Advanced Supercomputing Division and on Seaborg at the National Energy Research Scientific Computing Center (NERSC).
cut-off energy and reflection are obtained and. in most cases. these are compatible with the results reported in Tables 4 and 5.,"cut-off energy and reflection are obtained and, in most cases, these are compatible with the results reported in Tables 4 and 5."
 However. due to the non-simultaneity of the and observations. spectral and/or flux variability could play an important role in the determination of the spectral parameters (as in the case of Fairall 1146 where the spectral slope varied significantly between two different observations).," However, due to the non-simultaneity of the and observations, spectral and/or flux variability could play an important role in the determination of the spectral parameters (as in the case of Fairall 1146 where the spectral slope varied significantly between two different observations)."
 In the following discussion. we choose to adopt those fits where C ts left free to vary.," In the following discussion, we choose to adopt those fits where $C$ is left free to vary."
 Even in this case. some caution is still worthwhile. but we hope that the sampling of several objects dilutes any remaining effects of combining non-simultaneous data sets and provides some indications on the average high energy properties of type | AGN.," Even in this case, some caution is still worthwhile, but we hope that the sampling of several objects dilutes any remaining effects of combining non-simultaneous data sets and provides some indications on the average high energy properties of type 1 AGN."
 In the following. we discuss in detail the main results of our analysis.," In the following, we discuss in detail the main results of our analysis."
" In five objects of the sample. mild neutral absorption in excess of the Galactic value is highly required to improve the quality of the fit: the observed column densities range from 0.09 to 9.8 x107! em""."," In five objects of the sample, mild neutral absorption in excess of the Galactic value is highly required to improve the quality of the fit; the observed column densities range from 0.09 to 9.8 $\times 10^{21}$ $^{-2}$."
 In the case of two sources. the absorption is complex as it partially covers one source (IGR J16558-5203). or. as in the case of 4U1344-60. is formed by two layers of material partially obseuring the central source.," In the case of two sources, the absorption is complex as it partially covers one source (IGR J16558-5203), or, as in the case of 4U1344-60, is formed by two layers of material partially obscuring the central source."
 In the case of intermediate Seyfert galaxies. such as 4U1344-60. this is 1n agreement with the Unified Model predictions. since at intermediate angles of the line of sight only the outer part of the obscuring torus Is intercepted by the observer (e.g.. see Matolino 2001 and references therein).," In the case of intermediate Seyfert galaxies, such as 4U1344-60, this is in agreement with the Unified Model predictions, since at intermediate angles of the line of sight only the outer part of the obscuring torus is intercepted by the observer (e.g., see Maiolino 2001 and references therein)."
 In the case of IGR J16558-5203. the high value of its absorption could be instead ascribed to an intercepting cloud. à concept discussed. for instance. in Lamer et al. (," In the case of IGR J16558-5203, the high value of its absorption could be instead ascribed to an intercepting cloud, a concept discussed, for instance, in Lamer et al. ("
2003) and also envisaged in the clumpy torus model proposed by Elitzur Shlosman (2006).,2003) and also envisaged in the clumpy torus model proposed by Elitzur Shlosman (2006).
 In several type | Seyfert galaxies. complex absorption has also been found in the form of a warm absorber (Gondoin et al.," In several type 1 Seyfert galaxies, complex absorption has also been found in the form of a warm absorber (Gondoin et al."
 2003. Schurch Warwick 2003: Feldmeier et al.," 2003, Schurch Warwick 2003; Feldmeier et al."
" 1999), often used to describe the soft X-ray spectrum of type | AGN."," 1999), often used to describe the soft X-ray spectrum of type 1 AGN."
 Since it is beyond the scope of this work to assess the ionization state and temporal variability of this absorber. we have chosen to describe the soft part of the spectrum with a simple model adequate to ensure a proper parameterization of the X-ray/zamma-ray spectrum.," Since it is beyond the scope of this work to assess the ionization state and temporal variability of this absorber, we have chosen to describe the soft part of the spectrum with a simple model adequate to ensure a proper parameterization of the X-ray/gamma-ray spectrum."
 In fact. a soft power-law with [D = 3.8 (for LEDA 168563). a black body with temperature 0.09 and 0.05 keV (for IGR JO7597-3842 and ESO 209-12. respectively) and a MEKAL model with &7 of 0.15 and 0.19 keV (for FRL 1146 and IGR J18027-1455 respectively) provide quite good fit to the soft energy continuum of our sources.," In fact, a soft power-law with $\Gamma$ = 3.8 (for LEDA 168563), a black body with temperature 0.09 and 0.05 keV (for IGR J07597-3842 and ESO 209-12, respectively) and a MEKAL model with $kT$ of 0.15 and 0.19 keV (for FRL 1146 and IGR J18027-1455 respectively) provide quite good fit to the soft energy continuum of our sources."
 Clearly a more detailed analysis of the high-resolution data is needed to assess the nature of the soft component present in some of our sources and we defer this study to a future work., Clearly a more detailed analysis of the high-resolution data is needed to assess the nature of the soft component present in some of our sources and we defer this study to a future work.
 In Fig., In Fig.
 3 we show the photon index distribution obtained from data in Table 4.. where a cut-off power-law model is used.," \ref{figure=gamma} we show the photon index distribution obtained from data in Table \ref{table=cut}, where a cut-off power-law model is used."
 The mean Γ is 1.73 with a standard deviation of 0.24., The mean $\Gamma$ is 1.73 with a standard deviation of 0.24.
 This value is consistent. within errors. with the 2-10 keV mean slope found for other sample of AGN (r.e.. <[> ~ 1.8-2. Reeves Turner 2000. Piconcelli et al.," This value is consistent, within errors, with the 2-10 keV mean slope found for other sample of AGN (i.e., $< \Gamma >$ $\sim$ 1.8-2, Reeves Turner 2000, Piconcelli et al."
 2005. Dadina 2008).," 2005, Dadina 2008)."
 Four sources (LEDA 168563. IGR JO7597-3842. IGRJI6482-3036 and IGRJISO027-1455) in our sample have very flat spectra. Le. E ~ L5-10.6. providing the low Γ peak seen in Fig. 3..," Four sources (LEDA 168563, IGR J07597-3842, IGRJ16482-3036 and IGRJ18027-1455) in our sample have very flat spectra, i.e., $\Gamma$ $\sim$ 1.5-1.6, providing the low $\Gamma$ peak seen in Fig. \ref{figure=gamma}."
 Our photon index distribution is similar to the one reported for a sample of nearby Seyfert 1-1.5 galaxies by Cappi et al. (, Our photon index distribution is similar to the one reported for a sample of nearby Seyfert 1-1.5 galaxies by Cappi et al. (
2006) who found an even flatter weighted mean value for Γ (1.56+0.04 compared to our 1.68+ 0.02).,2006) who found an even flatter weighted mean value for $\Gamma$ $1.56 \pm 0.04$ compared to our $1.68 \pm 0.02$ ).
 Interestingly. flat photon indices have been invoked to account for the X-ray background spectral shape in synthesis models recently proposed (Gilli et al.," Interestingly, flat photon indices have been invoked to account for the X-ray background spectral shape in synthesis models recently proposed (Gilli et al."
 2007)., 2007).
 There are several examples in the literature of type | sources with flat spectra (Mkn 841. Petrucet et al.," There are several examples in the literature of type 1 sources with flat spectra (Mkn 841, Petrucci et al."
 2007: PG 1416-129. Porquet et al.," 2007; PG 1416-129, Porquet et al."
 2007; NGC 4051. Ponti et al.," 2007; NGC 4051, Ponti et al."
 2006: NGC 3516. Turneret al.," 2006; NGC 3516, Turner et al."
 2005; NGC 3227. Gondoin et al.," 2005; NGC 3227, Gondoin et al."
 2003: ΤΗ 0419-577. Pounds et al.," 2003; 1H 0419-577, Pounds et al."
 2004): all of these sources are characterized by puzzling spectral and temporal behaviors., 2004); all of these sources are characterized by puzzling spectral and temporal behaviors.
 In general. the rather flat spectra of type 1 AG can be ascribed to either the presence of à warm and/or complex absorber. or alternatively to a reflection bump as all of these components conspire to flatten the primary continuum.," In general, the rather flat spectra of type 1 AGN can be ascribed to either the presence of a warm and/or complex absorber, or alternatively to a reflection bump as all of these components conspire to flatten the primary continuum."
 Another possible explanation for the detection of many flat spectrum sources could be the hard X-ray selection of our sample. 1.89. AGN with a flat l'and a significant reflection component (when present) are more easily detected at energies > 10 keV than objects with a steep continuum and no reflection.," Another possible explanation for the detection of many flat spectrum sources could be the hard X-ray selection of our sample, i.e. AGN with a flat $\Gamma$ and a significant reflection component (when present) are more easily detected at energies $>$ 10 keV than objects with a steep continuum and no reflection."
 However. the average photon index found in hard X-rays surveys is Γ ~ 2.1 (see Beckmann et al.," However, the average photon index found in hard X-rays surveys is $\Gamma$ $\sim$ 2.1 (see Beckmann et al."
 2006. Deluit Courvoisier 2003.," 2006, Deluit Courvoisier 2003,"
"Expanding the left hand side. we have the smoothing length is a given function of the density. then the SPH continuity equation is given by (329) and (37)) becomes dB. in one dimension these terms must cancel to give 2, =const. and thus we deduce that the correct form of the induction equation is therefore dB. in the form (36)) we would have d Using (39)) or (403) and (329) as constraints we may then derive the equations of motion using the variational principle described in to give The total energy equation is given by whilst the internal energy equation is found using the first law of thermodynamics and (322). that is We show in refsecimwav. that including the correction terms for a variable smoothing length in this manner significantly improves the numerical wave speed in the propagation of MHD waves and enables the shock tube problems considered in paper I to be computed with no smoothing of the initial conditions.","Expanding the left hand side, we have If the smoothing length is a given function of the density, then the SPH continuity equation is given by \ref{eq:sphctygradh}) ) and \ref{eq:Bevolgradh}) ) becomes However in one dimension these terms must cancel to give $B_x =$ const, and thus we deduce that the correct form of the induction equation is therefore or in the form \ref{eq:brhonormal}) ) we would have Using \ref{eq:Bgradh}) ) or \ref{eq:Brhogradh}) ) and \ref{eq:sphctygradh}) ) as constraints we may then derive the equations of motion using the variational principle described in \\ref{sec:sphmom} to give The total energy equation is given by whilst the internal energy equation is found using the first law of thermodynamics and \ref{eq:sphctygradh}) ), that is We show in \\ref{sec:mwav} that including the correction terms for a variable smoothing length in this manner significantly improves the numerical wave speed in the propagation of MHD waves and enables the shock tube problems considered in paper I to be computed with no smoothing of the initial conditions."
 The equations of motion conserve linear momentum exactly., The equations of motion conserve linear momentum exactly.
 However. angular momentum is not conserved exactly because the stress force between a pair of particles is not along the line joining them.," However, angular momentum is not conserved exactly because the stress force between a pair of particles is not along the line joining them."
" Returning to C413). and considering motion in 2 dimensions .r and y. the change in angular momentum of the system is given by where Yon=HaoMoe FabShap 07mSUOp and ση=a|a)’, "," Returning to \ref{eq:spmhdmomgradh}) ), and considering motion in 2 dimensions $x$ and $y$ , the change in angular momentum of the system is given by where $y_{ab} = y_a - y_b$, $x_{ab} = x_a - x_b$, $\sigma^{ij} = S^{ij}/
\Omega \rho^2$ and $\tilde\sigma^{ij}_{ab} = \sigma_a^{ij} + \sigma_b^{ij} $."
"We have replaced VM, by pine.", We have replaced $\nabla W_{ab}$ by ${\bf r}_{ab} F_{ab}$.
 It ean be seen from (44) that if the stress is isotropic. and proportional to the identity tensor. as is the case for isotropic fluids. the rate of change of angular momentum vanishes.," It can be seen from \ref{eq:angmom}) ) that if the stress is isotropic, and proportional to the identity tensor, as is the case for isotropic fluids, the rate of change of angular momentum vanishes."
 If. however. the stress is not proportional to the identity tensor then the total angular momentum of the system will change.," If, however, the stress is not proportional to the identity tensor then the total angular momentum of the system will change."
 It can be shown that when the summations can be converted to integrals the angular momentum is conserved exactly., It can be shown that when the summations can be converted to integrals the angular momentum is conserved exactly.
 The same problem arises in the case of elastic stresses where the problem is exacerbated by the fact that the particles near the edge of a solid have densities similar to the interior and the particles do not have neighbours exterior to the solid., The same problem arises in the case of elastic stresses where the problem is exacerbated by the fact that the particles near the edge of a solid have densities similar to the interior and the particles do not have neighbours exterior to the solid.
 In this case the conservation of angular momentum is significantly in error., In this case the conservation of angular momentum is significantly in error.
 ? showed. however. that angular momentum could be conserved by altering the gradient of the kernel to a matrix operator.," \citet{bl99} showed, however, that angular momentum could be conserved by altering the gradient of the kernel to a matrix operator."
 The astrophysical problem could be solved in the same way but we expect the astrophysical conservation to be very much better without changing the kernel. because edges are associated with low density and correspondingly low angular momentum.," The astrophysical problem could be solved in the same way but we expect the astrophysical conservation to be very much better without changing the kernel, because edges are associated with low density and correspondingly low angular momentum."
 We demonstrate the usefulness of thevariable smoothing length terms in the MHD case by the simulation of MHD waves and the ?.» shock, We demonstrate the usefulness of thevariable smoothing length terms in the MHD case by the simulation of MHD waves and the \citet{bw88} shock
monotonic functions of lass loss. it is a sufficient condition that MT be stable at the ouset of RLOF in order to ensure stability throughout.,"monotonic functions of mass loss, it is a sufficient condition that MT be stable at the onset of RLOF in order to ensure stability throughout."
 We reject system configurations in which this condition is violated., We reject system configurations in which this condition is violated.
 We realise that there is a difference between a true dynamical stability (or instability) the oue arises ou time-scales shorter than dyvuaiical-timescale. before a star obtain hydrostatic equilibrium and the dyuaniical stability used conuuoulv for the purpose— of studies of lnass transfer stability.," We realise that there is a difference between a true dynamical stability (or instability) — the one arises on time-scales shorter than dynamical-timescale, before a star obtain hydrostatic equilibrium — and the dynamical stability used commonly for the purpose of studies of mass transfer stability."
 The latter one. as described earlier ∙∙∣iu &1L. operates ou timescales. louger than the dynamical timescale (as all the analyzed stellar iuodel are in livdrodvuamical equilibriun) but much shorter than thermal tiuescale. so the cutropy of the stellar lavers is not changed.," The latter one, as described earlier in 4, operates on timescales longer than the dynamical timescale (as all the analyzed stellar model are in hydrodynamical equilibrium) but much shorter than thermal timescale, so the entropy of the stellar layers is not changed."
" The code we use always generating stellar inodels in hydrostatic equilibriuu. aud as such not of modelling a true dynanical-fiiescale isinstability, capablehowever is able work on a timescale much shorter than is required to change the entropy,"," The code we use always generating stellar models in hydrostatic equilibrium, and as such is not capable of modelling a true dynamical-timescale instability, however is able work on a timescale much shorter than is required to change the entropy."
" As such, through out mass transfer sequences. when the rate of the MT exceeds TTAT. we efficiently obtain Gaq asdiscussed above. but for actual stellar models Gusteacd of Composite polvtropes)."," As such, through out mass transfer sequences, when the rate of the MT exceeds TTMT, we efficiently obtain $\zeta_\mathrm{ad}$ as discussed above, but for actual stellar models (instead of composite polytropes)."
" We find that with § close to the 1iaxininua stable value, we obtain MT rates exceeding the thermaltimescale MIT rate. although this is achieved ouly after ~Ty has passed after the onset of RLOF,"," We find that with $\beta$ close to the maximum stable value, we obtain MT rates exceeding the thermal-timescale MT rate, although this is achieved only after $\sim \tau_\mathrm{th}$ has passed after the onset of RLOF."
 As an example. we model the case of a 12M. red giant with a LLAL.. companion. with au initial period of 100 davs. which initiates AIT at a core mass of approximately 0.315M... and with a donor radins of 1G.LR..," As an example, we model the case of a $1.2\,M_\odot$ red giant with a $1.1\,M_\odot$ companion, with an initial period of 100 days, which initiates MT at a core mass of approximately $0.345\,M_\odot$ and with a donor radius of $46.4\,R_\odot$."
 For a conservation factor greater than hus©0.89. runway APT eusues (see retig:compa;l)): ALP stabilityisanabletorecoceronthetherimadtineased 0.9. leading to the code crashing.," For a conservation factor greater than $\beta_\mathrm{max} \approx 0.89$, runaway MT ensues (see \\ref{fig:comp_MT}) ): MT stability is unable to recover on the thermal timescale for $\beta = 0.9$ , leading to the code crashing."
 We interpret this as nmeieative of a runaway MT event., We interpret this as indicative of a runaway MT event.
 In this case the AIT rate approaches and finally exceeds the thermaltimescale-AIT rate;, In this case the MT rate approaches and finally exceeds the thermal-timescale-MT rate.
" Note that the maxima couscrvation factor fouud here is considerably higher than that found when taking the donor as a condensed polytrope considered with the core aud the total masses as in the described above giaut. in which case yas,20.32."," Note that the maximum conservation factor found here is considerably higher than that found when taking the donor as a condensed polytrope considered with the core and the total masses as in the described above giant, in which case $\beta_\mathrm{max} \approx 0.32$."
 Note frou cshthatthe ALT phascappcarstopassthroughtwodist inet stuges., Note from \\ref{fig:comp_mesh} that the MT phase appears to pass through two distinct sub-stages.
"Usingtheceaimpleabocc(al.2 |1.13M... progenitor system with P=100dd) for the case 3=0.3. we observe that there are iu fact tlaee such stages,"," Using the example above (a $1.2+1.1\,M_\odot$ progenitor system with $P_\mathrm{i}=100$ d) for the case $\beta = 0.3$, we observe that there are in fact three such stages."
 At the ouset. the MT rapidly accelerates to a timescale conmparable to the donor's thermal timescale. reaching a dramatic peak M. before rapidly falling off.," At the onset, the MT rapidly accelerates to a timescale comparable to the donor's thermal timescale, reaching a dramatic peak $\dot M$ before rapidly falling off."
" This turn-off occurs approximately ty, after the coudition qur(4)«Coq is net. (sce reffie:lst xàaseend)) as the amass ratio reaches qu."," This turn-off occurs approximately $\tau_\mathrm{th}$ after the condition $\zeta_\mathrm{RL} (q) < \zeta_\mathrm{eq}$ is met (see \\ref{fig:1stphaseend}) ), as the mass ratio reaches $q_\mathrm{crit}$ ."
 TUs initial stage strips the envelope down (removing ~50το of the envelope mass). to which the donor reacts by contracting until the binary becomes detached (underfilling the Roche lobe by ~5%).," This initial stage strips the envelope down (removing $\sim 50-70\%$ of the envelope mass), to which the donor reacts by contracting until the binary becomes detached (underfilling the Roche lobe by $\sim 5 \%$ )."
 This results in a pause in MT lasting for ~ ΛΙ (this recovery tine is approximately the thermal tine of the whole donor. whereas the thermal time of only its outers layers played a role in the determination of the TTMT rate). during which tine the donors core erows slightly until RLOF FOSS.," This results in a pause in MT lasting for $\sim 1-4$ Myr (this recovery time is approximately the thermal time of the whole donor, whereas the thermal time of only its outers layers played a role in the determination of the TTMT rate), during which time the donor's core grows slightly until RLOF resumes."
" This pause is followed by another stage of MT on the star's unclear timescale. in which the remainder of the envelope is trausferred, save for a final ~10.3AL."," This pause is followed by another stage of MT on the star's nuclear timescale, in which the remainder of the envelope is transferred, save for a final $\sim 10^{-3}\,M_\odot$."
 While often neglected (?).. iu the course of the pause aud unclear-timescale phase of AIT the donor's core niass can increase by ~ο 30%. having a profound effect ou the outcome of the sv«teus," While often neglected \citep{Han1998}, in the course of the pause and nuclear-timescale phase of MT the donor's core mass can increase by $\sim 20-30\%$ , having a profound effect on the outcome of the system."
 As for the donor remaining envelope mass. at the end of AIT this collapses (ou its thermal timescale) outo the surface of the Aoldegenerate model.core (2??)..," As for the donor's remaining envelope mass, at the end of MT this collapses (on its thermal timescale) onto the surface of the degenerate core \citep{DS70,Ivanova10, Justham10}."
 The same behavior aud the amount that reni1s in the cuvelope at the eud of MT is generally ~3% ofthe original cuvelope mass.," The same behavior is observed in our model, and the amount that remains in the envelope at the end of MT is generally $\sim 3 \%$ of the original envelope mass."
" This means that for smaller core masses, we see thicker envelopes remaining."," This means that for smaller core masses, we see thicker envelopes remaining."
 However. using our code it is difficult to make a precise estimate of the final mass of the euvelope remuaut. as our model breaks down at the collapse of the euvelope for low core masses.," However, using our code it is difficult to make a precise estimate of the final mass of the envelope remnant, as our model breaks down at the collapse of the envelope for low core masses."
 For the purpose of this study. we asstune that the MT euds very shortly after the code breaks down. aud that the remainingmass in the envelope will beburned. lo. we take the total mass at the end of the AIT phase," For the purpose of this study, we assume that the MT ends very shortly after the code breaks down, and that the remainingmass in the envelope will beburned, i.e., we take the total mass at the end of the MT phase"
sinall sizes of (he emitting plasma in the chunpy jet can also amplily the energy density of the svuchrotron photons to a level leading to domination of the SSC component over the EIC one.,Small sizes of the emitting plasma in the clumpy jet can also amplify the energy density of the synchrotron photons to a level leading to domination of the SSC component over the EIC one.
 Note that. for the electron energv spectrum usually considered in the ELC model. the photon energy range of the SSC enission corresponds roughly with the spectral range of the EIC radiation.," Note that, for the electron energy spectrum usually considered in the EIC model, the photon energy range of the SSC emission corresponds roughly with the spectral range of the EIC radiation."
 The ratio of observed SSC to EIC luminosity is where .N is (he nunber of (he emitting clumps with radius δὲ per knot. z is a redshift of the source and 0=L/T(1—4p) is the jet Doppler factor for its bulk velocity 3=(1-T2)? and inclination @=costy (Appendix C).," The ratio of observed SSC to EIC luminosity is where $N$ is the number of the emitting clumps with radius $R_{\rm c}$ per knot, $z$ is a redshift of the source and $\delta = 1 / \Gamma (1 - \beta \, \mu)$ is the jet Doppler factor for its bulk velocity $\beta = (1 - \Gamma^{-2})^{1/2}$ and inclination $\theta \equiv \cos^{-1} \mu$ (Appendix C)."
 It is always. possible to adjust the unknown parameters 0. A. and N in order to obtain Li2Lee.," It is always possible to adjust the unknown parameters $\delta$, $R_{\rm c}$ and $N$ in order to obtain $L_{\rm ssc} > L_{\rm eic}$."
 As a result. it is possible to model the observed X-ray. emission of large-scale quasar jets by SSC emission. and hence there are no obvious constraints on the large-scale jet parameters [rom X-ray observations.," As a result, it is possible to model the observed X-ray emission of large-scale quasar jets by SSC emission, and hence there are no obvious constraints on the large-scale jet parameters from X-ray observations."
" In particular. the Doppler factor of the jet in the SSC model can be smaller (han that required by the EIC model,"," In particular, the Doppler factor of the jet in the SSC model can be smaller than that required by the EIC model."
 Modifications to the EIC model. which are required in the case of knots treated. as slalionary regions of enerev dissipation. decrease the models alivactiveness.," Modifications to the EIC model, which are required in the case of knots treated as stationary regions of energy dissipation, decrease the model's attractiveness."
 ‘Therefore. alternative scenarios postulating a svnclirotron origin of (he X-ray emission should be considered.," Therefore, alternative scenarios postulating a synchrotron origin of the X-ray emission should be considered."
 llowever. in (his case the X-ray photons would have to be produced by a different electron population than the one responsible for the radio-to-optical emission. as the X-ray. [lax is usually above (he extrapolated racdio-to-optical power-law continuum: or else deviations from a single power-law behavior in (he electron energy distribution — high energy particle in particular have to be invoked.," However, in this case the X-ray photons would have to be produced by a different electron population than the one responsible for the radio-to-optical emission, as the X-ray flux is usually above the extrapolated radio-to-optical power-law continuum; or else deviations from a single power-law behavior in the electron energy distribution — high energy particle pile-up in particular — have to be invoked."
 Furthermore. to reconcile the observed. flat X-ray spectral indices with strong cooling of the highlv energetic electrons aud large observed sizes of the emission regions (seediscussioninAharonian2002).. one must have particle acceleration occurring over extended. volumes.," Furthermore, to reconcile the observed flat X-ray spectral indices with strong cooling of the highly energetic electrons and large observed sizes of the emission regions \citep[see discussion in][]{aha02}, one must have particle acceleration occurring over extended volumes."
 This can be illustrated by rewriting the observed propagation length of the electrons radiating svnchrotron photons with Irequency Dag 11 a form, This can be illustrated by rewriting the observed propagation length of the electrons radiating synchrotron photons with frequency $\nu_{\rm syn}$ in a form
vr.1 (Skopal et al.,"$^{-1}$ (Skopal et al.,"
 1996). Viu—20 kms ! (Vogel ot al.," 1996), $V_{\rm
wind}$ =20 km $^{-1}$ (Vogel et al.,"
 1994)) it is clear that the ionised cavity clue to the hot component. will be density bounded. and. much smaller than the binary separation., 1994)) it is clear that the ionised cavity due to the hot component will be density bounded and much smaller than the binary separation.
 The Hipparcos distance to CLL Cveni is 268+66 pe (Viotti et al., The Hipparcos distance to CH Cygni is $268\pm66$ pc (Viotti et al.
" 1998). meaning that the maximum extent of the 30,4. contour of radio emission at 19561 in 1986 js —500.AU."," 1998), meaning that the maximum extent of the $3\sigma_{\rm rms}$ contour of radio emission at 15GHz in 1986 is $\sim 500$ AU."
 Phe most likely origin of of extended nonthermal emission is svnchrotron emission from relativistic electrons in à magnetic field., The most likely origin of of extended non–thermal emission is synchrotron emission from relativistic electrons in a magnetic field.
 Η CL €veni. follows the model proposed. for 11M Sagittae by IZvres ct al. (, If CH Cygni follows the model proposed for HM Sagittae by Eyres et al. (
1995). then what is being observed are regions of shocked material. caused when high velocity gecta expand. into the relatively dense. circunitrinary envelope created. by the winds of the giant. stars in the svsteor.,"1995), then what is being observed are regions of shocked material, caused when high velocity ejecta expand into the relatively dense circumtrinary envelope created by the winds of the giant stars in the system."
 Evidence for this scenario comes from infrared spectroscopy Cl'aranova Yuelin. 1988). carried out around the period of the end of the optical outburst in 1983.1987. showing changes in the cireumtrinary cust envelope.," Evidence for this scenario comes from infrared spectroscopy (Taranova Yudin, 1988), carried out around the period of the end of the optical outburst in 1983–1987, showing changes in the circumtrinary dust envelope."
 They sugeested that the dust was disrupted at the time of the radio jet emergence. probably as it was swept up by the expanding matter.," They suggested that the dust was disrupted at the time of the radio jet emergence, probably as it was swept up by the expanding matter."
 The positions of the NW and SE extended knots were nmieasured. on the 1986 15C6llIz radio map., The positions of the NW and SE extended knots were measured on the 1986 15GHz radio map.
 The angular separations between the peak in each. knot and the central bright peak were and for the NW and. SE knots. respectively., The angular separations between the peak in each knot and the central bright peak were and for the NW and SE knots respectively.
 Phe greater uncertainty in the SIZ position is due to the fact that the SE component has lower surface brightness than the the NW one., The greater uncertainty in the SE position is due to the fact that the SE component has lower surface brightness than the the NW one.
 In à 1985 VLA 1561 map (Fig. 5)).," In a 1985 VLA 15GHz map (Fig. \ref{fig:85}) ),"
 these two knots were not visible. and hence the material must have been ected within 422 days before the 1986 observation.," these two knots were not visible, and hence the material must have been ejected within 422 days before the 1986 observation."
 This places a lower limit on the expansion velocity., This places a lower limit on the expansion velocity.
 Assuming a distance to CLL Cve of 268+66 pe the velocities are found to be [or the NW component and for the SE component. with the uncertainties dominated by the uncertainty on the Llippareos distance.," Assuming a distance to CH Cyg of $268\pm 66$ pc the velocities are found to be for the NW component and for the SE component, with the uncertainties dominated by the uncertainty on the Hipparcos distance."
 These results correspond well with those derived. previously. in particular with the expansion velocity of 1400. km 7 derived. from," These results correspond well with those derived previously, in particular with the expansion velocity of 1400 km $^{-1}$ derived from"
 These results correspond well with those derived. previously. in particular with the expansion velocity of 1400. km 7 derived. from.," These results correspond well with those derived previously, in particular with the expansion velocity of 1400 km $^{-1}$ derived from"
phase with the planetary orbit.,phase with the planetary orbit.
" The lead angles observed by Shkolniketal.(2003) and Shkolniketal.(2005) were recently explained with an Alfvénn-wing model using realistic stellar wind parameters obtained from the stellar wind model by Weber and Davis (Preusse,2006;Preusseetal., 2006)."," The lead angles observed by \citet{Shkolnik03} and \citet{Shkolnik05} were recently explained with an Alfvénn-wing model using realistic stellar wind parameters obtained from the stellar wind model by Weber and Davis \citep{PreussePHD05,Preusse06}."
. This indicates that a magnetised planet is not required to describe the present data., This indicates that a magnetised planet is not required to describe the present data.
" The presence of a planetary magnetic field could, however, be proven by the existence of planetary radio emission."," The presence of a planetary magnetic field could, however, be proven by the existence of planetary radio emission."
" Although our model does not predict high radio fluxes from these planets (see table 1), the high chromospheric flux shows that a strong interaction is taking place."," Although our model does not predict high radio fluxes from these planets (see table 1), the high chromospheric flux shows that a strong interaction is taking place."
" As a possible solution of this problem, an intense stellar magnetic field was suggested (Zarka,2006,2007).."," As a possible solution of this problem, an intense stellar magnetic field was suggested \citep{Zarka06PREVI,Zarka06PSS}."
" In that case, table 1 underestimates the radio emission of Ups And b, c, d and HD 179949 b, making these planets interesting candidates for radio observations (eg."," In that case, table 1 underestimates the radio emission of Ups And b, c, d and HD 179949 b, making these planets interesting candidates for radio observations (eg."
 through the model or the model)., through the model or the model).
" For this reason, it would be especially interesting to obtain measurements of the stellar magnetic fieldfor these two planet-hosting stars (e.g.bythemethodofCatalaetal.,2007)."," For this reason, it would be especially interesting to obtain measurements of the stellar magnetic fieldfor these two planet-hosting stars \citep[e.g.~by the method of][]{Catala07}."
". Considering the uncertainties mentioned above, it is important not to limit observations attempts to these best cases."," 		 Considering the uncertainties mentioned above, it is important not to limit observations attempts to these best cases."
" The estimated radio characteristics should only be used as a guide (e.g. for the target selection, or for statistical analysis), but individual results should not be regarded as precise values."," The estimated radio characteristics should only be used as a guide (e.g. for the target selection, or for statistical analysis), but individual results should not be regarded as precise values."
 It may seem surprising that so few good candidates are found among the 197 examined exoplanets., It may seem surprising that so few good candidates are found among the 197 examined exoplanets.
" However, when one checks the list of criteria for “good” candidates (e.g.GrieBmeieretal.,2006a),, it is easily seen that only a few good targets can be expected: (a) the planet should be close to the Earth (otherwise the received flux is too weak)."," However, when one checks the list of criteria for “good” candidates \citep[e.g.][]{Griessmeier51PEG05}, it is easily seen that only a few good targets can be expected: (a) the planet should be close to the Earth (otherwise the received flux is too weak)."
" About of the known exoplanets are located within 50 pc, so that this is not a strong restriction. ("," About of the known exoplanets are located within 50 pc, so that this is not a strong restriction. ("
b) A strongly magnetised system is required (especially for frequencies above the ionospheric cutoff).,b) A strongly magnetised system is required (especially for frequencies above the ionospheric cutoff).
" For this reason, the planet should be massive (as seen above, we find magnetic moments M>2M, only for planets with masses M> 2Μ1)."," For this reason, the planet should be massive (as seen above, we find magnetic moments $\mathcal{M}\ge2\mathcal{M}\J$ only for planets with masses $M\ge2M\J$ )."
 About of the known exoplanets are at least as massive as Jupiter (but only have My> 2.0Λ41). (, About of the known exoplanets are at least as massive as Jupiter (but only have $M\p \ge 2.0 M\J$ ). (
"c) The planet should be located close to its host star to allow for strong interaction (dense stellar wind, strong stellar magnetic field).","c) The planet should be located close to its host star to allow for strong interaction (dense stellar wind, strong stellar magnetic field)."
 Only of the known exoplanets are located within 0.1 AU of their host star., Only of the known exoplanets are located within 0.1 AU of their host star.
" By multiplying these probabilities, one finds that close (s€50 pc), heavy (My> 2.0Μ1). close-in (d€0.1 AU) planets would represent (5 15 of 197 planets) of the current total if the probabilities for the three conditions were independent."," By multiplying these probabilities, one finds that close $s \le 50$ pc), heavy $M\p \ge 2.0 M\J$ ), close-in $d \le 0.1$ AU) planets would represent $\approx$ 15 of 197 planets) of the current total if the probabilities for the three conditions were independent."
" However, this is not the case."," However, this is not the case."
" In the current census of exoplanets, a correlation between planetary mass and orbital distance is clearly evident, with a lack of close-in massive planets (seee.g.Udryetal., 2003)."," In the current census of exoplanets, a correlation between planetary mass and orbital distance is clearly evident, with a lack of close-in massive planets \citep[see e.g.][]{Udry03}."
". This is not a selection effect, as massive close-in planets should be easier to detect than low-mass planets."," This is not a selection effect, as massive close-in planets should be easier to detect than low-mass planets."
" This correlation was explained by the stronger tidal interaction effects for massive planets, leading to a faster decrease of the planetary orbital radius until the planet reaches the stellar Roche limit and is effectively destroyed (Pátzold&Rauer,2002;Jiangetal.,2003)."," This correlation was explained by the stronger tidal interaction effects for massive planets, leading to a faster decrease of the planetary orbital radius until the planet reaches the stellar Roche limit and is effectively destroyed \citep{Paetzold02,Jiang03}."
". Because of this mass-orbit correlation, the fraction of good candidates is somewhat lower (approx. 2%,,"," Because of this mass-orbit correlation, the fraction of good candidates is somewhat lower (approx. ,"
 namely 3 of, namely 3 of
the hot interior plasma gradually become uniform through thermal conduction (e.g. Coxetal.(1909))) or evolution in a medium with a density eracicnt viewed along the line of sight (Petruk2001).,the hot interior plasma gradually become uniform through thermal conduction (e.g. \citet {b10}) ) or evolution in a medium with a density gradient viewed along the line of sight \citep {b26}.
. Phe evaporation moclel requires dense clouds. the thermal conduction mocdoel requires a relatively high density ambient medium.," The evaporation model requires dense clouds, the thermal conduction model requires a relatively high density ambient medium."
 CTD 37X is located. in a region of greatly varving density. with OLL maser sources indicating interaction with molecular clouds.," CTB 37A is located in a region of greatly varying density, with OH maser sources indicating interaction with molecular clouds."
 In this τοσα]. the center-filled N-ray morphology of CPB 37 is consistent with evaporating clouds model.," In this regard, the center-filled X-ray morphology of CTB 37A is consistent with evaporating clouds model."
" The racial temperature variation in the plasma of CPB 387A (E, ~ 0.6-0.8 keV) is consistent with other MM SNRs such as W4E al.1994:Shelton.IXuntz&Petre 2004).. 3€391. Petre1996:Chenetal.2004) and 221 (Pannutiοἱal. 2010)."," The radial temperature variation in the plasma of CTB 37A $kT_{\rm e}$ $\sim$ 0.6-0.8 keV) is consistent with other MM SNRs such as W44 \citep {b29,b21}, 3C391 \citep {b32,b33} and HB21 \citep {b27}."
. Verv small temperature variation in the plasma of CPB 37A as shown Fig., Very small temperature variation in the plasma of CTB 37A as shown Fig.
 4 can be explained by both evaporation and thermal conduction models., 4 can be explained by both evaporation and thermal conduction models.
 Future deep X-rav observations and. detailed: spectral. analysis of this remnant would give more detailed information to compare with theoretical models that produce MM SNRs., Future deep X-ray observations and detailed spectral analysis of this remnant would give more detailed information to compare with theoretical models that produce MM SNRs.
 The X-rav emission of CPB 37A is dominated by thermal emission. that can be best deseribed by an absorbed CLE plasma moclel (VMEIAL) with an absorbing column density of Ng~35107 em7?7. an electron temperature of Kk.0.6 keV. and solar abunclances of Mg. Si. S. and. Ar. which indicate a shocked interstellar/cireumstellar material origin.," The X-ray emission of CTB 37A is dominated by thermal emission that can be best described by an absorbed CIE plasma model (VMEKAL) with an absorbing column density of $N_{\rm H}\sim
3\times10^{22}$ $\rm cm^{-2}$, an electron temperature of $kT_{\rm
e}\sim0.6$ keV, and solar abundances of Mg, Si, S, and Ar, which indicate a shocked interstellar/circumstellar material origin."
 For full ionization equilibrium. the ionization timescale. T=qnd. ds required. to be 1077 cem s. where t is the plasma age or the time since the gas was shock-heated (Masa19:S4)..," For full ionization equilibrium, the ionization timescale, $\tau=n_{\rm e}t$, is required to be $\geq$ $10^{12}$ $\rm
cm^{-3}$ s, where t is the plasma age or the time since the gas was shock-heated \citep {b14}."
 To determine the age of the remnant. n. should. be estimated. from the emission. measure. n.ngl. which is related to the normalization of the VMERAL model according. to the equation.. normrnmgl: (παΩΙ lo). where V is the N-rav. emitting volume. ay is the volume density of hydrogen. and diis the distance.," To determine the age of the remnant, $n_{\rm e}$ should be estimated from the emission measure, $n_{\rm
e}n_{\rm H}V$, which is related to the normalization of the VMEKAL model according to the equation, $n_{\rm e}n_{\rm H}
V$ $4\pi d^{2}$$10^{14}$ ), where V is the X-ray emitting volume, $n_{\rm H}$ is the volume density of hydrogen and d is the distance."
 For simplicity. we assumed. the emitting region to be a sphere of radius 5.5 arcmin.," For simplicity, we assumed the emitting region to be a sphere of radius 5.5 arcmin."
 Considering the possibility that less than the entire volume is filled. we write the volume V=\if. where Vo is the full spherical volume. f is the filling factor.," Considering the possibility that less than the entire volume is filled, we write the volume $V_{\rm
s}f$, where $V_{\rm s}$ is the full spherical volume, $f$ is the filling factor."
 We then carry the f factor through our calculations to show the explicit depencenee of each derived. quantity on this factor., We then carry the $f$ factor through our calculations to show the explicit dependence of each derived quantity on this factor.
" Knowing that the SNR is at a clistanee of 11.3 kpc and n,=L2ng. we estimated the emission. volume to be VoGTs107 emt."," Knowing that the SNR is at a distance of 11.3 kpc and $n_{\rm e}=1.2n_{\rm H}$, we estimated the emission volume to be $V\sim 6.7\times10^{59}f$ ${\rm cm^{3}}$."
 Consequently. we find an ambient eas density of ~Lff.EU? em* and age of —3«101f? vr (assuming n.d~1107 em. 3s). implving that CPB 37A is a midcdle-aged SNR.," Consequently, we find an ambient gas density of $\sim$ $f^{-1/2}$ ${\rm cm}^{-3}$ and age of $\sim$$3\times10^{4}f^{1/2}$ yr (assuming $n_{\rm e}t\sim 1\times10^{12}$ $\rm cm^{-3}$ s), implying that CTB 37A is a middle-aged SNR."
 Finally. we caleulated total mass of the X-ray emitting plasma. Ale. bv ManmgncV530/72AL. where mg is mass of a hydrogen atom. (/0.604 is the mean atomic weight.," Finally, we calculated total mass of the X-ray emitting plasma, $M_{\rm x}$, by $M_{\rm
x}$ $m_{\rm H}n_{\rm e}V$$\sim 530 f^{1/2}{M\sun}$, where $m_{\rm
H}$ is mass of a hydrogen atom, $\mu$ =0.604 is the mean atomic weight."
 The Suzaku X-ray spectral. data of CPB 37A. is. well fitted. with a thermal component and. an additional hard component., The Suzaku X-ray spectral data of CTB 37A is well fitted with a thermal component and an additional hard component.
 “Phere could be a few reasons for the hard. X-ray emision: (i) an association with a classical voung pulsar. (ii) a contribution from an extended non-thermal X-ray source (CNOU J171419.8-383023). (iii) overionization of the plasma which produces excess hard emission as has been the case [or IC443 (Yamaguchietal.2009).," There could be a few reasons for the hard X-ray emision: (i) an association with a classical young pulsar, (ii) a contribution from an extended non-thermal X-ray source (CXOU J171419.8-383023), (iii) overionization of the plasma which produces excess hard emission as has been the case for IC443 \citep {b60}."
. The hard. component is well fitted by a PL model with a photon index value of 71.6., The hard component is well fitted by a PL model with a photon index value of $\sim$ 1.6.
 This value is consistent with that of classical voung pulsar value ranging in between 1.1 and 1.7 (Chakrabartyetal.2001)., This value is consistent with that of classical young pulsar value ranging in between 1.1 and 1.7 \citep {b37}.
. However. there is no pulsar reported that. is associated with this remnant.," However, there is no pulsar reported that is associated with this remnant."
" In the Northwest region of the CPB 37X. an extended non-thermal X-ray source (CXOU J171419.8-383023) is reported. (RA(2000))=πα Dee.(2000)--38°30°20"") by Abaronianetal.(2008)."," In the Northwest region of the CTB 37A, an extended non-thermal X-ray source (CXOU J171419.8-383023) is reported $\rmn{RA}(2000)=17^{\rmn{h}} 14^{\rmn{m}} 20^{\rmn{s}}$, $\rmn{Dec.}~(2000)=-38\degr 30\arcmin 20\arcsec$ ) by \citet {b20}."
. In their work. a non-thermal emission. from the source with vspectral index of ~1.32 is found. which is lower (harder) mn our best-fitting value of ~1.6.," In their work, a non-thermal emission from the source with a spectral index of $\sim$ 1.32 is found which is lower (harder) than our best-fitting value of $\sim$ 1.6."
 Although we excluclec ο.'NOU J171419.8-383023 (with racüus 2.1 arcmin) from our spectra during our spectral analvsis. our fits required. a non-thermal component.," Although we excluded CXOU J171419.8-383023 (with radius $2.1$ arcmin) from our spectra during our spectral analysis, our fits required a non-thermal component."
 To investigate this. we performed μα»ectral analysis also for individual regions by selecting gamall rectangular regions that are being further away [rom 10 known extended: non-thermal source.," To investigate this, we performed spectral analysis also for individual regions by selecting small rectangular regions that are being further away from the known extended non-thermal source."
 The non-thermal ux is found to be stronger for the selected small regions nearby the source compared to the ones further away., The non-thermal flux is found to be stronger for the selected small regions nearby the source compared to the ones further away.
" We rave obtained an unabsorbed flux value of ky~I410."" erg stem7 for the non-thermal extended. source in the 10 keV energy range."," We have obtained an unabsorbed flux value of $F_{\rm
x}\sim1.4\times10^{-9}$ erg $\rm s^{-1}$$\rm cm^{-2}$ for the non-thermal extended source in the $-$ 10 keV energy range."
 When we compare it with the unabsorbed Hux value (FX~0.14.10 “eres tem7) o£ PL component of best-fitting. we find a factor of ten dillerence tween them.," When we compare it with the unabsorbed flux value $F_{\rm
x}\sim0.14\times10^{-9}$ erg $\rm s^{-1}$$\rm cm^{-2}$ ) of PL component of best-fitting, we find a factor of ten difference between them."
 This dillerence indicates that the extended source is most likely the origin of the PL component and emission scattered from the source into the field of the rest of he remnant by a broad. point spread function of theSuzaku mirrors., This difference indicates that the extended source is most likely the origin of the PL component and emission scattered from the source into the field of the rest of the remnant by a broad point spread function of the mirrors.
 The spectral studies of CPB 37 indicate that the Mdasma is best described by a thermal component in CLE condition with solar elemental abundances ancl a non-hermal component with a photon index of ~1.6., The spectral studies of CTB 37A indicate that the plasma is best described by a thermal component in CIE condition with solar elemental abundances and a non-thermal component with a photon index of $\sim$ 1.6.
 Thermal emission. possibly originates from. the shocked. interstellar material with ambient gas density of ~Lftem7., Thermal emission possibly originates from the shocked interstellar material with ambient gas density of $\sim$ $f^{-1/2}$${\rm cm^{-3}}$.
" The nest speetral [its require an ionization timescale of zz 107 ""RED. ≼∙⊔↓≻⊳∖⊳↓⊔↓↓≻⇂∙∖⇁↓⊔⋏∙≟⋜⋯⋜↧⋏∙≟⋖⋅∪⇂∿∆∫≻↓∪⇠∕ ⋅⋅ ⊥↝⊥⊐ vr."," The best spectral fits require an ionization timescale of $\tau\geq$ $10^{12}$ $\rm cm^{-3}$ s, implying an age of $\sim$ $\times10^{4}f^{1/2}$ yr."
 mThe originDa of he power-law component is more Likely the elleet of the contribution from the extended source (CXOU J171419.8-383023) located in the Northwest part of the remnant., The origin of the power-law component is more likely the effect of the contribution from the extended source (CXOU J171419.8-383023) located in the Northwest part of the remnant.
 CPB 31X is most likely anew member of mixed-morphology SNR., CTB 37A is most likely a new member of mixed-morphology SNR.
 We thank Dr. Patrick Slane for his valuable comments and sugeestions which helped to improve the overall quality of the manuscript., We thank Dr. Patrick Slane for his valuable comments and suggestions which helped to improve the overall quality of the manuscript.
 AS ids supported. by LUBBITTAN PostDoctoral Fellowship., AS is supported by TÜBBİTTAK PostDoctoral Fellowship.
 Vhis work is supported by the Akcdeniz University Scientific Research Project Management and by PUBBIPTAI under project codes 1081226. and 109092., This work is supported by the Akdeniz University Scientific Research Project Management and by TÜBBİTTAK under project codes 108T226 and 109T092.
 “Phe authors also acknowledge the support. by Bogaazicii University Research Foundation. under. 2010- Research Project Support (BAP) project no:5052., The authors also acknowledge the support by Boğaaziçii University Research Foundation under 2010-Scientific Research Project Support (BAP) project no:5052.
"For the 90 galaxies, which include 21 BCGs, we make a linear error-weighted fit of the form to the g—r colour profile over all annular bins from an inner radius 0.67 arcsec to the outer limit of the tabulated profile, usually 28 arcsec, each fit by eye.","For the 90 galaxies, which include 21 BCGs, we make a linear error-weighted fit of the form to the $g-r$ colour profile over all annular bins from an inner radius 0.67 arcsec to the outer limit of the tabulated profile, usually 28 arcsec, examining each fit by eye."
 Figure 5 shows the gradient examiningd(log“=2r) plotted against our colour gradient -;d—1., Figure 5 shows the gradient ${{d(g-r)}\over{d(\rm log~r)}}$ plotted against our colour gradient ${{{\rm r}_{eff}(g)}\over{{\rm r}_{eff}(r)}}-1$.
" It is clearly correlated with a linear correlation coefficient 0.768 and best fit relation 0.0119(+0.0038)—0.9398(--0.0336)x, passing very close to the origin as expected, but the scatter of 0.122 is rather large."," It is clearly correlated with a linear correlation coefficient 0.768 and best fit relation $-0.0119(\pm 0.0038)-0.9398(\pm 0.0336)x$, passing very close to the origin as expected, but the scatter of 0.122 is rather large."
" This is in part because a significant minority of the ellipticals have colour profiles not linear in log radius; we see non-monotonic gradients for about 1096 and in these cases, the rer ratio tends to be sensitive to the colour profile at a larger radius than the direct fit (which is weighted towards smaller radii where the error bars are smaller)."," This is in part because a significant minority of the ellipticals have colour profiles not linear in log radius; we see non-monotonic gradients for about $10\%$ and in these cases, the $r_{eff}$ ratio tends to be sensitive to the colour profile at a larger radius than the direct fit (which is weighted towards smaller radii where the error bars are smaller)."
" Despite this, BCGs and high and low luminosity E/S0s, considered separately (Figure 6), show similar relations between the two colour gradient measures."," Despite this, BCGs and high and low luminosity E/S0s, considered separately (Figure 6), show similar relations between the two colour gradient measures."
" However, the relation is much tighter for the BCGs with a scatter of only 0.053, compared to 0.123 (high L E/SO0) and 0.150 (low L E/S0)."," However, the relation is much tighter for the BCGs with a scatter of only 0.053, compared to 0.123 (high L E/S0) and 0.150 (low L E/S0)."
" a further test, we examine (Figure 7) the residuals of the2AS to the best-fit linearrelation, as a function of M, and ELAXEapparent refs (in the r-band); a significant trend could introduce a bias into the investigations of this paper."," As a further test, we examine (Figure 7) the residuals of the ${{d(g-r)}\over{d(\rm log~r)}}$ to the best-fit linearrelation, as a function of $M_r$ and apparent $r_{eff}$ (in the $r$ -band); a significant trend could introduce a bias into the investigations of this paper."
 We find the scatter tends to increase at lower luminosity but there is not an obvious systematic trend., We find the scatter tends to increase at lower luminosity but there is not an obvious systematic trend.
" Neither do we see a trend with apparent radius, down to about 1.8 arcsec."," Neither do we see a trend with apparent radius, down to about 1.8 arcsec."
" However, for galaxies smaller than this radius the scatter increases greatly and asymmetrically, which is probably unacceptable for our purposes."," However, for galaxies smaller than this radius the scatter increases greatly and asymmetrically, which is probably unacceptable for our purposes."
 For galaxies with Teff«1.8 arcsec it may not be possible to meaningfully characterize the colour gradient at all using SDSS data., For galaxies with $r_{eff}<1.8$ arcsec it may not be possible to meaningfully characterize the colour gradient at all using SDSS data.
" For early-type galaxies of larger apparent size, including the BCGs, the ratio of de Vaucoleurs radii does appear to be a valid, consistent and approximately linear colour gradient measure."," For early-type galaxies of larger apparent size, including the BCGs, the ratio of de Vaucoleurs radii does appear to be a valid, consistent and approximately linear colour gradient measure."
" Returning to Figure 5, if all repr<1.8 arcsec galaxies are excluded, leaving 51, the best-fit linear relation changes only slightly to —0.0089(+0.0039)—0.8736(2:0.0346)z, but the scatter is decreased by more than a factor of two to a much more acceptable 0.056 (similar to the scatter for BCGs only), and the correlation coefficient is increased to 0.862."," Returning to Figure 5, if all $r_{eff}<1.8$ arcsec galaxies are excluded, leaving 51, the best-fit linear relation changes only slightly to $-0.0089(\pm 0.0039) -0.8736(\pm 0.0346)x$, but the scatter is decreased by more than a factor of two to a much more acceptable 0.056 (similar to the scatter for BCGs only), and the correlation coefficient is increased to 0.862."
 Some galaxies in our sample have very strong (> 0.5) or inverted (« 0) colour gradients (ie. rerg(g)«rer f(7))-, Some galaxies in our sample have very strong $>0.5$ ) or inverted $<0$ ) colour gradients (i.e. ${\rm r}_{eff}(g)<{\rm r}_{eff}(r)$ ).
" Examining some of these, we find that some are galaxies confused with or very close to (red or blue) stars, and that there are also some misclassified spirals present, despite our strict selection criterion of fracpey=1 in both g and r."," Examining some of these, we find that some are galaxies confused with or very close to (red or blue) stars, and that there are also some misclassified spirals present, despite our strict selection criterion of $frac_{Dev}=1$ in both $g$ and $r$."
" To reduce any biases that these types of objects may introduce, we exclude some galaxies from the colour gradient analysis."," To reduce any biases that these types of objects may introduce, we exclude some galaxies from the colour gradient analysis."
" Firstly we excluded the objects with gradients (i.e. Tepf(g)f(r)— 1) calculated as <—0.5 or > 1, far out of the normal rangereg (there were only 130/70378)."," Firstly, we excluded the objects with gradients (i.e. ${{{\rm r}_{eff}(g)}\over {{\rm r}_{eff}(r)}}-1$ ) calculated as $<-0.5$ or $>1$ , far out of the normal range (there were only 130/70378)."
" Secondly, we examined"," Secondly, we examined"
at the surface of a ueutrou star. Le.. less than a few huudred Hz.,"at the surface of a neutron star, i.e., less than a few hundred Hz."
 It is inportaut to uote that [or larger spin frequeucies. the ellipticity of the neutron stars induced by the rotation can be as large as 0.3. dependiug ou the equation of state (Cook et 1199[). vielkdiug an additioual broadeniug as large as 215S," It is important to note that for larger spin frequencies, the ellipticity of the neutron stars induced by the rotation can be as large as 0.3, depending on the equation of state (Cook et 1994), yielding an additional broadening as large as $\simeq 15$."
 Iu the calculations presented here. we show for clarity euission lines: absorption lines are allectecd in the same way due to the linear character of the equatious.," In the calculations presented here, we show for clarity emission lines; absorption lines are affected in the same way due to the linear character of the equations."
 Moreover. for numerical reasOns. we asstune an intrinsic fractional line width of 0.01. which is much sinaller than the Doppler width for the cases shown here.," Moreover, for numerical reasons, we assume an intrinsic fractional line width of $0.01$, which is much smaller than the Doppler width for the cases shown here."
 Finally. we assume that the observer is on the rotational equator of the star in order to show the maximum rotational effects.," Finally, we assume that the observer is on the rotational equator of the star in order to show the maximum rotational effects."
 The line profiles imeasurecl at infinity coming from the surface of a 1.LAL..10 km neutron star are shown in Figure 1 for different values of the spin frequency.," The line profiles measured at infinity coming from the surface of a $1.4 M_\odot, 10$ km neutron star are shown in Figure 1 for different values of the spin frequency."
 As the spin frequency is increased. the lines become weaker aud broader. aud their peak emission shifts towards larger energies.," As the spin frequency is increased, the lines become weaker and broader, and their peak emission shifts towards larger energies."
 Lu this, In this
source conünuum. the less extended it appears to be.,"source continuum, the less extended it appears to be."
 The II5 components also decrease in intensity with distance., The $_2$ components also decrease in intensity with distance.
" This behavior could be explained by the cooling. decreased excitation and expansion of ""packets"" of gas as they. travel away from the source."," This behavior could be explained by the cooling, decreased excitation and expansion of “packets” of gas as they travel away from the source."
 A decrease in gas density and excitation temperature is inferred from the excitation analvsisof (2005)., A decrease in gas density and excitation temperature is inferred from the excitation analysisof \citet{tak05}.
. A similar trend is also seen in small-scale jets from T Tauri stars 2002).," A similar trend is also seen in small-scale jets from T Tauri stars \citep{bac00,woi02}."
. Directly behind a fast-moving shock the very hot (T~10*—10? IX) post shock gas will raciativelv cool very rapidly. before the region has (ime to expand.," Directly behind a fast-moving shock the very hot $T \sim
10^3-10^5$ K) post shock gas will radiatively cool very rapidly, before the region has time to expand."
 However. the bulk of the nualerial in the gas packet.behind (he shock Ivont working surface. may expand adiabatically.," However, the bulk of the material in the gas packet, the shock front working surface, may expand adiabatically."
 If the pressure inside (he warm (Z7100 IX) eas packet approaches (hat of the surrounding nedium as it expands. decreasing bv a [actor of 710-100. and if at (he same time the eas temperature in the packet decreases by a factor of 3-10 as it travels a distance of a ew arcseconds (equivalent to the inter-knot spacing). then the packet might be expected to increase in volume by a factor of 1-30. or in diameter by a factor of 1-3.," If the pressure inside the warm $T
\sim 100$ K) gas packet approaches that of the surrounding medium as it expands, decreasing by a factor of $\sim$ 10-100, and if at the same time the gas temperature in the packet decreases by a factor of 3-10 as it travels a distance of a few arcseconds (equivalent to the inter-knot spacing), then the packet might be expected to increase in volume by a factor of 1-30, or in diameter by a factor of 1-3."
 Isothermal expansion would result in greater expansion. while a lower pressure gradient would suppress expansion.," Isothermal expansion would result in greater expansion, while a lower pressure gradient would suppress expansion."
 Either way. the ratio ispotentially consistent with (he relative sizes of the Ile components in Table ..," Either way, the ratio ispotentially consistent with the relative sizes of the $_2$ components in Table \ref{table1}."
 By comparing theVLT data with the earlier observations of Takamietal.(2005) we ean measure. or at least set upper limits on. the proper motions (PM) of the [Fe ΠΠ] and IH» components.," By comparing the data with the earlier observations of \citet{tak05} we can measure, or at least set upper limits on, the proper motions (PMs) of the [Fe ] and $_2$ components."
 The observations. although at higher spectral resolution (12 L.1x 107). were not obtained with AO correction.," The observations, although at higher spectral resolution $R\sim1.1\times10^4$ ), were not obtained with AO correction."
" However. theSubaru pixel scale (£0.002"")) does [fullv sample the seeing and the same slit position angle (159°) was used with both instruments."," However, the pixel scale $\pm$ )) does fully sample the seeing and the same slit position angle ) was used with both instruments."
 Offsets of emission features along the jet axis can therefore be measured accurately aud a direct comparison made between the and observations (see Table 2))., Offsets of emission features along the jet axis can therefore be measured accurately and a direct comparison made between the and observations (see Table \ref{table2}) ).
" Note. however. that the Subaru slit was slightly wider than the slit: vversus 0.172"".."," Note, however, that the slit was slightly wider than the slit; versus ."
Fig.3 presents the V—(BV) color-magnitude diagram for horizontal branch of w Cen.,3 presents the $V-(B\!-\!V)$ color-magnitude diagram for horizontal branch of $\omega$ Cen.
 It is worth noting that RRe and RR«b regions overlap significantly., It is worth noting that $c$ and $ab$ regions overlap significantly.
 There is a clear scatter in mean V magnitude of the horizontal branch stars. which is most likely caused by differences in their chemical composition.," There is a clear scatter in mean $V$ magnitude of the horizontal branch stars, which is most likely caused by differences in their chemical composition."
 It is known that stars of ω Cen can differ in metallicity by factor of up to 100 (Sollima et al., It is known that stars of $\omega$ Cen can differ in metallicity by factor of up to 100 (Sollima et al.
 2005)., 2005).
 Six double mode variables discussed in the previous section are displayed with filled triangles., Six double mode variables discussed in the previous section are displayed with filled triangles.
 Because they are strongly dominated by the first overtone. we will compare them with the RRc stars.," Because they are strongly dominated by the first overtone, we will compare them with the $c$ stars."
 Five of the double mode variables are located on the cooler side of the RRe region. but without any significant trend or clumping.," Five of the double mode variables are located on the cooler side of the $c$ region, but without any significant trend or clumping."
 The clear exception is V350. which seems to be as red as the redest fundamental mode pulsators.," The clear exception is V350, which seems to be as red as the redest fundamental mode pulsators."
 This variable is a new detection made by Kaluzny et al. (, This variable is a new detection made by Kaluzny et al. (
2004) with the image subtraction technique.,2004) with the image subtraction technique.
 It is located in a very crowded region. where significant blending can affect both mean magnitude of the star and its color.," It is located in a very crowded region, where significant blending can affect both mean magnitude of the star and its color."
 Typical period-amplitude diagram for RR Lyr. stars of a globular cluster shows roughly linear trend for RRab stars. with smaller amplitudes at longer periods. and a clump of RRe stars with no clear structure.," Typical period-amplitude diagram for RR Lyr stars of a globular cluster shows roughly linear trend for $ab$ stars, with smaller amplitudes at longer periods, and a clump of $c$ stars with no clear structure."
 Some investigators try to divide this clump by amplitude into two subgroups. containing second and first overtone pulsators. respectively Clement Rowe 2000).," Some investigators try to divide this clump by amplitude into two subgroups, containing second and first overtone pulsators, respectively Clement Rowe 2000)."
 This is not well justified. as the shortest period first overtone pulsators can have very small amplitudes as well (Bono et al.," This is not well justified, as the shortest period first overtone pulsators can have very small amplitudes as well (Bono et al."
 1997)., 1997).
 The period-amplitude diagram for RR Lyr stars of co Cen is shown in Fig.4., The period-amplitude diagram for RR Lyr stars of $\omega$ Cen is shown in 4.
 The double mode pulsators are plotted with filled triangles., The double mode pulsators are plotted with filled triangles.
 All of them are located firmly among RRe variables., All of them are located firmly among $c$ variables.
 We note. however. that they all have high pulsation amplitudes. one of the highest among overtone pulsators.," We note, however, that they all have high pulsation amplitudes, one of the highest among overtone pulsators."
 Fourier coefficients (amplitudes Aj. amplitude ratios A;; and phase differences d;j) could be used to characterize the shape of the pulsation light curves and to discriminating between different modes of pulsation.," Fourier coefficients (amplitudes $A_j$, amplitude ratios $R_{ij}$ and phase differences $\phi_{ij}$ ) could be used to characterize the shape of the pulsation light curves and to discriminating between different modes of pulsation."
 We decided to compare Fourier coefficients of our six double mode variables with those of the RRe pulsators., We decided to compare Fourier coefficients of our six double mode variables with those of the $c$ pulsators.
 The results are shown in 5., The results are shown in 5.
 In all cases. the position of the double mode stars is typical for RRe variables. without any trend or clumping.," In all cases, the position of the double mode stars is typical for $c$ variables, without any trend or clumping."
 It confirms conclusions which could be drawn form the visual inspection of the light curves of the variables., It confirms conclusions which could be drawn form the visual inspection of the light curves of the variables.
 They look quite typical for RRe stars. without any significant pecularity. indicating that influence of the seconadry mode is weak and this mode does not affect the global shape of the light curve.," They look quite typical for $c$ stars, without any significant pecularity, indicating that influence of the seconadry mode is weak and this mode does not affect the global shape of the light curve."
 The only surprising thing is large pulsation amplitude which was mentioned in the previous paragraph., The only surprising thing is large pulsation amplitude which was mentioned in the previous paragraph.
 Systematic. frequency analysis of RR Lyr. stars of globular cluster c) Cen resulted in discovery of six RRc variables. which in addition to the dominant first radial overtone. display also a weak secondary mode of higher frequency.," Systematic frequency analysis of RR Lyr stars of globular cluster $\omega$ Cen resulted in discovery of six $c$ variables, which in addition to the dominant first radial overtone, display also a weak secondary mode of higher frequency."
 These are the first double mode RR Lyr stars identified in this cluster., These are the first double mode RR Lyr stars identified in this cluster.
 In variable V10 the most probable period ratio of the two modes is 0.80., In variable V10 the most probable period ratio of the two modes is 0.80.
 This value points towards pulsations in the first and second radial overtones., This value points towards pulsations in the first and second radial overtones.
 In three other stars. the period ratios are either ~0.80 or ~0.61. depending on the choice of aliases.," In three other stars, the period ratios are either $\sim\! 0.80$ or $\sim\! 0.61$, depending on the choice of aliases."
 Finally. in the last two stars (V19 and V105) an unambiguous period ratio of 0.61 was found.," Finally, in the last two stars (V19 and V105) an unambiguous period ratio of 0.61 was found."
 Such a period ratio cannot be explained by two radial modes. which implies that the secondary mode must be nonradial Moskalik Kolaezkowski 2009 for discussion of this point).," Such a period ratio cannot be explained by two radial modes, which implies that the secondary mode must be nonradial Moskalik aczkowski 2009 for discussion of this point)."
 Thus. V19 and V105 belong to a new class of double mode RR Lyr pulsators.," Thus, V19 and V105 belong to a new class of double mode RR Lyr pulsators."
 We recall. that a similar period ratio of ~0.61 was also discovered in the LMC first overtone Cepheids (Moskalik Kolaezkowski 2008: Soszyfisski et al.," We recall, that a similar period ratio of $\sim\! 0.61$ was also discovered in the LMC first overtone Cepheids (Moskalik aczkowski 2008; Soszyńsski et al."
 2008) and in the field double mode RR Lyr star AQ Leo (Gruberbauer et al., 2008) and in the field double mode RR Lyr star AQ Leo (Gruberbauer et al.
 2007)., 2007).
 Discovery of RR Lyr stars pulsating in the first and second overtones has been claimed previously in the LMC (Alcock et al., Discovery of RR Lyr stars pulsating in the first and second overtones has been claimed previously in the LMC (Alcock et al.
 2000)., 2000).
 However. Soszynisski et al. (," However, Soszyńsski et al. ("
2003) have shown. that all these objects are about mag brighter thàn typical RR Lyr stars in the LMC. and suggested that they might be short-pertod Cepheids instead.,"2003) have shown, that all these objects are about mag brighter than typical RR Lyr stars in the LMC, and suggested that they might be short-period Cepheids instead."
 In contrast. all six double mode variables discovered in ω Cen belong to the RR Lyr population of the cluster without any doubt.," In contrast, all six double mode variables discovered in $\omega$ Cen belong to the RR Lyr population of the cluster without any doubt."
 Thus. VIO is the first solid candidate for the FO/SO double mode RR Lyr pulsator.," Thus, V10 is the first solid candidate for the FO/SO double mode RR Lyr pulsator."
Two of the major new insights of the 1990s into cosmology and the history of galaxy formation were the discovery of the Cosmic. Infrared. Background. (CIB: Puget ct al..,"Two of the major new insights of the 1990s into cosmology and the history of galaxy formation were the discovery of the Cosmic Infrared Background (CIB: Puget et al.,"
 1996: Lixsen et aL.," 1996; Fixsen et al.,"
 1998) and the measurement of a significant dark energv term. in the expansion of the universe through the use of high redshift tvpe la supernovae as standard candles (Riess et al.," 1998) and the measurement of a significant 'dark energy' term in the expansion of the universe through the use of high redshift type 1a supernovae as standard candles (Riess et al.,"
 1998. HZT: Perlmutter et al.," 1998, HZT; Perlmutter et al.,"
 1999. SCP).," 1999, SCP)."
 The discovery of the CLB indicated. that dust enshrouded star formation is a significant aspect of the star formation history of the universe. amounting to or more of all star formation (Gispert et al..," The discovery of the CIB indicated that dust enshrouded star formation is a significant aspect of the star formation history of the universe, amounting to or more of all star formation (Gispert et al.,"
 2000)., 2000).
 At the same time surveys with SCUBA (ee., At the same time surveys with SCUBA (eg.
 Small et al..," Smail et al.,"
 LOOT: Hughes et al.," 1997; Hughes et al.,"
 1998: Eales et abl.," 1998; Eales et al.,"
 2000: Mortier et. al..," 2000; Mortier et al.,"
 2005) and other submillimetre array detectors have begun to find the objects that make up the CLB., 2005) and other submillimetre array detectors have begun to find the objects that make up the CIB.
 These objects are [largely interpreted as being similar to local Ultraluminous Infrared Galaxies (ULIICGs). and are thought to contain large dust masses at a temperature T-40Ilx. (Blain et al.," These objects are largely interpreted as being similar to local Ultraluminous Infrared Galaxies (ULIRGs), and are thought to contain large dust masses at a temperature $\sim$ 40K (Blain et al.,"
 1999) and to be the hosts of massive bursts of star formation. 1001000AZ.yr ," 1999) and to be the hosts of massive bursts of star formation, $100-1000 M_{\odot} yr^{-1}$ ."
Llowever. substantial uncertainties remain.," However, substantial uncertainties remain."
 Most. of these submillimetre galaxies (SAIGs) do not have well determined redshifts (hough see Chapman et al..," Most of these submillimetre galaxies (SMGs) do not have well determined redshifts (though see Chapman et al.,"
 2005)., 2005).
 The degeneracy between. temperature ancl redshift. (Blain 1999) thus means that their dust. temperature is. highly uncertain a low dust temperature object at low recishift (z~0.5r1) looks much the same as a high cust temperature object at high redshift (z~ 23)., The degeneracy between temperature and redshift (Blain 1999) thus means that their dust temperature is highly uncertain — a low dust temperature object at low redshift $\sim$ 0.5—1) looks much the same as a high dust temperature object at high redshift $\sim$ 2—3).
 Since Luminosity is a strong power of temperature. typically 2° for a standard SMCG spectral energy. distribution (SED). this leads to a considerable uncertainty in the cerivect Luminosity anc star formation rates for those SALGs without measured redshilts.," Since luminosity is a strong power of temperature, typically $T^6$ for a standard SMG spectral energy distribution (SED), this leads to a considerable uncertainty in the derived luminosity and star formation rates for those SMGs without measured redshifts."
 Indeed some authors have suggested (Rowan-Robinson 2001. ]xaviani ct al.," Indeed some authors have suggested (Rowan-Robinson 2001, Kaviani et al."
 2003. Efstathiou Rowan-Robinson. 2008) that a substantial fraction of the SMG population may be cooler and closer than originally thought. and there is some observational evidence to back up," 2003, Efstathiou Rowan-Robinson, 2003) that a substantial fraction of the SMG population may be cooler and closer than originally thought, and there is some observational evidence to back up"
we adopt as the systeuatic uncertainty in Quaoars size measureimen due to our assumption about its unknown hall-lieht diameter.,we adopt as the systematic uncertainty in Quaoar's size measurement due to our assumption about its unknown half-light diameter.
 Adding in quadrature this uncertaiuty. aud the random aud remaining systermalic uncertainties in the Hubble measurement. the total uncertainty iu Quaoar's diameter is. or 115 kin.," Adding in quadrature this uncertainty, and the random and remaining systematic uncertainties in the Hubble measurement, the total uncertainty in Quaoar's diameter is, or $115$ km."
 Unlike the size iuferred from adopting a lambert profile. the corrected size measuremet tis compatible with both Spitzer size measure:jents. leucine confidence in those measurements aic our use of the icy satellites as proxies for QuaoarW. surface.," Unlike the size inferred from adopting a lambert profile, the corrected size measurement is compatible with both Spitzer size measurements, lending confidence in those measurements and our use of the icy satellites as proxies for Quaoar's surface."
 We adopt as a size of Quaoar. the weighted average of tie Spitzer and corrected HST estu—es. Douavar=890-5TO kin.," We adopt as a size of Quaoar, the weighted average of the Spitzer and corrected HST estimates, $D_{\rm{Quaoar}} = 890 \pm 70$ km."
 The adopted size ancl inferred mass of Quaoar imply that Quaoar’s density is ?. , The adopted size and inferred mass of Quaoar imply that Quaoar's density is $\rho = 4.2\pm1.3 \dense$ .
This is only mareinally compatible with the density of the next most dense Ixuiper belt object. Haumea (Rabinowitzetal.2006:Lacerda&Jewitt2007) aud we conclude that Quaoar is likely the most deuse Ixuiper belt object currently knowu.," This is only marginally compatible with the density of the next most dense Kuiper belt object, Haumea \citep{Rabinowitz2006,Lacerda2007} and we conclude that Quaoar is likely the most dense Kuiper belt object currently known."
 Quaoar's unusually high density implies that this Ixuiper belt object has little ice content., Quaoar's unusually high density implies that this Kuiper belt object has little ice content.
 A thin veneer of surface ice is required. [or Quaoar to exhibit its absorption leatures indicative of water. methane. aud ethane ices (Jewitt&Luu2001:SchallerBrown2007).," A thin veneer of surface ice is required for Quaoar to exhibit its absorption features indicative of water, methane, and ethane ices \citep{Jewitt2004,Schaller2007}."
. But this ice cannot be a substautial compouerit ofthe bodys mass., But this ice cannot be a substantial component of the body's mass.
 Quaoar's high density is reminiscent of the asteroid belt., Quaoar's high density is reminiscent of the asteroid belt.
 It may be possible that. in the early Solar system. duriug some dynamical event. such as tte migration of Jupiter. a series of scattering events eimplaced. asteroids iuto the Ixuiper belt regior.," It may be possible that, in the early Solar system, during some dynamical event, such as the migration of Jupiter, a series of scattering events emplaced asteroids into the Kuiper belt region."
 Indeed. it has been shown that migration can emplace Ixuiper belt «)bjeets in the stable asteroid belt region (Levisouetal.2009).," Indeed, it has been shown that migration can emplace Kuiper belt objects in the stable asteroid belt region \citep{Levison2009}."
. Thus it seetus possible that the reverse process could occur sug:Dmyesting that Quaoar might ouce lave been an asteroid which lost tle majoriv of its ice content cdi eto rapid sublimation from Solar insolation. or never had a substantia ice Content. and was scatteος onto its Current orbit.," Thus it seems possible that the reverse process could occur suggesting that Quaoar might once have been an asteroid which lost the majority of its ice content due to rapid sublimation from Solar insolation, or never had a substantial ice content, and was scattered onto its current orbit."
 [t is also possible that Quaoar's high density is collisionally produced., It is also possible that Quaoar's high density is collisionally produced.
 The stall satellites of the largest Ixuiper belt οjects. which presumably Lo1ued through massive collisions. appear icy (Marcialisetal.1957:Ba‘ume2006:Fraser&Brown2009).. cousistent with the idea that the satellites are ejected maerial from the ice surface layers of large differentiated: parent bodies.," The small satellites of the largest Kuiper belt objects, which presumably formed through massive collisions, appear icy \citep{Marcialis1987,Barkume2006,Fraser2009b}, consistent with the idea that the satellites are ejected material from the ice surface layers of large differentiated parent bodies."
 Presumably. the resultau density of the remainine body is a function of the inipact. properties fimpact augle. velocity. e.," Presumably, the resultant density of the remaining body is a function of the impact properties (impact angle, velocity, etc.)."
 Given the lack of uuderstauding of large-scale collisious. it. may be possible that with a particular impact scenario. a collision can strip nearly of the surface laver of a parent body. leaving the rocky-core that is Quaoar virtually intact.," Given the lack of understanding of large-scale collisions, it may be possible that with a particular impact scenario, a collision can strip nearly of the surface layer of a parent body, leaving the rocky-core that is Quaoar virtually intact."
 Weywot’s orbit is clifficilt to explain with a collisional genesis., Weywot's orbit is difficult to explain with a collisional genesis.
 Ejecta form disks from which a satellite might coalesce., Ejecta form disks from which a satellite might coalesce.
 The satellite then tidally evolves outwards on a circular orbit rather than the elliptical orbit of Weywot., The satellite then tidally evolves outwards on a circular orbit rather than the elliptical orbit of Weywot.
demonstrates that the same basic phenomenon acts to alien periceuters as well.,demonstrates that the same basic phenomenon acts to align pericenters as well.
 Thus Collisions can indeed align pericenters aud nodes. provided the collisions are frequent. (aud lossy) enough. and provided the particles rmaiutaiu some finite (free) eccentricity aud πομα1ο.," Thus collisions can indeed align pericenters and nodes, provided the collisions are frequent (and lossy) enough, and provided the particles maintain some finite (free) eccentricity and inclination."
 The requirement that collisious are frequent enough to align pericenters is probably met for the Charming Rinelet., The requirement that collisions are frequent enough to align pericenters is probably met for the Charming Ringlet.
 While this ringlet has a low normal optical depth (roughly 10.7). the orbital period is sulliciently short (arouud 0.5 days) that the collisional timescale is still only a few years or decades. much less than the typical erosion timescales of thousauds of years (Burusefαἱ.2001).," While this ringlet has a low normal optical depth (roughly $^{-3}$ ), the orbital period is sufficiently short (around 0.5 days) that the collisional timescale is still only a few years or decades, much less than the typical erosion timescales of thousands of years \citep{BHS}."
. On the other hand. the persistance of the nonzero free eccentricities aud inclinations probably requires some moclifications to the individual particles’ dyuamics.," On the other hand, the persistance of the nonzero free eccentricities and inclinations probably requires some modifications to the individual particles' dynamics."
 If the particles equations of motion were just giveu by Eqs L7-- 060 above. dissipative collisious would (assuming the initial conditious were not highly asyiunetric) tend to produce a riuglet with €;=70.," If the particles' equations of motion were just given by Eqs \ref{heqm}- - \ref{qeqm} above, dissipative collisions would (assuming the initial conditions were not highly asymmetric) tend to produce a ringlet with $e_l=i_l=0$."
 Thus. we probably need to add some acdditioual terius to these equatious to produce something similar to the Charming Biuglet's observed shape.," Thus, we probably need to add some additional terms to these equations to produce something similar to the Charming Ringlet's observed shape."
 One relatively simple way to accomplish this is to add non-linear clamping terms iuto the equatious: where 55.55fÁ<<zxoO and |ryl.1ᾳ««[| quantify the magnitudeo of the dampingὃν terms.," One relatively simple way to accomplish this is to add non-linear damping terms into the equations: where $\gamma_h, \gamma_k << \dot{\varpi}'_o$ and $|\gamma_p|, |\gamma_q| << |\dot{\Omega}'_o|$ quantify the magnitude of the damping terms."
 These terms transform the [/.4] and [p.g] systems from simple harmonic oscillators iuto van der Pol oscillators (Baierlein1983).," These terms transform the $[h,k]$ and $[p,q]$ systems from simple harmonic oscillators into van der Pol oscillators \citep{Baierlein}."
. Such oscillators are characterized by a Limit evcle which the system will asyintotically approach no matter where it is started in [h.] and [p.q] space.," Such oscillators are characterized by a limit cycle which the system will asymtotically approach no matter where it is started in $[h,k]$ and $[p,q]$ space."
 These limit cycles are circles centered at [h.&]=|—65.0] and [p.q]=[0.tij] with radii of e; aud ij. and the orbit traces out the circles at rates given by a) aud OF.," These limit cycles are circles centered at $[h,k]=[-e_f,0]$ and $[p,q]=[0,\pm i_f]$ with radii of $e_l$ and $i_l$, and the orbit traces out the circles at rates given by $\dot{\varpi}'_o$ and $\dot{\Omega}'_o$."
 These equations of motion therefore cause auy particles orbit to evolve to tlie same path as the observed riuglet., These equations of motion therefore cause any particle's orbit to evolve to the same path as the observed ringlet.
 Ou their own. particles started at differeut. points iu pliase space will wind up at clifferent poiuts alone tliis evcle.," On their own, particles started at different points in phase space will wind up at different points along this cycle."
 However. if the relative motions amoue the particles are efficiently. dissipated. then all the particles should eventually elump together in phase space such that they all move around the limit cycle together. as observe.," However, if the relative motions among the particles are efficiently dissipated, then all the particles should eventually clump together in phase space such that they all move around the limit cycle together, as observed."
 Models of this sort have the advantage that the additional termes in the equatious of motion do not have explicit [requency-dependent teris that can only be effective at specilic, Models of this sort have the advantage that the additional terms in the equations of motion do not have explicit frequency-dependent terms that can only be effective at specific
require extinctions in excess of Ay=100” 2220 1s still IR-bright despite this extinction).,require extinctions in excess of $A_{\rm V}=100^m$ 220 is still IR-bright despite this extinction).
 Huynhetal.(2010) and Norrisetal.(2010) also consider the possibility that IFRS are pulsars., \cite{Huynh2010} and \cite{Norris2010} also consider the possibility that IFRS are pulsars.
 While it cannot be ruled out that pulsars are among the IFRS (in fact. a pulsar is likely to look like an IFRS). the density of pulsars at high galactic latitudes is of the order of ddeg7* (Manchesteretal. 2005)). so they cannot account for the majority of the A significant population of AGN which have as yet escaped detection also has cosmological implications.," While it cannot be ruled out that pulsars are among the IFRS (in fact, a pulsar is likely to look like an IFRS), the density of pulsars at high galactic latitudes is of the order of $^{-2}$ \citealt{Manchester2005}) ), so they cannot account for the majority of the A significant population of AGN which have as yet escaped detection also has cosmological implications."
 For example. the cosmic X-ray background (CXB) has an unresolved component which makes up around (Morettietal. 2003)). and IFRS could in principle account for a significant fraction of that (Zinetal. 20100).," For example, the cosmic X-ray background (CXB) has an unresolved component which makes up around \citealt{Moretti2003}) ), and IFRS could in principle account for a significant fraction of that \citealt{Zinn2010}) )."
 Also models of structure formation will have to consider a significant additional fraction of high-redshift The vast majority of IFRS do not have visible counterparts in co-located. deep optical images. and no redshift has yet been measured for an IFRS.," Also models of structure formation will have to consider a significant additional fraction of high-redshift The vast majority of IFRS do not have visible counterparts in co-located, deep optical images, and no redshift has yet been measured for an IFRS."
 Almost the only information available comes from observations in the radio regime., Almost the only information available comes from observations in the radio regime.
 Useful evidence can be gathered from broad-band radio spectra. to determine the emission mechanisms at work.," Useful evidence can be gathered from broad-band radio spectra, to determine the emission mechanisms at work."
 Here we present an analysis of 18 “bright” IFRS. using both archival radio data and new radio observations.," Here we present an analysis of 18 “bright” IFRS, using both archival radio data and new radio observations."
 The goal of the new observations was to mmage a significant sample of sources with high. angular resolution. to determine their structure on kpe scales. and to obtain more spectral points for an analysis of their spectral indices.," The goal of the new observations was to image a significant sample of sources with high angular resolution, to determine their structure on kpc scales, and to obtain more spectral points for an analysis of their spectral indices."
 To construct our sample we used the Australia Telescope Large Area Survey (ATLAS) GGHz catalogues (Norrisetal.2006 and Middelbergetal. 2008a))., To construct our sample we used the Australia Telescope Large Area Survey (ATLAS) GHz catalogues \citealt{Norris2006a} and \citealt{Middelberg2008a}) ).
 Our targets had been classified as IFRS at the time of the publication of the catalogues by visual inspection of the radio and gam images. and have ratios of GGHz flux density to jm flux density. $20/S3.6. of between 500 and 10000.," Our targets had been classified as IFRS at the time of the publication of the catalogues by visual inspection of the radio and $\mu$ m images, and have ratios of GHz flux density to $\mu$ m flux density, S20/S3.6, of between 500 and 10000."
 Furthermore. existing. yet unpublished GGHz survey data (Zinn et al..," Furthermore, existing, yet unpublished GHz survey data (Zinn et al.,"
 in prep) were used to measure the spectral indices. α (S.o v). of the sources and to predict their higher-frequency flux densities.," in prep) were used to measure the spectral indices, $\alpha$ $S\propto\nu^\alpha$ ), of the sources and to predict their higher-frequency flux densities."
" We selected those 18 IFRS with Sj4Gu, »1mmJy which did have reliable GGHz detections. with the exception of CS215. where the GGHz emission merged inseparably with a nearby. strong source."," We selected those 18 IFRS with $S_{\rm 1.4\,GHz}>$ mJy which did have reliable GHz detections, with the exception of CS215, where the GHz emission merged inseparably with a nearby, strong source."
 We note that all targets had a signal-to-noise ratio exceeding 9. so were unquestionably real and not spurious sources. such as sidelobes.," We note that all targets had a signal-to-noise ratio exceeding 9, so were unquestionably real and not spurious sources, such as sidelobes."
 Based on their spectra it was expected that signal-to-noise ratios of 5 or more could be achieved with new observations at GGHz and GGHz for all targets. using reasonable integration times.," Based on their spectra it was expected that signal-to-noise ratios of 5 or more could be achieved with new observations at GHz and GHz for all targets, using reasonable integration times."
 Source names are taken from the short names used by Norrisetal.(2006) and Middelbergetal.(2008a).. with a prefix of ES for the European Large Area ISO Survey - SI (ELAIS-SI) field and CS for the CDFS field.," Source names are taken from the short names used by \cite{Norris2006a} and \cite{Middelberg2008a}, with a prefix of ES for the European Large Area ISO Survey - S1 (ELAIS-S1) field and CS for the CDFS field."
 The following observations were carried out by us either for this project only or as part of other observing programmes., The following observations were carried out by us either for this project only or as part of other observing programmes.
 The targets were observed during five observing runs on 21 to 25 October 2008 when the Australia Telescope Compact Array (ATCA) was in the 6A configuration., The targets were observed during five observing runs on 21 to 25 October 2008 when the Australia Telescope Compact Array (ATCA) was in the 6A configuration.
 The correlator was configured to allow simultaneous observations at both GGHz and GGHz with a bandwidth of MMHz for each frequeney band., The correlator was configured to allow simultaneous observations at both GHz and GHz with a bandwidth of MHz for each frequency band.
 In processing. each band ts divided into 13 independent MMHz channels. resulting in an effective bandwidth of MMHz per band.," In processing, each band is divided into 13 independent MHz channels, resulting in an effective bandwidth of MHz per band."
 Three to five sources were imaged during each observing session. and sources were switched rapidly to fill the uv plane.," Three to five sources were imaged during each observing session, and sources were switched rapidly to fill the uv plane."
 More time was spent on weaker targets to increase the likelihood of detection: the net ntegration times. after flagging. are given in Table |.," More time was spent on weaker targets to increase the likelihood of detection; the net integration times, after flagging, are given in Table 1."
 The flux density scale was set relative to observations of the primary flux density calibrator BB1934-638 with assumed flux densities of JJy at GGHz and JJy at GGHz., The flux density scale was set relative to observations of the primary flux density calibrator B1934-638 with assumed flux densities of Jy at GHz and Jy at GHz.
 The gain and bandpass calibration were performed relative to the secondarycalibrators BB0237-233 and BB0022-[123 for the CDFS and ELAIS fields. respectively.," The gain and bandpass calibration were performed relative to the secondarycalibrators B0237-233 and B0022-423 for the CDFS and ELAIS fields, respectively."
 Data calibration was carried out with the Miriad. package (Saultetal. 1995)) and followed standard procedures as described in the Miriad. User's Guide., Data calibration was carried out with the Miriad package \citealt{Sault1995}) ) and followed standard procedures as described in the Miriad User's Guide.
 Naturally-weighted images with matched resolution were made at GGHz and GGHz by excluding the shortest baseline (CA04-CAO03) in the GGHz data sets and the longest three baselines (CA06-CAO0|1|2]|3]) at GGHz to reduce the effects of resolution on the measured spectral indices between these two frequencies., Naturally-weighted images with matched resolution were made at GHz and GHz by excluding the shortest baseline (CA04-CA05) in the GHz data sets and the longest three baselines $|$ $|$ 3]) at GHz to reduce the effects of resolution on the measured spectral indices between these two frequencies.
 However. resolution. effects can still occur between the lower three frequencies described below and these higher two frequencies presented here. since the resolutions vary by more than an order of magnitude.," However, resolution effects can still occur between the lower three frequencies described below and these higher two frequencies presented here, since the resolutions vary by more than an order of magnitude."
 These observations resulted in resolutions of j.6x aaresec- on average., These observations resulted in resolutions of $\times$ $^2$ on average.
 Both the ATLAS/ELAIS and ATLAS/CDFS fields were imaged at GGHz with the ATCA in 2006-2008., Both the ATLAS/ELAIS and ATLAS/CDFS fields were imaged at GHz with the ATCA in 2006-2008.
 The data were imaged and source extraction and publication is underway (Zinn et al.," The data were imaged and source extraction and publication is underway (Zinn et al.,"
 in prep)., in prep).
 For our purpose here we extracted only the flux densities of the IFRS., For our purpose here we extracted only the flux densities of the IFRS.
 The array was in one of the four available 750mm configurations due to scheduling constraints and to ensure that short-spacing information was not missed at this higher frequency., The array was in one of the four available m configurations due to scheduling constraints and to ensure that short-spacing information was not missed at this higher frequency.
 The observations therefore yielded much lower resolution than at GGHz., The observations therefore yielded much lower resolution than at GHz.
 The final Το noise levels are jJy/beam in the ATLAS/ELAIS field and uJv/beam in the ATLAS/CDFS field. owing to a difference in the integration times.," The final $\sigma$ noise levels are $\mu$ Jy/beam in the ATLAS/ELAIS field and $\mu$ Jy/beam in the ATLAS/CDFS field, owing to a difference in the integration times."
 Uniform weighting was used to image both fields. resulting in resolutions of 33.6x19.9 aaresec and 54.3x20.6 aarcsec. respectively.," Uniform weighting was used to image both fields, resulting in resolutions of $\times$ $^2$ and $\times$ $^2$ , respectively."
the disk.,the disk.
 Finally. after a steady increase in mass. the host halo is accreted by a much more massive halo at 2=1.1. when the most massive progenitor becomes a satellite galaxy.," Finally, after a steady increase in mass, the host halo is accreted by a much more massive halo at $z=1.1$, when the most massive progenitor becomes a satellite galaxy."
 The day galaxy is a satellite in a halo of mass 10715.+AL..., The present-day galaxy is a satellite in a halo of mass $10^{14} h^{-1}M_{\odot}$.
 The next most massive galaxy (middle panels Fig. 23) , The next most massive galaxy (middle panels Fig. \ref{GMT}) )
displays two epochs at which the most massive progenitor is a bright LBG ες—6 and 2o 3.6).," displays two epochs at which the most massive progenitor is a bright LBG $z \sim
6$ and $z \sim 3.6$ )."
 The most massive progenitor branch in the most massive galaxy (bottom panels of Fig. 29 , The most massive progenitor branch in the most massive galaxy (bottom panels of Fig. \ref{GMT}) )
again shows several instances when the progenitor is a bright LBG., again shows several instances when the progenitor is a bright LBG.
 It undergoes a major merger at zz1.5 which increases the stellar mass by (barely visible in the figure). triggers a bright LBG phase. and changes the morphology from D/T= Oto D/Tex].," It undergoes a major merger at $z \approx 1.5$ which increases the stellar mass by (barely visible in the figure), triggers a bright LBG phase, and changes the morphology from $B/T \approx 0$ to $B/T \approx 1$."
 Itis interesting to note that in all cases shown. the stellar mass of the most massive progenitor branch (shown by the blue points in the right-hand panels) increases steadily with redshift. without displaying any sudden large jumps.," It is interesting to note that in all cases shown, the stellar mass of the most massive progenitor branch (shown by the blue points in the right-hand panels) increases steadily with redshift, without displaying any sudden large jumps."
 This implies that the bursts of star formation in these examples are not responsible for large changes in the stellar mass of the galaxy., This implies that the bursts of star formation in these examples are not responsible for large changes in the stellar mass of the galaxy.
 This is a result in part of the large recycled fraction (2= 0.91) for stars forming with the top-heavy IMF. together with the strong feedback from supernova explosions.," This is a result in part of the large recycled fraction $R=0.91$ ) for stars forming with the top-heavy IMF, together with the strong feedback from supernova explosions."
 We can use the formation histories of model LBGs to answer some important questions., We can use the formation histories of model LBGs to answer some important questions.
 The first of these is: what is the mechanism of the star formation reponsible for the galaxy being seen as an LBG at a particular redshift?, The first of these is: what is the mechanism of the star formation reponsible for the galaxy being seen as an LBG at a particular redshift?
 In the present model. the possibilities are: a starburst triggered by a minor galaxy merger: a starburst triggered by a major galaxy merger: and quiescent star formation in a galaxy disk.," In the present model, the possibilities are: a starburst triggered by a minor galaxy merger; a starburst triggered by a major galaxy merger; and quiescent star formation in a galaxy disk."
 To determine which of these dominates in a particular case. we move back in time through the galaxy formation history. starting at the redshift at which a galaxy is identified as an LBG.," To determine which of these dominates in a particular case, we move back in time through the galaxy formation history, starting at the redshift at which a galaxy is identified as an LBG."
 If at any time during the current LBG phase the burst and quiescent SFRs satisfy the condition SERauisu7ΕΕRivas: then we classify he LBG phase as being produced by quiescent star formation. otherwise we find the first galaxy merger (going back in time) and identify whether it is a minor or major merger.," If at any time during the current LBG phase the burst and quiescent SFRs satisfy the condition ${\rm SFR}_{\rm quiescent}> 4\, {\rm SFR}_{\rm burst}$ then we classify the LBG phase as being produced by quiescent star formation, otherwise we find the first galaxy merger (going back in time) and identify whether it is a minor or major merger."
 We include he factor + in the condition on the SFRs because stars forming with the top-heavy burst IMF produce roughly 4 times higher UV uminosities than the same mass of stars formed with the quiescent IMF., We include the factor 4 in the condition on the SFRs because stars forming with the top-heavy burst IMF produce roughly 4 times higher UV luminosities than the same mass of stars formed with the quiescent IMF.
 The results of this classification exercise are shown in Fig. 3.. ," The results of this classification exercise are shown in Fig. \ref{fig:trigger}, ,"
"or bright LBGs (LicLi identified at >=3 and 6 ttop yanel). and for faint LBGs (Li>> O.LL;-,-) identified at >=3. 6 and 10 (bottom panel)."," for bright LBGs $L_{UV} > L^{*}_{UV}$ ) identified at $z=3$ and $6$ (top panel), and for faint LBGs $L_{UV} > 0.1 L^{*}_{UV}$ ) identified at $z=3$, $6$ and $10$ (bottom panel)."
 The fractions shown there are calculated or a volume-Iimited sample of LBGs at the identification redshift., The fractions shown there are calculated for a volume-limited sample of LBGs at the identification redshift.
 We see from the tigure that LBGs are predicted to be dominated by starbursts triggered by minor galaxy mergers (around of cases) in all of the cases examined here., We see from the figure that LBGs are predicted to be dominated by starbursts triggered by minor galaxy mergers (around of cases) in all of the cases examined here.
 Minor mergers dominate over major mergers by a factor 2—4., Minor mergers dominate over major mergers by a factor 2–4.
 Quiescent star formation is predicted to account for at most a few percent of LBGs. with the exception of faint LBGs at 2=3. where this fraction increases to around206c.," Quiescent star formation is predicted to account for at most a few percent of LBGs, with the exception of faint LBGs at $z=3$, where this fraction increases to around."
. We also see that the quiescent fraction decreases with increasing redshift for both bright and faint LBGs. and is much smaller for bright LBGs than for faint LBGs at the same redshift.," We also see that the quiescent fraction decreases with increasing redshift for both bright and faint LBGs, and is much smaller for bright LBGs than for faint LBGs at the same redshift."
 These results about the dominance of bursts over quiescent star formation inLBGs are in agreement with the analysis by 2.., These results about the dominance of bursts over quiescent star formation inLBGs are in agreement with the analysis by \citet{Lacey10b}. .
inverse Fourier transformed in real space to produce ór.,inverse Fourier transformed in real space to produce $\phi_{\rm L}$.
 The final ® is obtained using eq. (, The final $\Phi$ is obtained using eq. (
1).,1).
" Finally, back in Fourier space, we modulate the power-law spectrum using the transfer functionsof the ACDM model."," Finally, back in Fourier space, we modulate the power-law spectrum using the transfer functionsof the $\Lambda$ CDM model."
 We also run some other simulations at higher resolutions to check for numerical convergence., We also run some other simulations at higher resolutions to check for numerical convergence.
" In particular we have performed a (20,384) simulation run to analyse the flux PDF."," In particular we have performed a $(20,384)$ simulation run to analyse the flux PDF."
" For the (20,256) models the flux probability distribution function has numerically converged only below z=3 (see ?))."," For the $(20,256)$ models the flux probability distribution function has numerically converged only below $z=3$ (see \cite{bolton07}) )."
" However, since our results will always be quoted in comparison with the fw,=0 case (ie. as a ratio of two different quantities) we expect the resolution errors to be unimportant (i.e. we assume the same resolution corrections should be applied to all the models, even though this assumption should be explicitly checked)."," However, since our results will always be quoted in comparison with the $f_{\rm NL}=0$ case (i.e. as a ratio of two different quantities) we expect the resolution errors to be unimportant (i.e. we assume the same resolution corrections should be applied to all the models, even though this assumption should be explicitly checked)."
" A projected density slice of the gas (IGM) distribution for the (20,256) simulation of thickness 1.5 comoving Mpc/h is shown in Figure "," A projected density slice of the gas (IGM) distribution for the (20,256) simulation of thickness 1.5 comoving $h$ is shown in Figure \ref{fig_slice}."
We focus on this simulation because at z—3 the flux [I].probability distribution function has numerically converged., We focus on this simulation because at $z=3$ the flux probability distribution function has numerically converged.
" In the middle panel we plot the gas density in the Gaussian case, while residuals in the two models with fw;=—200 and fy,=+200 are shown in the left and right panel, respectively."," In the middle panel we plot the gas density in the Gaussian case, while residuals in the two models with $f_{\rm NL}=-200$ and $_{\rm NL}=+200$ are shown in the left and right panel, respectively."
 On average regions of the cosmic web below the mean density appear to be ~10% less (more) dense in the negative (positive) fwr case., On average regions of the cosmic web below the mean density appear to be $\sim 10\%$ less (more) dense in the negative (positive) $f_{\rm NL}$ case.
 This trend is apparent not only near the centre of these regions but also in the matter surrounding them (see for example the void at (a=17;y8) comoving Mpc/h)., This trend is apparent not only near the centre of these regions but also in the matter surrounding them (see for example the void at $(x=17; y=8)$ comoving $/h$ ).
 The same qualitative behavior can be observed in the distribution of the dark matter particles (see Figure 2 of ?))., The same qualitative behavior can be observed in the distribution of the dark matter particles (see Figure 2 of \cite{grossi08}) ).
 In the NG models considered here the growth of structures in terms of density PDF is different., In the NG models considered here the growth of structures in terms of density PDF is different.
 As discussed in Grossi et al. (, As discussed in Grossi et al. (
"2008), the maps of residuals in the non-Gaussian cases reflect the differences in the primordial PDF of the mass overdensity.","2008), the maps of residuals in the non-Gaussian cases reflect the differences in the primordial PDF of the mass overdensity."
 As shown in Figures 1 and 5 of Grossi et al. (, As shown in Figures 1 and 5 of Grossi et al. (
"2008) the mass PDF is skewed towards positive (negative) overdensities in the non-Gaussian models with positive (negative) fwr, values, compared to the Gaussian case.","2008) the mass PDF is skewed towards positive (negative) overdensities in the non-Gaussian models with positive (negative) $f_{\rm NL}$ values, compared to the Gaussian case."
" As a consequence, since the gas traces well the underlying mass distribution at these redshifts, voids look emptier in the [ντ=—200 case (map on the left) while denser environments like filaments and knots look more prominent in the fwr,=+200 case (map on the right) with respect to the Gaussian case."," As a consequence, since the gas traces well the underlying mass distribution at these redshifts, voids look emptier in the $f_{\rm
 NL}=-200$ case (map on the left) while denser environments like filaments and knots look more prominent in the $f_{\rm NL}=+200$ case (map on the right) with respect to the Gaussian case."
 These differences in the tails of the density PDF also impact on the filaments at around the mean density that surround the voids., These differences in the tails of the density PDF also impact on the filaments at around the mean density that surround the voids.
" In fact the size of the voids is slightly different in the negative and positive NG models: for negative fxr values the emptier voids grow in size faster than for the Gaussian case and even faster than for positive fwr values, displacing the filaments at around the mean densities at different positions in the three cases and giving rise to the filamentary pattern of residuals of the panels."," In fact the size of the voids is slightly different in the negative and positive NG models: for negative $f_{\rm NL}$ values the emptier voids grow in size faster than for the Gaussian case and even faster than for positive $f_{\rm NL}$ values, displacing the filaments at around the mean densities at different positions in the three cases and giving rise to the filamentary pattern of residuals of the panels."
 'To perform our analysis we have extracted several mock QSO absorption spectra from the simulation box., To perform our analysis we have extracted several mock QSO absorption spectra from the simulation box.
" All spectra are drawn in redshift space taking into account the effect of the IGM peculiar velocities along the line-of-sight vpec,||."," All spectra are drawn in redshift space taking into account the effect of the IGM peculiar velocities along the line-of-sight $v_{\rm pec,\parallel}$."
" Basically, the simulated flux at the redshift-space coordinate u (in km/s) is F(u)=exp[—r(u)] with: (x) ]dz ,, where 00,4=4.45x107 cm? is the hydrogen cross-section, H(z) is the Hubble constant at redshift 2, v is the realspace coordinate (in km s!) b=(2kT/mc!)/? is the velocity dispersion in units of c, G=(nb)exp[-(u—y(y))?/b?] is the Gaussian profile that well! approximatesΌρος the Voigt profile in the regime considered here."," Basically, the simulated flux at the redshift-space coordinate $u$ (in km/s) is $F(u)=\exp[-\tau(u)]$ with: (x) ]dx , where $\sigma_{0,\alpha} = 4.45 \times 10^{-18}$ $^2$ is the hydrogen cross-section, $H(z)$ is the Hubble constant at redshift $z$, $x$ is the real-space coordinate (in km $^{-1}$ ), $b=(2k_BT/mc^2)^{1/2}$ is the velocity dispersion in units of $c$, ${\cal G}=(\sqrt{\pi}
b)^{-1}\exp[-(u-y-v_{\rm pec,\parallel}^{\rm IGM}(y))^2/b^2]$ is the Gaussian profile that well approximates the Voigt profile in the regime considered here."
" The neutral hydrogen density in real-space, that enters the equation above, could be related to the underlying gas density by the following expression (e.g. ??)): with Ὦ.1ο is the hydrogen photoionization rate in units of s!, T is the IGM temperature, and TiGw(z) is the mean IGM density at that redshift."," The neutral hydrogen density in real-space, that enters the equation above, could be related to the underlying gas density by the following expression (e.g. \cite{huignedin97,schaye}) ): with $\Gamma_{-12}$ is the hydrogen photoionization rate in units of $s^{-1}$ , $T$ is the IGM temperature, and $\overline{n}_{\rm IGM}(z)$ is the mean IGM density at that redshift."
" However, this equation is not explicitly used since the neutral hydrogen fraction is computed self-consistently for each gas particles during the simulation run."," However, this equation is not explicitly used since the neutral hydrogen fraction is computed self-consistently for each gas particles during the simulation run."
 The integral in eq. (25) , The integral in eq. \ref{eq1}) )
"to obtain the optical depth along each simulated line-of-sight is thus performed using the relevant hydrodynamical quantities from the numerical simulations: diam,T,Όρος,NHI-"," to obtain the optical depth along each simulated line-of-sight is thus performed using the relevant hydrodynamical quantities from the numerical simulations: $\delta_{\rm
 IGM}, T, v_{\rm pec}, n_{\rm HI}$."
 More details on how to extract a mock QSO spectrum from an hydrodynamical simulation using the SPH formalism can be found in ?.., More details on how to extract a mock QSO spectrum from an hydrodynamical simulation using the SPH formalism can be found in \cite{theuns98}.
" An example of line-of-sight is shown in the top panel of Figure D], while the bottom panel shows the ratio of the gas density along the line-of-sight of NG and Gaussian models (in real space) In the following we will focus on high transmissivity in which the transmitted flux is close to unity (upper panel)."," An example of line-of-sight is shown in the top panel of Figure \ref{fig_los}, while the bottom panel shows the ratio of the gas density along the line-of-sight of NG and Gaussian models (in real space) In the following we will focus on high transmissivity in which the transmitted flux is close to unity (upper panel)."
" Three QSO spectra are shown with different line styles and correspond to the Gaussian case (dashed, red line), and to [νι=+200 (solid black and solid blue, respectively)."," Three QSO spectra are shown with different line styles and correspond to the Gaussian case (dashed, red line), and to $f_{\rm NL}=\pm200$ (solid black and solid blue, respectively)."
" The transmitted flux (no noise is added in this case) is almost identical for the two NG models in magnitude but not in sign, as expected."," The transmitted flux (no noise is added in this case) is almost identical for the two NG models in magnitude but not in sign, as expected."
 One can better appreciate the differences among the models by looking at the gas density (bottom panel)., One can better appreciate the differences among the models by looking at the gas density (bottom panel).
" On average differences are of the order10%,, even if in some cases they can rise above 30-4096."," On average differences are of the order, even if in some cases they can rise above ."
". The fact that the corresponding variations in the flux are comparatively smaller (usually less than few percent) is somehow expected, since differences in the gas density are exponentiallysuppressed by the non- transformation between fluxand matter (and by other non-linear effects as well)."," The fact that the corresponding variations in the flux are comparatively smaller (usually less than few percent) is somehow expected, since differences in the gas density are exponentiallysuppressed by the non-linear transformation between fluxand matter (and by other non-linear effects as well)."
" However, despite their small"," However, despite their small"
generation.,generation.
 The consequence of larger energy generation is much faster system evolution., The consequence of larger energy generation is much faster system evolution.
 The cluster lives shorter., The cluster lives shorter.
" Therefore, not only BH with masses of several hundred Mo (IMBH) can influence the system structure, which can be detected by observations, but also presence in the system of several massive stellar mass BHs can leave observational imprint on the cluster structure."," Therefore, not only BH with masses of several hundred $M_{\odot}$ (IMBH) can influence the system structure, which can be detected by observations, but also presence in the system of several massive stellar mass BHs can leave observational imprint on the cluster structure."
 That is a very interesting possibility worth to further check., That is a very interesting possibility worth to further check.
" Similar behaviour was reported in Hurley(2007) for stochastic core radius evolution powered by single rather massive BH and in Merrittetal.(2004), Mackeyetal.(2008) for strong core expansion of massive star cluster powered by large number of stellar mass BHs (in this case the core radius evolution is rather smooth because of a large number of BHs which forms bound subsystem in the central part of the system)."," Similar behaviour was reported in \citet{Hu2007} for stochastic core radius evolution powered by single rather massive BH and in \citet{Merrittetal2004}, \citet{Mackeyetal2008} for strong core expansion of massive star cluster powered by large number of stellar mass BHs (in this case the core radius evolution is rather smooth because of a large number of BHs which forms bound subsystem in the central part of the system)."
 The behaviour of the half mass and the core radii described above for N=100000 is also visible for N=200000., The behaviour of the half mass and the core radii described above for $N=100000$ is also visible for $N=200000$.
" The fact that in this case, for different kfallbs the number of BHs and BH- binaries are very similar, is interesting."," The fact that in this case, for different $kfallbs$ the number of BHs and BH-BH binaries are very similar, is interesting."
 This suggests that not the number of BH-BH binaries is crucial for the discussed above behaviour but the mass of BH-BH binary., This suggests that not the number of BH-BH binaries is crucial for the discussed above behaviour but the mass of BH-BH binary.
 For kfallb—1 case more massive BHs can be formed than in other kfalbs because of the mass fallback during SN explosion., For $kfallb = 1$ case more massive BHs can be formed than in other $kfalbs$ because of the mass fallback during SN explosion.
" Therefore, the most massive binary which can form in this case is substantially more massive than in other cases."," Therefore, the most massive binary which can form in this case is substantially more massive than in other cases."
 Such a binary can generate more energy in interactions and remove more stars and binaries from the system than a less massive binary., Such a binary can generate more energy in interactions and remove more stars and binaries from the system than a less massive binary.
" It is possible that in the case when two or more massive BH-BH binaries are formed in the system, they will interact between themselves and quickly harden."," It is possible that in the case when two or more massive BH-BH binaries are formed in the system, they will interact between themselves and quickly harden."
" There is a non zero probability that before they escape, they will merge in collision interactions with ""ordinary"" stars/binaries and form more massive BH, which very quickly will form again binary."," There is a non zero probability that before they escape, they will merge in collision interactions with ""ordinary"" stars/binaries and form more massive BH, which very quickly will form again binary."
 The sequence can be repeated a few times forming a seed IMBH in the system., The sequence can be repeated a few times forming a seed IMBH in the system.
 That is an interesting new road for the possible creation of IMBH in globular clusters., That is an interesting new road for the possible creation of IMBH in globular clusters.
" This possible scenario strongly relay on the SN kick velocity distribution for BHs, initial mass function for massive stars and initial cluster concentration."," This possible scenario strongly relay on the SN kick velocity distribution for BHs, initial mass function for massive stars and initial cluster concentration."
 It is worth to stress that fast MOCCA-NoFB code can be used for projects which investigate the evolution of star clusters from the point of view their global properties., It is worth to stress that fast MOCCA-NoFB code can be used for projects which investigate the evolution of star clusters from the point of view their global properties.
" If one is interested in properties of ""peculiar"" objects and their distributions should use slower MOCCA code."," If one is interested in properties of ""peculiar"" objects and their distributions should use slower MOCCA code."
 At the end of this section we would like to refer to the choice of the best value of rpmax., At the end of this section we would like to refer to the choice of the best value of $r_{pmax}$.
" We argued that from the point of view of the number of BSS in the system the best choice of rpmaz is about A, but from the point of view of the number of binaries or the distribution of the binary binding energy larger values of about 9A are more appropriate."," We argued that from the point of view of the number of BSS in the system the best choice of $r_{pmax}$ is about $A$, but from the point of view of the number of binaries or the distribution of the binary binding energy larger values of about $9A$ are more appropriate."
" The best compromise, taking into account statistical fluctuations, seems to be rpj,a;=2A."," The best compromise, taking into account statistical fluctuations, seems to be $r_{pmax} = 2A$."
 This means that we put more emphasise on the limitations given by BSS than ones given by binaries., This means that we put more emphasise on the limitations given by BSS than ones given by binaries.
 The reason for that is as follows., The reason for that is as follows.
 The BSS definition in N-body and MOCCA is exactly the same and the fluctuations in BSS number are smaller than the its value itself., The BSS definition in N-body and MOCCA is exactly the same and the fluctuations in BSS number are smaller than the its value itself.
 So the sharp increase in the maximum number of BSS with larger Tpmaz (Observed in Fig.7)) is real and can not be attributed only to fluctuations., So the sharp increase in the maximum number of BSS with larger $r_{pmax}$ (observed in \ref{fig:Nbs-rp-100k}) ) is real and can not be attributed only to fluctuations.
" For the evolution of the number of binaries in the system and for the binary binding energy distributions the statistical fluctuations are practically negligible, so we could expect that observed dependences on Τρπιαα are real."," For the evolution of the number of binaries in the system and for the binary binding energy distributions the statistical fluctuations are practically negligible, so we could expect that observed dependences on $r_{pmax}$ are real."
 But there are some doubts about the binary definition in N-body and MOCCA., But there are some doubts about the binary definition in N-body and MOCCA.
" In N-body simulation it is easy to count regularised binaries (KS binaries), but it is not quite so straightforward to find all non KS binaries."," In N-body simulation it is easy to count regularised binaries (KS binaries), but it is not quite so straightforward to find all non KS binaries."
 In MOCCA all binaries are directly followed., In MOCCA all binaries are directly followed.
" As we pointed out in Sec.??,, however, the number of non KS binaries is rather small and can not be entirely responsible for the observed differences."," As we pointed out in \ref{sec:free}, however, the number of non KS binaries is rather small and can not be entirely responsible for the observed differences."
" For binary binding energy distribution evidences are rather indirect and the observed dependence on rp;,5; could be also, at least partially, attributed to unidentified yet physical processes or some systematical errors in MOCCA code."," For binary binding energy distribution evidences are rather indirect and the observed dependence on $r_{pmax}$ could be also, at least partially, attributed to unidentified yet physical processes or some systematical errors in MOCCA code."
" Therefore, we decided to opt for the compromise vale of rpmaz than use larger values suggested by the total number of binaries and their distributions."," Therefore, we decided to opt for the compromise vale of $r_{pmax}$ than use larger values suggested by the total number of binaries and their distributions."
" We estimate that the error made in the total number of binaries by use of this compromise value is of order 5 per cent of the number of binaries In this paper we have presented an advanced Monte Carlo code (MOCCA) for the evolution of rich star clusters, including most aspects of dynamical interactions involving binary and single stars, internal evolution of single and binary stars and complicated process of escape in the static tidal field."," We estimate that the error made in the total number of binaries by use of this compromise value is of order $5$ per cent of the number of binaries In this paper we have presented an advanced Monte Carlo code (MOCCA) for the evolution of rich star clusters, including most aspects of dynamical interactions involving binary and single stars, internal evolution of single and binary stars and complicated process of escape in the static tidal field."
 The direct integration of a few body problem was introduced on the base of FewBody code, The direct integration of a few body problem was introduced on the base of FewBody code
 (22222).. (2?).. (????).. (222227) II» 0 ," \citep{wong02a, kennicutt07a, bigiel08a, leroy08a, blanc09a}. \citep{blitz06b, krumholz09b}, \citep{obreschkow09b, obreschkow09a, fu10a, dutton10a},"
(77).. (?77)..," \citep{pelupessy06a, robertson08b, pelupessy09a, ng:gtk09, ng:gk10a, ng:gk10b} $_2$ $\alpha$ \citep{wolfe06a, wild07a}. \citep{krumholz09e,ng:gk10b}."
 ose their outer gas disks but retain high colt density. nolecule-vich ceuters coutiuue to form stars; while those hat lose their mner gas disks cease to formi molecules and stars (?)..," lose their outer gas disks but retain high column density, molecule-rich centers continue to form stars, while those that lose their inner gas disks cease to form molecules and stars \citep{fumagalli09a}."
 While many of these authors have compared their nodels or simulations to observed molecular fractious iu rearby galaxies. these observations cover only a limited dvnaiic rauge mm imoetalliity: radiation environment. aud other quantities that may be relevant to the o Πο transition.," While many of these authors have compared their models or simulations to observed molecular fractions in nearby galaxies, these observations cover only a limited dynamic range in metallicity, radiation environment, and other quantities that may be relevant to the to $_2$ transition."
 We cannot vet test the models iu nore extreme environments with observations. but we can check for cousisteney between the models.," We cannot yet test the models in more extreme environments with observations, but we can check for consistency between the models."
 Such checks provide at least a minima level of coufidence iu extrapolating the model predictions bevoud the range of environments in which they have heen calibrated., Such checks provide at least a minimum level of confidence in extrapolating the model predictions beyond the range of environments in which they have been calibrated.
 Cross-conrparisons are particularly important eiven the rauge of complexity of the models. which go from steady-state analytic approxination formulae to sophisticated timec-dependent radiation plus chemistry modules.," Cross-comparisons are particularly important given the range of complexity of the models, which go from steady-state analytic approximation formulae to sophisticated time-dependent radiation plus chemistry modules."
 Oulv the former are suitable for implementation m seni-analvtic models. aud thus such a test is necessary to ensure that semi-analytic models that rely on them are able to faithfully reproduce the results of ummerical simulations.," Only the former are suitable for implementation in semi-analytic models, and thus such a test is necessary to ensure that semi-analytic models that rely on them are able to faithfully reproduce the results of numerical simulations."
 Our goal in this paper is to provide such an inter-mode conrparison., Our goal in this paper is to provide such an inter-model comparison.
 We use a suite of nunerical iodels by ?.hereafterCULO:see§2.1. for a detaileddescription. ar we conipare them to one of the most conmionbv-usec analytic approximations (777.see82.2. for a doetaile for the tto Πο transition.," We use a suite of numerical models by \citet[hereafter GK10; see \S~\ref{sec:numerical} for a detailed, and we compare them to one of the most commonly-used analytic approximations \citep[see \S\ref{sec:analytic} for a detailed for the to $_2$ transition."
 Both of the analytic aud nuuerica models have been tested against observations of locaealaxics. and have Όσοι. found to provide a goo description of the molecular coutent iu This," Both of the analytic and numerical models have been tested against observations of localgalaxies, and have been found to provide a good description of the molecular content in This"
 We consider metric perturbations which are produced by some isotropic raucdom process (for example during inflation)., We consider metric perturbations which are produced by some isotropic random process (for example during inflation).
 After production. they evolve according to a ceteruinistic equation of motion.," After production, they evolve according to a deterministic equation of motion."
" The correlation fictions of h;;j(k.f) have to be of the form. Uk.An}, = [bbsTEUtH) | | | |tH)."," The correlation functions of $h_{ij}({\bf k},t)$ have to be of the form ,t) = [k_ik_jk_lk_mH_1(k,t,t') + + + +."
" Iere the functions /£, are functions of the modulus &=|k| ouly.", Here the functions $H_a$ are functions of the modulus $k=|{\bf k}|$ only.
 Furthermore. all of them except Ls are herimitian in f aud £," Furthermore, all of them except $H_3$ are hermitian in $t$ and $t'$."
 This is the most seueral ansatz for au isotropic correlation tensor satisfving the sviuuetries required., This is the most general ansatz for an isotropic correlation tensor satisfying the symmetries required.
" To project out the tensorial part of this correlation tensor we act ou fj; it with the teusor projection operator. = ke""j This vieldsIK | | Lhe,hjhyο) From Eq. (12))."," To project out the tensorial part of this correlation tensor we act on $h_{ij}$ it with the tensor projection operator, = _j. This yields+ + - + k_ik_jk_lk_m] From Eq. \ref{dT}) ),"
 we then obtain ilem XM dr x) (i. ) y dt df! «πω ik-n(fy0). ΚΕΜΕΤΗ D, we then obtain ( ( d^3x ) ( ) = )^3 dt dt' (t_0-t)) (t_0-t')) ) n_in_jn'_ln'_m ] .
previous section.,previous section.
 We have also considered the region between galaxies as backeround for the sources associated with the eroup members. and we fouud entirely cousistcut results in the derived quautities. with ouly a siuall decrease --i the net count rates (120%... for NGC 92 and NGC 89 respectively).," We have also considered the region between galaxies as background for the sources associated with the group members, and we found entirely consistent results in the derived quantities, with only a small decrease in the net count rates $4-20$, for NGC 92 and NGC 89 respectively)."
 We binned the data to increase the photon ⋅⋅ ⋅ ↴∖↴⋜↧↑↕↴∖↴⊓↸⊳↴∖↴↻↸∖↥⋅↴∖↴⋉∖↸⊳⊓⋅⋜↧⊓⋝↕∐↑∪↸∖∐↴∖↴↿∐⋅↸∖↑∐⋜↧↑↑↕∐∖∖−↴∖↴↑⋜↧↑↕↴∖↴↑↕↸⊳↴∖↴ ⋅≻ ⋅⋅ can be applied., We binned the data to increase the photon statistics per spectral bin to ensure that the $\chi^2$ statistics can be applied.
 We have used a binning based on a minimum nuniber of comnts iu the total data (typically ! counts por bin) or based on a nium signal-to-noise ratio in the net data. depending on the observed uuuber of photons. while at the same time ensuriug that there was a reasonable number of bius for the spectral fit.," We have used a binning based on a minimum number of counts in the total data (typically 30 counts per bin) or based on a minimum signal-to-noise ratio in the net data, depending on the observed number of photons, while at the same time ensuring that there was a reasonable number of bins for the spectral fit."
 The data are fitted in NSPEC (version. 11.3.1) with either a plasina with low energv absorption (c.g. MERAL) or a combination of plasma auc bremsstrahlung or power law to account for Ligh οπσον tails., The data are fitted in XSPEC (version 11.3.1) with either a plasma with low energy absorption (e.g. MEKAL) or a combination of plasma and bremsstrahlung or power law to account for high energy tails.
 We adopt the tables of for the abundances and a Galactic value of Ny=2.741029 cin?1990)., We adopt the tables of for the abundances and a Galactic value of $_H = 2.7 \times 10^{20}$ $^{-2}$.
. Quoted errors correspoud to a A\7=2.7 unless specified otherwise., Quoted errors correspond to a $\Delta \chi^2$ =2.7 unless specified otherwise.
 The A-ray spectra of NCC 92 can be paramoeterised by a combination of a power law with D—2.2£0.6 aud a solar abundance plasma with kT~0.31025.0.55} keV (Fig 6))., The X-ray spectrum of NGC 92 can be parameterised by a combination of a power law with $\Gamma \sim 2.2 \pm 0.6$ and a solar abundance plasma with $\sim 0.3\ [0.22-0.55]$ keV (Fig \ref{spec-92}) ).
 A relatively. huge amount of low cucrey absorption is required. correspoudiug to Ny~Lb«1074 7. consistent with the presence and amount of neutral hydrogen observed in HI emissiou2007).," A relatively large amount of low energy absorption is required, corresponding to $_H \sim 4 \times 10^{21}$ $^{-2}$, consistent with the presence and amount of neutral hydrogen observed in HI emission."
".. The iutrinsic Iuninositv of the power law component. L,~Ls10 jin the 0.5-10 keV baud. points to the prescuce of au ACN. albeit of very low Iuninosity."," The intrinsic luminosity of the power law component, $_x \sim 4 \times 10^{40}$ in the 0.5-10 keV band, points to the presence of an AGN, albeit of very low luminosity."
" The absorption corrected plasma luminosity of ~10 1(0.5-2 keV. within a 30"" radius). is relatively Ligh for a jornial spiral galaxy. but is consisteut with the presence of starburst activity."," The absorption corrected plasma luminosity of $\sim 2 \times 10^{40}$ (0.5-2 keV, within a $''$ radius), is relatively high for a normal spiral galaxy, but is consistent with the presence of starburst activity."
 Uufortunatelv we cannot study the spectral properties of the emission in different regions: however. given its extended nature. also testifiec by the fit paraiucters with a πο οἱ (see previous sections). we speculate that the ciission is not to be attributed exchisively to the nuclear starburst region. but is most likely distributed throughout the body of the ealaxy.," Unfortunately we cannot study the spectral properties of the emission in different regions; however, given its extended nature, also testified by the fit parameters with a $\beta$ -model (see previous sections), we speculate that the emission is not to be attributed exclusively to the nuclear starburst region, but is most likely distributed throughout the body of the galaxy."
 The euerev distribution of the signal allows a ~20 binning of the net spectrum only at low energies. up to ~2 keV. In the 2-10 keV range. too few photons (28£8) are detected. for a mucanineful spectral analvsis.," The energy distribution of the signal allows a $\sim 2 \sigma$ binning of the net spectrum only at low energies, up to $\sim 2$ keV. In the 2-10 keV range, too few photons $ 28 \pm 8$ ) are detected, for a meaningful spectral analysis."
 However. taking into account that this object has a Sevtert 2 uncleus. from the optical line ratios. we will first use the spectral data at low energies. to obtain oeiforiiation on the N-ray spectral properties of the object.," However, taking into account that this object has a Seyfert 2 nucleus, from the optical line ratios, we will first use the spectral data at low energies, to obtain information on the X-ray spectral properties of the object."
 aVo will then add the high energy rauge to obtain some oeiformiation on possible uuclear emission., We will then add the high energy range to obtain some information on possible nuclear emission.
" A singleC» component plasia uodel does not fit the ata well: a single temperature breimsstraliluug or a power law inodel could eive significautlv etter fits. but with ureasonable parameters (kT~0.5 κο, which is also obtained with a zero abundauce MEIKAL model. or T=I. respectively)."," A single component plasma model does not fit the data well; a single temperature bremsstrahlung or a power law model could give significantly better fits, but with unreasonable parameters $\sim
0.5$ keV, which is also obtained with a zero abundance MEKAL model, or $\Gamma=4$, respectively)."
 We obtain a reasonable fit (47=1 for 16- degrees of freedom iu EPIC-pu) with a two-componcn model (two thin plasimas at 0.25. 1. keV. solar abundance or one plasma at ~1 keV. solar abundance and a power law component with D fixed a 1.9).," We obtain a reasonable fit $\chi^2 \sol
1$ for 16-17 degrees of freedom in EPIC-pn) with a two-component model (two thin plasmas at 0.25, 1.4 keV, solar abundance or one plasma at $\sim 0.4$ keV, solar abundance and a power law component with $\Gamma$ fixed at 1.9)."
 Either models could )o Interpreted in the framework of he emission from spira and starburst galaxies. resulting youn to the combined contribution of a population of resolved compact sources aud a diffuse enission. nios ikelv due to a hot phase of the ISM.," Either models could be interpreted in the framework of the emission from spiral and starburst galaxies, resulting from to the combined contribution of a population of unresolved compact sources and a diffuse emission, most likely due to a hot phase of the ISM."
 The line-ofseht absorption is always consistent with the Galactic value., The line-of-sight absorption is always consistent with the Galactic value.
" The unabsorbed total flux from this object is ~~lads101ον, Whichcorres corresponds↴. to a otal iutriusie Luminosity of L,~εν10°"" hone2.0 keV). with a contribution of 1/3 frou the softer (plasina) component and 2/3 arising frou the larder (higher temperature/power law) compoucnt. respectively."," The unabsorbed total flux from this object is $_x \sim 1.4 \times 10^{-14}$, which corresponds to a total intrinsic luminosity of $_x \sim 4\times10^{39} $ (0.5-2.0 keV), with a contribution of 1/3 from the softer (plasma) component and 2/3 arising from the harder (higher temperature/power law) component, respectively."
 The power aw CODI]rent could however also be interpreted as due to a central ACN. visible in the optical ata.," The power law component could however also be interpreted as due to a central AGN, visible in the optical data."
" Towever. its mtriusic luminosity would oulv be Ly~ 1(2.0-10 keV). indicative of a very faint ACN, unless it were interprete as the scattered comuponcut of a heavily obscured object."," However, its intrinsic luminosity would only be $_x \sim 4\times10^{39} $ (2.0-10 keV), indicative of a very faint AGN, unless it were interpreted as the scattered component of a heavily obscured object."
 Optical line. cussion ratios, Optical line emission ratios
located near the magnetic poles.,located near the magnetic poles.
 Hence the bursts would be associated with a particular aclive region on the surface. resulüng in a correlation with pulse phase.," Hence the bursts would be associated with a particular active region on the surface, resulting in a correlation with pulse phase."
 Lyutikoy(2002) proposed another burst emission mechanism within (he framework of je magnetar model., \citet{lyu02} proposed another burst emission mechanism within the framework of the magnetar model.
 Ie suggested that the bursting activity of ANPs and SGRs is due to 1e release of magnetic energv stored in non-potential magnetic fields by reconnection-tvpe evenis in (he magnetosphere., He suggested that the bursting activity of AXPs and SGRs is due to the release of magnetic energy stored in non-potential magnetic fields by reconnection-type events in the magnetosphere.
 Ii this model. bursts occur at random. phases because the enussion site is high in the magnetosphere.," In this model, bursts occur at random phases because the emission site is high in the magnetosphere."
 Hence we observe all bursts., Hence we observe all bursts.
 This mechanism will —sroducem harder ancl shorter bursts as compared to the ones due to surface Iracturing., This mechanism will produce harder and shorter bursts as compared to the ones due to surface fracturing.
 Solter il longer bursts are achieved by a combination of reconnection and a small contribution Tom surface cooling. as energetic reconnection events will precipitate particles which will veal (he surface.," Softer and longer bursts are achieved by a combination of reconnection and a small contribution from surface cooling, as energetic reconnection events will precipitate particles which will heat the surface."
 Since there is a cdiuration-Eluence correlation in both GR. (Gógüs and ANP (Gavriletal.2004) bursts. this model suggests that the shorter unminous) bursts are harder (han the longer (more luminous) bursts.," Since there is a duration-fluence correlation in both SGR \citep{gkw+01} and AXP \citep{gkw04} bursts, this model suggests that the shorter (less-luminous) bursts are harder than the longer (more luminous) bursts."
 A hardness-Iluence correlation was found for SGR bursts (Gógüsetal.2001).. but an anti-correlation was found or the 80 bursts from ANP citepekw04..," A hardness-fluence correlation was found for SGR bursts \citep{gkw+01}, but an anti-correlation was found for the 80 bursts from AXP \\citep{gkw04}."
 It should also be noted that for aand {(he more energetic bursts are the hardest. although only three bursts have been observed (hus far.," It should also be noted that for and the more energetic bursts are the hardest, although only three bursts have been observed thus far."
 Hence the aspects Chat differentiate (he surface-cooling model [rom the reconnection model for bursts seem to be the same aspects Chat separate (he canonical SGR bursts from ihe long-duration AXP bursts., Hence the aspects that differentiate the surface-cooling model from the reconnection model for bursts seem to be the same aspects that separate the canonical SGR bursts from the long-duration AXP bursts.
 In the surface-cooling model one expects longer durations. a correlation wilh pulse phase and a fluence-hardness anti-correlation.," In the surface-cooling model one expects longer durations, a correlation with pulse phase and a fluence-hardness anti-correlation."
 It is possible that both mechanisms (surface and magnetospheric) are responsible for creating ANP and SGR bursts. but that magnetospheric bursts are more common in SCGlis.," It is possible that both mechanisms (surface and magnetospheric) are responsible for creating AXP and SGR bursts, but that magnetospheric bursts are more common in SGRs."
 This is not unreasonable if we consider the (wisted-magnetosphere model proposed by Thompsonetal.(2002)., This is not unreasonable if we consider the twisted-magnetosphere model proposed by \citet{tlk02}.
. In this extension (o the magnetar model. Thompsonetal.(2002) suggested that the highly twisted internal magnetic field of a magnetar imposes stresses on (he erust which in (urn twist the external dipole field.," In this extension to the magnetar model, \citet{tlk02} suggested that the highly twisted internal magnetic field of a magnetar imposes stresses on the crust which in turn twist the external dipole field."
 The twisted external fields induce currents in the magnetosphere., The twisted external fields induce large-scale currents in the magnetosphere.
 The inferred dipole magnetic field strengths. Iuminosity and spectra of SGRs all suggest that the global “twists” of their magnetic fields are greater than those of the AXPs.," The inferred dipole magnetic field strengths, luminosity and spectra of SGRs all suggest that the global “twists” of their magnetic fields are greater than those of the AXPs."
" If the external fields of SGRs are much more ""twisted"" than those ol the AXPs. that would make them more susceptible to reconnection tvpe events in (heir magnetosphere."," If the external fields of SGRs are much more “twisted” than those of the AXPs, that would make them more susceptible to reconnection type events in their magnetosphere."
 Furthermore. if SGRs have stronger magnetic fields than the AXPs. then they would be less susceptible to surface fracture events because at high field strengths the crustal motions are expected to become plastic.," Furthermore, if SGRs have stronger magnetic fields than the AXPs, then they would be less susceptible to surface fracture events because at high field strengths the crustal motions are expected to become plastic."
critical mass-to-Ilux ratio as (i=(ALS)/(AL/laa. where & is the magnetic Hux.,"critical mass-to-flux ratio as $\mu = (M/\Phi)/(M/\Phi)_{\text{crit}}$, where $\Phi$ is the magnetic flux."
 For a spherical configuration. the critical value is given bv (Md)zm0.125€.7 (?)..," For a spherical configuration, the critical value is given by $(M/\Phi)_{\text{crit}} \approx 0.125\, \text{G}^{-1/2}$ \citep{Mouschovias1976dz}."
" Choosing so=20 the initial magnetic field strength is given w 30.7μέ, and the plasma beta is given by Oyu=56. TheAlfvén "," Choosing $\mu=20$ the initial magnetic field strength is given by $30.7\,\mug$, and the plasma beta is given by $\beta_{\text{plasma}} = 56$."
speed is ey=Bofapo3.910kms," The speed is $v_A=B_0 / \sqrt{4 \pi \rho_0}= 3.9 \times 10^{-2}\,\unit{km}\,\unit{s}^{-1}$."
 The initial angular velocity is Ου=43-10.+s+ for he cloud which is in solid body rotation. corresponding to Qufy= 0.4.," The initial angular velocity is $\Omega_0 = 4.3\cdot 10^{-13}\,\unit{s}^{-1}$ for the cloud which is in solid body rotation, corresponding to $\Omega_0 \tff = 0.4$ ."
 Using these choices. we get for the energy ratios Athen=Éaesa/£s]O87 and ua=EsaEl 045.," Using these choices, we get for the energy ratios $\alpha_{\text{therm}} = E_{\text{therm}}/\left| E_{\text{grav}}\right| = 0.37$ and $\beta_{\text{rot}} = E_{\text{rot}}/\left| E_{\text{grav}}\right| = 0.045$ ."
 ? characterize their models. by a. cimensionless xwameter o=Oy/api resulting for our choice of initial conditions in a value of ξ0.2. thus comparable with the rapid rotating model considered by these authors.," \cite{Machida2008fk} characterize their models by a dimensionless parameter $\omega = \Omega_0/\sqrt{4\pi G \rho_0}$ resulting for our choice of initial conditions in a value of $\omega=0.2$, thus comparable with the rapid rotating model considered by these authors."
 The Jeans condition lor SPL given by 2 requires that the mass of the cloud needs to be sulliciently resolved. and that the particle softening length needs to be equal to the smoothing length. in order to avoid numerical artefacts during cloud. collapse.," The Jeans condition for SPH given by \cite{Bate1997sj} requires that the mass of the cloud needs to be sufficiently resolved, and that the particle softening length needs to be equal to the smoothing length, in order to avoid numerical artefacts during cloud collapse."
 They proved. that. the minimum number of particles required. to. resolve. the cloud. mass is given by Nin=2AoNeinMas where Ma ds. the Jeans mass.," They proved, that the minimum number of particles required to resolve the cloud mass is given by $N_{\text{min}} = 2 M_0 N_{\text{neigh}}/M_{\text{J}}$, where $M_{\text{J}} $ is the Jeans mass."
 Phere exist several formulations of the Jeans mass which dilfer. as was pointed out by 2.. by numerical prefactors.," There exist several formulations of the Jeans mass which differ, as was pointed out by \cite{Nelson2006fk}, , by numerical prefactors."
 We usethe most conservative formulation that eives the lowest value for the Jeans mass: lor Japc£p 2.al posi we. get. using: eq. (1).," We usethe most conservative formulation that gives the lowest value for the Jeans mass: For $c_{\textrm{s}}^3/\rho^{-1/2}$ at $\rho_{\text{crit}}$ we get, using eq. \ref{eq:eos}) ),"
 hl27620p31/2 and thus a value of Nun~48000 [or Nuus=04.," $2^{3/4} c_{\textrm{s},0}^3\rho_{\text{crit}}^{-1/2}$ and thus a value of $N_{\text{min}} \sim 48000$ for $N_{\text{neigh}} = 64$."
" Enmploving V=4-10"" particles within the cloud (6-107 in the ambient medium). we have NV~83Nii and thus meet the requirements imposed by the Jeans condition."," Employing $N=4 \cdot 10^6$ particles within the cloud $6 \cdot 10^5$ in the ambient medium), we have $N \sim 83\,N_{\text{min}}$ and thus meet the requirements imposed by the Jeans condition."
 Actelitionall. we would like to emphasize that we also cid. simulations with 1/5 of the particles and found qualitatively the same behaviour as described here.," Additionally, we would like to emphasize that we also did simulations with $\sim 1/5 $ of the particles and found qualitatively the same behaviour as described here."
 Reearcding the evolution of the magnetic field. we show in Fie. (1))," Regarding the evolution of the magnetic field, we show in Fig. \ref{fig:ncore_bfield}) )"
 the dependeney of the magnetic field £ on the core density ni., the dependency of the magnetic field $B$ on the core density $n_c$.
 Assuming a scaling relation parametrized as Boxn. às is usually cone in the literature (e.ο.?).. we performed a fit which gave a result of &=0.58.," Assuming a scaling relation parametrized as $B\propto n^{\kappa}$, as is usually done in the literature \citep[e. g.][]{Heilesuq}, we performed a fit which gave a result of $\kappa = 0.58$."
 For this fit we considered only the region of the highest density Minas Within the collapsing cloud., For this fit we considered only the region of the highest density $n_{\text{max}}$ within the collapsing cloud.
 Increasing the considered density range used for averaging up to μονSStas. as in ?.. we see the same trend only slightly steeper with Bo=0.64 (not shown).," Increasing the considered density range used for averaging up to $n_{\max}/2 \leq n \leq n_{\max}$, as in \cite{Banerjee2006uq}, we see the same trend only slightly steeper with $\kappa = 0.64$ (not shown)."
 This is in good agreement with ? and. νι who find a value of &~0.6. but in disagreement with other studies (e.ο.?22?)..," This is in good agreement with \cite{Banerjee2006uq} and \cite{Price2007tg}, who find a value of $\kappa \sim 0.6$, but in disagreement with other studies \citep[e. g.][]{Desch2001fk,Li2004uq,Burzle2011fk}."
 However. the scaling relation depends strongly on the geometry of the magnetic field.," However, the scaling relation depends strongly on the geometry of the magnetic field."
 We define the aciabatic. or first. core as the space occupied bv the material exceeding the eritical density. posi. that is where the eas becomes optically thick.," We define the adiabatic, or 'first', core as the space occupied by the material exceeding the critical density $\rho_{\textrm{crit}}$, that is where the gas becomes optically thick."
 We find that. the first core has formed at à time of 1.1fy or 33000 vears.," We find that the first core has formed at a time of $1.1 \tff$ or $33000\, \unit{years}$ ."
 At this time the central density has reached a value of nas&10em.7. and the mass of the first core is M=0:02i.," At this time the central density has reached a value of $n_{\max} \simeq 10^{11}\,\unit{cm}^{-3}$ , and the mass of the first core is $M \approx 0.02\,\msun$."
" Due to the fast rotation the first core has an oblate structure. with an equatorial radius of re,=48.5AU inthe sy plane. and a polar radius of μα29.5XU parallel to the c-axis at formation time."," Due to the fast rotation the first core has an oblate structure, with an equatorial radius of $r_{\textrm{eq}} = 43.5\,\textrm{AU}$ in the $x-y$ plane, and a polar radius of $r_{\textrm{pol}} =9.5\,\textrm{AU}$ parallel to the $z$ -axis at formation time."
 Defining the oblateness as usual. we find a value of 2=1.raraO78.," Defining the oblateness as usual, we find a value of $\varepsilon = 1-r_{\textrm{pol}}/r_{\textrm{eq}}=0.78$."
 Only shortly after formation of the first core. at Lilt. a slow bipolar outllow with peak velocities of LOkmsis ejected [rom the disc.," Only shortly after formation of the first core, at $\sim 1.11 \tff$ , a slow bipolar outflow with peak velocities of $\sim 1.9\,\unit{km}\,\unit{s}^{-1}$ is ejected from the disc."
 This can be seen in Fig. (2)).," This can be seen in Fig. \ref{fig:rho}) ),"
 which shows the normalized density near the x-z plane or different timesteps. and the vectors show the velocity ield (arrows have equal. magnitude for better. visibility).," which shows the normalized density near the x-z plane for different timesteps, and the vectors show the velocity field (arrows have equal magnitude for better visibility)."
 This outflow. is accompanied. with the build-up of a strong oroidal magnetic field. as shown in Fig. (3)).," This outflow is accompanied with the build-up of a strong toroidal magnetic field, as shown in Fig. \ref{fig:btor}) ),"
 where the ratio BurlBuealin the outllow regions., where the ratio $B_{\text{tor}}/B_{\text{pol}} > 1$ in the outflow regions.
 This kind of ow-velocitv outflow. which is frequently found. in other simulations (o.g.????).0 is usually considered as magnetic ower (22?)..," This kind of low-velocity outflow, which is frequently found in other simulations \citep[e. g.][]{Tomisaka1998fk,Banerjee2006uq,Hennebelle2008uq,Machida2008fk}, is usually considered as magnetic tower \citep{Lynden-Bell1996fk,Lynden-Bell2003fk,Kato2004uq}."
 In à magnetic tower. the toroidal component of he magnetic field is continuously generated by the rotating disc and pushes material into the surrounding medium by means of magnetic pressure.," In a magnetic tower, the toroidal component of the magnetic field is continuously generated by the rotating disc and pushes material into the surrounding medium by means of magnetic pressure."
 Additionally. this can be proven » considering the ratio of thermal to magnetic pressure which. in the outflow region. is given bv. Jupaua~OL indicating magnetic pressure dominating thermal pressure here.," Additionally, this can be proven by considering the ratio of thermal to magnetic pressure which, in the outflow region, is given by $\beta_{\text{plasma}} \sim 0.1$ indicating magnetic pressure dominating thermal pressure there."
 This magnetic tower [Dow creates a torus-like structure hat further expands into the surrounding gas. also visible in Fig. (2)).," This magnetic tower flow creates a torus-like structure that further expands into the surrounding gas, also visible in Fig. \ref{fig:rho}) )."
 We note that our results suggesting toroidal magnetic oressire as driving mechanism are in good. agreement with results presented by ? and ?.. but. however. in disagreement o the findings by 7..," We note that our results suggesting toroidal magnetic pressure as driving mechanism are in good agreement with results presented by \cite{Banerjee2006uq} and \cite{Hennebelle2008uq}, , but, however, in disagreement to the findings by \cite{Machida2008fk}."
 The latter authors attribute the emergence of the slow outllow to magneto-rotational effects rather than magnetic pressure., The latter authors attribute the emergence of the slow outflow to magneto-rotational effects rather than magnetic pressure.
 On the other hand. they had included the elleets of non-ideal MED: (ambipolar cilfusion and resistivity) which are absent in this work and in ? and 7 which might have an important influence on the magnetic field structure.," On the other hand, they had included the effects of non-ideal MHD (ambipolar diffusion and resistivity) which are absent in this work and in \cite{Banerjee2006uq} and \cite{Hennebelle2008uq} which might have an important influence on the magnetic field structure."
 Later in our simulation. at 1.17fp. also a fast outflow. with peak velocities of ~28kms|. emerges [rom the central parts of the first core. visible in the last panel of Eig. (2))," Later in our simulation, at $1.17\,\tff$, also a fast outflow, with peak velocities of $\sim 28\,\unit{km}\,\unit{s}^{-1}$, emerges from the central parts of the first core, visible in the last panel of Fig. \ref{fig:rho}) )"
 and Fig. (3)).," and Fig. \ref{fig:btor}) ),"
 respectively., respectively.
 A similar structure is also visible in ? in the weak field. case. probably also at the same simulation time.," A similar structure is also visible in \cite{Hennebelle2008uq} in the weak field case, probably also at the same simulation time."
 Llowever. since. we use a comparable set-up as these authors. the same restrictions regarding the thermal structure of the protostar also apply to our work.," However, since we use a comparable set-up as these authors, the same restrictions regarding the thermal structure of the protostar also apply to our work."
 So. although the velocities found. here are comparable to those obtained in other work (o.&.2?2).. an identification of this [ast flow component with optical jets seen in observations. which believed to be launched during second collapse. sectis to be doubtful at this stage.," So, although the velocities found here are comparable to those obtained in other work \citep[e. g.][]{Banerjee2006uq,Machida2008fk}, an identification of this fast flow component with optical jets seen in observations, which believed to be launched during second collapse, seems to be doubtful at this stage."
 Certainlv. further investigations considering a more correct treatment of the thermodynamics within molecular cloud core are necessary.," Certainly, further investigations considering a more correct treatment of the thermodynamics within molecular cloud core are necessary."
 Finally. in ((4)) we show a sequence of spatial averages of theratio Dis/Byer from 1.10fr to.1.16 fr. calculated in the central parts of the cloud. core.," Finally, in \ref{fig:btorbpol_plot}) ) we show a sequence of spatial averages of theratio $B_{\textrm{tor}}/B_{\textrm{pol}}$ from $1.10\,\tff$ to$1.16\,\tff$ , calculated in the central parts of the cloud core."
 Here we see the generation of the toroidal part of the magneticfield. as well as itsoutward. propagation with time.," Here we see the generation of the toroidal part of the magneticfield, as well as itsoutward propagation with time."
 However. at 1.15fy it is also visible that the toroidal part is re-generated in the very central parts of the disc.," However, at $1.15\,\tff$ it is also visible that the toroidal part is re-generated in the very central parts of the disc."
 Thus. this proves the connection of the outflow with the evolution of the toroidal Ποιά component.," Thus, this proves the connection of the outflow with the evolution of the toroidal field component."
" Rowe~1 BR. 7g (p~Le sim?) M,~ M. Rp~(AL/p)5m] BR. Az My~10%101"" 3 Mz to the WD.", $R_{out}\sim 1$ $_\odot$ $R_R$ $\rho\sim 1$ $^{-3}$ $M_\star\sim$ $_\odot$ $R_R\sim (M_\star/\rho)^{1/3}\approx 1$ $_\odot$ $\dot M_Z$ $\dot M_Z\sim 10^6-10^{10}$ $^{-1}$ $\dot M_Z$ to the WD.
 IIowever. he question of how hieh-Z eleiieuts eet transported to the WD atmosphere frou the ring of solid particles. which docs not extend all the way to the WD surface. has not vet been auswered.," However, the question of how high-Z elements get transported to the WD atmosphere from the ring of solid particles, which does not extend all the way to the WD surface, has not yet been answered."
 Tn principle. a dense ring of particles should evolve siuplv because of the angular momentum trausfer due to iuter-particle collisions. in full analogy with the rines of Saturn.," In principle, a dense ring of particles should evolve simply because of the angular momentum transfer due to inter-particle collisions, in full analogy with the rings of Saturn."
 However. the evolution time scale of Saturu's riugs due to this process is too long. ~10? vr (Salinou 2010). aud resultant values of Mz are negligible.," However, the evolution time scale of Saturn's rings due to this process is too long, $\sim 10^9$ yr (Salmon 2010), and resultant values of $\dot M_Z$ are negligible."
 Another natural mechanisin driving debris towards the WD is due to stellar radiation iuteracting with the disk aud eiviug rise to the Poiutines-Bobertson. (PR) drag (Durus 1979)., Another natural mechanism driving debris towards the WD is due to stellar radiation interacting with the disk and giving rise to the Pointing-Robertson (PR) drag (Burns 1979).
 Previously. Farili (2010) claimed that PR drag cannot provide Mz higher than 105 10556 Land dismissed this process as irrelevant.," Previously, Farihi (2010) claimed that PR drag cannot provide $\dot M_Z$ higher than $10^3-10^4$ g $^{-1}$ and dismissed this process as irrelevant."
 The goal of this paper is to critically re-exauine the effect of radiative forces on the debris disk evolution. aud to show in particular that PR drag can give rise to My interred from observations.," The goal of this paper is to critically re-examine the effect of radiative forces on the debris disk evolution, and to show in particular that PR drag can give rise to $\dot M_Z$ inferred from observations."
" We envisage the following conceptual picture of the cireuui-WD ονομα,", We envisage the following conceptual picture of the circum-WD environment.
 A dense disk (or ring) of particles lies inside the Roche radius Ry of the WD aud evolves uudoer the action of external agents. e.g. radiation forces.," A dense disk (or ring) of particles lies inside the Roche radius $R_R$ of the WD and evolves under the action of external agents, e.g. radiation forces."
" Particles mügrate through the disk towards the sublanation radius ων where thei equilibria temperature equals the sublimation temperature Ti: where δὲ,isthe WD radius.T;z:L500 I& for silicate exams. and T,,=T,/104 K is the normalized stellar"," Particles migrate through the disk towards the sublimation radius $R_s$, where their equilibrium temperature equals the sublimation temperature $T_s$ :22^2 )^2, where $R_\star$isthe WD radius,$T_s\approx 1500$ K for silicate grains, and $T_{\star,4}\equiv T_\star/10^4$ K is the normalized stellar"
between the components.,between the components.
 However. for successful fitting of the slight asymmetry in the light curves. the optimal model of the system needs a bright spot located in the neck region of the more massive. hotter component.," However, for successful fitting of the slight asymmetry in the light curves, the optimal model of the system needs a bright spot located in the neck region of the more massive, hotter component."
 This result agrees with the analysis by Qianetal.(2007).. who find that mass transfer from the less massive to the more massive component. indicated by their O-C analysis. could justify a possible hot spot in the neck region of the more massive component.," This result agrees with the analysis by \citet{qiana07}, who find that mass transfer from the less massive to the more massive component, indicated by their O-C analysis, could justify a possible hot spot in the neck region of the more massive component."
 With the large difference in the masses of components. their equal temperatures suggest a significant energy exchange through the neck region.," With the large difference in the masses of components, their equal temperatures suggest a significant energy exchange through the neck region."
 Because of the specific light curve shape with almost equal depths of the primary and secondary eclipses and a relatively small amplitude resulting from the low orbital inclination 55°). we also tested the hypothesis that the system is in à W subtype W UMa configuration.," Because of the specific light curve shape with almost equal depths of the primary and secondary eclipses and a relatively small amplitude resulting from the low orbital inclination $i\approx 55^\circ$ ), we also tested the hypothesis that the system is in a W subtype W UMa configuration."
 However. this model gave a significantly worst fit to the observations.," However, this model gave a significantly worst fit to the observations."
" In comparison with previous studies of QX And by Miloneal.(1995) and Qianetal.(2007).. who used the underestimated mass ratio of q=0.2 obtained from the radial velocities of Miloneetal.(1905). our solution yields a significantly more massive secondary (Atewii;=0.24M... Meguia=9.27Me. and Alqius=0.45 MJ. an overcontact parameter that is between their estimated values (Patilone=2196. fouan= 55%. and fai,sudy= 35%). somewhat larger radit of the components (Re.ijs;=0.68Res. Rn.Mitone=39 Re. and Rethisstudy=0.88Re. Ro.thisstudy=136 Re). and a lower inclination Cyr3σως55”. fOuian>Nu~567. and Api,study9 557)."," In comparison with previous studies of QX And by \citet{mila95} and \citet{qiana07}, who used the underestimated mass ratio of $\rm q \approx 0.2$ obtained from the radial velocities of \citet{mila95}, our solution yields a significantly more massive secondary ${\cal M}_{\rm c,\ Milone}=0.24\ M_\odot$, ${\cal M}_{\rm c,\ Quian}=0.27\ M_\odot$, and ${\cal M}_{\rm c,\ this\ study}=0.45\ M_\odot$ ), an overcontact parameter that is between their estimated values $f_{\rm Milone}=21\%$, $f_{\rm Quian}=55\%$ , and $f_{\rm this\ study}=35\%$ ), somewhat larger radii of the components ${\cal R}_{\rm c,\ Milone}=0.68\ R_\odot$, ${\cal R}_{\rm h,\ Milone}=1.39\ R_\odot$ , and ${\cal R}_{\rm c,\ this\ study}=0.88\ R_\odot$, ${\cal R}_{\rm h,\ this\ study}=1.46\ R_\odot$ ), and a lower inclination $i_{\rm Milone}\approx58^\circ$, $i_{\rm Quian}\approx56^\circ$, and $i_{\rm this\ study}\approx55^\circ$ )."
 The temperatures. absolute bolometric magnitudes. and the estimated distance of the system agree well between these two studies and our own.," The temperatures, absolute bolometric magnitudes, and the estimated distance of the system agree well between these two studies and our own."
 RW Com (HIP 61243) is à short-period eclipsing binary., RW Com (HIP 61243) is a short-period eclipsing binary.
 Its variability was first recognized by Jordan(1923).. who discovered it while observing the Cepheid variable S Comae and classified it as 6 Lyrae type binary.," Its variability was first recognized by \citet{jor23}, who discovered it while observing the Cepheid variable S Comae and classified it as $\beta$ Lyrae type binary."
 Struve(1950) performed the first spectral observations of the system and suggested that the emission components in the Ca II absorption line. observed to be strong in both conjunctions and weak in quadratures. originated in both stars.," \citet{stra50} performed the first spectral observations of the system and suggested that the emission components in the Ca II absorption line, observed to be strong in both conjunctions and weak in quadratures, originated in both stars."
 O'Connell(1951) noted the asymmetry and variability of the light curves. and Milone(1976). interpreted them as evidence of mass loss from the system. primarily through the outer Lagrangian point. facing the observer at primary minimum.," \citet{oconn51} noted the asymmetry and variability of the light curves, and \citet{mila76} interpreted them as evidence of mass loss from the system, primarily through the outer Lagrangian point, facing the observer at primary minimum."
 Miloneetal.(1980) constructed light curves based on all data up to the time of their study. and also noted the variability in the light curves and the differences between the light levels of maxima.," \citet{mila80} constructed light curves based on all data up to the time of their study, and also noted the variability in the light curves and the differences between the light levels of maxima."
 The asymmetry was reported às increasing with wavelength by Davidgeetal.(1981)., The asymmetry was reported as increasing with wavelength by \citet{dav81}.
 From their spectroscopic study. Miloneetal.(1985) found the mass ratio of 0.34 and classified the system as a W- W UMa binary of spectral type G5-G8.," From their spectroscopic study, \citet{mila85} found the mass ratio of 0.34 and classified the system as a W-subtype W UMa binary of spectral type G5-G8."
 Based on the results of this study. Miloneetal.(1987) analyzed UBV light curves of the system with the Wilson-Devinney code.," Based on the results of this study, \citet{mila87} analyzed UBV light curves of the system with the Wilson-Devinney code."
 Fixing the temperature to three different values (5400 K. 5600 K. and 5800 K) according to the estimated spectral type range (G5-G8). they tested different solutions. including both cold and hot photospheric spot configurations. and gave the absolute parameters of the solution that fit the observations best.," Fixing the temperature to three different values (5400 K, 5600 K, and 5800 K) according to the estimated spectral type range (G5-G8), they tested different solutions, including both cold and hot photospheric spot configurations, and gave the absolute parameters of the solution that fit the observations best."
 Srivastava(1987) published the first O-C curve of the system based on the previously published times of minima. and found a eyelie variation in the orbital period.," \citet{sriv87} published the first O-C curve of the system based on the previously published times of minima, and found a cyclic variation in the orbital period."
 Relying on the closely spaced data obtained between 1967 and 1986. Srivastava(1987) suggested that a third body with an orbital period of 16 years was causing the period to vary in time. Qian(2002).," Relying on the closely spaced data obtained between 1967 and 1986, \citet{sriv87} suggested that a third body with an orbital period of 16 years was causing the period to vary in time. \citet{qiana02},"
. however. found that the variation caused by the third body had a 13.3 year period. and was superimposed on a decreasing trend that the author explained by angular momentum loss from the system.," however, found that the variation caused by the third body had a 13.3 year period, and was superimposed on a decreasing trend that the author explained by angular momentum loss from the system."
 Yang&Liu(2003) considered both mass exchange and mass loss mechanisms thatcould cause the observed decrease in the period but found that the cyclic variation superimposed on the decreasing trend was quasi-periodic: hence. it could only be attributed to magnetic activity.," \citet{yangli03} considered both mass exchange and mass loss mechanisms thatcould cause the observed decrease in the period but found that the cyclic variation superimposed on the decreasing trend was quasi-periodic; hence, it could only be attributed to magnetic activity."
direction.,direction.
 This approach is justified if the snow line location is sufficiently far from the inner edee., This approach is justified if the snow line location is sufficiently far from the inner edge.
 The 2D structure of the inner disk region (the pulfed-up inner rim and the adjacent shadowed region) seems to be important only in (he innermost part of the disk around a T Tami star judging from results for Herbig Ae/Be stars by Dullemond (2002)., The 2D structure of the inner disk region (the puffed-up inner rim and the adjacent shadowed region) seems to be important only in the innermost part of the disk around a T Tauri star judging from results for Herbig Ae/Be stars by Dullemond (2002).
 Though the shacdowecl region extends to slightly large heliocentric distances. it does not matter for the scope of (his study because it only lowers the disk temperature ancl does not shilt the snow line location outward.," Though the shadowed region extends to slightly large heliocentric distances, it does not matter for the scope of this study because it only lowers the disk temperature and does not shift the snow line location outward."
 Details are given in Appendix., Details are given in Appendix.
 The radial distribution of the gas surface density is modeled assuming Chat (he disk is in the steady accretion state. Le.. the mass aceretion rate Af is constant along the racial direction A.," The radial distribution of the gas surface density is modeled assuming that the disk is in the steady accretion state, i.e., the mass accretion rate $\dot{M}$ is constant along the radial direction $R$."
" The gas surface density in a region where /229HR, (the stellar raclius) is given as (e.g.. Pringle 1931). where νι) is the viscosity in the disk."," The gas surface density in a region where $R \gg R_{*} $ (the stellar radius) is given as (e.g., Pringle 1981), where $\nu_{t}(R)$ is the viscosity in the disk."
 The assumption of the steady. accretion is justified in the region around the snow line because the snow lineis usually located within LOAU and the viscous diffusion timescale there is sufficiently smaller than the entire disk evolution timescale., The assumption of the steady accretion is justified in the region around the snow line because the snow lineis usually located within $10$ AU and the viscous diffusion timescale there is sufficiently smaller than the entire disk evolution timescale.
" The viscositv 5, is modeled with the o-prescription (Shakura Suuvaev 1973) as p,=acz/Og. where a is a non-dimensional parameter. e,=kT/(jm,) is the isothermal sound velocity of gas. & is the Boltzmann constant. 7 is the gas temperature. ji is the mean molecular weight. ni is the atomic mass unit. Oy=G.M,/IP is the Ixepler angular velocity. G is the gravitational constant. and AM, is the stellar mass. respectively."," The viscosity $\nu_{t}$ is modeled with the $\alpha$ -prescription (Shakura Sunyaev 1973) as $ \nu_{t} = \alpha c_{s}^{2}/\Omega_{\mathrm{K}}$, where $\alpha$ is a non-dimensional parameter, $c_{s}=\sqrt{kT / (\bar{\mu} m_{u})}$ is the isothermal sound velocity of gas, $k$ is the Boltzmann constant, $T$ is the gas temperature, $\bar{\mu}$ is the mean molecular weight, $m_{u}$ is the atomic mass unit, $\Omega_{\mathrm{K}} = \sqrt{GM_{*} / R^{3}}$ is the Kepler angular velocity, $G$ is the gravitational constant, and $M_{*}$ is the stellar mass, respectively."
 The value ol a ranges from 0.001 to 0.1 according to ideal MIID simulations (Ilawleva, The value of $\alpha$ ranges from $0.001$ to $0.1$ according to ideal MHD simulations (Hawley.
f 1995. 1996).," 1995, 1996)."
 The value of a=0.01 is adopted as a fiducial one throughout the disk in this study except for 83.3., The value of $\alpha = 0.01$ is adopted as a fiducial one throughout the disk in this study except for 3.3.
 In the evaluation of η. the sound velocity ὃς at the midplane (Z= 0) is used.," In the evaluation of $\nu_{t}$ , the sound velocity $c_{s}$ at the midplane $Z=0$ ) is used."
 As for the mean molecular weight. ji=2.3 is used.," As for the mean molecular weight, $\bar{\mu} = 2.3$ is used."
left panel of relcentroid.. where the arms of the green crosses show the uncertainty in RA and DEC.,"left panel of \\ref{centroid}, where the arms of the green crosses show the uncertainty in RA and DEC."
 We see (hat in all quarters (he transit signal location is consistently offset to the west by about 0.1 arcsec., We see that in all quarters the transit signal location is consistently offset to the west by about 0.1 arcsec.
 The robust average across quarters. weighted by (he quarterly uncertainty. is shown by (the magenta cross. with the solid circle giving its 2-s1gma uncertaintv radius.," The robust average across quarters, weighted by the quarterly uncertainty, is shown by the magenta cross, with the solid circle giving its 3-sigma uncertainty radius."
 This average centroid observation is offset by about 0.1 arcsec with a significance of 5.7 signa., This average centroid observation is offset by about 0.1 arcsec with a significance of 5.7 sigma.
 The right panel of relcentroid shows the (ransit. signal source. estimated. by correlating the transit model wilh observed photocenter motion (Jenkins et al., The right panel of \\ref{centroid} shows the transit signal source estimated by correlating the transit model with observed photocenter motion (Jenkins et al.
 90110)., 2011b).
 Photocenter motion also shows a statistically significant (17 sigma) transit signal location offset. but the offsets from the two methods are in significant disagreement. suggesting Chat these offsets are due to measurement bias.," Photocenter motion also shows a statistically significant (17 sigma) transit signal location offset, but the offsets from the two methods are in significant disagreement, suggesting that these offsets are due to measurement bias."
 The uncertainty in PRE-fit centroids is based on (he propagation of pixel-level uncertainty and does not include a possible PRE fit bias., The uncertainty in PRF-fit centroids is based on the propagation of pixel-level uncertainty and does not include a possible PRF fit bias.
 Sources of PRE fit bias include scene crowding. because the fit is of a single PRF assuming a single star. as well as PRF error.," Sources of PRF fit bias include scene crowding, because the fit is of a single PRF assuming a single star, as well as PRF error."
 The measured olfset is the difference between the centroids of the difference and out-ofF-transit images. so common biases such as PRE error should cancel.," The measured offset is the difference between the centroids of the difference and out-of-transit images, so common biases such as PRF error should cancel."
 Bias due (ο crowding. however. will not cancel because. to the extent that variations in other field stars are not correlated. with transits. field stars will not contribute to the difference image.," Bias due to crowding, however, will not cancel because, to the extent that variations in other field stars are not correlated with transits, field stars will not contribute to the difference image."
 In other words the difference image wil have (he appearance of a single star where (he transit occurs. so (there is no crowding bias in (he difference image PRE fit.," In other words the difference image will have the appearance of a single star where the transit occurs, so there is no crowding bias in the difference image PRF fit."
 To investigate the possibility that the observed offsets are due to PRE-lt bias caused by crowding we modeled the local scene using stars Irom the Ixepler Input Catalog supplemented by UIXIRT observations (see section 3.2) and the measured PREF. induced the transit on ]xepler-15 in (he model. and performed (he above PREF fit analysis on (he model difference ancl out-ol-Utransit images.," To investigate the possibility that the observed offsets are due to PRF-fit bias caused by crowding we modeled the local scene using stars from the Kepler Input Catalog supplemented by UKIRT observations (see section 3.2) and the measured PRF, induced the transit on Kepler-15 in the model, and performed the above PRF fit analysis on the model difference and out-of-transit images."
 The resulting moclel offsets lor quarters one through four is shown on 3 as open diamonds. (, The resulting model offsets for quarters one through four is shown on \ref{centroid} as open diamonds. (
Only four quarters are shown because the model is very nearly periodic with a period of one vear.),Only four quarters are shown because the model is very nearly periodic with a period of one year.)
 The robust average of the model offsets. again weighted by propagated uncertainty. is shown as the filled diamond. with the dotted circle showing the average model 3-sigina uncertainty.," The robust average of the model offsets, again weighted by propagated uncertainty, is shown as the filled diamond, with the dotted circle showing the average model 3-sigma uncertainty."
 We see that the model points are consistently offset (o the west. and the observed average is well-contained within the model 3-sigma uneertainty.," We see that the model points are consistently offset to the west, and the observed average is well-contained within the model 3-sigma uncertainty."
 This is consistent with the observed in-transit centroid offsets being due to PRE fit bias (mostly) due to crowding., This is consistent with the observed in-transit centroid offsets being due to PRF fit bias (mostly) due to crowding.
 We therefore can be highly confident that the transit signal is due {ο transits on Ixepleir-15., We therefore can be highly confident that the transit signal is due to transits on Kepler-15.
]t is commonly. accepted that “Pype la supernovae are the result. of the thermonuclear explosion of a mass accreting CO white dwarf.,It is commonly accepted that Type Ia supernovae are the result of the thermonuclear explosion of a mass accreting CO white dwarf.
 In the outburst. high amounts of “Ni and other radioactive isotopes are produced. opening the possibility to use 5-ravs as a diagnostic tool.," In the outburst, high amounts of $^{56}$ Ni and other radioactive isotopes are produced opening the possibility to use $\gamma$ -rays as a diagnostic tool."
 Although there is an agreement about the basic. properties of such SUpernovac. There are several theories to account. for these events.," Although there is an agreement about the basic properties of such supernovae, there are several theories to account for these events."
 One class of models assumes that the parent white cdwarf is very close to the Chandrasekhar mass and. that he thermonuclear runaway starts at the center., One class of models assumes that the parent white dwarf is very close to the Chandrasekhar mass and that the thermonuclear runaway starts at the center.
 According o the properties of the burning front. three cases can be considered: cletonation model. (Arnett 1969)... dellagration moclel (Nomotoetal.1984). and delaved detonation mociel (Ixhokhloyv.1991).," According to the properties of the burning front, three cases can be considered: detonation model \cite{Ar69}, , deflagration model \cite{No84} and delayed detonation model \cite{Kh91}."
 Reeenthy. a fourth model based on a sub-Chandrasekhar mass progenitor has gained popularity clue o some observational evidences (Phillips 1993: Maza et al.," Recently, a fourth model based on a sub-Chandrasekhar mass progenitor has gained popularity due to some observational evidences (Phillips 1993; Maza et al."
 904: Lamu et αἱ., 1994; Hamuy et al.
 1995)., 1995).
 In. this case. the explosion. is triggered. by the ignition of a freshly accreted. Le mantle (Ruiz-Lapucnte et al.," In this case, the explosion is triggered by the ignition of a freshly accreted He mantle (Ruiz-Lapuente et al."
 1993: Livne et al., 1993; Livne et al.
 1993: Wosslev et al., 1993; Wossley et al.
 1994: Arnett 1994)., 1994; Arnett 1994).
 Reearding the amount of radioactive material svnthesized. the chemical composition ancl the density ancl velocity profiles. the properties of ejecta are cillerent for each one of these models.," Regarding the amount of radioactive material synthesized, the chemical composition and the density and velocity profiles, the properties of ejecta are different for each one of these models."
 These. dillerences allect the evolution of the total intensity of the «-ray lines. their relative ratios anc even their widths ancl shapes as well as the importance and extension of the continuum component ofthe spectrum.," These differences affect the evolution of the total intensity of the $\gamma$ -ray lines, their relative ratios and even their widths and shapes as well as the importance and extension of the continuum component of the spectrum."
 Several authors have already investigated: the 5-ràv emission of type la supernovae (Gehrels ο al., Several authors have already investigated the $\gamma$ -ray emission of type Ia supernovae (Gehrels et al.
 LOST: Ambwani Burrows 1988: Burrows The 1990. Burrows 1991: Phe et al.," 1987; Ambwani Burrows 1988; Burrows The 1990, Burrows 1991; The et al."
 1993: Ituiz-Lapuente et al., 1993; Ruiz-Lapuente et al.
 199091: Lotflich Whoklov 1994: Kumagai Nomoto 1905: Wooslev limmes 1996) for different SNla models., 1993b; Höfflich Khoklov 1994; Kumagai Nomoto 1995; Woosley Timmes 1996) for different SNIa models.
 Lo most of these works a reduced number of SNelascenarios were stucliccl," In most of these works a reduced number of SNeIascenarios were studied,"
 Lo most of these works a reduced number of SNelascenarios were stucliccl.," In most of these works a reduced number of SNeIascenarios were studied,"
The two templates are fouud to be mareially correlated with the 19 CGIIz map. while all three. DIRBE £u-iufrared. templates show a siguificaut correlation.,"The two templates are found to be marginally correlated with the 19 GHz map, while all three DIRBE far-infrared templates show a significant correlation."
 When a aud a DIRBE template are snuultaueouslv fit to the 19 CGIIz map (via linear regression) the correlation cocficiceuts do not chauge sieuificautlv from those listed in Table 1 aud. in addition. the two fit parameters are esseutialv uncorrelated ([p|Zi 0.05).," When a and a DIRBE template are simultaneously fit to the 19 GHz map (via linear regression) the correlation coefficients do not change significantly from those listed in Table 1 and, in addition, the two fit parameters are essentially uncorrelated $|\rho|\simlt 0.05)$ ."
 We conclude that the correlatious with DIRBE dust cunission are independent of the correlations with cuuission., We conclude that the correlations with DIRBE dust emission are independent of the correlations with emission.
 The ampliude of the signal is much larger than expected for ordinary (vibrational) dust Cluission. as shown iu.," The amplitude of the signal is much larger than expected for ordinary (vibrational) dust emission, as shown in."
. Moreover. there is now good agrecincut between different experiments that this correlated component is brighter at lower frequeucies.," Moreover, there is now good agreement between different experiments that this correlated component is brighter at lower frequencies."
 So what physical compoucut is this?, So what physical component is this?
 Two couteudoers have been proposed., Two contenders have been proposed.
 I&96ab argue ou pliysical erouuds that free-free emission might be spatially correlated with dust., K96ab argue on physical grounds that free-free emission might be spatially correlated with dust.
 ILlowever. the correlations between Ho. (which is normally a good tracer of frece-free emission) and CMD maps. aud between Ila aud the DIRBE maps. are weak (L97: -].5c1a -].2«c1," However, the correlations between $\alpha$ (which is normally a good tracer of free-free emission) and CMB maps, and between $\alpha$ and the DIRBE maps, are weak (L97; -1.8cm -1.2cm"
 ILlowever. the correlations between Ho. (which is normally a good tracer of frece-free emission) and CMD maps. aud between Ila aud the DIRBE maps. are weak (L97: -].5c1a -].2«c1a," However, the correlations between $\alpha$ (which is normally a good tracer of free-free emission) and CMB maps, and between $\alpha$ and the DIRBE maps, are weak (L97; -1.8cm -1.2cm"
analysis. so we are simply fitting normalisations to the relation as a proxy for relative jet power.,"analysis, so we are simply fitting normalisations to the relation as a proxy for relative jet power."
 Note that for 4U 1543-47. XTE and A 0620-00 we only have a single datum. and so the “fit” is a simple sealing. no more.," Note that for 4U 1543-47, XTE J1550-564 and A 0620-00 we only have a single datum, and so the `fit' is a simple scaling, no more."
 Note also that we do not consider upper limits. and that for Cygnus X-] we do not include points which include any evidence for suppression of the radio emission as the source enters softer X-ray states (see Fig 3 of Gallo. Fender Pooley 2003 for an illustration of this).," Note also that we do not consider upper limits, and that for Cygnus X-1 we do not include points which include any evidence for suppression of the radio emission as the source enters softer X-ray states (see Fig 3 of Gallo, Fender Pooley 2003 for an illustration of this)."
 The normalisations. c. are simply fitted as This process can be repeated with near-infrared data. which dave been convincingly demonstrated to have a large contribution rom the jet (e.g. Homan et al.," The normalisations, $c$, are simply fitted as This process can be repeated with near-infrared data, which have been convincingly demonstrated to have a large contribution from the jet (e.g. Homan et al."
 2005: Russell et al., 2005; Russell et al.
 2006)., 2006).
 In Fig 3 we plot the equivalant ensemble of near-infrared data. and perform he same analysis of normalisations.," In Fig \ref{IR} we plot the equivalant ensemble of near-infrared data, and perform the same analysis of normalisations."
 For XTE 11550-564 we plot data both in the rise and decline phases of an outburst. which show different normalisations — see Russell et al.," For XTE J1550-564 we plot data both in the rise and decline phases of an outburst, which show different normalisations – see Russell et al."
 2007 and our discussion ater., 2007 and our discussion later.
 Note also that the correlation in Russell et al. (, Note also that the correlation in Russell et al. (
2006) extends o lower luminosities because it also utilizes optical data: however hose data are generally dominated by the irradiated accretion dise and are not suitable for estimating the jet power.,2006) extends to lower luminosities because it also utilizes optical data; however those data are generally dominated by the irradiated accretion disc and are not suitable for estimating the jet power.
" For both the radio and infrared data sets. we include a ‘representative’ measurement for the hard ""plateau state of GRS 19154105 (Fender Belloni 2004)."," For both the radio and infrared data sets, we include a `representative' measurement for the hard `plateau' state of GRS 1915+105 (Fender Belloni 2004)."
 These measurements should be interpreted with caution as this system — persistently very luminous since entering outburst in 1992 — has not been observed to enter a true canonical hard state., These measurements should be interpreted with caution as this system – persistently very luminous since entering outburst in 1992 – has not been observed to enter a true canonical hard state.
 Nevertheless. the properties of the source in this plateau state (which is probably a “hard intermediate’ state in the terminology of Belloni 2009). including a steady powerful radio jet. are rather similar to those of the canonical hard state.," Nevertheless, the properties of the source in this plateau state (which is probably a `hard intermediate' state in the terminology of Belloni 2009), including a steady powerful radio jet, are rather similar to those of the canonical hard state."
 We can now compare these measurements of the radio and near-IR normalisations. as proxies for jet power. with the reported measurements of black hole spin from reflection and disc modelling.," We can now compare these measurements of the radio and near-IR normalisations, as proxies for jet power, with the reported measurements of black hole spin from reflection and disc modelling."
 This is done in Fig +. where for each normalisation measurement we estimate a systematic uncertainty of 0.3 dex.," This is done in Fig \ref{spincomp}, where for each normalisation measurement we estimate a systematic uncertainty of 0.3 dex."
 There is clearly no correlation in any of the four panels., There is clearly no correlation in any of the four panels.
 Notably. for the reflection fits. (νο X-I appears to have more or less average radio power despite a low reported spin.," Notably, for the reflection fits, Cyg X-1 appears to have more or less average radio power despite a low reported spin."
 Equally. A 0620-OO has a strong radio normalisation (admittedly based on a single measurement). compared to a low reported spin from dise fits.," Equally, A 0620-00 has a strong radio normalisation (admittedly based on a single measurement), compared to a low reported spin from disc fits."
 Note that we indicate (with solid red circles) all three of the other reported spin measurements for GRS 19154105., Note that we indicate (with solid red circles) all three of the other reported spin measurements for GRS 1915+105.
 The lower panels also clearly illustrate the large difference in relative jet power fitted to the source XTE 11550-564 (indicated with dashed blue circles), The lower panels also clearly illustrate the large difference in relative jet power fitted to the source XTE J1550-564 (indicated with dashed blue circles)
parallaxes. for IX. Vel (HLPPARCOS) and SS Cve (Llarrison et al.,"parallaxes, for IX Vel ) and SS Cyg (Harrison et al."
 2001). respectively.," 2001), respectively."
 “Phe seeming precdeliction for carbon line emission may be due toa carbon over-abuncdance in the emission line gas., The seeming predeliction for carbon line emission may be due to a carbon over-abundance in the emission line gas.
 Doth the question of the distance to QU Car and the abundances issue are focused on in a separate study (Drew ct al., Both the question of the distance to QU Car and the abundances issue are focused on in a separate study (Drew et al.
 2002)., 2002).
 Although wind signatures are scarcely apparent in the QU Car spectrum shown in figure 6.. the comparison with archive dedata (section 5)) showed. that they have been more apparent at other epochs.," Although wind signatures are scarcely apparent in the QU Car spectrum shown in figure \ref{fig:comp}, the comparison with archive data (section \ref{s:mag}) ) showed that they have been more apparent at other epochs."
 However there is a clear point of contrast with objects like SS ονο and IX Vel with regard to he maxiniun oulllow velocities observed., However there is a clear point of contrast with objects like SS Cyg and IX Vel with regard to the maximum outflow velocities observed.
 In. QU Car they are usually about 2000I. whilst in both SS Cvg and IX. Vel this is in the region of 4000+.," In QU Car they are usually about 2000, whilst in both SS Cyg and IX Vel this is in the region of 4000."
 This higher igure is indeed. tvpical of IInMC' (see c.g. Prinja Rosen 1995)., This higher figure is indeed typical of HnMCV (see e.g. Prinja Rosen 1995).
 Vers erudelv. if it is assumed these speeds scale as he rotation speeds in the accretion disc where presumably he wind is launched. this factor of 2 dillerence may. be viewed as implying a substantially larger launch radius in QU Car perhaps up to a factor of4 Larger.," Very crudely, if it is assumed these speeds scale as the rotation speeds in the accretion disc where presumably the wind is launched, this factor of 2 difference may be viewed as implying a substantially larger launch radius in QU Car – perhaps up to a factor of 4 larger."
 Quantitatively his conclusion is somewhat dependent on both the binary inclination and accretor mass — qualitatively it will be hard o avoid., Quantitatively this conclusion is somewhat dependent on both the binary inclination and accretor mass – qualitatively it will be hard to avoid.
 Its implication. like the impression of relatively jiigh ionization. is a higher than typical mass aceretion rate.," Its implication, like the impression of relatively high ionization, is a higher than typical mass accretion rate."
 In the above we have assumed that the UV continuum emission in QU Car is dominated by. disc accretion., In the above we have assumed that the UV continuum emission in QU Car is dominated by disc accretion.
 This seems uncontroversial given the similarity. between the slope of its dereddened: energy. distribution and. that. of inclisputably accretion-dominated HnMCV (see section 3))., This seems uncontroversial given the similarity between the slope of its dereddened energy distribution and that of indisputably accretion-dominated HnMCV (see section \ref{s:mean}) ).
 Lt is likely that all absorption features. including those seen superposed on theCin. aand eemission profiles. form in the disc atmosphere.," It is likely that all absorption features, including those seen superposed on the, and emission profiles, form in the disc atmosphere."
 This view is supported by the way in which the pattern of variability seen in and aabsorption during the Q3 observation is also apparent in the aabsorption component., This view is supported by the way in which the pattern of variability seen in and absorption during the Q3 observation is also apparent in the absorption component.
 The less variable aabsorption component can be viewed as mimicking the less variable pprofile., The less variable absorption component can be viewed as mimicking the less variable profile.
 We now consider the likely origin of the line emission., We now consider the likely origin of the line emission.
 Figure T shows the emission. from the three ionization stages of carbon present in the spectrum. plotted on a common velocity scale.," Figure \ref{fig:c} shows the emission, from the three ionization stages of carbon present in the spectrum, plotted on a common velocity scale."
 The line. is clearly the narrowest with a LIWZL of. orderο, The line is clearly the narrowest with a HWZI of order.
"ι, Phe LIWZlIs in the aand lines are not so easy to tell apart.", The HWZIs in the and lines are not so easy to tell apart.
 On fitting a single eaussian through the line wines we find that the FWIIAI. respectively for these two lines. is 950 and ~1100kmis+.," On fitting a single gaussian through the line wings we find that the FWHM, respectively for these two lines, is $\sim$ and $\sim$."
 Phese figures translate ας of 71200 and 14001., These figures translate to HWZIs of $\sim$ 1200 and $\sim$.
 We do not correct for intrinsic multiplet splitting because the magnitude of the correction depends on the unknown flux ratios among the multiplet components., We do not correct for intrinsic multiplet splitting because the magnitude of the correction depends on the unknown flux ratios among the multiplet components.
 Fortunately these splittings are not so large awl correction for them would. alter the basic [inding namely. that broacer emission is associated: with higher ionization.," Fortunately these splittings are not so large that correction for them would alter the basic finding -- namely, that broader emission is associated with higher ionization."
 The near equality of the aand eemission widths probably indicates that the excited Iline contains a substantial contribution from recombination., The near equality of the and emission widths probably indicates that the excited line contains a substantial contribution from recombination.
 To see all three carbon ion stages. simultaneously. with this pattern of velocity widths probably points to an origin in a disc ‘chromosphere’.," To see all three carbon ion stages simultaneously, with this pattern of velocity widths probably points to an origin in a disc `chromosphere'."
 This might be created by irradiation from the EUV-brieht inner disc and accreting object., This might be created by irradiation from the EUV-bright inner disc and accreting object.
 Eniission produced by an outllow from the accretor or the innermost disc is rendered. less likely bv the mocest ionization of the aand lines (with the emissive [ux in the line only a little less than that in Civ)., Emission produced by an outflow from the accretor or the innermost disc is rendered less likely by the modest ionization of the and lines (with the emissive flux in the line only a little less than that in ).
 Since the emission component in each of theCL. aand lines is broader than the superposed absorption. we would jwe to refer to a specific kinematic mocel for the system to »osition the emission line region relative to the absorption ine region.," Since the emission component in each of the, and lines is broader than the superposed absorption, we would have to refer to a specific kinematic model for the system to position the emission line region relative to the absorption line region."
 In the absence of this. we cannot distinguish whether the line emission. is optically thin ancl overlies he source of line absorption. or whether it comes from a different part of the disc.," In the absence of this, we cannot distinguish whether the line emission is optically thin and overlies the source of line absorption, or whether it comes from a different part of the disc."
 The emergent picture of QU Car is then that it is relatively highlv-ionized. comparecl to the more typical properties of HEnMC'V., The emergent picture of QU Car is then that it is relatively highly-ionized compared to the more typical properties of HnMCV.
 Phe narrowness of the UY spectral, The narrowness of the UV spectral
(by 7O%) anc planets with mass less than 20AL (by ~35%).,"(by $\sim70\%$ ) and planets with mass less than $20
M_\oplus$ (by $\sim35\%$ )."
 The average number of planets character3zed with masses less than 34/0 would be reduced by 105€ compared to the a ten year survey with twice as many observations of hall as many target stars., The average number of planets characterized with masses less than $3 M_\oplus$ would be reduced by $\sim10\%$ compared to the a ten year survey with twice as many observations of half as many target stars.
 If SIM were to observe each extrasolar planet already known from racial velocity surveys. then it would be able to make accurate measurements of the mass aud orbital elements for 80c3. TLE Lor 6F+5 of the 99 known planets using 21 two dimensional meastwements at 1. 2. or L µας precision (see ledSigual)).," If SIM were to observe each extrasolar planet already known from radial velocity surveys, then it would be able to make accurate measurements of the mass and orbital elements for $80\pm3$, $74\pm4$, or $67\pm5$ of the 99 known planets using 24 two dimensional measurements at $1$, $2$, or 4 $\mu$ as precision (see \\ref{RvScaledSignal}) )."
 Of the eleven known multiple planet systems. 1 ras or 2 gras astrometry would allow acc‘urate orbital determinations for at least. two planets in seven or five of those systems. assuming that SIMs ability to measure orbits is not dimiuislied in multiple planet systems.," Of the eleven known multiple planet systems, 1 $\mu$ as or 2 $\mu$ as astrometry would allow accurate orbital determinations for at least two planets in seven or five of those systems, assuming that SIM's ability to measure orbits is not diminished in multiple planet systems."
 Lu practice. the primary importauce of these measurements would be to confirm the interpretation of the raclia| velocity measurements and to coustrain the iuclinatious of the orbits.," In practice, the primary importance of these measurements would be to confirm the interpretation of the radial velocity measurements and to constrain the inclinations of the orbits."
 All «X our results are based on the assumption that the mass functiou for terrestrial-uiass planets ¢an be obtained by extrapolating the mass function lor giant. planets determined by radia velocity surveys., All of our results are based on the assumption that the mass function for terrestrial-mass planets can be obtained by extrapolating the mass function for giant planets determined by radial velocity surveys.
 IE this assumption is correct. then we find that a ten-year planet search with SIM uueht detect a few Earth mass planets.," If this assumption is correct, then we find that a ten-year planet search with SIM might detect a few Earth mass planets."
 SIM could be expected to measure the masses aud orbita parameters with accuracy for planets with masses as small as ~2AL., SIM could be expected to measure the masses and orbital parameters with accuracy for planets with masses as small as $\sim2 M_\oplus$.
 While SIM could fine more low mass planets if they are more Common than current estimates. a null result would wot demoustr‘ate that planets with masses less than LOA are less common than presently expectec ou the b:isis of extrapolating the results of radial velocity surveys.," While SIM could find more low mass planets if they are more common than current estimates, a null result would not demonstrate that planets with masses less than $\sim10 M_\oplus$ are less common than presently expected on the basis of extrapolating the results of radial velocity surveys."
 Includiug elaut planets. SIM is expected to detect ~21—162 planets: the higher uumber results [rom the ten-year surveys whi target a aree number of stars at relatively low precision.," Including giant planets, SIM is expected to detect $\sim24-162$ planets; the higher number results from the ten-year surveys which target a large number of stars at relatively low precision."
 Of these. a significant fraction. 25—65% could also be discovered by a 3125 vacdial velocity survey.," Of these, a significant fraction, $25-65\%$, could also be discovered by a 3 radial velocity survey."
 With the observing strategies that we have exanined SIM will measure the masses and orbits of 16—106 planets with accuracy and the 1nasses ancl orbits of 13—81 planets with accuracy., With the observing strategies that we have examined SIM will measure the masses and orbits of $\sim16-106$ planets with accuracy and the masses and orbits of $\sim13-84$ planets with accuracy.
 Of these. 30—τούς could be 1110ΑΡος by aB3ans radial velocity survey. We hank Stefano Casertano. Jeremy Coodman. Debra Fischer. Geoff Marcy. Michael Shao. Alessandro Sozzetti. David Spergel. auc Edwin Turner for stimulating discussions.," Of these, $\sim30-70\%$ could be measured by a 3 radial velocity survey, We thank Stefano Casertano, Jeremy Goodman, Debra Fischer, Geoff Marcy, Michael Shao, Alessandro Sozzetti, David Spergel, and Edwin Turner for stimulating discussions."
 This research was supported in part by NASA grant NAC5-1L0156 aud the EPIcS SIM Ixey. Project., This research was supported in part by NASA grant NAG5-10456 and the EPIcS SIM Key Project.
pre-naxinuun shell. after undergoing a shock. with a post-shock density of the order 3x105 em?,"pre-maximum shell, after undergoing a shock, with a post-shock density of the order $\times 10^8$ $^{-3}$."
 If our interpretation is correct. the physical couditious of tlie early N-ray. emission source in iis orders of inagnitudes denser than in supernova remuauts. aud orders of maguitucles more rarified than in accretion shocks in CVs. two well-studied classes of shock heated. X-ray emitting. plasmas.," If our interpretation is correct, the physical conditions of the early X-ray emission source in is orders of magnitudes denser than in supernova remnants, and orders of magnitudes more rarified than in accretion shocks in CVs, two well-studied classes of shock heated, X-ray emitting, plasmas."
 Although it may be comparable to stellar coronae in density alone. the heating mechanism aud the environment are different.," Although it may be comparable to stellar coronae in density alone, the heating mechanism and the environment are different."
 Applicatious of existing spectral models (widely tested iu supernova remuauts and stellar corouae) must therefore proceed with caution., Applications of existing spectral models (widely tested in supernova remnants and stellar coronae) must therefore proceed with caution.
 Such an internal shock model has already been suggested as a possibile explanation of the early ddetection of V838 Her (Lloydetal1992)., Such an internal shock model has already been suggested as a possibile explanation of the early detection of V838 Her \citep{ll92}.
. O'Brienetal(1991). has developed this iuto a detailed numerical model assuming a constant mass loss rate. with ejection velocity of 1000 ! for the Ist day. increasing linearly to 3600 | by day 5. and remaining constant thereafter.," \citet{o94} has developed this into a detailed numerical model assuming a constant mass loss rate, with ejection velocity of 1000 $^{-1}$ for the 1st day, increasing linearly to 3600 $^{-1}$ by day 5, and remaining constant thereafter."
 Our model aud theirs are situilar in that N-rays are generated from au internal shock., Our model and theirs are similar in that X-rays are generated from an internal shock.
 However. aud we lave chosen different sets of simplyfiug assumptions.," However, \citet{o94}
 and we have chosen different sets of simplyfing assumptions."
 assulue a constant mass loss rate. with a smoothly changiug ejection velocity: iu contrast. we have assumed a two distinct. phases of mass loss with a discontinuous change in velocity.," \citet{o94}
 assume a constant mass loss rate, with a smoothly changing ejection velocity; in contrast, we have assumed a two distinct phases of mass loss with a discontinuous change in velocity."
 Are the differences significant. and if so. which is the better [framework on which to build future. more detailed. models?," Are the differences significant, and if so, which is the better framework on which to build future, more detailed, models?"
 Let us first examine how the specific preclictious of the O'Brienetal(1991). utmelical mocel compare with our data ouVel: we find two significant differences.," Let us first examine how the specific predictions of the \citet{o94}
 numelical model compare with our data on: we find two significant differences."
 First clifference coucerus the predicted temperature of the X-ray emitting region., First difference concerns the predicted temperature of the X-ray emitting region.
 The model predicts 105 to 2:10* Ix. (or ~0.2-2 keV) X-ray emitting plasma. matching oue of the two thermal plasma model parameters that fit the PPSPC spectrum of V838 Her (model RS2 in Table 2 of O'Brienetal. (1991))). whereas we observe INT—10 keV on Day 20.5 inVel.," The \citet{o94} model predicts $\times 10^6$ to $\times 10^7$ K (or $\sim$ 0.2–2 keV) X-ray emitting plasma, matching one of the two thermal plasma model parameters that fit the PSPC spectrum of V838 Her (model RS2 in Table 2 of \citet{o94}) ), whereas we observe $\sim$ 10 keV on Day 20.5 in."
" Secondly. O'Brienetal(1991). claims that ""Lor these parameter values the cousequent reduction iun low-energy X-rays is stuall.” whereas low-energy rRm)10tous are decimated by intrinsic absorption in the sspectrum ofVel."," Secondly, \citet{o94} claims that “for these parameter values the consequent reduction in low-energy X-rays is small,” whereas low-energy photons are decimated by intrinsic absorption in the spectrum of."
 Note that. while the O’Brienetal(1991) tmocel does predict a high temperature region (T~ 105I&) 10 days after eruption. the density. predicted in this region is orders of maguitude too low to result in sienilicant[e X-ray. emission (from their Figuree 1. we estimate einissiou measure of order LOM oκ7. compared to >10?* ccm? estimated from aand sspectra).," Note that, while the \citet{o94} model does predict a high temperature region $\sim 10^8$ K) 10 days after eruption, the density predicted in this region is orders of magnitude too low to result in significant X-ray emission (from their Figure 1, we estimate emission measure of order $^{46}$ $^{-3}$, compared to $> 10^{57}$ $^{-3}$ estimated from and spectra)."
 Moreover. since this high temperature is seen at the outermost edge of the ejecta. little," Moreover, since this high temperature is seen at the outermost edge of the ejecta, little"
velocity dispersion calculations.,velocity dispersion calculations.
 This leads to a significantly higher systemic velocity for the cluster. ez=7328c105 km L (5—=0.0244+ 0.0004) with σ.=283(1109.52) kms +.," This leads to a significantly higher systemic velocity for the cluster, $c\overline{z}
= 7328\pm 105$ km $^{-1}$ $\overline{z}= 0.0244 \pm 0.0004$ ) with $\sigma_{z}= 283\, (+109, -52)$ km $^{-1}$."
 Lo this case. NGC 6251 is one of the slowest-moving members of the cluster with a peculiar velocity of 128 101 kms+," In this case, NGC 6251 is one of the slowest-moving members of the cluster with a peculiar velocity of 128 $\pm$ 107 km $^{-1}$."
 Lleckman et ((1985b) measured the rotation curves of several radio-Ioud: and raclio-quict elliptical. galaxies to est theories that the rotation axis might coincide with the radio axis in powerful radio galaxies (log LissΗν= 24 WO Dy, Heckman et (1985b) measured the rotation curves of several radio-loud and radio-quiet elliptical galaxies to test theories that the rotation axis might coincide with the radio axis in powerful radio galaxies (log $P_{\rm 178\ MHz} \geq$ 24 W $^{-1}$ ).
 They present rotation curves for NGC 6251 in xosition angles of 27 and 124 and conclude that the galaxy rotates about an axis at DX. —δρ£28*° with a velocity of Vo~47416 km ," They present rotation curves for NGC 6251 in position angles of $27^{\circ}$ and $124^{\circ}$ and conclude that the galaxy rotates about an axis at P.A. $\sim 85^{\circ} \pm 28^{\circ}$ with a velocity of $V \sim 47
\pm 16$ km $^{-1}$."
"We measured rotation curves for two position angles. 25.3"" and 115.3"" (Table 2)). the latter being aligned. with the jet."," We measured rotation curves for two position angles, $^{\circ}$ and $^{\circ}$ (Table \ref{tab:obsh}) ), the latter being aligned with the jet."
" Phe results of the slit in PA. = 25.8"" suggest a slow rotation of the order of 50 km * about the jet. consistent with Lleckman et al"," The results of the slit in P.A. = $^{\circ}$ suggest a slow rotation of the order of 50 km $^{-1}$ about the jet, consistent with Heckman et al."
s result in PLA. = 277.,'s result in P.A. = $^{\circ}$.
 The velocities the jet were inconclusive., The velocities the jet were inconclusive.
 Deeper. observations. are required to obtain sullicient signal-to-noise in the outer parts of the galaxy. (at à racius z oor  6 kpe) if more precise information on the rotation axis or velocity than that found by Lleckman et iis to be obtained., Deeper observations are required to obtain sufficient signal-to-noise in the outer parts of the galaxy (at a radius $\geq$ or $\sim$ 6 kpc) if more precise information on the rotation axis or velocity than that found by Heckman et is to be obtained.
 The jet of the powerful radio galaxy ALST has been detected: at optical wavelengths. and many authors report imaging ancl spectroscopic studies (see Weel LOSS and references therein).," The jet of the powerful radio galaxy M87 has been detected at optical wavelengths, and many authors report imaging and spectroscopic studies (see Keel 1988 and references therein)."
 Keel subsequently detected: optical continuum emission from the NGC 6251 jet. and. his D-. V- and R-bancl Fluxes of feature A oor ~ 99 kpc from the nucleus) imply a spectrum much steeper than AIST or other similar jets.," Keel subsequently detected optical continuum emission from the NGC 6251 jet, and his B-, V- and R-band fluxes of feature A – or $\sim$ 7 – 29 kpc from the nucleus) imply a spectrum much steeper than M87 or other similar jets."
 Our observations were not deep enough to reveal significant continuum emission from [feature A. but we searched. for line emission from ο HH]. He and N IH].," Our observations were not deep enough to reveal significant continuum emission from feature A, but we searched for line emission from [O III], $\alpha$ and [N II]."
" Νο emission lines in the jet were found. at an upper limit (for Ua)of 10%10m ""erg em22g s© lora range of sline widths. of 3001000A.. respectively."," No emission lines in the jet were found, at an upper limit (for $\alpha$ ) of $10^{-17}-10^{-16}$ erg $^{-2}$ $^{-1}$ for a range of line widths of $300-1000$, respectively."
 Poor weather prevented: us from obtaining the planned. much deeper. exposures.," Poor weather prevented us from obtaining the planned, much deeper, exposures."
 Considering our redshifts in the context of the two subsystems that make up cluster Zw 1609.0]8212. (sec section. 7?)). it is clear that our sample does not. include any members of the subcluster separately listed: as (2247 (cz=11670 km +). and situated in the Eastern part of the Zwicky cluster. South-East of NGC 6251.," Considering our redshifts in the context of the two subsystems that make up cluster Zw 1609.0+8212 (see section \ref{sec:intro}) ), it is clear that our sample does not include any members of the subcluster separately listed as A2247 $c\overline{z} = 11670$ km $^{-1}$ ), and situated in the Eastern part of the Zwicky cluster, South-East of NGC 6251."
 Objects 12 and 19 appear to belong to a slightly closer group or small cluster on the Western edge of Zw 1600.0]8212 and. we have accordingly argued for their removal from the velocity dispersion calculations in section ??.., Objects 12 and 13 appear to belong to a slightly closer group or small cluster on the Western edge of Zw 1609.0+8212 and we have accordingly argued for their removal from the velocity dispersion calculations in section \ref{sec:veldisp}.
 Objects 7 and LO have redshifts unlike those of other objects in the sample. and appear to be more or less isolated field galaxies.," Objects 7 and 10 have redshifts unlike those of other objects in the sample, and appear to be more or less isolated field galaxies."
 Vhis leaves us with S companion galaxies (two with double nuclei) near the velocity of NGC 6251. and these seem to form a third sub-cluster within the limits of Zw 1609.0|8212.," This leaves us with 8 companion galaxies (two with double nuclei) near the velocity of NGC 6251, and these seem to form a third sub-cluster within the limits of Zw 1609.0+8212."
 It is clear that not all the brightest galaxies within Zwickys boundary are physically. associatec., It is clear that not all the brightest galaxies within Zwicky's boundary are physically associated.
 Figure 2. shows the positions of our sources. as well as rough outlines of clusters A2247 and Zw 1609.0|S212.," Figure \ref{fig:dssfield} shows the positions of our sources, as well as rough outlines of clusters A2247 and Zw 1609.0+8212."
 The one-dimensional velocity. dispersion of a cluster. of ealaxies is related to the X-ray gas temperature of the eluster atmosphere (Lubin, The one-dimensional velocity dispersion of a cluster of galaxies is related to the X-ray gas temperature of the cluster atmosphere (Lubin
 of the NGC 3311 CCS. Wehner Ihburis (2007: their Figure 1) find aun “upward” extension towards brighter magnitudes of the red subpopulation.," of the NGC 3311 GCS, Wehner Harris (2007; their Figure 1) find an ""upward"" extension towards brighter magnitudes of the red subpopulation."
 This coutiuuation to brighter magnitudes (and higher masses) is absent αλλος the blue subpopulation., This continuation to brighter magnitudes (and higher masses) is absent among the blue subpopulation.
 Wehner ανν (2007) postulate that given their magnitudes (7<22.5 mag) aud iuferred masses (06& 109A/.). the extension of the CMD corresponds to Ultra-Compact Dwarts (UCDs. Phillipps et 22001).," Wehner Harris (2007) postulate that given their magnitudes $i' \leq 22.5$ mag) and inferred masses $>6\times10^6 M_{\odot}$ ), the extension of the CMD corresponds to Ultra-Compact Dwarfs (UCDs, Phillipps et 2001)."
 While Wehner ILhuris (2007) sugecst that UCDs are the bright extension of the GCS. the ground-based data used for their work do not allow them to derive NN radii for them UCD candidates.," While Wehner Harris (2007) suggest that UCDs are the bright extension of the GCS, the ground-based data used for their work do not allow them to derive characteristic radii for their UCD candidates."
 Peng et um((2009) over-plotted 18 objects with extended effective (ry>10 pe) on their CAID of the M87 GCS., Peng et (2009) over-plotted 18 objects with extended effective radii $r_{h} > 10$ pc) on their CMD of the M87 GCS.
 Some of these objects are coufirmed UCDs or Dwiuf/Clobulu Transition tle Objects(IHasegau 22005) and most of them le exac at the bright cud of the blue subpopulation of globular clusters., Some of these objects are confirmed UCDs or Dwarf/Globular Transition Objects (Hasegan et 2005) and most of them lie exactly at the bright end of the blue subpopulation of globular clusters.
 Ultra-compact dwarts are a relatively newly discovered class of stellar system (Iilker et 11999: Diiukwater et al., Ultra-compact dwarfs are a relatively newly discovered class of stellar system (Hilker et 1999; Drinkwater et al.
 2000) aud thei origin is uot vet clearly established., 2000) and their origin is not yet clearly established.
 Iu color. aud structural parameters. UCDs le between supermassive elobulay clusters and conrpact clwart elliptical galaxies.," In color, and structural parameters, UCDs lie between supermassive globular clusters and compact dwarf elliptical galaxies."
 Not surprisingly. the origiu of UCDs has been linked to both globular clusters and chart elliptical galaxies(Ililker 2006. aud references therein).," Not surprisingly, the origin of UCDs has been linked to both globular clusters and dwarf elliptical galaxies (Hilker 2006, and references therein)."
 UCDs are typically associated with ealaxy clusters aud, UCDs are typically associated with galaxy clusters and
cell voltune V. (se6eg.?.orSection3.below).,"cell volume $V$ \citep[see
e.g.][or Section~\protect\ref{sec:pl} ."
 There are. however. several potential practical difüculties with this simple approach.," There are, however, several potential practical difficulties with this simple approach."
 While the correlation function of ealaxies is typically welbapproxiuated bv a power law in the strougly non-linear regime (rZ10-15 Ape). on larger scales. iu the linear reginac. the correlation function is expected to deviate from the power-law slope measured on smaller scales.," While the correlation function of galaxies is typically well-approximated by a power law in the strongly non-linear regime $r
\la 10$ -15 Mpc), on larger scales, in the linear regime, the correlation function is expected to deviate from the power-law slope measured on smaller scales."
 Also. estimating the correlation fuuctiou (especially its slope) of an observed population 1s more difficult than estimating the number density. so often the latter quantity is known while the former is not.," Also, estimating the correlation function (especially its slope) of an observed population is more difficult than estimating the number density, so often the latter quantity is known while the former is not."
 Iu this situation. we cau use the theory of clustering and bias in the Cold Dark Matter (CDAD) paradigm to estimate the cosmic variance for a population with a known nean redshift aud average comoving nuuber density.," In this situation, we can use the theory of clustering and bias in the Cold Dark Matter (CDM) paradigm to estimate the cosmic variance for a population with a known mean redshift and average comoving number density."
 Iu thisLetter. we estimate the uncertainty due to cosmic variance for several populations that have beeu identified in the GOODS survey. and present eeneral results based on CDM theory that can be used to estimate the cosmic variance for populations at τς6.," In this, we estimate the uncertainty due to cosmic variance for several populations that have been identified in the GOODS survey, and present general results based on CDM theory that can be used to estimate the cosmic variance for populations at $z<6$."
" Throughout. we assume cosmological parameters consistent with the recent analysis of ddata ελα matter density O,,= 0.3. barvon deusitv QO,=OOLL cosmological constant O40.70. ποιο pirauecter Ty=TO kimn/s/Mpe. fluctuation amplitude σς=0.9. and a scale-free primordial power spectra neal."," Throughout, we assume cosmological parameters consistent with the recent analysis of data \citep{spergel:03}: matter density $\Omega_m = 0.3$ , baryon density $\Omega_b =0.044$, cosmological constant $\Omega_{\Lambda}=0.70$, Hubble parameter $H_0=70$ km/s/Mpc, fluctuation amplitude $\sigma_8 = 0.9$, and a scale-free primordial power spectrum $n_s=1$."
 The Creat Observatories Origins Deep Survey (GOODS) covers two fields. the Chandra Deep Ficld South (CDFS) and the IIubble Deep Field North (IIDEN).," The Great Observatories Origins Deep Survey (GOODS) covers two fields, the Chandra Deep Field South (CDFS) and the Hubble Deep Field North (HDFN)."
 The CDFS field has dimensions 416. and the GOODS IIDEN field has similar dimensions.," The CDFS field has dimensions $\times$ 16', and the GOODS HDFN field has similar dimensions."
 For more details aud a general overview of the GOODS program. see 2..," For more details and a general overview of the GOODS program, see \citet{giavalisco:03}."
 Hore. we treat the case of a single CDFS-sizec field.," Here, we treat the case of a single CDFS-sized field."
 For widely separated fields. the cosmic variance goes as l/Ngqa. πο he variance will decrease by a factor of two when the second feld is included.," For widely separated fields, the cosmic variance goes as $1/N_{\rm field}$, so the variance will decrease by a factor of two when the second field is included."
 In Fig. 1..," In Fig. \ref{fig:scale},"
 we show the comoving vohuue per unit redshift for several recent. ougoiug. and Xauned deep OST strvers: the original Ibble Deep Field North (?).. the GOODS CDES field. the GEMS (Calaxyv Evolution frou Morphology aud SEDs: Rix et al.," we show the comoving volume per unit redshift for several recent, ongoing, and planned deep HST surveys: the original Hubble Deep Field North \citep{williams}, the GOODS CDFS field, the GEMS (Galaxy Evolution from Morphology and SEDs; Rix et al."
 iu prep)Πο]... and the planned Ultra Deep Field (UDF)°.," in prep), and the planned Ultra Deep Field (UDF)."
. For redshifts :.= Land Az~0.5 1. GOODS samples a voluue of afew «10?Mpec?.," For redshifts $z\ga1$ and $\Delta z \sim 0.5$ –1, GOODS samples a volume of a few $\times
10^5\, {\rm Mpc^3}$."
 Fig., Fig.
" 1. also shows the average rausverse size (L=10ς16"" 12.77) of the GOODS field as a functionof redshift. again compared with the original TDF (£L=Vh5.7arcuuin? 2.1)."," \ref{fig:scale} also shows the average transverse size $L = \sqrt{10'\times 16'} = 12.7'$ ) of the GOODS field as a functionof redshift, again compared with the original HDF $L = \sqrt{5.7 \rm arcmin^2} = 2.4'$ )."
 The relative cosmic variance for a population with known two-point correlation fiction (0) is elven by: (soc.c.g.7.p.231).," The relative cosmic variance for a population with known two-point correlation function $\xi(r)$ is given by: \citep[see, e.g.][p. 234]{peebles:80}."
" Tf the correlation function cau be represented by a power-law (7)=(ryfry. then this expression can be evaluated in closed. fori: where J,=τος51.σα5)27] (2.p.230)."," If the correlation function can be represented by a power-law $\xi(r) = (r_0/r)^\gamma$, then this expression can be evaluated in closed form: where $J_2 = 72.0/[(3-\gamma)(4-\gamma)(6-\gamma)2^\gamma]$ \citep[][p. 230]{peebles:80}."
 Asstuing spherical cells. the variance may be equivalently expressed im terms of the cell radius # or the cell volume P=lrR?/3.," Assuming spherical cells, the variance may be equivalently expressed in terms of the cell radius $R$ or the cell volume $V\equiv 4 \pi R^3/3$."
 For objects with a known correlation function that is well represented by a power-law. we cau simply use Equ.," For objects with a known correlation function that is well represented by a power-law, we can simply use Eqn."
 3 to compute the cosniüc variance for a eiven effective volume. as illustrated in Fie. 2..," \ref{eqn:cv_pl} to compute the cosmic variance for a given effective volume, as illustrated in Fig. \ref{fig:var_pl}."
" We show o, as a function of volume. for three populations with correlation function estimates from the Literature: Extremely Rec Objects (EROs) at mean redshift 1.2. U-baud dropouts at 2~ (also known as Lyinan break galaxies (LDGU)). aud D-baud dropouts at 2~1."," We show $\sigma_v$ as a function of volume, for three populations with correlation function estimates from the literature: Extremely Red Objects (EROs) at mean redshift $\bar{z}\sim
1.2$, U-band dropouts at $\bar{z}\sim 3$ (also known as Lyman break galaxies (LBG)), and B-band dropouts at $\bar{z}\sim 4$."
 The maguitude limit and color selection used for cach of these populations selects objects in a given redshift ranec. resulting in an effective volume Va ," The magnitude limit and color selection used for each of these populations selects objects in a given redshift range, resulting in an effective volume $V_{\rm eff}$."
Characteristic nunuber densities for cach of these populations. along with correlation function parameters and the relevant references. are summarized in Table 1..," Characteristic number densities for each of these populations, along with correlation function parameters and the relevant references, are summarized in Table \ref{tab:param}."
" For example. for EROs in the COODS field. σι0.1.0.6. while for the less clustered. LBGs. o,0.150.2."," For example, for EROs in the GOODS field, $\sigma_v \sim 0.4-0.6$, while for the less clustered LBGs, $\sigma_v \sim 0.15-0.2$."
 Note that we have asstuued here a spherical ecometry for the cells. while in fact for the GOODS siuvev the cells are very clongated. with the redshift dimension beiug mach louger (about a factor of ten) than the transverse cimicusion in comoving distance units.," Note that we have assumed here a spherical geometry for the cells, while in fact for the GOODS survey the cells are very elongated, with the redshift dimension being much longer (about a factor of ten) than the transverse dimension in comoving distance units."
 We have also ignored the evolution iu clustering that occurs over the time interval )etween the ας aud the οι of the cell., We have also ignored the evolution in clustering that occurs over the time interval between the `back' and the `front' of the cell.
 It should © noted that. for two fields with the same volume. the cosnüe variance is for au elongated (parallelepiped or exliudrical)field thu or a compact (cubical or spherical) field (seee.g.2)..," It should be noted that, for two fields with the same volume, the cosmic variance is for an elongated (parallelepiped or cylindrical)field than for a compact (cubical or spherical) field \citep[see
e.g.][]{newman:02}. ."
 This is because au elongated field. suuples more iudepenudoeut (uncorrelated) regions., This is because an elongated field samples more independent (uncorrelated) regions.
 Therefore. the estimates eiveu here xovide au upper bound ou the cosmic variance.," Therefore, the estimates given here provide an upper bound on the cosmic variance."
A halo population of exclusively low-mass stars contributing to dark matter might be supposed to be systematically metal-poor.,A halo population of exclusively low-mass stars contributing to dark matter might be supposed to be systematically metal-poor.
 Phe elective temperature scale is dependant on metallicity. in à manner which is not well calibrated.," The effective temperature scale is dependant on metallicity, in a manner which is not well calibrated."
 The general ellect is to associate svstematically higher temperatures with a given mass than those listed in table ??.., The general effect is to associate systematically higher temperatures with a given mass than those listed in table \ref{lowmassfn}.
 Since LSO is sensitive to cool stars. this reduces our sensitivity for this experiment.," Since ISO is sensitive to cool stars, this reduces our sensitivity for this experiment."
 A conservative caleulation of the amplitude of this effect. is possible by adoption of the isochrones for stars with 2 (approximately 2.35) and age I0Cvr from Baralle. Chabrier. Allard Hauschildt (1997).," A conservative calculation of the amplitude of this effect is possible by adoption of the isochrones for stars with $-2$ (approximately $-2.35$ ) and age 10Gyr from Baraffe, Chabrier, Allard Hauschildt (1997)."
" ""μονο isochrones lie svstematically hotter than the observations of metal-poor elobular cluster and field subcdwar stars at low masses (figures 5. 6. and S of Baralle et al). and so provide an upper limit."," These isochrones lie systematically hotter than the observations of metal-poor globular cluster and field subdwarf stars at low masses (figures 5, 6, and 8 of Baraffe et al), and so provide an upper limit."
 These values are also listed in table ??.., These values are also listed in table \ref{lowmassfn}.
 The range of calibrations available corresponds to à systematic change in the expected flux in the L2 band by a factor of about three at à mass ofOAL... rising to a reduction by a factor of about 10 at à mass of... with metal-poor stars being svstematically hotter. and hence less luminous for LSO. relative to metal-rich stars.," The range of calibrations available corresponds to a systematic change in the expected flux in the LW2 band by a factor of about three at a mass of, rising to a reduction by a factor of about 10 at a mass of, with metal-poor stars being systematically hotter, and hence less luminous for ISO, relative to metal-rich stars."
 Since the sources are now quite warm. LWS3 sensitivity is reduced below useful limits for the hottest mass-temperature calibration at the lowest masses.," Since the sources are now quite warm, LW3 sensitivity is reduced below useful limits for the hottest mass-temperature calibration at the lowest masses."
 The conclusions from the LNV2 limits are however not strongly dependant on the calibration adopted., The conclusions from the LW2 limits are however not strongly dependant on the calibration adopted.
 The adopted. black-body Ilux approximation should be more accurate for the more metal-poor sources., The adopted black-body flux approximation should be more accurate for the more metal-poor sources.
 Some remarks concerning cool white dwarls as major contributors to dark halos are noted in the introduction., Some remarks concerning cool white dwarfs as major contributors to dark halos are noted in the introduction.
 Chabrier (1997) presents à recent summary of theoretical work on cooling theory., Chabrier (1997) presents a recent summary of theoretical work on cooling theory.
 Masses for WDs vary (comparativelv) little (from about to 2)., Masses for WDs vary (comparatively) little (from about to ).
" For a typical WD of mass )). at ages of 10 Civr. we expect the bolometric luminosity to be ο!.) = -5.0. and 1) ,=2900K. That is. old white dwarls have a bolometric mass to light ratio which a factor of approximately 100 higher than that of stars of similar temperature. near the hydrogen burning limit."," For a typical WD of mass ), at ages of 10 Gyr, we expect the bolometric luminosity to be $\lg(L/L_{\odot})$ = -5.0, and $T_{eff}$ =2900K. That is, old white dwarfs have a bolometric mass to light ratio which a factor of approximately 100 higher than that of stars of similar temperature, near the hydrogen burning limit."
 Correspondinglv. they are hard to sec.," Correspondingly, they are hard to see."
 Given the high gravity. and (probable) low metallicity. the spectra should be adequately approximated by a black-bods.," Given the high gravity, and (probable) low metallicity, the spectra should be adequately approximated by a black-body."
 As indicated in figure ?2?.. objects of this temperature are too warm to allow sensitive direct detections with ISO.," As indicated in figure \ref{filtersens}, objects of this temperature are too warm to allow sensitive direct detections with ISO."
 We quantify this in model W1 below. which is the power per unit mass in the [ISO filters for ao function mass distribution of white chwarts. all of mass and age 10Civr.," We quantify this in model W1 below, which is the power per unit mass in the ISO filters for a $\delta-$ function mass distribution of white dwarfs, all of mass and age 10Gyr."
 Brown cwarls are those objects of mass below the minimum mass for hvdrogen burning., Brown dwarfs are those objects of mass below the minimum mass for hydrogen burning.
 Considerable progress has been made recently in understanding their properties., Considerable progress has been made recently in understanding their properties.
 Extensive numerical work by Stevenson (1986) led to à set of scaling relations for, Extensive numerical work by Stevenson (1986) led to a set of scaling relations for
The Mg II lines undergo significant. changes in their line profiles during the Lavine intervals.,The Mg II lines undergo significant changes in their line profiles during the flaring intervals.
 Figure 4 shows the Me II k line profiles for the individual flares (F1-10). obtained from the summed spectra over the extent of each [Marine episode.," Figure 4 shows the Mg II k line profiles for the individual flares (F1-10), obtained from the summed spectra over the extent of each flaring episode."
 Flares F2 ancl FO were large enough that it was possible to split them up into impulsive. peak and decay. phases. shown as F2abc and F9abe in Figure 4.," Flares F2 and F9 were large enough that it was possible to split them up into impulsive, peak and decay phases, shown as F2abc and F9abc in Figure 4."
 The quiet flare profile is shown for comparison as the dotted line in each panel., The quiet flare profile is shown for comparison as the dotted line in each panel.
 It is clear that the quiet [lux dominates the total even during flares. indicating that the flare area coverage is verv small. and that Mg II k is already a very strong line even in the «quiet chromosphere.," It is clear that the quiet flux dominates the total even during flares, indicating that the flare area coverage is very small, and that Mg II k is already a very strong line even in the quiet chromosphere."
 This behavior is similar to La. which also responds only slightly to flares in early-micl Al clwarls (e.g. Hawley et al.," This behavior is similar to $\alpha$, which also responds only slightly to flares in early-mid M dwarfs (e.g. Hawley et al."
" 2003). though 1t responds more stronelv in late M dwarls (ef,"," 2003), though it responds more strongly in late M dwarfs (cf."
 Liebert et al., Liebert et al.
 1999)., 1999).
 This is in contrast to lines such as He I and ΠΠ. and the higher order Balmer lines. which become significantly stronger during flares. often. clwarling the «quiet. contribution to the line flux (IIawlev Pettersen 1991).," This is in contrast to lines such as He I and II, and the higher order Balmer lines, which become significantly stronger during flares, often dwarfing the quiet contribution to the line flux (Hawley Pettersen 1991)."
 Figure 5 shows the subtracted profiles for each flare (i.e. flare - equiet. as in Figure 3). in order to examine possible velocity shifts during the flare.," Figure 5 shows the subtracted profiles for each flare (i.e. flare - quiet, as in Figure 3), in order to examine possible velocity shifts during the flare."
 The flares are shown on the sime verlical seale such that strong flares have significant excess emission. ancl small flares have very little.," The flares are shown on the same vertical scale such that strong flares have significant excess emission, and small flares have very little."
 It is clear that some flares (F1. F2. F3. FT. FLO) show a blue wing enhancement and ved wing deficit. while others show the opposite behavior (red wing enhancement ancl blue wing deficit - F4. F9) aud still others show both blue and red enhancements (F5. F3) or deficits (FG).," It is clear that some flares (F1, F2, F3, F7, F10) show a blue wing enhancement and red wing deficit, while others show the opposite behavior (red wing enhancement and blue wing deficit - F4, F9) and still others show both blue and red enhancements (F5, F8) or deficits (F6)."
 For simplicity. we use only the Mg IE k line in the following analvsis. as the Ae II h line exhibited very similar behavior in all cases.," For simplicity, we use only the Mg II k line in the following analysis, as the Mg II h line exhibited very similar behavior in all cases."
 The fares are grouped according to the appearance of (he excess flare emission in Figure 6 (blue enhancements) aud Figure 7 (red enhancements). with the left panels showing Ale II k and the right panels the strong Fe II UVI line at2600.," The flares are grouped according to the appearance of the excess flare emission in Figure 6 (blue enhancements) and Figure 7 (red enhancements), with the left panels showing Mg II k and the right panels the strong Fe II UV1 line at."
2A.. In general. the enhancements seen in Me II k are also seen. albeit al a lower level ancl with poorer signal-to-noise ratio. in the Fe II data. as expected since these lines are formed in approximately (he same temperature reeion of the atmosphere.," In general, the enhancements seen in Mg II k are also seen, albeit at a lower level and with poorer signal-to-noise ratio, in the Fe II data, as expected since these lines are formed in approximately the same temperature region of the atmosphere."
 Simple Gaussian [its to the enhancement features eive wavelength shilis for each of these flares. as shown in Table 4.," Simple Gaussian fits to the enhancement features give wavelength shifts for each of these flares, as shown in Table 4."
 The shifts are not large. tvpicallv a few km/sec in both the upward (blue shift) and dowuward (red shift) directions.," The shifts are not large, typically a few km/sec in both the upward (blue shift) and downward (red shift) directions."
 The Sun also shows such velocity shifts even outside of obvious flares., The Sun also shows such velocity shifts even outside of obvious flares.
 These have been attributed to asvmmetric heating in active region loops (Winebarger el al., These have been attributed to asymmetric heating in active region loops (Winebarger et al.
 2002)., 2002).
 To verify that these apparent velocity shifts are not artifacts of the data reduction. we compared (he magnitude anc sense of the shift in each flare with the peculiar velocities of LIST and the Earth during the tme period in the orbit that the Hare occurred. and found no correlation.," To verify that these apparent velocity shifts are not artifacts of the data reduction, we compared the magnitude and sense of the shift in each flare with the peculiar velocities of HST and the Earth during the time period in the orbit that the flare occurred, and found no correlation."
 We see no evidence (hat the observed. velocity shifts are instrumental in nature.," We see no evidence that the observed velocity shifts are instrumental in nature,"
"The correlation of nuclear black hole mass M, and bulge stellar velocity dispersion o, is now well established in nearby galaxies (Tremaineetal.2002).",The correlation of nuclear black hole mass ${\rm M_{\bullet}}$ and bulge stellar velocity dispersion $\sigma_{\ast}$ is now well established in nearby galaxies \citep{tremaineetal02}.
. The possibility of extending (he study of (his relationship to active galaxies. using diagnostics (hat can be easily measured even al substantial redshifts. has been explored as a result of two techniques: (1) the use of reverberation mapping to calibrate a relation between luminosity ancl radius of the broad line region (DLI). and (2) the use of the narrow |O III] AS007 emission line width as a surrogate for stellar velocity dispersion.," The possibility of extending the study of this relationship to active galaxies, using diagnostics that can be easily measured even at substantial redshifts, has been explored as a result of two techniques: (1) the use of reverberation mapping to calibrate a relation between luminosity and radius of the broad line region (BLR), and (2) the use of the narrow [O III] $\lambda$ 5007 emission line width as a surrogate for stellar velocity dispersion."
 If the BLR is in virial equilibrium. the mass of the central black hole is given bv AL=>a4cHpu/C6. where e and Rep are the characteristic. velocity. and radius. of. (he BLK.," If the BLR is in virial equilibrium, the mass of the central black hole is given by $_{\bullet} = v^2 {\rm R_{BLR}} / G$, where $v$ and ${\rm R_{BLR}}$ are the characteristic velocity and radius of the BLR."
 scale factors for converting measured quantiles to truly representative ancl corresponding velocities and radii depend on (he unknown kinematic structure of the DLR., Scale factors for converting measured quantities to truly representative and corresponding velocities and radii depend on the unknown kinematic structure of the BLR.
 Iowever. several studies have shown that estimates of the black hole mass (hat are consistent with other methods can be derived in this way.," However, several studies have shown that estimates of the black hole mass that are consistent with other methods can be derived in this way."
 Gebhardtetal.(2000) and, \citet{gebhardtetal00} and
"The variations of ¢, T(¢) and V(9) against a in Case II have been drawn in figs.","The variations of $\phi$ , $T(\phi)$ and $V(\phi)$ against $a$ in Case II have been drawn in figs."
" 5, 6 and 7 respectively for A=1/3,B0.5,C0.5,a0.6,¢010."," 5, 6 and 7 respectively for $A=1/3,B=0.5,C=0.5,\alpha=0.6,\phi_{0}=10$."
" From these figures, we see that DBI scalar field ¢ and potential V are increasing and warped brane tension T is decreasing with the evolution of the Universe."," From these figures, we see that DBI scalar field $\phi$ and potential $V$ are increasing and warped brane tension $T$ is decreasing with the evolution of the Universe."
" So the DBI scalar field, potential and warped brane tension can be reconstructed by modified Chaplygin gas model."," So the DBI scalar field, potential and warped brane tension can be reconstructed by modified Chaplygin gas model."
" Gibbons Hawking conjectured that event horizon area, including cosmological event horizons, might quite generally have associated entropy Gibbons&Hawk-ing (1977)."," Gibbons Hawking conjectured that event horizon area, including cosmological event horizons, might quite generally have associated entropy \cite{hawking}."
. A prominent example is de Sitter space., A prominent example is de Sitter space.
" We consider the FRW Universe as a thermodynamical system with the future even horizon surface as a boundary of the system, which is a valid assumption Davisetal(2003)."," We consider the FRW Universe as a thermodynamical system with the future even horizon surface as a boundary of the system, which is a valid assumption \cite{davis}."
". This horizon has got recent attention since it yields a correct equation of state of dark energy, namely for the holographic dark energy Jamiletal(2009)."," This horizon has got recent attention since it yields a correct equation of state of dark energy, namely for the holographic dark energy \cite{li}."
". In general, the radius of the event horizon Hjis not constant but changes with time (or expansion of the Universe)."," In general, the radius of the event horizon $R_h$is not constant but changes with time (or expansion of the Universe)."
" Let dH, be an infinitesimal change in the radius of the future event horizon during a time of interval dt.", Let $dR_h$ be an infinitesimal change in the radius of the future event horizon during a time of interval $dt$.
" This small displacement dR», will produce an infinitesimal change dV in the volume V of the event horizon.", This small displacement $dR_h$ will produce an infinitesimal change $dV$ in the volume $V$ of the event horizon.
" Each spacetime describing a thermodynamical system and satisfying Einstein’s equations differs infinitesimally in the extensive variables volume, energy and entropy by dV, dE and dS, respectively, while having the same values for theintensive variables temperature T' and pressure p."," Each spacetime describing a thermodynamical system and satisfying Einstein's equations differs infinitesimally in the extensive variables volume, energy and entropy by $dV$, $dE$ and $dS$, respectively, while having the same values for theintensive variables temperature $T$ and pressure $p$ ."
" Thus, for these two spacetimes describing two thermodynamical states, there must exist some"," Thus, for these two spacetimes describing two thermodynamical states, there must exist some"
disrupt the convection laver.,disrupt the convection layer.
 We intend to carry out a more extensive investigation of intermediate parameter ranges in which the role of downward pumping is important in counteracting the buovancy cllects (Lobiasefαἱ2001)., We intend to carry out a more extensive investigation of intermediate parameter ranges in which the role of downward pumping is important in counteracting the buoyancy effects \citep{TBC2}.
". Finally, we intend to explore. the interactions between shear-driven buovaney instabilities ane convective [lows ab higher Richardson numbers (with a hydrodvnamically stable shear)."," Finally, we intend to explore the interactions between shear-driven buoyancy instabilities and convective flows at higher Richardson numbers (with a hydrodynamically stable shear)."
 This will be a challenging problem to tackle numerically (requiring high numerical resolution). but results from these preliminary calculations constitute a firm foundation for future work.," This will be a challenging problem to tackle numerically (requiring high numerical resolution), but results from these preliminary calculations constitute a firm foundation for future work."
 The authors thank Nie Brummell. Nigel Weiss and. Cieolf Vasil for stimulating cliscussions.," The authors thank Nic Brummell, Nigel Weiss and Geoff Vasil for stimulating discussions."
 The numerical calculations. were carried out on the UINMILD. cluster based in St Andrews. which is partially funded by STEC.," The numerical calculations were carried out on the UKMHD cluster based in St Andrews, which is partially funded by STFC."
 This research. is supported: via a rolling erant from STEC that is held at DAAITPP. University of Cambridge.," This research is supported via a rolling grant from STFC that is held at DAMTP, University of Cambridge."
 PIB and LJS also wish to acknowledge support from the WEED. Santa Barbara and travel grants from the RAS to facilitate attendance at a workshop where some of the work was clone.," PJB and LJS also wish to acknowledge support from the KITP, Santa Barbara and travel grants from the RAS to facilitate attendance at a workshop where some of the work was done."
to cause the individual stars in the binary to coalesce and form a single highly rotating object. thereby preventing additional binary evolution and the formation of a double compact object.,"to cause the individual stars in the binary to coalesce and form a single highly rotating object, thereby preventing additional binary evolution and the formation of a double compact object."
 Because of significant radial expansion. stars crossing the Hertzsprung gap (HG) very frequently initiate a common envelope phase.," Because of significant radial expansion, stars crossing the Hertzsprung gap (HG) very frequently initiate a common envelope phase."
 HG stars do not have a clear entropy jump at the core-envelope transition(2): if such a star overflows its Roche lobe and initiates a common envelope phase. the inspiral is expected to lead to a coalescence (?)..," HG stars do not have a clear entropy jump at the core-envelope transition\citep{2004ApJ...601.1058I}; if such a star overflows its Roche lobe and initiates a common envelope phase, the inspiral is expected to lead to a coalescence \citep{2000ARA&A..38..113T}."
 In particular. it has been estimated that for a solar metallicity environment (e.g.. our Galaxy). properly accounting for the HG gap may lead to a reduction in the merger rates of BH-BH binaries by ~2-3 orders of magnitude (?)..," In particular, it has been estimated that for a solar metallicity environment (e.g., our Galaxy), properly accounting for the HG gap may lead to a reduction in the merger rates of BH-BH binaries by $\sim 2-3$ orders of magnitude \citep{2007ApJ...662..504B}."
 In contrast. in a low metallicity environment this suppression ts much less severe (~| order of magnitude: ?)).," In contrast, in a low metallicity environment this suppression is much less severe $\sim 1$ order of magnitude; \citet{2010ApJ...715L.138B}) )."
 The details of the common envelope phase are not yet fully understood. thus in what follows we consider two set of models. one that does not take into account the suppression (optimistic models: marked with A). and another that assumes the maximum suppression (pessimistic models: marked with B).," The details of the common envelope phase are not yet fully understood, thus in what follows we consider two set of models, one that does not take into account the suppression (optimistic models: marked with A), and another that assumes the maximum suppression (pessimistic models: marked with B)."
 Solar metallicity and 10% of solar metallicity are labeled with Z and z. respectively.," Solar metallicity and $10\%$ of solar metallicity are labeled with Z and z, respectively."
 In the case of NSs. we adopt natal kick distributions from observations of single Galactic pulsars (?) with c=265 km/s. However. for BHs we draw kicks from the same distribution (but at a lower magnitude). which is inverse proportional to the amount of fall back expected at BH formation (e.g..?)..," In the case of NSs, we adopt natal kick distributions from observations of single Galactic pulsars \citep{2005MNRAS.360..974H} with $\sigma =265$ km/s. However, for BHs we draw kicks from the same distribution (but at a lower magnitude), which is inverse proportional to the amount of fall back expected at BH formation \citep[e.g.,][]{2001ApJ...554..548F}."
 In particular. for most massive BHs that form with the full fall back (direct BH formation). the amount of natal kick is zero.," In particular, for most massive BHs that form with the full fall back (direct BH formation), the amount of natal kick is zero."
 In addition. we test one more set of models in which the magnitude of the NS kicks is lower by a factor of 2. to c=132.5 km/s. as some observations and empirically based arguments seem to indicate that natal kicks in close binaries are lower than for single stars (22)..," In addition, we test one more set of models in which the magnitude of the NS kicks is lower by a factor of 2, to $\sigma=132.5$ km/s, as some observations and empirically based arguments seem to indicate that natal kicks in close binaries are lower than for single stars \citep{2006ApJ...644.1063D,2006A&A...450..345K}."
 The BH kicks are decreased in the similar fashion as in models with the full NS kicks., The BH kicks are decreased in the similar fashion as in models with the full NS kicks.
 The standard value of c parameter is denoted by K and the smaller value by k. The detailed list of models considered in this paper is presented in Table 2.., The standard value of $\sigma$ parameter is denoted by K and the smaller value by k. The detailed list of models considered in this paper is presented in Table \ref{Models}.
 Model AZK ts a standard set of parameters described in detail by ?.., Model AZK is a standard set of parameters described in detail by \citet{2002ApJ...572..407B}.
 The evolution of the orbit of compact object binary under the influence of gravitational radiation had been calculated by ?2..," The evolution of the orbit of compact object binary under the influence of gravitational radiation had been calculated by \citet{1963PhRv..131..435P,1964PhRv..136.1224P}."
" In the quadrupole approximation. the orbit decays às where a is the great semi-axis. e is the eccentricity of binary. Mj, is the mass of the first component. M» is the mass of second component. and While the eccentricity decaysMi asM» Using the above formulae we can express the fundamental gravitational wave frequency as a function of the eccentricity where cy=(1[1-4972294etl Py is the initial orbital period. and ων) is re]the first non-zero harmonic."," In the quadrupole approximation, the orbit decays as where $a$ is the great semi-axis, $e$ is the eccentricity of binary, $M_1$ is the mass of the first component, $M_2$ is the mass of second component, and While the eccentricity decays as Using the above formulae we can express the fundamental gravitational wave frequency as a function of the eccentricity where $c_0=(e_0^{12/19}[1+\frac{121}{304}e_0^2]^{1305/2299})(1-e_0^2)^{-1}$, $P_0$ is the initial orbital period, and $f_{GW}(e)$ is the first non-zero harmonic."
 The gravitational wave frequency is twice the orbital frequency. Le. faw=2foreτ," The gravitational wave frequency is twice the orbital frequency, i.e., $f_{GW}=2f_{orb}=\frac{2}{P_{orb}}$."
 We present the evolution of eccentricity as a function of gravitational wave frequency in Figure | for a binary neutron star with components of equal masses of 1.4M...," We present the evolution of eccentricity as a function of gravitational wave frequency in Figure \ref{Ecevol} for a binary neutron star with components of equal masses of $ 1.4 \,M_{\odot}$."
 The initial frequency corresponds to a semi-major axis such that the merger time is set to be Tere=107 Myr., The initial frequency corresponds to a semi-major axis such that the merger time is set to be $T_{merg}=10^4$ Myr.
 Figure 1. contains several different cases of evolution in the plane stretched by eccentricity and gravitational wave frequency., Figure \ref{Ecevol} contains several different cases of evolution in the plane stretched by eccentricity and gravitational wave frequency.
 We start with an initial population created using the code., We start with an initial population created using the code.
 We present the properties of the population, We present the properties of the population
The characteristic gravitational wave amplitudes are calculated in a similar wav as before. under the assumption Chat the core collapse leads to asyinnmetrical blobs which undergo a merger leading to a DII. which then undergoes a ring-down phase.,"The characteristic gravitational wave amplitudes are calculated in a similar way as before, under the assumption that the core collapse leads to asymmetrical blobs which undergo a merger leading to a BH, which then undergoes a ring-down phase."
 The parameters chosen are plausible but. arbitrarily chosen (o represent the maximum level of signals that could be expected., The parameters chosen are plausible but arbitrarily chosen to represent the maximum level of signals that could be expected.
 These are shown in figure 7.. where we assumed mq=msad. with a<1 (representing blobs which become the DII) and we assumed that the merging phase starts when the blobs are separated by r~10* em.," These are shown in figure \ref{fig:colla}, where we assumed $m_1=m_2= \alpha M_\odot$ with $\alpha \lesssim 1$ (representing blobs which become the BH) and we assumed that the merging phase starts when the blobs are separated by $r\sim10^7$ cm."
 A rough estimate on the maximal enussion from an unstable accretion disk is given by (he gravitational wave amplilucles from bars of m=dM... am!=3M. and r=6Gin’/e? where 3<1.," A rough estimate on the maximal emission from an unstable accretion disk is given by the gravitational wave amplitudes from bars of $m=\beta M_\odot$, $m^\prime= 3 M_\odot$ and $r=6Gm^\prime/c^2$ where $\beta \lesssim 1$."
 We have calculated these amplitudes for the distances derived from the occurrence rates of Type I collapsars derived bv Frver et al. (, We have calculated these amplitudes for the distances derived from the occurrence rates of Type I collapsars derived by Fryer et al. (
1999b).,1999b).
 Type IL rates were not computed. but i we take into account the Type IE as well. using the mass function ratio in the next (o last paragraph. the amplitude of gravitational waves from collapsars should be stronger than what is shown in figure 7.. which corresponds to Type I only.," Type II rates were not computed, but if we take into account the Type II as well, using the mass function ratio in the next to last paragraph, the amplitude of gravitational waves from collapsars should be stronger than what is shown in figure \ref{fig:colla}, which corresponds to Type I only."
 A complete set of theoretical wavelorm templates will be available for the in-spiral and rine-down phases of compact binaries such as DII-DII. aud presumably also for DII-NS.," A complete set of theoretical waveform templates will be available for the in-spiral and ring-down phases of compact binaries such as BH-BH, and presumably also for BH-NS, NS-NS."
 These are directly applicable to the first two GRB scenarios. and may be of some limited use in other scenarios. e.g. if core collapse leads to break-up into very dense (NS-like) blobs.," These are directly applicable to the first two GRB scenarios, and may be of some limited use in other scenarios, e.g. if core collapse leads to break-up into very dense (NS-like) blobs."
 When templates can be used. one can employ the matched filtering technique (e.g. Thorne 1987) to optimize the search for gravitational wave signals in (he observational data stream.," When templates can be used, one can employ the matched filtering technique (e.g. Thorne 1987) to optimize the search for gravitational wave signals in the observational data stream."
 This technique is useful especially for in-spiral binaries emitting signals of many cvcles., This technique is useful especially for in-spiral binaries emitting signals of many cycles.
 The signal-Lo-noise ratio (S/N) p is given by where ο) is the noise power spectral densitv of the detector., The signal-to-noise ratio (S/N) $\rho$ is given by where $S_h(f)$ is the noise power spectral density of the detector.
 The gravitational wave signal is detectable if the S/N exceeds a threshold ο). as a rough rule of thumb taken as Phm™-o).," The gravitational wave signal is detectable if the S/N exceeds a threshold $\rho_{th}$, as a rough rule of thumb taken as $\rho_{th}\sim 5$."
 ‘The matched filtering technique can in general be applied only {ο (he in-spiral phases of NS-NS and BII-NS binaries., The matched filtering technique can in general be applied only to the in-spiral phases of NS-NS and BH-NS binaries.
 Unfortunately. the rine-down frequencies of the equasimormal modes of stellar mass black holes are too hieh to be optimal for the advanced LIGO.," Unfortunately, the ring-down frequencies of the quasi-normal modes of stellar mass black holes are too high to be optimal for the advanced LIGO."
 Furthermore. the in-spiral signal from DII-WD and BII-IIe binaries ends below the seismic cutoff Irequency. ~10 Hz.," Furthermore, the in-spiral signal from BH-WD and BH-He binaries ends below the seismic cutoff frequency $\sim 
10$ Hz."
 For the nearest NS-NS binary in-spiral which, For the nearest NS-NS binary in-spiral which
of ealasics with known redshifts.,of galaxies with known redshifts.
 If then applies tle same forimla to photometry data of new ealaxy samples to deteriuue their photometric redshifts., It then applies the same formula to photometry data of new galaxy samples to determine their photometric redshifts.
 This method is superior to the other in the point that the more galaxies we observe for the training set. the more accurate photometric redshifts we obtain.," This method is superior to the other in the point that the more galaxies we observe for the training set, the more accurate photometric redshifts we obtain."
 Therefore. Yee (1998) called it the cClupizical traimime-sct method.," Therefore, Yee (1998) called it the empirical training-set method."
 For galaxies. the rainine-set method secs to work more robust than the uinethod. because it is based on real observed ealaxv spectra and because the enrpiical formula cau ο determined accurately using ai large nuniber of spectroscopic seüuples (Connolly et al.," For galaxies, the training-set method seems to work more robust than the method, because it is based on real observed galaxy spectra and because the empirical formula can be determined accurately using a large number of spectroscopic samples (Connolly et al."
 1997)., 1997).
 Recently. comparably accurate redshifts are obtained by a simpler raining-sct method which adopts binning of galaxics according to observed colors (Wane. Dahcall Turner 1998: Wang. Turner. Dahcall 1999).," Recently, comparably accurate redshifts are obtained by a simpler training-set method which adopts binning of galaxies according to observed colors (Wang, Bahcall Turner 1998; Wang, Turner, Bahcall 1999)."
 Csabai. Connolly. Szalav (1999) also succeeded. iu obtaining accurate photometric redshifts by combining the trainiug-set uethod aud the method.," Csabai, Connolly, Szalay (1999) also succeeded in obtaining accurate photometric redshifts by combining the training-set method and the method."
 IHowever. it is difficult to make a good traimiug set for high redshift ealaxies. since the uunber of ealaxics with spectroscopic redshifts is still small.," However, it is difficult to make a good training set for high redshift galaxies, since the number of galaxies with spectroscopic redshifts is still small."
 Also we should © cautious in applying the enpirical formmla obtained at low redshifts to high redshift ealaxics. since siguificaut evolution is expected in their SEDs.," Also we should be cautious in applying the empirical formula obtained at low redshifts to high redshift galaxies, since significant evolution is expected in their SEDs."
 Hence. in this study. we use the nuuiniizugiuethod which cau inchide spectral evolution of galaxies directly.," Hence, in this study, we use the minimizing method which can include spectral evolution of galaxies directly."
 This method searches for the best-fit SED aud the redshift of à ealaxy by comparing the observed SED of the ealaxy with templates prepared in advance., This method searches for the best-fit SED and the redshift of a galaxy by comparing the observed SED of the galaxy with templates prepared in advance.
 In general. templates are made either frou observed spectra of nearby ealaxics or from simulated spectra based on a population svuthesis model.," In general, templates are made either from observed spectra of nearby galaxies or from simulated spectra based on a population synthesis model."
 Coleman. Wu. Weediman (1980: hereafter CWW) and Iiunev et al. (," Coleman, Wu, Weedman (1980; hereafter CWW) and Kinney et al. ("
1993. 1996) are widely used sources of observed. spectra for the IIDE. galaxies.,"1993, 1996) are widely used sources of observed spectra for the HDF galaxies."
 Lauzetta et al. (, Lanzetta et al. (
1996. 1998) aud Fernanudez-Soto et al. (,"1996, 1998) and Fernánndez-Soto et al. ("
1999) used CWWNVs aud Kiuuev ct al,1999) used CWW's and Kinney et al.
 spectra.,'s spectra.
 However. the use of the observed. SEDs of nearby galaxies miav inake it dificult to directly take the effects of galaxy evolution iuto account.," However, the use of the observed SEDs of nearby galaxies may make it difficult to directly take the effects of galaxy evolution into account."
 Accordingly. oei this paper we use simulated spectra based. on a recent population svuthesis model.," Accordingly, in this paper we use simulated spectra based on a recent population synthesis model."
 Caryn Uartwick (1996) also used simulated spectra based on Bruzual Charlot (1993)., Gwyn Hartwick (1996) also used simulated spectra based on Bruzual Charlot (1993).
 Sawicki ct al. (, Sawicki et al. (
1997) made their templates based ou both observed spectra (CWW) aud. simulated spectra by Bruzual Charlot (1996: hereafter DC96).,1997) made their templates based on both observed spectra (CWW) and simulated spectra by Bruzual Charlot (1996; hereafter BC96).
 We use a stellar population svuthesis model by Ποανα Avimoto (1997: hereafter NAOT) to make template SEDs., We use a stellar population synthesis model by Kodama Arimoto (1997; hereafter KA97) to make template SEDs.
 IXA97 includes the stellar evolitionary tracks after the asviuptotic elant brauch iu addition to the conventional tracks., KA97 includes the stellar evolutionary tracks after the asymptotic giant branch in addition to the conventional tracks.
 Hence the model predicts UW fiux of galaxies reasonably well. or at least. as good as any previous models.," Hence the model predicts UV flux of galaxies reasonably well, or at least, as good as any previous models."
 NAQT was successfully used. to obtain photometric redshifts of low redshift ealaxies yoda. Bell. Bower 1999).," KA97 was successfully used to obtain photometric redshifts of low redshift galaxies (Kodama, Bell, Bower 1999)."
 Our work is the first to use KAQ? to obtain photometric redshifts of ligh-~ galaxies., Our work is the first to use KA97 to obtain photometric redshifts of $z$ galaxies.
 The template SEDs cousist of the spectra of pure disks. pure bulges. and composites made by interpolating the two as shown in Table 1..," The template SEDs consist of the spectra of pure disks, pure bulges, and composites made by interpolating the two as shown in Table \ref{table:sedparam}."
 The parameters for the SEDs are the power-law index at of the initial mass function (MIF). the time scale of star formation Typ. the time scale of gas intall from a ealactic halo iuto a disk rg. aud the time when the ealactic wind blows feyy.," The parameters for the SEDs are the power-law index $x^{\rm IMF}$ of the initial mass function (IMF), the time scale of star formation $\tau_{\rm SF}$, the time scale of gas infall from a galactic halo into a disk $\tau_{\rm
infall}$, and the time when the galactic wind blows $t_{\rm GW}$."
 The star formation rate of a galaxw is set to be zero after fei., The star formation rate of a galaxy is set to be zero after $t_{\rm GW}$ .
" For disks. we adopt MF=1,35. rug=5C. ng=56r. and fei=20C€vr (G6. longer than the preseut age of the universe). which are close to the values estimated for the disk of our Galaxy."," For disks, we adopt $x^{\rm IMF}=1.35$, $\tau_{\rm SF}=5$ Gyr, $\tau_{\rm
infall}=5$ Gyr, and $t_{\rm GW}=20$ Gyr (i.e., longer than the present age of the universe), which are close to the values estimated for the disk of our Galaxy."
" We adopt from IA97 ΟΗΕ=41,10. zug=0.1 sx. Tinfall=0. Cur. and fea=0.353C€0vr for bulges. which are known to reproduce the average color of ellipticals iu clusters of galaxies."," We adopt from KA97 $x^{\rm IMF}=1.10$, $\tau_{\rm
SF}=0.1$ Gyr, $\tau_{\rm infall}=0.1$ Gyr, and $t_{\rm GW}=0.353$ Gyr for bulges, which are known to reproduce the average color of ellipticals in clusters of galaxies."
 We make intermediate SED types by combining a disk component aud a bulee component with the same age., We make intermediate SED types by combining a disk component and a bulge component with the same age.
 The ratio of the bulge luninosity to the total luminosity in theD baud. which we define as D/T. is changed from 0.1 to 0.9 with an interval of 0.1.," The ratio of the bulge luminosity to the total luminosity in the band, which we define as B/T, is changed from 0.1 to 0.9 with an interval of 0.1."
 Pure disk SEDs correspoud to young or active star-forming galaxies. and pure bulee SEDs correspond to elliptical galaxies.," Pure disk SEDs correspond to young or active star-forming galaxies, and pure bulge SEDs correspond to elliptical galaxies."
 We also prepare very blue SEDs of agecICvr. corresponding to blue star-forming galaxies reported by recent deep surveys.," We also prepare very blue SEDs of $<$ 1Gyr, corresponding to blue star-forming galaxies reported by recent deep surveys."
 In total. our basic teuplate set consists of LS7 SEDs.," In total, our basic template set consists of 187 SEDs."
 To simmilate the observed SEDs. we take iuto account two absorption effects.," To simulate the observed SEDs, we take into account two absorption effects."
 One is the internal absorption due to dust iu cach galaxy., One is the internal absorption due to dust in each galaxy.
 More light is scattered and absorbed by dust eraius in shorter waveleusths., More light is scattered and absorbed by dust grains in shorter wavelengths.
 Therefore. internal absorption is oue of the Κον parameters for photometric redshift technique which is scusitive to wavelength dependent effects.," Therefore, internal absorption is one of the key parameters for photometric redshift technique which is sensitive to wavelength dependent effects."
 For simplicity. we assume that all galaxies have the same extinction curve. although we change the absolute amount of extinction. indicated by E(DbWV). as a free parameter.," For simplicity, we assume that all galaxies have the same extinction curve, although we change the absolute amount of extinction, indicated by $E(B-V)$, as a free parameter."
 Typical features of extinction curves of nearby. ealaxies including our Galaxy are as follows: (1) The amount of absorption basically inereases from the infra-red to the ultraviolet. (, Typical features of extinction curves of nearby galaxies including our Galaxy are as follows: (1) The amount of absorption basically increases from the infra-red to the ultraviolet. (
2) Some extinction curves have a bump at2175AÀ.. which is usually explained mainly by eraphite.,"2) Some extinction curves have a bump at, which is usually explained mainly by graphite."
 The existence of the bump is reported for our Galaxy (Seatou 1979: Cardelli et al., The existence of the bump is reported for our Galaxy (Seaton 1979; Cardelli et al.
 1989). LAIC (Fitzpatrick 1985). and AD (Bianchi et al.," 1989), LMC (Fitzpatrick 1985), and M31 (Bianchi et al."
 1996)., 1996).
 ITowever. no buiip is reported imn the extinction curve of SAIC (Prévvot et al.," However, no bump is reported in the extinction curve of SMC (Prévvot et al."
 1981: Bouchet etal., 1984; Bouchet et al.
 1985)., 1985).
 Gordon. Calzetti. Witt (1997) showed that whether the bump is preseut or nof cannot be explained by scattering or eeonietrical effects. aud that galaxies with ligh star formation activity tend to have no bump iu their extinction curves.," Gordon, Calzetti, Witt (1997) showed that whether the bump is present or not cannot be explained by scattering or geometrical effects, and that galaxies with high star formation activity tend to have no bump in their extinction curves."
 There are some studies in which an analytical Γον] was fitted to observed. extinction curves (Cardelli et al., There are some studies in which an analytical formula was fitted to observed extinction curves (Cardelli et al.
 1989: Fitzpatrick 1986.1998).," 1989; Fitzpatrick 1986,1998)."
 Calzetti (1997a). proposed an analvtical foriuula for nearby star-forming galaxies. including the effect of scattering through star-forming regions.," Calzetti (1997a) proposed an analytical formula for nearby star-forming galaxies, including the effect of scattering through star-forming regions."
 Te inferred that his formula holds for distant voung ealaxies because these galaxies are probably simular to nearby star-formune galaxies., He inferred that his formula holds for distant young galaxies because these galaxies are probably similar to nearby star-forming galaxies.
 We calculated. photometric redshifts using the Milky- extinction curve by Cardelli. Clavton. Mathis (1989) aud the SMClike curve by Calzetti (1997).," We calculated photometric redshifts using the Milky-Way-like extinction curve by Cardelli, Clayton, Mathis (1989) and the SMC-like curve by Calzetti (1997b)."
 Asa, Asa
cold accretion-gencerated IIT clouds. aud therefore we cannot make a definitive statement abou the role of cold accretion.,"cold accretion-generated HI clouds, and therefore we cannot make a definitive statement about the role of cold accretion."
 If HII clouds tracing cold accretion exist iu our observed. position. velocity. and mass regimes. as the siuulation of[eres&Ieruquist(2009) predict they ough (scoTable 1)). they should have been observe in all eroups instead of only one eroup.," If HI clouds tracing cold accretion exist in our observed position, velocity, and mass regimes, as the simulation of\citet{keres09} predict they ought (seeTable \ref{millertable}) ), they should have been observed in all groups instead of only one group."
 It the HI clouds we have detected tracers of cold accretion. this result indicates that the preseuce or lack of cold accretiou-related HI clouds is strongly euvironnmieut-depeudent. requiring a deuse euviromnenut and/or the preseuce of curent. strong interactions such as those in the M81 eroup.," If the HI clouds we have detected tracers of cold accretion, this result indicates that the presence or lack of cold accretion-related HI clouds is strongly environment-dependent, requiring a dense environment and/or the presence of current, strong interactions such as those in the M81 group."
 Teoutativelv. we state that 1ο observed IIT clouds are not likely to ve a product of cold accretion.," Tentatively, we state that the observed HI clouds are not likely to be a product of cold accretion."
 Certainly. more modeling aud simmlatious of cold accretion. especially in the verv cold II regime. are needed to properly address this question.," Certainly, more modeling and simulations of cold accretion, especially in the very cold HI regime, are needed to properly address this question."
 Future work towards determining the origin of UT clouds in galaxy eroups should iuclude high-resolution UT observations with the EVLA to determine their substructure: UV ane optical observations to search for a stellar compoucut: and coluparison with simulations of the AMIS Group that include all the relevant eas plivsics aud low for cold accretion., Future work towards determining the origin of HI clouds in galaxy groups should include high-resolution HI observations with the EVLA to determine their substructure; UV and optical observations to search for a stellar component; and comparison with simulations of the M81 Group that include all the relevant gas physics and allow for cold accretion.
 These studies would place stronger constraints ou the origius of HI clouds in ealaxy groups. aud determine whether such clouds are analogs to the Milkv Way IIVC's.," These studies would place stronger constraints on the origins of HI clouds in galaxy groups, and determine whether such clouds are analogs to the Milky Way HVCs."
 Finally. hese future observations will place stronger constraints on cosinological models of galaxy formation.," Finally, these future observations will place stronger constraints on cosmological models of galaxy formation."
 KAIC acknowledges the NRC Research Associateship prograin. the NRÀO Pre-Doctoral Fellowship program. aud Vauderbilt Universitv for fuudiug support.," KMC acknowledges the NRC Research Associateship program, the NRAO Pre-Doctoral Fellowship program, and Vanderbilt University for funding support."
 EP acknowledges support under the Edison Memorial Graduate Training Program at the Naval Research Laboratory. GDT.., EP acknowledges support under the Edison Memorial Graduate Training Program at the Naval Research Laboratory. .
on the particle magnetic moment.,on the particle magnetic moment.
 We therefore consider non-zero gradient. and curvature drifts., We therefore consider non-zero gradient and curvature drifts.
 We estimate that. dift and resulting displacement alter a (nme shorter (han the correlation time., We estimate that drift and resulting displacement after a time shorter than the correlation time.
 The guiding position X(/)=CX.Y.Z) lor a particle of mass m. charge Ze and momentum p having coordinate x(/)=(Cr.y.z) is described. in ce.g.s.," The guiding position ${\bf X} (t) = (X, Y , Z)$ for a particle of mass $m$ , charge $Ze$ and momentum $\bf{p}$ having coordinate ${\bf x} (t) = (x, y, z)$ is described, in c.g.s."
" units. by If the scales of magnetic fluctuation are much larger than the gvroradius r,. the guiding center motion delined in Eq. (5))"," units, by If the scales of magnetic fluctuation are much larger than the gyroradius $r_g$, the guiding center motion defined in Eq. \ref{GCmotion}) )"
 has (he role of effective evroperiod-averaged motion., has the role of effective gyroperiod-averaged motion.
 Therefore. Eq. (5))," Therefore, Eq. \ref{GCmotion}) )"
 can well describe the motion perpendicular to the local magnetic field., can well describe the motion perpendicular to the local magnetic field.
" In the case of ""finite Larmor radius. the gvroradius only represents the tvpical scale οἱ particle motion and Eq. (5))"," In the case of “finite Larmor radius”, the gyroradius only represents the typical scale of particle motion and Eq. \ref{GCmotion}) )"
 provides the instantaneous guiding center position whereas evroperiod-average becomes meaningless., provides the instantaneous guiding center position whereas gyroperiod-average becomes meaningless.
 In (he magnetostatic field described above. the euiding center velocity. transverse {ο the field B(x) is given at the first order in 0D(x)/Dy bv the gvroperiod average (Rossi&Olbert1970) where a is the particle pitch angle anc fo=cosa.," In the magnetostatic field described above, the guiding center velocity transverse to the field ${\bf B (x)}$ is given at the first order in $\delta B({\bf x})/B_0$ by the gyroperiod average \citep{ro70}
 where $\alpha$ is the particle pitch angle and $\mu = {\rm cos}\alpha$."
 Eq. (6)), Eq. \ref{Vperp}) )
 gives the first order most general expression of the guiding center velocity orthogonal to the local magnetic field direction (Dalescu1988)., gives the first order most general expression of the guiding center velocity orthogonal to the local magnetic field direction \citep{b88}.
. Tere the variation of à is assumed to be negligible over a gvroperiod., Here the variation of $\alpha$ is assumed to be negligible over a gyroperiod.
 Being VC(I) a gvroperiod average. magnetic field can be computed at the euiding center position during that gvroperiod.," Being ${\bf V}_{\perp}^G (t)$ a gyroperiod average, magnetic field can be computed at the guiding center position during that gyroperiod."
 In contrast to Matthaeusetal.(2003).. the transverse motion of the guiding center [rom the field line is not parametrized in the present paper through some constants to be inferred [rom numerical simulations. bul described directlv. from (he equation of motion of the guiding center.," In contrast to \citet{mqbz03}, the transverse motion of the guiding center from the field line is not parametrized in the present paper through some constants to be inferred from numerical simulations, but described directly from the equation of motion of the guiding center."
 The finite-timeaverage square transverse displacement of the particle from the direction of local B due to drift dp(/) can, The finite-timeaverage square transverse displacement of the particle from the direction of local $B$ due to drift $d_D (t)$ can
the two stars.,the two stars.
 Η this is tlie case. the phase lag between emission and absorption must be 0.5 cycles — this is a necessary. but uot sufficient. condition for the estimate to be trustworthy.," If this is the case, the phase lag between emission and absorption must be 0.5 cycles – this is a necessary, but not sufficient, condition for the estimate to be trustworthy."
 In the present case. this coucdition is margiually fulfilled — the discrepaucey is lormally three staucard deviations.," In the present case, this condition is marginally fulfilled – the discrepancy is formally three standard deviations."
 If we assume the A-velocities do reflect the center-of-nass motion. we find q=Ale/AL0.8340.13.," If we assume the $K$ -velocities do reflect the center-of-mass motion, we find $q = M_2 / M_1 = 
0.83 \pm 0.13$."
 Combining us with a broadly typical white dwarf mass of 0.7 M... vields a secondary. mass uear 0.55 M... si-—ilar to what the Baralle&νου(2000) models would suggestMOD at this period aud spectral type.," Combining this with a broadly typical white dwarf mass of 0.7 $_\odot$ yields a secondary mass near 0.55 $_\odot$, similar to what the \citet{bk00} models would suggest at this period and spectral type."
 While these mass calculatious are somewhat fanciful. the moclest value of νο does firmly coustraiu the orbital inclination 7 to be fairly low.," While these mass calculations are somewhat fanciful, the modest value of $K_2$ does firmly constrain the orbital inclination $i$ to be fairly low."
 Evenwe take M4 to be a very low Q.1 ML. and 4 to be 0.6 — pushiug both quantities to values that increase i — tlie inclination is ouly ~ 25 degrees., Evenwe take $M_1$ to be a very low $0.4$ $_{\odot}$ and $q$ to be 0.6 – pushing both quantities to values that increase $i$ – the inclination is only $\sim$ 25 degrees.
 The apparent lack of eclipses is therefore not unexpected., The apparent lack of eclipses is therefore not unexpected.
 The Baraffe&Ixolb(2000) evolutionary models that best mateh this system are those iu which mass transfer begins after hydrogeu has been substantially depleted in the core., The \citet{bk00} evolutionary models that best match this system are those in which mass transfer begins after hydrogen has been substantially depleted in the core.
 The spectral type of the secondary is situilar to that in other CVs with similar orbital periods (Ixnigge2006).., The spectral type of the secondary is similar to that in other CVs with similar orbital periods \citep{kniggedonor}.
 No dwarf uova outbursts have been reported from this svstem., No dwarf nova outbursts have been reported from this system.
 In many respects it resembles LY UMa (= CW 10154525). a 0.271-d emission-line binary with a strong late-Ix coutribution aud uo reported outbursts (Tappertetal.2001).," In many respects it resembles LY UMa (= CW 1045+525), a 0.271-d emission-line binary with a strong late-K contribution and no reported outbursts \citep{tappert01}."
. V1062 Tau is the optical counterpart of the X-ray source 1HO1294-216. which was discovered in the HEAO-2 Large Area Sky Survey (Woodetal.198D).," V1062 Tau is the optical counterpart of the X-ray source 1H0459+246, which was discovered in the HEAO-2 Large Area Sky Survey \citep{wood84}."
. Remillarcdetal.(1991). found an X-ray inoculation near 62 minutes. aud classified the object as an intermediate polar. or DQ Her star.," \citet{remillard94} found an X-ray modulation near 62 minutes, and classified the object as an intermediate polar, or DQ Her star."
 The 62-1niuute X-ray inoculation was couliriued aud refined by Hellieretal., The 62-minute X-ray modulation was confirmed and refined by \citet{hellier02}. .
 (2002).. (1991). also published au optical spectrum. aud uoted the features ofa CV and a Ix star.," \citet{remillard94} also published an optical spectrum, and noted the features of a CV and a K star."
 They obtained V. aud / time series photometry that showed ellipsoidal variation at a period of 9.95£0.07 lh. Lipkinetal.(2001) monitored V1062 Tau photometrically. aud. refined the orbital period to 9.0809+0.0006LA.," They obtained $V$ and $I$ time series photometry that showed ellipsoidal variation at a period of $9.95 \pm 0.07$ h. \citet{lipkin04} monitored V1062 Tau photometrically, and refined the orbital period to $9.9802 \pm 0.0006$."
 They also detected the 62-minute period. and the beat between this and the orbit.," They also detected the 62-minute period, and the beat between this and the orbit."
 Their data showed two short. low-amplitude outbursts. with M.~1.2 mae.," Their data showed two short, low-amplitude outbursts, with $\Delta I \sim 1.2$ mag."
 For the most part. our spectra of V1062 Tau appeared similar to the average shown in Fie. 9..," For the most part, our spectra of V1062 Tau appeared similar to the average shown in Fig. \ref{fig:spectra1},"
 which iu turn is generally similar to that shown by Remillardetal.(1991). (their Figure 3)., which in turn is generally similar to that shown by \citet{remillard94} (their Figure 3).
 The excitation is high: Hell A1686 emission is similar in streugth to He. and our long cumulative exposure also shows eunission at Hell A5111.," The excitation is high; HeII $\lambda 4686$ emission is similar in strength to $\beta$, and our long cumulative exposure also shows emission at HeII $\lambda 5411$ ."
 The Schlegel.Fiukbeiner.&Davis(1998) map iudicates areddening E(5—V)=0.63 at this position (f=178.08.6= —10.31). aud the continuuui does suggest substautial redcenine.," The \citet{schlegel98} map indicates areddening $E(B-V) = 0.63$ at this position $l = 178.08,\, b = -10.31$ ), and the continuum does suggest substantial reddening."
 The presence ofdiffuse interstellar bands wear ASTSO aud AG2S| , The presence of diffuse interstellar bands near $\lambda 5780$ and $\lambda 6284$ 
"ranges (e.g.,vanDyketal.2001).","ranges \citep[e.g.,][]{vandyk01}."
. MCMC methods require the specification of priors on parameters to be determined (as described below)., MCMC methods require the specification of priors on parameters to be determined (as described below).
" The spectrum of the northern, radio-bright rim is shown in the upper panel of Figure 3.."," The spectrum of the northern, radio-bright rim is shown in the upper panel of Figure \ref{spec}."
 Spectral lines typical of strongly underionized plasma are apparent (such plasma is expected in G1.9+0.3 because of its youth and the low density of the ambient ISM)., Spectral lines typical of strongly underionized plasma are apparent (such plasma is expected in G1.9+0.3 because of its youth and the low density of the ambient ISM).
" SN 1006 has a very similar X-ray spectrum; in the same spectral range of Figure 3,, Yamaguchietal.(2008) find prominent Ko lines of abundant elements such as Si, S, Ar, Ca, and Fe, with line centroids at 1.815 keV, 2.36 keV, 3.01 keV, 3.69 keV, and 6.43 keV. (As in SN 1006, O, Ne, and Mg lines might also be present at lower energies, but cannot be seen because of the high absorption.)"," SN 1006 has a very similar X-ray spectrum; in the same spectral range of Figure \ref{spec},, \citet{yamaguchi08} find prominent $\alpha$ lines of abundant elements such as Si, S, Ar, Ca, and Fe, with line centroids at 1.815 keV, 2.36 keV, 3.01 keV, 3.69 keV, and 6.43 keV. (As in SN 1006, O, Ne, and Mg lines might also be present at lower energies, but cannot be seen because of the high absorption.)"
" In addition to these lines produced in hot shocked plasma, the radioactive decay of tto aand finally to the stable isotope “Ca will result in the emission of X-ray and -ray lines in very young remnants (“Tiwithameanlifeof85.0--0.4yr,Ahmadet2006)."," In addition to these lines produced in hot shocked plasma, the radioactive decay of to and finally to the stable isotope $^{44}$ Ca will result in the emission of X-ray and $\gamma$ -ray lines in very young remnants \citep[\ti\ decays with a mean life of $85.0 \pm
0.4$ yr,][]{ahmad06}."
".decays This decay commences via an electron capture toSc,, leaving a K-shell vacancy followed rapidly either by Auger decay or by emission of a fluorescence photon of energy 4.09 keV (theis0.172photonspereach“Tidecay;Béetal.2004)."," This decay commences via an electron capture to, leaving a K-shell vacancy followed rapidly either by Auger decay or by emission of a fluorescence photon of energy 4.09 keV \citep[the yield is 0.172 
photons per each \ti\ decay;][]{be04}."
".yield Nuclear de-excitation Sc y-ray lines at 78.4 and 67.9 keV are also emitted, followed by Ca gamma rays at 1.157 MeV (mean life of Sc is 5.4 hr)."," Nuclear de-excitation Sc $\gamma$ -ray lines at 78.4 and 67.9 keV are also emitted, followed by Ca gamma rays at 1.157 MeV (mean life of $^{44}$ Sc is 5.4 hr)."
" An inspection of the radio-bright rim spectrum (Figure 3)) reveals the presence of Si, S, Ar, and Fe Ko lines, and a broad feature near 4 keV that may be a blend of Doppler-broadened Ca and Sc Kao lines."," An inspection of the radio-bright rim spectrum (Figure \ref{spec}) ) reveals the presence of Si, S, Ar, and Fe $\alpha$ lines, and a broad feature near 4 keV that may be a blend of Doppler-broadened Ca and Sc $\alpha$ lines."
" Lines are weaker in the low-surface brightness interior (lowergenerally panel of Figure 3)), with Ar and Sc lines being the most prominent."," Lines are generally weaker in the low-surface brightness interior (lower panel of Figure \ref{spec}) ), with Ar and Sc lines being the most prominent."
" We modeled the spectra of the northern, radio-bright rim and the faint interior with an absorbed power law plus emission lines of Si, S, Ar, Ca, Sc, and Fe."," We modeled the spectra of the northern, radio-bright rim and the faint interior with an absorbed power law plus emission lines of Si, S, Ar, Ca, Sc, and Fe."
" This simple model does not account for dust scattering and does not separate the underlying continuum into thermal and nonthermal components, but it suffices for the determination of line strengths, centroids, and widths."," This simple model does not account for dust scattering and does not separate the underlying continuum into thermal and nonthermal components, but it suffices for the determination of line strengths, centroids, and widths."
" We used a normal (Gaussian) prior for the absorbing column density Ng, with mean (standard deviation) of 6.89(0.11)x1077 cm, based on our multiregion spectral fit without dust scattering to the 2007 data (Paper II). ("," We used a normal (Gaussian) prior for the absorbing column density $N_H$, with mean (standard deviation) of $6.89 (0.11) \times 10^{22}$ $^{-2}$, based on our multiregion spectral fit without dust scattering to the 2007 data (Paper II). ("
Solar abundances of the absorbing ISM are those of Grevesse Sauval 1998; fits with dust scattering resulted inNy lower by 25%..),Solar abundances of the absorbing ISM are those of Grevesse Sauval 1998; fits with dust scattering resulted in$N_H$ lower by .)
" Noninformative, uniform and logarithmic priors were assumed for the power-law index I and the (unabsorbed) 5-10 keV continuum flux 75.10xev, respectively."," Noninformative, uniform and logarithmic priors were assumed for the power-law index $\Gamma$ and the (unabsorbed) 5–10 keV continuum flux $F_{5-10\ {\rm keV}}$, respectively."
" We used normal priors for line setting mean thermal line energies equal to theenergies, values measured by Yamaguchietal.(2008) for SN 1006, and to 4.09 keV for the Sc line."," We used normal priors for line energies, setting mean thermal line energies equal to the values measured by \citet{yamaguchi08} for SN 1006, and to 4.09 keV for the Sc line."
" In view of the 14,000 km s! blast wave speed, significant bulk Doppler shifts are possible, so we chose a large (c=10* km s!) width for these priors. ("," In view of the 14,000 km $^{-1}$ blast wave speed, significant bulk Doppler shifts are possible, so we chose a large $\sigma=10^4$ km $^{-1}$ ) width for these priors. ("
"For numerical stability, these normal priors were truncated to include only a finite range in line energies; we verified that our results are not affected by this procedure.)","For numerical stability, these normal priors were truncated to include only a finite range in line energies; we verified that our results are not affected by this procedure.)"
" Thermal lines in a young remnant arise in a fast-moving, shocked shell bounded by forward and reverse shocks."," Thermal lines in a young remnant arise in a fast-moving, shocked shell bounded by forward and reverse shocks."
" An optically and geometrically thin shell with velocity γω produces flat-topped lines with Doppler expandingwidths of 2v,;,4;.", An optically and geometrically thin shell expanding with velocity $v_{shell}$ produces flat-topped lines with Doppler widths of $2v_{shell}$.
 We assumed flat-topped profiles with the same (but unknown) Doppler width for all thermal lines. (, We assumed flat-topped profiles with the same (but unknown) Doppler width for all thermal lines. (
"Thermal broadening is likely of only modest importance, (KT;/m;)1/2~0.2Vsnez, based on models of Dwarkadas&Chevalier(1998) with exponential ejecta profiles.","Thermal broadening is likely of only modest importance, $\left(kT_i/m_i\right)^{1/2} \sim 0.2v_{shell}$, based on models of \citet{dwarkadas98} with exponential ejecta density profiles."
" But it may still be in off-center densitylocations suchas the north rim, where bulk appreciableradial motions contribute less to the line broadening.)"," But it may still be appreciable in off-center locations suchas the north rim, where bulk radial motions contribute less to the line broadening.)"
" A truncated normal prior was assumed for νεο, with mean of 14,000 km s! and 1c width of 5000 km s'!, from 0 to 50,000 km !.The Sc line was modeled by a extendingGaussian with width o5°; we assumed a prior with o—0.15 keV for 03°."," A truncated normal prior was assumed for $v_{shell}$, with mean of 14,000 km $^{-1}$ and $\sigma$ width of 5000 km $^{-1}$, extending from 0 to 50,000 km $^{-1}$ .The Sc line was modeled by a Gaussian with width $\sigma_v^{Sc}$ ; we assumed a prior with $\sigma = 0.15$ keV for $\sigma_v^{Sc}$ ."
" These priors for line widths exclude very large (> 50,000 km s!) widths, but otherwise provide weak constraints."," These priors for line widths exclude very large $>$ 50,000 km $^{-1}$ ) widths, but otherwise provide weak constraints."
Fordetal.(2003). lead us to conclude that formaldehyde is a molecule produced by the photodissociation of an unknown parent molecule. and that the parent molecule is produced bv vaporization from the surfaces of cometary nuclei orbiting IC210216 in a Ixuiper Dell analog.,"\citet{for03} lead us to conclude that formaldehyde is a molecule produced by the photodissociation of an unknown parent molecule, and that the parent molecule is produced by vaporization from the surfaces of cometary nuclei orbiting IRC+10216 in a Kuiper Belt analog."
 We did not detect methanol around IRC+10216. despite our deep search. aud our upper limits on the methanol abundance (<0.077% relative to water vapor) imply that anv comelary svstem around IRC--10216 contains significantly less methanol than (vpical Solar Svslem comets.," We did not detect methanol around IRC+10216, despite our deep search, and our upper limits on the methanol abundance $<0.077\%$ relative to water vapor) imply that any cometary system around IRC+10216 contains significantly less methanol than typical Solar System comets."
 Chemical characterization of extrasolar cometary svstenis is important for a variety of reasons., Chemical characterization of extrasolar cometary systems is important for a variety of reasons.
 The chemical composition of cometary svstenis can tell us something about the conditions in protoplanetary disks around forming stars. and therefore can provide us with interesting information on (he process of star formation.," The chemical composition of cometary systems can tell us something about the conditions in protoplanetary disks around forming stars, and therefore can provide us with interesting information on the process of star formation."
 The study of extrasolar cometary svslenms also bears directly on the emerging field of astrobiology. (IE£hrenlreund2000:Oro.Miller&Lazcano 1990).," The study of extrasolar cometary systems also bears directly on the emerging field of astrobiology \citep{EC00,OML90}."
. In our own Solar System. it is believed that much of the volatile carbon present on the voung Earth was delivered by comets (Chyba&Sagan1992)..," In our own Solar System, it is believed that much of the volatile carbon present on the young Earth was delivered by comets \citep{CS92}."
 Comets contributed volatile carbon both in the form of simple molecules like formaldehyde and methanol and as more complex molecules like amino acids Pierazzo&Chvba 1999).," Comets contributed volatile carbon both in the form of simple molecules like formaldehyde and methanol and as more complex molecules like amino acids \citep{and89,chy90,PC99}."
. It has been suggested (Cronin&Chang1993:Ore1997) that this extraterrestrial volatile carbon. contribution formed (he basis of the carbon chemistry which led to (the formation of extremely complex molecules and eventually to single-celled organisms and all life on Earth.," It has been suggested \citep{CC93,OL97} that this extraterrestrial volatile carbon contribution formed the basis of the pre-biotic carbon chemistry which led to the formation of extremely complex molecules and eventually to single-celled organisms and all life on Earth."
 Thus. the chemistry of extrasolar comelarv svslems nav have important consequences for the probability of lile lormine on otherwise habitable exoplanets.," Thus, the chemistry of extrasolar cometary systems may have important consequences for the probability of life forming on otherwise habitable exoplanets."
 Ultimately. we would like to survey (he chemical composition of a large number of extrasolar cometary svstems and compare their compositions to the chemical composition of Solar Svstem comets.," Ultimately, we would like to survey the chemical composition of a large number of extrasolar cometary systems and compare their compositions to the chemical composition of Solar System comets."
 We are extremely grateful to Silvia Leurini for taking most of our followup observations., We are extremely grateful to Silvia Leurini for taking most of our followup observations.
 We would also like to thank Axel Weiss and Clemens Thum for their help with the service observing program and for eiving us the opportunity to work with an experimental receiver selup., We would also like to thank Axel Weiss and Clemens Thum for their help with the service observing program and for giving us the opportunity to work with an experimental receiver setup.
 Thanks as well to Sergio. Martin for his help at the telescope., Thanks as well to Sergio Martin for his help at the telescope.
 D.A.N. gratefully acknowledges the support of NASA grants NÀG5-13114 [rom the Long Term Space Astrophysics Program and NAS5-30702 from the SWAS program., D.A.N. gratefully acknowledges the support of NASA grants NAG5-13114 from the Long Term Space Astrophysics Program and NAS5-30702 from the SWAS program.
" IX. E. ο, F. was partially supported by an American Dissertation Fellowship from the American Association of University Women (AAUW).", K. E. S. F. was partially supported by an American Dissertation Fellowship from the American Association of University Women (AAUW).
The quasar “broacd-line region” (BLR) from which high-velocity. gas produces correspondingly broad spectral emission lines. with typical EFWILM in the 2000-20000 Καινής range.,"The quasar ""broad-line region"" (BLR) from which high-velocity gas produces correspondingly broad spectral emission lines, with typical FWHM in the 2000-20000 km/s range."
 Prominent emission lines visible in optical spectra at >290.5 include. from ionization potential placing them nearest to the central black hole.CIV. a broad. component of 110. andMelt.," Prominent emission lines visible in optical spectra at $z > 0.5$ include, from ionization potential placing them nearest to the central black hole, a broad component of $\beta$, and."
 For some individual active galactie nuclei. reverberation mapping (??) has been able to confirm the locations of broad emission lines.," For some individual active galactic nuclei, reverberation mapping \citep{Peterson2004,Bentz2009} has been able to confirm the locations of broad emission lines."
 In a time series of spectra for the same object. an increase in the continuum Iuminosity is followed. often hundreds of days later. by a similar flare in and then 111.," In a time series of spectra for the same object, an increase in the continuum luminosity is followed, often hundreds of days later, by a similar flare in and then $\beta$."
 Assuming the Lare propagates outward at the speed of light. the delay can be used to infer a radius to BLE spectral lines.," Assuming the flare propagates outward at the speed of light, the delay can be used to infer a radius to BLR spectral lines."
 Lt is hoped that. broad-line region velocities are predominantly virial., It is hoped that broad-line region velocities are predominantly virial.
 For reverberation-mappecd quasars. this approximation. combined with lxeplers Laws then allows the use of and 111 to infer a black hole mass.," For reverberation-mapped quasars, this approximation combined with Kepler's Laws then allows the use of and $\beta$ to infer a black hole mass."
 An empirical relationship between the reverberation radii andthe continuum Ilux allows ‘virial mass estimators’ (2227777) that can be used on just one spectrum rather than a time series.," An empirical relationship between the reverberation radii andthe continuum flux allows `virial mass estimators' \citep{McLure2002,McLure2004,Vestergaard2006,Wang2009,Onken2008,Risaliti2009,Rafiee2011} that can be used on just one spectrum rather than a time series."
 Mass estimates have allowed a dramatic iniprovement in our understanding of distant quasars in several wavs. including the tight AZ@ correlation between black hole mass ancl stellar dispersion in the host. ealactic bulgeμισο (2?)(72)... analysis| of[ the ququasar: mass distributionlistribut as a function of redshift (?).. and analysis of the quasar mass-luminosity plane (??)..," Mass estimates have allowed a dramatic improvement in our understanding of distant quasars in several ways, including the tight $M - \sigma$ correlation between black hole mass and stellar dispersion in the host galactic bulge \citep{msigma1,msigma2}, analysis of the quasar mass distribution as a function of redshift \citep{Vestergaard2008}, and analysis of the quasar mass-luminosity plane \citep{Steinhardt2010a,Steinhardt2010b}."
 Phe last two of these entirely depend upon virial mass estimates. while the others would. require virial mass estimates if considered at higher redshift.," The last two of these entirely depend upon virial mass estimates, while the others would require virial mass estimates if considered at higher redshift."
 Llowever. in particular may. also be substantially broadened by. radiation pressure anc quasar outflows (?)..," However, in particular may also be substantially broadened by radiation pressure and quasar outflows \citep{Marconi2009}."
 If so. this extra velocity would result in an overestimate of the mass of the central black hole.," If so, this extra velocity would result in an overestimate of the mass of the central black hole."
 It has recently been reported that ~25% of quasars at 0.2<zOLS have anomalous narrow lines. and that these ANL quasars are associated with broadened 1132 but not broacenecMgll.," It has recently been reported that $\sim 25$ of quasars at $0.2 < z < 0.8$ have anomalous narrow lines, and that these ANL quasars are associated with broadened $\beta$ but not broadened."
 In this paper. we consider the implications of this broadening on virial mass estimation.," In this paper, we consider the implications of this broadening on virial mass estimation."
 In 2. we describe our line-Litting for the LL2/ ΟΙ] complex and identification of ANLs.," In \ref{sec:sample}, we describe our line-fitting for the $\beta$ ] complex and identification of ANLs."
 We also examine the response of other emission lines to an increased narrow L3 width., We also examine the response of other emission lines to an increased narrow $\beta$ width.
 Ehe resulting response of virial mass estimates in ANLs is exaniinect in 3.., The resulting response of virial mass estimates in ANLs is examined in \ref{sec:vme}.
 Finally. the possible implications ol these objects upon the validity of virial mass estimation are discussed in 4..," Finally, the possible implications of these objects upon the validity of virial mass estimation are discussed in \ref{sec:discussion}. ."
 We investigate the properties of the LL? anc OLI] lines. as in 7.. with a fitting prescriptionsimilar to ?..," We investigate the properties of the $\beta$ and ] lines, as in \citet{Steinhardt2011a}, , with a fitting prescriptionsimilar to \citet{Shen2008}. ."
 First. the," First, the"
rad m7.,rad $^{-2}$.
 Several spectra to its east contain +50 rad m7 and +100 rad m (spectrum 60)., Several spectra to its east contain $+50$ rad $^{-2}$ and $+100$ rad $^{-2}$ (spectrum 60).
 See for example the patches between lines of sight 60. 82. 75. and 61 at ὁ=+84 rad m.," See for example the patches between lines of sight 60, 82, 75, and 61 at $\phi=+84$ rad $^{-2}$."
 Of course there is to east gradient between ὁ=+18 rad m and ó=+60 rad m. and lower Faraday depths occur throughout the mosaic.," Of course there is to east gradient between $\phi=+18$ rad $^{-2}$ and $\phi=+60$ rad $^{-2}$, and lower Faraday depths occur throughout the mosaic."
" The highest absolute Faraday depths complex Faraday dispersion spectra occur in fields E. G. and H in areas that can not be associated with the cluster. of the “front” (+42 to +48 rad m77). ""lens"" {5+50 rad m). ""doughnut (=+50 rad m). “blob” (+60 rad m7). and “bar? (+78 rad m7) are neither extreme. nor special when compared to the range of Faraday depths observed in this mosaic."," The highest absolute Faraday depths complex Faraday dispersion spectra occur in fields E, G, and H in areas that can not be associated with the of the “front” $+42$ to $+48$ rad $^{-2}$ ), “lens” $\approx +50$ rad $^{-2}$ ), “doughnut” $\approx
+50$ rad $^{-2}$ ), “blob” $+60$ rad $^{-2}$ ), and “bar” $+78$ rad $^{-2}$ ) are neither extreme, nor special when compared to the range of Faraday depths observed in this mosaic."
 distinguish between Galactic polarized emission. and. cluster related polarized emission in this field based solely on the value of the Faraday depth if it is in the range from —48 rad m to +100 rad m7., distinguish between Galactic polarized emission and cluster related polarized emission in this field based solely on the value of the Faraday depth if it is in the range from $-48$ rad $^{-2}$ to $+100$ rad $^{-2}$.
 Figures 4 and 5 show the position angleof the electric field on top of polarized intensity contours.," Figures \ref{brentjens_perseusmosaic_fig:lens-doughnut-zoom}
 and \ref{brentjens_perseusmosaic_fig:patches+84} show the position angleof the electric field on top of polarized intensity contours."
 The position angles have been derotated to 0 wavelength because the Ic uncertainty of the Faraday depth at ὁ>+18 rad m7 was generally worse than 0.5 rad m7.," The position angles have been derotated to 0 wavelength because the $1\sigma$ uncertainty of the Faraday depth at $\phi >
+18$ rad $^{-2}$ was generally worse than 0.5 rad $^{-2}$."
 Instead. the vectors reflect the position angles at A;=0.73275 m7 (350.22 MHz). hence no conclusions can be drawn from the absolute position angles in the images.," Instead, the vectors reflect the position angles at $\lambda_0^2 =
0.73275$ $^{-2}$ (350.22 MHz), hence no conclusions can be drawn from the absolute position angles in the images."
 The images are only used to estimate typical scales at which the position angle changes by a radian or more at 350.22 MHz., The images are only used to estimate typical scales at which the position angle changes by a radian or more at 350.22 MHz.
 The area of the “lens”. “doughnut”. and “blob” is shown in Fig. 4.," The area of the “lens”, “doughnut”, and “blob” is shown in Fig. \ref{brentjens_perseusmosaic_fig:lens-doughnut-zoom}."
 The lens is difficult to recognize due to the lower signal to noise ratio compared to the observations by ?.., The lens is difficult to recognize due to the lower signal to noise ratio compared to the observations by \citet{DeBruynBrentjens2005}.
 angles are fairly uniform in patches of the order of 15’ across. changing abruptly at the borders between these patches.," angles are fairly uniform in patches of the order of $15\arcmin$ across, changing abruptly at the borders between these patches."
" The polarized patches at the same Faraday depth in field D. north of the “lens”. “doughnut”. and ""blob"". are comparable. but are too far away from to be associated with the Perseus cluster."," The polarized patches at the same Faraday depth in field D, north of the “lens”, “doughnut”, and “blob”, are comparable, but are too far away from to be associated with the Perseus cluster."
 The polarized emission in fields G and H at o=+84 rad m7 has fairly uniform polarization angles across each emission patch. (, The polarized emission in fields G and H at $\phi=+84$ rad $^{-2}$ has fairly uniform polarization angles across each emission patch. (
see Fig. 55.,see Fig. \ref{brentjens_perseusmosaic_fig:patches+84}) ).
 The polarization angle structure of a few representative images from the full RM-cube is shown in Figs., The polarization angle structure of a few representative images from the full RM-cube is shown in Figs.
 AS and A6.., \ref{brentjens_perseusmosaic_fig:polangles-1} and \ref{brentjens_perseusmosaic_fig:polangles-2}.
" At ὁ=+6 rad m the position angles are fairly uniform at scales of 30’ to 90""."," At $\phi =
+6$ rad $^{-2}$ the position angles are fairly uniform at scales of $30\arcmin$ to $90\arcmin$."
 At=+30 rad m7 it changes at 20 to 30’ scales., At $\phi =+30$ rad $^{-2}$ it changes at $20\arcmin$ to $30\arcmin$ scales.
 At ó=+42 rad m7 the typical scale is 10’ to 30’. and at higher Faraday depths scales range from 3’ to 20’.," At $\phi=+42$ rad $^{-2}$ the typical scale is $10\arcmin$ to $30\arcmin$, and at higher Faraday depths scales range from $3\arcmin$ to $20\arcmin$."
 These changes can be due to differences 1n intrinsic polarization. changes in Faraday rotation. or a combination of the two effects.," These changes can be due to differences in intrinsic polarization, changes in Faraday rotation, or a combination of the two effects."
" Because of the uncertainty of the precise Faraday depth. it is not possible to discriminate between these possibilities.size at which the polarization angles change decrease with increasing ό]. but not limited to the area and tthe scales at which the polarization angles at 350.22 MHz change in the ""lens"". “doughnut”. “front”. and “blob” are comparable to"," Because of the uncertainty of the precise Faraday depth, it is not possible to discriminate between these possibilities.size at which the polarization angles change decrease with increasing $|\phi|$ , but not limited to the area and the scales at which the polarization angles at 350.22 MHz change in the “lens”, “doughnut”, “front”, and “blob” are comparable to"
The intrinsic polarization of a synchrotron emitting source together with knowledge of propagation effects through intervening media provide critical diagnostics for magnetic field orientation and fluctuations in a wide range of astrophysical contexts.,The intrinsic polarization of a synchrotron emitting source together with knowledge of propagation effects through intervening media provide critical diagnostics for magnetic field orientation and fluctuations in a wide range of astrophysical contexts.
 Faraday rotation is a physical phenomenon where the position angle of linearly polarized radiation propagating through a magneto-ionic medium is rotated as a function of frequency., Faraday rotation is a physical phenomenon where the position angle of linearly polarized radiation propagating through a magneto-ionic medium is rotated as a function of frequency.
" As introduced in ? and ?,, Faraday rotation measure synthesis is an important tool for analysing radio polarization data where multiple emitting regions are present along a single line of sight."," As introduced in \citet{Brentjens:2005p3385} and \citet{Heald:2009p3423}, Faraday rotation measure synthesis is an important tool for analysing radio polarization data where multiple emitting regions are present along a single line of sight."
" Observations of extragalactic sources, which by necessity must be viewed through the Faraday rotating and emitting Galactic interstellar-medium (????), are an obvious example of this regime."," Observations of extragalactic sources, which by necessity must be viewed through the Faraday rotating and emitting Galactic interstellar-medium \citep{de2006radio, brown2009diffuse, schnitzeler2007wsrt, schnitzeler2009wsrt}, are an obvious example of this regime."
" ? introduced the Faraday dispersion function F(9), which describes the intrinsic polarized flux per unit Faraday depth $ (in 2), and its relationship with the complex polarized emission P(A?) as where 4 is the wavelength."," \citet{Burn:1966p3487} introduced the Faraday dispersion function $F(\phi)$, which describes the intrinsic polarized flux per unit Faraday depth $\phi$ (in $^{-2}$ ), and its relationship with the complex polarized emission $P(\lambda^2)$ as where $\lambda$ is the wavelength."
" Note that P can also be written as P=Q+iU, where Q and U represent the emission of Stokes Q and Stokes U, respectively."," Note that $P$ can also be written as $P=Q+\mathrm{i}U$, where $Q$ and $U$ represent the emission of Stokes $Q$ and Stokes $U$, respectively."
" To study multiple emitting and Faraday rotating regions along each line of sight, we need to reconstruct the Faraday dispersion function, which is, in general, a complex-valued function of the Faraday depth $."," To study multiple emitting and Faraday rotating regions along each line of sight, we need to reconstruct the Faraday dispersion function, which is, in general, a complex-valued function of the Faraday depth $\phi$."
" From Eq. (T)),"," From Eq. \ref{e:faradaytransform}) ),"
" we can invert the expression to yield: However, the problem is that we can not observe the polarized emission at wavelengths where A?<0."," we can invert the expression to yield: However, the problem is that we can not observe the polarized emission at wavelengths where $\lambda^2<0$."
" Even for the wavelength range A?> 0, it is impossible to observe all wavelengths or frequencies."," Even for the wavelength range $\lambda^2>0$ , it is impossible to observe all wavelengths or frequencies."
 ? propose a synthesis method by first introducing an observing window function M(4?)., \cite{Brentjens:2005p3385} propose a synthesis method by first introducing an observing window function $M(\lambda^2)$.
" The observed complexpolarized emission can then be described as In this paper, the tilde denotes the observed quantities."," The observed complexpolarized emission can then be described as In this paper, the tilde denotes the observed quantities."
" If the observing window function is M(2) with m channels, the RM spread function (RMSF) is be defined by where the parameter AG is the mean of the sampled values between A7 and 42, within the observation window M22); i is the / channel in the observation window, and K is a normalising constant of the window function M(A?)."," If the observing window function is $M(\lambda^2)$ with $m$ channels, the RM spread function (RMSF) is be defined by where the parameter $\lambda^2_0$ is the mean of the sampled values between $\lambda^2_1$ and $\lambda^2_m$ within the observation window $M(\lambda^2)$; $i$ is the $i^{\rm{th}}$ channel in the observation window, and $K$ is a normalising constant of the window function $M(\lambda^2)$."
" In this paper, we assume as a simplification that all channels have uniform weights for the m channels in the observing window function."," In this paper, we assume as a simplification that all channels have uniform weights for the $m$ channels in the observing window function."
" In ?,, the reconstructed Faraday rotation measure synthesis can be written in discrete form as where F(¢) is the reconstructed Faraday dispersion function."," In \citet{Brentjens:2005p3385}, the reconstructed Faraday rotation measure synthesis can be written in discrete form as where $\widetilde{F}(\phi)$ is the reconstructed Faraday dispersion function."
" From Eq. (5)),"," From Eq. \ref{e:discrete_invfaradaytransform}) ),"
 we can see that the Faraday dispersion function can be reconstructed provided that the spectral coverage is sufficient., we can see that the Faraday dispersion function can be reconstructed provided that the spectral coverage is sufficient.
" However, the reconstructed results generally include some side lobes."," However, the reconstructed results generally include some side lobes."
" Using the terminology of radio interferometry, the result of Brentjens de Bruyn’ method is a dirty version of the Faraday dispersion function and is abbreviated as “the dirty curve""."," Using the terminology of radio interferometry, the result of Brentjens de Bruyn' method is a dirty version of the Faraday dispersion function and is abbreviated as “the dirty curve""."
" It is the convolution of F($) and the RMSF, and a deconvolution step may be used to clean it up."," It is the convolution of $F(\phi)$ and the RMSF, and a deconvolution step may be used to clean it up."
 By borrowing the cleaning procedure in the image deconvolution method of Hóggbom CLEAN (?).., By borrowing the cleaning procedure in the image deconvolution method of Höggbom CLEAN \citep{Hogbom:1974p1206}.
 ? proposes the RM-CLEAN method which deconvolves F(¢) with the RMSF to remove the sidelobe response., \cite{Heald:2009p3423} proposes the RM-CLEAN method which deconvolves $\widetilde{F}(\phi)$ with the RMSF to remove the sidelobe response.
" Recently, ? proposed a wavelet-based Faraday RM synthesis method."," Recently, \cite{Frick:2010p3495} proposed a wavelet-based Faraday RM synthesis method."
" In that approach, the authors assume specific magnetic field symmetries in order to project the observed polarization emissions onto 17<0."," In that approach, the authors assume specific magnetic field symmetries in order to project the observed polarization emissions onto $\lambda^2<0$."
 Compressive sensing/sampling (CS) (???) has been one of the most active areas in signal and image processing over the last few years.," Compressive sensing/sampling (CS) \citep{Candes:2008p14, Candes:2006p23,Wakin:2008p1623} has been one of the most active areas in signal and image processing over the last few years."
" Since CS was proposed, it has attracted very substantial interest, and has been applied in many research areas (?????).."," Since CS was proposed, it has attracted very substantial interest, and has been applied in many research areas\citep{Wakin:2006p1437,Lustig:2007p1719,Puy:2010p1807, Mishali:2009p2147,Bobin:2009p2006}. ."
" In radio astronomy, CS has attracted attention as a tool for image deconvolution."," In radio astronomy, CS has attracted attention as a tool for image deconvolution."
 ? compare the CS-based deconvolution methods with the Hóggbom CLEAN method (?) on simulated uniform random sensing, \citet{Wiaux:2009p2267} compare the CS-based deconvolution methods with the Höggbom CLEAN method \citep{Hogbom:1974p1206} on simulated uniform random sensing
on all davs during the outburst.,on all days during the outburst.
 Phe source and background spectra were extracted. from Standard2 mode cata of the PCA detectors., The source and background spectra were extracted from Standard2 mode data of the PCA detectors.
 The background. spectrum. was simulated using thepeabackes! tool with appropriate background models. provided. by theRANTLE euest observer. facility (GOL)., The background spectrum was simulated using the tool with appropriate background models provided by the guest observer facility (GOF).
 To fit the 3-30 keV energy spectrum of GX 304-1. we first tried a model consisting of an absorbed: power-law with a high energy. cut-olf ancl a Gaussian component for iron Iluorescence line emission for all of these spectra.," To fit the 3-30 keV energy spectrum of GX 304-1, we first tried a model consisting of an absorbed power-law with a high energy cut-off and a Gaussian component for iron fluorescence line emission for all of these spectra."
 This simple model fits the energy. spectrum. over the outburst with a reduced 47 in the range 2.24., This simple model fits the energy spectrum over the outburst with a reduced $\chi^{2}$ in the range $-$ 2.24.
 For some days. ike during the peak of the outburst. the 47. value. is relatively larger.," For some days, like during the peak of the outburst, the $\chi^{2}$ value is relatively larger."
 To get a clearer idea. we performed. pulse johase resolved: spectral. analysis for. two of the relatively ong and bright observations and found that for some phase intervals. this model does not. provide a good Lit. with a large reduced. 47. value of as much as 10.," To get a clearer idea, we performed pulse phase resolved spectral analysis for two of the relatively long and bright observations and found that for some phase intervals, this model does not provide a good fit, with a large reduced $\chi^{2}$ value of as much as 10."
 Phis rellects he complex nature of the energy. dependence of the pulse xofiles shown in Figure 3. and can be due to the presence of two dillerent spectral components prominent at dillerent energies., This reflects the complex nature of the energy dependence of the pulse profiles shown in Figure \ref{fig3} and can be due to the presence of two different spectral components prominent at different energies.
 We find that the 3-30 keV spectrum of GX 304-1 during most of the outburst can be well fitted by a mocel consisting of a partial covering power-law with a high enerey cut-olf ancl an iron fluorescent line emission., We find that the 3-30 keV spectrum of GX 304-1 during most of the outburst can be well fitted by a model consisting of a partial covering power-law with a high energy cut-off and an iron fluorescent line emission.
 With his model. we could also fit the phase resolved spectra with »etter reduced x7 at all the pulse phases.," With this model, we could also fit the phase resolved spectra with better reduced $\chi^{2}$ at all the pulse phases."
 The iron emission ine is found to be quite weak. with equivalent width always ess than 100 eV. Since for such weak emission line. the line xuwameters cannot be measured accurately with the PCA. we have fixed. the line centre energy to G4 keV ancl fixed he line width to 100 eV as the iron emission line is known o be narrow in accretion powered. pulsars.," The iron emission line is found to be quite weak, with equivalent width always less than 100 eV. Since for such weak emission line, the line parameters cannot be measured accurately with the PCA, we have fixed the line centre energy to 6.4 keV and fixed the line width to 100 eV as the iron emission line is known to be narrow in accretion powered pulsars."
 The analytical form of the model describing the 3-30 keV spectrum of GX 304-1 is given by. where. N(E) is the observed. intensity. Way and Nye are the two equivalent hyelrogen column densities. EP is the photon index. & is the photo-electric cross-section. Sj and 5$» corresponds to the respective power-Iaw normalizations. £5. is the cut.olf energy and £i. the οfolding or. in NSPEC notation: wabss(pefabsspoxhighec | One representative spectrum (obtained οἳ 15th August. ALJD 55423) along with the best. fitted mocdel and 10 corresponding residuals are shown in Figure 8..," The analytical form of the model describing the 3-30 keV spectrum of GX 304-1 is given by, where, N(E) is the observed intensity, $N_{H1}$ and $N_{\mathrm H2}$ are the two equivalent hydrogen column densities, $\Gamma$ is the photon index, $\sigma$ is the photo-electric cross-section, $S_{1}$ and $S_{2}$ corresponds to the respective power-law normalizations, $E_{\mathrm c}$ is the cut–off energy and $E_{\mathrm f}$, the e–folding or, in XSPEC $:$ $*$ $*$ $*$ $+$ One representative spectrum (obtained on 15th August, MJD 55423) along with the best fitted model and the corresponding residuals are shown in Figure \ref{peakspec}."
 The source showed a significant spectral. evolution. during the outburst., The source showed a significant spectral evolution during the outburst.
 To illustrate this. ratios of the 3-30 keV. X-ray spectrum obtained. on cilferent cays of observations with 16 spectrum obtained on August 15 are shown in the lef panel of Figure 9..," To illustrate this, ratios of the 3-30 keV X-ray spectrum obtained on different days of observations with the spectrum obtained on August 15 are shown in the left panel of Figure \ref{ratiospec}."
 A softening of the spectrum below abou 18 keV and a hardening above 18 keV is evident during the ecay of the outburst., A softening of the spectrum below about 18 keV and a hardening above 18 keV is evident during the decay of the outburst.
 During most of the outburst. the 3-30 keV spectrum of GX 304-1 can be well fitted with a partia covering power-law model with a high energy. cutoll anc iron Iluorescent line emission.," During most of the outburst, the 3-30 keV spectrum of GX 304-1 can be well fitted with a partial covering power-law model with a high energy cutoff and iron fluorescent line emission."
 For a few of the observations carried: out during the decay of the outburst. the partia covering absorption component is founc to change to single component absorption.," For a few of the observations carried out during the decay of the outburst, the partial covering absorption component is found to change to single component absorption."
 Evolution of the spectra parameters during the outburst is shown in the righ panel of Figure 9.., Evolution of the spectral parameters during the outburst is shown in the right panel of Figure \ref{ratiospec}.
 Phe errors given here are for the 1 σ confidence level determined using the NSPECerror comand., The errors given here are for the 1 $\sigma$ confidence level determined using the XSPEC comand.
 As mentioned in section 3 and shown in Figures 3 and 4. the xulse shape of GX 304-1 changes dramatically with energy.," As mentioned in section 3 and shown in Figures 3 and 4, the pulse shape of GX 304-1 changes dramatically with energy."
 ‘To have a better understanding of how the energy spectrum changes as the highly magnetised pulsar spins. we performed oulse. phase resolved: spectral analysis.," To have a better understanding of how the energy spectrum changes as the highly magnetised pulsar spins, we performed pulse phase resolved spectral analysis."
 X strong energy dependence of the pulse profile is detected till 26th August (NLID 55434)., A strong energy dependence of the pulse profile is detected till 26th August (MJD 55434).
 The pattern of energy. dependence is similar during 13 August to 26th August., The pattern of energy dependence is similar during 13 August to 26th August.
 Not all the observations wave good enough statistics (count rate observation duration) to carry out. pulse phase resolved: spectroscopy., Not all the observations have good enough statistics (count rate $\times$ observation duration) to carry out pulse phase resolved spectroscopy.
 We have selected two long observations for phase resolved spectroscopy. one near the peak of the outburst (15th August) and one in the middle of the decay (24th August).," We have selected two long observations for phase resolved spectroscopy, one near the peak of the outburst (15th August) and one in the middle of the decay (24th August)."
chance wander into the densest part of the core or have the lowest relative velocity with respect to the surrounding gas experience the highest accretion rates.,chance wander into the densest part of the core or have the lowest relative velocity with respect to the surrounding gas experience the highest accretion rates.
 Thev become massive. experience orbit decay. and migrate to the center of the model where they form a cyvuaniucally unstable nultiple system.," They become massive, experience orbit decay, and migrate to the center of the model where they form a dynamically unstable multiple system."
 4) The kinetic energy of the stars and the outflow could have been generated by release ol gravitational binding energy accompanying the formation of a compact binary. most likely radio source I. If source I consists of a pair of 10. M. stars. then to produce the observed kinetic energv of the ejected stars and the outflow. between 2 to 6x10/5 eres. the mean separation of the binary must be between 2.2 and 0.7 AU.," 4) The kinetic energy of the stars and the outflow could have been generated by release of gravitational binding energy accompanying the formation of a compact binary, most likely radio source I. If source I consists of a pair of 10 $_{\odot}$ stars, then to produce the observed kinetic energy of the ejected stars and the outflow, between $2$ to $6 \times 10^{46}$ ergs, the mean separation of the binary must be between 2.2 and 0.7 AU."
" 5) In the proposed scenario. the outflow is driven by (he energy and momentum stored in orbital motion prior to dynamical decay,"," 5) In the proposed scenario, the outflow is driven by the energy and momentum stored in orbital motion prior to dynamical decay."
 Previous studies of gas Lows in multiple-star svstenis show that orbiting material tends to be organized in a hierarchy consisting of tightlv bound circumstellar disks with outer radii less (han about 1/3 of the periastron separation ancl relatively loosely bound. envelopes with inner radii several (mes the apastron separation., Previous studies of gas flows in multiple-star systems show that orbiting material tends to be organized in a hierarchy consisting of tightly bound circumstellar disks with outer radii less than about 1/3 of the periastron separation and relatively loosely bound envelopes with inner radii several times the apastron separation.
 Such a scenario is envisaged {ο to have been present in OMCI prior to the ejection of its Düasslve stars., Such a scenario is envisaged to to have been present in OMC1 prior to the ejection of its massive stars.
 6) Stellar ejection mav contribute to the formation of an explosive outflow bv three mechanisms:envelope: The removal of stellar mass [rom (he center of the envelope would result in the conversion of its orbital motion into linear motion., 6) Stellar ejection may contribute to the formation of an explosive outflow by three mechanisms: The removal of stellar mass from the center of the envelope would result in the conversion of its orbital motion into linear motion.
 The final penetrating encounter that Formed a compact binary would eject the inner parts of pre-existing disks to produce the fastest ejecta., The final penetrating encounter that formed a compact binary would eject the inner parts of pre-existing disks to produce the fastest ejecta.
stress: Magnetic enereyv potentially produced by shear-cyvuamo action in both jrcumstellar disks ancl (he envelope might boost the velocities of the ejecta., Magnetic energy potentially produced by shear-dynamo action in both circumstellar disks and the envelope might boost the velocities of the ejecta.
 In this scenario. 1e fastest ejecta is launched first from deep inside (he gravitational potential of the decaving ‘luster.," In this scenario, the fastest ejecta is launched first from deep inside the gravitational potential of the decaying cluster."
 This material must plow through the slower-moving and later ejected envelope., This material must plow through the slower-moving and later ejected envelope.
 Such mnt(eractions are prone to Ravleigh-Tavlor (vpe instabilities as shown by models of last-winels V.amning into slower. previously ejected winds.," Such interactions are prone to Rayleigh-Taylor type instabilities as shown by models of fast-winds slamming into slower, previously ejected winds."
 Order-o[-magnitude energy. estimates show iw all three mechanisms are. plausible. and that all three may contribute to the energv budget.," Order-of-magnitude energy estimates show that all three mechanisms are plausible, and that all three may contribute to the energy budget."
 7) The ejected high-velocity stars may have accreted new cireiumstellar material as (hey (raversecd the dense OMCL core., 7) The ejected high-velocity stars may have accreted new circumstellar material as they traversed the dense OMC1 core.
 In the presence of oOgradients in the medium. the angulare momentum vectors of accreting gas tend to be orthogonal to the stellar velocity vectors.," In the presence of gradients in the medium, the angular momentum vectors of accreting gas tend to be orthogonal to the stellar velocity vectors."
 Therefore. for stellar motions close to the plane of the sky. disk major axes will be aliened (in projection) with the stellar proper motion vectors. as observed for both radio source I and DN.," Therefore, for stellar motions close to the plane of the sky, disk major axes will be aligned (in projection) with the stellar proper motion vectors, as observed for both radio source I and BN."
 Consequently. any. recent outflow activity produced by the ejected stars will have axes orthogonal to the stellar proper motion vector.," Consequently, any recent outflow activity produced by the ejected stars will have axes orthogonal to the stellar proper motion vector."
 The voungest ejecta [rom radio source, The youngest ejecta from radio source
SED fitting mav not be a sensitive enough. method. to distinguish between the cdillerences introduced by the two approaches. because of the width of the filters and the scarce scumpling of the observed. SEDs. but also because the various characteristics of the torus component can be altered or cliluted by. for example. the presence ofa starburst component.,"SED fitting may not be a sensitive enough method to distinguish between the differences introduced by the two approaches, because of the width of the filters and the scarce sampling of the observed SEDs, but also because the various characteristics of the torus component can be altered or diluted by, for example, the presence of a starburst component."
 Notwithstanding these limitations. SED fitting is still the best tool available for extracting the maximum information [rom large photometric AGN sunples and is now proving to be a powerful technique in relating the dust. properties to the aceretion properties as well as the properties of the larger host galaxy.," Notwithstanding these limitations, SED fitting is still the best tool available for extracting the maximum information from large photometric AGN samples and is now proving to be a powerful technique in relating the dust properties to the accretion properties as well as the properties of the larger host galaxy."
 Decause AGN are of order hundred times less numerous, Because AGN are of order hundred times less numerous
In this work we have presented. the results of high-speed photometric and low resolution spectroscopic observations of the m stars. 998851. and. 1102480.,In this work we have presented the results of high-speed photometric and low resolution spectroscopic observations of the Am stars 98851 and 102480.
 Analyses of the available data show tha 1102480 is pulsating mainly in two frequencies. mmllz and mnmllz corresponding to periods 2.6 hr and 1l. hr.," Analyses of the available data show that 102480 is pulsating mainly in two frequencies, mHz and mHz corresponding to periods 2.6 hr and 1.4 hr."
 Similarly. 998851 is. pulsating mainty with two frequencies mnillz and mamllIz. corresponding to periods 1.34 hr and 2.70 hr.," Similarly, 98851 is pulsating mainly with two frequencies mHz and mHz, corresponding to periods 1.34 hr and 2.70 hr."
 Deside the (wo main frequencies. we can see evidence of one other frequency in the amplitude spectra of both stars.," Beside the two main frequencies, we can see evidence of one other frequency in the amplitude spectra of both stars."
 The effective temperature and logg for the stars are determined to be 700043:250 Ix. 3.5+0.5 ancl 67504250 Why. 3.0d:0.5 for 998851 and 1102480. respectively.," The effective temperature and $\log g$ for the stars are determined to be $7000 \pm 250$ K, $3.5 \pm 0.5$ and $6750 \pm250$ K, $3.0 \pm 0.5$ for 98851 and 102480, respectively."
 The corresponding equivalent hydrogen. line spectral tvpes. are found to be FILLY and E3ILLZINV., The corresponding equivalent hydrogen line spectral types are found to be F1IV and F3III/IV.
 We conclude that 998851. and 1102480. are unusual variables lving near the red edge of the instability strip., We conclude that 98851 and 102480 are unusual variables lying near the red edge of the instability strip.
 Their Am spectral types are securely established: given their luminosities these stars belong to the p Pup group (previously known as ὁ Del) of evolved. Ani stars., Their Am spectral types are securely established; given their luminosities these stars belong to the $\rho$ Pup group (previously known as $\delta$ Del) of evolved Am stars.
 Their unusual nearly. harmonic (or sub-harmonic) period. ratios. unusually high overtones and Am spectral tvpes make these stars especially interesting objects for further observational and theoretical studies.," Their unusual nearly harmonic (or sub-harmonic) period ratios, unusually high overtones and Am spectral types make these stars especially interesting objects for further observational and theoretical studies."
 We are thankful to the referee for constructive suggestions which improved the scientific content of the paper., We are thankful to the referee for constructive suggestions which improved the scientific content of the paper.
" This work was carried out. under the Lncdo-South African Science and Technology Cooperation Programme joint project titled “Nain d""-Cape Survey for roAp stars.” funded by. the Indian and South African governments."," This work was carried out under the Indo-South African Science and Technology Cooperation Programme joint project titled “Naini Tal-Cape Survey for roAp stars,” funded by the Indian and South African governments."
three planets have higher densities that have partly protected them against erosion.,three planets have higher densities that have partly protected them against erosion.
 No significant evaporation is currently underway in Solar System planets. consistent with their location in Figs. ].. 2..," No significant evaporation is currently underway in Solar System planets, consistent with their location in Figs. \ref{masses}, , \ref{agemasses}."
" It is interesting to see that. when life appeared on Earth. the planet was well below the ""erosion line"". so probably suffering little or no erosion."," It is interesting to see that, when life appeared on Earth, the planet was well below the “erosion line”, so probably suffering little or no erosion."
 Even 100 Myr after the Sun was born. the Earth was still below the the erosion line.," Even 100 Myr after the Sun was born, the Earth was still below the the erosion line."
 By contrast. any atmosphere on Mereury. much nearer the Sun (0.47 a.u.).," By contrast, any atmosphere on Mercury, much nearer the Sun (0.47 a.u.),"
 would have been stripped away., would have been stripped away.
 The sample of known exoplanets is by no means complete., The sample of known exoplanets is by no means complete.
 Several selection effects could be present. (/), Several selection effects could be present. )
 With the methods used in exoplanet surveys. it is easier to detect massive planets close to stars.," With the methods used in exoplanet surveys, it is easier to detect massive planets close to stars."
 This should bring more massive planets with high Fx into our sample. thereby yielding a positive relation of Fx with planet mass.," This should bring more massive planets with high $F_{\rm X}$ into our sample, thereby yielding a positive relation of $F_{\rm X}$ with planet mass."
 This bias reinforces our conclusions. since we find the opposite effect: the more massive planets receive a lower Fx. Gi)," This bias reinforces our conclusions, since we find the opposite effect: the more massive planets receive a lower $F_{\rm X}$. )"
 Initial conditions 1n the disk could yield to more massive planets placed at longer distances., Initial conditions in the disk could yield to more massive planets placed at longer distances.
 The current sample of extrasolar planets has a deficit of massive planets at the shortest distances., The current sample of extrasolar planets has a deficit of massive planets at the shortest distances.
 We assume that initial conditions have little impact within this range of distances but we cannot exclude that the observed distribution is an effect of planet formation. (ii), We assume that initial conditions have little impact within this range of distances but we cannot exclude that the observed distribution is an effect of planet formation. )
 X-ray luminous stars are easier to detect 1 X-rays surveys. so we should be biased towards planets with high Fy (very few present m our sample). independent on planet mass.," X-ray luminous stars are easier to detect in X-rays surveys, so we should be biased towards planets with high $F_{\rm X}$ (very few present in our sample), independent on planet mass."
 In the other side. the planet-hunting programs generally discard the active (young) stars.," In the other side, the planet-hunting programs generally discard the active (young) stars."
" Among these stars we would likely find more planets above the ""erosion line"". but the planet would still be under heavy erosion for a young star. in good agreement with our interpretation of the data. (/)"," Among these stars we would likely find more planets above the “erosion line”, but the planet would still be under heavy erosion for a young star, in good agreement with our interpretation of the data. )"
" Finally. most of the planets in the sample have M,sin?<2.5 MMj. with few planets above this mass. that would actually be the most useful objects for confirming our conclusions."," Finally, most of the planets in the sample have $M_{\rm p}
\sin i < 2.5$ $_{\rm J}$, with few planets above this mass, that would actually be the most useful objects for confirming our conclusions."
 Our approach is an alternative to the one followed by LecavelierDesEtangs(2007).. who balances the potential energy of the planet with the EUV flux received from the star. based on a number of assumptions for estimating the present and past EUV flux (with no estimation of the age of each star). and the radius and composition of the planet.," Our approach is an alternative to the one followed by \citet{lec07}, who balances the potential energy of the planet with the EUV flux received from the star, based on a number of assumptions for estimating the present and past EUV flux (with no estimation of the age of each star), and the radius and composition of the planet."
 In particular. the EUV flux is estimated using the flux in the range 110—200 ttypical of each spectral type. and then scaled to the range 100— bbased on the solar pattern. an approach discouraged by the differences seen in the few known EUV spectra in the literature (see.e.g..Sanz-Foreadaetal..2003a).," In particular, the EUV flux is estimated using the flux in the range 110–200 typical of each spectral type, and then scaled to the range 100--1200 based on the solar pattern, an approach discouraged by the differences seen in the few known EUV spectra in the literature \citep[see, e.g.,][]{san03b}."
. LecavelierDesEtangs(2007) extend this caleulation. for individual cases. most notably claiming that Gj 876 b must be dense to have survived the large estimated EUV flux.," \citet{lec07} extend this calculation for individual cases, most notably claiming that Gj 876 b must be dense to have survived the large estimated EUV flux."
 Our real measurements (close to the ROSAT value of logLx.= 26.5) indicate that this planet receives less coronal radiation than others with low density. such as HD 189733 b. Davis&Wheatley(2009) instead balance the potential energy with the X-ray flux that would arrive just during the saturation period of stellar evolution. averaged according to spectral type.," Our real measurements (close to the ROSAT value of $\log L_{\rm X}=26.5$ ) indicate that this planet receives less coronal radiation than others with low density, such as HD 189733 b. \citet{dav09} instead balance the potential energy with the X-ray flux that would arrive just during the saturation period of stellar evolution, averaged according to spectral type."
 This would be a lower limit of the XUV flux. as the EUV band is missing.," This would be a lower limit of the XUV flux, as the EUV band is missing."
" As a result they suggest there is a ""destruction limit below which only dense planets would survive.", As a result they suggest there is a “destruction limit” below which only dense planets would survive.
 The present sample of exoplanets has at least three planets (GJ. 1214 b. GJ 436 b. HAT-P- b) with low densities (p.=1.58. 1.06. and 0.30 gcem. respectively) below this limit.," The present sample of exoplanets has at least three planets (GJ 1214 b, GJ 436 b, HAT-P-12 b) with low densities $\rho=$ 1.58, 1.06, and 0.30 $^{-3}$, respectively) below this limit."
" Among 75 extrasolar planets. only 3 out of 34 high-mass planets of M,sin?>1.5 (one of them still young) have been exposed to the levels of radiation suffered by most of the low-mass planets in the sample."," Among 75 extrasolar planets, only 3 out of 34 high-mass planets of $M_{\rm p} \sin i>1.5$ (one of them still young) have been exposed to the levels of radiation suffered by most of the low-mass planets in the sample."
 We suggest that this ts a consequence of the long-term effects of erosion of gaseous planets by coronal radiation., We suggest that this is a consequence of the long-term effects of erosion of gaseous planets by coronal radiation.
" We propose the existence of an ""erosion line"" that depends on the planet mass for the mass range explored. indicating that erosion. would have stronger effects for more massive planets."," We propose the existence of an “erosion line” that depends on the planet mass for the mass range explored, indicating that erosion would have stronger effects for more massive planets."
 The heterogeneity of our sample makes it difficult to apply the thermal erosion models in the long-term. but these models cannot explain the observed dependence on mass.," The heterogeneity of our sample makes it difficult to apply the thermal erosion models in the long-term, but these models cannot explain the observed dependence on mass."
 More complex models are required that consider the chemical composition that could be very different among planets: different molecules and ionization stages have different responses to XUV radiation., More complex models are required that consider the chemical composition that could be very different among planets: different molecules and ionization stages have different responses to XUV radiation.
 Non-thermal losses should also be considered. against which the presence of a planetary magnetic field might provide protection.," Non-thermal losses should also be considered, against which the presence of a planetary magnetic field might provide protection."
 Planets above the erosion line. such as the young 7 Boo b. would be good candidates to search for current effects of erosion by coronal radiation.," Planets above the erosion line, such as the young $\tau$ Boo b, would be good candidates to search for current effects of erosion by coronal radiation."
 Finally we cannot exclude that the observed distribution is not partly an effect of planetary formation processes that would result in massive planets on wider orbits., Finally we cannot exclude that the observed distribution is not partly an effect of planetary formation processes that would result in massive planets on wider orbits.
" More observations of X-ray emission ofplanets with MM, are needed to confirm our conclusions.", More observations of X-ray emission ofplanets with $M_{\rm p} \sin i \ga 2.5$ $_{\rm J}$ are needed to confirm our conclusions.
of pseudo spectrum coellicients have to be used as input to the likelihood.,of pseudo spectrum coefficients have to be used as input to the likelihood.
 How many multipoles depends on the width A of the Gabor kernel for a given window which is discussed in more detail in The power spectra were estimated in bins defined as where fj is the first multipole in bin 6., How many multipoles depends on the width $\Delta\ell$ of the Gabor kernel for a given window which is discussed in more detail in The power spectra were estimated in bins defined as where $\ell_b$ is the first multipole in bin $b$.
 A similar binning does not work for for the temperature-polarisation cross correlation power spectrum., A similar binning does not work for for the temperature-polarisation cross correlation power spectrum.
 The reason for this is the Schwarz inequality ἐνxVCECE., The reason for this is the Schwarz inequality $C^C_\ell\leq\sqrt{C^T_\ell C^E_\ell}$.
 During likelihood maximisation one must make sure that the estimated. value of --C5. never exceeds yyCAECPOE eq, During likelihood maximisation one must make sure that the estimated value of $C^C_\ell$ never exceeds $\sqrt{C^T_\ell C^E_\ell}$.
sThe way we solved this. problem was to estimate. for CFἑψέFC under the constraint that this value never exceeds 1., The way we solved this problem was to estimate for $C^C_\ell/\sqrt{C^T_\ell C^E_\ell}$ under the constraint that this value never exceeds $1$.
" So the binning is then where as before £jx(mfy,1. As an example we simulated a sky using Vo;=512 resolution in Llealpix (CGórski.Hivonand.Wandelt1998). and a LO’ beam.", So the binning is then where as before $\ell_b\leq\ell<\ell_{b+1}$ As an example we simulated a sky using $N_{side}=512$ resolution in Healpix \cite{healpix} and a $10'$ beam.
 We added non-uniform noise to the map., We added non-uniform noise to the map.
 A reasonable assumption about the size of the noise deviations for polarisation is. to take ojn=20° Yo(Zaldarriaga.&Seljakva.|-1997).., A reasonable assumption about the size of the noise deviations for polarisation is to take $\sigma^P_j=\sqrt{2}\sigma^T_j$ \cite{pol1}.
 Phis wesis what we used in. this. test. but note that the formalism. clo not require anv relation between e and ap.," This is what we used in this test, but note that the formalism do not require any relation between $\sigma_T$ and $\sigma_P$."
 Phe noise level was set so that the signal to noise ration for the temperature power, The noise level was set so that the signal to noise ration for the temperature power
into eight IDL jobs running in parallel+..,into eight IDL jobs running in parallel		.
" Among the 11600 inverted profiles, 925 (c8 of the total number) show invertible linear polarization signals."," 	Among the $11600$ inverted profiles, $925$ $\simeq8$ of the total 	number) show invertible linear polarization signals."
 These profiles have been found mainly in correspondence with patches of strong polarization (see the upper panel in Fig. 5)), 	These profiles have been found 	mainly in correspondence with patches 	of strong polarization (see the upper panel in Fig. \ref{figf}) ).
 Here we present the results obtained from the inversion of Stokes I and V profiles alone., 	Here we present the results obtained from the inversion 	of Stokes $I$ and $V$ profiles alone.
" Full Stokes inversions using modified MISMA models having inclination and azimuth as free parameters have been performed with success (e.g., Fig. 5)),"," 	Full Stokes inversions using modified MISMA models having inclination and azimuth 	as free parameters have been performed with success (e.g., Fig. \ref{figf}) ),"
" but they are less representative from a statistical point of view, and they provide similar results."," 	but they are less representative from a statistical 	point of view, and they provide similar results."
" In fact, magnetic field strengths from few hG to kG fields are measured in fully inverted pixels, with a slightly higher probability for kG fields."," 	In fact, magnetic field strengths 	from few hG to kG fields are measured in fully inverted 	pixels, with a slightly higher probability for kG fields."
 We focus our analysis on the statistical properties of the magnetic field strength and occupation fraction at the photosphere as retrieved by the inversion code (the occupation fraction is just the volume filling factor)., 	We focus our analysis on the statistical properties of the 	magnetic field strength and occupation fraction 	at the photosphere as retrieved by the inversion code 	(the occupation fraction is just the volume filling factor).
" Assuming the model atmospheres to be in lateral pressure balance, each value of total pressure defines the same geometrical height in all model MISMAs."," 	Assuming the model atmospheres to be in lateral pressure 	balance, each value of total pressure defines the same geometrical 	height in all model MISMAs."
" We decided to take as reference height in the atmosphere the one corresponding to the base of the photosphere in typical ID quiet Sun model atmospheres (e.g.,Maltbyetal.1986)."," We decided to take as reference 	height in the atmosphere the one corresponding to the base of the photosphere 	in typical 1D quiet Sun model atmospheres \citep[e.g.,][]{Mal86}."
". The photospheric lower boundary in such models is defined as the height where the continuum optical depth at 500 nm equals one, which corresponds to a pressure of about 1.3x10? dyn cm-?."," 	The photospheric lower boundary in such models 	is defined as the height where the 	continuum optical depth at $500$ nm equals one, which 	corresponds to a pressure of about $1.3\times10^{5}$ dyn $^{-2}$."
" Unless otherwise is mentioned explicitly, all the parameters discussed hereafter refer to this reference height or, equivalently, to this reference total pressure."," 	Unless otherwise is mentioned explicitly, all 	the parameters discussed hereafter refer to this reference height or, equivalently, to this reference total pressure."
 Fig., 	 	Fig.
" 6 shows six maps summarizing the inversion at the reference height, together with the COG magnetogram, used here to show the context."," \ref{fig3} shows six maps summarizing the 	inversion at the reference height, together with the COG magnetogram, used 	here to show the context."
 The red contours on the COG magnetogram separate network and IN regions in the selected subfield., 	The red contours on the COG magnetogram 	separate network and IN regions in the selected subfield.
 Network patches have been identified using an algorithm which takes into account two properties of the IN and network regions. t," 	Network patches have been identified using an algorithm which 	takes into account two properties of the IN and network regions. 	First,"
"he IN covers most of the solar photosphere at any time (morethan9096forHarvey-Angle1993,whichisthefigureweusein calculations).."," the IN covers most of the solar photosphere at any time \citep[more than $90$~\% for ][which is the figure
	we use in the calculations]{Har93}."
" Second, network patches are magnetic concentrations showing a spatial coherence."," Second, 	network patches are magnetic concentrations showing a spatial 	coherence."
 The network must be identified not just asa strongly polarized region; it is expected to be also spatially extended., The network must be identified not just 	as a strongly polarized region; it is expected to be also spatially extended.
 The procedure to define the network works as follows: (1) it automatically finds the threshold on the total polarization that makes the patches of large signal to cover a few percent of the FOV (c4 %))., 	The procedure to define the network works as follows: (1) it automatically finds the 	threshold on the total polarization that makes the patches of large signal to cover 	a few percent of the FOV $\simeq4$ ).
Lastly. we must assign velocity dispersions ancl truncation radii to the haloes of cach of the Alonte Carlo ealaxies.,"Lastly, we must assign velocity dispersions and truncation radii to the haloes of each of the Monte Carlo galaxies."
 To do this. we assume that the galaxies follow a Faber-Jackson or Tullv-Fisher type of relationship and have constant mass-to-light. ratio (see. e.g. BBS).," To do this, we assume that the galaxies follow a Faber-Jackson or Tully-Fisher type of relationship and have constant mass-to-light ratio (see, e.g., BBS)."
 The velocity dispersion. σοι of the halo of a galaxy with luminosity. L. is then given by where a;i is the velocity dispersion of the halo of an L ealaxy.," The velocity dispersion, $\sigma_v$, of the halo of a galaxy with luminosity, $L$, is then given by where $\sigma_v^\ast$ is the velocity dispersion of the halo of an $L^\ast$ galaxy."
 The truncation radius. τε. of the halo of a galaxy with luminosity.£L. is given hy where wy ds the truncation radius of the halo of an L galaxv.," The truncation radius, $x_t$, of the halo of a galaxy with luminosity,$L$, is given by where $x_t^\ast$ is the truncation radius of the halo of an $L^\ast$ galaxy."
 The luminosity of each Monte Carlo galaxy. is obtained from its observed. {ρα apparent magnitude and the redshift. z. that was assigned to the galaxy based on equation (8)) above.," The luminosity of each Monte Carlo galaxy is obtained from its observed $I$ -band apparent magnitude and the redshift, $z$ , that was assigned to the galaxy based on equation \ref{zdist}) ) above."
 Accounting for the Ix-correction. we have where à=flidepyLy (c.g.. BBS).," Accounting for the K-correction, we have where $\alpha = -\frac{d \log_{10} L_\nu}{d \nu}$ (e.g., BBS)."
 For simplicity. we take a=0.42. which is the mean slope of the spectral enerey distribution between the Johnson {παπά and D-band from the Caltech Faint Galaxy Recshilt Survey (Cohen et 11999ab).," For simplicity, we take $\alpha = 0.42$, which is the mean slope of the spectral energy distribution between the Johnson $R$ -band and $B$ -band from the Caltech Faint Galaxy Redshift Survey (Cohen et 1999ab)."
 For cach Monte Carlo simulation then: Each Alonte Carlo. simulation then proceeds by computing the weak lensing shear. 5. that is induced. as light ravs emanating [rom distant galaxies encounter the eravitational potentials of foreground: galaxies.," For each Monte Carlo simulation then: Each Monte Carlo simulation then proceeds by computing the weak lensing shear, $\vec{\gamma}$, that is induced as light rays emanating from distant galaxies encounter the gravitational potentials of foreground galaxies."
 As we will see below. most of the distant galaxies with redshift 2; are lensed. by numerous foreground. galaxies with redshifts 2j€n;," As we will see below, most of the distant galaxies with redshift $z_i$ are lensed by numerous foreground galaxies with redshifts $z_j < z_i$."
" We define the intrinsic (unlensed) shape of cach Iuminous Monte Carlo galaxy to be where eq, in the intrinsic (unlensed) ellipticitv of the galaxy image and Oy is the intrinsic (unlensed). position angle.", We define the intrinsic (unlensed) shape of each luminous Monte Carlo galaxy to be where $\epsilon_{\rm in}$ in the intrinsic (unlensed) ellipticity of the galaxy image and $\phi_{\rm in}$ is the intrinsic (unlensed) position angle.
 Since we are dealing with the weak lensing regime. all lensing events may be considered to be independent. (e.g. Bartelmann Schneider 2001) and the final image shape of cach Iensed ealaxy is given by where 7; is the shear induced by foreground lens galaxy. j. and Ny is the net shear due to all foreground lenses.," Since we are dealing with the weak lensing regime, all lensing events may be considered to be independent (e.g., Bartelmann Schneider 2001) and the final image shape of each lensed galaxy is given by where $\vec{\gamma}_j$ is the shear induced by foreground lens galaxy, $j$, and $\vec{\chi}_{\rm net}$ is the net shear due to all foreground lenses."
" The real (5,1) and imaginary (52) components of the shear are given by equations (4) through (6) above.", The real $\gamma_1$ ) and imaginary $\gamma_2$ ) components of the shear are given by equations (4) through (6) above.
 Computation of the net shear for each of the galaxies due to literallyaff potential foreground: lens galaxies. is extremely time-consuming and. from a practical standpoint. is unnecessary since foreground lenses that induce negligible shear (sav. v;~10°) can be neglected. in comparison to foreground. lenses that. induce substantial shear (sav. T;m 0.005).," Computation of the net shear for each of the galaxies due to literally potential foreground lens galaxies is extremely time-consuming and, from a practical standpoint, is unnecessary since foreground lenses that induce negligible shear (say, $\vec{\gamma}_j \sim 10^{-9}$ ) can be neglected in comparison to foreground lenses that induce substantial shear (say, $\vec{\gamma}_j > 0.005$ )."
" From. Brainerd (2010). we know that source ealaxies with a median redshift ος=0.96 that have been lensecl by a population of foreground galaxies with z;=0.55 experience Little shear due to lenses that are located at projected radii @>60""."," From Brainerd (2010), we know that source galaxies with a median redshift $z_s = 0.96$ that have been lensed by a population of foreground galaxies with $z_l = 0.55$ experience little shear due to lenses that are located at projected radii $\theta > 60''$."
" Scaling to the BPC4O0 galaxies. we lind that for τν100"" the contribution to the net galaxy- lensing shear will be negligible."," Scaling to the BTC40 galaxies, we find that for $\theta > 100''$ the contribution to the net galaxy-galaxy lensing shear will be negligible."
" Hence. in our Monte Carlo simulations we compute the net shear experienced by cach D'T€40 galaxy. due to all foreground. galaxies that are located within a projected radius of 100"". and we do not include any contribution to the net shear from lenses located at projected. radii -100H"," Hence, in our Monte Carlo simulations we compute the net shear experienced by each BTC40 galaxy due to all foreground galaxies that are located within a projected radius of $100''$, and we do not include any contribution to the net shear from lenses located at projected radii $> 100''$."
 In the next section we will analyse the output of our Alonte Carlo simulations in a manner that is similar to the wav in which an observational galaxv-galaxy lensing data set is analvsed., In the next section we will analyse the output of our Monte Carlo simulations in a manner that is similar to the way in which an observational galaxy-galaxy lensing data set is analysed.
 In the case that neither spectroscopic nor photometric redshifts ave available for an observational data set (as is the case for the D'TCAO data). one can make only a crude distinction between “foreground” and “backerouncl” ealaxies using apparent magnitudes.," In the case that neither spectroscopic nor photometric redshifts are available for an observational data set (as is the case for the BTC40 data), one can make only a crude distinction between “foreground” and “background” galaxies using apparent magnitudes."
 From the probability distribution. above. we know that. on average. galaxies with bright apparent magnitudes tend. to be located. at lower redshifts than galaxies with faint apparent magnitudes (though there is certainly a good deal of overlap)," From the probability distribution above, we know that, on average, galaxies with bright apparent magnitudes tend to be located at lower redshifts than galaxies with faint apparent magnitudes (though there is certainly a good deal of overlap)."
" If we consider galaxies with ISxfig20. we find a median redshift of 24,44=0.29 for our DTCO sample."," If we consider galaxies with $18 \le I_{AB} \le 20$, we find a median redshift of $z_{\rm med} = 0.29$ for our BTC40 sample."
 Lowe consider ealaxies with 20</igx22.5. we find a mean redshift of Luaed=0.61 for our BPCALO sample.," If we consider galaxies with $20 < I_{AB} \le 22.5$, we find a mean redshift of $z_{\rm med} = 0.61$ for our BTC40 sample."
" These magnitude cuts therefore vield a rough division of our D'TCHO sample into 38.879 σι foreground (18xLig 20) objects and 225.5]8 ""faint background (20</i1gx 22.5) objects."," These magnitude cuts therefore yield a rough division of our BTC40 sample into 38,879 “bright” foreground $18 \le I_{AB} \le 20$ ) objects and 225,518 “faint” background $20 < I_{AB} \le 22.5$ ) objects."
 The redshiftἱ distributions adopted for these objects are shown Figure 3., The redshift distributions adopted for these objects are shown Figure 3.
" Lt is important to remember that in the Monte Carlo simulations. all galaxies with redshifts 2; have been lense by all other galaxies with redshifts 2;M< that are located within a projected radius 6=100""H of the galaxy at recishift 2."," It is important to remember that in the Monte Carlo simulations, all galaxies with redshifts $z_i$ have been lensed by all other galaxies with redshifts $z_j < z_i$ that are located within a projected radius $\theta = 100''$ of the galaxy at redshift $z_i$ ."
 We illustrate this in Figure 4. where we show an example of a Monte. Carlo simulation.," We illustrate this in Figure 4, where we show an example of a Monte Carlo simulation."
 The image corresponds to a single CCD frame from the 1Ες) survey (0.25 deg 0.25 deg). where the dots indicatethe locations of galaxies," The image corresponds to a single CCD frame from the BTC40 survey (0.25 deg $\times$ 0.25 deg), where the dots indicatethe locations of galaxies"
"and reddening are derived by fitting solar-metallicity Padova isochrones (Girardietal. 2002; Bonatto,Bica&Girardi 2004)) to the CMDs.",and reddening are derived by fitting solar-metallicity Padova isochrones \citealt{Girardi2002}; ; \citealt{TheoretIsoc}) ) to the CMDs.
 The derived fundamental parameters (Table 1)) are similar to those in WEBDA., The derived fundamental parameters (Table \ref{tab1}) ) are similar to those in WEBDA.
" After isolating the probable member stars with the colour-magnitude filters, we use them to build the stellar radial density profile (RDP), which is the projected stellar number density profile around the cluster centre (Fig. 3))."," After isolating the probable member stars with the colour-magnitude filters, we use them to build the stellar radial density profile (RDP), which is the projected stellar number density profile around the cluster centre (Fig. \ref{fig3}) )."
" Note that the cluster centres have been computed by an algorithm that searches for the highest stellar density in the innermost bin and, at the same time, the smoothest RDP (Bonatto&Bica 2010a))."," Note that the cluster centres have been computed by an algorithm that searches for the highest stellar density in the innermost bin and, at the same time, the smoothest RDP \citealt{vdB92}) )."
 Working with colour-magnitude filtered photometry minimises field contamination and enhances the RDP contrast with the fore/background., Working with colour-magnitude filtered photometry minimises field contamination and enhances the RDP contrast with the fore/background.
 The position (and error) of each RDP point along the R axes in Fig., The position (and error) of each RDP point along the $R$ axes in Fig.
 3 corresponds to the average (and 1e uncertainty) distance to the cluster centre of the stars within each bin., \ref{fig3} corresponds to the average (and $1\sigma$ uncertainty) distance to the cluster centre of the stars within each bin.
We,We
The illumiuation of molecular clouds by CRs from supernova remuauts (SNRs) was first suggested by BlackaudFazio(1973):Moutmerle(1979).,"The illumination of molecular clouds by CRs from supernova remnants (SNRs) was first suggested by \cite{black_fazio1973,montmerle1979}."
. Most recently. observatious performed with the Fermi Telescope have revealed high-enerey emission from several regious associated with. a SNB located in close proximity to molecular clouds (MICs).," Most recently, observations performed with the Fermi Telescope have revealed high-energy emission from several regions associated with a SNR located in close proximity to molecular clouds (MCs)."
 Iu particular. emission at 0.2 to 200 GeV has been detected towards the SNRs W21C (Abdoetal.2009).. W28 (Abdoetal.2010a).. ΤΕΙ (Abdoetal. 2010b).. WL9B (Abdoetal.20106) and ICII3 (Abdoetal.2010d)..," In particular, emission at 0.2 to 200 GeV has been detected towards the SNRs W51C \citep{abdo_w51c}, , W28 \citep{abdo_w28}, W44 \citep{abdo_w44}, , W49B \citep{abdo_w49b} and IC443 \citep{adbo_ic443}."
 SNRs are oue of the primary cauclicates [or CR acceleration. as discussed [or example by (2009).," SNRs are one of the primary candidates for CR acceleration, as discussed for example by \cite{biermann_prl2009}."
. The observed gamma-ray signatures could therefore be interpreted as m?—decay products from high-energy CR interactions with the MC., The observed gamma-ray signatures could therefore be interpreted as $\pi^{0}-$ decay products from high-energy CR interactions with the MC.
" The data for these particular objects actually seem. to favor a hacrouic scenario over a leptouic one. see cltepabcdo,LL"," The data for these particular objects actually seem to favor a hadronic scenario over a leptonic one, see \\citep{abdo_w44}."
 Duelotheambignilyofthesignal. however. οἱΕΙ ασεσος Rsareneededtohaved finalproe f.," Due to the ambiguity of the signal, however, other tracers of CRs are needed to have a final proof."
 Iu this paper. we quantify a new method to identify SNRs as CR sources. based ou CI-induced ionization.," In this paper, we quantify a new method to identify SNRs as CR sources, based on CR-induced ionization."
 When CRs are accelerated ina SNR aud then iujected iuto a nearby MC. the ionization rate in the ambient gas is expected to be enhanced compared with the iouization caused by the eeneral background of Galactic CRs.," When CRs are accelerated in a SNR and then injected into a nearby MC, the ionization rate in the ambient gas is expected to be enhanced compared with the ionization caused by the general background of Galactic CRs."
" The imunediate products are hydrogen ious. αμά H,. which react rapidly with Ha» and oxygen to form molecular ions."," The immediate products are hydrogen ions, $^+$ and $_2^+$ , which react rapidly with $_2$ and oxygen to form molecular ions."
" lous like H,. . ΠΟ . and H3O ας spectroscopically observable at infrared aud submin wavelengths and their abundauces are predictable as functions of the lonizatiou rate citepblack1908.:montmerle2000))."," Ions like $_3^+$, $^+$, $_2$ $^+$, and $_3$ $^+$ are spectroscopically observable at infrared and submm wavelengths and their abundances are predictable as functions of the ionization rate \\citep{black1998,montmerle2009}) )."
 Among the 15 molecular catious now identified iu the interstellar mediun. it is the reactive ious H4. . and HeO that are expected to be the most specific tracers of the CR ionization rate (Black1998.2007).. aud it was only curing the last year that the latter two species have been detected (Benzetal.2010:Bruderer 2010)..," Among the 18 molecular cations now identified in the interstellar medium, it is the reactive ions $_3^+$, $^+$, and $_2$ $^+$ that are expected to be the most specific tracers of the CR ionization rate \citep{black1998,black2007}, and it was only during the last year that the latter two species have been detected \citep{Benz2010_hyd_ion,
Bruderer2010_hyd2591,Gerin2010_Oions,Gupta2010OHp_Orion,Krelowski2010,
Neufeld2010_OHp,Ossenkopf2010H2Op,Schilke2010_H2Op_oprat,
Wyrowski2010_H2Op}."
 Analysis of anc H»O absorption it liffuse interstellar gas of low molecular fraction (H2/H. <10% )) serves to calibrate the background ionizing frequency of interstellar hydrogen at a level Qj=(0.6—2.1)-10.16 ! per atom (Cerinetal. 2010a.b)..," Analysis of $^+$ and $_2$ $^+$ absorption in diffuse interstellar gas of low molecular fraction $_2$ /H $<10$ ) serves to calibrate the background ionizing frequency of interstellar hydrogen at a level $\zeta_{\rm Gal} = (0.6 - 2.4) \cdot 10^{-16}$ $^{-1}$ per atom \citep{Gerin2010_Oions,Neufeld2010_OHp,black_ionization_rate}."
 Here. we estimate the eubauced interstellar ionization rates expected from the observed fluxes ol high-euergy gamma rays toward SNRs aud predict the abuudauces of reactive molecular ions to be expected. in associated MCs.," Here, we estimate the enhanced interstellar ionization rates expected from the observed fluxes of high-energy gamma rays toward SNRs and predict the abundances of reactive molecular ions to be expected in associated MCs."
 We show how correlations between GeV-TeV emission and vibrational and rotational spectra of molecular ious could be used to identify the sites of CR acceleration., We show how correlations between GeV-TeV emission and vibrational and rotational spectra of molecular ions could be used to identify the sites of CR acceleration.
 Observational tests will be possible through astronomical spectroscopy at infrared and mm/subimm wavelengths., Observational tests will be possible through astronomical spectroscopy at infrared and mm/submm wavelengths.
 CRs of kineticenergies between Ey~1 MeV aud ~1 GeV ionize the interstellar meditun. while those at lower enerey hardly escape their sources.," CRs of kineticenergies between $E_p\sim 1$ MeV and $\sim 1$ GeV ionize the interstellar medium, while those at lower energy hardly escape their sources."
 Weinvestigate five SNRslocated in or close to MCs. which are detected in ganumna-rays.," Weinvestigate five SNRslocated in or close to MCs, which are detected in gamma-rays."
The consequence of a dead-zone on planet migration was studied by Matsumura et al. (,The consequence of a dead-zone on planet migration was studied by Matsumura et al. (
2003).,2003).
 These authors found that a dead-zone significantly slows down the nigration of low-mass planets undergoing Type [ migration., These authors found that a dead-zone significantly slows down the migration of low-mass planets undergoing Type I migration.
" ThisT. arises, because the dead-zone creates a jump in surface density. which changed the balance between inner and outer Lindblad torques in their model."," This arises because the dead-zone creates a jump in surface density, which changed the balance between inner and outer Lindblad torques in their model."
 A surface density transition. however. can also create a planet trap where the corotation torque exerted on the protoplanet equals the differential Lindblad torque (Masset et al.," A surface density transition, however, can also create a planet trap where the corotation torque exerted on the protoplanet equals the differential Lindblad torque (Masset et al."
 2006)., 2006).
 Concerning gap-opening giant planets which migrate o1 a viscous timescale. Matsumura et al. (," Concerning gap-opening giant planets which migrate on a viscous timescale, Matsumura et al. ("
2003) found. unsurprisingly. that a dead-zone slows down Type II migration due to the low value for the viscosity there.,"2003) found, unsurprisingly, that a dead-zone slows down Type II migration due to the low value for the viscosity there."
 However. it should be noted that this work did not consider how the existence of a live-zone near the disk surface affects this latter result.," However, it should be noted that this work did not consider how the existence of a live-zone near the disk surface affects this latter result."
 In this paper. we present the results of 3D hydrodynamical simulations of giant-planets embedded in layered protoplanetary disks and in which the dead-zone is modelled using a vertical. profile for the laminar viscosity which increases as a function of height in the disk.," In this paper, we present the results of 3D hydrodynamical simulations of giant-planets embedded in layered protoplanetary disks and in which the dead-zone is modelled using a vertical profile for the laminar viscosity which increases as a function of height in the disk."
 The aim of this work ts to investigate how the evolution depends on the size of the dead-zone Hpz. subject to the condition that all our disk models have the same vertically integrated viscous stress and associated radial mass flux.," The aim of this work is to investigate how the evolution depends on the size of the dead-zone $\hdz$, subject to the condition that all our disk models have the same vertically integrated viscous stress and associated radial mass flux."
" To address this issue. we consider a model in which a 30M protoplanet is embedded in the disk on a fixed circular orbit. and can slowly accrete gas until its mass 71, becomes the same as that of Saturn (n,=| Ms) or Jupiter Gv,=1 Mj)."," To address this issue, we consider a model in which a $30\;M_\oplus$ protoplanet is embedded in the disk on a fixed circular orbit, and can slowly accrete gas until its mass $m_p$ becomes the same as that of Saturn $m_p=1$ $_S$ ) or Jupiter $m_p=1$ $_J$ )."
 The planet is then released and allowed to evolve under the action of disk forces., The planet is then released and allowed to evolve under the action of disk forces.
 The results of these simulations suggest that for a given accretion rate through the disk. Jupiter migrates more slowly as the size of the dead-zone increases.," The results of these simulations suggest that for a given accretion rate through the disk, Jupiter migrates more slowly as the size of the dead-zone increases."
 However. we find that provided the size of the dead-zone is small enough. both the accretion rate onto the planet and the migration of Saturn-mass planets depend only weakly on Hy.," However, we find that provided the size of the dead-zone is small enough, both the accretion rate onto the planet and the migration of Saturn-mass planets depend only weakly on $\hdz$."
 This paper is organized as follows., 	 This paper is organized as follows.
 In Sect., In Sect.
 2. we describe the hydrodynamical model and the numerical setup.," 2, we describe the hydrodynamical model and the numerical setup."
 In Sect., In Sect.
 3. we present the results of our simulations.," 3, we present the results of our simulations."
 We finally summarize and draw our conclusions in Sect., We finally summarize and draw our conclusions in Sect.
 4., 4.
 In order to study the evolution of a giant planet in a dead- which ts represented in the simulations as a disk region where the viscosity. profile depends on the distance from the equatorial plane. we adopt a 3-dimensional disk model.," 	 In order to study the evolution of a giant planet in a dead-zone, which is represented in the simulations as a disk region where the viscosity profile depends on the distance from the equatorial plane, we adopt a 3-dimensional disk model."
 In spherical coordinates (7.8.) and in a frame centred on the central star. the continuity equation reads: where p is the disk density.," In spherical coordinates $(r,\theta,\phi)$ and in a frame centred on the central star, the continuity equation reads: where $\rho$ is the disk density."
 The equations for the radial. meridional. and angular components of the disk velocity are given. respectively. by: — In the above equations. p is the pressure. fj. fy and fy are respectively the radial. meridional and azimuthal components of the viscous force per unit volume.," The equations for the radial, meridional, and angular components of the disk velocity ${\bf v}=(v_r,v_\theta,v_\phi)$ are given, respectively, by: and In the above equations, $p$ is the pressure, $f_r$, $f_\theta$ and $f_\phi$ are respectively the radial, meridional and azimuthal components of the viscous force per unit volume."
 Expressions for f. fj and f» can be found for example in Klahr et al.(1999).," Expressions for $f_r$, $f_\theta$ and $f_\phi$ can be found for example in Klahr et al.(1999)."
" @ is the gravitational potential and can be written as: where M, and ji, are the masses of the star and planet. respectively. and where e is a softening length."," $\Phi$ is the gravitational potential and can be written as: where $M_\star$ and $m_p$ are the masses of the star and planet, respectively, and where $\epsilon$ is a softening length."
" 0;,; 1s an indirect term arising from the fact that the star-centered frame is not inertial.", $\Phi_{ind}$ is an indirect term arising from the fact that the star-centered frame is not inertial.
 This term reads: where the integral is performed over the volume of the disk., This term reads: where the integral is performed over the volume of the disk.
 In this work the planet can experience the gravitational acceleration arising from both the disk and the central star., In this work the planet can experience the gravitational acceleration arising from both the disk and the central star.
 Therefore. the equation of motion for the planet is given by: where fap is the force due to the disk which is defined by: Note that we exclude the material contained in the planet Hill sphere when calculating the gravitational force acting on the planet.," Therefore, the equation of motion for the planet is given by: where ${\bf f_{dp}}$ is the force due to the disk which is defined by: Note that we exclude the material contained in the planet Hill sphere when calculating the gravitational force acting on the planet."
 Moreover. in the simulations presented here. the smoothing length € is set to the diagonal length of one grid cell.," Moreover, in the simulations presented here, the smoothing length $\epsilon$ is set to the diagonal length of one grid cell."
Despite the uncertaiufies iu our imeasurenments. jt appears that the standard models uM Reseonly3 excess of the values observed ii our jects.,"Despite the uncertainties in our measurements, it appears that the standard models produce in excess of the values observed in our objects."
 The exception is for the two lowest mass stars ((0.9 and 1.0 AL.) computed by WC which agree with the ratios measured iu MA-17 and NGC 6781., The only exception is for the two lowest mass stars (0.9 and 1.0 $M_\odot$ ) computed by HG which agree with the ratios measured in M1-17 and NGC 6781.
 Although Fig., Although Fig.
 3 iucicates a marked discrepancy between observed and theoretical values. one should be aware of the scusitivity of the predicted vields ou the model assumptions.," 3 indicates a marked discrepancy between observed and theoretical values, one should be aware of the sensitivity of the predicted yields on the model assumptions."
 Iu particular. the isotopic ratios (not only jJ) depeud rather strouglv on the adopted mass loss rate during the AGB ase. ou the thi dredee-up effcieucy. and on stellar mctallicity.," In particular, the isotopic ratios (not only ) depend rather strongly on the adopted mass loss rate during the AGB phase, on the third dredge-up efficiency, and on stellar metallicity."
 Their combined effects have been thoroughly discussed by FC and WC aud need not to be repeated rere., Their combined effects have been thoroughly discussed by FC and HG and need not to be repeated here.
 Iu Senera. a shorter phase of nass loss audor lower mass loss rateμα tend to decrease the surface. iratio.," In general, a shorter phase of mass loss and/or lower mass loss rates tend to decrease the surface ratio."
 However. a more effücient convective penetratio- results ina higher pollution ofthe envelope from pulse te pulse and a higher‘ ratio.," However, a more efficient convective penetration results in a higher pollution of the envelope from pulse to pulse and a higher ratio."
 Finally. stars with initial metallicities lower tha- solar vield higher ratios.," Finally, stars with initial metallicities lower than solar yield higher ratios."
 BRotunimg to Fig., Returning to Fig.
 3. we see that several PNe lie in the region of the diagram with low and low lius.," 3, we see that several PNe lie in the region of the diagram with low and low mass."
 For these objects we should expect the standard models to become inaccurate insofar as they neelect the possible occurrence of mixing niechanisnis of non-convective origin which can alter the composition of the stellar ejecta., For these objects we should expect the standard models to become inaccurate insofar as they neglect the possible occurrence of mixing mechanisms of non-convective origin which can alter the composition of the stellar ejecta.
 Low values of the carbon isotopic ratio have also been measured in field population II stays aud iu elobular cluster eiaut (0.8. Sneden et al., Low values of the carbon isotopic ratio have also been measured in field population II stars and in globular cluster giant (e.g. Sneden et al.
 1956: Cülrov Brown 1991: Pilachowski et al., 1986; Gilroy Brown 1991; Pilachowski et al.
 1997) iux have provided the inofivation to introduce extra-cmnixius; processes du the standard evolution (e.g. Charbounel 1995)., 1997) and have provided the motivation to introduce extra-mixing processes in the standard evolution (e.g. Charbonnel 1995).
 Receutly. Charbounel do Nascimento (1998) fiud that more than of a sample of |91 field aud cluster rec ejauts presents carbon isotopic ratios incousisteut with those predicted by standard uucleosvuthliesis.," Recently, Charbonnel do Nascimento (1998) find that more than of a sample of 191 field and cluster red giants presents carbon isotopic ratios inconsistent with those predicted by standard nucleosynthesis."
 The observational situation in ACB stars is less clear. because of the extreme sensitivity of the determination of isotopic ratios on excitation temperatures and modcl atinospheres.," The observational situation in AGB stars is less clear, because of the extreme sensitivity of the determination of isotopic ratios on excitation temperatures and model atmospheres."
 For example. Greaves Tolland↽↼(1997) have measured a ratio. varvius. between 12 aud36 ina xanuple of 9 carbon stars with high unass-loss rates (~107 MD; 4). in accordance with simular results previously obtained by Wanner Sahai (1987) on seven other carbon stars.," For example, Greaves Holland (1997) have measured a ratio varying between 12 and 36 in a sample of 9 carbon stars with high mass-loss rates $\sim 10^{-5}$ $_{\sun}$ $^{-1}$ ), in accordance with similar results previously obtained by Wannier Sahai (1987) on seven other carbon stars."
 Ou the other hid. Lainbert ct al. (," On the other hand, Lambert et al. ("
1986) 11easured the rratio in 30 cool carbon stars and found values hetween 30 and τίV.,1986) measured the ratio in 30 cool carbon stars and found values between 30 and 70.
" More recently, Ohnalka Tsuji (1996) 1report ratios between 20 and 30 for 21 N-type carbon stars in common with the sample of Lambert et al. ("," More recently, Ohnaka Tsuji (1996) report ratios between 20 and 30 for 24 N-type carbon stars in common with the sample of Lambert et al. ("
1986).,1986).
 These values are about a facor of 2 smaller than those derived by Lambert et al. (, These values are about a factor of 2 smaller than those derived by Lambert et al. (
see however the discussion iu de Lavery Gustafsson 1998 aud Olnaka Tsuji 1995). but are consistent with those ound for our PN sample.,"see however the discussion in de Laverny Gustafsson 1998 and Ohnaka Tsuji 1998), but are consistent with those found for our PN sample."
 If these samples are representative of the population of both carbon stars and PNe. the low ratios provide ↴∖↴⊓⋅∪∐∶↴∙⊾↕∐≼∐↸⊳⋜↧↑↕∪∐ that ∐↓∪↴∖↴↑↴∖↴↑⋜∐⋅↴∖↴ should experience ⋅⋅ ⋅≽ ⋅ ↴∖↴∪⋯↸∖↸∖⊼⊓⋅⋜⊢∐∐⊼↕∐∶↴∙⊾⋜⋯≼↧≼∐∖↻↕↸∖↑↸∖∟≼⊲↖↖⇁↕↑∐↥⋅↸∖↴∖↴⋉∖↸⊳↑↑∪↓⊽⋟≼⊲∙ According to this conjecture. it appears that in order to match the observations.," If these samples are representative of the population of both carbon stars and PNe, the low ratios provide strong indication that most stars should experience some extra-mixing and deplete $^{12}$ C with respect to $^{13}$ C. According to this conjecture, it appears that in order to match the observations,."
" Theoretical models predict that stars with low values of should also have low ""He abundances.", Theoretical models predict that stars with low values of should also have low $^3$ He abundances.
 Iu (ΤΙ. we estimated that to obtain consistency between 1ο observed Pe abuudances aud chemical evolution nodels. the majority of the Calactic PNe (70% )) should lave a ratio well below the standard value.," In GSTP, we estimated that to obtain consistency between the observed $^3$ He abundances and chemical evolution models, the majority of the Galactic PNe $>$ ) should have a ratio well below the standard value."
 In js section we test this sueecstion using the coustrait xovidedby πο observations in PNe., In this section we test this suggestion using the constraint provided by the observations in PNe.
 Chenucal evolution models offer je adequate tool to follow simmultancously the evolution of aud Πο over the Galactic lifetime., Chemical evolution models offer the adequate tool to follow simultaneously the evolution of and $^3$ He over the Galactic lifetime.
We generate over 1 million GES-ISCCDP data pairs of every initialization. forecast time point and cloud tvpe for the entire time period of interest.,"We generate over 1 million GFS-ISCCP data pairs of every initialization, forecast time point and cloud type for the entire time period of interest."
 To get a more objective evaluation of the model forecast skill for total cloud cover. we compose three additional models that are to be compared with the ISCCP. data: Limiting bv computational resource. we randomly choose July 2006 for such comparisons.," To get a more objective evaluation of the model forecast skill for total cloud cover, we compose three additional models that are to be compared with the ISCCP data: Limiting by computational resource, we randomly choose July 2006 for such comparisons."
 We will show that monthly variation of lorecast error is not significant in the period of study. so (he July 2006 result is representative.," We will show that monthly variation of forecast error is not significant in the period of study, so the July 2006 result is representative."
 We use a different evaluation scheme lor convective cloud., We use a different evaluation scheme for convective cloud.
 Although we are dealing with the term “convective cloucl cover” or “fractional convective cloud”. there is virtually no scientific/observational meaning in this term.," Although we are dealing with the term “convective cloud cover” or “fractional convective cloud”, there is virtually no scientific/observational meaning in this term."
 It is due to the small scales of most convective clouds comparing wilh the spatial resolution of global model or satellite camera (which are mostly at tens of kilometers). so such cloud can only be represented in fractional numbers in model outputs or observations.," It is due to the small scales of most convective clouds comparing with the spatial resolution of global model or satellite camera (which are mostly at tens of kilometers), so such cloud can only be represented in fractional numbers in model outputs or observations."
 Therefore. in addition to fractional comparisons. we also binary degenerate the modeling and observational data. so binary statistical indicators can be used {ο assess the forecast skill (see 823.4.2).," Therefore, in addition to fractional comparisons, we also binary degenerate the modeling and observational data, so binary statistical indicators can be used to assess the forecast skill (see 3.4.2)."
 Figure 1. shows the 3-vear mean of forecast minus observation (abbreviated as fe—obs below) of total cloud cover forecast al 7=3h at 12Z initialization: we notice that the, Figure \ref{fig1} shows the 3-year mean of forecast minus observation (abbreviated as $fc-obs$ below) of total cloud cover forecast at $\tau=3h$ at 12Z initialization; we notice that the
measuring the distance from the centre where the cluster RDP and residual background are statistically indistinguishable.,measuring the distance from the centre where the cluster RDP and residual background are statistically indistinguishable.
" In this sense, ccan be considered as an observational truncation radius, whose value depends both on the radial distribution of member stars and the field density."," In this sense, can be considered as an observational truncation radius, whose value depends both on the radial distribution of member stars and the field density."
" The above RDPs are fitted with the function o(R)=+σο/(1(R/ R;)?), where σο and o, are the central and residual background stellar densities, and iis the core radius."," The above RDPs are fitted with the function $\sigma(R)=\sigma_{bg}+\sigma_0/(1+(R/R_c)^2)$ , where $\sigma_0$ and $\sigma_{bg}$ are the central and residual background stellar densities, and is the core radius."
" When applied to star counts, this function is similar to that used by King(1962) to the surface-brightness profiles in the central parts of globular clusters."," When applied to star counts, this function is similar to that used by \cite{King1962} to the surface-brightness profiles in the central parts of globular clusters."
" Degrees of freedom are minimised by allowing only co and tto vary in the fits, while oy, is previously measured in the surrounding field and kept fixed."," Degrees of freedom are minimised by allowing only $\sigma_0$ and to vary in the fits, while $\sigma_{bg}$ is previously measured in the surrounding field and kept fixed."
" The best-fit solutions are shown in Fig. 7,,"," The best-fit solutions are shown in Fig. \ref{fig7}, ,"
 and the corresponding structural parameters are given in Table 2.., and the corresponding structural parameters are given in Table \ref{tab2}.
" Within uncertainties, the adopted King-like function provides a reasonable description along the full radial range of the RDPs for most of the sample (Fig. 7))."," Within uncertainties, the adopted King-like function provides a reasonable description along the full radial range of the RDPs for most of the sample (Fig. \ref{fig7}) )."
" The exceptions are 227, Ru441, and 1174, which present a pronounced cusp (density excess over the King-like fit) in the innermost RDP bin."," The exceptions are 27, 41, and 174, which present a pronounced cusp (density excess over the King-like fit) in the innermost RDP bin."
" The same appears to apply to Ru223 and Ru663, although only at the lo level."," The same appears to apply to 23 and 63, although only at the $1\sigma$ level."
 This feature has been attributed to a post-core collapse structure in some globular clusters (e.g. 1995))., This feature has been attributed to a post-core collapse structure in some globular clusters (e.g. ).
" However, such a dynamical evolution-related feature has also been detected in the RDP of some Gyr-old OCs, e.g. 33960 (Bonatto&Bica2006)) and 110 (Bonatto&2009a))."," However, such a dynamical evolution-related feature has also been detected in the RDP of some Gyr-old OCs, e.g. 3960 \citealt{N3960}) ) and 10 \citealt{LKstuff}) )."
" Alternatively, clusters that form dynamically cool and with significant substructure will probably develop an irregular central region, unless such a region collapses and smooths-out the initial substructure (Allisonetal.2009))."," Alternatively, clusters that form dynamically cool and with significant substructure will probably develop an irregular central region, unless such a region collapses and smooths-out the initial substructure \citealt{Allison09}))."
 Compared to the distribution of core radii derived for a sample of relatively nearby OCs by Piskunov - their Fig., Compared to the distribution of core radii derived for a sample of relatively nearby OCs by \citet{Piskunov07} - their Fig.
" 3, the present clusters occupy the tail."," 3, the present clusters occupy the tail."
" However, we find significant differences, especially inR.,, for the 3 clusters in common with (2005)."," However, we find significant differences, especially in, for the 3 clusters in common with \citet{Kharch05}."
". While they find angular values of aabout twice those we derive, their angular values of aare ©5 (Ru227) and z15 (Rull and Ru226) times larger."," While they find angular values of about twice those we derive, their angular values of are $\approx5$ 27) and $\approx15$ 1 and 26) times larger."
" This, in turn, would imply core radii of the order of ~2.5 ppc to ~4.0 ppc, bigger than most of the Galactic globular clusters (see, e.g. Fig."," This, in turn, would imply core radii of the order of $\sim2.5$ pc to $\sim4.0$ pc, bigger than most of the Galactic globular clusters (see, e.g. Fig."
 8 of Bonatto&Bica2008b))., 8 of \citealt{Struc11GCs}) ).
 These discrepancies probably arise from the fact that they do not field-decontaminate their photometry., These discrepancies probably arise from the fact that they do not field-decontaminate their photometry.
" Because of the low-contrast RDPs that result when field stars are not eliminated, structural radii derived from RDP fits may not be robust."," Because of the low-contrast RDPs that result when field stars are not eliminated, structural radii derived from RDP fits may not be robust."
" Finally, according to Bonatto&Bica(2008a), the depth-limited 2MASS photometry has only a small effect on the core radius determination (by means of the King-like fit), but may be somewhat more important forRrpp,, especially in 337, for which stars fainter than the sequence turnoff (MSTO) are not detected."," Finally, according to \citet{StrucPar}, the depth-limited 2MASS photometry has only a small effect on the core radius determination (by means of the King-like fit), but may be somewhat more important for, especially in 37, for which stars fainter than the main-sequence turnoff (MSTO) are not detected."
 In the previous sections we derived a set of fundamental and structural parameters for a sample of 15 overlooked Ruprecht clusters., In the previous sections we derived a set of fundamental and structural parameters for a sample of 15 overlooked Ruprecht clusters.
" Now we use these parameters for comparison with the previously analysed Ruprecht clusters listed in WEBDA, as well as to investigate relations among parameters."," Now we use these parameters for comparison with the previously analysed Ruprecht clusters listed in WEBDA, as well as to investigate relations among parameters."
" WEBDA contains 171 such clusters with coordinates, but only 79 have age, reddening and distance from the Sun been determined so far."," WEBDA contains 171 such clusters with coordinates, but only 79 have age, reddening and distance from the Sun been determined so far."
 The 6 and b distribution of the Ruprecht clusters in WEBDA is shown in Fig. 8., The $\ell$ and $b$ distribution of the Ruprecht clusters in WEBDA is shown in Fig. \ref{fig8}.
" By far, most of them are located in the 3""? and 4*” quadrants, and within |b| 8?."," By far, most of them are located in the $3^{rd}$ and $4^{th}$ quadrants, and within $|b|\la8\degr$."
 Our sample shares the same b distribution but is restricted essentially to the 3/4 quadrant., Our sample shares the same $b$ distribution but is restricted essentially to the $3^{rd}$ quadrant.
" With respect to the age and reddening distributions, our sample basically maps those of the WEBDA clusters."," With respect to the age and reddening distributions, our sample basically maps those of the WEBDA clusters."
" However, our sample is biased towards larger values ofthe distance from the Sun, which is consistent with the fact that they still haven't been studiedin detail."," However, our sample is biased towards larger values ofthe distance from the Sun, which is consistent with the fact that they still haven't been studiedin detail."
" The positions of the sample clusters, projected onto the Galactic plane, are shown in Fig. 9,,"," The positions of the sample clusters, projected onto the Galactic plane, are shown in Fig. \ref{fig9}, ,"
 which contains the, which contains the
rrotation does not affect the upper and lower bounds on ο.,rotation does not affect the upper and lower bounds on $E_{\rm p}/E$.
 Having derived some stability criteria for a mixed. toroidal field. it remains to see what this means for the stability of a global magnetic field. configuration.," Having derived some stability criteria for a mixed poloidal-toroidal field, it remains to see what this means for the stability of a global magnetic field configuration."
 Clearly. a globally stable configuration needs to be locally stable against the Tayler instability at each point in the star. as well as being stable in the neighbourhood of the neutral line.," Clearly, a globally stable configuration needs to be locally stable against the Tayler instability at each point in the star, as well as being stable in the neighbourhood of the neutral line."
 There are two obvious ways to proceed., There are two obvious ways to proceed.
 The first is to find a global configuration and then check that a local analysis predicts stability at every location in the star for both types of instability., The first is to find a global configuration and then check that a local analysis predicts stability at every location in the star for both types of instability.
 The second way is to construct a global configuration and then numerically follow its evolution in time., The second way is to construct a global configuration and then numerically follow its evolution in time.
 The basis for constructing axisymmetric field contigurations whose stability we can probe will be the result of numerical simulations similar to those performed in Paper I. to where the reader is referred for a fuller account of the setup of the model: a brief outline is given here.," The basis for constructing axisymmetric field configurations whose stability we can probe will be the result of numerical simulations similar to those performed in Paper I, to where the reader is referred for a fuller account of the setup of the model; a brief outline is given here."
 The code used is the (Nordlund&Galsgaard 1995.. Gudiksen&Nordlund 20053). a high-order finite-difference Cartesian MHD code which uses a “hyper-diffusion” scheme. a system whereby diffusivities are scaled with the length scales present so that badly resolved structure near the Nyquist spatial frequency is damped whilst preserving well-resolved structure on longer length scales.," The code used is the \citealt{NorandGal:1995}, \citealt{GudandNor:2005}) ), a high-order finite-difference Cartesian MHD code which uses a `hyper-diffusion' scheme, a system whereby diffusivities are scaled with the length scales present so that badly resolved structure near the Nyquist spatial frequency is damped whilst preserving well-resolved structure on longer length scales."
 This. and the high-order spatial interpolation and derivatives (sixth order) and time-stepping (third order) increase efficiency by giving a low effective diffusivity at modest resolution (128° here).," This, and the high-order spatial interpolation and derivatives (sixth order) and time-stepping (third order) increase efficiency by giving a low effective diffusivity at modest resolution $128^3$ here)."
 The code includes Ohmic and well as thermal and kinetic diffusion., The code includes Ohmic and well as thermal and kinetic diffusion.
 Using Cartesian coordinates avoids problems with singularities and simplifies the boundary conditions: periodic boundaries are used here., Using Cartesian coordinates avoids problems with singularities and simplifies the boundary conditions: periodic boundaries are used here.
 The simulations model the star as a self-gravitating ball of ideal gas €= 5/3) of radius # in hydrostatic equilibrium with radial density and pressure profiles obeying the polytrope relation 17. . ⋅ ∫↗∖∕⇂⊥⊓⋅∖∏↾∣∏∣↧∁⋯↲∁⋅∖⊔⊰∁⊓∩⇀∫≻∣↧∁⇂⊾∁⋅⊰⋯∁∁↾∣∏⊰∙⋮↾↥∖⊽∁⊰⊰↾∸∣∣↴∣∁ stratitication and is a reasonable approximation to an upper-main-sequence star.," The simulations model the star as a self-gravitating ball of ideal gas $\gamma=5/3$ ) of radius $R$ in hydrostatic equilibrium with radial density and pressure profiles obeying the polytrope relation $P \propto \rho^{1+\frac{1}{n}}$, with the index $n$ set to $3$ here, since this gives stable stratification and is a reasonable approximation to an upper-main-sequence star."
 It seems unlikely that a different EOS. for instance that of a neutron star. will make even much quantitative difference to the results.," It seems unlikely that a different EOS, for instance that of a neutron star, will make even much quantitative difference to the results."
 The important point is the stable stratification — the issue of Magnetic equilibria in a non-stably-stratified star will be explored in a forthcoming paper., The important point is the stable stratification – the issue of magnetic equilibria in a non-stably-stratified star will be explored in a forthcoming paper.
 The star is given an initially random magnetic Ποιά containing energy at all length scales down to a limit of a ew grid-spacings. and the MHD equations are integrated in time o follow the evolution of the field.," The star is given an initially random magnetic field containing energy at all length scales down to a limit of a few grid-spacings, and the MHD equations are integrated in time to follow the evolution of the field."
 Within a few Alfvénn crossing-imes. a stable equilibrium is reached.," Within a few Alfvénn crossing-times, a stable equilibrium is reached."
 In the ease where the field is ess centrally concentrated. the equilibrium is non-axisymmetric. consisting of twisted flux tubes meandering at roughly constant depth under the surface of the star.," In the case where the field is less centrally concentrated, the equilibrium is non-axisymmetric, consisting of twisted flux tubes meandering at roughly constant depth under the surface of the star."
 This case was examined in detail in Paper II., This case was examined in detail in Paper II.
 In the case of more centrally-concentrated (1.8. deeply-buried) initial fields. an approximately axisymmetric field forms.," In the case of more centrally-concentrated (i.e. deeply-buried) initial fields, an approximately axisymmetric field forms."
" Ignoring the small deviations from axisymmetry. there appear to be wo busic degrees offreedom: the concentration of the field into he centre of the star. which can be parametrized as ιν. the distance between the axis of symmetry and the neutral line. and the poloidal Traction of total energy £5,/££."," Ignoring the small deviations from axisymmetry, there appear to be two basic degrees of: the concentration of the field into the centre of the star, which can be parametrized as $r_{\rm n}$ the distance between the axis of symmetry and the neutral line, and the poloidal fraction of total energy $E_{\rm p}/E$."
" In this two-dimensional parameter space lies an area of stability through which the star slowly moves in time. as a result of diffusive processes such as finite conductivity. o ever increasing 7, and the eventual end of its stable axisymmetric ife. as described above and in Paper IT."," In this two-dimensional parameter space lies an area of stability through which the star slowly moves in time, as a result of diffusive processes such as finite conductivity, to ever increasing $r_{\rm n}$ and the eventual end of its stable axisymmetric life, as described above and in Paper II."
 It is the aim here to tind the boundaries of that area of stability., It is the aim here to find the boundaries of that area of stability.
 The first step is to produce a stable field in a simulation (1.9. run with arbitrary initial conditions for a few Alfvénn crossing imes until the field has settled down into an equilibrium) and axisymmetrise it. using an axis defined by {r.Bel.," The first step is to produce a stable field in a simulation (i.e. run with arbitrary initial conditions for a few Alfvénn crossing times until the field has settled down into an equilibrium) and axisymmetrise it, using an axis defined by $\int \mathbf{r} \times \mathbf{B} dV$."
 Although he tields produced in the simulations are already approximately axisymmetric. perfect axisymmetry simplities the stability analysis.," Although the fields produced in the simulations are already approximately axisymmetric, perfect axisymmetry simplifies the stability analysis."
 Also. the small asymmetry between the two hemispheres is removed so that the field is symmetrical about the +=0 plane.," Also, the small asymmetry between the two hemispheres is removed so that the field is symmetrical about the $z=0$ plane."
" Now. this symmetrised star can be put back into the simulation and evolved in time (the ‘fiducial simulation). where it slowly diffuses outwards. the value of ry, rising as it does so."," Now, this symmetrised star can be put back into the simulation and evolved in time (the `fiducial simulation'), where it slowly diffuses outwards, the value of $r_{\rm n}$ rising as it does so."
 Its stability can then be examined at various points along this diffusive evolution track. both analytically. using the methods described in Sect. 2..," Its stability can then be examined at various points along this diffusive evolution track, both analytically, using the methods described in Sect. \ref{sec:analytic},"
 and numerically. by ehanging the relative strengths of the poloidal and toroidal parts and using that as the initial conditions for a new simulation.," and numerically, by changing the relative strengths of the poloidal and toroidal parts and using that as the initial conditions for a new simulation."
 In this way.the boundaries of the stable area in ry — LVf/E parameter space can be found. [," In this way,the boundaries of the stable area in $r_{\rm n}$ – $E_{\rm p}/E$ parameter space can be found. ["
In the simulations,In the simulations
either with full resolution at 3.Gem or with tapering al 2 em. consistent wilh the predications ol the models presented here.,"either with full resolution at 3.6cm or with tapering at 2 cm, consistent with the predications of the models presented here."
 Thus. the plasmoids that are considered here are too small {ο have (heir sizes accurately fit wilh state of the art interferometry. except possibly if thev are observed al very. high frequency with VLBA.," Thus, the plasmoids that are considered here are too small to have their sizes accurately fit with state of the art interferometry, except possibly if they are observed at very high frequency with VLBA."
 One can also look at the time evolution of D and N for component C2., One can also look at the time evolution of $B$ and $N$ for component C2.
 Figures 7 ancl 8 plot JJ and AN. respectively. for the allowed. plasmoids models of C2 at all three epochs.," Figures 7 and 8 plot $B$ and $N$, respectively, for the allowed plasmoids models of C2 at all three epochs."
 Figures 7 and 3 show that the plasmoll is expanding lor anyreasonable value of D and AN., Figures 7 and 8 show that the plasmoid is expanding for anyreasonable value of $B$ and $N$ .
 Furthermore. Figure 7 indicates that £ is decreasing as the plasmoid propagates away [rom the central engine.," Furthermore, Figure 7 indicates that $B$ is decreasing as the plasmoid propagates away from the central engine."
 Again. on December 14. C2 is still too small to be resolved except mareinally with high frequeney with VLBA.," Again, on December 14, C2 is still too small to be resolved except marginally with high frequency with VLBA."
 In order to discuss. the possibility of protonic plasmoils versus positronic plasmoids. one needs to separate the energv content into (vo pieces.," In order to discuss, the possibility of protonic plasmoids versus positronic plasmoids, one needs to separate the energy content into two pieces."
 The first is the kinetic energy of the protons. E(proton).," The first is the kinetic energy of the protons, $E(\mathrm{proton})$."
 The other piece is namecl (he lepto-magnetic energy. Z(In). and is composed of (he volume integral of the leptonic thermal energy densityv. OY. and (he magnetic Ποιά energv density. Uy.," The other piece is named the lepto-magnetic energy, $E(\mathrm{lm})$, and is composed of the volume integral of the leptonic thermal energy density, $U_{e}$, and the magnetic field energy density, $U_{B}$."
 It is straightforward (to compute the lepto-magnetic energv in a spherical volume from the solutions in Figures 5 to 8 for D and NV. The kinetic enereve. of the protonic component is where DL is the bulk Lorentz [actor and M is the mass of the plasmoid.," It is straightforward to compute the lepto-magnetic energy in a spherical volume from the solutions in Figures 5 to 8 for $B$ and $N$, The kinetic energy of the protonic component is where $\Gamma$ is the bulk Lorentz factor and $M$ is the mass of the plasmoid."
 There is no hieh resolution multi-epoch radio imagine of the ejected plasmoils for the December 1993 flare. so one cannot estimate {hese kinematic values directly [rom observation.," There is no high resolution multi-epoch radio imaging of the ejected plasmoids for the December 1993 flare, so one cannot estimate these kinematic values directly from observation."
 ILowever. GRS 19154-105 has shown fairly similar kinematics of the ejected plamsoids lor the various flares that have been monitored since 1994 (MirabelandRoclriguez1994:Rodriguezοἱal1995:Fenderetal1999:Dhawan2000:Miller-Jones 2005).," However, GRS 1915+105 has shown fairly similar kinematics of the ejected plamsoids for the various flares that have been monitored since 1994 \citep{mir94,rod95,fen99,dha00,mil05}."
. The kinematic fits of the plasmoid motion for the March 1994 major flare indicate that the motion is consistent with a bulk velocity is 7=0.92 and the Lorentz factor associated with this motion is P=2.55 (MirabelanclRodriguez1994:andAlirabel 1999)..," The kinematic fits of the plasmoid motion for the March 1994 major flare indicate that the motion is consistent with a bulk velocity is $v=0.92c$ and the Lorentz factor associated with this motion is $\Gamma=2.55$ \citep{mir94,rod99}. ."
 Thevalues are not that much different than those inferred lor other major flares, Thevalues are not that much different than those inferred for other major flares
For the determination of spectroscopic stellar parameters. one needs high resolution spectra with high signal to noise ratio.,"For the determination of spectroscopic stellar parameters, one needs high resolution spectra with high signal to noise ratio."
 These spectra are available from radial velocity surveys and are often used to determine stellar parameters., These spectra are available from radial velocity surveys and are often used to determine stellar parameters.
 For instance. properties of cool stars from the Keck. Lick and AAT planet search are described by?..," For instance, properties of cool stars from the Keck, Lick and AAT planet search are described by\citet{valenti2005}."
 Atmospheric parameters for stars observed by the N2K consortium (?) are described by ?.., Atmospheric parameters for stars observed by the N2K consortium \citep{fischer2005a} are described by \citet{robinson2007}.
 ?? present stellar parameters and metallicities from the planet search using ESO facilities and the ELODIE spectrograph at the 1.93 m telescope at the Observatoire de Haute Provence.," \citet{santos2004,santos2005} present stellar parameters and metallicities from the planet search using ESO facilities and the ELODIE spectrograph at the 1.93 m telescope at the Observatoire de Haute Provence."
 Also. basic stellar parameters for 72 evolved stars. previously studied for radial velocity variations. are presented by ?..," Also, basic stellar parameters for 72 evolved stars, previously studied for radial velocity variations, are presented by \citet{dasilva2006}."
 Some of these results are not only interesting in terms of the stellar parameters. but also reveal which stars are most likely to harbour sub-stellar companions.," Some of these results are not only interesting in terms of the stellar parameters, but also reveal which stars are most likely to harbour sub-stellar companions."
 As first shown by ?.. and confirmed with larger samples by ? and ?.. metal rich stars are more likely to harbour companions than metal poor ones.," As first shown by \citet{gonzalez1997}, , and confirmed with larger samples by \citet{fischervalenti2005} and \citet{santos2005}, metal rich stars are more likely to harbour companions than metal poor ones."
 Spectroscopic stellar. parameters are most commonly determined by fitting the observed spectrum directly. see for instance ?.. or by imposing excitation and ionisation equilibrium for metal lines. using an LTE analysis and a grid of model atmospheres. see for instance ??.. 2.. ? and ?..," Spectroscopic stellar parameters are most commonly determined by fitting the observed spectrum directly, see for instance \citet{valenti2005}, or by imposing excitation and ionisation equilibrium for metal lines, using an LTE analysis and a grid of model atmospheres, see for instance \citet{santos2004,santos2005}, \citet{dasilva2006}, \citet{takeda2002} and \citet{luck2007}."
 Rotational velocity and macro turbulence can only be determined directly with the Fourier. transform technique. see for instance 2..," Rotational velocity and macro turbulence can only be determined directly with the Fourier transform technique, see for instance \citet{gray1989}."
 2?) have shown that accurate rotational velocities can also be deduced for dwarfs from à cross correlation function. by performing a calibration with the direct measurements of ?..," \citet{benz1981} have shown that accurate rotational velocities can also be deduced for dwarfs from a cross correlation function, by performing a calibration with the direct measurements of \citet{gray1989}."
 ? extended this technique for giant stars., \citet{demedeiros1999} extended this technique for giant stars.
 ? used the full width at half maximum (FWHM) of weak to moderate spectral lines to determine rotational velocities. also by performing a calibration with the results of ?..," \citet{fekel1997} used the full width at half maximum (FWHM) of weak to moderate spectral lines to determine rotational velocities, also by performing a calibration with the results of \citet{gray1989}."
" In 1999, a radial velocity survey of about 180 K giant stars was started at UCO/Lick Observatory. USA."," In 1999, a radial velocity survey of about 180 K giant stars was started at UCO/Lick Observatory, USA."
 This ongoing survey has recently been expanded to about 380 G and K giants., This ongoing survey has recently been expanded to about 380 G and K giants.
 From the initial sample of 180 stars. companions have been announced for¢ Draconis (2?) and Pollux (2)..," From the initial sample of 180 stars, companions have been announced for $\iota$ Draconis \citep{frink2002} and Pollux \citep{reffert2006}."
 Stars with radial velocity variations of less than 20 ms! were presented as stable stars by ?.. and an investigation into the mechanism(s) causing the radial velocity variations is presented by ?..," Stars with radial velocity variations of less than 20 $^{-1}$ were presented as stable stars by \citet{hekker2006a}, and an investigation into the mechanism(s) causing the radial velocity variations is presented by \citet{hekker2007}."
 Some binaries discovered with this survey. as well as an extensive overview of the sample. will be presented in forthcoming papers.," Some binaries discovered with this survey, as well as an extensive overview of the sample, will be presented in forthcoming papers."
 In this paper. we determine stellar parameters. t.e. effective temperature (Ty). surface gravity (log σ) and metallicity ({Fe/H]). as well as rotational velocity (esin/) for all stars in the sample.," In this paper, we determine stellar parameters, i.e. effective temperature $_{\rm{eff}}$ ), surface gravity $\log$ g) and metallicity ([Fe/H]), as well as rotational velocity $\varv \sin i$ ) for all stars in the sample."
 In Sect., In Sect.
 2. we describe the observations.," 2, we describe the observations."
 In Sects., In Sects.
 3 and 4. we present the methods used. and results for the stellar parameters and rotational velocity. respectively.," 3 and 4, we present the methods used, and results for the stellar parameters and rotational velocity, respectively."
 In Sect., In Sect.
 5 a summary of our results is presented., 5 a summary of our results is presented.
 Por the radial velocity survey. giants were selected from the Hippareos catalog (?).. based on the criteria described by ?..," For the radial velocity survey, giants were selected from the Hipparcos catalog \citep{esa1997}, based on the criteria described by \citet{frink2001}."
 The selected stars are all brighter than 6 mag. are presumably single and have photometric variations <0.06 mag.," The selected stars are all brighter than 6 mag, are presumably single and have photometric variations $< 0.06$ mag."
 These criteria are the same for the initial sample (ΚΙ and later giants) as well as for the extension (G and ΚΟ. ΚΙ giants).," These criteria are the same for the initial sample (K1 and later giants) as well as for the extension (G and K0, K1 giants)."
 The survey started in 1999 at Lick observatory using the Coude Auxiliary Telescope (CAT) in conjunction with the Hamilton echelle spectrograph (R = 600000)., The survey started in 1999 at Lick observatory using the Coude Auxiliary Telescope (CAT) in conjunction with the Hamilton echelle spectrograph (R = 000).
 The radial velocity measurements are performed with an iodine cell in the light path as deseribed by ?. and ?.., The radial velocity measurements are performed with an iodine cell in the light path as described by \citet{marcy1992} and \citet{valenti1995}.
 Radial velocities are determined from the comparison of a stellar spectrum obtained with an todine cell in the light path. and the convolution of a template todine spectrum and a template stellar spectrum obtained without an todine cell in the light path (2)..," Radial velocities are determined from the comparison of a stellar spectrum obtained with an iodine cell in the light path, and the convolution of a template iodine spectrum and a template stellar spectrum obtained without an iodine cell in the light path \citep{butler1996}."
 For each target star we have a high signal to noise ratio template spectrum., For each target star we have a high signal to noise ratio template spectrum.
 These templates are used for the determination of the stellar parameters described in this paper., These templates are used for the determination of the stellar parameters described in this paper.
 Thortum-Argon images taken at the beginning and end of each night are used for wavelength calibration., Thorium-Argon images taken at the beginning and end of each night are used for wavelength calibration.
 Spectroscopic stellar parameters (Των. log g and [Fe/H]) aredetermined by measuring the equivalent width (EW) of tron lines.," Spectroscopic stellar parameters $_{\rm{eff}}$ , $\log$ g and [Fe/H]) aredetermined by measuring the equivalent width (EW) of iron lines."
 The tron lines used in this work are listed in Table 1.., The iron lines used in this work are listed in Table \ref{Felines}. .
"Rather than measuring SFR via the resolved stellar populations of the MCs, we can trace it by means of Ha emission, which gives us a third probe of gasdensity.","Rather than measuring SFR via the resolved stellar populations of the MCs, we can trace it by means of $\alpha$ emission, which gives us a third probe of gasdensity."
" Ha is principally powered by photoionisation from O-type stars, whose numbers are proportional to the SFR."," $\alpha$ is principally powered by photoionisation from O-type stars, whose numbers are proportional to the SFR."
 The Schmidt law again connects this SFR to the gas mass column., The Schmidt law again connects this SFR to the gas mass column.
 We have examined the continuum-subtracted Ho emission maps of the LMC and SMC from the SHASSA survey of Gaustadetal.(2001) 8., We have examined the continuum-subtracted $\alpha$ emission maps of the LMC and SMC from the SHASSA survey of \citet{gaustad01:SHASSA} .
". Figure 7 shows that both the LMC and the SMC have distributions of Ho surface brightness that follow power laws of index ~—1, this time over 2 orders of magnitude for the SMC, and almost 3 for the LMC."," Figure \ref{HaHist} shows that both the LMC and the SMC have distributions of $\alpha$ surface brightness that follow power laws of index $\sim -1$, this time over 2 orders of magnitude for the SMC, and almost 3 for the LMC."
" As before, through the Schmidt law, this implies a power law with index —1 for the gas density distribution over 1-2 orders of magnitude in density."," As before, through the Schmidt law, this implies a power law with index $-1$ for the gas density distribution over 1-2 orders of magnitude in density."
" Surface brightness is independent of distance for such nearby galaxies, and can therefore be compared directly between the LMC and SMC."," Surface brightness is independent of distance for such nearby galaxies, and can therefore be compared directly between the LMC and SMC."
" The density tracers that we have examined here are not free of biases, but they should provide a fairly accurate picture of the density distribution in the interstellar medium of the MCs."," The density tracers that we have examined here are not free of biases, but they should provide a fairly accurate picture of the density distribution in the interstellar medium of the MCs."
" Specific regions within the Clouds, like the LMC bar or 30 Dor, will probably have density distributions that are different from the simple powerlaws we have found here; our analysis only applies to the bulk, statistical properties of the gas on galactic scales."," Specific regions within the Clouds, like the LMC bar or 30 Dor, will probably have density distributions that are different from the simple powerlaws we have found here; our analysis only applies to the bulk, statistical properties of the gas on galactic scales."
" Several theoretical studies have adressed the probability distribution of densities in the interstellar medium: see Padoanetal.(1997),, PassotVázquez-Semadeni (1998),, Scaloetal. (1998),, and Wada&Norman (2001).."," Several theoretical studies have adressed the probability distribution of densities in the interstellar medium: see \cite{padoan97:IMF_universality}, \cite{passot98:density_distribution_ISM}, \cite{scalo98:interstellar_gas_density_distribution}, and \cite{wada01:multiphase_ISM}."
" The consensus of these studies is that, despite local inhomogeneities and deviations, a combination of galaxy-wide and local mechanisms conspire to produce a lognormal distribution of densities in the gas for a wide range of conditions."," The consensus of these studies is that, despite local inhomogeneities and deviations, a combination of galaxy-wide and local mechanisms conspire to produce a lognormal distribution of densities in the gas for a wide range of conditions."
" At the higher densities where most stars are formed and most SNe explode, the tail of the lognormal distribution is well reproduced by a power law with an index —] (seefigure19inWada&Norman2007).."," At the higher densities where most stars are formed and most SNe explode, the tail of the lognormal distribution is well reproduced by a power law with an index $\sim -1$ \citep[see figure 19 in][]{wada07:density_structure_ISM}."
 This is consistent with our findings for the MCs., This is consistent with our findings for the MCs.
" The derivation in 4 ignores many subtleties in what is clearly a complex problem, involving different physical processes and temporal scales."," The derivation in \ref{physics} ignores many subtleties in what is clearly a complex problem, involving different physical processes and temporal scales."
" In this context, the fact that the distribution of gas densities in the MCs seems to behave like a power law with an index ~—1 does not that our proposed picture for the evolution of SNRs is correct."," In this context, the fact that the distribution of gas densities in the MCs seems to behave like a power law with an index $\sim-1$ does not that our proposed picture for the evolution of SNRs is correct."
" However, our simple (but physically motivated) scenario appears to explain the available observations quite well, and is consistent with what we know about the bulk properties of the interstellar gas in the MCs."," However, our simple (but physically motivated) scenario appears to explain the available observations quite well, and is consistent with what we know about the bulk properties of the interstellar gas in the MCs."
" Furthermore, there are indirect ways to test that the basic scenario is sound."," Furthermore, there are indirect ways to test that the basic scenario is sound."
" In Paper II, we use the compilation of SNR observations from Table 1 and the SFH maps of Harris&Zaritsky(2004) and Harris&Zaritsky(2009) to derive the SN rate and delay time distribution in the Magellanic Clouds."," In Paper II, we use the compilation of SNR observations from Table 1 and the SFH maps of \citet{harris04:SMC_SFH} and \citet{harris09:LMC_SFH} to derive the SN rate and delay time distribution in the Magellanic Clouds."
" Some key results from that exercise, which we describe briefly here, serve as plausibility arguments for our picture of SNR evolution."," Some key results from that exercise, which we describe briefly here, serve as plausibility arguments for our picture of SNR evolution."
" A basic ingredient in the derivation of SN rates is the “visibility time"" of SNRs (i.e., the time during which a SNR would be visible, if it were there)."," A basic ingredient in the derivation of SN rates is the “visibility time” of SNRs (i.e., the time during which a SNR would be visible, if it were there)."
" We have identified this time with the transition to the radiative phase in 4,, but without assigning any specific value to it."," We have identified this time with the transition to the radiative phase in \ref{physics}, but without assigning any specific value to it."
" This cannot be done using theoretical arguments alone, because many of the necessary parameters are not known with sufficient accuracy, like the distribution of SN kinetic energies or the normalization of the cooling function (see Eq. 11))."," This cannot be done using theoretical arguments alone, because many of the necessary parameters are not known with sufficient accuracy, like the distribution of SN kinetic energies or the normalization of the cooling function (see Eq. \ref{rmaxwithepsilon}) )."
" The visibility time cannot be calibrated using individual objects either, because the only SNRs that have reliable ages from light echoes or historical observations are much younger than the old SNRs in the Sedov stage that form the bulk of our sample."," The visibility time cannot be calibrated using individual objects either, because the only SNRs that have reliable ages from light echoes or historical observations are much younger than the old SNRs in the Sedov stage that form the bulk of our sample."
" In Paper II, this conundrum is solved by imposing a condition on the delay time distribution: that the vast majority of stars more massive than 8Meo explode as core collapse SNe, with very few ""silent"" events that collapse directly to form a black hole without much ejection of material and hence without leaving a SNR behind."," In Paper II, this conundrum is solved by imposing a condition on the delay time distribution: that the vast majority of stars more massive than $8\,\mathrm{M_{\odot}}$ explode as core collapse SNe, with very few “silent” events that collapse directly to form a black hole without much ejection of material and hence without leaving a SNR behind."
" If this condition holds, an absolute value for the SNR visibility time can be obtained by equating the time-integrated SN rate in the temporal bin of the delay time distribution that is associated with core collapse SNe (in the binning used in Paper II, that is all SNe with delays shorter than 35 Myr) to the number of massive stars per total stellar mass formed."," If this condition holds, an absolute value for the SNR visibility time can be obtained by equating the time-integrated SN rate in the temporal bin of the delay time distribution that is associated with core collapse SNe (in the binning used in Paper II, that is all SNe with delays shorter than 35 Myr) to the number of massive stars per total stellar mass formed."
" This procedure yields SNR visibility times that depend on the tracer used to determine the local density, and vary between 13.3 kyr (for the HI density tracer) and 22.5 kyr (for the SFR-based density tracer — see table 2 in Paper II)."," This procedure yields SNR visibility times that depend on the tracer used to determine the local density, and vary between $13.3$ kyr (for the HI density tracer) and $22.5$ kyr (for the SFR-based density tracer – see table 2 in Paper II)."
" These ages are for regions where the local density corresponds to the mean value of the tracer, 1.5x10?!cm""? and 3.3x10Moyr !cell respectively (see Figures 5 and 6)); for values 10 times !,lower than the mean, the visibility times could be a factor 3 to 4 longer (see Paper II"," These ages are for regions where the local density corresponds to the mean value of the tracer, $1.5\times
10^{21}~{\rm cm}^{-2}$ and $3.3\times10^{-4}~M_\odot ~{\rm yr}^{-1}\,\mathrm{cell}^{-1}$ , respectively (see Figures \ref{HIHist} and \ref{SFHist}) ); for values 10 times lower than the mean, the visibility times could be a factor 3 to 4 longer (see Paper II"
at the midplane is of order unity (or ay=1: &Hawley 1991)).,at the midplane is of order unity (or $a_{\rm 0} \lesssim 1$ ; \citealt{BH91}) ).
 Tlowever. calculations by Salmeron&Wardle(2003) aud WSII show that when iy«0 the instability may erow for super-equipartition (supra-thermal) fields.," However, calculations by \citet{SW03} and WS11 show that when $\eta_{\rm H} < 0$ the instability may grow for super-equipartition (supra-thermal) fields."
 This is the result of Tall diffusion in this case exteudiic the unstable wavelengths to shorter values., This is the result of Hall diffusion in this case extending the unstable wavelengths to shorter values.
 These results demonstrate fhat the AIRT grows over a wide range cft magnetic field strengths once dust erains have setted out of the eas phase. even in the Inner regions of wealsly-iouised disces;," These results demonstrate that the MRI grows over a wide range of magnetic field strengths once dust grains have settled out of the gas phase, even in the inner regions of weakly-ionised discs."
 Note also that 1c Wan)uma field sreneth for which perturbations erow is inversely related to the redius., Note also that the maximum field strength for which perturbations grow is inversely related to the radius.
 This is expected. as bo the midplane gas deusity py and the isothermal sound spec ος decrease wit itje radial location.," This is expected, as both the midplane gas density $\rho_{\rm 0}$ and the isothermal sound speed $c_{\rm s}$ decrease with the radial location."
 As a result. the value of ay=Μα...e associated with particular field strength Increases With rs causing 1C instavility to be damIOC at progressively weaker fields as the radius Increases.," As a result, the value of $a_{\rm 0} \equiv B_{\rm 0}/[(4 \pi \rho_{\rm 0})^{1/2} c_{\rm s}]$ associated with a particular field strength increases with $r$, causing the instability to be damped at progressively weaker fields as the radius increases."
 The magnetic acivitv of discs is also stronely depeident ou the presence and size distribution of dust eyalis μήκος with the eas., The magnetic activity of discs is also strongly dependent on the presence and size distribution of dust grains mixed with the gas.
 This is the result of rapid recolbinatious aking place on their surfaces. as well as their relatively arge cross-sections. Which caises them to ecouple froi the magnetic feld at deusities for which other Ulnaller particle sare still well ied to it.," This is the result of rapid recombinations taking place on their surfaces, as well as their relatively large cross-sections, which causes them to decouple from the magnetic field at densities for which other – smaller – particles are still well tied to it."
 The vertical sticture aud growh ofthe fastes-orowlue AIRI modes as a function of t1ο preseice and size of dust erains susvended in the oeas phase is 1lustrated in Fig., The vertical structure and growth of the fastest-growing MRI modes as a function of the presence and size of dust grains suspended in the gas phase is illustrated in Fig.
 10. for he ΠΕ solar uchla model at r= AU, \ref{fig:MRI3} for the minimum-mass solar nebula model at $r = 5$ AU.
LTιο leftmost cohiin of the figure shows the magnetic field perturbations when he erains have settled out of the gas phase. or ive agerceated to sizes sieuificautv lareer to those shown.," The leftmost column of the figure shows the magnetic field perturbations when the grains have settled out of the gas phase, or have aggregated to sizes significantly larger to those shown."
 The other cols display the correspoidiug resIts when a population of single-sized grains. of the radius (064) imdicated at the top of each cohnun aud coustitutius a cousta (ο1ο percent) fractio rof the ujass of the eas. rena suspended with the uid.," The other columns display the corresponding results when a population of single-sized grains, of the radius $a_{\rm g}$ ) indicated at the top of each column and constituting a constant (one percent) fraction of the mass of the gas, remains suspended with the fluid."
 All the magnetic diffusivi componens have been incorporate in the caleulatio aud DB.> 0., All the magnetic diffusivity components have been incorporated in the calculations and $B_z > 0$ .
 The owest row shows the imaxiuu fied streneth for wuch the 4oerturbationus grow (for Gul aud 0.1 jna). or the results for B=LOO mC (for the no grains. OY Uy3 ya cases)," The lowest row shows the maximum field strength for which the perturbations grow (for $a_{\rm g} = 1$ and $0.1 \ \mu$ m), or the results for $B = 100$ mG (for the no grains, or $a_{\rm g} = 3 \ \mu$ m cases)."
 Note the CXended: magneticaIw-inactive| zone adjacent to the disc mudplanue when the grains are stnall (sub-micron sized)., Note the extended magnetically-inactive zone adjacent to the disc midplane when the grains are small (sub-micron sized).
 Tn this case. severe magneic diffuion iu the disc iuterior prevents the maguetic feld from couplius to the eas below ~2.5 scale-heights.," In this case, severe magnetic diffusion in the disc interior prevents the magnetic field from coupling to the gas below $\sim 2.5$ scale-heights."
" When the erai15 have agerceatedOO to about a micron in size. however. 1ο disc midplane remains miagnueticallvy coupled for all 1ο field streugths for which the iustability grows (BSKn mG. see the cohun for a,L jan in Fig. 10))."," When the grains have aggregated to about a micron in size, however, the disc midplane remains magnetically coupled for all the field strengths for which the instability grows $B \lesssim 100$ mG, see the column for $a_{\rm g} = 1 \ \mu$ m in Fig. \ref{fig:MRI3}) )."
 In contrast. the NRI exows for BS1G when Lo eral are present at this (Salmeron&War‘dle2005).," In contrast, the MRI grows for $B \lesssim 1$ G when no grains are present at this \citep{SW05}."
. These results hold when the uagnetic feld is aligned with the rotation axis of the disc. rendoeri18o apco.," These results hold when the magnetic field is aligned with the rotation axis of the disc, rendering $\eta_{\rm H} > 0$."
 When the field is couuter-aligned to it. however. onlv a sunall fraction of the dIsc Is acive even after the eraius ageregate. unless the field is i the range o 90 SU C. (WSIL).," When the field is counter-aligned to it, however, only a small fraction of the disc is active even after the grains aggregate, unless the field is in the range of 20 – 80 G (WS11)."
 Fig., Fig.
 11 displavs the erowth rate of the fastest-erowing MBRI perturb:ions a r= AU. for cüffereut assunptions regarding the presence and size of dist eyali mnixed with the gas aud D.>0.," \ref{fig:MRI4} displays the growth rate of the fastest-growing MRI perturbations at $r = 5$ AU, for different assumptions regarding the presence and size of dust grains mixed with the gas and $B_z > 0$."
 The Tage of Beld streneths over wlich the MRI oerates is snialler as the grain size diniuishes., The range of field strengths over which the MRI operates is smaller as the grain size diminishes.
 This is expected. given t1ο reduction iu magnetic coupling for a particular D he dust particles are smaller.," This is expected, given the reduction in magnetic coupling for a particular $B$ as the dust particles are smaller."
 Note. however. that t stabilising effect assoclated with the presence of nal eyalisis not strong enoueh to completely suppress the oerturbatious. even when sinall paricles (0.1.pau in size) are present.," Note, however, that the stabilising effect associated with the presence of small grains is not strong enough to completely suppress the perturbations, even when small particles $0.1 \ \mu$ m in size) are present."
 In this case uustable modes are stil able to erow over a finite section of the disc away roni the midplane aix for a restriced rauge of felk streneths., In this case unstable modes are still able to grow over a finite section of the disc away from the midplane and for a restricted range of field strengths.
 All the results discussed. so far in this section were obtained assunune tha the surface deusitv profile of the disc is that of the nünimunun-niss solar nebula model Xr)=L700x£AU562 o 2. where rap is the radial distance from re central object measured in astronomical wits.," All the results discussed so far in this section were obtained assuming that the surface density profile of the disc is that of the minimum-mass solar nebula model, $\Sigma(r) = 1700\ r_{\rm AU}^{-3/2}$ g $^{-2}$, where $r_{\rm AU}$ is the radial distance from the central object measured in astronomical units."
 This vields a surface deitv of 150 ο 7 at 5 AU and ~50 ο at 10 AU., This yields a surface density of $\sim 150$ g $^{-2}$ at 5 AU and $\sim 50$ g $^{-2}$ at 10 AU.
 Wowever. the surace density profile iu real discs uav well be cdiffereut from these iuferred vaues.," However, the surface density profile in real discs may well be different from these inferred values."
 Iu act. recent observatkuns by Iitammuractal.(2002) and Andrews&Wiluus(2007) secu to imply hat the surface deusiv declines more eradualv with radius than predicted by this model.," In fact, recent observations by \citet{Kitamura02a} and \citet{AW07} seem to imply that the surface density declines more gradually with radius than predicted by this model."
 Moreover. the actual surface deusity iuntre disc der regions nav ο smaller than that «Mf a uiimniun-nass solar nebula disc CAndrews&Willi:uus2007).," Moreover, the actual surface density in the disc inner regions may be smaller than that of a minimum-mass solar nebula disc \citep{AW07}."
. This would facilitate a deeper penetration of he jonising sources iuto he dise. and would resul oeji an increased ioulsatiou yaction closer to the iüdpluie.," This would facilitate a deeper penetration of the ionising sources into the disc, and would result in an increased ionisation fraction closer to the midplane."
 This effect would. iu urn. modify the provertices of MBLEunustabe modes in this region and. nrore generally. the presence and confieuration of the naenetically dead zone iu the dise duterior.," This effect would, in turn, modify the properties of MRI-unstable modes in this region and, more generally, the presence and configuration of the magnetically dead zone in the disc interior."
 On the otherhaud. protostelar discs nav have surface deusities roughly up to ~5O tics the values implied by he uinimnnuunnss solu nebula model without becoming eravitatiouallv uusable.," On the otherhand, protostellar discs may have surface densities roughly up to $\sim 50$ times the values implied by the minimum-mass solar nebula model without becoming gravitationally unstable."
 An increased surface deusi vowillresult in à more exteuded, An increased surface density willresult in a more extended
"The Anomalous XN-rav Pulsars (ANPs) are a sinall eroup of isolated. voung neutron stars having N-rav huninosities ereater than their rotational cucrev loss rates,","The Anomalous X-ray Pulsars (AXPs) are a small group of isolated, young neutron stars having X-ray luminosities greater than their rotational energy loss rates."
 Thev are believed to be maguetars. neutron stars possessing ~104! C magnetic fields. with N-ray cmission powered by the decay of their superstrong maguetic fields (Thompson&Duncan1996).," They are believed to be magnetars, neutron stars possessing $\sim$ $^{14}$ G magnetic fields, with X-ray emission powered by the decay of their superstrong magnetic fields \citep{td96}."
. The magnetar nature of ANPs has been strongly supported by their hieh spin-down rates aud similar radiative properties to soft Sauna repeaters. inchiding short ταν bursts (Woods&Thompson 2006: Iaspi 2007)).," The magnetar nature of AXPs has been strongly supported by their high spin-down rates and similar radiative properties to soft gamma repeaters, including short X-ray bursts \citealt{wt06}; \citealt{kas07}) )."
 The bursting activity ikelv reflects structural changes in the surface magnetic Ποια of a magnetar., The bursting activity likely reflects structural changes in the surface magnetic field of a magnetar.
 As the brightest and nearest among the currently: shown ANPs. ws been well studied over wavelength ranges from he N-rav to miuc-infrared (MIB).," As the brightest and nearest among the currently known AXPs, has been well studied over wavelength ranges from the X-ray to mid-infrared (MIR)."
 Its N-rav emission in the 0.510 keV range cau be well described by a dackbody (k= 0.5 keV) plus power law (photon index P= 3.4 es. Pateletal. 2003)). which i$ believed o arise from the surface and maguetosphere of the star (e.g.. ΜΗ 2002)).," Its X-ray emission in the 0.5–10 keV range can be well described by a blackbody $kT$ = 0.5 keV) plus power law (photon index $\Gamma$ = 3.4; e.g., \citealt{pat03}) ), which is believed to arise from the surface and magnetosphere of the star (e.g., \citealt*{tlk02}) )."
 Its optical eniission is pulsed at the δι7-« spin period (Iker&Martin2002:Dhillonetal. 2005)) and appears to have a power-lawlike spectrum (ITullenian.vanI[kerk-wijk.&Ixullkaurni 20003.. likely also originating from the magnetosphere (although no apparent connection cau be established between the optical and N-ray spectra).," Its optical emission is pulsed at the 8.7-s spin period \citealt{km02, dhi+05}) ) and appears to have a power-law–like spectrum \citep*{hvk00}, likely also originating from the magnetosphere (although no apparent connection can be established between the optical and X-ray spectra)."
 A surprise came from the detection of the source in the ATR (1.5 and 8.0 gan). which revealed a rising spectrum from the near-IR (NIR) to MIR. (Waug.Chakrabarty.&Isaplan 2006).," A surprise came from the detection of the source in the MIR (4.5 and 8.0 $\mu$ m), which revealed a rising spectrum from the near-IR (NIR) to MIR \citep*{wck06}."
. The detection can be interpreted as a surrounding debris disk (Wangctal.2006)., The detection can be interpreted as a surrounding debris disk \citep{wck06}.
. The putative disk. presumably formect from fallback material after the supernova explosion. is irradiated by the X-ravs from the central pulsar aud cuits mainly in the AOR.," The putative disk, presumably formed from fallback material after the supernova explosion, is irradiated by the X-rays from the central pulsar and emits mainly in the MIR."
 The existence and appearance of such a disk has been predicted (e.g.. Liu.Woosley.&Bodenheiuer1991:Perna.Heruquist.," The existence and appearance of such a disk has been predicted (e.g., \citealt*{lwb91, phn00}) )."
&Naravan 2000)). Πουσέν opticalNIR flux variability frou hhas been reported (Duraut&vanRkerkwijk2006).," Recently, optical/NIR flux variability from has been reported \citep{dv06}."
. Iu a total of only 9 observations. significant flux variations were detected. sugeesting such variability is very cohunon.," In a total of only 9 observations, significant flux variations were detected, suggesting such variability is very common."
 This variability is intriguing. since no such flux changes have been detected ii N-ravs. even though N-rav observations of the source have been mace much more frequently than the optical/NTR observations.," This variability is intriguing, since no such flux changes have been detected in X-rays, even though X-ray observations of the source have been made much more frequently than the optical/NIR observations."
 Aim obvious question is whether there is similar variability in the AUR., An obvious question is whether there is similar variability in the MIR.
 Rapid variability in the MIB. would be very hard to understand in the disk model iu the absence of N-rav variability., Rapid variability in the MIR would be very hard to understand in the disk model in the absence of X-ray variability.
 Ou 2007 February 7. a luge fastarise X-ray burst was detected during theEvcplorer (RNTE) mouitorime observations of citepgav| 07..," On 2007 February 7, a large fast-rise X-ray burst was detected during the ) monitoring observations of \\citep{gav+07}."
 The peak 8ux of the burst was more than two orders of mmaenitude larger than that in the sources quiescent state., The peak flux of the burst was more than two orders of magnitude larger than that in the source's quiescent state.
 This event provided an opportunity to test the fallback disk model. since a MIR flux increase is expected from an X-ray irradiated disk when the iuput X-ray flux is increased (see Figure 1)).," This event provided an opportunity to test the fallback disk model, since a MIR flux increase is expected from an X-ray irradiated disk when the input X-ray flux is increased (see Figure \ref{fig:disk}) )."
 For the purposes of searchiug for variability aud testing the fallback disk model. we observed with theTelescope.," For the purposes of searching for variability and testing the fallback disk model, we observed with the."
 bu this paper. we report ou the results of the observatious.," In this paper, we report on the results of the observations."
 We observed four times in 2007. February Ll21 with Spifzer.. following the February 7 burst.," We observed four times in 2007 February 14–21 with, following the February 7 burst."
 To catch fux variations from the source aud possibly coustrain their time scale. the observations were scheduled to be on days 2. 1. aud T after the first observation.," To catch flux variations from the source and possibly constrain their time scale, the observations were scheduled to be on days 2, 4, and 7 after the first observation."
 The exact observation dates are given in Table 2.., The exact observation dates are given in Table \ref{tab:obs}. .
 The imaging iustrumenut used was the Infrared) Array Camera (IB.AC: Fazioetal. 2001)., The imaging instrument used was the Infrared Array Camera (IRAC; \citealt{fha+04}) ).
2010).,.
". In order to reduce ringing, our filter consists of a high-pass filter with a turn on at 6 arcmin convolved with a o=1.8 arcmin Gaussian."," In order to reduce ringing, our filter consists of a high-pass filter with a turn on at 6 arcmin convolved with a $\sigma = 1.8$ arcmin Gaussian."
 Only the Lockman-SWIRE field is large enough to be significantly affected because the other fields are not much larger than this scale., Only the Lockman-SWIRE field is large enough to be significantly affected because the other fields are not much larger than this scale.
" Since the benefit of aanalyses is at faint flux densities where most of the CFIRB arises, and the shallow Lockman-SWIRE field has little constraining power here, our main scientific results are minimally affected by non-Poissonian clustering effects even if we ignore them."," Since the benefit of analyses is at faint flux densities where most of the CFIRB arises, and the shallow Lockman-SWIRE field has little constraining power here, our main scientific results are minimally affected by non-Poissonian clustering effects even if we ignore them."
" In fact, we find that the differences between fits to simulated data with and without clustering are well within the statistical errors even without filtering."," In fact, we find that the differences between fits to simulated data with and without clustering are well within the statistical errors even without filtering."
" Analysis of simulated data from Fernandez-Condeetal. (2008),, which has linear clustering based on the assumption that infrared galaxies are tracers of dark-matter fluctuations, shows that a high-pass filter is quite effective at removing clustering signal for this data set."," Analysis of simulated data from \citet{fer08}, which has linear clustering based on the assumption that infrared galaxies are tracers of dark-matter fluctuations, shows that a high-pass filter is quite effective at removing clustering signal for this data set."
" We construct two sets of simulated maps: one with clustering, and another using the same catalogue but with clustering removed by randomizing the source positions."," We construct two sets of simulated maps: one with clustering, and another using the same catalogue but with clustering removed by randomizing the source positions."
 We then compare fits and pixel histograms for both maps., We then compare fits and pixel histograms for both maps.
" Because filtering will affect the eeven in the absence of clustering, comparing these to unclustered, unfiltered maps is not useful."," Because filtering will affect the even in the absence of clustering, comparing these to unclustered, unfiltered maps is not useful."
" The fits recover the input model accurately in both cases, whereas if we do not filter dN/dS is slightly underestimated at low flux densities for the largest maps."," The fits recover the input model accurately in both cases, whereas if we do not filter $dN/dS$ is slightly underestimated at low flux densities for the largest maps."
 Smaller maps show no evidence for bias., Smaller maps show no evidence for bias.
 A pixel histogram from such a simulation is shown in figure 2.., A pixel histogram from such a simulation is shown in figure \ref{fig:filterhisto}.
" Such filtering is also effective at removing infrared cirrus, although we have not tested this explicitly in terms of the recovered fit parameters."," Such filtering is also effective at removing infrared cirrus, although we have not tested this explicitly in terms of the recovered fit parameters."
" However, it is possible that clustering signal on scales between one and six arcminutes could affect our results."," However, it is possible that clustering signal on scales between one and six arcminutes could affect our results."
 This regime is currently not well characterized and thus we could not model it quantitatively in our analysis., This regime is currently not well characterized and thus we could not model it quantitatively in our analysis.
 The best approach for comparing a particular model to SPIRE data using lis to generate pixel histograms as a function of the model parameters and compare directly with our data., The best approach for comparing a particular model to SPIRE data using is to generate pixel histograms as a function of the model parameters and compare directly with our data.
" However, not all models have smoothly adjustable parameters, and furthermore, if the model is a poor fit to the data this may provide little insight as to at which flux densities the model disagrees with observations."," However, not all models have smoothly adjustable parameters, and furthermore, if the model is a poor fit to the data this may provide little insight as to at which flux densities the model disagrees with observations."
" Hence, we have followed Ρ09 and fit simple, non-physical parametric models to our data."," Hence, we have followed P09 and fit simple, non-physical parametric models to our data."
 These models are defined by the values of the differential number counts dN/dS at a set of fixed flux densities (knots)., These models are defined by the values of the differential number counts $dN/dS$ at a set of fixed flux densities (knots).
" Observationally we can never do more than place a lower limit on the total number of sources fainter than S, N(«S) because we can never measure all the way down to zero flux density, but dN/dS is better behaved because it only depends on the number of sources in some small range."," Observationally we can never do more than place a lower limit on the total number of sources fainter than $S$, $N\left(< S\right)$ because we can never measure all the way down to zero flux density, but $dN/dS$ is better behaved because it only depends on the number of sources in some small range."
" The actual fit parameters are log,,dN/dS at the knot positions.", The actual fit parameters are $\log_{10} dN/dS$ at the knot positions.
 The differential number counts must become shallower than S? at low flux densities or else the contribution to the CFIRB diverges., The differential number counts must become shallower than $S^{-2}$ at low flux densities or else the contribution to the CFIRB diverges.
" However, this turn-over may lie below the flux densities probed by our data."," However, this turn-over may lie below the flux densities probed by our data."
" Therefore, in order to avoid biasing our fits by excluding models which are too steep within the range of our measurements (i.e., would overpredict the CFIRB if integrated down to zero flux density), we assume that the number counts outside the largest and smallest knot are zero; the problem of choosing the limits is discussed below."," Therefore, in order to avoid biasing our fits by excluding models which are too steep within the range of our measurements (i.e., would overpredict the CFIRB if integrated down to zero flux density), we assume that the number counts outside the largest and smallest knot are zero; the problem of choosing the limits is discussed below."
 A ffit requires that the number counts model is continuous., A fit requires that the number counts model is continuous.
" Therefore, we must choose a method of interpolating between the knots, and for a finite number of knots, the interpretation of our results depends on the interpolation method."," Therefore, we must choose a method of interpolating between the knots, and for a finite number of knots, the interpretation of our results depends on the interpolation method."
" We consider two methods of interpolation in this paper: first, as in PO9, using power law extrapolation between each knot (these are multiply-broken law fits), and second, using a cubic spline in log-log space."," We consider two methods of interpolation in this paper: first, as in P09, using power law extrapolation between each knot (these are multiply-broken power-law fits), and second, using a cubic spline in log-log space."
" The first code supports both methods, and the second only the former."," The first code supports both methods, and the second only the former."
" We do not expect the fit parameters (i.e., dN/dS at the knot positions) of these models to be identical, since they have different meaning."," We do not expect the fit parameters (i.e., $dN/dS$ at the knot positions) of these models to be identical, since they have different meaning."
 It is important to understand that the results of this paper are model fits., It is important to understand that the results of this paper are model fits.
" The fit results are not simply dN/dS at the flux densities of the knots, but instead are effectively integral constraints over some region surrounding each knot."," The fit results are not simply $dN/dS$ at the flux densities of the knots, but instead are effectively integral constraints over some region surrounding each knot."
" Any excursion in the number counts that lies entirely between two knots will affect at least both neighboring knots, and likely others as well."," Any excursion in the number counts that lies entirely between two knots will affect at least both neighboring knots, and likely others as well."
" The flux density range that each fit parameter is sensitive to depends on the interpolation scheme, with the spline response more local to the knot."," The flux density range that each fit parameter is sensitive to depends on the interpolation scheme, with the spline response more local to the knot."
" Therefore, simply reading off the values predicted by a theoretical or empirical number counts model at the knot positions and comparing that with our fit parameters is wrong since they are over a region surrounding the knot."," Therefore, simply reading off the values predicted by a theoretical or empirical number counts model at the knot positions and comparing that with our fit parameters is wrong since they are over a region surrounding the knot."
" This is also true for more traditional methods (i.e., simple number counts derived from individual galaxy detections) because of the importance of the de-boosting corrections for low signal-to-noise ratio detections."," This is also true for more traditional methods (i.e., simple number counts derived from individual galaxy detections) because of the importance of the de-boosting corrections for low signal-to-noise ratio detections."
" A preferable approach is to first find the best approximation to the differential counts of the theoretical (or empirical) number counts model chosen for comparison using either of our parametric models (for example, by fitting a multiply-broken power law to the dN/dS of the theoretical model giving equal weighting to all fluxes, not just the values at the knots) and comparing the parameters of that approximation to our results."," A preferable approach is to first find the best approximation to the differential counts of the theoretical (or empirical) number counts model chosen for comparison using either of our parametric models (for example, by fitting a multiply-broken power law to the $dN/dS$ of the theoretical model giving equal weighting to all fluxes, not just the values at the knots) and comparing the parameters of that approximation to our results."
 The highest and lowest knot positions must be chosen with some care because the differential number counts are assumed to, The highest and lowest knot positions must be chosen with some care because the differential number counts are assumed to
= |). ancl Poisson's equation. VP COmputational where f is the distribution function. of the particles. describing their position r and velocity v at a time /. and o is the gravitational potential at (7./) due to all the particles.,"= 0, and Poisson's equation, ^2 = 4 G ), where $f$ is the distribution function of the particles, describing their position $\bmath r$ and velocity $\bmath v$ at a time $t$, and $\Phi$ is the gravitational potential at $(\bmath{r},t)$ due to all the particles."
 The density of the svstem is related to f by p= [see C is the universal gravitational constant ancl hereafter is taken to be unity., The density of the system is related to $f$ by = f. $G$ is the universal gravitational constant and hereafter is taken to be unity.
 The acceleration can then be found from the potential.Veo.," The acceleration can then be found from the potential,."
 Apart from a number of exact equilibrium. solutions of the collisionless Boltzmann equations. in general this function of seven independent variables cannot be solved.," Apart from a number of exact equilibrium solutions of the collisionless Boltzmann equations, in general this function of seven independent variables cannot be solved."
 A [easible way of solving for the time evolution of equations (2)) and (3)) is to construct an N-bocly realisation of the SVSLCHL w sampling the phase space (roe) JN times. subject ο the obabilitv density. f(r.ο).," A feasible way of solving for the time evolution of equations \ref{cbe}) ) and \ref{poiss}) ) is to construct an N-body realisation of the system by sampling the phase space $(\bmath{r},\bmath{v})$ $N$ times, subject to the probability density $f(\bmath{r},\bmath{v})$."
 Phe N-body. system. of xuwticles is then evolved. according to Newton's laws., The N-body system of particles is then evolved according to Newton's laws.
 Lt is clesiralXe for the sample No to be as large as possible to recluce he effects of statistical noise in the sample. lessening he ellects of numerical twobody relaxation. and increasing he possible spatial resolution.," It is desirable for the sample $N$ to be as large as possible to reduce the effects of statistical noise in the sample, lessening the effects of numerical two–body relaxation, and increasing the possible spatial resolution."
 Memory and processing time of coniputing resources constrain the value of No that is achievable. and thus N-body codes generally employ. various approximations to counter the problems raised with smaller CN.," Memory and processing time of computing resources constrain the value of $N$ that is achievable, and thus N-body codes generally employ various approximations to counter the problems raised with smaller $N$."
 In general techniques address: citier one problem. or another. and so choice of appropriat«| algorithms is. very important.," In general techniques address either one problem or another, and so choice of appropriate algorithms is very important."
 One must ensure. that. the| [limitations of any particular algorithm does not invalidae dUs application to the physical system uncer consideration., One must ensure that the limitations of any particular algorithm does not invalidate it's application to the physical system under consideration.
 In the following section OlUline some of the major techniques that have been emXoved in the study of stellar dynamical problems sce. also. Hernequist. (1987) [or a comprehensive review]. and explain why it ijs we implemented the two methods used in SCITIUL.," In the following section we outline some of the major techniques that have been employed in the study of stellar dynamical problems [see also Hernquist (1987) for a comprehensive review], and explain why it is we implemented the two methods used in SCFTREE."
 Perhaps the most straightforward way to evolve the system is to calculate directly all the interparticle accelerations., Perhaps the most straightforward way to evolve the system is to calculate directly all the interparticle accelerations.
 The combined acceleration. &;. on a particle is where r;. rj. m;. and m; are the positions and masses of the particles 7 and j. ο is the softening parameter.," The combined acceleration, ${\bmath a}_i$, on a particle is = , where ${\bmath{r}_i}$, ${\bmath{r}_j}$, $m_i$, and $m_j$ are the positions and masses of the particles $i$ and $j$, $\epsilon$ is the softening parameter."
 These particle (PP) or direct summation methods have two important aspects in their favour. the resolution scale is determined. solely by. c. aneL there are no constraints on the geometry of the system.," These particle–particle (PP) or direct summation methods have two important aspects in their favour, the resolution scale is determined solely by $\epsilon$, and there are no constraints on the geometry of the system."
 Phe greatest drawback Ὁ cost. at best the CPU time scales as OCN7).," The greatest drawback is in computational cost, at best the CPU time scales as ${\cal
O}(N^2)$."
 Integration techniques have become quite ellicient (Aarseth1972:Aarseth1985)... |oit. CPU expensive lor Αα10? (although new dedicated. hardware has improved the situation. see below).," Integration techniques have become quite efficient \cite{aa72,aa85}, but CPU expensive for $N\go 10^4$ (although new dedicated hardware has improved the situation, see below)."
 An extension of the PP echnique is the particlemesh (PM) technique (Hlocknev&Eastwood.1981)., An extension of the PP technique is the particle--mesh (PM) technique \cite{he81}.
.. This method. imposes à grid upon the system and. densities are assigned to cach eric ce|l., This method imposes a grid upon the system and densities are assigned to each grid cell.
 Applying Last Fourier ‘Transform (Cooley&Turkey1965). to PAL methods makes hem hiehly ellicient at. dealing. withlarge. numbers of xuticles. thus minimizing statisical Iuctuations in particle distribution.," Applying Fast Fourier Transform \cite{ct65} to PM methods makes them highly efficient at dealing withlarge numbers of particles, thus minimizing statistical fluctuations in particle distribution."
 Llowever spatial resolution is constrained: by he grid spacing., However spatial resolution is constrained by the grid spacing.
 A hwbrid. technique has been. developec incorporating PP and PAL schernes. unsurprisingly. referrec o as P°AL (Eastwood&Lockney1974).," A hybrid technique has been developed incorporating PP and PM schemes, unsurprisingly referred to as $^3$ M \cite{eh74}."
. TFhis technique ws been usefullv implement| for simulations of large-scale structure. where high density. contrasts are expectec (Efstathiou&Eastwood1981).. however when densities eet high the number of close neighbours. which are deal with bv the PP algorithm. beconies large and prohibitively engthen the computation time.," This technique has been usefully implemented for simulations of large-scale structure, where high density contrasts are expected \cite{ee81}, however when densities get high the number of close neighbours, which are dealt with by the PP algorithm, becomes large and prohibitively lengthen the computation time."
 Geometric constraints are also imposed. by the existence of the fixed. eric., Geometric constraints are also imposed by the existence of the fixed grid.
 Further refinement to the PM technicjue has been to introduce an adaptive grid. (APPL Couchman 1991. Couchman 1995).," Further refinement to the $^3$ M technique has been to introduce an adaptive grid $^3$ M, Couchman 1991, Couchman 1995)."
 Examples of further variants of the adaptive mesh technique are the adaptive ParticleMultiple.Mesh (PAIF) of Gelato. Chernoll. Wasserman (1996). and the ivdrodynamic ancl N-body unstructurecl adaptive mesh of Xu (1995).," Examples of further variants of the adaptive mesh technique are the adaptive Particle–Multiple–Mesh $^2$ ) of Gelato, Chernoff, Wasserman (1996), and the hydrodynamic and N-body unstructured adaptive mesh of Xu (1995)."
 For systems with a fairly high degree of svmimetry it is »ossible to represent the potentiul of the svstem as a series of erms in a multipole expansion àrout the centre of symmetry of the system., For systems with a fairly high degree of symmetry it is possible to represent the potential of the system as a series of terms in a multipole expansion about the centre of symmetry of the system.
 Various basis functions for the expansion 1e been emploved (CCTutton-DrockLOTS:vanAlbacla&Gorkom1977:MeCGlyan1984:|ernquist&Ostriker 1992). depending on the elobal geonretry of the system. being modelled.," Various basis functions for the expansion have been employed \cite{cb73,vv77,mg84,ho92}, depending on the global geometry of the system being modelled."
 Phe expansion is truncated at a specified. order. n. this governs the elfective resoution of the technique.," The expansion is truncated at a specified order, $n$, this governs the effective resolution of the technique."
 The ηΙαν advantage of this technique is that. computation ime scales as O(N). making Large No an attractive xossibilitv.," The primary advantage of this technique is that computation time scales as ${\cal O}(nN)$, making large $N$ an attractive possibility."
 Weinberg. (1996) has recently presented an advance on the expansion technique whereby the expansion xis and number of expansion terms are matched to the system its time-evolution-, Weinberg \shortcite{w96} has recently presented an advance on the expansion technique whereby the expansion basis and number of expansion terms are matched to the system its time-evolution.
 Phe main drawback is that expansion techniques do not consider individual particle-xwticle interactions and so loca| substructure is ostensivelv suppressed., The main drawback is that expansion techniques do not consider individual particle-particle interactions and so local substructure is ostensively suppressed.
 The SCE method of Llernquist Ostriker (1992) (hereafter HO). is particularly suited to the observed. mass distribution in ellipticals. we expand. upon this method in some moredetail in 82.," The SCF method of Hernquist Ostriker (1992) (hereafter HO), is particularly suited to the observed mass distribution in ellipticals, we expand upon this method in some moredetail in ."
2.. The advantages of the particle in a field. approach of expansion techniques and the geometrical Hlexibilitv of PP methods are combined. in. what are ecnerically described, The advantages of the particle in a field approach of expansion techniques and the geometrical flexibility of PP methods are combined in what are generically described
We first assess the optimal galaxy population to target for BAO measurements using a WEMOSlike instrument.,We first assess the optimal galaxy population to target for BAO measurements using a WFMOS–like instrument.
 This is achieved by studying the trade-olf between exposure time and areal coverage for the four galaxy classes considered., This is achieved by studying the trade-off between exposure time and areal coverage for the four galaxy classes considered.
" For the z=1 blue (emission-line) galaxies. we assume a ealaxy bias factor (relative to the underlying dark matter rower spectrum) of b=1.3. whilst for the 2=1 ""ped"" (passive) galaxies. we assume b—2."," For the $z=1$ “blue” (emission-line) galaxies, we assume a galaxy bias factor (relative to the underlying dark matter power spectrum) of $b=1.3$, whilst for the $z=1$ “red” (passive) galaxies, we assume $b=2$."
 We assume b=3 or both of the z=3 galaxy samples considered., We assume $b=3$ for both of the $z=3$ galaxy samples considered.
 We do not attempt to model the dependence of bias on redshift or uniinosityv., We do not attempt to model the dependence of bias on redshift or luminosity.
 We consider surveys where galaxies are observed at roth high and low redshifts. and the FoAL comes from the combination of the two redshift bins.," We consider surveys where galaxies are observed at both high and low redshifts, and the FoM comes from the combination of the two redshift bins."
" For this initial study we fix the two redshift regimes at O5<2.13 for “low redshift"" galaxies (2;,,,,=0.9 ancl dopa. 0.4) and 25«23.5 for ""high redshift"" galaxies (25745=3.0 and (dστι 0.5)."," For this initial study we fix the two redshift regimes at $0.5
< z < 1.3$ for “low redshift” galaxies $z_{low} =0.9$ and $dz_{low}=0.4$ ) and $2.5 < z < 3.5$ for “high redshift” galaxies $z_{high}=3.0$ and $dz_{high}=0.5$ )."
" We also fix the total time spent observing in each regime. 75,4= SOO hrs anc Thigh= τοῦ hrs."," We also fix the total time spent observing in each regime, $\tau_{low}=$ 800 hrs and $\tau_{high}=$ 700 hrs."
 We vary only the areas and exposure times for surveys based on these four galaxy classes., We vary only the areas and exposure times for surveys based on these four galaxy classes.
 Note that ifthe total survey time is fixed. then the exposure times and areas are linked through the number of repeat. pointings for cach field-of-view.," Note that if the total survey time is fixed, then the exposure times and areas are linked through the number of repeat pointings for each field-of-view."
 This parameter (ην) is selected by an algorithm that makes best use of the available number of fibres., This parameter $n_p$ ) is selected by an algorithm that makes best use of the available number of fibres.
 The results. of this study. are presented. in Table 7 where we list the optimal survey for cach of the four possible combinations of the four galaxy. classes considered. i0... (1) emission-line galaxies in. both the low anc high redshift regimes. (2) continuum (or passive) galaxies at low redshift and emission-line. galaxies at high redshift. (3) emission-line galaxies at low redshift and continuum galaxies at high redshift and (4) continuum galaxies at both redshifts.," The results of this study are presented in Table \ref{galaxytypetable}
 where we list the optimal survey for each of the four possible combinations of the four galaxy classes considered, i.e., (1) emission-line galaxies in both the low and high redshift regimes, (2) continuum (or passive) galaxies at low redshift and emission-line galaxies at high redshift, (3) emission-line galaxies at low redshift and continuum galaxies at high redshift and (4) continuum galaxies at both redshifts."
 We provide the optimal areas ancl exposure times in the table (with their Dlexibilitv bounds) as well as the overall PoM for the optimal survey., We provide the optimal areas and exposure times in the table (with their flexibility bounds) as well as the overall FoM for the optimal survey.
 The Figure-of-Merit as a function of galaxy tvpe. ancl area and exposure times for the low and high redshift bins. are plotted in Figure 3..," The Figure-of-Merit as a function of galaxy type, and area and exposure times for the low and high redshift bins, are plotted in Figure \ref{areatime}."
 The for the high redshift surveys implicitly. includes the best low-z component. and. vice versa.," The for the high redshift surveys implicitly includes the best low-z component, and vice versa."
" ‘Table 7 demonstrates that the z=1 ιο (emission- galaxy population does significantly better than the 2=1 cred? (passive) population. as he FoM for these ""blue? ealaxies (in case 1) is a [actor of 25 higher (than in case 2)."," Table \ref{galaxytypetable} demonstrates that the $z=1$ “blue” (emission-line) galaxy population does significantly better than the $z=1$ “red” (passive) population, as the FoM for these “blue” galaxies (in case 1) is a factor of 25 higher (than in case 2)."
" This corresponds to a factor of 25~5 improvement in the area of the error ellipse in the wy tw, parameter space.", This corresponds to a factor of $\sqrt{25} \simeq 5$ improvement in the area of the error ellipse in the $w_0$ $w_a$ parameter space.
 For circular error ellipses. this is a factor of 2:2.2 improvement in cach parameter.," For circular error ellipses, this is a factor of $\simeq 2.2$ improvement in each parameter."
 This advantage is due to the speed at which redshifts can be obtained for these >=] blue? galaxies (from the OLI] emission linc). which allows the survey to cover more area per unit time compared to targetting “red” galaxies (even though these red &alaxies have a higher bias factor).," This advantage is due to the speed at which redshifts can be obtained for these $z=1$ “blue” galaxies (from the [OII] emission line), which allows the survey to cover more area per unit time compared to targetting “red” galaxies (even though these red galaxies have a higher bias factor)."
 ‘Table 7 demonstrates that observing either line or continuum galaxies at high redshift does not improve the FoAL no matter what type of galaxies are observed at. low redshift.," Table \ref{galaxytypetable} demonstrates that observing either line or continuum galaxies at high redshift does not improve the FoM, no matter what type of galaxies are observed at low redshift."
 This manifests itself in the Hatness of the FoM plots for the high. redshift bin area and. exposure time in Figure 3.. and the corresponding width of the Dexibility bars.," This manifests itself in the flatness of the FoM plots for the high redshift bin area and exposure time in Figure \ref{areatime}, and the corresponding width of the flexibility bars."
 Phe inelfectiveness of the high-redshift: bin is due to the small energy density of the dark energy at this recdshift for our assumed Cosmological constant. [idducial model. and may change for more general dark energy moclels.," The ineffectiveness of the high-redshift bin is due to the small energy density of the dark energy at this redshift for our assumed cosmological constant fiducial model, and may change for more general dark energy models."
 In the previous subsection. we held. fixed ie limits of the two redshift regimes and the total time spent in each. whilst varving the area ancl exposure times of surveys for. the four different galaxy simples.," In the previous subsection, we held fixed the limits of the two redshift regimes and the total time spent in each, whilst varying the area and exposure times of surveys for the four different galaxy samples."
 Here. we address the issue of the optimal redshift range for constraining dark energy models by allowing the total times [τωνand. Τρ). the central recishift (2;). and width: (dz;). of the two redshift regimesto vary as free parameters in our ΑΟΧΙΟ search.," Here, we address the issue of the optimal redshift range for constraining dark energy models by allowing the total times $\tau_{low}$and $\tau_{high}$ ), the central redshift $z_i$ ), and width $dz_i$ ), of the two redshift regimesto vary as free parameters in our MCMC search."
 We still however impose the &elobal redshift constraints of O5<2.<L5 and 2.5<23.5 to ensure we obtain realistic survey configurations., We still however impose the global redshift constraints of $0.5<z<1.5$ and $2.5<z<3.5$ to ensure we obtain realistic survey configurations.
 The results of this search are presented in Figures 4 and 5.. as well as in Table δι. ," The results of this search are presented in Figures \ref{singlelowzbin} and \ref{twobins}, , as well as in Table \ref{binredshifttable}. ."
First. we consider a single “low," First, we consider a single “low"
In Bazot et al. (2005).,"In Bazot et al. \cite{bazot05}) ),"
 the effective temperatures anc lumimosities of the models were the first parameters usec for comparisons with the observations., the effective temperatures and luminosities of the models were the first parameters used for comparisons with the observations.
 We now prefer to compare the models with the spectroscopic observations in a more consistent way. by using the “triplets”Το. log e anc [Fe/H].," We now prefer to compare the models with the spectroscopic observations in a more consistent way, by using the “triplets”, log $g$ and [Fe/H]."
 These three parameters are indeed consistently giver be the same observers. while the luminosities are obtained i a different way. using Hipparcos parallaxes.," These three parameters are indeed consistently given be the same observers, while the luminosities are obtained in a different way, using Hipparcos parallaxes."
 Here we compare the luminosities as a second step., Here we compare the luminosities as a second step.
 For this reason. we do not use exactly the same set of references as given by Bazot et al. (2005)).," For this reason, we do not use exactly the same set of references as given by Bazot et al. \cite{bazot05}) ),"
 as we only keep those which give constraints on the surface gravity (see Table 1))., as we only keep those which give constraints on the surface gravity (see Table \ref{tab1}) ).
 The visual magnitude of µ Arae is V.=5.15 (SIMBAD Astronomical data base)., The visual magnitude of $\mu$ Arae is $V=5.15$ (SIMBAD Astronomical data base).
 Van Leeuwen (2007)) carried out a new analysis of the Hipparcos data., Van Leeuwen \cite{leeuwen07}) ) carried out a new analysis of the Hipparcos data.
 He derived a new value of the parallax of µ Arae: 7=64.48+0.31 mas. which is lower than the first one derived by Perryman et al. (1997))," He derived a new value of the parallax of $\mu$ Arae: $\pi = 64.48 \pm 0.31$ mas, which is lower than the first one derived by Perryman et al. \cite{perryman97}) )"
 and has a reduced error., and has a reduced error.
 Using this new value. we deduced an absolute magnitude of My=4.20+0.04.," Using this new value, we deduced an absolute magnitude of $M_{V}=4.20 \pm 0.04$."
 From Table 1.. we have an average value of effective temperature for uj Arae of = 5800 + 100 K. Using the tables of Flower (1996)). we obtained BC=—0.08+0.02 for the bolometric correction.," From Table \ref{tab1}, we have an average value of effective temperature for $\mu$ Arae of = 5800 $\pm$ 100 K. Using the tables of Flower \cite{flower96}) ), we obtained $BC=-0.08\pm0.02$ for the bolometric correction."
 With a solar absolute magnitude of My;=4.75 (Lejeune et al. 1998)).," With a solar absolute magnitude of $M_{bol,\odot}=4.75$ (Lejeune et al. \cite{lejeune98}) ),"
 we deduced for pe Arae a luminosity of log (L/L.))=0.25+0.03., we deduced for $\mu$ Arae a luminosity of log $=0.25\pm0.03$.
 This value is lower than the one derived by Bazot et al (2005)) in their analysis of this star. namely log (L/L..))20.28+0.0012.," This value is lower than the one derived by Bazot et al \cite{bazot05}) ) in their analysis of this star, namely log $=0.28\pm0.0012$."
 The star jt Arae was observed with the HARPS spectrograph. dedicated to the search for exoplanets by the means of precise radial velocity measurements.," The star $\mu$ Arae was observed with the HARPS spectrograph, dedicated to the search for exoplanets by the means of precise radial velocity measurements."
 HARPS ts installed on the ESO telescope at la Silla Observatory. Chile.," HARPS is installed on the 3.6m-ESO telescope at la Silla Observatory, Chile."
 These measurements led to the identification of 43 p-modes of degrees (= Oto £=3 with frequencies between 1.3 and 2.6 mHz (Bouchy et al. 2005))., These measurements led to the identification of 43 p-modes of degrees $\ell=0$ to $\ell=3$ with frequencies between 1.3 and 2.6 mHz (Bouchy et al. \cite{bouchy05}) ).
 The frequency resolution of the time-series was 1.56 Hz. and the uncertainty on the oscillation modes has been evaluated to 0.78 pHz.," The frequency resolution of the time-series was 1.56 $\mu$ Hz, and the uncertainty on the oscillation modes has been evaluated to 0.78 $\mu$ Hz."
 The mean large separation between two modes of consecutive order. computed in the observed range of frequencies. is Avo= 90 uHz. with an uncertainty of 1.1 p Hz.," The mean large separation between two modes of consecutive order, computed in the observed range of frequencies, is $\Delta\nu_0=$ 90 $\mu$ Hz, with an uncertainty of 1.1 $\mu$ Hz."
 The small separations present variations which are clearly. visible in the echelle diagram., The small separations present variations which are clearly visible in the echelle diagram.
 Their average value in the observedrange of frequencies is «ὃν >= 5.7 μΗΖ., Their average value in the observedrange of frequencies is $<\delta\nu>$ = 5.7 $\mu$ Hz.
 We computed evolutionary tracks with the TGEC code (Hui Bon Hoa 2008:: Richard et al. 1996)).," We computed evolutionary tracks with the TGEC code (Hui Bon Hoa \cite{hui08}; Richard et al. \cite{richard96}) ),"
 with the OPAL equations of state and opacities (Rogers Nayfonov 2002:: Iglesias Rogers 1996)) and the NACRE nuclear reaction rates (Angulo et al. 1999))., with the OPAL equations of state and opacities (Rogers Nayfonov \cite{rogers02}; Iglesias Rogers \cite{iglesias96}) ) and the NACRE nuclear reaction rates (Angulo et al. \cite{angulo99}) ).
 For all models. the microscopic diffusion was included as in. Paquette et al. (1986))," For all models, the microscopic diffusion was included as in Paquette et al. \cite{paquette86}) )"
 and Michaud et al. (2004)., and Michaud et al. \cite{michaud04}) ).
 The treatment of the convection 1s done in the framework of the mixing length theory and the mixing length parameter is adjusted as in the Sun: a=1.8 (Richard et al. 2004))., The treatment of the convection is done in the framework of the mixing length theory and the mixing length parameter is adjusted as in the Sun: $\alpha=1.8$ (Richard et al. \cite{richard04}) ).
 We also computed cases with a=1.7 and e=1.9 to test the corresponding uncertainties., We also computed cases with $\alpha=1.7$ and $\alpha=1.9$ to test the corresponding uncertainties.
 We found that for 1.10 and «=1.7. the track is very close to that of 1.12 and a=1.8.," We found that for 1.10 and $\alpha=1.7$, the track is very close to that of 1.12 and $\alpha=1.8$."
 On the other side. the 1.10 and a=1.9 track is close to the 1.08 and a=1.8 one.," On the other side, the 1.10 and $\alpha=1.9$ track is close to the 1.08 and $\alpha=1.8$ one."
 This was taken into account in the determination of the uncertainties on the final results (Sect., This was taken into account in the determination of the uncertainties on the final results (Sect.
 5)., 5).
 From the literature. we found two values for the metallicity of it Arae: [Fe/H|20.29 (Laws et al. 2003.. ," From the literature, we found two values for the metallicity of $\mu$ Arae: [Fe/H]=0.29 (Laws et al. \cite{laws03}, ,"
Fischer Valenti 2005)) and |Fe/H|20.32 (Bensby et al. 2003..," Fischer Valenti \cite{fischer05}) ) and [Fe/H]=0.32 (Bensby et al. \cite{bensby03},"
 Santos et al., Santos et al.
 2004a and 2004b)., \cite{santos04a} and \cite{santos04b}) ).
 For each value of [Fe/H]. we first computed two series of evolutionary tracks for two different values of the helium abundance: The results obtained in the log g - log and log (L/L..)) - planes are displayed in Fig.1..," For each value of [Fe/H], we first computed two series of evolutionary tracks for two different values of the helium abundance: The results obtained in the log $g$ - log and log ) - planes are displayed in \ref{fig1}."
 Each graph corresponds to one value of the metallicity., Each graph corresponds to one value of the metallicity.
 On each graph. the five error boxes are plotted. but those that correspond to the same value of [Fe/H] as given by the groups of observers are drawn in thicker lines.," On each graph, the five error boxes are plotted, but those that correspond to the same value of [Fe/H] as given by the groups of observers are drawn in thicker lines."
 We then computed two similar series including overshooting at the edge of the convective core., We then computed two similar series including overshooting at the edge of the convective core.
 Here overshooting is simply described as an extension of the convective core by a length Hp. where is the overshooting parameter. and Hp the pressure scale height.," Here overshooting is simply described as an extension of the convective core by a length $_P$, where is the overshooting parameter, and $_P$ the pressure scale height."
 In these two series. the overshooting parameter is fixed at = 0.2 (Fig. 6)).," In these two series, the overshooting parameter is fixed at = 0.2 (Fig. \ref{fig6}) )."
 Finally. we tested more precisely the seismic. constraints. on overshooting by varying in small steps between 0.0 and 0.2 for models of masses 1.1 (Fig. 7)).," Finally, we tested more precisely the seismic constraints on overshooting by varying in small steps between 0.0 and 0.2 for models of masses 1.1 (Fig. \ref{fig7}) )."
 We computed the adiabatic oscillation frequencies for a large number of models along each evolutionary track with the PULSE code (Brassard Charpinet 2008))., We computed the adiabatic oscillation frequencies for a large number of models along each evolutionary track with the PULSE code (Brassard Charpinet \cite{brassard08}) ).
 These frequencies were computed for degrees (=0 to £23. and for radial orders typically ranging from 4 to 100.," These frequencies were computed for degrees $\ell=0$ to $\ell=3$, and for radial orders typically ranging from 4 to 100."
 For each track. we selected the model that has a mean large separation of 90 μΗΖ. computed in the same frequency range as the observed one.," For each track, we selected the model that has a mean large separation of 90 $\mu$ Hz, computed in the same frequency range as the observed one."
 We plotted on each graph (Fig. 1)), We plotted on each graph (Fig. \ref{fig1}) )
 the corresponding 1s0-Avo 90 uHz line., the corresponding $\Delta\nu_0$ 90$\mu$ Hz line.
 The parameters of these models are given in Tables 2. to 5.., The parameters of these models are given in Tables \ref{tab2} to \ref{tab5}. .
 We can check that all the models that fit the same large separation, We can check that all the models that fit the same large separation
5ulace photometry was extracted from the ellipse fitting using the standard tecliniques outliued in Schombert (2007).,Surface photometry was extracted from the ellipse fitting using the standard techniques outlined in Schombert (2007).
 Due to their typically irregular morphology. LSB galaxies are notoriously ciffieut to simplify into a 1D light proile.," Due to their typically irregular morphology, LSB galaxies are notoriously difficult to simplify into a 1D light profile."
 The procedure used herein is to couvert the best fit ellidses into a surface brightuess profile of intensity versus semi-major axis., The procedure used herein is to convert the best fit ellipses into a surface brightness profile of intensity versus semi-major axis.
 A section of the πιr[ace rightless proile is selected in the outer 'egions of the galaxy with the most linear appearance., A section of the surface brightness profile is selected in the outer regions of the galaxy with the most linear appearance.
 This 'eelon is then il ο a stralght liue. iuterpolating to the core to extract the central surface briel{less (Ho ) ixl expoellial scale leneth (a).," This region is then fit to a straight line, interpolating to the core to extract the central surface brightness $\mu_o$ ) and exponential scale length $\alpha$ )."
" Athough the interiors of LSB galaxies are frequently poorly i ""v all expoellial prolie. the exteriο! peglous are ofteu easily described by au expouentia law."," Although the interiors of LSB galaxies are frequently poorly fit by an exponential profile, the exterior regions are often easily described by an exponential law."
 Tis is surprising glven ueir irregular outer isophotes aud is probably due to the fact tha ally je1 surface b‘igl[n](ness [uiips are restricted to their core regions., This is surprising given their irregular outer isophotes and is probably due to the fact that any high surface brightness lumps are restricted to their core regions.
 A series of exaiuple surface brieluess fits are found in Figure 3., A series of example surface brightness fits are found in Figure 3.
 These profiles are a 5tbset ‘the total sauple demoustrating good aud poor (e.g.. F561-1) fits. as well as examples where t1 exponential Tm lay no be appropjate.," These profiles are a subset of the total sample demonstrating good and poor (e.g., F561-1) fits, as well as examples where an exponential fit may not be appropriate."
 The ful set of surface brightness fits cau be fouxl αἱ w data website., The full set of surface brightness fits can be found at our data website.
 As can ye seen [rom several of tle surface brightness fits. te. fitting technique can lead to a iuisuatch beween the central surface wightness as described by a lit to the galaxys outer regions. versls a cellral surface brightuess tha actually represents the Iuuinosity of tlie core regions.," As can be seen from several of the surface brightness fits, the fitting technique can lead to a mismatch between the central surface brightness as described by a fit to the galaxy's outer regions, versus a central surface brightness that actually represents the luminosity of the core regions."
" To fix l ΒΡΕch. the inner five aresecs are also fit to extract a rue ceutral surface bdehtuess (wh1 we will ¢esiguate as fre to distiugiish it [rom yr, [rom exponential fits) except iu uses where the‘e is a clear blee-like central regioi (e.g.. F571-1)."," To fix this mismatch, the inner five arcsecs are also fit to extract a true central surface brightness (which we will designate as $\mu_c$ to distinguish it from $\mu_o$ from exponential fits) except in cases where there is a clear bulge-like central region (e.g., F574-1)."
 No inclinalon corrections are yplied to fr siice the int‘Tusic 3D shaye of LSB galaxies is unknown (some are rotators. others ‘e pot. so a thin or thick disk correctio1i would vary [rom galaxy to galaxy).," No inclination corrections are applied to $\mu_o$ since the intrinsic 3D shape of LSB galaxies is unknown (some are rotators, others are not, so a thin or thick disk correction would vary from galaxy to galaxy)."
 The rauge of size ane ceural surfice. brightness is shown tn Figure L, The range of size and central surface brightness is shown in Figure 4.
 Here size (1095) is elined by the 25. V hag 1 lsopi0te tnajor axis in kpes., Here size $R_{V25}$ ) is defined by the 25 $V$ mag $^{-1}$ isophote major axis in kpcs.
 Central strlace brightness is the ---mer interpolation to zero raclius (ii the case of a bulge aud disk. interpolation of the disk).," Central surface brightness is the inner interpolation to zero radius (in the case of a bulge and disk, interpolation of the disk)."
 Sizes ange from 0.3 kpe to 10 kpe., Sizes range from 0.3 kpc to 10 kpc.
 LSB gaaxles iiclude both the smallest of dwarf galaxies up to --jecliuui sized disk galaxies., LSB galaxies include both the smallest of dwarf galaxies up to medium sized disk galaxies.
" TI οσοιral surface xiehtuesses are all [ainter than the Freeman value (21m Vr mag D? 7). hi| do not include the exremely faint surface brightjesses (nt> 23 10 21 --laes > ~) DouudJ i"" recent digital strTveys (Zhone 2008. Aclami 2006). primarily ue to the limitations in the photographic mediun used to discover tle saliple."," The central surface brightnesses are all fainter than the Freeman value (21 $V$ mag $^{-2}$ ), but do not include the extremely faint surface brightnesses $mu_o >$ 23 to 24 mags $^{-2}$ ) found in recent digital surveys (Zhong 2008, Adami 2006), primarily due to the limitations in the photographic medium used to discover the sample."
 To further display t1e range in size and morphology. Figures 5 ane 6 clisplay a greyscale image ol selected. galaxies (stars removed) witli 'espec to their central surface briglituess aud disk scale leneth.," To further display the range in size and morphology, Figures 5 and 6 display a greyscale image of selected galaxies (stars removed) with respect to their central surface brightness and disk scale length."
 Irregular morphoogy is most common at sinall scale leneths. athough it would be difficult to predict which galaxies were cdwarls siiiply from au estimate base Ol their appearance.," Irregular morphology is most common at small scale lengths, although it would be difficult to predict which galaxies were dwarfs simply from an estimate based on their appearance."
 LSB ealaxies with smooth uxxphlologies wouk probably be dE’s aud their lack of HI gas for redshift determination would exclude them (rom our samples., LSB galaxies with smooth morphologies would probably be dE's and their lack of HI gas for redshift determination would exclude them from our samples.
 Flocculate spiral j»alterus are evident at scale leneths greater thau 1 kpc (uote. UGC 128 is a HSB counter-example).," Flocculate spiral patterns are evident at scale lengths greater than 1 kpc (note, UGC 128 is a HSB counter-example)."
We would like to thank Telescope System Specialist Jim Ποσο as well as the entire supporting team of the James Clerk Maxwell Telescope for conducting a superb set of measurements on March 15th 2009 that made this work possible.,We would like to thank Telescope System Specialist Jim Hoge as well as the entire supporting team of the James Clerk Maxwell Telescope for conducting a superb set of measurements on March 15th 2009 that made this work possible.
 Moreover we would like to thank Dr Satoki Matsushita lor informing us about some issues with the SMA data. and Dr Loretta Dunne for discussions regarding SCUDA calibration issues.," Moreover we would like to thank Dr Satoki Matsushita for informing us about some issues with the SMA data, and Dr Loretta Dunne for discussions regarding SCUBA calibration issues."
 PPP would like to thank Dr Xilouris of the National Observatory of Athens for helpful discussions. and assistance with eatherimeg/plotüng literature data.," PPP would like to thank Dr Xilouris of the National Observatory of Athens for helpful discussions, and assistance with gathering/plotting literature data."
 Finally we would like to thank the anonvimous referee for his/hers pointed ancl clear suggestions that led to critical improvements of the original nianuscript., Finally we would like to thank the anonymous referee for his/hers pointed and clear suggestions that led to critical improvements of the original manuscript.
 lecent results from Herschel Space Observatory suggest a CO J=65 line-integrated flix 2-2.5 times higher than that measured by the JCAIT and the SALA., Recent results from Herschel Space Observatory suggest a CO J=6–5 line-integrated flux 2-2.5 times higher than that measured by the JCMT and the SMA.
 Pending solution of various calibration issues with the Ilerschel FTS instrument. we note that such values still leave our main conclusions intact (section 3.1)," Pending solution of various calibration issues with the Herschel FTS instrument, we note that such values still leave our main conclusions intact (section 3.1)"
igh intensity (Bieberοἱal.2002:Falcone&Rvan1999:SwinsonShea1990).. as well as the enhancement of muons al ground level from solar flares of large scale has been reported (Poirier&D'Andrea2002:Απιπακαίαοἱal.2001).,"high intensity \citep{bieber02,falcone99,swinson90}, as well as the enhancement of muons at ground level from solar flares of large scale has been reported \citep{poirier02,munakata01}."
. However. the enhancement of muons ad eround trom GRBs remains open. at least thev have not been observed with hieh confidence evel.," However, the enhancement of muons at ground from GRBs remains open, at least they have not been observed with high confidence level."
 The Milagrito experiment. a predecessor of the (water Cherenkov) Milagro experiment. ws reported evidence for the TeV counterpart of a DATSE GRB (970417) 2000).," The Milagrito experiment, a predecessor of the (water Cherenkov) Milagro experiment, has reported evidence for the TeV counterpart of a BATSE GRB (970417) \citep{atkins00}."
. The GRAND project (muon detectors array at ground. level) has reported some evidence of GRB detections in coincidence with one BATSE GRB (971110) 2).. even if with a low significance.," The GRAND project (muon detectors array at ground level) has reported some evidence of GRB detections in coincidence with one BATSE GRB (971110) \citep{poirier03}, even if with a low significance."
 Besides the experimental evidence. several models for the origin of GRBs predict a Τον component (Totani1996;Dermerοἱal.2000;Pillaet1998).," Besides the experimental evidence, several models for the origin of GRBs predict a TeV component \citep{totani99,dermer00,pilla98}."
.. A plausible explanation for the extremely low rate of events observed in the TeV region is to invoke the attenuation of TeV photons by interaction with the intergalactic infrared radiation., A plausible explanation for the extremely low rate of events observed in the TeV region is to invoke the attenuation of TeV photons by interaction with the intergalactic infrared radiation.
 This process would be responsible for a cut off for TeV GRBs whose sources are at distances larger (han z~0.3., This process would be responsible for a cut off for TeV GRBs whose sources are at distances larger than $z \sim 0.3$.
" llowever. for GRBs with E,>20 GeV. the cut off can be shifted to z~2."," However, for GRBs with $E_{\gamma}> 20$ GeV, the cut off can be shifted to $z\sim 2$."
 Consequently. in order (o increase the GRBs rate detected αἱ ground level a search for GRBs in a energy region above ~20 GeV has to be undertaken.," Consequently, in order to increase the GRBs rate detected at ground level a search for GRBs in a energy region above $\sim 20$ GeV has to be undertaken."
 A primary photon converts to ane¢ pair alter 1 radiation length (on average). in the atmosphere.," A primary photon converts to an $e^+e^-$ pair after 1 radiation length (on average), $\lambda_R\sim 37\;g/cm^2$ in the atmosphere."
 In a subsequent radiation length the electromagnetic particles further lose enerey by bremsstralling e=—5e-., In a subsequent radiation length the electromagnetic particles further lose energy by bremsstrahlung $e^{\pm}\rightarrow \gamma e^{\pm}$.
 The processes are repeated forming an electromagnetic air shower., The processes are repeated forming an electromagnetic air shower.
 All shower gamma ravs (including (he primary) above the ¢ross section can contribute to the muon content in the shower., All shower gamma rays (including the primary) above the photo-production cross section can contribute to the muon content in the shower.
 Despite the fact (hat gamma-ravs in the enerev band of 30 GeV to several TeV have only a to chance of undergoing interactions in the atmosphere vielding pions. the photons are more efficient at producing energetic. forward directed pions.," Despite the fact that gamma-rays in the energy band of 30 GeV to several TeV have only a to chance of undergoing interactions in the atmosphere yielding pions, the photons are more efficient at producing energetic, forward directed pions."
 The result comes from the distribution of charged pions obtained by using the FLUKA Monte Carlo simulation 2000).., The result comes from the Feynman-x distribution of charged pions obtained by using the FLUKA Monte Carlo simulation \citep{fasso01}.
 The 45—Avr interaction has a large fraction on hieh-x secondaries (pious) than p—Vr interaction., The $\gamma-Air$ interaction has a large fraction on high-x secondaries (pions) than $p-Air$ interaction.
 The ΕΠΙΝΑ results also show that the distribution of height above sea level al which the detected muons are produced has a peak at ~20hun for proton showers (Datistoneetal.1998) and ~12fin Lor photon showers (Poirieretal.2001)., The FLUKA results also show that the distribution of height above sea level at which the detected muons are produced has a peak at $\sim 20\;km$ for proton showers \citep{batistone98} and $\sim 12\;km$ for photon showers \citep{poirier01}.
. In addition the distribution of the generation number of the grandparent of the sea level muon in gamma showers is a verv narrow distribution aud is peaked al generation one lor energies below a few hundred where the parent is mainly produced in a photo-production process of (he primary photon., In addition the distribution of the generation number of the grandparent of the sea level muon in gamma showers is a very narrow distribution and is peaked at generation one for energies below a few hundred where the parent is mainly produced in a photo-production process of the primary photon.
" This means that"" photo-muons have a good chance of reaching eround level."," This means that ""photo-muons"" have a good chance of reaching ground level."
 In order to estimate the number of muons reaching detection level which are initiated by, In order to estimate the number of muons reaching detection level which are initiated by
acceleration since. according to eq.(3)). this changes the turbulence (hus improving particle confinement near (he shock [ront ancl thus making acceleration faster (smaller &)).,"acceleration since, according to \ref{delB}) ), this changes the turbulence thus improving particle confinement near the shock front and thus making acceleration faster (smaller )."
 llowever. the formation of a long CR precursor (ii which the upstream flow is gradually decelerated bv the pressure of CRs.£.)) influences the of the turbulence bv affecting the propagation and excitation of the Alfven waves.," However, the formation of a long CR precursor (in which the upstream flow is gradually decelerated by the pressure of CRs, ) influences the of the turbulence by affecting the propagation and excitation of the Alfven waves."
 This effect is twolold., This effect is twofold.
 First the waves are compressed in the converging plasma flow upstream and are thus blue-shifted. eliminating the long waves needed to keep exactly the highest energy. particles dillusively bound to the accelerator.," First the waves are compressed in the converging plasma flow upstream and are thus blue-shifted, eliminating the long waves needed to keep exactly the highest energy particles diffusively bound to the accelerator."
 Second. and as a result of the first. at highest energies (here remain fewer particles than expected so that the level of resonant waves is smaller ancl hence the acceleration rate is lower.," Second, and as a result of the first, at highest energies there remain fewer particles than expected so that the level of resonant waves is smaller and hence the acceleration rate is lower."
 We believe that these effects have been largely overlooked before which max have substantially overestimated the particle maximum energy in stronely nonlinear regimes., We believe that these effects have been largely overlooked before which may have substantially overestimated the particle maximum energy in strongly nonlinear regimes.
 We use the standard diffusion-convection equation for describing (he transport of hieh enerev particles (CRs) near a CR modified shock., We use the standard diffusion-convection equation for describing the transport of high energy particles (CRs) near a CR modified shock.
 First. we normalize the distribution function f(p) to p?dp:: llere wv is directed. along the shock normal which for simplicity is assumed to be the direction of the ambient magnetic field.," First, we normalize the distribution function f(p) to dp: Here x is directed along the shock normal which for simplicity is assumed to be the direction of the ambient magnetic field."
 The (wo quantities that control the acceleration process are the flow profile C(.r) and (he particle diffusivity aCe.p).," The two quantities that control the acceleration process are the flow profile U(x) and the particle diffusivity (x,p)."
. The fist one is coupled to the particle distribution f through the equations of mass and momentum conservation where, The first one is coupled to the particle distribution f through the equations of mass and momentum conservation where
similar order could be expected.,similar order could be expected.
 The correction is in the sense of reducing the LDB ages by19-1354... with the larger impact occuring al the low Iuminositv/old age end.," The correction is in the sense of reducing the LDB ages by, with the larger impact occuring at the low luminosity/old age end."
 Alternatively. the (V-I) colors of the isochrones ean be reconciled with the observations by a reduction of Tell~150 Ix in the isochrones (hemselves.," Alternatively, the (V-I) colors of the isochrones can be reconciled with the observations by a reduction of $\sim$ 150 K in the isochrones themselves."
 Reclucing the effective temperatures of (he reference calculation by 150 Ix results in a age reduction for the oldest clusters decreasing (o a age reduction for the voungest clusters., Reducing the effective temperatures of the reference calculation by 150 K results in a age reduction for the oldest clusters decreasing to a age reduction for the youngest clusters.
 The reduction in LDD ages is for the bolometric correction only and is independent of the effect (he cooler temperatures would have on the theoretical LDB ages., The reduction in LDB ages is for the bolometric correction only and is independent of the effect the cooler temperatures would have on the theoretical LDB ages.
 For a simple analvtical l-o error in the LDB ages resulüing [rom uncertainties in the bolometric correction. we adopt a constant error of lor log( L/L.. )2»-2.6 and increasing linearly to at log(L/L.. )—-3.0.," For a simple analytical $\sigma$ error in the LDB ages resulting from uncertainties in the bolometric correction, we adopt a constant error of for $\log$ $_{\odot}$ $>$ -2.6 and increasing linearly to at $\log$ $_{\odot}$ )=-3.0."
 The column labeled oy in Table 1. gives the l-o error in the reference LDB ages as a funetion of luminosity., The column labeled $\sigma_{BC}$ in Table \ref{reftab} gives the $\sigma$ error in the reference LDB ages as a function of luminosity.
 The last column in Table 1. gives the absolute I-band magnitude of the LDB using the bolometric corrections of Hauschildt.Baron (1999)., The last column in Table \ref{reftab} gives the absolute I-band magnitude of the LDB using the bolometric corrections of \citet{hau99}.
. We adopt Mi. —4.74 and reduce the bolometric correction by 0.04 magnitudes to account for the systematically lower gravitv at lithium depletion.," We adopt $M_{bol\, \odot}$ =4.74 and reduce the bolometric correction by 0.04 magnitudes to account for the systematically lower gravity at lithium depletion."
 In conclusion. we employ our error models for the theoretical aud bolometric correction uncertainties to reclerive LDB ages and errors for the four clusters will previous LDD age determinations (Vleiacles - Stauffer.Schultz.&Wirkpatrick(1998): a Per - Staufferetal.(1999): IC. 2391 - DarradoνNavasceués.Stauffer.&Patten(1999): NGC 2597 - Oliveiraetal. (2003))).," In conclusion, we employ our error models for the theoretical and bolometric correction uncertainties to rederive LDB ages and errors for the four clusters with previous LDB age determinations (Pleiades - \citet{sta98}; $\alpha$ Per - \citet{sta99}; IC 2391 - \citet{bar99}; NGC 2597 - \citet{oli03}) )."
 We adopt the same apparent I magnitude of tbe LDL. distance modulus. aud reddening as in the original study.," We adopt the same apparent I magnitude of the LDB, distance modulus, and reddening as in the original study."
 Table 2. repeats the observational parameters. along with their adopted. errors.," Table \ref{obstab} repeats the observational parameters, along with their adopted errors."
 We combine (he observational errors of the LDB location. reddening. aud absolute distance modulus in quadrature to derive (he error in the absolute I magnitude of the LDB.," We combine the observational errors of the LDB location, reddening, and absolute distance modulus in quadrature to derive the error in the absolute I magnitude of the LDB."
 The observational error along with the observed LDB luminosity lor each cluster is shown as the labeled crosses in Figure δ., The observational error along with the observed LDB luminosity for each cluster is shown as the labeled crosses in Figure \ref{errfig}.
", We then caleulate the LDB age and errors that result [rom observational. theoretical. and bolometric correction uncertainties using our reference calculation and error moclels."," We then calculate the LDB age and errors that result from observational, theoretical, and bolometric correction uncertainties using our reference calculation and error models."
 The total percentage age error is a sum in euadrature of these (hree error sources., The total percentage age error is a sum in quadrature of these three error sources.
 We derive a LDD age of 148 + 19 Myr lor the Pleiades open cluster., We derive a LDB age of 148 $\pm$ 19 Myr for the Pleiades open cluster.
 Thus. the LDD age technique rules out ages vounger than 91 Myr.," Thus, the LDB age technique rules out ages younger than 91 Myr."
 For the Pleiades. the difference in the LDB age and the upper main-secquence-fitng age without convective-core overshoot (70-80 Myr - (1981))) is highly significant.," For the Pleiades, the difference in the LDB age and the upper main-sequence-fitting age without convective-core overshoot (70-80 Myr - \citet{mer81}) ) is highly significant."
 Even a maximally plausible 0.30 magnitude change in the bolometrie correction (consistent with reconciling the theoretical isochrone fits to the, Even a maximally plausible 0.30 magnitude change in the I-band bolometric correction (consistent with reconciling the theoretical isochrone fits to the
measurements support the conclusion of Bouwens et al. (,measurements support the conclusion of Bouwens et al. (
2009) that Lyman break galaxies are bluer at ο=56 than at. =4. with £25 having moved from 69)=15d:0.15 ats =d to jj—240.20 (see our Fig.,"2009) that Lyman break galaxies are bluer at $z \simeq 5-6$ than at $z \simeq 4$ , with $\langle \beta \rangle$ having moved from $\langle \beta \rangle = -1.5 \pm 0.15$ at $z \simeq 4$ to $\langle \beta \rangle = -2 \pm 0.20$ (see our Fig."
 6 and the values given in Table 4 of Bouwens et al., 6 and the values given in Table 4 of Bouwens et al.
 2009)., 2009).
 There is thus no serious doubt that the brighter Lyman break galaxies have become significantly bluer with increasing redshift. and the idea that this change is primarily due to decreasing dust content gains support from the very low (generally. negligible) values of εν inferred from the best-fitting SED models at >>>6.5 deduced by MeLure et al. (," There is thus no serious doubt that the brighter Lyman break galaxies have become significantly bluer with increasing redshift, and the idea that this change is primarily due to decreasing dust content gains support from the very low (generally negligible) values of $A_V$ inferred from the best-fitting SED models at $z > 6.5$ deduced by McLure et al. ("
2011).,2011).
 Therefore the key question now is whether the οAr relation essentially plateaus at. 2— at 2<>5 due to the near absence of dust at all luminosities. or whether there is indeed evidence for a continuing dependence of 100 Mi. albeit perhaps with a different slope.," Therefore the key question now is whether the $\beta - M_{UV}$ relation essentially plateaus at $\beta \simeq -2$ at $z > 5$ due to the near absence of dust at all luminosities, or whether there is indeed evidence for a continuing dependence of $\beta$ on $M_{UV}$, albeit perhaps with a different slope."
 Our own results. as shown in Fig.," Our own results, as shown in Fig."
 6. support the former scenario. but as already discussed. our analysis also emphasizes the vital importance of deeper WFC3/IR data to establish the true values ofthe typical UV slopes of the very faintest galaxies at 2—7.," 6, support the former scenario, but as already discussed, our analysis also emphasizes the vital importance of deeper WFC3/IR data to establish the true values of the typical UV slopes of the very faintest galaxies at $z \simeq 7$."
 We have undertaken a critical study of the evidence for extremely blue UV continuum slopes in the highest redshift galaxies. focussing on the robust determination of the UV power-law index jJ (where fxA Y.," We have undertaken a critical study of the evidence for extremely blue UV continuum slopes in the highest redshift galaxies, focussing on the robust determination of the UV power-law index $\beta$ (where $f_{\lambda} \propto \lambda^{\beta}$ )."
 Our analysis is based on three new WFC3/IR-selected samples of galaxies spanning nearly two decades in UV luminosity over the redshift range >24.5.5 (MeLure et al., Our analysis is based on three new WFC3/IR-selected samples of galaxies spanning nearly two decades in UV luminosity over the redshift range $z \simeq 4.5-8$ (McLure et al.
 2011)., 2011).
 We have explored the impact of inclusion/exclusion of less robust high-redshift candidates. and have used the varying depths of the samples to explore the effects of noise and selection bias ata given UV luminosity.," We have explored the impact of inclusion/exclusion of less robust high-redshift candidates, and have used the varying depths of the samples to explore the effects of noise and selection bias at a given UV luminosity."
 Simple data-consistency arguments indicate that artificially blue average values of 7 can result when the analysis is extended into the deepest  0.5-magnitude bin ofthese WFC3/IR- galaxy samples. regardless of the actual luminosity or redshift range probed.," Simple data-consistency arguments indicate that artificially blue average values of $\beta$ can result when the analysis is extended into the deepest $\simeq 0.5$ -magnitude bin of these WFC3/IR-selected galaxy samples, regardless of the actual luminosity or redshift range probed."
 By contining attention to robust. high-redshift galaxy candidates. with at least one ὃ-σ detection in theWFC3/IR imaging. we find that the average value of «7 is consistent with £o;=2.05+0.10 over the redshift range 2=5T. and the UV absolute magnitude range 22«Mirage15. and that £25 shows no significant trend with either redshift or Mii.," By confining attention to robust high-redshift galaxy candidates, with at least one $\sigma$ detection in theWFC3/IR imaging, we find that the average value of $\beta$ is consistent with $\langle \beta \rangle = -2.05 \pm 0.10$ over the redshift range $z = 5-7$, and the UV absolute magnitude range $-22 < M_{UV,AB} < -18$, and that $\langle \beta \rangle$ shows no significant trend with either redshift or $M_{UV}$."
" We have created and analysed a set of simple end-to-end simulations based on the WPC3/IR+ACS HUDF and ERS datasets which demonstrate that a bias towards artifically low/blue average values of «7 is indeed ""expected"" when the UV slope analysis is extended towards the source detection threshold. and conclude that there is as yet no clear evidence for UV slopes signiticantly bluer than.=2. the typical value displayed by the bluest star-forming galaxies at more modest redshifts (e.g. NGCI705: 2= 2.15)"," We have created and analysed a set of simple end-to-end simulations based on the WFC3/IR+ACS HUDF and ERS datasets which demonstrate that a bias towards artifically low/blue average values of $\beta$ is indeed “expected” when the UV slope analysis is extended towards the source detection threshold, and conclude that there is as yet no clear evidence for UV slopes significantly bluer than $\beta \simeq -2$, the typical value displayed by the bluest star-forming galaxies at more modest redshifts (e.g. NGC1705; $\beta = -2.15$ )."
 A robust measurement of (7) for the faintest galaxies at 2—7 (and indeed >& 5) remains a key observational goal. as it provides a fundamental test for high escape fractions from a potentially abundant source of reionizing photons.," A robust measurement of $\langle \beta \rangle$ for the faintest galaxies at $z \simeq 7$ (and indeed $z \simeq 8$ ) remains a key observational goal, as it provides a fundamental test for high escape fractions from a potentially abundant source of reionizing photons."
 This goal is achievable withAST. but requires still deeper WFC3/IR imaging in the HUDF.," This goal is achievable with, but requires still deeper WFC3/IR imaging in the HUDF."
 We note. however. that. due to degeneracies between escape fraction and metallicity. it may prove hard to establish robust evidence for a high escape fraction from the measurement of 7 extreme values of 15—3 are indeed confirmed for faint galaxies at 2>7 (in which case both low metallicity a high escape fraction are required).," We note, however, that, due to degeneracies between escape fraction and metallicity, it may prove hard to establish robust evidence for a high escape fraction from the measurement of $\beta$ extreme values of $\beta = -3$ are indeed confirmed for faint galaxies at $z > 7$ (in which case both low metallicity a high escape fraction are required)."
 JSD acknowledges the support of the Royal Society via à Wolfson Research Merit award. and also the support of the European Research Council via the award of an Advanced Grant.," JSD acknowledges the support of the Royal Society via a Wolfson Research Merit award, and also the support of the European Research Council via the award of an Advanced Grant."
 RIM acknowledges the support of the Royal Society via a University Research Fellowship., RJM acknowledges the support of the Royal Society via a University Research Fellowship.
 BER is supported by a Hubble Fellowship grant. program number HST-HF-51262.01-A. provided by NASA from the Space Telescope Science Institute. which is operated by which is operated by the Association of Universities for Research in Astronomy. Inc. under NASA contract NAS5-26555.," BER is supported by a Hubble Fellowship grant, program number HST-HF-51262.01-A, provided by NASA from the Space Telescope Science Institute, which is operated by which is operated by the Association of Universities for Research in Astronomy, Inc, under NASA contract NAS5-26555."
 DPS. MC and LdR acknowledge the support of the UK Science Technology Facilities Council via the award of a Post-Doctoral Fellowship. an Advanced Fellowship. and a Post-Doctoral Research Associate position respectively.," DPS, MC and LdR acknowledge the support of the UK Science Technology Facilities Council via the award of a Post-Doctoral Fellowship, an Advanced Fellowship, and a Post-Doctoral Research Associate position respectively."
 This work is based in part on observations made with the NASA/ESATelescope. which is operated by the Association of Universitiesfor Research in Astronomy. Inc. under NASA contract NAS5-26555.," This work is based in part on observations made with the NASA/ESA, which is operated by the Association of Universitiesfor Research in Astronomy, Inc, under NASA contract NAS5-26555."
 This work is also based in part on observations made with the Telescope. which is operated by the Jet Propulsion Laboratory. California Institute of Technology under NASA contraet 1407.," This work is also based in part on observations made with the , which is operated by the Jet Propulsion Laboratory, California Institute of Technology under NASA contract 1407."
"age of about 0.2 Myr, confirming that EC 95 is a precursor of an intermediate mass star.","age of about 0.2 Myr, confirming that EC 95 is a precursor of an intermediate mass star."
" In spite of their large uncertainties, the dynamical mass estimates given above are also consistent with that suggestion."," In spite of their large uncertainties, the dynamical mass estimates given above are also consistent with that suggestion."
 Our observations further show that EC 95 is a binary system where the primary is significantly more massive than the secondary., Our observations further show that EC 95 is a binary system where the primary is significantly more massive than the secondary.
" As a consequence, we idenuly the proto-Herbig AeBe star with EC 95a, and argue that EC 95b must be a low-mass T Tauri companion."," As a consequence, we identify the proto-Herbig AeBe star with EC 95a, and argue that EC 95b must be a low-mass T Tauri companion."
" [tis clear that in such à situation, both the bolometric luminosity and the spectral type of the system will be almost enürely dominated by the more massive component."," It is clear that in such a situation, both the bolometric luminosity and the spectral type of the system will be almost entirely dominated by the more massive component."
" We should point out, also, that another young star (EC 92), located about 5"" (— 2000 AU) to the north of EC 95, has been argued to be gravilauonally bound to it HHaisch et 22002)."," We should point out, also, that another young star (EC 92), located about $''$ $\sim$ 2000 AU) to the north of EC 95, has been argued to be gravitationally bound to it Haisch et 2002)."
" If that were indeed the case, then EC 92/EC 95 would constitute a rare example of a very young, intermediate-mass, hierarchical triple system."," If that were indeed the case, then EC 92/EC 95 would constitute a rare example of a very young, intermediate-mass, hierarchical triple system."
" In spite of its youth, EC 95 does not appear to contain large quantities of circumstellar material."," In spite of its youth, EC 95 does not appear to contain large quantities of circumstellar material."
" It shows only a modest mid-inlrared excess (Preibish 1999, Haisch et 22002, Pontoppidan et 22004), lile veiling (Doppmann et 22005), and fairly weak CO overtone rovibrational absorption lines."," It shows only a modest mid-infrared excess (Preibish 1999, Haisch et 2002, Pontoppidan et 2004), little veiling (Doppmann et 2005), and fairly weak CO overtone rovibrational absorption lines."
" This has led some authors to classify it as a Class II source EEiroa et 22005), although others have favored a flat spectrum HHarvey et 22007) or even Class 0/I classification (Winston et 22007)."," This has led some authors to classify it as a Class II source Eiroa et 2005), although others have favored a flat spectrum Harvey et 2007) or even Class 0/I classification (Winston et 2007)."
" We note, in particular. that the fairly large rotational velocity of EC 95 (56 km !: Doppmann et 22005) would be more consistent with a Class Lor flat spectrum classification."," We note, in particular, that the fairly large rotational velocity of EC 95 (56 km $^{-1}$; Doppmann et 2005) would be more consistent with a Class I or flat spectrum classification."
" It is interesung to compare these characteristics with those of the nearby, possibly associated, source EC 92."," It is interesting to compare these characteristics with those of the nearby, possibly associated, source EC 92."
" From its location on the HR diagram, Preibisch (1999) estimate that EC 92 is a 0.5 M. star with an age of the order of 10? yr."," From its location on the HR diagram, Preibisch (1999) estimate that EC 92 is a 0.5 $M_\odot$ star with an age of the order of $^5$ yr."
 This suggests that EC 92 and EC 95 are nearly coeval (as would be natural if they belonged to a common multiple system)., This suggests that EC 92 and EC 95 are nearly coeval (as would be natural if they belonged to a common multiple system).
" Unlike EC 95, however, EC 92 does exhibit a significant mid-inlrared excess, and has been almost unanimously classified as a [lat-spectrum Class I source (see PPontoppidan et 22004)."," Unlike EC 95, however, EC 92 does exhibit a significant mid-infrared excess, and has been almost unanimously classified as a flat-spectrum Class I source (see Pontoppidan et 2004)."
" Thus, while EC 92 and EC 95 appear to have similar ages and might be physically associated, they diller significantly in their circumstellar content."," Thus, while EC 92 and EC 95 appear to have similar ages and might be physically associated, they differ significantly in their circumstellar content."
 The fact that EC 95 is a tight binary system could naturally explain the relative paucity of its circumstellar content because tidal [orces tend to be elTecüve at clearing out circumstellar material., The fact that EC 95 is a tight binary system could naturally explain the relative paucity of its circumstellar content because tidal forces tend to be effective at clearing out circumstellar material.
" In particular, any disk exisüng around the members of the EC 95 system are expected to be truncated down to a radius at most about a third of the physical separation between the stars:  5 mas (— 2 AU)."," In particular, any disk existing around the members of the EC 95 system are expected to be truncated down to a radius at most about a third of the physical separation between the stars: $\sim$ 5 mas $\equiv$ 2 AU)."
" Low-mass young stars TT Tauri stars) have long been known to often be magnetically active FFeigelson Montmerle 1999),", Low-mass young stars T Tauri stars) have long been known to often be magnetically active Feigelson Montmerle 1999).
 The accepted explanation for this activity is based on a scaled-up version of the situation. with the Sun., The accepted explanation for this activity is based on a scaled-up version of the situation with the Sun.
" While they move down the Hayashi track towards the main sequence, stars less massive than about 2 M. are fully convective PPalla Stahler 1993),"," While they move down the Hayashi track towards the main sequence, stars less massive than about 2 $M_\odot$ are fully convective Palla Stahler 1993)."
" As a consequence, they can generale strong superficial magnetic fields (~ 1 kG) through the dynamo mechanism (Parker 1955)."," As a consequence, they can generate strong superficial magnetic fields $\sim$ 1 kG) through the dynamo mechanism (Parker 1955)."
" This leads to the appearance of magnetic loops anchored on the stellar surface, and extending up to à maximum height of a few stellar radii."," This leads to the appearance of magnetic loops anchored on the stellar surface, and extending up to a maximum height of a few stellar radii."
" When two loops interact, flares associated with magnetic reconnection events can occur, leading to the sudden release of large quantities of energy initially stored in the magneuc field."," When two loops interact, flares associated with magnetic reconnection events can occur, leading to the sudden release of large quantities of energy initially stored in the magnetic field."
 Part of that energy can accelerate electrons initially trapped in the loops to mildly relativistic speeds., Part of that energy can accelerate electrons initially trapped in the loops to mildly relativistic speeds.
 These, These
Preibisch Zinnecker (1999) observed a very similar PAIS CMD in the Upper Seo OB association. with à similar vertical scatter of about £0.6 mag about the isochrones.,"Preibisch Zinnecker (1999) observed a very similar PMS CMD in the Upper Sco OB association, with a similar vertical scatter of about $\pm 0.6$ mag about the isochrones."
 They showed. that if one takes into account unresolved binaries. photometric errors and allowed a ~I0'4 range in distance. that the scatter around. the PAIS isochrones was exactly as expected for a coeval population at 5 MMwyr.," They showed that if one takes into account unresolved binaries, photometric errors and allowed a $\sim10\%$ range in distance, that the scatter around the PMS isochrones was exactly as expected for a coeval population at $\sim5$ Myr."
 We therefore similarly conclude that the CALD in Fig., We therefore similarly conclude that the CMD in Fig.
 2 shows no evidence for a large spread in the age or distance of the PAIS population we have found., 2 shows no evidence for a large spread in the age or distance of the PMS population we have found.
 In. particular. we can rule out any distance modulus spread in a coeval population that is larger than a few tenths of à magnitude. or any age spread in à co-spatial population of more than à Myr or so (for à mean age of 4 Myr).," In particular, we can rule out any distance modulus spread in a coeval population that is larger than a few tenths of a magnitude, or any age spread in a co-spatial population of more than a Myr or so (for a mean age of $\sim4$ Myr)."
 Thus unless there is à conspiracy to place older sars closer to us. the PAIS association seenis likely to have a relatively narrow spread around an age and distance that are incompatible with the deduced age for > Vel and its Hipparcos distance.," Thus unless there is a conspiracy to place older stars closer to us, the PMS association seems likely to have a relatively narrow spread around an age and distance that are incompatible with the deduced age for $\gamma^{2}$ Vel and its Hipparcos distance."
 Our findings challenge. the conclusions of several recent papers which use the Lipparcos parallax of 27. Vel and its error to derive: the absolute magnitude of the system and its components: svstem masses from the interferometric binary separation of Llanbury-Brown (1970): the O star luminosity. mass and age from stellar evolution models and. hence the orbital inclination and further mass estimates from racial velocity. curves (see van der. Hucht et al.," Our findings challenge the conclusions of several recent papers which use the Hipparcos parallax of $\gamma^{2}$ Vel and its error to derive: the absolute magnitude of the system and its components; system masses from the interferometric binary separation of Hanbury-Brown (1970); the O star luminosity, mass and age from stellar evolution models and hence the orbital inclination and further mass estimates from radial velocity curves (see van der Hucht et al."
 1997: Schacrer et al., 1997; Schaerer et al.
 1997. Schmutz et al.," 1997, Schmutz et al."
 1997. de Marco. Schmutz 999).," 1997, de Marco Schmutz 1999)."
 A distance as large as ppe for <> Vel significantly 'hanges the system parameters deduced in these papers., A distance as large as pc for $\gamma^{2}$ Vel significantly changes the system parameters deduced in these papers.
 The system luminosity increases by a [actor 2.5., The system luminosity increases by a factor 2.5.
 The ellective emperature and. Luminosity deduced for the O star would jen give Hb a Mass >40 vind an age «3 MMyr. compared with the values of and MMyr quoted by de Marco Schmutz (1999).," The effective temperature and luminosity deduced for the O star would then give it a mass $>40$ and an age $<3$ Myr, compared with the values of and Myr quoted by de Marco Schmutz (1999)."
 At us larger distance. an age of MMyr could be compatible with the low mass PAIS stars we have found.," At this larger distance, an age of Myr could be compatible with the low mass PMS stars we have found."
 The absolute magnitude of the O star would decrease to 6.000.3 (van er Llucht et al., The absolute magnitude of the O star would decrease to $-6.0\pm0.3$ (van der Hucht et al.
 1997). which argues for a supergiant rather han a giant classification.," 1997), which argues for a supergiant rather than a giant classification."
 Van der Llueht et al., Van der Hucht et al.
 comment hat this would be in better agreement with published spectra of Conti Smith (1972) and. Niemel&a Sahace (1980)., comment that this would be in better agreement with published spectra of Conti Smith (1972) and Niemelä Sahade (1980).
 As the mass ratio from the radial velocity curves is ixed. the WI mass increases by a sipilar fraction.," As the mass ratio from the radial velocity curves is fixed, the WR mass increases by a similar fraction."
 Phe total system mass. based on a binary separation of 4.3d:0.5 mas. increases from 30+10 to 120€40 ((now comfortably exceeding the minimum mass from racial velocity. curves Niemelà Sahade 1980) and the binary inclination is reduced to around 50° to explain the radial velocity curves.," The total system mass, based on a binary separation of $4.3\pm0.5$ mas, increases from $30\pm10$ to $120\pm40$ (now comfortably exceeding the minimum mass from radial velocity curves – Niemelä Sahade 1980) and the binary inclination is reduced to around $50^{\circ}$ to explain the radial velocity curves."
 From our discussion there seem to be two possible scenarios. (, From our discussion there seem to be two possible scenarios. (
1) That he PMS stars are approximately at the same distance and age as 57. Vel. and. that this distance places +2 Vel within the Vela OB2 association at ppc. (,"1) That the PMS stars are approximately at the same distance and age as $\gamma^{2}$ Vel, and that this distance places $\gamma^{2}$ Vel within the Vela OB2 association at pc. ("
2) That the PAIS stars are part of the Vela OD2 association. possibly surrounding «+ Vel. but that 57 Vel is an isolated foreground object with no surrounding low mass stars at a similar age.,"2) That the PMS stars are part of the Vela OB2 association, possibly surrounding $\gamma^{1}$ Vel, but that $\gamma^{2}$ Vel is an isolated foreground object with no surrounding low mass stars at a similar age."
 We believe that (1) isfar more plausible than (2) because of the dispersion in the Vela OD2 Llipparcos parallaxes and the likely association o£ ++ and 5? Vel., We believe that (1) is more plausible than (2) because of the dispersion in the Vela OB2 Hipparcos parallaxes and the likely association of $\gamma^{1}$ and $\gamma^{2}$ Vel.
 Recently. the idea that 5? Vel could form in isolation without accompanying low mass stars has also been challenged. by the near Hi detection of a Ix-tvpe PAIS companion only 4.7 aresee distant. (Tokovinin et al.," Recently, the idea that $\gamma^{2}$ Vel could form in isolation without accompanying low mass stars has also been challenged by the near IR detection of a K-type PMS companion only 4.7 arcsec distant (Tokovinin et al."
 1999)., 1999).
 If the low mass PAIS stars we have ound are truly in the vicinity of 57. Vel. they. represent an exciting opportunity to explore the influence of adj:cent high. mass loss stars arc ionizing UV radiation fields on the mass function and circumstellar cisc lifetimes of low mass stars.," If the low mass PMS stars we have found are truly in the vicinity of $\gamma^{2}$ Vel, they represent an exciting opportunity to explore the influence of adjacent high mass loss stars and ionizing UV radiation fields on the mass function and circumstellar disc lifetimes of low mass stars."
 Lt will be interesting to compare the frequencies of T-Fauri discs. around hese stars with the frequencies found in T associations and OB associations with similar ages., It will be interesting to compare the frequencies of T-Tauri discs around these stars with the frequencies found in T associations and OB associations with similar ages.
 The PAIS stars in Fig.2 have masses. found from the 1)Antona Mazztelli (1997) models. down to (an age dependent) mass of aboutM.," The PMS stars in Fig.2 have masses, found from the D'Antona Mazzitelli (1997) models, down to (an age dependent) mass of about."
.. Phe mass function will be addressed when we have a better census of the association membership., The mass function will be addressed when we have a better census of the association membership.
 ‘This research has made use oROSA data obtained [rom the Leicester Database ArchivὉ Service at the Department of Physics and Astronomy. Lcicester. University. Ulx.," This research has made use of data obtained from the Leicester Database Archive Service at the Department of Physics and Astronomy, Leicester University, UK."
 The Cerro Vololo Interamoerican Oυπονα(ον is operated by the Association of Universities for Research in Astronomy. I1nc.. under contract to the US National Science Foundation.," The Cerro Tololo Interamerican Observatory is operated by the Association of Universities for Research in Astronomy, Inc., under contract to the US National Science Foundation."
 TN was supported by a Ulx Particle and Physies and Astronomy Research Council (PPARC) Advanced. Fellowship., TN was supported by a UK Particle and Physics and Astronomy Research Council (PPARC) Advanced Fellowship.
 SL was supported by a Nullield. Foundation. Undergraduate Research Bursary (NUE-URDOS)., SH was supported by a Nuffield Foundation Undergraduate Research Bursary (NUF-URB98).
 ο is a PPARC postdoctoral research associate., EJT is a PPARC postdoctoral research associate.
 MIN was. supported. by an undergraduate research. bursary from Ixeele. University., MK was supported by an undergraduate research bursary from Keele University.
 Computational work for this paper was performed on the Ixeele node of the Starlink network funded by PPABC., Computational work for this paper was performed on the Keele node of the Starlink network funded by PPARC.
convection to show that the dissipative properties of the turbulent convective flow are indeed well approximated bv an effective viscosity. coefficieut.,convection to show that the dissipative properties of the turbulent convective flow are indeed well approximated by an effective viscosity coefficient.
 Therefore the siuulatious allow us to derive its theoretical value., Therefore the simulations allow us to derive its theoretical value.
 Iu this paper we combine these uew results to construct a complete prescription for the effective viscosity and show that the resulting dissipation. iu the absence of resonantly excited tidal waves. produces nmuch higher Q. values than those found observationallv for main sequence stars. and that those values are consistent with even the strongest current constraints on the tidal dissipation cficiency.," In this paper we combine these new results to construct a complete prescription for the effective viscosity and show that the resulting dissipation, in the absence of resonantly excited tidal waves, produces much higher $Q_*$ values than those found observationally for main sequence stars, and that those values are consistent with even the strongest current constraints on the tidal dissipation efficiency."
 In addition we derive the magnitude of the expected transit timing variations (TTV) due to orbital decay and conrpare them to possible observational coutraints (6.9. bv the ορια nussion) that could provide a direct test of the proposed viscosity prescription., In addition we derive the magnitude of the expected transit timing variations (TTV) due to orbital decay and compare them to possible observational contraints (e.g. by the Kepler mission) that could provide a direct test of the proposed viscosity prescription.
 The organization of the paper is as follows: in Section 2. we introduce what is usually wuderstood by the Q paralucter. i Section 3 we discuss how we arrive at the turbulent viscosity we use to caleulate orbital decay. in Section 1 we follow ?? to convert our turbulent viscosity to a tidal torque. in Section 5. woe present the stellar structure and evolution models used in the calculation of the torque. in Section 6 we calculate the effective Q. Which correspouds to this torque. the TTVs that our estimate of the dissipation would result in aud the future lifetimes of close in extrasolar planets. finally iu Section T we summarize our results.," The organization of the paper is as follows: in Section \ref{sec: classical}
 we introduce what is usually understood by the $Q_*$ parameter, in Section \ref{sec: viscosity} we discuss how we arrive at the turbulent viscosity we use to calculate orbital decay, in Section \ref{sec: torque} we follow \citet{Scharlemann_81, Scharlemann_82} to convert our turbulent viscosity to a tidal torque, in Section \ref{sec: stellar models} we present the stellar structure and evolution models used in the calculation of the torque, in Section \ref{sec: orbit} we calculate the effective $Q_*$ which corresponds to this torque, the TTVs that our estimate of the dissipation would result in and the future lifetimes of close in extrasolar planets, finally in Section \ref{sec: discussion} we summarize our results."
 The tide raised by a planet ou its star is a quadrupole wave of amplitude 5: the tidal motious are of order (ωOYA which set up shear inside the star., The tide raised by a planet on its star is a quadrupole wave of amplitude $h$; the tidal motions are of order $({\omega}-{\Omega})h$ which set up shear inside the star.
 The orbital aneular frequency. w. exceeds the stellar spin onc. Q. iu the case we cousider here. and the tidal forcing due to we occurs with timescales that are much shorter than the correlation time of the turbulence iu the stars convection Zone.," The orbital angular frequency, $\omega$, exceeds the stellar spin one, $\Omega$, in the case we consider here, and the tidal forcing due to $\omega$ occurs with timescales that are much shorter than the correlation time of the turbulence in the star's convection zone."
 Dissipation iu the star causes the tidal bulee 7 to lag behind by an angle 3. which is determined by the zinouut of coupling between the tide aud the source of the dissipation. presumably the turbulent eddies in the convection zone.," Dissipation in the star causes the tidal bulge $h$ to lag behind by an angle ${\delta}$, which is determined by the amount of coupling between the tide and the source of the dissipation, presumably the turbulent eddies in the convection zone."
 One could compare the response of the star to that of a forced harmonic oscillator aud relate à to a specific dissipation function Q—(wQ)EQ/E=1/26 εν., One could compare the response of the star to that of a forced harmonic oscillator and relate ${\delta}$ to a specific dissipation function $Q = ({\omega}-{\Omega})E_0/{\dot{E}} = 1/2\delta$ \citep{Murray_Dermott_99}.
 This is how the tidal dissipation quality factor (2 is defined. with £y being the energv stored iu the tidal bulge. aud. E. the rate of viscous dissipation of energy.," This is how the tidal dissipation quality factor $Q_*$ is defined, with $E_0$ being the energy stored in the tidal bulge, and $\dot{E}$, the rate of viscous dissipation of energy."
 This is another wav to determine the lag angle à., This is another way to determine the lag angle ${\delta}$.
 The turbulent viscosity is iutroduced iu the sense of Ravleigh-Benard incompressible convection. 14 Pfr. for a low forcing frequency.," The turbulent viscosity is introduced in the sense of Rayleigh-Benard incompressible convection, ${\nu}_{\rm t}={\frac{1}{3}}vl\approx l^2/{{\tau}}$ , for a low forcing frequency."
 Here. { is the convective nusing leugth. e is the convective velocity. and 7 is the convective thuescale (eddy turnover time).," Here, $l$ is the convective mixing length, $v$ is the convective velocity, and ${\tau}$ is the convective timescale (eddy turnover time)."
 Then basically Q.XGM racis. where AL and rs are the stellar miass and radius (see?.formoredetails)..," Then basically $Q_*\propto GM/r_*{\omega}{\nu}_{\rm t}$ where $M$ and $r_*$ are the stellar mass and radius \citep[see][for more
details]{Sasselov_03}."
 We need to combine the perturbatively derived effective viscosity of ? based on realistic low niass star convective models with the ? direct Viscosity from simulations with external forcing in order to ect a coniplete and reliable prescription for the full viscosity tensor., We need to combine the perturbatively derived effective viscosity of \citet{our_k_dwarfs} based on realistic low mass star convective models with the \citet{our_direct_viscosity} direct viscosity from simulations with external forcing in order to get a complete and reliable prescription for the full viscosity tensor.
 As discussed in ?/— the viscosity tensor is specified conipletelv from five independent quantities: Aj. Ay. Koo. vy. Ivo.," As discussed in \citet{our_k_dwarfs} the viscosity tensor is specified completely from five independent quantities: $K_0$, $K_{0'}$, $K_{00'}$, $K_1$, $K_2$ ."
 Two of these (Ay and νο) were calculated directly in ὃν and for the other three ? provide perturbative values.," Two of these $K_1$ and $K_2$ ) were calculated directly in \citet{our_direct_viscosity}, and for the other three \citet{our_k_dwarfs}
 provide perturbative values."
" In terms of these quautities the time and volume averaged rate of energy dissipation due to the turbuleut flow is eiven by (7.equation13): where the [.4,,|"" quantities- are root ican square shear colmpoucuts defined by: with the augle brackets denoting a time average.", In terms of these quantities the time and volume averaged rate of energy dissipation due to the turbulent flow is given by \citep[][equation 13]{our_k_dwarfs}: where the $|A_m|^2$ quantities are root mean square shear components defined by: with the angle brackets denoting a time average.
 Equation 1l is simply the volume aud time average of the rate of svork done by an anisotropic viscous force on a stratified fluid subject to some externally iniposed shear., Equation \ref{eq: viscous power} is simply the volume and time average of the rate of work done by an anisotropic viscous force on a stratified fluid subject to some externally imposed shear.
 The particular forma of Eq., The particular form of Eq.
 1 asstunes that locally the Viscosity tensor is luvariant uuder rotations around the axis of eravity (2). which must be true if stellar rotation Is ignored.," \ref{eq:
viscous power} assumes that locally the viscosity tensor is invariant under rotations around the axis of gravity $z$ ), which must be true if stellar rotation is ignored."
 The directly obtained effective. viscosity of 7?— and the perturbative estimates based on realistic low uass stay simulations (7?) aud on an idealized simulation (2) all produce a linear scaling of the effective viscosity with period. for the rauge of periods available to those simulations.," The directly obtained effective viscosity of \citet{our_direct_viscosity} and the perturbative estimates based on realistic low mass star simulations \citep{our_k_dwarfs} and on an idealized simulation \citep{our_code} all produce a linear scaling of the effective viscosity with period, for the range of periods available to those simulations."
 As is discussed in these works the linear scaling is not expected to hold for arbitrarily small 21ος». because at such timescales Kolmogorov cascade should be a good approximation to the flow and iu hat case 7. show that the loss of cficiency shouldbe quadratic with period.," As is discussed in these works the linear scaling is not expected to hold for arbitrarily small periods, because at such timescales Kolmogorov cascade should be a good approximation to the flow and in that case \citet{Goodman_Oh_97} show that the loss of efficiency shouldbe quadratic with period."
 Iu addition. the direct calculations (7). show that the effective viscosity saturates at lone »oriods.," In addition, the direct calculations \citep{our_direct_viscosity} show that the effective viscosity saturates at long periods."
 To acconunodate these three scalings.we will assuue hefollowiug form for the viscosity cocficicuts: witli:," To accommodate these three scalings,we will assume thefollowing form for the viscosity coefficients: with:"
We ca1 also estimate the influeuce o error in adopted solar radius on the secondary inversions by using sound speed aix density profiles obtained witi different values of the radius and these results are stown in Fie. Ll.,We can also estimate the influence of error in adopted solar radius on the secondary inversions by using sound speed and density profiles obtained with different values of the radius and these results are shown in Fig. \ref{txrad}.
 These erors can be seen to be comyarable to those due to uwcertaintics in frequencies, These errors can be seen to be comparable to those due to uncertainties in frequencies.
 The properties of these seisie mnodels are sunununudzed in Table 1.. which also gives the estimated errors in each qiantitv cue to those in the GONG mouths 10 data.," The properties of these seismic models are summarized in Table \ref{tab1}, which also gives the estimated errors in each quantity due to those in the GONG months 4-10 data."
" Iu this fade T, is the central temmpcrature. oUCl) the neutrino fux iu the Chlorine detector. of!Ca) the neutriιο flux in the Calli detector. while o(*B) is the flux of B neutrinos."," In this table $T_c$ is the central temperature, $\phi(^{37}\mathrm{Cl})$ the neutrino flux in the Chlorine detector, $\phi(^{71}\mathrm{Ga})$ the neutrino flux in the Gallium detector, while $\phi(^8\mathrm{B})$ is the flux of $^8$ B neutrinos."
 Tt can be seen that a reduction im radniw by. 210 kin Increases the computed hpmuuinosiy by 0.0VLE. aud the, It can be seen that a reduction in radius by 210 km increases the computed luminosity by $0.004L_\odot$ and the
CAZ.) al.,$M_*$ al.
 2007: Όσιο et al., 2007; Peng et al.
 2010). as well as at intermediate redshifts 0.5<2«23 (Noeske et al.," 2010), as well as at intermediate redshifts $0.5<z<3$ (Noeske et al."
 2007: Elbaz ct al., 2007; Elbaz et al.
 2007: Daddi ct al., 2007; Daddi et al.
 2007: Pannella et al., 2007; Pannella et al.
 2009: Rodighicro et al., 2009; Rodighiero et al.
 20104. Rariu et al.," 2010a, Karim et al."
 2011). aud bevond (Daddi et al.," 2011), and beyond (Daddi et al."
 2009: Conzalez ot al., 2009; Gonzalez et al.
 2010)., 2010).
 With SFR xAL. the slope a can differ substantially depeudiug ou sample selection aud the procedures for measmine SER aud AL... with values in the above literature ranginge frou ~0.6 to ~ 1l. Moreover. its normalization rapidly rises from 2= Oto.~ 225 as (1127??. then fatteniug all the way to the highest redshifts (Daddi et al.," With SFR $\propto M_*^{\alpha}$ , the slope $\alpha$ can differ substantially depending on sample selection and the procedures for measuring SFR and $M_*$, with values in the above literature ranging from $\sim 0.6$ to $\sim 1$ Moreover, its normalization rapidly rises from $z=0$ to $z\sim2$ –2.5 as $(1+z)^{\sim3.5}$, then flattening all the way to the highest redshifts (Daddi et al."
 200σα Rodighicro et al.," 2007, Rodighiero et al."
 20102: ναι ct al., 2010a; Karim et al.
 2011)., 2011).
 Slope and normalization of the AV. relation play a crucial role in the erowth of galaxies and in the evolution of theira. mass function (Reuzini 2009: Pene et al., Slope and normalization of the $-M_*$ relation play a crucial role in the growth of galaxies and in the evolution of their mass function (Renzini 2009; Peng et al.
 2010. 2011).," 2010, 2011)."
 Observations of the CO molecular gas content of MS ealaxies indicate that their star formation cficiency docs not depend strougly ou cosinic epoch to 2~2. with the SER increase being due to higher molecular gas fractions (Daddi et al.," Observations of the CO molecular gas content of MS galaxies indicate that their star formation efficiency does not depend strongly on cosmic epoch to $z\sim2$, with the SFR increase being due to higher molecular gas fractions (Daddi et al."
 2008: 20102: Tacconi et al., 2008; 2010a; Tacconi et al.
 2010: Geach et al., 2010; Geach et al.
 2011)., 2011).
 Ou the other haud. outliers are kuown to exist. with very high specific SER (SSFR) compared to normal MS ealaxies. such as local ultra-hbuninous infrared ealaxics (ULIRG. Saunders Mirabel 1996. Elbaz et al.," On the other hand, outliers are known to exist, with very high specific SFR (SSFR) compared to normal MS galaxies, such as local ultra-luminous infrared galaxies (ULIRG, Sanders Mirabel 1996, Elbaz et al."
 2007). and at least some of the subuuu-selected galaxies (SAIC) at dκτς[E CTaecoui oet al.," 2007), and at least some of the submm-selected galaxies (SMG) at $1<z<4$ (Tacconi et al."
 2008: Daddi et al., 2008; Daddi et al.
 2007: 2009: Takaei et al., 2007; 2009; Takagi et al.
 2008)., 2008).
 What docs differentiate such active behemoths frou the cominaut MS. population?, What does differentiate such active behemoths from the dominant MS population?
 Outlicrs are galaxies in which the SSER has been boosted by sole event. possibly a major mereer (c.g... Milos Ucruquist 1996:di Matteo et al.2008: Martig et al.," Outliers are galaxies in which the SSFR has been boosted by some event, possibly a major merger (e.g., Mihos Hernquist 1996;di Matteo et al.2008; Martig et al."
 2010:, 2010;
"we inferred the phase of the modulation by fitting each individual folded profile with the fundamental plus three higher As a first step, we fit the phases of fundamental harmonic obtained from the ddata divided into four segments of approximately equal length and from the aand HHRC-S and ACIS-I observations.","we inferred the phase of the modulation by fitting each individual folded profile with the fundamental plus three higher As a first step, we fit the phases of fundamental harmonic obtained from the data divided into four segments of approximately equal length and from the and HRC-S and ACIS-I observations."
" At this stage, the dral//ACIS-S observation was left out, because of its very different pulse profile."," At this stage, the /ACIS-S observation was left out, because of its very different pulse profile."
 The time-evolution of the phase can be followed unambiguously throughout all the data and described with a linear relation of the form ¢=$o+2n(t—to)/P., The time-evolution of the phase can be followed unambiguously throughout all the data and described with a linear relation of the form $\phi=\phi_0+2\pi(t-t_0)/P$.
" We assumed the start of the mmonitoring, MJD 558804.0, as the reference epoch to and the fit (v2=0.88 for 5 dof) gives Ρα=24030.42(2) s (1c uncertainty, valid over the range MJD 6632)."," We assumed the start of the monitoring, MJD 804.0, as the reference epoch $t_0$ and the fit $\chi^2_\nu=0.88$ for 5 dof) gives $P_{\mathrm{A}}=24\,030.42(2)$ s $\sigma$ uncertainty, valid over the range MJD 632)."
 We designate this rotational ephemeris ‘solution A’., We designate this rotational ephemeris `solution A'.
" A quadratic term —n(t—to)?P/P?, which would reflect the presence of a period derivative (P), is not required."," A quadratic term $-\pi(t-t_0)^2\dot{P}/P^2$, which would reflect the presence of a period derivative $\dot{P}$ ), is not required."
 This implies an upper limit on the period derivative of oof |PA|«3.3x107? s s! (3c confidence level)., This implies an upper limit on the period derivative of of $|\dot{P}_{\mathrm{A}}|<3.3\times10^{-9}$ s $^{-1}$ $\sigma$ confidence level).
 In Fig., In Fig.
 we show the epoch-folded pulse profiles (including the dral/ACIS-S one) obtained using this solution., \ref{pprofiles} we show the epoch-folded pulse profiles (including the /ACIS-S one) obtained using this solution.
 We note that the oobservation was affected by rather intense proton flares., We note that the observation was affected by rather intense proton flares.
" The removal of the intervals of flaring background, because of the few cycles contained in the observation, significantly affects the pulse profiles."," The removal of the intervals of flaring background, because of the few cycles contained in the observation, significantly affects the pulse profiles."
" As a check of the robustness of our results, we repeated the timing analysis using the unfiltered EPIC data and we obtained virtually identical results (both filtered and unfiltered profiles are plotted in Fig. 4))."," As a check of the robustness of our results, we repeated the timing analysis using the unfiltered EPIC data and we obtained virtually identical results (both filtered and unfiltered profiles are plotted in Fig. \ref{pprofiles}) )."
" Using solution A, we are able to predict for tthe phase of the fundamental harmonic at the epoch of the dral/ACIS-S observation within 40.03 cycles (at 3c)."," Using solution A, we are able to predict for the phase of the fundamental harmonic at the epoch of the /ACIS-S observation within $\pm$ 0.03 cycles (at $\sigma$ )."
 The phase of the fundamental harmonic in the Chandra/ACIS-S data nicely dovetails with the predicted value., The phase of the fundamental harmonic in the Chandra/ACIS-S data nicely dovetails with the predicted value.
" Thus we derived a new coherent timing solution, which we denote with 'B', including the Chandra//ACIS-S data and therefore valid over the range MJD 6632."," Thus we derived a new coherent timing solution, which we denote with `B', including the /ACIS-S data and therefore valid over the range MJD 632."
" Again, the phases ofthe fundamental harmonic can be fit with a linear relation (x?=0.77 for 6 dof) which yields Pg=24030.42(2) s (lo uncertainty; epoch MJD 8804.0)."," Again, the phases ofthe fundamental harmonic can be fit with a linear relation $\chi^2_\nu=0.77$ for 6 dof) which yields $P_{\mathrm{B}}=24\,030.42(2)$ s $\sigma$ uncertainty; epoch MJD 804.0)."
" While the best-fitting period is equal to that of solution A, the limit on the period derivative is slightly more constraining: |Pg|<1.6x107° ss~! (3c confidence level)."," While the best-fitting period is equal to that of solution A, the limit on the period derivative is slightly more constraining: $|\dot{P}_{\mathrm{B}}|<1.6\times10^{-9}$ s $^{-1}$ $\sigma$ confidence level)."
 We presented the analysis of the first five years (2006 April-2011 April) of the Swift//XRT monitoring of the enigmatic X-ray source aat the centre of the SNR103., We presented the analysis of the first five years (2006 April–2011 April) of the /XRT monitoring of the enigmatic X-ray source at the centre of the SNR.
". During this time span, the source remained in a quiescent state, with an average observed 1—10 keV flux of ~1.7x10713s-1,, 20-30 times lower than the historical maximum attained in the 1999—2000 outburst (~5x1071s~!;; Garmireetal. 2000))."," During this time span, the source remained in a quiescent state, with an average observed 1--10 keV flux of $\sim$$1.7\times10^{-12}$, 20–30 times lower than the historical maximum attained in the 1999–2000 outburst $\sim$$5\times10^{-11}$; \citealt{garmire00}) )."
 The timing study of the ddata yielded an accurate measure of the modulation period of wwhich allowed us to phase-connect the XRT data with archival aand oobservations., The timing study of the data yielded an accurate measure of the modulation period of which allowed us to phase-connect the XRT data with archival and observations.
" We derived two timing solutions, labelled A and B, both consistent with the same constant period Pa=Pp24030.42(2) s but with somewhat different upper limits on the period derivative."," We derived two timing solutions, labelled A and B, both consistent with the same constant period $P_{\mathrm{A}}=P_{\mathrm{B}}=24\,030.42(2)$ s but with somewhat different upper limits on the period derivative."
 Solution A (|PA|«3.3x107? s s MID 6632) is based on the single-peaked pulse profiles*; observed while wwas in quiescence., Solution A $|\dot{P}_{\mathrm{A}}|<3.3\times10^{-9}$ s $^{-1}$; MJD 632) is based on the single-peaked pulse profiles observed while was in quiescence.
 Solution B (|Ps|«1.6x107? s s; MJD 6632) is a natural extension of solution A including the multi-peaked Chandra//ACIS-S profile obtained on 2002 March, Solution B $|\dot{P}_{\mathrm{B}}|<1.6\times10^{-9}$ s $^{-1}$ ; MJD 632) is a natural extension of solution A including the multi-peaked /ACIS-S profile obtained on 2002 March
ractional escape rates of the FG aud SC stars due to evaporation tend to equalize. stabilizing the SC fraction (see also Decressin et al.,"fractional escape rates of the FG and SG stars due to evaporation tend to equalize, stabilizing the SG fraction (see also Decressin et al."
 2008 for another study of io mixing process)., 2008 for another study of the mixing process).
 Thus the vast majority of escapers roni the cluster are FO stars., Thus the vast majority of escapers from the cluster are FG stars.
 Two recent spectroscopic studies (Caretta ct al., Two recent spectroscopic studies (Carretta et al.
 2010. Martell ζαουο 2010) ave found that the vast majority of halo stars studied ive abundances typical of FCO stars in clusters: ouly about of the stars are Na-rich (Caretta ct al.," 2010, Martell Grebel 2010) have found that the vast majority of halo stars studied have abundances typical of FG stars in clusters; only about of the stars are Na-rich (Carretta et al."
 2010)x and CN-strong (Mairtell Crebel 2010). aud hence classifiable as SCC stars.," 2010) and CN-strong (Martell Grebel 2010), and hence classifiable as SG stars."
 Alauv general studies have addressed the evolution of the Galactic elobular cluster svstceu aud the dispersal of cluster stars in the halo (see ce. IKroupa Doilv 2002. Bamuegardt et al.," Many general studies have addressed the evolution of the Galactic globular cluster system and the dispersal of cluster stars in the halo (see e.g. Kroupa Boily 2002, Baumgardt et al."
 2008. Portegics Zwart et al.," 2008, Portegies Zwart et al."
 2010. Vesperini 2010 and references therein).," 2010, Vesperini 2010 and references therein)."
 However. is Letter ds specifically focused on SG. stars.," However, this Letter is specifically focused on SG stars."
 Our goals here are to estimate both the number of SCG stars rat may have formed in the Galactic globular cluster system aud the fraction. facii of SCC stars formed in elobular clusters that now populate the Galactic stellar iilo. and to illustrate the link between SC formation. elobular cluster evolution aud the formation history of he Galactic halo.," Our goals here are to estimate both the number of SG stars that may have formed in the Galactic globular cluster system and the fraction, $\fsge$, of SG stars formed in globular clusters that now populate the Galactic stellar halo, and to illustrate the link between SG formation, globular cluster evolution and the formation history of the Galactic halo."
 In refsecihvdro.. we preseut the results of hvdrodyvuauical sinulatious exploring the depeudence of the mass of SC stars formed on cluster initial properties.," In \\ref{sec:hydro}, we present the results of hydrodynamical simulations exploring the dependence of the mass of SG stars formed on cluster initial properties."
 Iu refsecisehalo we imtroduce our numerical framework to estimate the fraction of SC stars iu the halo. aud discuss its theoretical aud observational iugredieuts.," In \\ref{sec:sghalo} we introduce our numerical framework to estimate the fraction of SG stars in the halo, and discuss its theoretical and observational ingredients."
 Iu refsecóies we present and discuss our results., In \\ref{sec:res} we present and discuss our results.
 Iu order to calculate the total mass of SCO stars formed in a cluster as a function of cluster initial properties. we have carried out a series of ouc-dimensional bydrodvuamical simulations modclne the SC. formation process.," In order to calculate the total mass of SG stars formed in a cluster as a function of cluster initial properties, we have carried out a series of one-dimensional hydrodynamical simulations modeling the SG formation process."
 The techuical details of our sinulatious are described iu D'Ercole (2008)., The technical details of our simulations are described in D'Ercole (2008).
 We outline here only the aspects relevaut to this Letter., We outline here only the aspects relevant to this Letter.
 We asstune that the FC cluster initially follows a Nine (1962) density profile out to some truncation radius £A., We assume that the FG cluster initially follows a King (1962) density profile out to some truncation radius $R$.
 Stellar masses are distributed in the range 0.1«nmi.100 according to either a Ixroupa ct al. (, Stellar masses are distributed in the range $0.1<m/m_{\odot}<100$ according to either a Kroupa et al. (
"1993: hereafter 1893) or a Iroupa (2001: hereafter EKO1) stellar ΤΝΤ,",1993; hereafter K93) or a Kroupa (2001; hereafter K01) stellar IMF.
 We model the formation of SC stars from the ejecta of ACD stars and assume that the SC formation phase extends from about 30 Myr after the FC cluster forms until ~100 Alvr (should the SC. star formation epoch exteud to 150 Myr. aud hence include ejecta of stars down to LAL... the SCC mass can be obtained by multiplying the values presented below by a factor ~ 1.1).," We model the formation of SG stars from the ejecta of AGB stars and assume that the SG formation phase extends from about 30 Myr after the FG cluster forms until $\sim100$ Myr (should the SG star formation epoch extend to $\sim 150$ Myr, and hence include ejecta of stars down to 4 $M_{\odot}$, the SG mass can be obtained by multiplying the values presented below by a factor $\sim
1.4$ )."
 As discussed. πι D'Ercole. (2008) and D'Ercole. (2010) in order to explain the chemical properties of SC. stars it is necessary to iuvoke the presence of pristine eas wunxed iu with the matter from which SG stars formed (sce also Pfinu-Alteubure I&roupa 2009 for a study of the possible accretion of eas from the ISM. curing the SC. formation process)., As discussed in D'Ercole (2008) and D'Ercole (2010) in order to explain the chemical properties of SG stars it is necessary to invoke the presence of pristine gas mixed in with the matter from which SG stars formed (see also Pflamm-Altenburg Kroupa 2009 for a study of the possible accretion of gas from the ISM during the SG formation process).
 As shown by D'Ercole et al. (, As shown by D'Ercole et al. (
2008. 2010). a mass of pristine gas equal to about of the total mass of SC star-formine gas is required to reproduce the abundance patterns (Na-O. Ale-Al anticorrelations aud the belium cistribution function) observed in the massive cluster NGC2808 aud iu the low-mass cluster ALL (see also Veutura 2009. Ventura D'Antona 2009).,"2008, 2010), a mass of pristine gas equal to about of the total mass of SG star-forming gas is required to reproduce the abundance patterns (Na-O, Mg-Al anticorrelations and the helium distribution function) observed in the massive cluster NGC2808 and in the low-mass cluster M4 (see also Ventura 2009, Ventura D'Antona 2009)."
 ILlowever. additional systematic stuclies of the chemical properties of the iudivicual clusters for which spectroscopic data are available will be required to explore the allowed mass range of pristine gas and any possible dependences ou. protocluster conditious.," However, additional systematic studies of the chemical properties of the individual clusters for which spectroscopic data are available will be required to explore the allowed mass range of pristine gas and any possible dependences on protocluster conditions."
 Tere we smnplv assume that pristine material makes up of the total mass of gas forming the SC stars., Here we simply assume that pristine material makes up of the total mass of gas forming the SG stars.
 Results for differeut pristine gas fractions cau be easilv obtained from those preseuted in this Letter., Results for different pristine gas fractions can be easily obtained from those presented in this Letter.
 The two panels of Fig., The two panels of Fig.
" 1. show the fractional mass of SC. stars formed. £=(Mage;/M);,;. as à fiction of the total cluster mass (AS). for models with differeut colubinationus of values of the halfiuass radius (2),=2.| pc) of the truncatiou radius (RP=20. 10. and SO pe: these values encompass the range of R for he majority of Galactic elobular clusters. for which the nodal value is R—LO pe: see e.g. Mackey van den Borel 2005) aud for a IK93 or IKOL EME."," \ref{fig:hydrofig} show the fractional mass of SG stars formed, $\xi\equiv (M_{SG}/M)_{init}$, as a function of the total cluster mass $M$ ), for models with different combinations of values of the half-mass radius $R_h=1,~2,~4$ pc), of the truncation radius $R=20$, 40, and 80 pc; these values encompass the range of R for the majority of Galactic globular clusters, for which the modal value is $R\sim 40
$ pc; see e.g. Mackey van den Bergh 2005) and for a K93 or K01 IMF."
 As the cluster lass ducreascs for given values of Rand 2). so too do the cluster escape speed. the fraction of AGB ejecta retained. and the total mass of SG stars formed.," As the cluster mass increases for given values of $R$ and $R_h$, so too do the cluster escape speed, the fraction of AGB ejecta retained, and the total mass of SG stars formed."
 For the structural xwanmieters explored. oulv clusters initially more massive hau ~d0510°AZ. can retain enough. AGB ejecta to orn an appreciable fraction of SC stars.," For the structural parameters explored, only clusters initially more massive than $\sim 10^{4.8}-10^5~M_{\odot}$ can retain enough AGB ejecta to form an appreciable fraction of SG stars."
 The ditfereuce )etween the values of & obtained for the N93 aud the 01 IME is a consequence of the fact that the Io. IME contains a larger fraction of the cluster mass in the mass range ofthe polluting AGB stars., The difference between the values of $\xi$ obtained for the K93 and the K01 IMF is a consequence of the fact that the K01 IMF contains a larger fraction of the cluster mass in the mass range of the polluting AGB stars.
 A complete model for the determination of the fraction of SC. stars in the Galactic halo would require accurate snowledge of the initial global properties of the Galactic elobular cluster svsteni as well as its dyizunuical history. he iuitial internal structure and subsequent dyvuamical evolution of clusters with multiple stellar populations. and a comprehensive theory of how the stellar halo formed.," A complete model for the determination of the fraction of SG stars in the Galactic halo would require accurate knowledge of the initial global properties of the Galactic globular cluster system as well as its dynamical history, the initial internal structure and subsequent dynamical evolution of clusters with multiple stellar populations, and a comprehensive theory of how the stellar halo formed."
 Much work remains to be done on all of these woblems., Much work remains to be done on all of these problems.
 Considering the uncertainties involved in all 6 these kev ineredicuts. we elect to proceed here iu a simplified wav. aud our estimation of proceeds as ollows.," Considering the uncertainties involved in all of these key ingredients, we elect to proceed here in a simplified way, and our estimation of proceeds as follows."
" For as eiven value of the total amass of the Galactic globular cluster system. AMI. and a given initial elobular cluster svstem mass function (hereafter IGCME), we calculate the total mass of SC stars formed iu the cluster system. MUess. using the results of the lydrodvuamiical sinulatious described iu the previous section."," For a given value of the total mass of the Galactic globular cluster system, $M_{GCS}^{init}$, and a given initial globular cluster system mass function (hereafter IGCMF), we calculate the total mass of SG stars formed in the cluster system, $M_{SG,GCS}^{init}$, using the results of the hydrodynamical simulations described in the previous section."
 MUTees may be written. iu general. as an iutegral over cluster structural properties where fGU.Ry.R) is the joiut distribution fiction of initial cluster mass and structural parameters.," $M_{SG,GCS}^{init}$ may be written, in general, as an integral over cluster structural properties where $f(M, R_h, R)$ is the joint distribution function of initial cluster mass and structural parameters."
Having obtained the scalefactors for the optical depths iu the simulations we can derive a lower limit on O5.,Having obtained the scalefactors for the optical depths in the simulations we can derive a lower limit on $\Omega_b$.
" For au independent estimate of the radiation backeround intensity we adopt a temporally constant UV background with ΓονioPb) 1,", For an independent estimate of the radiation background intensity we adopt a temporally constant UV background with $\Gamma > 7\times10^{-13}$ $^{-1}$.
" This value correspouds to J,z:2.3«10.7? (depending ou the spectral shape)."," This value corresponds to $J_{\nu} \approx 2.3 \times
10^{-22}$ (depending on the spectral shape)."
 It is aDit in that it icludes ouly the radiation backgrouud from known QSOs alone., It is a in that it includes only the radiation background from known QSOs alone.
" From the firma lower limit ou P due to QSOs alone we can determine a lower limit for the amount of barvous in the universe: Our measurement (described in more detail iu [5|)) supports a high 5,45; (low D/II) universe. still consistent with the upper rauge permitted bv the solar system light clement abundances |] and with the ων derived from the D/II measurements by Tytler et al. ("," From the firm lower limit on $\Gamma$ due to QSOs alone we can determine a lower limit for the amount of baryons in the universe: Our measurement (described in more detail in \cite{rau}) ) supports a high $\Omega_{baryon}$ (low D/H) universe, still consistent with the upper range permitted by the solar system light element abundances \cite{hata} and with the $\Omega_{baryon}$ derived from the D/H measurements by Tytler et al. ("
these proceedings).,these proceedings).
 Remaining uncertainties stem from the assuuued intensity of the ionizing radiation backeround. and the temperature the lower columu deusitv gas has attained by the time relonization is complete.," Remaining uncertainties stem from the assumed intensity of the ionizing radiation background, and the temperature the lower column density gas has attained by the time reionization is complete."
 Moreover. the data sample is still relatively sinall. especially at lower redshifts.," Moreover, the data sample is still relatively small, especially at lower redshifts."
 The validity of these results depends of course not only the correct cosmological uodel. but also on its technical realisation: how can we be sure that we are iof missing structure on very σα scales. which are not resolved by the sinulatious?," The validity of these results depends of course not only the correct cosmological model, but also on its technical realisation: how can we be sure that we are not missing structure on very small scales, which are not resolved by the simulations?"
 If there were clampiness on sub-kpe scales (iresolved by current echuiques). the eas could be locally more neutral auc a smaller amount of xuwvous could conceivably account for the same amount of opacity iu the Lun à forest.," If there were clumpiness on sub-kpc scales (unresolved by current techniques), the gas could be locally more neutral and a smaller amount of baryons could conceivably account for the same amount of opacity in the Lyman $\alpha$ forest."
 From some point on such structure willdiverge from the xoperties of the CDM. based cosinological models [12]. but the only way to find out for sure whether it exists is to search directly for climrpinecss in the eas respousible for most of the Lya forest absorption.," From some point on such structure willdiverge from the properties of the CDM based cosmological models \cite{wein}
 but the only way to find out for sure whether it exists is to search directly for clumpiness in the gas responsible for most of the $\alpha$ forest absorption."
 The presence or absence of density aud velocity structure on very θα scales at hieh z can best be tested for bv searching for differences between the absorption svstenis in adjacent lines of sight to multiple (leused) QSO images., The presence or absence of density and velocity structure on very small scales at high z can best be tested for by searching for differences between the absorption systems in adjacent lines of sight to multiple (lensed) QSO images.
 We have eiibarked ou a project to (re-)Jobserve high redshitt lensed QSOs with the Ίνους TIRES spectrograph. auoue them the two cases UM 673 and. ITE 1101-1805. studied in the important papers by Sette ct al. 9.10]..," We have embarked on a project to (re-)observe high redshift lensed QSOs with the Keck HIRES spectrograph, among them the two cases UM 673 and HE 1104-1805, studied in the important papers by Smette et al. \cite{sme1,sme2}."
 The difference to earlier work is that with eck we are able to resolve the line widths even of iiost metal absorption svstcis. and cau measure the column densities directly.," The difference to earlier work is that with Keck we are able to resolve the line widths even of most metal absorption systems, and can measure the column densities directly."
 The coluun density differences over a known separation in the plane ofthe sky can be translated into eradicuts in the barvon density., The column density differences over a known separation in the plane of the sky can be translated into gradients in the baryon density.
 We have completely profile-fitted a Lyinan a forest region around z= 2.6 iu both the A and P images of the OSO UNMGT2 and measured the columu differences amoung those Voiet profile components agrecing in velocity position to within 10 +., We have completely profile-fitted a Lyman $\alpha$ forest region around z= 2.6 in both the $A$ and $B$ images of the QSO UM673 and measured the column differences among those Voigt profile components agreeing in velocity position to within 10 $^{-1}$ .
 We, We
"distance increases approximately with the square of the density, so that in very optically thick cells, photon packets may become effectively trapped.","distance increases approximately with the square of the density, so that in very optically thick cells, photon packets may become effectively trapped."
 This problem can be avoided by locally making use of the diffusion approximation to solve the radiative transfer in these regions., This problem can be avoided by locally making use of the diffusion approximation to solve the radiative transfer in these regions.
" For example, ? developed a modified random walk procedure based on the diffusion approximation that can dramatically reduce the number of steps required for a photon to escape from a grid cell of arbitrarily large optical depth."," For example, \citet{min:09:155} developed a modified random walk procedure based on the diffusion approximation that can dramatically reduce the number of steps required for a photon to escape from a grid cell of arbitrarily large optical depth."
" A large collection of dust continuum Monte-Carlo radiative transfer codes has been developed (e.g.7??777??77?7?777??7), each including some or all of the above optimizations, as well as other optimizations not mentioned here."," A large collection of dust continuum Monte-Carlo radiative transfer codes has been developed \citep[e.g.][]{wolf:99:839, harries:00:722, gordon:01:269, misselt:01:277, wood:01:299, wood:02:1183, wood:02:887, wolf:03:99, stamatellos:03:941, whitney:03:1079, whitney:03:1049, whitney:04:1177, dullemond:04:159, jonsson:06:2, pinte:06:797, min:09:155}, each including some or all of the above optimizations, as well as other optimizations not mentioned here."
" While some of the early codes assumed spherical or axis-symmetric geometries for simplicity, many have since been adapted to compute fully arbitrary three-dimensional distributions."," While some of the early codes assumed spherical or axis-symmetric geometries for simplicity, many have since been adapted to compute fully arbitrary three-dimensional distributions."
" In addition to dust continuum radiative transfer, some codes can also compute non-LTE line transfer (??),, or photoionization (e.g.???).."," In addition to dust continuum radiative transfer, some codes can also compute non-LTE line transfer \citep{carciofi:06:1081, carciofi:08:1374}, or photoionization \citep[e.g.][]{ercolano:03:1136, ercolano:05:1038, ercolano:08:534}."
" This paper presentsHYPERION, a new dust-continuum Monte-Carlo radiative transfer code that is designed to be applicable to a wide range of problems."," This paper presents, a new dust-continuum Monte-Carlo radiative transfer code that is designed to be applicable to a wide range of problems."
" implements many of the recent optimizations to the Monte-Carlo technique discussed above, was written from the start to be a parallel code that can scale to thousands of processes, and is written in a modular and extensible way so as to be easily improved in future."," implements many of the recent optimizations to the Monte-Carlo technique discussed above, was written from the start to be a parallel code that can scale to thousands of processes, and is written in a modular and extensible way so as to be easily improved in future."
" It can treat the emission from an arbitrary number of sources, can include multiple dust types, and can compute the anisotropic scattering of polarized radiation using fully numerical scattering phase functions."," It can treat the emission from an arbitrary number of sources, can include multiple dust types, and can compute the anisotropic scattering of polarized radiation using fully numerical scattering phase functions."
" It uses the ? iterative method to determine the radiative equilibrium temperature, but does not use the ? temperature correction technique, as the latter is much more challenging to parallelize efficiently."," It uses the \citet{Lucy:99:282} iterative method to determine the radiative equilibrium temperature, but does not use the \citet{bjorkman:01:615} temperature correction technique, as the latter is much more challenging to parallelize efficiently."
" Thanks to the modular nature of the code, the radiative transfer can be computed on a number of different three-dimensional grid types, and additional grid types can be added in future."," Thanks to the modular nature of the code, the radiative transfer can be computed on a number of different three-dimensional grid types, and additional grid types can be added in future."
 can compute SEDs and multi-wavelength images and polarization maps., can compute SEDs and multi-wavelength images and polarization maps.
" The code is released under an open source license, and is hosted on a service that allows members of the community to easily contribute to the code and documentation."," The code is released under an open source license, and is hosted on a service that allows members of the community to easily contribute to the code and documentation."
 Section 2. gives an overview of the implementation of the code., Section \ref{sec:overview} gives an overview of the implementation of the code.
 Section 3 discusses the efficiency of the parallelized code., Section \ref{sec:parallel} discusses the efficiency of the parallelized code.
 Section 4 presents the results for two benchmark models of protoplanetary disks., Section \ref{sec:benchmarks} presents the results for two benchmark models of protoplanetary disks.
" Finally, Section 5 demonstrates the capabilities of the code by computing temperatures, SEDs, and synthetic images for a simulation of a star-formation region."," Finally, Section \ref{sec:simulation} demonstrates the capabilities of the code by computing temperatures, SEDs, and synthetic images for a simulation of a star-formation region."
 The availability of the code and plans for the future are discussed in Section 6.., The availability of the code and plans for the future are discussed in Section \ref{sec:future}.
 'The code is split into two main components., The code is split into two main components.
" The first, which carries out the core of the radiative transfer calculation, is implemented in Fortran 95/2003 for high performance."," The first, which carries out the core of the radiative transfer calculation, is implemented in Fortran 95/2003 for high performance."
" This part of the code is problem-independent: the input (bundled into a single file) consists of an arbitrary three-dimensional density structure as well as dust properties, a list of sources, and output parameters."," This part of the code is problem-independent: the input (bundled into a single file) consists of an arbitrary three-dimensional density structure as well as dust properties, a list of sources, and output parameters."
" This input is used by the Monte-Carlo radiative transfer code to compute temperatures, SEDs, and images."," This input is used by the Monte-Carlo radiative transfer code to compute temperatures, SEDs, and images."
" Therefore, it is possible to use either gridded analytical density structures, or arbitrary density grids from simulations."," Therefore, it is possible to use either gridded analytical density structures, or arbitrary density grids from simulations."
" At the moment, supports several types of three-dimensional grids refsec:grid)) and the modular nature of the code will make it easy to add support for additional grid types in the future."," At the moment, supports several types of three-dimensional grids \\ref{sec:grid}) ) and the modular nature of the code will make it easy to add support for additional grid types in the future."
" It is possible to specify an arbitrary number of dust types (within computational limits), which allows models to have different effective grain size distributions and compositions in different grid cells."," It is possible to specify an arbitrary number of dust types (within computational limits), which allows models to have different effective grain size distributions and compositions in different grid cells."
 The second component of the code consists of an object-oriented Python library that makes it easy to set up the input file for arbitrary problems from a single script., The second component of the code consists of an object-oriented Python library that makes it easy to set up the input file for arbitrary problems from a single script.
 This library includes pre-defined analytical density structures for common problems such as flared disks and rotationally flattened envelopes and will also include scripts to import density structures from simulations., This library includes pre-defined analytical density structures for common problems such as flared disks and rotationally flattened envelopes and will also include scripts to import density structures from simulations.
 Post-processing tools are also provided in the Python library to analyze the results of radiative transfer models., Post-processing tools are also provided in the Python library to analyze the results of radiative transfer models.
 The present section describes the algorithm for the main radiative transfer code., The present section describes the algorithm for the main radiative transfer code.
" The code first reads in the inputs refsec:input)), then propagates photon packets through the grid refsec:propagation)) for multiple iterations to compute the energy absorbed in each cell refsec:temperature))."," The code first reads in the inputs \\ref{sec:input}) ), then propagates photon packets through the grid \\ref{sec:propagation}) ) for multiple iterations to compute the energy absorbed in each cell \\ref{sec:temperature}) )."
" Once the absorbed energy calculation has converged refsec:convergence)), the code computes SEDs and images refsec:seds))."," Once the absorbed energy calculation has converged \\ref{sec:convergence}) ), the code computes SEDs and images \\ref{sec:seds}) )."
 A model can include any number of sources of emission (within computational limits), A model can include any number of sources of emission (within computational limits).
" Each source is characterized by a bolometric luminosity, and the frequencies of the emitted photon packets are randomly sampled such that the emergent frequency distribution of the packets reproduces a user-defined spectrum."," Each source is characterized by a bolometric luminosity, and the frequencies of the emitted photon packets are randomly sampled such that the emergent frequency distribution of the packets reproduces a user-defined spectrum."
 The total number of photons to emit from sources is set by the user., The total number of photons to emit from sources is set by the user.
" A number of different source types can be used - at the moment, the code supports:"," A number of different source types can be used – at the moment, the code supports:"
or in the derived inclination owing to the less than perfect phase coverage and errors im measuring the contamination from the aceretion disk.,or in the derived inclination owing to the less than perfect phase coverage and errors in measuring the contamination from the accretion disk.
 It was straightforward to perform two fitting sequences to see what effect including the rotational velocity as a fitting constraint had on the outcome., It was straightforward to perform two fitting sequences to see what effect including the rotational velocity as a fitting constraint had on the outcome.
 It is less straightforward to quantify the effects. of incomplete phase coverage or imperfect disk/stellar decomposition., It is less straightforward to quantify the effects of incomplete phase coverage or imperfect disk/stellar decomposition.
 However. we can say with some confidence that since our derived inclination is already quite high and near the upper limit imposed by the lack of X-ray eclipses. it is unlikely that we have underestimated the true inclination significantly.," However, we can say with some confidence that since our derived inclination is already quite high and near the upper limit imposed by the lack of X-ray eclipses, it is unlikely that we have underestimated the true inclination significantly."
 Ultimately one would need to obtain additional data to see if similar light curves are observed., Ultimately one would need to obtain additional data to see if similar light curves are observed.
" The distance to the source is a function of four parameters: The mass M» and temperature Ίο of the secondary star fix its luminosity (see refden)): interstellar extinction (Ay) makes the source appear fainter: and extra light from the accretion disk (parameterized by the V-band ""disk fraction"" Ky) makes the source appear brighter.", The distance to the source is a function of four parameters: The mass $M_2$ and temperature $T_{\rm eff}$ of the secondary star fix its luminosity (see \\ref{den}) ); interstellar extinction $A_V$ ) makes the source appear fainter; and extra light from the accretion disk (parameterized by the $V$ -band “disk fraction” $k_V$ ) makes the source appear brighter.
 We have reasonably good values for all of these parameters., We have reasonably good values for all of these parameters.
 As noted in refsecsec.. Ayz4.75 can be derived by modelling the X- spectrum and assuming a typical gas to dust ratio for the interstellar medium: Ayz:0.30 was determined from our spectral decomposition reffig3aa and 4bb); and a temperature range of 4100<Tay K was deduced for the secondary star.," As noted in \\ref{secsec}, $A_V \approx 4.75$ can be derived by modelling the X-ray spectrum and assuming a typical gas to dust ratio for the interstellar medium; $k_V
\approx 0.30$ was determined from our spectral decomposition \\ref{fig3}a a and \ref{fig3}b b); and a temperature range of $4100\le T_{\rm eff} \le 5100$ K was deduced for the secondary star."
 Using these results and a simple Monte Carlo procedure. we computed the distance and its uncertainty for various. values of the secondary star mass M».," Using these results and a simple Monte Carlo procedure, we computed the distance and its uncertainty for various values of the secondary star mass $M_2$."
 We used the synthetic photometry computed from the to determine the expected absolute V magnitude of thestar from its temperature. radius. and surface gravity.," We used the synthetic photometry computed from the to determine the expected absolute $V$ magnitude of thestar from its temperature, radius, and surface gravity."
" For this procedure we adopted 4100<Tay5100 K. ky20.300.05. à mean apparent V. magnitude of 22.0+0.2. and Nj,=(8.5E2.3)«10?! emo? confidence) and Ay=Ny/1.79«107! (exact)."," For this procedure we adopted $4100\le T_{\rm eff}\le 5100$ K, $k_V = 0.30\pm
0.05$, a mean apparent $V$ magnitude of $22.0\pm 0.2$, and $N_H=(8.5\pm
2.3)\times 10^{21}$ $^{-2}$ confidence) and $A_V=N_H/1.79\times 10^{21}$ (exact)."
 The results are displayed in Table 6 for a wide range of secondary star masses., The results are displayed in Table \ref{tabdist} for a wide range of secondary star masses.
 For masses in the range of 0.15 to 3.0M.. the computed distance is in the range 3.0 to 7.6 kpe.," For masses in the range of 0.15 to $3.0\,M_{\odot}$ the computed distance is in the range 3.0 to 7.6 kpc."
 However. at a fixed mass. the formal error on the distance is rather large due to the relatively large adopted temperature range and to the relatively large error in Nj.," However, at a fixed mass, the formal error on the distance is rather large due to the relatively large adopted temperature range and to the relatively large error in $N_H$."
 The distance for the case of M»=1.31M.. is 5.9kpe. again with a rather large formal error (10 range of 2.8 to 7.6 kpe).," The distance for the case of $M_2=1.31\,M_{\odot}$ is 5.9kpc, again with a rather large formal error $1\sigma$ range of 2.8 to 7.6 kpc)."
 We can make an independent estimate of the distance if we assume the observed systemic velocity of +=—6812 km s! is entirely due to differential galactic rotation., We can make an independent estimate of the distance if we assume the observed systemic velocity of $\gamma=-68\pm 12$ km $^{-1}$ is entirely due to differential galactic rotation.
 We use the rotation curve of Fich. Blitz. Stark (1989) and the standard IAU rotation constants of Ro=8.5 kpe and Oy=220 km s.," We use the rotation curve of Fich, Blitz, Stark (1989) and the standard IAU rotation constants of $R_0=8.5$ kpc and $\Theta_0=220$ km $^{-1}$."
" The rotation curve for asource with galactic coordinates of (—325.88"" and 5b=—1.83 is roughly parabolic. with a minimum radial velocity of =—95 km s! at a distance of z7 kpe."," The rotation curve for asource with galactic coordinates of $\ell-325.88^{\circ}$ and $b=-1.83^{\circ}$ is roughly parabolic, with a minimum radial velocity of $\approx -95$ km $^{-1}$ at a distance of $\approx 7$ kpc."
 The expected distance for a source with ?=—68 km s! is either z4.4 kpe or z9.7 kpe., The expected distance for a source with $\gamma=-68$ km $^{-1}$ is either $\approx 4.4$ kpc or $\approx 9.7$ kpc.
 Considering the errors on +. the kinematic distance can be anywhere between ~3.2 kpe and zz10.8 kpe at the Io level. which is entirely consistent with the ranges derived above.," Considering the errors on $\gamma$, the kinematic distance can be anywhere between $\approx 3.2$ kpc and $\approx 10.8$ kpc at the $1\sigma$ level, which is entirely consistent with the ranges derived above."
 Given the general agreement between the two distance estimates we conclude that XTE J1550-564 has essentially no (radial) velocity with respect to its local standard of rest., Given the general agreement between the two distance estimates we conclude that XTE J1550-564 has essentially no (radial) velocity with respect to its local standard of rest.
 We can use the distance estimates for XTE J1550-564 to calculate an order of magnitude estimate for the maximum X-ray luminosity seen during outbursts., We can use the distance estimates for XTE J1550-564 to calculate an order of magnitude estimate for the maximum X-ray luminosity seen during outbursts.
 The spectral analysis of Sobezaketal.(2000) for the intense flare of 1998 September 19 implies an unabsorbed flux of 3.7«107 ere em s! over the range of 1-20 keV. with the spectrum dominated by the power-law component.," The spectral analysis of \citet{sob00}
 for the intense flare of 1998 September 19 implies an unabsorbed flux of $3.7 \times 10^{-7}$ erg $^{-2}$ $^{-1}$ over the range of 1-20 keV, with the spectrum dominated by the power-law component."
 For our favored distance of 5.3 kpe. the isotropic luminosity is then 1.77«10°° ere s! (with a large error owing to the uncertainty in the distance).," For our favored distance of 5.3 kpc, the isotropic luminosity is then $1.77\times10^{39}$ erg $^{-1}$ (with a large error owing to the uncertainty in the distance)."
 This its just slightly above the Eddington luminosity for a 10.56M.. black hole. which is a remarkable coincidence given the significant uncertainty in the distance.," This is just slightly above the Eddington luminosity for a $10.56\,M_{\odot}$ black hole, which is a remarkable coincidence given the significant uncertainty in the distance."
 Bailynetal.(1998) analyzed. the distribution of black hole masses in seven systems and found a high probability that six of the seven systems (GRO 10342232. A0620-00. GS 1124-683. GRO J1655-40. H1705-250. and GS 2000-25) have masses which are consistent with z7M...," \citet{bai98} analyzed the distribution of black hole masses in seven systems and found a high probability that six of the seven systems (GRO J0422+32, A0620-00, GS 1124-683, GRO J1655-40, H1705-250, and GS 2000+25) have masses which are consistent with $\approx 7\,M_{\odot}$."
 The seventh system. V404 Cyg. has a mass which ts significantly larger (about 12M.: Shahbaz et 11994).," The seventh system, V404 Cyg, has a mass which is significantly larger (about $12\,M_{\odot}$; Shahbaz et 1994)."
 The mass of the black hole in XTE J1S550-564 is well above 7M...," The mass of the black hole in XTE J1550-564 is well above $7\,M_{\odot}$."
" With M,>8.1M.. at 3c confidence (Table 3)). its mass may in fact be similar to the mass of the black hole in V404 Cyg."," With $M_1\ge 8.1\,M_{\odot}$ at $3\sigma$ confidence (Table \ref{parm}) ), its mass may in fact be similar to the mass of the black hole in V404 Cyg."
 Since the work of Bailynetal.(1998).. the mass functions for seven additional systems have been measured. and improved parameters for some of the original seven systems have been measured.," Since the work of \citet{bai98}, the mass functions for seven additional systems have been measured, and improved parameters for some of the original seven systems have been measured."
 Thus the issue of the observed black hole mass distribution should be revisited to see if the clustering of black hole masses near 7M... is still significant.," Thus the issue of the observed black hole mass distribution should be revisited to see if the clustering of black hole masses near $7\,M_{\odot}$ is still significant."
 Given the new data. we can begin to make meaningful comparisons with formation theory.," Given the new data, we can begin to make meaningful comparisons with formation theory."
 For example. the detailed formation models of Fryer&Kalogera(2001) predict a mass distribution which 15 continuous and which extends over a broad range (in particular. they predict no peak at ~7M..).," For example, the detailed formation models of \citet{fry01} predict a mass distribution which is continuous and which extends over a broad range (in particular, they predict no peak at $\approx 7\,M_{\odot}$ )."
 The determination of the black hole mass for XTE J1550-564 is especially important for the interpretation of the high-frequency X-ray quasi-periodic oscillations (QPOs) observed for this system (Remillard et al., The determination of the black hole mass for XTE J1550-564 is especially important for the interpretation of the high-frequency X-ray quasi-periodic oscillations (QPOs) observed for this system (Remillard et al.
 2002: Homan et al., 2002; Homan et al.
 2001)., 2001).
 Models for several types of oscillations predicted in general relativity are under investigation as possible causes of these QPOs (e.g. Remillard 2001. and references therein): all of these depend on both the mass and spin of the black hole. and possibly also on conditions in the inner aceretion disk.," Models for several types of oscillations predicted in general relativity are under investigation as possible causes of these QPOs (e.g. Remillard 2001, and references therein); all of these depend on both the mass and spin of the black hole, and possibly also on conditions in the inner accretion disk."
 Despite considerable uncertainties 1n. the models. we can offer a few comments on the implications of our mass determination for XTE J1550-564.," Despite considerable uncertainties in the models, we can offer a few comments on the implications of our mass determination for XTE J1550-564."
 At the nominal mass of 10.7M... oscillations at the frequency of the last stable orbit for a Schwarzschild black hole (spin parameter. 4.= 0) would be seen at a frequency. »/=2199μμ/M..)208.2 Hz (Shapiro&Teukolsky 1983).," At the nominal mass of $10.7\,M_{\odot}$, oscillations at the frequency of the last stable orbit for a Schwarzschild black hole (spin parameter, $a_* = 0$ ) would be seen at a frequency, $\nu = 2199 / (M_{\rm BH} / M_{\odot}) = 208.2 $ Hz \citep{sha83}."
. Since XTE J1550-564 has exhibited QPOs with frequencies up to 284 Hz (Homanetal. 2001).. it appears that plausible mechanisms require o.> 0. (," Since XTE J1550-564 has exhibited QPOs with frequencies up to 284 Hz \citep{hom01}, , it appears that plausible mechanisms require $a_* > 0$ . ("
The oscillation frequency would be 284 Hz (for a.= 0) if Myy=7.7AM ... which is below the 36 lower limit on the black hole mass.),"The oscillation frequency would be 284 Hz (for $a_*=0$ ) if $M_{\rm BH}=7.74\,M_{\odot}$ , which is below the $3\sigma$ lower limit on the black hole mass.)"
 This argument was used by Strohmayer(2001) to suggest that the 450 Hz QPO in GRO J1655-40 implies appreciable spin for the black hole in that system.," This argument was used by \citet{str01}
 to suggest that the 450 Hz QPO in GRO J1655-40 implies appreciable spin for the black hole in that system."
" We further note that the ratio of the black hole masses for XTE J1550-564 (M,=10.6M ..."," We further note that the ratio of the black hole masses for XTE J1550-564 $M_1=10.6\,M_{\odot}$ ,"
2.,2.
 Persistent precessional variability in lard XN-ravs was discovered with the maxima to nininuiua fux ratio —1. which is twice as large as in the softer X-ray baud.," Persistent precessional variability in hard X-rays was discovered with the maximum to minimum flux ratio $\sim 4$, which is twice as large as in the softer X-ray band."
 3., 3.
 The observed lard N-ray orbital eclipse is found to be in phase with the optical aud near infrared eclipses., The observed hard X-ray orbital eclipse is found to be in phase with the optical and near infrared eclipses.
 The hard X-ray eclipse is observed to be at least two tines deeper than the sof N-rav eclipse., The hard X-ray eclipse is observed to be at least two times deeper than the soft X-ray eclipse.
 The width of the N-rav eclipse increases with cucrey. which is opposite to what is observed iu classical N-ray binary svstenis.," The width of the X-ray eclipse increases with energy, which is opposite to what is observed in classical X-ray binary systems."
 1., 4.
 The broadbaud X-ray spectrin 2-100 keV of SS133 simultaneously obtained by aud RNTE in March 2001 when he source was in its faring state cau be fitted by bremsstralilung cussion from optically thin plasma with a cluperature ADτε30 keV. 5., The broadband X-ray spectrum 2-100 keV of SS433 simultaneously obtained by and RXTE in March 2004 when the source was in its flaring state can be fitted by bremsstrahlung emission from optically thin plasma with a temperature $kT\approx 30$ keV. 5.
" Optical spectroscopic observations of $8133 on the SAO ο telescope which were performed iu the framework ofthe multiwaveleneth canrpaien of the source confirmed the spectral class of the optical star to be AS-ATI. The radial velocity curve of the optical component was obtained with a semu-amplitude A,=13249 kin/s near the maxuuuni disk openius precession phase (T3).", Optical spectroscopic observations of SS433 on the SAO 6-m telescope which were performed in the framework of the multiwavelength campaign of the source confirmed the spectral class of the optical star to be A5-A7I. The radial velocity curve of the optical component was obtained with a semi-amplitude $K_v=132\pm 9$ km/s near the maximum disk opening precession phase (T3).
 The spectroscopic data revealed a heating effect of the hemisphere of the optica star illuminated by the accretion disk., The spectroscopic data revealed a heating effect of the hemisphere of the optical star illuminated by the accretion disk.
 6., 6.
 From the analysis of the hard X-rav eclipse ane precession variability in $$133 we estimate the mass ratio in this binary svstem to be q~0.3., From the analysis of the hard X-ray eclipse and precession variability in SS433 we estimate the mass ratio in this binary system to be $q\sim 0.3$.
" This mass ratio iux radial velocity measurements corrected for the heatingo effect enable us to evaluate the masses of the optical aux colmpact star in 88133 to ve Mom0M LM,zmOM... respectively,"," This mass ratio and radial velocity measurements corrected for the heating effect enable us to evaluate the masses of the optical and compact star in SS433 to be $M_v\approx 30 M_\odot$, $M_x \approx 9 M_\odot$, respectively."
 This finding lends further support to the presence of a black hole in this peculiar superaccretiug ealactic niücroquasar., This finding lends further support to the presence of a black hole in this peculiar superaccreting galactic microquasar.
ssludy evolve rapidly and become sufficiently. Iumninous to drive widespread sublimation of interstellar ices in their vicinitv. whereas the lower-mass objects in our sample have less impact on their environment.,"study evolve rapidly and become sufficiently luminous to drive widespread sublimation of interstellar ices in their vicinity, whereas the lower-mass objects in our sample have less impact on their environment."
 For a voung star of a given mass. the degree of depletion of CO and other molecules in the envelope is likely to evolve with time (e.g.. Thomas Fuller 2008).," For a young star of a given mass, the degree of depletion of CO and other molecules in the envelope is likely to evolve with time (e.g., Thomas Fuller 2008)."
 Rettig (2005) estimate Chat the solid CO abundance exceeds the gas phase abundance by a factor ~6 toward the eruptive T Tauri star VI64T Orionis. which implies 0(CO)=0.85 in this ine of sight.," Rettig (2005) estimate that the solid CO abundance exceeds the gas phase abundance by a factor $\sim6$ toward the eruptive T Tauri star V1647 Orionis, which implies $\delta({\rm CO})\ga 0.85$ in this line of sight."
 It would clearly be important to obtain data for a larger sample of low and intermediate-niass. YSOs., It would clearly be important to obtain data for a larger sample of low and intermediate-mass YSOs.
 In the case of one object in our sample. the intermeciate-amass voung star Elias 18 JO439557442515020). a notable discrepancy is apparent between our value of 1.0x10%em? from the radio survey data and that of Shuping (2001). who obtain a value a factor ~LOO less from a study of the infrared spectrum of this source.," In the case of one object in our sample, the intermediate-mass young star Elias 18 (J04395574+2545020), a notable discrepancy is apparent between our value of $N({\rm CO})_{\rm gas} \approx 1.0 \times 10^{18}~{\rm cm^{-2}}$ from the radio survey data and that of Shuping (2001), who obtain a value a factor $\sim100$ less from a study of the infrared spectrum of this source."
 It is possible that the difference might arise because of the finite beam size of (he radio observations. ancl (he possibilitv of dense material behind the source. as previously discussed in Section 1.," It is possible that the difference might arise because of the finite beam size of the radio observations, and the possibility of dense material behind the source, as previously discussed in Section 1."
 Shuping ppropose that CO is highly depleted in the circumstellar disk of Elias 15 and that it suffers very little loreeround absorption in the molecular cloud: however. we consider this unlikely. eiven that the abundance of solid CO is actually less toward Elias 18 compared. with the Taurus field stars wilh respect to both II50--ice and total extinction (ly22 mag) in the line of sight (Chiar 11995: Nummelin 22001).," Shuping propose that CO is highly depleted in the circumstellar disk of Elias 18 and that it suffers very little foreground absorption in the molecular cloud; however, we consider this unlikely, given that the abundance of solid CO is actually less toward Elias 18 compared with the Taurus field stars with respect to both -ice and total extinction $\av\approx 22$ mag) in the line of sight (Chiar 1995; Nummelin 2001)."
 ence. the CO as well as the gas-phase CO toward Elias 13 must be unusually low if the Shupping rresult is accurate.," Hence, the CO as well as the gas-phase CO toward Elias 18 must be unusually low if the Shupping result is accurate."
 In (his section we briefly review and discuss theoretical constraints on the timescale lor CO depletion in molecular clouds. ancl examine the degree to which {μον are consistent with our results.," In this section we briefly review and discuss theoretical constraints on the timescale for CO depletion in molecular clouds, and examine the degree to which they are consistent with our results."
 The rate at which gaseous atoms or molecules accumulate onto the dust depends on the collision rate and the probability (hat a collision will lead to attachment., The rate at which gaseous atoms or molecules accumulate onto the dust depends on the collision rate and the probability that a collision will lead to attachment.
 The collision rate depends on the thermal speed of the gaseous species and (he surface area of the dust., The collision rate depends on the thermal speed of the gaseous species and the surface area of the dust.
 The latter may be expressed in terms of the total erain geometric cross-sectional area per 1I atom:, The latter may be expressed in terms of the total grain geometric cross-sectional area per H atom:
Is (here evidence for such higher electron densities in stellar [Iare loops?,Is there evidence for such higher electron densities in stellar flare loops?
 Recent reviews (e.g.. 810 in Güddel 2004: Ness et al.," Recent reviews (e.g., 10 in Güddel 2004; Ness et al."
" 2004) of electron density measurements in stellar flare loops based on densitv-sensitive iron line pairs quote a typical range of n,22x101122x10"" 7", 2004) of electron density measurements in stellar flare loops based on density-sensitive iron line pairs quote a typical range of $n_e \approx 2 \times 10^{11}-2 \times 10^{13}$ $^{-3}$.
" A density of p,23x10! em? and a spatial scale of 0.1 stellar radius (Lzz200 Alm) was measured in a spatially resolved flare on the eclipsing binary Aleol B (Schmitt οἱ al.", A density of $n_e \approx 3 \times 10^{11}$ $^{-3}$ and a spatial scale of 0.1 stellar radius $L\approx 200$ Mm) was measured in a spatially resolved flare on the eclipsing binary Algol B (Schmitt et al.
 2003)., 2003).
 This range of observed densities (1?zz2xLOM—10M 7) brackets our theoretically. predicted range., This range of observed densities $n_e^{obs} \approx 2 \times 10^{11}-2 \times 10^{13}$ $^{-3}$ ) brackets our theoretically predicted range.
 We have also to keep in mind that previously measured densities [rom stellar spectroscopy Crom Ile-like triplets of OV II. Ne LX. Mg XI. $i XIII. and densitv-sensitive line ratios) have severe sensitivity limitations for densities above 2LOY *.," We have also to keep in mind that previously measured densities from stellar spectroscopy (from He-like triplets of OV II, Ne IX, Mg XI, Si XIII, and density-sensitive line ratios) have severe sensitivity limitations for densities above $\gapprox 10^{12}$ $^{-3}$."
 So our densities predicted by the RTV law are in the same ballpark as the observed stellar [lare densiGies., So our densities predicted by the RTV law are in the same ballpark as the observed stellar flare densities.
 The RTV law seems to be a good. prediction tool. and the effects ofshort heating times. which can be a factor of £z2 lower than the RTV predicted densities (Appendix A: Fig.," The RTV law seems to be a good prediction tool, and the effects ofshort heating times, which can be a factor of $\approx 2$ lower than the RTV predicted densities (Appendix A; Fig."
 9). lareely cancel out the effects of short heating scale heieths. which can reach up to a [actor of 2 higher densities than predicted by the RIV law.," 9), largely cancel out the effects of short heating scale heigths, which can reach up to a factor of $\approx 2$ higher densities than predicted by the RTV law."
" A correlation between the volume emission measure. LAL,=mV and the flare peak temperature 7), was extended from solar flares to stellar faves (e.g.. Feldman et al."," A correlation between the volume emission measure $EM_p=n_p^2 V$ and the flare peak temperature $T_p$ was extended from solar flares to stellar flares (e.g., Feldman et al."
 1995b: Stern 1992: Shibata Yokovama 1999. 2002).," 1995b; Stern 1992; Shibata Yokoyama 1999, 2002)."
" A theoretical attempt was made to explain the solar/stellar EM,--T,Pp correlation with a universal flare model in terms of magnetic reconnection by Shibata Yokovama (1999. 2002)."," A theoretical attempt was made to explain the solar/stellar $EM_p-T_p$ correlation with a universal flare model in terms of magnetic reconnection by Shibata Yokoyama (1999, 2002)."
" Using the result of numerical MIID simulations of flares conducted in Yokovama Shibata (L998). where the flare peak temperature scales as NE (with 2 the magnetic field strength and ny the electron density outside the reconnection region). sel(ing the thermal pressure equal to the magnetic pressure. /82. and assuming Euclidian volume scaling. EM,x Web®. they arrived al an “universal scaling law’ of (their Eq."," Using the result of numerical MHD simulations of flares conducted in Yokoyama Shibata (1998), where the flare peak temperature scales as $T_p \propto B^{6/7} n_0^{-1/7} L^{2/7}$ (with $B$ the magnetic field strength and $n_0$ the electron density outside the reconnection region), setting the thermal pressure equal to the magnetic pressure, $2 n_p k_B T_p \approx B^2/8 \pi$ , and assuming Euclidian volume scaling, $EM_p \propto n_p^2 L^3$ , they arrived at an “universal scaling law” of (their Eq."
" 5) so (he emission measure scales with a power of EM,xT?", 5) so the emission measure scales with a power of $EM_p \propto T_p^{8.5}$.
" If we introduce the fractal scaling of the flare volume. EM,xnob? the universal scaling law of Shibata and Yokovama.(1999) takes the following form."," If we introduce the fractal scaling of the flare volume, $EM_p \propto
n_p^2 L^{D_V}$ , the universal scaling law of Shibata and Yokoyama(1999) takes the following form,"
of emploving lines far apart in wavelength. albeit not. to the same extent as 257.25/345.74.,"of employing lines far apart in wavelength, albeit not to the same extent as 257.25/345.74."
" We note that the average electron density for the SEIS.SO active region from Table 7 ds log N, = 9.60.3. similar to that cerived from line ratios in species formed at temperatures close to that ofFex."," We note that the average electron density for the SERTS–89 active region from Table 7 is log $_{e}$ = $\pm$ 0.3, similar to that derived from line ratios in species formed at temperatures close to that of."
. For example. from line ratios (formed at d; = 105 KK) ]xeenan et al. (," For example, from line ratios (formed at $_{e}$ = $^{6.1}$ K) Keenan et al. ("
"2000) derived log N, = 9.20.2. while from CD. = 10 WR) Keenan et al. (","2000) derived log $_{e}$ = $\pm$ 0.2, while from $_{e}$ = $^{6.3}$ K) Keenan et al. ("
2002) found log NX. = 0.50.3.,2002) found log $_{e}$ = $\pm$ 0.3.
" An inspection of “Tables 7 and S clearly reveals that the best N, diagnostics for lie in the second-order wavelength range AA)) covered. by the SERTS95 active region spectrum.", An inspection of Tables 7 and 8 clearly reveals that the best $_{e}$ –diagnostics for lie in the second-order wavelength range ) covered by the SERTS–95 active region spectrum.
 In particular. the 175.27/174.53 ancl 175.27/177.24 ratios involve transitions which are strong and unblended: plus close in wavelength.," In particular, the 175.27/174.53 and 175.27/177.24 ratios involve transitions which are strong and unblended plus close in wavelength."
" AXdeditionallv. both ratios vary by large [actors (13) between N, = LO” and 10 7."," Additionally, both ratios vary by large factors (13) between $_{e}$ = $^{8}$ and $^{11}$ $^{-3}$."
 Phe 175.27/184.53 and 190.05/175.27 ratios also. potentially provide good diagnostics. although the relevant transitions are somewhat further apart in wavelength and hence more susceptible to possible errors in the instrument intensity calibration.," The 175.27/184.53 and 190.05/175.27 ratios also potentially provide good diagnostics, although the relevant transitions are somewhat further apart in wavelength and hence more susceptible to possible errors in the instrument intensity calibration."
" We note that the values of N, deduced for the SERES95 active region from the 4 ratios above are all consistent. with an average of log N. = 9440.1."," We note that the values of $_{e}$ deduced for the SERTS–95 active region from the 4 ratios above are all consistent, with an average of log $_{e}$ = $\pm$ 0.1."
" This is in excellent agreement. with the value of log N, = 9440.2 derived. by Brosius οἱ al. (", This is in excellent agreement with the value of log $_{e}$ = $\pm$ 0.2 derived by Brosius et al. (
1998b) from Fe ions formed at similar temperatures tox.,1998b) from Fe ions formed at similar temperatures to.
. Previously. Foster et al. (," Previously, Foster et al. ("
"1996). calculated the 175.27/174.53 and 175.27/1177.24ratios of using the electron impact excitation rates of Mohan. Libbert Ixingston (1994). ancl emploved. these as ΑΝ, cliagnostics for Procyon and a Cen via a comparison with observations from the Extreme Ultraviolet Explorer (IZUVIZ) satellite.","1996) calculated the 175.27/174.53 and 175.27/177.24ratios of using the electron impact excitation rates of Mohan, Hibbert Kingston (1994), and employed these as $_{e}$ --diagnostics for Procyon and $\alpha$ Cen via a comparison with observations from the Extreme Ultraviolet Explorer (EUVE) satellite."
 However. Foster et al.," However, Foster et al."
 found. that. the electron densities derived (rom showed [age discrepancies (up (ο an order of magnitude) with those deduced from other densitv-sensitive line ratios in the EUVIE spectra., found that the electron densities derived from showed large discrepancies (up to an order of magnitude) with those deduced from other density-sensitive line ratios in the EUVE spectra.
 To investigate this. in Table 9 we list the EUVIE line ratio measurements for along with the electron densities derived from the Foster et al.," To investigate this, in Table 9 we list the EUVE line ratio measurements for along with the electron densities derived from the Foster et al."
 and. present. line ratio calculations., and present line ratio calculations.
 An inspection of the table reveals that the electron densities. deduced from the current theoretical estimates of 175.T/174.53 and Ίοο/177.24 are consistent. ancl furthermore agree with the values of N. determined. [rom other line ratios. hence resolving the discrepancies found by Foster et al.," An inspection of the table reveals that the electron densities deduced from the current theoretical estimates of 175.27/174.53 and 175.27/177.24 are consistent, and furthermore agree with the values of $_{e}$ determined from other line ratios, hence resolving the discrepancies found by Foster et al."
 However. we should point out that the discrepancies are also resolved if theoretical line ratios from are emploved.," However, we should point out that the discrepancies are also resolved if theoretical line ratios from are employed."
 Finally. we note that Datla. Blaha Ixunze (1975) have measured several extreme-ultraviolet linc ratios in a @-pineh uncer well-determined. plasma conditions. hence allowing some independent. assessment of the accuracy of our theoretical results.," Finally, we note that Datla, Blaha Kunze (1975) have measured several extreme-ultraviolet line ratios in a $\theta$ -pinch under well-determined plasma conditions, hence allowing some independent assessment of the accuracy of our theoretical results."
 In. “Table LO we sununarise their experimental line ratios. along with the theoretical values for the measured plasma conditions from both the present calculations audCHIANTI.," In Table 10 we summarise their experimental line ratios, along with the theoretical values for the measured plasma conditions from both the present calculations and."
 An inspection of the table reveals that the measured 190.05/174.53 ratios are always larger than theory. which is expected as the line will be blended with lin the 6-pinch spectra. as these are of somewhat lower resolution (approximately AA)) than the SERTS data. where the two features are resolved. (sec above).," An inspection of the table reveals that the measured 190.05/174.53 ratios are always larger than theory, which is expected as the line will be blended with in the $\theta$ -pinch spectra, as these are of somewhat lower resolution (approximately ) than the SERTS data, where the two features are resolved (see above)."
 For the other ratios. agreement between theory and experiment is reasonable. eiven that the nmieasurements are estimated to be accurate to only 20.30 per cent.," For the other ratios, agreement between theory and experiment is reasonable, given that the measurements are estimated to be accurate to only 20–30 per cent."
 In most instances. agreement is slightly better with the present line ratio caleulations. but once uncertainties are taken into account the observations are consistent with both sets of theoretical results.," In most instances, agreement is slightly better with the present line ratio calculations, but once uncertainties are taken into account the observations are consistent with both sets of theoretical results."
 The Datla et al., The Datla et al.
 measurements therefore. provide some experimental support for the two atomic physics data sets adopted in the relevant line ratio calculations., measurements therefore provide some experimental support for the two atomic physics data sets adopted in the relevant line ratio calculations.
 Our comparison of theoretical emission-line intensity. ratios with solar active region spectra from the SEIS 1989 and 1995 [üghts reveals generally very good agreement between theory and experiment. with several features identified for the first time in the SEIUES data sets. including 193.72. 220.26 andAA... plus aand theήν blend atAA.," Our comparison of theoretical emission-line intensity ratios with solar active region spectra from the SERTS 1989 and 1995 flights reveals generally very good agreement between theory and experiment, with several features identified for the first time in the SERTS data sets, including 193.72, 220.26 and, plus and the blend at."
. In addition. the transition of is detected for the first time (to our knowledge) in an astronomical source.," In addition, the transition of is detected for the first time (to our knowledge) in an astronomical source."
" We find that the ratios 175.27/174.53.— and 175.27177.24 provide the best electron density diagnostics. as they involve lines which are strong and free [rom blends. are close in wavelength and the ratios are highly N, sensitive."," We find that the ratios 175.27/174.53 and 175.27/177.24 provide the best electron density diagnostics, as they involve lines which are strong and free from blends, are close in wavelength and the ratios are highly $_{e}$ –sensitive."
 Should these lines not be available. then the 257.25/345.74 ratio may be emploved as a diagnostic. although this requires an accurate determination of the instrument intensity calibration over a relatively large wavelength range.," Should these lines not be available, then the 257.25/345.74 ratio may be employed as a diagnostic, although this requires an accurate determination of the instrument intensity calibration over a relatively large wavelength range."
 However. if the weak lline is reliably detected. then the use of 324.73/345.74 or 257.25/324.73 is. recommended in preference to ," However, if the weak line is reliably detected, then the use of 324.73/345.74 or 257.25/324.73 is recommended in preference to 257.25/345.74."
WALA acknowledges financial support. from EPSRC. while DI) is grateful to the Department of Education and Learning (Northern Ireland) ancl NASA's Goddard Space Flight Center for the award of a studentship.," KMA acknowledges financial support from EPSRC, while DBJ is grateful to the Department of Education and Learning (Northern Ireland) and NASA's Goddard Space Flight Center for the award of a studentship."
 The SERS rocket programme is supported by IPOD! grants from the Solar Physies Ollice of NASAs Space Physics Division., The SERTS rocket programme is supported by RTOP grants from the Solar Physics Office of NASA's Space Physics Division.
 JW acknowledges additional NASA support under erant. NACH13321., JWB acknowledges additional NASA support under grant NAG5--13321.
 EPI is grateful to AWE Alclermaston for the award of a William Penney Fellowship., FPK is grateful to AWE Aldermaston for the award of a William Penney Fellowship.
 The authors thank Peter van Lloof for the use of his Atomic Line List., The authors thank Peter van Hoof for the use of his Atomic Line List.
 ΤΙ is à collaborative project involving the Naval Hesearch, is a collaborative project involving the Naval Research
returned by shapolets decomposition will. iu fact. not have auv information.,"returned by shapelets decomposition will, in fact, not have any information."
 Thus. the above inversion will vield a systematic underestimate of the truce image flexion.," Thus, the above inversion will yield a systematic underestimate of the true image flexion."
 Above. we describe a truncation which minimizes this effect.," Above, we describe a truncation which minimizes this effect."
 While the flexion inversion is. at its core. linear algebra. it involves an enormous number of terms.," While the flexion inversion is, at its core, linear algebra, it involves an enormous number of terms."
 We have thus provided an inversion code for shapelots estinates of flexion along with examples on the flexion webpage., We have thus provided an inversion code for shapelets estimates of flexion along with examples on the flexion webpage.
 Okura et al. (, Okura et al. (
2006) receutly related. flexion directlv to the 3rd moments of observed images.,2006) recently related flexion directly to the 3rd moments of observed images.
 This is a siguificaut extension of flexion. and ναν iuuch along the lines of Goldberg Natarajan’s (2002) original work which talked about “arciness” in terms of the measured octopole moments.," This is a significant extension of flexion, and very much along the lines of Goldberg Natarajan's (2002) original work which talked about “arciness” in terms of the measured octopole moments."
 Throughout our discussion. we will use the notation: to refer. in this case. to the wmmveighted quadrpole moments. with all higher moments being defined by exact analogy.," Throughout our discussion, we will use the notation: to refer, in this case, to the unweighted quadrupole moments, with all higher moments being defined by exact analogy."
 In this context.£F refers to the unwoiehted integrated fux.," In this context,$F$ refers to the unweighted integrated flux."
 Thev define the complex terms: aud where These terms are collectively referred. to as TOLICS., They define the complex terms: and where These terms are collectively referred to as HOLICs.
 If a ealaxy ds otherwise perfectly circular (ie. no ellipticity). aud in the absence of noise. then the TOLICSs iia be directly related to estimators of the flexion (subject to an unknown bias of Lor).," If a galaxy is otherwise perfectly circular (i.e. no ellipticity), and in the absence of noise, then the HOLICs may be directly related to estimators of the flexion (subject to an unknown bias of $1-\kappa$ )."
 Namely: where the latter teria iu thedenominator of F docs not appear in the Okura oet al., Namely: where the latter term in thedenominator of ${\cal F}$ does not appear in the Okura et al.
 analysis., analysis.
 Bacon aud Goldberg (2005) show that a flexion induces a shift iu the centroid proportional to the quadrupole 1oimoeuts., Bacon and Goldberg (2005) show that a flexion induces a shift in the centroid proportional to the quadrupole moments.
 Iu order to correctly iuvert the TOLICs. this tei needs to be incorporated explicitly.," In order to correctly invert the HOLICs, this term needs to be incorporated explicitly."
 The simplicity of the extra term results from au approxiuation of near circularity., The simplicity of the extra term results from an approximation of near circularity.
 The beauty of this approach is that it gives us a very intuitive feel for what flexion means du an observational way., The beauty of this approach is that it gives us a very intuitive feel for what flexion means in an observational way.
 We thus introduce the terii “skewucss” to the intrinsic properties of a galaxy as measured frou equation (27)) whether or not the galaxy is otherwise circular. and whether or not it is lensed.," We thus introduce the term “skewness” to the intrinsic properties of a galaxy as measured from equation \ref{eq:skewness}) ) whether or not the galaxy is otherwise circular, and whether or not it is lensed."
 The siewuess iav be thought of as the intrinsic property. much as the vellipticity” is the intrinsic property related to the “shear.”," The skewness may be thought of as the intrinsic property, much as the “ellipticity” is the intrinsic property related to the “shear.”"
 Likewise. the intrinsie property associated witli equation (351) will be referred to as the varciness.”," Likewise, the intrinsic property associated with equation \ref{eq:arciness}) ) will be referred to as the “arciness.”"
 Tn reality. however. equations (27)) aud (28)) are not sufficient to perform a flexion estimate even if a galaxy has an ellipticity of only a few percent.," In reality, however, equations \ref{eq:skewness}) ) and \ref{eq:arciness}) ) are not sufficient to perform a flexion estimate even if a galaxy has an ellipticity of only a few percent."
 Okura et al provide a general relationship between estimators for flexion aud HOLICs. though the relation is best expressed iu matrix form: where Mois a 1d<Lo matrix consisting of elements proportional to sius of Q;jj;; aud Qi;Qi. the former of which can be found by explicitly expaudiug the expressions in Okura et al.," Okura et al provide a general relationship between estimators for flexion and HOLICs, though the relation is best expressed in matrix form: where ${\cal M}$ is a $4\times 4$ matrix consisting of elements proportional to sums of $Q_{ijkl}$ and $Q_{ij}Q_{kl}$, the former of which can be found by explicitly expanding the expressions in Okura et al.,"
 and the latter of which is again derived from the shift iu the centroid., and the latter of which is again derived from the shift in the centroid.
 For the convenience of the reader. we write out the explicit form of Min Appendix A. It mav be seen by examining the elements of Ad why this iuversion ΙΕ be done explicitly for even ilv elliptical sources.," For the convenience of the reader, we write out the explicit form of ${\cal M}$ in Appendix A. It may be seen by examining the elements of ${\cal M}$ why this inversion must be done explicitly for even mildly elliptical sources."
 For fully circular sources. if iiiv be secu by inspection that Mis diagonal.," For fully circular sources, it may be seen by inspection that ${\cal
M}$ is diagonal."
 However. when a source has au cllipticity even as σπα as 1054. it can bo shown that [AL|~[M45]. and thus equatious (27)) and (28)) are no longer even approximately correct.," However, when a source has an ellipticity even as small as $10\%$, it can be shown that $|M_{11}|\simeq |M_{12}|$, and thus equations \ref{eq:skewness}) ) and \ref{eq:arciness}) ) are no longer even approximately correct."
 The application of the HOLICsS technique would be rial if there were no measurement noise., The application of the HOLICs technique would be trivial if there were no measurement noise.
" Iu the xesence of noise. and especially, when the sky dominates. ucasureienut of unweighted moments is muhereutlv quite roisy."," In the presence of noise, and especially, when the sky dominates, measurement of unweighted moments is inherently quite noisy."
 Iu a case where we are mieasurmeg the 3rd aud 1th nonients. if is even niore so.," In a case where we are measuring the 3rd and 4th moments, it is even more so."
 Iudser. Squires Broadhurst (1995: see also a nice review by Bartchuann Schneider. 2001) developed xhaps the most comprehensive approach to dealing with he secoud moments (the ellipticity) with noisy observing. and with a (potentially anisotropic) PSF.," Kaiser, Squires Broadhurst (1995; see also a nice review by Bartelmann Schneider, 2001) developed perhaps the most comprehensive approach to dealing with the second moments (the ellipticity) with noisy observing, and with a (potentially anisotropic) PSF."
 Our approach is similar., Our approach is similar.
 We have ouly worked with a Gaussian window thus far. but the approach is eeneralizable for auv circularly svuuuetriic weighting.," We have only worked with a Gaussian window thus far, but the approach is generalizable for any circularly symmetric weighting."
 We thus define a window fiction: where the origin is taken to be the center of light. aud the integral is normalized to unity.," We thus define a window function: where the origin is taken to be the center of light, and the integral is normalized to unity."
 Further. we define the weighted monents as. for example: We can thus redefine all IEOLICs aud moments similarly.," Further, we define the weighted moments as, for example: We can thus redefine all HOLICs and moments similarly."
 We have found through experimentation (see below) that for a «kv noise linited source. a reasonable value of ay Is 1.5 times the halflielt radius.," We have found through experimentation (see below) that for a sky noise limited source, a reasonable value of $\sigma_W$ is 1.5 times the half-light radius."
 Tf we were to simply replace all clemeuts in M. ¢. aud à from equation (29)) with their weielted counterparts we would not eet an unbiased estimate of the flexion.," If we were to simply replace all elements in ${\cal M}$ $\zeta$ , and $\delta$ from equation \ref{eq:Fsolve}) ) with their weighted counterparts we would not get an unbiased estimate of the flexion."
effects of narrow absorption troughs.,effects of narrow absorption troughs.
 We then subtract the pseudo-continuum plus emission. line emission from. the spectrum to get the residual spectrum., We then subtract the pseudo-continuum plus emission line emission from the spectrum to get the residual spectrum.
 aabsorption doublets are then identified on both sides of the eemission line by fitting double-Gaussians to the absorption doublet., absorption doublets are then identified on both sides of the emission line by fitting double-Gaussians to the absorption doublet.
 We only keep absorbers that are detected at >3c for both Gaussian components., We only keep absorbers that are detected at $>3\sigma$ for both Gaussian components.
 We measure restframe equivalent widths (EW) of these AALs and uncertainties of EWs are estimated from the Gaussian fits., We measure restframe equivalent widths (EW) of these AALs and uncertainties of EWs are estimated from the Gaussian fits.
" reffig:aas,vampshowsanexampleo four fittingresults", \\ref{fig:aas_examp} shows an example of our fitting results.
 Althoughthis fyatenue cand negktreéoyulues; codacetecre shatted dowhdor ptionsont! ," Although this fitting recipe was developed to reduce the effects of narrow absorptions on the emission line measurements rather than a dedicated recipe for finding narrow absorption lines, it does a reasonably good job in identifying AALs."
"of the AALs in the DR3 sample of VandenBerketal. (2008). where most of the ""missing"" AALs are weak absorptions with otherwise normal quasar properties."," With this method we recovered $\sim 80\%$ of the AALs in the DR3 sample of \citet{Vanden_Berk_etal_2008}, where most of the “missing” AALs are weak absorptions with otherwise normal quasar properties."
 However. we do not intend to quantify the completeness in our AAL selection as functions of S/N and absorber strength. as such a task would require a more dedicated narrow absorption finder and Monte-Carlo simulations. which are unnecessary for the purposes of this paper.," However, we do not intend to quantify the completeness in our AAL selection as functions of S/N and absorber strength, as such a task would require a more dedicated narrow absorption finder and Monte-Carlo simulations, which are unnecessary for the purposes of this paper."
 To define an AAL one needs to know the systemic redshift of the quasar., To define an AAL one needs to know the systemic redshift of the quasar.
 Stellar absorption features are generally unavailable due to the overwhelming quasar light., Stellar absorption features are generally unavailable due to the overwhelming quasar light.
 The redshifts based on narrow lines such as aand aare generally consistent with stellar absorption. redshifts within X100kms7! (e.g..Richardsetal.2002)..," The redshifts based on narrow lines such as and are generally consistent with stellar absorption redshifts within $\la
100\,{\rm km\,s^{-1}}$ \citep[e.g.,][]{Richards_etal_2002b}."
 The redshifts based on the broad eemission line are consistent with those based on oor wwith a dispersion of ~380kms'! (e.g..Richardsetal.2002: 17).," The redshifts based on the broad emission line are consistent with those based on or with a dispersion of $\sim 350\,{\rm km\,s^{-1}}$ \citep[e.g.,][their fig.\ 17]{Richards_etal_2002b,Shen_etal_2011}."
. The high-ionization broad line is known to be systematically blueshifted (~ 700kms!) from low-ionization. lines such asMel. with a large dispersion of ~700kms7! (e.g..Gaskell1982:Tytler&Fan1992;Richardsetal.2002;Shen 2011).. and hence will bias the systemic redshift determination at high redshift.," The high-ionization broad line is known to be systematically blueshifted $\sim 700\,{\rm km\,s^{-1}}$ ) from low-ionization lines such as, with a large dispersion of $\sim 700\,{\rm km\,s^{-1}}$ \citep[e.g.,][]{Gaskell_1982,Tytler_Fan_1992,Richards_etal_2002b,Shen_etal_2011}, and hence will bias the systemic redshift determination at high redshift."
 Here we adopt the centroid of the broad eemission line as the quasar systemic redshift to calculate the absorber velocity offset. and use 3000kms7! as the velocity cut to define an AAL.," Here we adopt the centroid of the broad emission line as the quasar systemic redshift to calculate the absorber velocity offset, and use $3000\,{\rm km\,s^{-1}}$ as the velocity cut to define an AAL."
 Wecompared the absorber velocity offsets with those calculated by adopting the improved redshifts of SDSS quasars from Hewett&Wild (2011).. and found good agreements with a dispersion of ~300kms!.," Wecompared the absorber velocity offsets with those calculated by adopting the improved redshifts of SDSS quasars from \citet{Hewett_Wild_2011}, , and found good agreements with a dispersion of $\sim 300\,{\rm km\,s^{-1}}$."
 This dispersion is consistent with the redshift uncertainty 350kms7! based on the ccentroid.," This dispersion is consistent with the redshift uncertainty $\sim 350\,{\rm km\,s^{-1}}$ based on the centroid."
 Therefore we adopt a nominal uncertainty of Avo=350kms7! in absorber velocities. which is dominated by systemic redshift uncertainties.," Therefore we adopt a nominal uncertainty of $\Delta v_{\rm off}=350\,{\rm km\,s^{-1}}$ in absorber velocities, which is dominated by systemic redshift uncertainties."
 We finally arrived at a sample of ~1800 quasars with AALs. among which ~10% show multiple AALs in SDSS spectra2008).," We finally arrived at a sample of $\sim 1800$ quasars with AALs, among which $\sim 10\%$ show multiple AALs in SDSS spectra."
. The sample of AALs used in the following analysis is listed in Table l.., The sample of AALs used in the following analysis is listed in Table \ref{table:sample}.
 Additional information about these quasars can be retrieved from the value-added SDSS DR7 quasar catalog compiled in Shenetal.(2011)., Additional information about these quasars can be retrieved from the value-added SDSS DR7 quasar catalog compiled in \citet{Shen_etal_2011}.
 reffig:vdist shows the distribution of absorber velocity vog for the whole sample in black. and for a subset of z«1.4 quasars for which we have redshifts from oor iin red.," \\ref{fig:vdist} shows the distribution of absorber velocity $v_{\rm
off}$ for the whole sample in black, and for a subset of $z<1.4$ quasars for which we have redshifts from or in red."
 Positive values indicate blueshifted relative to the Wwe th, Positive values indicate blueshifted relative to the systemic and negative values indicate redshifted.
at the absorber velocity distribution using this systemic redshift definition is similar (albeit slightly broader due to the less accurate eemission line redshifts) to that using the subset of our sample with oor |--based redshifts., We found that the absorber velocity distribution using this systemic redshift definition is similar (albeit slightly broader due to the less accurate emission line redshifts) to that using the subset of our sample with or -based redshifts.
 The dispersion in. the vor distribution is ~600kms. larger than the typical uncertainty wg~350kms7! arising from systemic redshift uncertainties based onΠ.," The dispersion in the $v_{\rm off}$ distribution is $\sim 600\,{\rm km\,s^{-1}}$, larger than the typical uncertainty $\Delta v_{\rm off}\sim 350\,{\rm km\,s^{-1}}$ arising from systemic redshift uncertainties based on."
. It is thus dominated by an intrinsic dispersion., It is thus dominated by an intrinsic dispersion.
 Our composite spectra (see refsec:composite)) also confirm that this dispersion is not caused by incorrect systemic redshifts., Our composite spectra (see \\ref{sec:composite}) ) also confirm that this dispersion is not caused by incorrect systemic redshifts.
 As earlier studies already show (e.g..Weymannetal.1979;VandenBerketal. 2008).. there is a substantial fraction of AALs that are redshifted from the systemic velocity.," As earlier studies already show \citep[e.g.,][]{Weymann_etal_1979,Vanden_Berk_etal_2008}, there is a substantial fraction of AALs that are redshifted from the systemic velocity."
 These systems could either be truly infalling absorbers. or the emission lines used to estimate the systemic redshift have significant outflowing velocity.," These systems could either be truly infalling absorbers, or the emission lines used to estimate the systemic redshift have significant outflowing velocity."
 At wy>I500kms'!. the distribution flattens out and is consistent with the expectation from cosmologically intervening absorbers. as seen m earlier studies (e.g..Wildetal.2008).," At $v_{\rm off}>1500\,{\rm km\,s^{-1}}$, the distribution flattens out and is consistent with the expectation from cosmologically intervening absorbers, as seen in earlier studies \citep[e.g.,][]{Wild_etal_2008}."
. We thus argue that these high-velocity AALs are mostly classical intervening absorbers. which will be confirmed by our composite spectra in refsec:composite..," We thus argue that these high-velocity AALs are mostly classical intervening absorbers, which will be confirmed by our composite spectra in \\ref{sec:composite}."
" We divide our sample into three categories: 1) AAL quasars with vor21500kms! (the ""intervening-like"" sample): 2) AAL quasars with 0<vy1S00kms7! (the ""blueshifted"" sample): 3) AAL quasars with —3000<voyOkms7! (the ""redshifted"" sample)."," We divide our sample into three categories: 1) AAL quasars with $v_{\rm off}>1500\,{\rm km\,s^{-1}}$ (the “intervening-like” sample); 2) AAL quasars with $0<v_{\rm off}<1500\,{\rm
km\,s^{-1}}$ (the “blueshifted” sample); 3) AAL quasars with $-3000<v_{\rm off}<0 \,{\rm km\,s^{-1}}$ (the “redshifted” sample)."
 We have ~750 quasars each in the latter two samples. and ~370 quasars in the former.," We have $\sim 750$ quasars each in the latter two samples, and $\sim 370$ quasars in the former."
 To study the average properties of these three AAL quasar samples we create high S/N composite spectra in the restframe of thequasar., To study the average properties of these three AAL quasar samples we create high S/N composite spectra in the restframe of thequasar.
 SDSS spectra integrate all the light received within a ffiber radius. corresponding to ~10 Κρο at z I. hence they cover a substantial fraction of the quasar host.," SDSS spectra integrate all the light received within a fiber radius, corresponding to $\sim 10$ kpc at $z\sim 1$ , hence they cover a substantial fraction of the quasar host."
 For comparison purposes we construct a control sample of more than 9.000," For comparison purposes we construct a control sample of more than 9,000"
 , 
These are fairly modest. Lorentz factors considering the above estimate of the maximum Lorentz factor that can be achieved in the outer gap in the radiation reaction limit. Eq. (5)).,"These are fairly modest Lorentz factors considering the above estimate of the maximum Lorentz factor that can be achieved in the outer gap in the radiation reaction limit, Eq. \ref{1}) )."
 It can. therefore. be concluded. that inverse Compton scattering by (he primary beam takes place in the NN regime.," It can, therefore, be concluded, that inverse Compton scattering by the primary beam takes place in the KN regime."
" Adding losses due to inverse Compton scattering in the extreme KN limit into the balanced eain loss equation (2.1)) results in a net energy loss of Ruppel2010) (a)$242 24d(=)udPUnope. ic where C, is the energv density of the target photon field. εωμ is the tvpical energy of a soft photon. and ap is the Thompson cross-section."," Adding losses due to inverse Compton scattering in the extreme KN limit into the balanced gain loss equation \ref{01}) ) results in a net energy loss of \citep{1970RvMP...42..237B,2010NJPh...12c3044S}
 = e c B -^4 ( )^2- } ( )^2 _T c, where $U_{\rm soft}$ is the energy density of the target photon field, $\epsilon_{\rm soft}$ is the typical energy of a soft photon, and $\sigma_T$ is the Thompson cross-section."
 Note that both the acceleration term and the decelerating IC: term are independent of the energy of the particle., Note that both the acceleration term and the decelerating IC term are independent of the energy of the particle.
 Thus. if curvature losses were negligible. particles are either accelerated or decelerated without reaching a steady solution.," Thus, if curvature losses were negligible, particles are either accelerated or decelerated without reaching a steady solution."
 Onlv in the presence of curvature radiation is it possible to achieve a steady-state particle distribution., Only in the presence of curvature radiation is it possible to achieve a steady-state particle distribution.
 In order to better understand how curvature radiation ancl inverse-Compton scattering contribute to the radiation loss of the primary beam in Eq. (3.2)), In order to better understand how curvature radiation and inverse-Compton scattering contribute to the radiation loss of the primary beam in Eq. \ref{eKN1}) )
 we compare the two., we compare the two.
 In this comparison we assume (he curvature radiation-Imited Lorentz factor ((5)). ancl justify our choice by showing that curvature radiation and IC losses in the Crab pulsar are about equal.," In this comparison we assume the curvature radiation-limited Lorentz factor \ref{1}) ), and justify our choice by showing that curvature radiation and IC losses in the Crab pulsar are about equal."
 The soft photon luminosity that results in IC losses in the INN regime which are similar to curvature radiation losses is Byes= —, The soft photon luminosity that results in IC losses in the KN regime which are similar to curvature radiation losses is = = .
The launch of the X-ray satellite has broush ereat progress in understanding the origin of the X-ray background. (XIUB) (for à review see Fabian DBarcons 1992).,The launch of the X-ray satellite has brought great progress in understanding the origin of the X-ray background (XRB) (for a review see Fabian Barcons 1992).
 Deep X-ray surveys have resolved about 70 per cent of the XRB at soft energies (0.5-2 keV) (Hlasinger et al., Deep X-ray surveys have resolved about 70 per cent of the XRB at soft energies (0.5-2 keV) (Hasinger et al.
 1998)., 1998).
 Spectroscopic follow-up observations have demonstrate that the majority of these sources are broad-line. luminous AGN (QSOs) eg.," Spectroscopic follow-up observations have demonstrated that the majority of these sources are broad-line, luminous AGN (QSOs) eg."
 Shanks et al. (, Shanks et al. (
1991). Georgantopoulos e al. (,"1991), Georgantopoulos et al. ("
1996). Mellardy et al. (,"1996), McHardy et al. ("
1998). Schmidt. et al. (,"1998), Schmidt et al. ("
1998).,1998).
 The QSO luminosity function (LE) derived on the basis of these surveys (Bovle et al., The QSO luminosity function (LF) derived on the basis of these surveys (Boyle et al.
 1993. Boyle et al.," 1993, Boyle et al."
 1994. Page 6 al.," 1994, Page et al."
 1996. Jones ct al.," 1996, Jones et al."
 1997) suggests that QSOs canno contribute the bulk of the ΧΙΟ at these energies., 1997) suggests that QSOs cannot contribute the bulk of the XRB at these energies.
 Indeed. at faint X-rav [luxes there are many sources associaloc with optical galaxies which present narrow emission lines (Bovle ct al.," Indeed, at faint X-ray fluxes there are many sources associated with optical galaxies which present narrow emission lines (Boyle et al."
 1995. Cuilliths et al.," 1995, Griffiths et al."
 1996. Mellardy et al.," 1996, McHardy et al."
 1998)., 1998).
 Roche et al. (, Roche et al. (
1995. 1996). Almaini et al. (,"1995, 1996), Almaini et al. ("
1997) anc Soltan et al. (,1997) and Soltan et al. (
1997). quantified. the contribution of these NELGs by eross-correlating optically selected. galaxies wit-— ROSAT XRB Iluctuations.,1997) quantified the contribution of these NELGs by cross-correlating optically selected galaxies with ROSAT XRB fluctuations.
 Phey found that NELGs can easily contribute the bulk of the NRB together with QSOs at soft energies., They found that NELGs can easily contribute the bulk of the XRB together with QSOs at soft energies.
 Similar attempts were mace by Iefregier. Lelfancd McMahon. (1997) using. cata and also in the hard band. (2-10 keV) by Lahay et al. (," Similar attempts were made by Refregier, Helfand McMahon (1997) using data and also in the hard band (2-10 keV) by Lahav et al. ("
1993). Ανα ct al. (,"1993), Miyaji et al. ("
1994) and Carrera et. al. (,1994) and Carrera et al. (
1995) who cross-correlated nearbyLRAS galaxy. catalogues with or data.,1995) who cross-correlated nearby galaxy catalogues with or data.
 Although there is mounting evidence that most of these galaxies do present either high excitation lines or broad wings ancl thus they are associated with AGN activity (ος Schmidt et al., Although there is mounting evidence that most of these galaxies do present either high excitation lines or broad wings and thus they are associated with AGN activity (eg Schmidt et al.
 1998). their exact nature and contribution to the ΧΙΙ remains unclear.," 1998), their exact nature and contribution to the XRB remains unclear."
 Llere. we provide an independent estimate of the local galaxy X-ray LE ancl emissivity.," Here, we provide an independent estimate of the local galaxy X-ray LF and emissivity."
 More importantly. we assess the contribution of different classes of galaxies. (Sev[erts. LINERS. star-forming ancl passive galaxies) to the galaxy Xoray emissivitys," More importantly, we assess the contribution of different classes of galaxies (Seyferts, LINERS, star-forming and passive galaxies) to the galaxy X-ray emissivity."
 This is done by convolving the optical LE as derived from the Llo et al. (, This is done by convolving the optical LF as derived from the Ho et al. (
"1995) sample of nearby galaxies with the corresponding L,/Lg relation (section 2).",1995) sample of nearby galaxies with the corresponding $L_x/L_B$ relation (section 2).
 The same method has been employed. using LRASdata (Grilliths Padovani 1990. ‘Trever οἱ al.," The same method has been employed using data (Griffiths Padovani 1990, Treyer et al."
 1992. Barcons οἱ al.," 1992, Barcons et al."
 1995)., 1995).
 Schmidt. Boller Voges (1996) also present a preliminary analysis of the local galaxy luminosity function using allsky survey data.," Schmidt, Boller Voges (1996) also present a preliminary analysis of the local galaxy luminosity function using all-sky survey data."
 However. the use of the Llo et al.," However, the use of the Ho et al."
 sample presents the advantage that excellent quality nuclear spectra exist for cach galaxy: thus it provides us with one of the less biased samples against low-Iuminosity AGN., sample presents the advantage that excellent quality nuclear spectra exist for each galaxy; thus it provides us with one of the less biased samples against low-luminosity AGN.
 Moreover. the use of an optical sample may introduce less bias against passive galaxies ancl LINERS most. of which are associated with carly-type galaxies ancl thus are," Moreover, the use of an optical sample may introduce less bias against passive galaxies and LINERS most of which are associated with early-type galaxies and thus are"
is measured for each priu exposure.,is measured for each prism exposure.
 The average sky backeround im each individual exposure ds subtracted from cach flat-fielded priu nuage., The average sky background in each individual exposure is subtracted from each flat-fielded prism image.
 The spectra were extracted in PyRAF using the«Xe slitless spectroscopy reduction package (ver.1.62°).. specifically desigued for eer and prisni data.," The spectra were extracted in PyRAF using the slitless spectroscopy reduction package \citep[ver. 1.6][]{2006hstc.conf...79W,2006hstc.conf...85K}, specifically designed for grism and prism data."
 Iu the extraction. the position. of the galaxv on the direct nuage is used iu combination with the header dither paraiucters to locate the spectimm ou the dispersed image and assign a waveleneth to cach pixel in the spectrum.," In the extraction, the position of the galaxy on the direct image is used in combination with the header dither parameters to locate the spectrum on the dispersed image and assign a wavelength to each pixel in the spectrum."
 The spectral trace and wavelength solutions are defined with respect to a reference position. which is measured by runing SExtractor (2). ona direct inage for each orbit.," The spectral trace and wavelength solutions are defined with respect to a reference position, which is measured by running SExtractor \citep{1996A&AS..117..393B} on a direct image for each orbit."
 A aster catalog was generated for cach set of priu nuages taken in a siugle orbit., A master catalog was generated for each set of prism images taken in a single orbit.
 Using the master catalogs. the software eenerates pixel extraction tables (PETs). which contain a spectral mapping for cach pixel in the spectrum.," Using the master catalogs, the software generates pixel extraction tables (PETs), which contain a spectral mapping for each pixel in the spectrum."
 Various sizes for the extraction window were explored. with au extraction width approximately the size of the object maximizing the signal to noise of the spectra.," Various sizes for the extraction window were explored, with an extraction width approximately the size of the object maximizing the signal to noise of the spectra."
 The signal to noise was further increased (a factor of —1.1) by usings optimal weighting extraction. which weights the pixels as a function of distance from the spectral trace rather than eiviug cach pixel the same weight when genueratiug the oue dineusional spectra.," The signal to noise was further increased (a factor of $\sim$ 1.4) by using optimal weighting extraction, which weights the pixels as a function of distance from the spectral trace rather than giving each pixel the same weight when generating the one dimensional spectra."
 The waveleneth solution over .jsaccurate to within a few anestroms., The wavelength solution over is accurate to within a few angstroms.
 The spectra were flux calibrated using the standard seusitivitv curve for the PRI30L prin (?).., The spectra were flux calibrated using the standard sensitivity curve for the PR130L prism \citep{2006acs..rept....3L}.
 The dux and waveleneth-calibrated spectra for each priu nuage were co-added weighting cach exposure by the xius of the backeround in cach individual exposure., The flux and wavelength-calibrated spectra for each prism image were co-added weighting each exposure by the rms of the background in each individual exposure.
 This was done to account for increasing dark current with subsequent exposures., This was done to account for increasing dark current with subsequent exposures.
 For an individual target the dark current was a factor of | higher iu the forth orbit conmpxured to the first., For an individual target the dark current was a factor of 4 higher in the forth orbit compared to the first.
 The uncertainty iu the spectra flux was estimated differently for the waveleneth regions redward and blieward of the Lxauanu linit., The uncertainty in the spectral flux was estimated differently for the wavelength regions redward and blueward of the Lyman limit.
 Dluewar of912À.. where we typically measured no signal (i.e. uo detection of πο) we are csscutially probing the backerouud.," Blueward of, where we typically measured no signal (i.e., no detection of LyC) we are essentially probing the background."
 We extracted regions of blauk sky aud foe that the staudard deviation of the sky flux between the observed waveleusths typically used to measure the LyC in our ;~0.7 saunple was comparable to the παπαατς deviation of the fiw in our galaxies., We extracted regions of blank sky and found that the standard deviation of the sky flux between the observed wavelengths typically used to measure the LyC in our $z\sim0.7$ sample was comparable to the standard deviation of the flux in our galaxies.
 We therefore use the standard deviation of the fiux between 780 aud irest frame (the region used to iieasure LyC fax Πιτ) as a conservative estimate of the uncertiüntv., We therefore use the standard deviation of the flux between 780 and rest frame (the region used to measure LyC flux limits) as a conservative estimate of the uncertainty.
 However. recsvard of the Lyman break. where fux is detected. the errors at cach wavelength bin in the final onc-dinieusional co-added spectra are the la weighted standard deviation since there were lavecr.," However, redward of the Lyman break, where flux is detected, the errors at each wavelength bin in the final one-dimensional co-added spectra are the $1\sigma$ $weighted$ standard deviation since there were larger."
 The final one-dimensional spectra are preseuted in Fieure 5., The final one-dimensional spectra are presented in Figure 5.
 Accurate spectroscopic redshifts are required to identify the observed wavelengths correspouding to the rest-frame Lyinan limit aud LyC. Redshifts caunot be measured frou the PUV spectra tlemsclyes since the prisin probes blueward of Lvo in the rest frame aud the resolution is too poor for the identification of absorption lines., Accurate spectroscopic redshifts are required to identify the observed wavelengths corresponding to the rest-frame Lyman limit and LyC. Redshifts cannot be measured from the FUV spectra themselves since the prism probes blueward of $\alpha$ in the rest frame and the resolution is too poor for the identification of absorption lines.
 The photometric redshifts. although sufficient. for selection purposes. have au unucertaiuty corresponding to 200A. Jat 2~0.7.," The photometric redshifts, although sufficient for selection purposes, have an uncertainty corresponding to $\sim$ at $z\sim0.7$."
 Optical spectroscopy for six of our targets were taken from the public zZOSMOS (7).., Optical spectroscopy for six of our targets were taken from the public zCOSMOS \citep{2009ApJS..184..218L}.
 Au additional 23 spectra were obtained at the Palomar Tale 5 iu Telescope using the Double Spectrograph (hereafterDoubleSpec:7). in 2008 aud 2009 February with secing conditions raugineg from to 2755 for the majority of the observations aud lelit cimus., An additional 23 spectra were obtained at the Palomar Hale 5 m Telescope using the Double Spectrograph \citep[hereafter Double Spec;][]{1982PASP...94..586O} in 2008 and 2009 February with seeing conditions ranging from to 5 for the majority of the observations and light cirrus.
" This instrument uses a pair of CCD cameras which simultaneously obtain loug-slit spectra over a ""blue"" range of 3500- anda “red” range ofω", This instrument uses a pair of CCD cameras which simultaneously obtain long-slit spectra over a “blue” range of 3500- and a “red” range of.
ν The observiug strategy consisted of acquiring a series of 600-0008 exposures with a slit width of 1755., The observing strategy consisted of acquiring a series of 600-900s exposures with a slit width of 5.
 We obtained a total integration time of 10-90 nuünutes for cach of the 23 galaxies., We obtained a total integration time of 40-90 minutes for each of the 23 galaxies.
 The data were reduced using standard IRAF tasks aud waveleugth calibrated with Te. Ne. and Ar reference laps.," The data were reduced using standard IRAF tasks and wavelength calibrated with He, Ne, and Ar reference lamps."
 The spectral features used for the redshift determination were typically a combination of ΟΠ atο OL at and iu some cases IL? at ," The spectral features used for the redshift determination were typically a combination of O[II] at, O[III] at and in some cases $\beta$ at ."
The spectroscopic redshifts confirmed that all the observed galaxies were within the 0.6<:0.85 range needed to measure the escape fraction with the UV observations., The spectroscopic redshifts confirmed that all the observed galaxies were within the $0.6<z<0.85$ range needed to measure the escape fraction with the UV observations.
" The mean spectroscopic redshitt of the sample is 2=0.679,", The mean spectroscopic redshift of the sample is $z=0.679$.
 Due to poor observing conditions. three targets remain with no spectroscopic redshift comfirmation.," Due to poor observing conditions, three targets remain with no spectroscopic redshift confirmation."
 Since ouly one of these (CHUVLCE15) had a detectable UW spectrum and the rest of the salple had photometric redshifts within a few percent of the spectroscopic redshift we assiuned the photometric redshift for this galaxy., Since only one of these (C-UVLG-15) had a detectable UV spectrum and the rest of the sample had photometric redshifts within a few percent of the spectroscopic redshift we assumed the photometric redshift for this galaxy.
 Typically. the escape fraction of LyC photons is measured relative to the number of photons escapiug at Άμος=LS00A citep2001ÀpJ...5 16..665S..," Typically, the escape fraction of LyC photons is measured relative to the number of photons escaping at $\lambda_{\mathrm{rest}}=$ \\citep{2001ApJ...546..665S}."
 This allows a straightforward calculation of the escape fraction with oulv two fiux measurements fat and in the LyC) using the following equation: where Gfisoo/fiscdinr and CFisoo/Frsc)ons are the lutrinsic| and observed LyC πας density ratios., This allows a straightforward calculation of the escape fraction with only two flux measurements (at and in the LyC) using the following equation: where $(f_{1500}/f_{\mathrm{LyC}})_{\mathrm{int}}$ and $(f_{1500}/f_{\mathrm{LyC}})_{\mathrm{obs}}$ are the intrinsic and observed LyC flux density ratios.
" The ""LyCU refers to the waveleneth at which LyC is measured ffor this study}. 59 is the scaling factor discussed below and nenpLec is the IGAL optical depth for LyC photons along the line of sight to the galaxy."," The “LyC” refers to the wavelength at which LyC is measured for this study), $S$ is the scaling factor discussed below and $\tau_{\mathrm{IGM,LyC}}$ is the IGM optical depth for LyC photons along the line of sight to the galaxy."
 The iutrinsic drop between the rest-frame ΕΙΝ J)and the LyC J) dis highlwv uncertain and cannot be observed., The intrinsic drop between the rest-frame FUV )and the LyC ) is highly uncertain and cannot be observed.
" The assumed value of f,(500À. ", The assumed value of $f_{\nu}$ 
become important and diminish the resulting polarisation.,become important and diminish the resulting polarisation.
" Note also, that the Stokes flux from the double-cone results from integrating photons over its entire opening angle."," Note also, that the Stokes flux from the double-cone results from integrating photons over its entire opening angle."
 This leads to combining scattered photons having a large range of polarisation orientations and also diminishes the net polarised flux., This leads to combining scattered photons having a large range of polarisation orientations and also diminishes the net polarised flux.
" Overall, the case of Τεοπε=0.3 that we investigate produces a strong Stokes flux but at most inclinations it remains comparable to the polarised flux coming from the disc/torus system and therefore the rotation Aw is significant."," Overall, the case of $\tau_{\rm cone} = 0.3$ that we investigate produces a strong Stokes flux but at most inclinations it remains comparable to the polarised flux coming from the disc/torus system and therefore the rotation $\Delta \psi$ is significant."
" Having in mind the unified scheme of AGN, it is important that Tcone remains low enough as the ionised winds are seen in transmission in Seyfert-1 galaxies, where they produce warm absorption in the soft X-ray band."," Having in mind the unified scheme of AGN, it is important that $\tau_{\rm cone}$ remains low enough as the ionised winds are seen in transmission in Seyfert-1 galaxies, where they produce warm absorption in the soft X-ray band."
" Observations of the warm absorber rule out that the medium has a higher column density than 10? for most objects (seeTurner&Miller2009,andreferencescm""? therein).", Observations of the warm absorber rule out that the medium has a higher column density than $10^{23} {\rm cm}^{-2}$ for most objects \citep[see][and references therein]{turner2009}.
" Only a few exceptions exceed this threshold so that our choice of Tcone=0.3, which corresponds to a column density around 4.5x10? is a good estimate for the upper limit."," Only a few exceptions exceed this threshold so that our choice of $\tau_{\rm cone} = 0.3$, which corresponds to a column density around $4.5 \times 10^{23} {\rm cm}^{-2}$, is a good estimate for the upper limit."
" Note also cm-?,that for NGC 1068 the column density of the polar scattering medium has been constrained from the observed emission measure distribution to 4x10?!cm?«logNucone7x10?cm? (Kinkhabwalaetal.2002)."," Note also that for NGC 1068 the column density of the polar scattering medium has been constrained from the observed emission measure distribution to $4 \times 10^{21} {\rm cm}^{-2} < \log{N_{\rm H,Cone}} < 7 \times 10^{22} {\rm cm}^{-2}$ \citep{kinkhabwala2002}."
". Furthermore, we assume in our modelling that the matter is uniformly distributed inside the double-cone, whereas the approach by Dasetal.(2006) is based on outflows with a shell-structure, such as predicted for magnetically driven outflows (Konigl&Kartje 1994)."," Furthermore, we assume in our modelling that the matter is uniformly distributed inside the double-cone, whereas the approach by \citet{das2006} is based on outflows with a shell-structure, such as predicted for magnetically driven outflows \citep{konigl1994}."
". For all these reasons, the Stokes flux coming from the ionisation cones of NGC 1068 should be lower than we assume in our modelling, which enables a larger Av."," For all these reasons, the Stokes flux coming from the ionisation cones of NGC 1068 should be lower than we assume in our modelling, which enables a larger $\Delta \psi$."
 The misalignment of the ionisation cones with respect to the torus axis as derived by Rabanetal.(2009) refers to the projection of the double-cone onto the plane of the sky., The misalignment of the ionisation cones with respect to the torus axis as derived by \citet{raban2009} refers to the projection of the double-cone onto the plane of the sky.
" But if the outflows are rotated in azimuth with respect to the yz-plane, it is possible that the real misalignment with respect to the torus axis is larger than 18?."," But if the outflows are rotated in azimuth with respect to the $yz$ -plane, it is possible that the real misalignment with respect to the torus axis is larger than $18\degr$."
 Note that a slight inclination of the double-cone towards the observer is suggested by the kinematic modelling of Dasetal.(2006)., Note that a slight inclination of the double-cone towards the observer is suggested by the kinematic modelling of \citet{das2006}.
". Then, the average scattering angle for the polar electron scattering is no longer close to 90? but will shift towards forward and backward scattering."," Then, the average scattering angle for the polar electron scattering is no longer close to $90\degr$ but will shift towards forward and backward scattering."
 This reduces the polarised flux coming from the outflows., This reduces the polarised flux coming from the outflows.
" At the same time, a stronger inclination of the cones also requires a larger half-opening of the torus, otherwise the outflows would be blocked."," At the same time, a stronger inclination of the cones also requires a larger half-opening of the torus, otherwise the outflows would be blocked."
" The scattering distribution of the torus is thus geometrically flatter in this case, which should increase its Stokes flux."," The scattering distribution of the torus is thus geometrically flatter in this case, which should increase its Stokes flux."
 Both effects work in favour of higher values for Av than found from the models presented here., Both effects work in favour of higher values for $\Delta \psi$ than found from the models presented here.
 We are also pessimistic in our assumptions about the torus scattering properties., We are also pessimistic in our assumptions about the torus scattering properties.
" In our modelling we assume a maximum optical depth by setting Nu,tor=cm10?""?."," In our modelling we assume a maximum optical depth by setting $N_{\rm H,tor} = 10^{27} {\rm cm}^{-2}$."
 This agrees with previous spectroscopic studies showing that the obscuring material along the line-of-sight toward NGC 1068 is entirely opaque., This agrees with previous spectroscopic studies showing that the obscuring material along the line-of-sight toward NGC 1068 is entirely opaque.
" But for most viewing angles we are still more than one order above the lower threshold of the observed hydrogen column density, which was given by Mattetal.(1997) and Bianchietal.(2001) based on andBeppoSAX data."," But for most viewing angles we are still more than one order above the lower threshold of the observed hydrogen column density, which was given by \citet{matt1997} and \citet{bianchi2001} based on and data."
 It is thus likely that the torus is less optically thick than we assumed in our modelling., It is thus likely that the torus is less optically thick than we assumed in our modelling.
" A lower Nu,tor increases the polarised flux of the torus as we show in Fig. 7.."," A lower $N_{\rm H,tor}$ increases the polarised flux of the torus as we show in Fig. \ref{fig:torPF}."
" Between the cases of lower and higher Nu,tor there is an increase in Stokes flux at 20 keV by a factor of 2.5 at i=76° and of more than a factor of 10 at izz87°. The exact geometry of the obscuring dust region remains a matter of debate, although infrared interferometry observations start putting robust constraints on the geometrical size of the dusty region (Jaffeetal.2004;RamosAlmeidaetal.2009;Hónig 2010).."," Between the cases of lower and higher $N_{\rm H,tor}$ there is an increase in Stokes flux at 20 keV by a factor of 2.5 at $i \approx 76\degr$ and of more than a factor of 10 at $i \approx 87\degr$ The exact geometry of the obscuring dust region remains a matter of debate, although infrared interferometry observations start putting robust constraints on the geometrical size of the dusty region \citep{jaffe2004,ramos2009,hoenig2010a}."
" The latest generation of infrared radiative transfer models allows for a satisfying description of the data by assuming that the dust region is clumpy (Nenkovaetal.2008a,b;Schartmann 2010).."," The latest generation of infrared radiative transfer models allows for a satisfying description of the data by assuming that the dust region is clumpy \citep{nenkova2008a,nenkova2008b,schartmann2008,hoenig2010b}."
 Such a clumpy composition of the torus could also address criticism that the unified model could not properly explain how the observed spatial extension of the dust region can be maintained against self-gravity., Such a clumpy composition of the torus could also address criticism that the unified model could not properly explain how the observed spatial extension of the dust region can be maintained against self-gravity.
 The clumpy structure would argue for a dynamical model in which the torus is not in hydrostatic equilibrium (Krolik&Begelman1988)., The clumpy structure would argue for a dynamical model in which the torus is not in hydrostatic equilibrium \citep{krolik1988}.
. In the results presented here we do not include the effect of clumpiness on the resulting polarisation., In the results presented here we do not include the effect of clumpiness on the resulting polarisation.
" But if the torus medium is clumpy and at the same time dynamical, there is a better chance for fluctuations in the column density along a given line-of-sight."," But if the torus medium is clumpy and at the same time dynamical, there is a better chance for fluctuations in the column density along a given line-of-sight."
 Observing NGC 1068 with a lower opacity Nuyjtor is thus more likely if the medium is clumpy instead of uniform.," Observing NGC 1068 with a lower opacity $N_{\rm H,tor}$ is thus more likely if the medium is clumpy instead of uniform."
" As shown above, a lower opacity enhances the Stokes flux from the torus and thus the rotation Aw."," As shown above, a lower opacity enhances the Stokes flux from the torus and thus the rotation $\Delta \psi$."
 We assume that the polarisation coming from the accretion disc is based on reprocessing across the whole disk surface., We assume that the polarisation coming from the accretion disc is based on reprocessing across the whole disk surface.
 The extended disk has a large radius compared to the height of the X-ray source above., The extended disk has a large radius compared to the height of the X-ray source above.
" Then, the outer disc regions produce polarisation with y= 90°.This aligned polarisation"," Then, the outer disc regions produce polarisation with $\psi = 90\degr$ .This aligned polarisation"
"prior for j4 (between generous limits), and a uniform prior for black hole mass given jz, such that the predicted line widths are on the order of those in the data, reducing the volume of parameter space that needs to be explored.","prior for $\mu$ (between generous limits), and a uniform prior for black hole mass given $\mu$, such that the predicted line widths are on the order of those in the data, reducing the volume of parameter space that needs to be explored."
" We then assign cloud velocities in a probabilistic manner (note that we can assign multiple velocities to each cloud in order to improve sampling of the phase space in a computationally efficient way; throughout this paper we adopt 100 velocities for each of the 1,000 clouds)."," We then assign cloud velocities in a probabilistic manner (note that we can assign multiple velocities to each cloud in order to improve sampling of the phase space in a computationally efficient way; throughout this paper we adopt 100 velocities for each of the 1,000 clouds)."
" As in P11, we assume that the only force acting on the BLR clouds is gravity from the central black hole."," As in P11, we assume that the only force acting on the BLR clouds is gravity from the central black hole."
" The total energy of a cloud at a distance r from the black hole, moving with angular momentum J, is given by which has the minimum possible value If we knew the position, energy, and angular momentum of a cloud, we could solve for the radial velocity, We choose the negative (inbound) solution with probability q and the outbound with probability 1—q, 8 free parameter."," The total energy of a cloud at a distance $r$ from the black hole, moving with angular momentum $L$, is given by which has the minimum possible value If we knew the position, energy, and angular momentum of a cloud, we could solve for the radial velocity, We choose the negative (inbound) solution with probability $q$ and the outbound with probability $1-q$, a free parameter."
" For solutions to exist, the angular momentum must satisfy Circular orbits are obtained if we set the energy and angular momentum to To get elliptical orbits, instead of assigning E and L the exact circular values above, we assign them at random from the following probability distributions: These probability distributions are centered around the values for circular velocities, but the parameter A describes the dispersion, or how noncircular typical orbits will be."," For solutions to exist, the angular momentum must satisfy Circular orbits are obtained if we set the energy and angular momentum to To get elliptical orbits, instead of assigning $E$ and $L$ the exact circular values above, we assign them at random from the following probability distributions: These probability distributions are centered around the values for circular velocities, but the parameter $\lambda$ describes the dispersion, or how noncircular typical orbits will be."
 T'he circular orbit formulae are reproduced when λ—0., The circular orbit formulae are reproduced when $\lambda \to 0$.
" The probability distributions for E and L given three different values for A are shown in Figure 4,, along with the corresponding line shapes."," The probability distributions for $E$ and $L$ given three different values for $\lambda$ are shown in Figure \ref{EL}, along with the corresponding line shapes."
" For the inference, we use a uniform prior on A between 0 and 1."," For the inference, we use a uniform prior on $\lambda$ between 0 and 1."
 The main advantage of our implementation of this method with respect to that of Ρ11 is that we can generate relatively broad distributions of E and L with a smaller number of parameters., The main advantage of our implementation of this method with respect to that of P11 is that we can generate relatively broad distributions of $E$ and $L$ with a smaller number of parameters.
 The drawback is that this model is technically nonstationary (in the case of noncircular orbits) and would change if it were allowed to evolve in a dynamically self-consistent way., The drawback is that this model is technically nonstationary (in the case of noncircular orbits) and would change if it were allowed to evolve in a dynamically self-consistent way.
" Our model can be thought of as describing the time-invariant illuminated part of the full phase-space distribution, even though the underlying particles are actually flowing through the region."," Our model can be thought of as describing the time-invariant illuminated part of the full phase-space distribution, even though the underlying particles are actually flowing through the region."
 We checked that this simplifying assumption does not bias our inference on the black hole mass by analysis of the data with the code developed by P11., We checked that this simplifying assumption does not bias our inference on the black hole mass by analysis of the data with the code developed by P11.
 The results are consistent with the ones presented here., The results are consistent with the ones presented here.
 We then rotate the models (positions and velocities of the clouds) by an appropriate distribution of angles to generate an axisymmetric distribution of angular momentum vectors., We then rotate the models (positions and velocities of the clouds) by an appropriate distribution of angles to generate an axisymmetric distribution of angular momentum vectors.
 The first rotation is about the y axis by a small random angle; the typical size of these angles determines the opening angle of the disk or torus., The first rotation is about the $y$ axis by a small random angle; the typical size of these angles determines the opening angle of the disk or torus.
 We then rotate around the z axis by random angles to restore the axisymmetry of the model., We then rotate around the $z$ axis by random angles to restore the axisymmetry of the model.
" Finally, we rotate again about the y axis, by the inclination angle to model the inclination of the system with respect to the line of sight."," Finally, we rotate again about the $y$ axis, by the inclination angle to model the inclination of the system with respect to the line of sight."
" For the inference, we use uniform priors on the opening angle and the inclination angle."," For the inference, we use uniform priors on the opening angle and the inclination angle."
" To obtain non-axisymmetric models, in order to reproduce the line asymmetry, we weight each cloud by a simple spatially varying illumination function."," To obtain non-axisymmetric models, in order to reproduce the line asymmetry, we weight each cloud by a simple spatially varying illumination function."
" In spherical polar coordinates, this function is"," In spherical polar coordinates, this function is"
(2002).,.
. The code computes the dark matter correlation function using the transfer function given in Bardeenetal.(1986) and a window function which is | inside the volume V and 0 elsewhere., The code computes the dark matter correlation function using the transfer function given in \citet{bardeen1986} and a window function which is 1 inside the volume $V$ and 0 elsewhere.
 The volume elements are determined by the angular dimensions of the survey field and the redshift bin., The volume elements are determined by the angular dimensions of the survey field and the redshift bin.
 Finally. the cosmic variance for galaxies is computed using Equation(5).," Finally, the cosmic variance for galaxies is computed using Equation."
. Once cosmic variance has been determined for a number of individual survey fields that are widely separated on the sky. compared to the correlation length. as 1s often the case (e.g. for the various HST survey fields). one can easily derive the cosmic variance for the combined sample.," Once cosmic variance has been determined for a number of individual survey fields that are widely separated on the sky, compared to the correlation length, as is often the case (e.g. for the various HST survey fields), one can easily derive the cosmic variance for the combined sample."
 For the combination of fields / the total volume ts implying a cosmic variance for the total sample of where we have used since the galaxies 1n separated fields are uncorrelated., For the combination of fields $i$ the total volume is implying a cosmic variance for the total sample of where we have used since the galaxies in separated fields are uncorrelated.
" For a pencil beam geometry (angular extend <| radian) this can be written as where o, and o» are the angular dimensions of each field.", For a pencil beam geometry (angular extend $\ll 1$ radian) this can be written as where $\alpha_1$ and $\alpha_2$ are the angular dimensions of each field.
 Note that this volume-weighted average is identical to an inverse-variance-weighted average only in the range where the cosmic variance scales with volume., Note that this volume-weighted average is identical to an inverse-variance-weighted average only in the range where the cosmic variance scales with volume.
 In order to compute the cosmic variance for galaxies in à given volume in the universe one has to fix five parameters., In order to compute the cosmic variance for galaxies in a given volume in the universe one has to fix five parameters.
 The size of the volume is determined by two dimensions tangential to the line of sight and one dimension parallel to the line of sight., The size of the volume is determined by two dimensions tangential to the line of sight and one dimension parallel to the line of sight.
 The tangential dimensions we use are the angular size of the field a) and e». while the vertical dimension Is set by the size of the redshift bin under consideration Az.," The tangential dimensions we use are the angular size of the field $\alpha_1$ and $\alpha_2$, while the vertical dimension is set by the size of the redshift bin under consideration $\Delta z$."
 The fourth parameter 1s the mean redshift of the volume z. since the cosmic variance depends on the clustering strength which is a function of redshift.," The fourth parameter is the mean redshift of the volume $\bar{z}$, since the cosmic variance depends on the clustering strength which is a function of redshift."
 Moreover z determines the length scale of the volume bins by setting the conversion factor from angular dimensions and Az into comoving Mpe., Moreover $\bar{z}$ determines the length scale of the volume bins by setting the conversion factor from angular dimensions and $\Delta z$ into comoving Mpc.
 In order to determine the cosmic variance for galaxies one finally has to fix the stellar mass 71. of the sample under consideration. as the clustering strength and the bias depend strongly on stellar mass.," In order to determine the cosmic variance for galaxies one finally has to fix the stellar mass $m_*$ of the sample under consideration, as the clustering strength and the bias depend strongly on stellar mass."
 Thus the five parameters which have to be set are ay. ao. 5. Az and nn," Thus the five parameters which have to be set are $\alpha_1$, $\alpha_2$, $\bar{z}$, $\Delta z$ and $m_*$."
 The first step to calculate the cosmic variance i8 to fix the size of the volume element under consideration., The first step to calculate the cosmic variance is to fix the size of the volume element under consideration.
 For now we set the size of the redshift bin to a reference value of Az=0.2., For now we set the size of the redshift bin to a reference value of $\Delta z = 0.2$.
 This is à convenient bin size for low redshift while for higher redshift it ts rather small., This is a convenient bin size for low redshift while for higher redshift it is rather small.
 However. this choice can be changed at any redshift (for values Az50.05) using the recipe presented in section 3.2..," However, this choice can be changed at any redshift (for values $\Delta z \geq 0.05$ ) using the recipe presented in section \ref{sec:redshiftbins}."
 For the tangential dimensions. we choose five popular fields: the Hubble Ultra Deep Field (Beckwithetal.2006.UDF).. one field of the Great Observatories Origins Deep Survey (Giavaliscoetal.2004.GOODS).. the Extended Chandra Deep Field South (E-CDFS) used in the Galaxy Evolution From Morphology And SEDs survey (Rixetal.2004.GEMS).. the Extended Groth Strip (EGS) used in the All-wavelength Extended Groth strip International Survey (Davisetal.2007.AEGIS) and the field used in the Cosmic Evolution Survey (Scovilleetal.2007.COSMOS).," For the tangential dimensions, we choose five popular fields: the Hubble Ultra Deep Field \citep[UDF]{udf}, one field of the Great Observatories Origins Deep Survey \citep[GOODS]{goods}, the Extended Chandra Deep Field South (E-CDFS) used in the Galaxy Evolution From Morphology And SEDs survey \citep[GEMS]{gems}, the Extended Groth Strip (EGS) used in the All-wavelength Extended Groth strip International Survey \citep[AEGIS]{aegis} and the field used in the Cosmic Evolution Survey \citep[COSMOS]{cosmos}."
. The angular dimensions of the surveys and the resulting observation areas are summarized in. Table I.., The angular dimensions of the surveys and the resulting observation areas are summarized in Table \ref{t:surveyarea}.
 We note that due to the small scales for the UDF numerical uncertainties in the integration of the correlation function are likely to be high., We note that due to the small scales for the UDF numerical uncertainties in the integration of the correlation function are likely to be high.
 As a result the values for cosmic variance in the UDF computed here. especially for z«0.5 (where size of the volume elements is very small) have considerable uncertainties.," As a result the values for cosmic variance in the UDF computed here, especially for $z<0.5$ (where size of the volume elements is very small) have considerable uncertainties."
 At these scales. the assumption of linear biasing is also not accurate.," At these scales, the assumption of linear biasing is also not accurate."
 As a consequence the cosmic variance for the UDF presented here is to be treated with caution and is mainly included to demonstrate the large cosmic variance in small fields., As a consequence the cosmic variance for the UDF presented here is to be treated with caution and is mainly included to demonstrate the large cosmic variance in small fields.
Diffuse radio cussion that caunot be attributed oulv to individual galaxies iu a galaxy cluster is termed ahalo if the emission is ceutrallv located or arelic M it lies substantially away frou the (N-rav) cluster ceuter (for reviews sec. e.g. Feretti 2000: Sarazin 2000).,"Diffuse radio emission that cannot be attributed only to individual galaxies in a galaxy cluster is termed a if the emission is centrally located or a if it lies substantially away from the (X-ray) cluster center (for reviews see, e.g., Feretti 2000; Sarazin 2000)."
 Radio halos typically extend to 1 Alpe scales aud are characterized by a steep radio spectrum consistent with a svuchrotron origin., Radio halos typically extend to 1 Mpc scales and are characterized by a steep radio spectrum consistent with a synchrotron origin.
 Until receutlv radio halos were known to exist du only a handful of galaxy clusters with Coma being the best-studied example (c.e.. Giovannini et al.," Until recently radio halos were known to exist in only a handful of galaxy clusters with Coma being the best-studied example (e.g., Giovannini et al."
 1993: Deiss et al., 1993; Deiss et al.
 1997)., 1997).
 With the completion of the NRAO VLA Sky Survey (Condonetal.1998). the umuber of candidate radio halos has riseu to approximately 20 (Cdovanmini. Tordi. Feretti 1999: Cüovanuini Feretti 2000: Liane ct al.," With the completion of the NRAO VLA Sky Survey \citep{vlass} the number of candidate radio halos has risen to approximately 20 (Giovannini, Tordi, Feretti 1999; Giovannini Feretti 2000; Liang et al."
 2000)., 2000).
 Tlowever. these radio halos still represeut onlv ~10 of the cluster »opulatious studied indicating that they are indeed a rare phenomenon.," However, these radio halos still represent only $\sim 10\%$ of the cluster populations studied indicating that they are indeed a rare phenomenon."
 huportaut progress iu our understanding of the ornmation of radio halos has been made recently., Important progress in our understanding of the formation of radio halos has been made recently.
 First. Covonictal.(2001). have compared the poiut-to-poiut spatial distribution of the radio and X-ray cussion iu our clusters and lave found a linear relationship iu wo cases and a nearlv linear relationship iu the other wo.," First, \citet{govoni} have compared the point-to-point spatial distribution of the radio and X-ray emission in four clusters and have found a linear relationship in two cases and a nearly linear relationship in the other two."
 The similarity of the radio aud N-rav morphologies sugeests a direct connection between the thermal X-rav plasina aud the nou-theriual radio plasma., The similarity of the radio and X-ray morphologies suggests a direct connection between the thermal X-ray plasma and the non-thermal radio plasma.
" Secoud. Colafraucesco(1999). and Liangotal.(2000)— have discovered a correlation between radio power Pi, (at 1.1 CGIIz rest frame) aud Nav temperature (74)) such that Iq increases for larecr in their sample of 10 of the most securely detected radio halos."," Second, \citet{sergio} and \citet{liang} have discovered a correlation between radio power $P_{1.4}$ (at 1.4 GHz rest frame) and X-ray temperature ) such that $P_{1.4}$ increases for larger in their sample of 10 of the most securely detected radio halos."
" Liangctal.(2000) sneeest that the Pi,Ts correlation also indicates a direct connection between the radio aud X-ray plasinas.", \citet{liang} suggest that the $P_{1.4}-\tx$ correlation also indicates a direct connection between the radio and X-ray plasmas.
 Although there is mounting evidence that the thermal N-rav and nou-thermal racio emission are directly related. the source of the relativistic particles eiviug rise to the nou-thermal cussion. as well as the question of the rarity of radio halos. remains unexplained.," Although there is mounting evidence that the thermal X-ray and non-thermal radio emission are directly related, the source of the relativistic particles giving rise to the non-thermal emission, as well as the question of the rarity of radio halos, remains unexplained."
 Perhaps the most favored mechanisin to accelerate relativistic clectrous im clusters is that of mergers (e... Tribble 1993) owing to the considerable amount of enerev available during a jiereer (~1001 ere).," Perhaps the most favored mechanism to accelerate relativistic electrons in clusters is that of mergers (e.g., Tribble 1993) owing to the considerable amount of energy available during a merger $\sim 10^{64}$ erg)."
 The details of this process. however. reluain coutroversial because of the difficulty im clirectly acceleratiug the thermal clectrous to relativistic enereies (o.@.. Tribble 1993: Saraziu 2000: Brunetti et al.," The details of this process, however, remain controversial because of the difficulty in directly accelerating the thermal electrons to relativistic energies (e.g., Tribble 1993; Sarazin 2000; Brunetti et al."
 2001: Blasi 2001)., 2001; Blasi 2001).
 In fact. owing to this difficulty it is often assumed that a reservoir of relativistic particles is established at sole time in the past evolution of the cluster with the current merger merely serving to re-accelerate relativistic particles from this reservoir.," In fact, owing to this difficulty it is often assumed that a reservoir of relativistic particles is established at some time in the past evolution of the cluster with the current merger merely serving to re-accelerate relativistic particles from this reservoir."
 In this case it is unclear whether the current or the past ανασα state of the cluster is the primary factor in the creation of a radio halo., In this case it is unclear whether the current or the past dynamical state of the cluster is the primary factor in the creation of a radio halo.
 N-rav observations provide circtuustantial evidence for a connection between cluster mereie and radio halos (see Feretti 2000 and references therein) because. iu particular. radio halos are only found in clusters possessing X-ray substructure and weak (or non-existent) cooling flows.," X-ray observations provide circumstantial evidence for a connection between cluster merging and radio halos (see Feretti 2000 and references therein) because, in particular, radio halos are only found in clusters possessing X-ray substructure and weak (or non-existent) cooling flows."
 However. it las been argued (e.g. Ciovanuuini Feretti 2000: Liang et al.," However, it has been argued (e.g., Giovannini Feretti 2000; Liang et al."
 2000: Feretti 2000) that iiereiue cannot be solely responsible for the formation of radio alos because at least of clusters show evidence for N-rav substructure (CJoues Forman 1999) whereas, 2000; Feretti 2000) that merging cannot be solely responsible for the formation of radio halos because at least of clusters show evidence for X-ray substructure (Jones Forman 1999) whereas
be confused. (,be confused. (
1) Are the jets a series of isolated components or a continuous fluid flow? (,1) Are the jets a series of isolated components or a continuous fluid flow? (
2) For these two cases. how does the observed total intensity depend on Doppler boosting in a jet whose locus is a helix but whose motion is racial? (,"2) For these two cases, how does the observed total intensity depend on Doppler boosting in a jet whose locus is a helix but whose motion is radial? ("
3) Under what conditions can observations distinguish the the cases η=2 and »=3?DAP (,3) Under what conditions can observations distinguish the the cases $n=2$ and $n=3$? (
4) What do the data sav about the 4433 jets?,4) What do the data say about the 433 jets?
" A moving opticallv-thin svnehrotron source is Doppler boosted and Ix-corrected by a [actor of D"" because L,/7""7 is a Lorentz invariant and J,xv"" .", A moving optically-thin synchrotron source is Doppler boosted and K-corrected by a factor of $D^{3+\alpha}$ because $I_\nu / \nu^3$ is a Lorentz invariant and $I_\nu \propto \nu^{-\alpha}$ \citep{RL} .
In the case of a continuous jet we want to know the flux densitv of a segment of the jet defined by the observing beam., In the case of a continuous jet we want to know the flux density of a segment of the jet defined by the observing beam.
 As shown by Lind&Blandford(1985):al.(1997):DeYoung (2002).. and others. not all the material in that segment of jet at a eiven instant contributes to a particular image.," As shown by \cite{LindBlandford, Sikora,DeYoung}, and others, not all the material in that segment of jet at a given instant contributes to a particular image."
 This is purely a light travel time effect., This is purely a light travel time effect.
 The fraction of the jet segment that contributes is (1—2cos0)=1/4)., The fraction of the jet segment that contributes is $(1 - \beta\cos\theta) = 1/\gamma D$.
" The effect of this is that the boost [actor is modified [rom D*"" to D?""/5: in other words. Li!/=510|D?.."," The effect of this is that the boost factor is modified from $D^{3+\alpha}$ to $D^{2+\alpha}/\gamma$; in other words, $I_\nu^{jet} = \gamma I_\nu^{obs}/ D^{2+\alpha}$."
 This calculation assumes a straight jet with the velocity along the jet direction., This calculation assumes a straight jet with the velocity along the jet direction.
 In 4433 the locus of the jet is a helix even though the motion of the jet material is racial., In 433 the locus of the jet is a helix even though the motion of the jet material is radial.
 This means (hat the ime delay between (he arrival of photons from the near and [ar ends of the jet is no longer Al=Reos(#)/e. where His the length of the part of the jet defined by the beam and @ is the angle between the jet velocity ancl the line of sight.," This means that the time delay between the arrival of photons from the near and far ends of the jet is no longer $\Delta t = R \cos(\theta)/c$, where $R$ is the length of the part of the jet defined by the beam and $\theta$ is the angle between the jet velocity and the line of sight."
 Instead. it is Al2fecos())/e. where 7 is the angle between the tangent to the jet locus and the line of sight.," Instead, it is $\Delta t \simeq R \cos(\eta)/c$, where $\eta$ is the angle between the tangent to the jet locus and the line of sight."
" In addition. (he rate al which material is added to the observed part of the jet is no longer proportional to c;,. but is instead determined by the component of the jet velocity in the direction of the locus of the helix."," In addition, the rate at which material is added to the observed part of the jet is no longer proportional to $v_{jet}$, but is instead determined by the component of the jet velocity in the direction of the locus of the helix."
" We have made such caleulations using the known kinematics of each part of the jet. aud (he results are very. similar to (he continuousstraight jet case. that is. with effective boosts of approximately D? "". as observed."," We have made such calculations using the known kinematics of each part of the jet, and the results are very similar to the continuousstraight jet case, that is, with effective boosts of approximately $D^{2+\alpha}$ , as observed."
 Critical, Critical
between the optical emission and the radio position of D. this could be due to the poorer signal-to-noise or the extended nature of the optical emission near D. Both (1 and G2 are extended. suggesting that both are galaxies.,"between the optical emission and the radio position of B, this could be due to the poorer signal-to-noise or the extended nature of the optical emission near B. Both G1 and G2 are extended, suggesting that both are galaxies."
 Photometry and relative astrometry were performed on GI and G2 in { band. and only. photometry in V. band (Table 3).," Photometry and relative astrometry were performed on G1 and G2 in $I$ band, and only photometry in $V$ band (Table 3)."
 The V.1 colour indices of €1 and C2 are 1.9 and 2.0 mag. respectively.," The $V-I$ colour indices of G1 and G2 are 1.9 and 2.0 mag, respectively."
 The separation is 0.60 aresee and the position angle of the line 1-62 is 1207., The separation is 0.60 arcsec and the position angle of the line G1-G2 is $120^\circ$.
 In this section we present a model that. reproduces. the observed. properties. of. DI1127|385., In this section we present a model that reproduces the observed properties of B1127+385.
 We use à Singular ]sothermal Ellipsoid (SHE) mass. distribution. (IxXormann. Schneider Dartelmann 1994) to describe the lens galaxies.," We use a Singular Isothermal Ellipsoid (SIE) mass distribution (Kormann, Schneider Bartelmann 1994) to describe the lens galaxies."
 We assume a smooth EI universe., We assume a smooth FRW universe.
 1 not. mentioned otherwise. all errors 99 per indicatecent confidence intervals.," If not mentioned otherwise, all errors indicate 99 per cent confidence intervals."
 From the VLBA observations we obtain 10 constraints (8 from the image positions and 2 from the flux. density ratios)., From the VLBA observations we obtain 10 constraints (8 from the image positions and 2 from the flux density ratios).
 Phe two source positions give 4 [ree parameters and the mass model gives 3 (velocity dispersion. surface density (SD) axis ratio ancl position angle).," The two source positions give 4 free parameters and the mass model gives 3 (velocity dispersion, surface density (SD) axis ratio and position angle)."
 Phe number of degrees of freeclom (NDE) is therefore 3., The number of degrees of freedom (NDF) is therefore 3.
 Initially we try a mocel consisting of a single SIE galaxy., Initially we try a model consisting of a single SIE galaxy.
 We place the mass distribution on the surface brightness (SB) centre of Gil. determined by fitting a 2D-Gaussian profile to it.," We place the mass distribution on the surface brightness (SB) centre of G1, determined by fitting a 2D-Gaussian profile to it."
" Phe position ofG1 relative to the optical emission feature associated. with radio component A is (0.2287. 0,038""). with a le error of ~5 mas in both or and. y."," The position of G1 relative to the optical emission feature associated with radio component A is $(-0.228'', -0.038'')$ , with a $1\sigma$ error of $\sim$ 5 mas in both $x$ and $y$."
 Ehe parities of components A and D are taken as. Land |1. respectively.," The parities of components A and B are taken as –1 and +1, respectively."
 Choosing |l anc 1 for A and D. and letting the centre of the SD distribution move freely. give in all cases (both for the single and. double lens case) unsatislactory mocels (NC <5).," Choosing +1 and –1 for A and B, and letting the centre of the SD distribution move freely, give in all cases (both for the single and double lens case) unsatisfactory models $\chi^2\ga5$ )."
 Using the image positions and Ilux density ratios of the radio components from Tables 1 and 2. we project ravs back on the source plane through the lens.," Using the image positions and flux density ratios of the radio components from Tables 1 and 2, we project rays back on the source plane through the lens."
 For the two image pairs AI&DDI and A2&DD2 we simultaneously minimize the distance between the back-projected ravs and the dillerence »etween observed: ancl model [lux density ratios (Ixavser 1990)., For the two image pairs – B1 and B2 – we simultaneously minimize the distance between the back-projected rays and the difference between observed and model flux density ratios (Kayser 1990).
 We allow for a le error of 0.1 mas in the relative ro and y distances between the positions of the two back-xojected rays and their average position., We allow for a $1\sigma$ error of 0.1 mas in the relative $x$ and $y$ distances between the positions of the two back-projected rays and their average position.
 A la error of 0.15 is allowed. for the [Dux density ratios., A $1\sigma$ error of 0.15 is allowed for the flux density ratios.
 When the mocdel has converged. sulliciently. we use the average source positions o calculate the image positions in the lens plane.," When the model has converged sufficiently, we use the average source positions to calculate the image positions in the lens plane."
 These are subsequently used to caleulate a X7 from the mismatch with the observed image positions., These are subsequently used to calculate a $\chi^2$ from the mismatch with the observed image positions.
 The resulting mass moclel xuameters for minimum X7 (lens plane) are Listed in Table + (mocdel L)., The resulting mass model parameters for minimum $\chi^2$ (lens plane) are listed in Table 4 (model I).
 Although Cl is the primary lens. C2 cannot be neglected as it liesclose to Gil and is only —1 mag fainter.," Although G1 is the primary lens, G2 cannot be neglected as it liesclose to G1 and is only $\sim$ 1 mag fainter."
 We therefore, We therefore
Elliptical or cD Brightest Cluster Galaxies (BCGs) have long been used as cosmological probes. in attempts to determine parameters such as Ly and eo. (Sandage 1972: Sandage lard LOTS: Lloessel. Gunn ‘Thuan 1980: Sandage Tammann 1990).,"Elliptical or cD Brightest Cluster Galaxies (BCGs) have long been used as cosmological probes, in attempts to determine parameters such as $_0$ and $_0$ (Sandage 1972; Sandage Hardy 1973; Hoessel, Gunn Thuan 1980; Sandage Tammann 1990)."
 These stuclies make use of the ease of selection. of such objects. at cosmological distances. which is a result. of their bright optical luminosities and privileged locations defined by other ealaxies and by the centroids of cluster X-ray emission.," These studies make use of the ease of selection of such objects at cosmological distances, which is a result of their bright optical luminosities and privileged locations defined by other galaxies and by the centroids of cluster X-ray emission."
 They also appeal to another. more surprising property of BCGs: they appear to be excellent standard candles. with Sandage llardw (1973) finding a scatter of only 0.28 mag in visual absolute magnitude. after. correction for. cluster Dautz-Morgan (1970). and richness class.," They also appeal to another, more surprising property of BCGs: they appear to be excellent standard candles, with Sandage Hardy \shortcite{sa:73} finding a scatter of only 0.28 mag in visual absolute magnitude, after correction for cluster Bautz-Morgan \shortcite{ba:70} and richness class."
 Lauer Postman (1994).. in a study using more modern CCD techniques. founcl a scatter of 0.33 mag in R-band absolute magnitudes of BCGs.," Lauer Postman \shortcite{la:94}, in a study using more modern CCD techniques, found a scatter of 0.33 mag in R-band absolute magnitudes of BCGs."
" They were able to reduce this scatter to 0.25 mag by using the relation. of absolute magnitude. with the ""Structure Parameter’ à of Lloessel (1980).. which is defined where sr, is a metric radius of 9.6 kpc and L,, is the luminosity within that metric radius."," They were able to reduce this scatter to 0.25 mag by using the relation of absolute magnitude with the `Structure Parameter' $\alpha$ of Hoessel \shortcite{ho:80}, which is defined as where $r_m$ is a metric radius of 9.6 kpc and $L_m$ is the luminosity within that metric radius."
 Lloessel (1980) explains a as being a climensionless parametrization of ealaxy size. and empirically it is found to increase with BCC luminosity.," Hoessel \shortcite{ho:80} explains $\alpha$ as being a dimensionless parametrization of galaxy size, and empirically it is found to increase with BCG luminosity."
 Indeed he found a scatter in o-corrected. BCC absolute magnitudes of just 0.21 mag. even lower than that of Lauer Postman (1994).," Indeed he found a scatter in $\alpha$ -corrected BCG absolute magnitudes of just 0.21 mag, even lower than that of Lauer Postman \shortcite{la:94}."
. ‘This uniformity in BCC luminosities remains something of a mystery., This uniformity in BCG luminosities remains something of a mystery.
 There is indeed: &ood reason for expecting a wider disparity in BCG properties than in those of other ealaxy types., There is indeed good reason for expecting a wider disparity in BCG properties than in those of other galaxy types.
 Hoessel (1980). and Lauer (1988). showed that 3076 of BCOGs have multiple nuclei. a frequency. which is ereater than would. be predicted by chance superpositions. and which indicates that galactic cannibalism is. very common in BCGs at the present epoch.," Hoessel \shortcite{ho:80} and Lauer \shortcite{la:88} showed that $\sim$ of BCGs have multiple nuclei, a frequency which is greater than would be predicted by chance superpositions, and which indicates that galactic cannibalism is very common in BCGs at the present epoch."
 The continued accretion of cluster members would seem. to ensure that BCGs as a population should. have diverse properties. and it would. seem. probable that this should. be reflected. both in their total luminosity and in their. composition.," The continued accretion of cluster members would seem to ensure that BCGs as a population should have diverse properties, and it would seem probable that this should be reflected both in their total luminosity and in their composition."
 One motivation for the present paper is to test whether BC'CGs, One motivation for the present paper is to test whether BCGs
though the ILELS.S. source is outside the error box of IFGL J1357.12-0212c. an association can not be excluded a priori. because it is known that the Galactic diffuse model used to build the IFGL catalog has the highest uncertainties on (he Galactic plane. amounting to <6% as estimated in the case of the supernova remnants W51C and W49 (Abdo et al.,"though the H.E.S.S. source is outside the error box of 1FGL J1857.1+0212c, an association can not be excluded a priori, because it is known that the Galactic diffuse model used to build the 1FGL catalog has the highest uncertainties on the Galactic plane, amounting to $\leq 6\%$ as estimated in the case of the supernova remnants W51C and W49 (Abdo et al."
 2009 2010c: see also 4.7 of the IFGL catalog).," 2009, 2010c; see also 4.7 of the 1FGL catalog)."
 Furthermore. we are analvzing (his region using more than 2 vears of Fermi-LAT data. against the Ll months used for the IFGL. which may induce changes in (he position and fIuxes of the sources in the spatial-spectral moclel.," Furthermore, we are analyzing this region using more than 2 years of -LAT data, against the 11 months used for the 1FGL, which may induce changes in the position and fluxes of the sources in the spatial-spectral model."
 To invesügate the hypothesis of a possible association of ΤΕΙ J1357.12-0212c€. with HESS J1358-2-020. we performed (wo likelihood analvses.," To investigate the hypothesis of a possible association of 1FGL J1857.1+0212c with HESS J1858+020, we performed two likelihood analyses."
 i one we set in the model the coordinates of IFGL J1357.12-0212c at the LFGL position., In one we set in the spectral-spatial model the coordinates of 1FGL J1857.1+0212c at the 1FGL position.
 In the other. we sel it at (he position of the ILE.S.5. source.," In the other, we set it at the position of the H.E.S.S. source."
 The analvses are performed setting Iree the fhix parameters of all (he point-like sources closer than 3° to HESS J18582-020. and modeling 1FGL J1357.12-0212c with a power-law with index and Πας free.," The analyses are performed setting free the flux parameters of all the point-like sources closer than $^{\circ}$ to HESS J1858+020, and modeling 1FGL J1857.1+0212c with a power-law with index and flux free."
 The only difference between both analvses was the assumed position of LFGL J1857.12-0212c., The only difference between both analyses was the assumed position of 1FGL J1857.1+0212c.
 This method allows testing whether (he position listed in the 1FGL Catalog is sustained., This method allows testing whether the position listed in the 1FGL Catalog is sustained.
 Iu the first case we obtained a lest statistic value TS=863. whilein the secondcase. with IFGL J1851.12-0212e displaced. we obtained TS-509.," In the first case we obtained a test statistic value TS=863, while in the second case, with 1FGL J1857.1+0212c displaced, we obtained TS=509."
 The comparison of the two TS values obtained changing the coordinates ol 1FGL J1357.1--0212e suggests that the association is significantly unlikely. given that ATS>350," The comparison of the two TS values obtained changing the coordinates of 1FGL J1857.1+0212c suggests that the association is significantly unlikely, given that $\Delta TS > 350$."
 In order to take into account the svstematics due (o the uncertainties of the Galactic diffuse model. (he analyses were repeated by arGlicially changing the normalization of the Galactic diffuse model by 26% (see.," In order to take into account the systematics due to the uncertainties of the Galactic diffuse model, the analyses were repeated by artificially changing the normalization of the Galactic diffuse model by $\pm 6\%$ (see."
 ο... Abdo et al.," e.g., Abdo et al."
 2010d)., 2010d).
 Also in these cases. the differences of the TS values (for the putative chauge in position of LFGL J1551.12-0212c) was large (ATS> 300). and suggests that (he association is significantly unlikelv.," Also in these cases, the differences of the TS values (for the putative change in position of 1FGL J1857.1+0212c) was large $\Delta TS > 300$ ), and suggests that the association is significantly unlikely."
 Thus. we believe we can salely entertain the hypothesis that IIESS J18582-020 and 1EGL J1857.12-0212c are not associated and proceed to impose upper limits.," Thus, we believe we can safely entertain the hypothesis that HESS J1858+020 and 1FGL J1857.1+0212c are not associated and proceed to impose upper limits."
 Once the hypothesis of association is rejected. the significance of the plausible gamma-raxy emission from IIESS J13584-020 was evaluated by means of adding an extra source at its position in the spectral-spatial model for the likelihood analysis.," Once the hypothesis of association is rejected, the significance of the plausible gamma-ray emission from HESS J1858+020 was evaluated by means of adding an extra source at its position in the spectral-spatial model for the likelihood analysis."
 We model it with a, We model it with a
gravitational acceleration. inferred from all-sky surveys of galaxies (the dipole.,"gravitational acceleration, inferred from all-sky surveys of galaxies (the )."
" A serious problem plaguing such comparisons is that every survey called ""all-sky misses a significant amount of galaxies due to obscuration by dust. gas and stars in the disk of the Milky Way (the Zone of Avoidance. ZoA)."," A serious problem plaguing such comparisons is that every survey called `all-sky' misses a significant amount of galaxies due to obscuration by dust, gas and stars in the disk of the Milky Way (the Zone of Avoidance, ZoA)."
 To overcome this problem. in order to calculate the clustering dipole of the given survey. the ZoA is fillec with mock galaxies.," To overcome this problem, in order to calculate the clustering dipole of the given survey, the ZoA is filled with mock galaxies."
 Their properties are chosen in a way to reflec the true. although unknown. galaxy distribution in the obscured par! of the sky. basing on the one known from the rest of the celestia sphere.," Their properties are chosen in a way to reflect the true, although unknown, galaxy distribution in the obscured part of the sky, basing on the one known from the rest of the celestial sphere."
 A part ofthe ZoA intersects with a nearby void region. the Loca Void (LV).," A part of the ZoA intersects with a nearby void region, the Local Void (LV)."
 When the existence of such a structure is not accounted for in the calculation of the acceleration of the LG. a spurious term is generated.," When the existence of such a structure is not accounted for in the calculation of the acceleration of the LG, a spurious term is generated."
 In this paper we have calculated both the amplitude anc the direction of this spurious acceleration., In this paper we have calculated both the amplitude and the direction of this spurious acceleration.
 For simplicity we have assumed that the LV is spherical and for its size we have adopted the value estimated by Tullyetal.(2008)., For simplicity we have assumed that the LV is spherical and for its size we have adopted the value estimated by \citet{Tully.etal}.
. We have also made the assumption that the LV is completely empty., We have also made the assumption that the LV is completely empty.
 Even then the amplitude of the spurious component amounts only to 45kms+ in units of velocity., Even then the amplitude of the spurious component amounts only to $45\kms$ in units of velocity.
 Including the observed elongation of the LV increases this value by 1/3., Including the observed elongation of the LV increases this value by $1/3$.
 On the other hand. possible presence of massive structures inside the LV. hidden behind the ZoA. could only lower this value.," On the other hand, possible presence of massive structures inside the LV, hidden behind the ZoA, could only lower this value."
 This artificial acceleration changes also the direction of the calculated clustering dipole., This artificial acceleration changes also the direction of the calculated clustering dipole.
 We have shown that this change is comparable to the uncertainty in the direction of the peculiar velocity of the LG. determined from the dipole component of the CMB temperature distribution. reduced to the barycentre of the LG.," We have shown that this change is comparable to the uncertainty in the direction of the peculiar velocity of the LG, determined from the dipole component of the CMB temperature distribution, reduced to the barycentre of the LG."
 Moreover. it points almost perpendicularly to the misalignment vector (ie. the difference between the vectors of the velocity and acceleration of the LG).," Moreover, it points almost perpendicularly to the misalignment vector (i.e. the difference between the vectors of the velocity and acceleration of the LG)."
 This results in a negligible shift of the misalignment angle. by less than one degree.," This results in a negligible shift of the misalignment angle, by less than one degree."
" The tinal effeet that we considered is the error in the inferred value of the non-relativistic matter density (2,, resulting from the negligence of the LV.", The final effect that we considered is the error in the inferred value of the non-relativistic matter density $\Omega_\mrm$ resulting from the negligence of the LV.
 We have estimated the relative error in this parameter as approximately 57 per cent., We have estimated the relative error in this parameter as approximately $5\div7$ per cent.
" Therefore. up to this accuracy the influence of the Local Void on the determination of Qu, from velocity-density comparisons can be neglected."," Therefore, up to this accuracy the influence of the Local Void on the determination of $\Omega_\mrm$ from velocity–density comparisons can be neglected."
 On the other hand. this additional biasing should be taken into account in the total error budget of the density parameter determined by such a method.," On the other hand, this additional biasing should be taken into account in the total error budget of the density parameter determined by such a method."
 We would like to reiterate that our results do not negate the dynamical influence of the Local Void on the Local Group: on the contrary. Tullyetal.(2008). have shown that this influence is significant.," We would like to reiterate that our results do not negate the dynamical influence of the Local Void on the Local Group; on the contrary, \citet{Tully.etal} have shown that this influence is significant."
 It is only the effect of masking the intersection of the LV and the ZoA that seems to be of little importance for the purpose of calculation of the clustering dipole within the linear theory., It is only the effect of masking the intersection of the LV and the ZoA that seems to be of little importance for the purpose of calculation of the clustering dipole within the linear theory.
 This partially supports the claims that the Zone of Avoidance is not a crucial issue in determinations of the peculiar acceleration. of the LG from all-sky surveys. especially such as 2MASS. where Galactic extinction is much weaker than in optical wavelengths.," This partially supports the claims that the Zone of Avoidance is not a crucial issue in determinations of the peculiar acceleration of the LG from all-sky surveys, especially such as 2MASS, where Galactic extinction is much weaker than in optical wavelengths."
 The authors would like to thank R. Brent Tully for the idea of this study and for useful comments on an earlier version of this manuscript., The authors would like to thank R. Brent Tully for the idea of this study and for useful comments on an earlier version of this manuscript.
 We also appreciate valuable suggestions from. the refferree. Pirin This work was partially supported by the Polish Ministry of Science and Higher Education under grant N N203 0253 33. allocated for the period 2007-2010.," We also appreciate valuable suggestions from the ree, Pirin This work was partially supported by the Polish Ministry of Science and Higher Education under grant N N203 0253 33, allocated for the period 2007–2010."
"determined the K-band GLF using the same Vj,4, values.",determined the $K$ -band GLF using the same $\vmod$ values.
" For this, we used the K-band magnitude defined by K=Kauto—tauto+ tgersic, Where the photometry is from the r-defined catalogue (Hilletal.2011)."," For this, we used the $K$ -band magnitude defined by $K=K_{\rm auto} - i_{\rm auto} + i_{\rm Sersic}$ , where the photometry is from the $r$ -defined catalogue \citep{hill11}."
. The reason for this definition is that for low-SB galaxies an aperture is more accurately defined in the SDSS r-band (or {-ραπά) compared to the UKIDSS K-band., The reason for this definition is that for low-SB galaxies an aperture is more accurately defined in the SDSS $r$ -band (or $i$ -band) compared to the UKIDSS $K$ -band.
 This K—i colour is added to our fiducial i-bandSersic magnitude in order to be get a robust estimate of total K-band flux., This $K-i$ colour is added to our fiducial $i$ -bandSersic magnitude in order to be get a robust estimate of total $K$ -band flux.
" The resulting GLF was simply converted to a GSMF using M/Lx= 0.5, which was chosen to give approximate agreement with the GSMF derived using the Tayloretal.(2011) stellar masses."," The resulting GLF was simply converted to a GSMF using $_K =
0.5$ , which was chosen to give approximate agreement with the GSMF derived using the \citet{taylor11} stellar masses."
 The number densities were divided by an average completeness of 0.93 because of the reduced coverage in the K-band [fig., The number densities were divided by an average completeness of 0.93 because of the reduced coverage in the $K$ -band [fig.
 3 of Baldryetal. (2010)]]., 3 of \citet{baldry10}] ].
 This scaled GLF is shown by the blue line in Fig. 12((, This scaled GLF is shown by the blue line in Fig. \ref{fig:gsmf}( (
b).,b).
" Note that strictly the V;,4,. values should be recomputed because of the different coverage across the regions but this should have minimal impact on the shape.", Note that strictly the $\vmod$ values should be recomputed because of the different coverage across the regions but this should have minimal impact on the shape.
" We also show the GAMA /x-band GLF from Driveretal. (2012), which was derived from different sample (0.013«z0.1, rp««19.4 and Kap<18.1a with r-defined Kauto magnitudes) with the same M/Lx applied."," We also show the GAMA $K$ -band GLF from \citet{driver12}, , which was derived from a different sample $0.013 <
z < 0.1$, $r_{\rm Pet}<19.4$ and $K_{\rm AB}< 18.1$ with $r$ -defined $K_{\rm
 auto}$ magnitudes) with the same $_K$ applied."
 The flattening from 10'°°Mo to ~10!?M& and upturn below these masses shown in the i-band derived GSMF is also seen directly in the K-band GLF [Fig. 12((, The flattening from $10^{10.6}\Msun$ to $\sim 10^{10}\Msun$ and upturn below these masses shown in the $i$ -band derived GSMF is also seen directly in the $K$ -band GLF [Fig. \ref{fig:gsmf}( (
b)].,b)].
 Though in the case of the Driveretal.(2012) result (standard Vinax) it is less pronounced., Though in the case of the \citet{driver12} result (standard $\vmax$ ) it is less pronounced.
" This is an important confirmation of this upturn since, while there is some variation in M/Lx, the K-band GLF is often used as a proxy for the GSMF."," This is an important confirmation of this upturn since, while there is some variation in $_K$, the $K$ -band GLF is often used as a proxy for the GSMF."
" Previous measurements of the K-band field GLF had failed to detect this upturn using 2MASS photometry down to LxS10°Le (Coleetal.2001;Kochanek2001) or using UKIDSS with SDSS redshifts (Smith,Loveday,&Cross2009);; see fig oof Smithetal. for a compilation."," Previous measurements of the $K$ -band field GLF had failed to detect this upturn using 2MASS photometry down to $L_K \la 10^{9}\Lsun$ \citep{cole01,kochanek01} or using UKIDSS with SDSS redshifts \citep*{SLC09}; see fig of \citeauthor{SLC09} for a compilation."
 These measurements nominally probe far enough down the GSMF (~ 10?M;) that the upturn should have been noted., These measurements nominally probe far enough down the GSMF $\sim10^{9}\Msun$ ) that the upturn should have been noted.
" We note that Merluzzietal. (2010)""s measurement of the K-band GLF in the z=0.048 Shapley Cluster shows an upturn particularly in the lower-density environments, however, this does rely on statistical background subtraction."," We note that \citet{merluzzi10}' 's measurement of the $K$ -band GLF in the $z=0.048$ Shapley Cluster shows an upturn particularly in the lower-density environments, however, this does rely on statistical background subtraction."
 The explanation for 2MASS-based GLFs missing this could be the surface brightness limit., The explanation for 2MASS-based GLFs missing this could be the surface brightness limit.
" However, GAMA and Smithetal. bboth used UKIDSS photometry."," However, GAMA and \citeauthor{SLC09} both used UKIDSS photometry."
" The difference in this case is that GAMA has redone the near-IR photometry using r-band defined matched apertures (Hilletal.2011), and the magnitude limit is higher meaning the galaxies are typically further away (smaller on the sky) making near-IR photometry more reliable."," The difference in this case is that GAMA has redone the near-IR photometry using $r$ -band defined matched apertures \citep{hill11}, and the magnitude limit is higher meaning the galaxies are typically further away (smaller on the sky) making near-IR photometry more reliable."
" The shape of the GSMF is well fit with a double Schechter function with a single value for the break mass (M”*), aa five-parameter fit (BGDOS8; Pozzettietal. 2010))."," The shape of the GSMF is well fit with a double Schechter function with a single value for the break mass $\mass^{*}$ ), a five-parameter fit (BGD08; \citealt{pozzetti10}) )."
 This is given by where $4dM is the number density of galaxies with mass between M and M+dM; with a2<αι so that the second term dominates at the faintest magnitudes.," This is given by where $\phi_\mass \, \D \mass$ is the number density of galaxies with mass between $\mass$ and $\mass + \D \mass$; with $\alpha_2 < \alpha_1$ so that the second term dominates at the faintest magnitudes."
 Figure 13 shows this function fitted to the GSMF data providing a good fit.," Figure \ref{fig:gsmf-fit}
 shows this function fitted to the GSMF data providing a good fit."
" The fit was obtained using a Levenberg-Marquardt algorithm on the binned GSMF between 8.0 and 11.8 (Table 1)), and the fit parameters are given in the plot."," The fit was obtained using a Levenberg-Marquardt algorithm on the binned GSMF between 8.0 and 11.8 (Table \ref{tab:gsmf}) ), and the fit parameters are given in the plot."
" The fit to the Pozzettietal. GGSMF for z— 0.1-0.35 is also shown, which is similar."," The fit to the \citeauthor{pozzetti10} GSMF for $z=0.1$ –0.35 is also shown, which is similar."
 A natural explanation for this functional form was suggested by Pengetal. (2010b).., A natural explanation for this functional form was suggested by \citet{peng10}. .
" In their phenomenological model, star- (SF) galaxies have a near constantspecific star-formation rate (SFR) that is a function of epoch."," In their phenomenological model, star-forming (SF) galaxies have a near constantspecific star-formation rate (SFR) that is a function of epoch."
 Then there are two principle processes that turn SF galaxies into red-sequence orpassive galaxies: ‘mass quenching’ and ‘environmental quenching’., Then there are two principle processes that turn SF galaxies into red-sequence orpassive galaxies: `mass quenching' and `environmental quenching'.
" In the model, the probability of mass quenching is proportional to"," In the model, the probability of mass quenching is proportional to"
that may be plagued by systematic ellects. observational and/or physical (a common problem in the interpretation astronomical data),"that may be plagued by systematic effects, observational and/or physical (a common problem in the interpretation astronomical data)."
 Observationallv. there are essentially two classes. of. halo objects: globular clusters and dwarf. spheroidal galaxies: these overlap in mass but not in surface brightness or in age and uniformity of the stellar populations.," Observationally, there are essentially two classes of halo objects: globular clusters and dwarf spheroidal galaxies; these overlap in mass but not in surface brightness or in age and uniformity of the stellar populations."
 The globular clusters are generally comprised of ancient. though not necessarily coeval. stellar populations and they are numerous (several hundred: observed in. ane inferred. in the Galaxy).," The globular clusters are generally comprised of ancient, though not necessarily coeval, stellar populations and they are numerous (several hundred observed in and inferred in the Galaxy)."
 Γον are high surface brightness objects and garow no dynamical evidence for dark matter within the visible object. (dynamical mass-to-light ratios are typical of the observed stellar populations)., They are high surface brightness objects and show no dynamical evidence for dark matter within the visible object (dynamical mass-to-light ratios are typical of the observed stellar populations).
 The dwarf spheroidal ealaxies have low surface brightness and a large conventional dynamical M/L (M/L exceeding LOO in some cases)., The dwarf spheroidal galaxies have low surface brightness and a large conventional dynamical M/L (M/L exceeding 100 in some cases).
 They are few in number (about 20 cirectlv observed in the the Galaxy) and contain generally vounger stellar populations covering a range of ages., They are few in number (about 20 directly observed in the the Galaxy) and contain generally younger stellar populations covering a range of ages.
 In the context the LODAL paradigm. the explanation of the general properties of these halo objects. specifically he presence or absence of cdark matter”. resides in murky creation mythology.," In the context the LCDM paradigm, the explanation of the general properties of these halo objects, specifically the presence or absence of “dark matter"", resides in murky creation mythology."
 LODAL simulations predict that ealaxies. assembled over cosmic time via mergers of smaller ialos. should. contain a large number of dark matter sub-ialos (in the Galaxy more than 200 with velocity dispersion ercater than a few kms): this substructure is intrinsic to the heory and a fundamental constituent of galaxy scale halos.," LCDM simulations predict that galaxies, assembled over cosmic time via mergers of smaller halos, should contain a large number of dark matter sub-halos (in the Galaxy more than 200 with velocity dispersion greater than a few km/s); this substructure is intrinsic to the theory and a fundamental constituent of galaxy scale halos."
 ]t might seem more natural to icentify these dark matter sub-halos with globular clusters. the more numerous ane wimorcdial objects in the Galaxy.," It might seem more natural to identify these dark matter sub-halos with globular clusters, the more numerous and primordial objects in the Galaxy."
 However. these are barvon rather than dark matter dominated. so the identification is made with the dwarf. spheroidals.," However, these are baryon rather than dark matter dominated, so the identification is made with the dwarf spheroidals."
 Their. embarrassing scarcitv is then due the fact that most of the predicted dark matter sub-halos have remained cark because they never captured sullicient barvons to initiate star formation or the captured barvons have been blown away by early stellar processes., Their embarrassing scarcity is then due the fact that most of the predicted dark matter sub-halos have remained dark because they never captured sufficient baryons to initiate star formation or the captured baryons have been blown away by early stellar processes.
 “Phen a separate formation scenario must » invoked. for. globular clusters: e.g.. globular clusters are ormed in primordial clisk-bouncl supermassive molecular clouds with high barvon to dark matter ratio and. [ater attain a more spheroidal shape due to subsequent. mergers (Ixravtsov CGneden 2005).," Then a separate formation scenario must be invoked for globular clusters; e.g., globular clusters are formed in primordial disk-bound supermassive molecular clouds with high baryon to dark matter ratio and later attain a more spheroidal shape due to subsequent mergers (Kravtsov Gneden 2005)."
 These scenarios. while imaginative. are. ο sav the least. cillieult to falsify.," These scenarios, while imaginative, are, to say the least, difficult to falsify."
 In the context of MOND there is no need to speculate about formation processes in order to account for the perceived dark matter content in these two classes of objects., In the context of MOND there is no need to speculate about formation processes in order to account for the perceived dark matter content in these two classes of objects.
 MOND predicts. that high surface brightness. systems (svstems with high internal acceleration) should exhibit no evidence for a mass discrepancy within the visible object (conventionally. no dark matter).," MOND predicts that high surface brightness systems (systems with high internal acceleration) should exhibit no evidence for a mass discrepancy within the visible object (conventionally, no dark matter)."
 Conversely. ΜΟΝΟ oedicets that. low-surlace-brightness svstenis. such as the dwarf. spheroidal satellites of the Galaxy. should: exhibit a large discrepancy.," Conversely, MOND predicts that low-surface-brightness systems, such as the dwarf spheroidal satellites of the Galaxy, should exhibit a large discrepancy."
 These observed: properties of globular clusters and. dwarf spheroidals find. natural explanation in the context of MOND based on existent physical law. not on formation scenarios.," These observed properties of globular clusters and dwarf spheroidals find natural explanation in the context of MOND based on existent physical law, not on formation scenarios."
 Phat is not to say cüllering formation histories are unimportant in defining the overall observed properties of these two distinct classes of halo objects (such as the stellar populations)., That is not to say differing formation histories are unimportant in defining the overall observed properties of these two distinct classes of halo objects (such as the stellar populations).
 With MOND. globular clusters could. well be among the first objects formed. prior to or simultaneous with galaxies. as suggested by the old. stellar populations: whereas the dwarf spheroidals may have formed subsequently as tidal objects.," With MOND, globular clusters could well be among the first objects formed, prior to or simultaneous with galaxies, as suggested by the old stellar populations; whereas the dwarf spheroidals may have formed subsequently as tidal objects."
" But the magnitude of the apparent ""dark matter content” is clirectly related. to the internal acceleration or observed surface density and not to different formation histories."," But the magnitude of the apparent ""dark matter content"" is directly related to the internal acceleration or observed surface density and not to different formation histories."
 lt is of interest. that with MOND. non-isothermal systems. such as the high-order polvtropes shown here. have a cutoll radius (an edge) whieh is unrelated to the tidal racdius.," It is of interest that with MOND, non-isothermal systems, such as the high-order polytropes shown here, have a cutoff radius (an edge) which is unrelated to the tidal radius."
 Given the barvonic mass of NGC 2419. the tidal radius should be in excess of 1. kpe. and vet. the observed. truncation radius is on the order of 200 pc.," Given the baryonic mass of NGC 2419, the tidal radius should be in excess of 1 kpc, and yet, the observed truncation radius is on the order of 200 pc."
 In general the cutoll radii of dwarf spheroidals. which have comparable barvonic masses. are larger than those of the globular clusters (Zhao 2005a.b).," In general the cutoff radii of dwarf spheroidals, which have comparable baryonic masses, are larger than those of the globular clusters (Zhao 2005a,b)."
 Perhaps it is the case that the globular clusters do not fill their Roche lobe that the density cutoll is due to non-isothermal state., Perhaps it is the case that the globular clusters do not fill their Roche lobe – that the density cutoff is due to non-isothermal state.
 On the other hand. the cwarl spheroidals may well extend to their tidal radii because of the dillerent formation history.," On the other hand, the dwarf spheroidals may well extend to their tidal radii because of the different formation history."
 With respect to the specific example of NGC 2419 it has been claimed that simultaneously matching the radial distribution of starlight and. line-of-sight velocity dispersion is not possible in the context of MOND., With respect to the specific example of NGC 2419 it has been claimed that simultaneously matching the radial distribution of starlight and line-of-sight velocity dispersion is not possible in the context of MOND.
 This claim is mace in the context of a class of isothermal models in which the phase space distribution of stars as a [function of the integrals of motion is chosen to be of a quite specific form (the Alichie mocel)., This claim is made in the context of a class of isothermal models in which the phase space distribution of stars as a function of the integrals of motion is chosen to be of a quite specific form (the Michie model).
 This class nay » appropriate for Newtonian isothermal spheres with a constructed. radial cutolfl (identified with the tidal raclius) out dt is not clearly applicable to ALONDian objects which are intrinsically finite., This class may be appropriate for Newtonian isothermal spheres with a constructed radial cutoff (identified with the tidal radius) but it is not clearly applicable to MONDian objects which are intrinsically finite.
 L have presented: a counter-example which demonstrates no such inconsistency with he observations: a non-isothermal models. approximated by ugh order polvtropes.," I have presented a counter-example which demonstrates no such inconsistency with the observations: a non-isothermal models, approximated by high order polytropes."
 L attach no particular significance o the polvtropic relation between velocity dispersion and density: it is an idealizecl assumption., I attach no particular significance to the polytropic relation between velocity dispersion and density; it is an idealized assumption.
 But it does demonstrate that. given the uncertainties of anisotropy or isothermality.- it is perhaps rash to claim that this one particular object is problematic for MOND.," But it does demonstrate that, given the uncertainties of anisotropy or isothermality, it is perhaps rash to claim that this one particular object is problematic for MOND."
 Each single well-nmieasured rotation curve for a nearby disk galaxy missing these ambiguities is lar more of a crucible for gravity theories., Each single well-measured rotation curve for a nearby disk galaxy – missing these ambiguities – is far more of a crucible for gravity theories.
 Lam grateful to Moti. Alilgrom for helpful comments on the craft of this paper., I am grateful to Moti Milgrom for helpful comments on the draft of this paper.
 E also thank Roclerigo Ibata for pointing out an inconsistency in earlier results that led to a correction of my Jeans equation integrator., I also thank Roderigo Ibata for pointing out an inconsistency in earlier results that led to a correction of my Jeans equation integrator.
 Anc I thank Scott “Prager for a useful. discussion on the properties of elobular clusters., And I thank Scott Trager for a useful discussion on the properties of globular clusters.
funelion is steep. and the total LvC budget requires extrapolation to low-huminosity galaxies (Trenti 22010: Bouwens 22011b).,"function is steep, and the total LyC budget requires extrapolation to low-luminosity galaxies (Trenti 2010; Bouwens 2011b)."
 Moreover. the conversion from SFR to LyC production rate relies on insecure calibrations from theoretical models and comparison with high-anass. low-metallicity stars.," Moreover, the conversion from SFR to LyC production rate relies on insecure calibrations from theoretical models and comparison with high-mass, low-metallicity stars."
 We revisit (he calculation of LvC photon production and assess the high-z galaxy contribution {ο reionization., We revisit the calculation of LyC photon production and assess the $z$ galaxy contribution to reionization.
 We also analyze several factors. such as (he photon escape fraction (foe). IGM chunping factor (C5). and electron temperature (7.). which enter the calculation of the verilical star formation rate” (per) Necessary to maintain a photoionized IGM.," We also analyze several factors, such as the photon escape fraction $f_{\rm esc}$ ), IGM clumping factor $C_H$ ), and electron temperature $T_e$ ), which enter the calculation of the “critical star formation rate"" $\dot{\rho}_{\rm crit}$ ) necessary to maintain a photoionized IGM."
 In Section 2. we caleulate poi CM.ve+ *) in a filamentary IGM. equating the production rate of Lyman contünuum (LvC) photons with the hydrogen recombination rate.," In Section 2, we calculate $\dot{\rho}_{\rm crit}$ $M_{\odot}~{\rm yr}^{-1}$ $^{-3}$ ) in a filamentary IGM, equating the production rate of Lyman continuum (LyC) photons with the hydrogen recombination rate."
 The photoionization rate depends on (he mass function of stellar populations. their evolutionarv (racks and stellar atmospheres. and the escape Iraction. [ως of LvC photons awav [rom their galactic sources.," The photoionization rate depends on the mass function of stellar populations, their evolutionary tracks and stellar atmospheres, and the escape fraction, $f_{\rm esc}$ of LyC photons away from their galactic sources."
 The recombination rate depends on the density and temperature of the IGM. properties we explore wilh cosmological simulations.," The recombination rate depends on the density and temperature of the IGM, properties we explore with cosmological simulations."
 In Section 3. we give our results for the critical SFR at 2Z6 and. present our new SER. simulator. a user-[riendly interface for caleulating f44(2) and τσ).," In Section 3, we give our results for the critical SFR at $z \gsim 6$ and present our new SFR simulator, a user-friendly interface for calculating $\dot{\rho}_{\rm crit}(z)$ and $\tau_e(z)$."
" In Section 4. we discuss the implications for the hydrogen EoR. Consistency between high-redshilt galaxies and CMD optical depth appears lo require z,47 and a partially ionized IGM at 2>7."," In Section 4, we discuss the implications for the hydrogen EoR. Consistency between high-redshift galaxies and CMB optical depth appears to require $z_{\rm rei} \approx 7$ and a partially ionized IGM at $z > 7$."
 The peak signal fom recdshifted 2]-cm emission would likely occur during (he heating period between 2=7.7—8.5 (145163 MIIZ) when the hydrogen neutral fraction μι220.5 (Pritehard 22010: Lidz 22003)., The peak signal from redshifted 21-cm emission would likely occur during the heating period between $z = 7.7-8.8$ (145–163 MHz) when the hydrogen neutral fraction $x_{\rm HI} \approx 0.5$ (Pritchard 2010; Lidz 2008).
 We denote by fap CU...vetMpe *) the global star formation rate per co-moving volume., We denote by $\dot{\rho}_{\rm SFR}$ $M_{\odot}~{\rm yr}^{-1}~{\rm Mpc}^{-3}$ ) the global star formation rate per co-moving volume.
 Using a simple argument (Macau 11999). balancing photoionization wilh radiative recombination. we estimate the critical SFR ο maintain IGAL photoionization al 27. assuming that the ων photons are produced by populations of massive (OD-(vpe) stus.," Using a simple argument (Madau 1999), balancing photoionization with radiative recombination, we estimate the critical SFR to maintain IGM photoionization at $z > 7$, assuming that the LyC photons are produced by populations of massive (OB-type) stars."
 Because the mass in collapsed objects (clusters. eroups. galaxies) is still small at high redshift. the IGAI contains most of the cosmological barvons. al mean density," Because the mass in collapsed objects (clusters, groups, galaxies) is still small at high redshift, the IGM contains most of the cosmological baryons, at mean density"
and where ων is (he Éu-UV radiation field. ogi. is the photoclissociation cross section per PAIL molecule. nj is the number density of hvdrogen atoms. Ve: is the abundance of C in the ISM. ancl Aye. is the reaction rate for sticking of a carbon atom onto such a molecule.,"and where $F_{{\rm FUV}}$ is the far-UV radiation field, $\sigma _{{\rm diss}}$ is the photodissociation cross section per PAH molecule, $n_{{\rm H}}$ is the number density of hydrogen atoms, $X_{{\rm C}}$ is the abundance of C in the ISM, and $k_{{\rm acc}}$ is the reaction rate for sticking of a carbon atom onto such a molecule."
 For the far-UYV radiation fiekl. we take the total radiation field above the ionization potential adopted [ον these molecules ( >6 eV).," For the far-UV radiation field, we take the total radiation field above the ionization potential adopted for these molecules ( $\ge 6$ eV)."
 Putting together equations 1. and 2.. we see that the PAIIs will be destroved when Or We shall define H as theParameter. by analogy will the dimensionless Ionization Parameter 24 used in rreeion theory.," Putting together equations \ref{1} and \ref{2}, we see that the PAHs will be destroyed when or We shall define ${\cal H}$ as the, by analogy with the dimensionless Ionization Parameter ${\cal U}$ used in region theory."
 The advantage of (he use of this parameter is (hat all photocdissociation rates will scale in this wav. and therefore the local value of this dimensionless parameter will also determine the local chemistry. of photodissociation regions to [ist order.," The advantage of the use of this parameter is that all photodissociation rates will scale in this way, and therefore the local value of this dimensionless parameter will also determine the local chemistry of photodissociation regions to first order."
 The actual shape of the photodissociating spectrum will determine the chemistry (o second order., The actual shape of the photodissociating spectrum will determine the chemistry to second order.
 Since we do not know the absolute value of H above which PAIIs are destroved. we have to ask. what are the most extreme values of H observed in regions which still contain ΡΑΣ.," Since we do not know the absolute value of ${\cal H}$ above which PAHs are destroyed, we have to ask, what are the most extreme values of ${\cal H}$ observed in regions which still contain PAHs."
 From Allain et al. (, From Allain et al. (
"1996a). such extreme regions can be identified as in the diffuse ISM. high above the galactic plane where my,70.1 *. Frey~1.5x105 photons ? l'or in the planetary nebula NGCTO27 where py~7xI0!em ? and Freyc7.6x10! photons 7s +. corresponding to 74~0.05 and 7470.04 respectively.","1996a), such extreme regions can be identified as in the diffuse ISM, high above the galactic plane where $n_{{\rm H}}\sim 0.1$ $^{-3}$ , $F_{{\rm FUV}}\sim
1.5\times 10^{8}$ photons $^{-2}$ $^{-1}$ or in the planetary nebula NGC7027 where $n_{{\rm H}}\sim 7\times 10^{4}$ $^{-3}$ and $F_{{\rm FUV}}\sim 7.6\times
10^{13}$ photons $^{-2}$ $^{-1}$, corresponding to ${\cal H}\sim 0.05$ and ${\cal H}\sim 0.04$ respectively."
 We therefore adopt a thresholel of H~0.05 for the destruction of PAIIs.," We therefore adopt a threshold of ${\cal
H}\sim 0.05$ for the destruction of PAHs."
 This threshold is not reached for anv of ihe photoionization models presented here. so it is at least conceivable that charged PAL-llike molecules may survive in the environment of an rregion.," This threshold is not reached for any of the photoionization models presented here, so it is at least conceivable that charged PAH-like molecules may survive in the environment of an region."
 The photoionization modelling procedure adopted here closely follows that described in Dopitaetal.(2000) and. IXewley.etal.(2001)., The photoionization modelling procedure adopted here closely follows that described in \citet{Dopita00} and \citet{Kewley01}.
. For the central star cluster. we adopt a STARBURST99 (Leithererοἱal.1999). instantaneous-burst with a total huninositv. of 10 erg !1 and having an InitialMass. Function (MF) with a power-law slope of the," For the central star cluster, we adopt a STARBURST99 \citep{Leitherer99} instantaneous-burst with a total luminosity of $10^{40}$ erg $^{-1}$ and having an InitialMass Function (IMF) with a power-law slope of the"
lensing inversion to a different degree.,lensing inversion to a different degree.
 Since weak lensing PDFs span large ranges in both mass and concentration. the c(A7) prior can dominate the posterior resul by selecting a region which is always compatible with the likelihood.," Since weak lensing PDFs span large ranges in both mass and concentration, the $c(M)$ prior can dominate the posterior result by selecting a region which is always compatible with the likelihood."
 Then. the shapes of the PDFs for mass and concentration. with or without the prior on the c(A7) relation are very different.," Then, the shapes of the PDFs for mass and concentration with or without the prior on the $c(M)$ relation are very different."
 On the other hand. the concentration distribution from SL is already peaked and in good agreement with theoretical predictions.," On the other hand, the concentration distribution from SL is already peaked and in good agreement with theoretical predictions."
 Then. any ¢(A/) prior alleviates the over-concentration problem for the strong lensing analysis. favouring lesser values of cogo and smaller dispersions. but does not dramatically change the PDFs.," Then, any $c(M)$ prior alleviates the over-concentration problem for the strong lensing analysis, favouring lesser values of $c_{200}$ and smaller dispersions, but does not dramatically change the PDFs."
 Differently from any shear analysis in the outskirts. strong lensing can precisely estimate the projected ellipticity in the inner regions.," Differently from any shear analysis in the outskirts, strong lensing can precisely estimate the projected ellipticity in the inner regions."
 Whatever the priors on the axial ratios distributions. spherical shapes are quite disregarded.," Whatever the priors on the axial ratios distributions, spherical shapes are quite disregarded."
" Even assuming a priori flat distributions. values of d,=(0.8 are now excluded and final distributions are quite peaked favouring triaxial shapes."," Even assuming a priori flat distributions, values of $q_1 \gs 0.8$ are now excluded and final distributions are quite peaked favouring triaxial shapes."
" Using strong instead of weak lensing. the central momenta of the PDF for q, and qo shift by ~0.2 and ~0.1. respectively."," Using strong instead of weak lensing, the central momenta of the PDF for $q_1$ and $q_2$ shift by $\sim0.2$ and $\sim0.1$, respectively."
 As before. when we adopt ;V-body like prescriptions. posterior PDFs mimic the prior.," As before, when we adopt $N$ -body like prescriptions, posterior PDFs mimic the prior."
 In order to perform a weak+strong lensing inversion. we considered a combined likelihood ZuxLhCup.," In order to perform a weak+strong lensing inversion, we considered a combined likelihood ${\cal L}_\mathrm{All} \propto {\cal L}_\mathrm{WL} \times {\cal L}_\mathrm{SL}$."
 Since posterior distributions from either strong or weak lensing analyses are compatible. the combined investigation provides a meaningful compromise.," Since posterior distributions from either strong or weak lensing analyses are compatible, the combined investigation provides a meaningful compromise."
 Concentration values are a bit larger but still compatible with theoretical predictions., Concentration values are a bit larger but still compatible with theoretical predictions.
 With respect to the inversionusing only strong lensing. lesser values of the mass are preferred. Aou~ AL... with smaller dispersions.," With respect to the inversionusing only strong lensing, lesser values of the mass are preferred, $-\Delta M_{200} \sim (4-6) \times 10^{14}M_{\odot}$ , with smaller dispersions."
 On the other hand. concentrations are slightly higher. eoo;1— 1.5. but," On the other hand, concentrations are slightly higher, $\Delta c_{200} \sim 1-1.5$ , but"
is a = 0.64+0.09 and b = 0.11+0.16.,is $a$ = $\pm$ 0.09 and $b$ = $\pm$ 0.16.
 The slope is smaller than the values of DK Lac (a = 0.88) and V4745 Ser (a = 0.79) derived by ? and a = 0.79 for the 6 novae presented by ?.., The slope is smaller than the values of DK Lac $a$ = 0.88) and V4745 Sgr $a$ = 0.79) derived by \cite{2009ApJ...701L.119P} and a = 0.79 for the 6 novae presented by \cite{2010arXiv1010.5611T}.
" With only one J-class nova candidate in our catalog, we can not tell if this is a difference between the nova in M31 and Galactic novae, or it is simply a variation among individual novae."," With only one J-class nova candidate in our catalog, we can not tell if this is a difference between the nova in M31 and Galactic novae, or it is simply a variation among individual novae."
" Besides the above-mentioned classes, there remains three more classes in the taxonomy of ?:: Among our candidates, however, we do not find evident light curves belonging to these classes."," Besides the above-mentioned classes, there remains three more classes in the taxonomy of \cite{2010AJ....140...34S}: Among our candidates, however, we do not find evident light curves belonging to these classes."
 This could be partially attributed to the set-up of our observation campaign., This could be partially attributed to the set-up of our observation campaign.
" For example, the dust dip for the extreme shallow dips in ? occur more than 1 month after the peak, with the dip to be about 6 mag dimmer than the light curve maximum."," For example, the dust dip for the extreme shallow dips in \cite{2010AJ....140...34S} occur more than 1 month after the peak, with the dip to be about 6 mag dimmer than the light curve maximum."
" Such magnitude variation can hardly be observed in M31, because it is too faint to be discerned."," Such magnitude variation can hardly be observed in M31, because it is too faint to be discerned."
 This implies that we might misclassified the D-class novae into other classes., This implies that we might misclassified the D-class novae into other classes.
 The non-detection of the P-class novae can be explained by the filter system we used., The non-detection of the P-class novae can be explained by the filter system we used.
 ? pointed, \cite{2006ApJS..167...59H} pointed
"where <4)(1;)=3/5,Aj) 5 D) is the linear theory growth mode. and a,(/) is the expansion factor of a universe with initial density contrast 0;=$7,A(/;).","where $A_h(t_i)=3/\sum_k A_k(t_i)^{-1}$ , $D(t)$ is the linear theory growth mode, and $a_e(t)$ is the expansion factor of a universe with initial density contrast $\delta_i\equiv\sum_k \lambda_k(t_i)$."
 Note that the first term in the expression above is the Zeldovich approximation to the evolution., Note that the first term in the expression above is the Zeldovich approximation to the evolution.
 Also note that. if all three axis are initially the same. then all the Ajs are the same. and A=9;/2.," Also note that, if all three axis are initially the same, then all the $\lambda_j$ s are the same, and $\lambda = \delta_i/3$."
 In (his case. the perturbation is a sphere. and the expression above reduces to (1)4AC)αλαμ]. so the approximation (A7)) is exact.," In this case, the perturbation is a sphere, and the expression above reduces to $A(t) \to A(t_i)\, [a_e(t)/a_i]$, so the approximation \ref{mowhitesilk}) ) is exact."
 Figure 6 compares the full numerical evolution of the three axes in (his model (solid) with the Zeldovich approximation (dotted) and with equation (A7)) (dashed). when the initial values are (0.6.p)=(2/400.0.2.0) in an Einstein de-Sitter universe.," Figure \ref{bondmo} compares the full numerical evolution of the three axes in this model (solid) with the Zeldovich approximation (dotted) and with equation \ref{mowhitesilk}) ) (dashed), when the initial values are $(\delta,e,p)=(2/400,0.2,0)$ in an Einstein de-Sitter universe."
 This shows clearly that. at late times. equation(ÀY)) J is significantly more accurate than the Zeldovieh approximation.," This shows clearly that, at late times, equation\ref{mowhitesilk}) ) is significantly more accurate than the Zeldovich approximation."
of magnitude.,of magnitude.
 The trends do not depend on the details of the simulations’ MDF., The trends do not depend on the details of the simulations' MDF.
" In this paper, we have studied the chemical abundance trends of inner halo stars in four SPH+N-Body simulations of approximately L* disk galaxies."," In this paper, we have studied the chemical abundance trends of inner halo stars in four SPH+N-Body simulations of approximately L* disk galaxies."
 We investigate the possibility of using chemical abundance trends to discern the relative importance of in situ and accretion processes in building up the inner stellar halos of Milky Way-mass galaxies., We investigate the possibility of using chemical abundance trends to discern the relative importance of in situ and accretion processes in building up the inner stellar halos of Milky Way-mass galaxies.
 For each simulated galaxy we concentrated on a sample of halo stars located within 10 kpe of a simulated sun-like observer., For each simulated galaxy we concentrated on a sample of halo stars located within 10 kpc of a simulated sun-like observer.
" This sample included stars from two populations, one formed in situ, and one accreted."," This sample included stars from two populations, one formed in situ, and one accreted."
" We find that in the inner halos of galaxies where a recent binary merger did not occur, high [Fe/H] in situ halo stars are more [a/Fe] rich than accreted stars at similar [Fe/H]."," We find that in the inner halos of galaxies where a recent binary merger did not occur, high [Fe/H] in situ halo stars are more $\alpha$ /Fe] rich than accreted stars at similar [Fe/H]."
 The bimodal distribution of [a/Fe] at high for in situ and accreted stars is primarily due to the [Fe/H]different mass galaxies in which they formed., The bimodal distribution of $\alpha$ /Fe] at high [Fe/H] for in situ and accreted stars is primarily due to the different mass galaxies in which they formed.
" The in situ halo populations (in all but h258) were formed early on deep in the potential wells of the primary dark matter halos, where a high star formation rate ensured that only core-collapse SNe dominated the chemical enrichment up to high [Fe/H]."," The in situ halo populations (in all but h258) were formed early on deep in the potential wells of the primary dark matter halos, where a high star formation rate ensured that only core-collapse SNe dominated the chemical enrichment up to high [Fe/H]."
" The accreted stars, which formed later on average than the in situ stars, and in shallower potential wells, underwent a slower chemical evolution, where SNe Type Ia contributed iron at lower [Fe/H], resulting in a lower at a given "," The accreted stars, which formed later on average than the in situ stars, and in shallower potential wells, underwent a slower chemical evolution, where SNe Type Ia contributed iron at lower [Fe/H], resulting in a lower $\alpha$ /Fe] at a given [Fe/H]."
Such trends are expected given a [a/Fe]mass-metallicity [Fe/H].relation (Brooksetal.2007).., Such trends are expected given a mass-metallicity relation \citep{Brooks2007}.
" Though the satellite galaxies in our simulations are too bright, and hence too metal rich, we have found that the relative chemical abundance patterns between in situ and accreted stars is a qualitative trend that is robust to the details of the simulated halos’ MDFs."," Though the satellite galaxies in our simulations are too bright, and hence too metal rich, we have found that the relative chemical abundance patterns between in situ and accreted stars is a qualitative trend that is robust to the details of the simulated halos' MDFs."
 We predict that a large systematic survey of the detailed chemical abundances of inner halo stars in the Milky Way will exhibit such dual trends in [Fe/H] vs , We predict that a large systematic survey of the detailed chemical abundances of inner halo stars in the Milky Way will exhibit such dual trends in [Fe/H] vs $\alpha$ /Fe].
"At higher metallicities, —1.0, Milky Way [a/Fe].stars in the inner several kpc[Fe/H]> of the halo should exhibit a bimodal distribution in [a/Fe]."," At higher metallicities, $\geq -1.0$, Milky Way stars in the inner several kpc of the halo should exhibit a bimodal distribution in $\alpha$ /Fe]."
" Unless the Galaxy has experienced a recent major major, high stars in this metallicity range will have formed in the a/Fe]Milky Way’s disk or bulge, and then been displaced into halo orbits."," Unless the Galaxy has experienced a recent major major, high $\alpha$ /Fe] stars in this metallicity range will have formed in the Milky Way's disk or bulge, and then been displaced into halo orbits."
" Low [a/Fe] stars in this regime will likely have formed in smaller potential wells than the Milky Way, and were accreted from satellite companions at high redshift."," Low $\alpha$ /Fe] stars in this regime will likely have formed in smaller potential wells than the Milky Way, and were accreted from satellite companions at high redshift."
" In fact, such trends in a and Fe have already been observed in a small sample of 94 local Milky Way halo dwarfs (Nissen&Schuster2010)."," In fact, such trends in $\alpha$ and Fe have already been observed in a small sample of 94 local Milky Way halo dwarfs \citep{Nissen2010}."
". Larger planned surveys, like HERMES, which will obtain high resolution spectra of MW halo stars will be able to observe such patterns, and quantify the importance of different physical processes to the MW’s halo formation."," Larger planned surveys, like HERMES, which will obtain high resolution spectra of MW halo stars will be able to observe such patterns, and quantify the importance of different physical processes to the MW's halo formation."
 We thank the anonymous referee for helping to greatly improve the paper., We thank the anonymous referee for helping to greatly improve the paper.
" We thank Chris Brook for helpful conversations, and Joe Cammisa at Haverford for computing support."," We thank Chris Brook for helpful conversations, and Joe Cammisa at Haverford for computing support."
 A.Z. and B.W. acknowledge support from NSF grant AST-0908446., A.Z. and B.W. acknowledge support from NSF grant AST-0908446.
 All simulations were run using the NASA Advanced Supercomputer Pleiades., All simulations were run using the NASA Advanced Supercomputer Pleiades.
" FG acknowledges support from the HST GO-1125, NSF AST-0607819 and NASA ATP NNX08AGS4G grants."," FG acknowledges support from the HST GO-1125, NSF AST-0607819 and NASA ATP NNX08AG84G grants."
 A.B. acknowledges support from the Sherman Fairchild, A.B. acknowledges support from the Sherman Fairchild
Basic expressions to calculate. the covariance of. light intensity [uctuations in two photometric bands are given in the paper (2)..,Basic expressions to calculate the covariance of light intensity fluctuations in two photometric bands are given in the paper \citep{multi2011}.
" ""μον were obtained for the approximation of weak perturbations bv the method. previously used in (?)..", They were obtained for the approximation of weak perturbations by the method previously used in \citep{polychrom2003}.
" The starting relation for the covariance ο of normalised intensities. arising due to turbulence in the laver located at the distance z from the receiver. is the expression: where x, and X2 are the averaged over entrance aperture logarithms of wave amplitudes in the first. and the second channels. anc £)(A) and. £5(A) are normaliscd products of the photon sensitivity in the photometric bands with the energy. distribution of the source spectrum."," The starting relation for the covariance $c_{1,2}$ of normalised intensities, arising due to turbulence in the layer located at the distance $z$ from the receiver, is the expression: where $\bar\chi_1$ and $\bar\chi_2$ are the averaged over entrance aperture logarithms of wave amplitudes in the first and the second channels, and $F_1(\lambda)$ and $F_2(\lambda)$ are normalised products of the photon sensitivity in the photometric bands with the energy distribution of the source spectrum."
 This equation is approximate because the right-hand: side: is written for the log-amplitudes ancl the left-hand side. for the intensities., This equation is approximate because the right-hand side is written for the log-amplitudes and the left-hand side for the intensities.
 For weak scintillation. the expression can be regarded as accurate.," For weak scintillation, the expression can be regarded as accurate."
 Using the formulae 711. from the paper (?).. one can calculate the covariance of the. log-amplituctes VALνο(A23 where apertures of the photometric channels may be not be coincident. in general.," Using the formulae 7–11 from the paper \citep{polychrom2003}, , one can calculate the covariance of the log-amplitudes $\langle\bar\chi_1(\lambda_1)\bar\chi_2(\lambda_2)\rangle$ where apertures of the photometric channels may be not be coincident, in general."
 For coincicent circular apertures. the product. of the Fourier. transforms of the aperture functions Wills is replaced. by the axi-symmoeltric aperture filter ACf/) during further integration over the spatial frequency.," For coincident circular apertures, the product of the Fourier transforms of the aperture functions $\tilde W_1\tilde W_2$ is replaced by the axi-symmetric aperture filter $A(f)$ during further integration over the two-dimension spatial frequency."
 The relationship between the scintillation power inder) 87 and the turbulence intensity C5(2) at the distance z ids described. with help offunctions (WE). that is scintillation power produced. by a turbulent laver of unity intensity.," The relationship between the scintillation power ) $s^2$ and the turbulence intensity $C_n^2(z)$ at the distance $z$ is described with help of (WF), that is scintillation power produced by a turbulent layer of unity intensity."
 In the linear approximation of the weak perturbations where Q(z) is the respective WE and the integration is performed. over whole atmospheric depth., In the linear approximation of the weak perturbations where $Q(z)$ is the respective WF and the integration is performed over whole atmospheric depth.
 In. analogy with the expression. for Q(2) in (2). we can obtain an expression for the Bsz) which cleseribes the covariance of seintillation in two dillerent photometric channels: where the integration is performed: over the modulus the spatial frequeney f. ο) is the spectral aperture filter. equal to ACf)=(24GDf)GDY for the case of coincident circular apertures of the diameter. D. and. the kernel Syos.fi is thefiller.," In analogy with the expression for $Q(z)$ in \citep{polychrom2003}, we can obtain an expression for the $R_{1,2}(z)$ which describes the covariance of scintillation in two different photometric channels: where the integration is performed over the modulus the spatial frequency $f$, $A(f)$ is the spectral aperture filter, equal to $A(f) = (2J_1(\pi Df)/(\pi Df))^2$ for the case of coincident circular apertures of the diameter $D$ , and the kernel $S_{1,2}(z,f)$ is the."
 Vhis filter is a double integral which splits into a product of two integrals: Then. the observed covariance ¢y.2 of the scintillation in two channels (eross-inder) depends. on the vertical distribution of the structure cocllicient C5(z): ICD xnp=(Az)7). we can use the method of (?).. putting sin(xÀAz/)=zAzf.," This filter is a double integral which splits into a product of two integrals: Then, the observed covariance $c_{1,2}$ of the scintillation in two channels ) depends on the vertical distribution of the structure coefficient $C_n^2(z)$: If $D \gg r_F = (\lambda z )^{1/2}$ ), we can use the method of \citep{Roddier81}, putting $\sin(\pi\lambda zf^2) \approx \pi\lambda zf^2$."
 The asvmptotie dependence for the covariance WE Rys(z)=17.33.D7z? is obtained.," The asymptotic dependence for the covariance WF $R_{1,2} (z) = 17.33\,D^{-7/3}z^2$ is obtained."
 This expression is identical to the known relation for the scintillation power in the case of large telescopes., This expression is identical to the known relation for the scintillation power in the case of large telescopes.
 Correlation of the scintillation can be described in. terms of theindex the variance of the difference of normalised signals in two photometric channels. an analogue of dillerential spatial index (7).," Correlation of the scintillation can be described in terms of the — the variance of the difference of normalised signals in two photometric channels, an analogue of differential spatial index \citep{timeconst2002}."
 In the case of strong. correlation expected for large. telescopes. this approach is more practical for measurement anc analysis.," In the case of strong correlation expected for large telescopes, this approach is more practical for measurement and analysis."
 This colour scintillation arises from the dependence of the dillraction on the wavelength of light., This colour scintillation arises from the dependence of the diffraction on the wavelength of light.
 Based on the relation for the variance of acillerence: Returning to the expression (3)) and summing the corresponding integrands. we obtain where {τονf) is thefiller: If the usual Fresnel filter used for the Q(z) caleulation ας behaviour x[i near £=0. the cillerential Fresnel filter T(z.f) is proportional to /77 there and suppresses the low pequencies passed by the aperture filter very effectively.," Based on the relation for the variance of adifference: the colour weighting function $Q_{d}(z)$ can be represented as: Returning to the expression \ref{eq:r12}) ) and summing the corresponding integrands, we obtain where $T_{1,2}(z,f)$ is the: If the usual Fresnel filter used for the $Q(z)$ calculation has behaviour $\propto f^4$ near $F=0$, the differential Fresnel filter $T(z,f)$ is proportional to $f^{12}$ there and suppresses the low frequencies passed by the aperture filter very effectively."
 For apertures of arbitrary size ancl wide photometric mands. the functions {τος} and Qafs) can be obtained »v numerical integration with formulae (3)). (4)) and (8)). (9)). as done when calculating the Ws in the programabmos developed Lor processing of measurements with Multi-Aperture Scintillation Sensor (ALASS) (??)..," For apertures of arbitrary size and wide photometric bands, the functions $R_{1,2}(z)$ and $Q_{d}(z)$ can be obtained by numerical integration with formulae \ref{eq:r12}) ), \ref{eq:s12}) ) and \ref{eq:weight_qd}) ), \ref{eq:t12}) ), as done when calculating the WFs in the program developed for processing of measurements with Multi-Aperture Scintillation Sensor (MASS) \citep{MASS,mnras2003}."
 The computed unctions Qu(z) for the D and & photometric bands (elective wavelengths Ag=440 nm E Àj=690nm) aud or four dillerent telescope apertures are shown in Fig. 1., The computed functions $Q_{d}(z)$ for the $B$ and $R$ photometric bands (effective wavelengths $\lambda_B = 440$ nm É $\lambda_R = 690$nm) and for four different telescope apertures are shown in Fig. \ref{fig:wfs_large}.
.Inthe case of large apertures 2(Az PF the asvmptotic dependencies for both index and erosseindex are completely achromatic (2.1)).," .Inthe case of large apertures $D \gg (\lambda z)^{1/2}$ , the asymptotic dependencies for both index and cross-index are completely achromatic \ref{sec:theory-corr}) )."
 Fherefore. it is not possible to obtain the asvinplote of the colour index s; [rom the formula. (6).," Therefore, it is not possible to obtain the asymptote of the colour index $s_d^2$ from the formula \ref{eq:s2_diff}) )."
 , 
then |z(t)|+0 as t— oo.,then $|z(t)|\rightarrow 0$ as $t\rightarrow \infty$ .
 Setting z=0 in (22)) gives a lower bound on the velocity of orbits which escape on the SOS., Setting $z=0$ in \ref{eq:cond1}) ) gives a lower bound on the velocity of orbits which escape on the SOS.
 The solid black region at the top of Figure 2 (a) demonstrates how this condition over estimates the escape boundary., The solid black region at the top of Figure \ref{fig:two} (a) demonstrates how this condition over estimates the escape boundary.
 All energy and time values in this region do not return to the SOS., All energy and time values in this region do not return to the SOS.
" The map, y, provides an accurate way of determining escape and capture."," The map, $\varphi$, provides an accurate way of determining escape and capture."
" From equation (20)) it is found that the mapping q is defined in a region, for as time enters into the mapping with period 27."," From equation \ref{eq:map}) ) it is found that the mapping $\varphi$ is defined in a region, for as time enters into the mapping with period $2\pi$."
 The curve ODy is the escape boundary., The curve $\partial \mathcal{D}_0$ is the escape boundary.
 Time and energy values above ODp are said to have escaped., Time and energy values above $\partial \mathcal{D}_0$ are said to have escaped.
" The domain, Do, can be defined by (23)) and (24))."," The domain, $\mathcal{D}_0$, can be defined by \ref{eq:Ebound}) ) and \ref{eq:Tbound}) )."
" Initial conditions in Do are mapped into the region, Di, defined by for t€ [0,27]."," Initial conditions in $\mathcal{D}_0$ are mapped into the region, $\mathcal{D}_1$, defined by for $t\in[0,2\pi]$ ."
" Figure 4 shows how the boundaries OD and OD, intersect.", Figure \ref{fig:boundaries} shows how the boundaries $\partial \mathcal{D}_0$ and $\partial \mathcal{D}_1$ intersect.
" Orbits are mapped from the region under the curve OD, to the region under the curve 0D;.", Orbits are mapped from the region under the curve $\partial \mathcal{D}_0$ to the region under the curve $\partial \mathcal{D}_1$.
 The region Bo=DoXD| represents energy and time values for which orbits are captured., The region $\mathcal{B}_0=\mathcal{D}_0\backslash\mathcal{D}_1$ represents energy and time values for which orbits are captured.
" In the context of the differential equation, these are orbits which come from infinity and get captured by the binary."," In the context of the differential equation, these are orbits which come from infinity and get captured by the binary."
" Similarly, the initial conditions in the region B1=D,\Do are energy and time values for which q is undefined."," Similarly, the initial conditions in the region $\mathcal{B}_1=\mathcal{D}_1\backslash\mathcal{D}_0$ are energy and time values for which $\varphi$ is undefined."
" Again, in the context of the differential equation, the region B4 represents orbits which escape from the system."," Again, in the context of the differential equation, the region $\mathcal{B}_1$ represents orbits which escape from the system."
 Finally note that initial conditions for the differential equation are such that Z>0 and z=0 on the SOS.," Finally, note that initial conditions for the differential equation are such that $\dot{z}>0$ and $z=0$ on the SOS."
" So from (19)), the initial energy can be bounded from below by, for to€[0, 27]."," So from \ref{eq:spcenergy}) ), the initial energy can be bounded from below by, for $t_0 \in [0,2\pi]$ ."
 Initial conditions are chosen in Do with (26))for and plotted in Figure 2 (b)., Initial conditions are chosen in $\mathcal{D}_0$ with \ref{eq:below}) )for $e=0.61$ and plotted in Figure \ref{fig:two} (b).
 The colour ofeach point represents the number of periods of the binary determinedby £y/2* where M is the number of iterations of the, The colour ofeach point represents the number of periods of the binary determinedby $t_M/2\pi$ where $M$ is the number of iterations of the
 Astronomy Centre. Department of Physics and Astronomy. School of Maths. and Physical Sciences. Pevensey LL Building. UUniversity of Sussex. Falmer. Brighton. BNI 9011. iy ‘Department of⋅ Physics. and Astronomy. UniversityD.. of British Columbia. 6224 Agricultural Roacl. Vancouver. BC. V6TIZI. Canaca Leiden Observatory. Leiden University. PO. Box 9513. NL - 2300 RA Leiden. The ‘EuropeanOps Southern1 Observatory. Karl-Schwarzschilel-- 2. D-85748. Garching bei Münnchen. “Phe STEC Rutherlord Appleton Laboratory. Didcot. Oxfordshire.,"$^{16}$ Astronomy Centre, Department of Physics and Astronomy, School of Maths and Physical Sciences, Pevensey II Building, University of Sussex, Falmer, Brighton, BN1 9QH, $^{17}$ Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC, V6T1Z1, Canada $^{18}$ Leiden Observatory, Leiden University, P.O. Box 9513, NL - 2300 RA Leiden, The $^{19}$ European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748, Garching bei Münnchen, $^{20}$ The STFC Rutherford Appleton Laboratory, Didcot, Oxfordshire,"
"Although we cannot sav which parameter (C,(1/3)Mi or logo) is better. we can identify some of the advantages and disadvantages of cach.","Although we cannot say which parameter $C_{r_e}(1/3)$ or $\log \sigma$ ) is better, we can identify some of the advantages and disadvantages of each."
 Use of he concentration index. for studies such as this may rot be applicable to morphologically disturbed galaxies which may have undergone recent mergers or interactiois (this could also influence the stellar velocity dispersion), Use of the concentration index for studies such as this may not be applicable to morphologically disturbed galaxies which may have undergone recent mergers or interactions (this could also influence the stellar velocity dispersion).
 Dominant cD ealaxies that have acquired large extended envelopes cau also be diffieult to model aud. depening ou the exteut of the acereted iiaterial. their concenration ludex may be heavily biased.," Dominant cD galaxies that have acquired large extended envelopes can also be difficult to model and, depending on the extent of the accreted material, their concentration index may be heavily biased."
 The stellar velocity «lispersion may. on the other haud. be a more stable quanutitv in such cases.," The stellar velocity dispersion may, on the other hand, be a more stable quantity in such cases."
 Velocity dispersions have additionally been measured for uunerous (mostly nearby) galaxies., Velocity dispersions have additionally been measured for numerous (mostly nearby) galaxies.
 Oue obvious practical advantage that the concentration iudex has over stellar velocity dispersious is that images are far less expensive to acquire (in terms of telescope time) than stellar velocity dispersions: especially those at one effective radi, One obvious practical advantage that the concentration index has over stellar velocity dispersions is that images are far less expensive to acquire (in terms of telescope time) than stellar velocity dispersions; especially those at one effective radii.
 This i$ particularly nuportaut for studies of ligh-+vecdshift ealaxies., This is particularly important for studies of high-redshift galaxies.
 Second. use of the bulge concentration cirecunveuts conceerus that the SMDII may be influencing the Iuuinositvwceiehted iuclear velocity dispersion measurements Wandel 2001).," Second, use of the bulge concentration circumvents concerns that the SMBH may be influencing the luminosity-weighted nuclear velocity dispersion measurements Wandel 2001)."
" Similulv. while η aud €, are global parameters. velocity dispersion measurements are affected by: kinematical sub-structure at the ceuters of bulges. rotational velocity. seeing conditions. and aperture-size."," Similarly, while $n$ and $C_{\rm r_e}$ are global parameters, velocity dispersion measurements are affected by: kinematical sub-structure at the centers of bulges, rotational velocity, seeing conditions, and aperture-size."
 It should also be noted. however. that tle presence of bars. rines. and Ieuses within spiral galaxies can complicate the determination of the bulge concentration.," It should also be noted, however, that the presence of bars, rings, and lenses within spiral galaxies can complicate the determination of the bulge concentration."
 A fourth advantage that the concentration index has is that it can be measured from photometrically uncalibrated images. it docs not rely on distance measurements. redshift dependent corrections. or assunied mass-to-lieht ratios.," A fourth advantage that the concentration index has is that it can be measured from photometrically uncalibrated images, it does not rely on distance measurements, redshift dependent corrections, or assumed mass-to-light ratios."
 It appear that the formation mnmechiauusmn(s) behiud nmlees πι sHnaultaneousle determine thei total ΠΠ their eventual huuinous structure (as measured * concentration index and Sérrsic 0) ancl lass distribution. them stellar velocity dispersion. the final mass of the ceutral SMDIT.," It appear that the formation mechanism(s) behind bulges must simultaneously determine their total luminosity, their eventual luminous structure (as measured by concentration index and Sérrsic $n$ ) and mass distribution, their stellar velocity dispersion, the final mass of the central SMBH."
. Subsequent evolution. iucludins the effects of mergers (once this process las neared completion). evideutlv preserves the above connections.," Subsequent evolution, including the effects of mergers (once this process has neared completion), evidently preserves the above connections."
" To date. most models iucorporatiug SMDIIs wave addressed their formation from the standpoiut of he older Afi, Af relation. (Παπά Loch 1998: Richstoue ot 11998: Silk Rees 1998: Dlaudford 1999: Ixauffuiun Παομπο 2000: Archibald oet 22001: Uiienimra 2001): a few recent papers have offered possible explanations for the Mig, 6 correlation (achuelt Wanftinann 2000: Adams. Caaf Richstone 2001: Burkert Silk 2001)."," To date, most models incorporating SMBHs have addressed their formation from the standpoint of the older $M_{\rm bh}$ $M_{\rm bulge}$ relation (Haiman Loeb 1998; Richstone et 1998; Silk Rees 1998; Blandford 1999; Kauffmann Haehnelt 2000; Archibald et 2001; Umemura 2001); a few recent papers have offered possible explanations for the $M_{\rm bh}$ $\sigma$ correlation (Haehnelt Kauffmann 2000; Adams, Graff, Richstone 2001; Burkert Silk 2001)."
 We argue that a more complete uuderstanding will be achieved when the correlation between SAIBIT mass and bulge concentration is also explained., We argue that a more complete understanding will be achieved when the correlation between SMBH mass and bulge concentration is also explained.
 Move luninous (παςνο) bulees have lavecr values of n (Trujillo et 22001b. and references therein). ereater central concentrations. deeper eravitational potential wells with steeper central eradieuts (ποτά 1991. Trujillo et 22001a). and more massive SMDIIs," More luminous (massive) bulges have larger values of $n$ (Trujillo et 2001b, and references therein), greater central concentrations, deeper gravitational potential wells with steeper central gradients (Ciotti 1991, Trujillo et 2001a), and more massive SMBHs."
 One might expect these characteristics to result in bulges which are better able to fuel aud build their ceutral black holes., One might expect these characteristics to result in bulges which are better able to fuel and build their central black holes.
 It is however likely that the processes which shaped the galaxy and built the supermassive black hole operated im tandem., It is however likely that the processes which shaped the galaxy and built the supermassive black hole operated in tandem.
 Velocity dispersion measurenmients iuav simply be a solewhat inore expensive tracer of the fundamental nuderling mass distribution which cau be more cheaply (in terms of telescope time) measured from galaxy lieht profiles., Velocity dispersion measurements may simply be a somewhat more expensive tracer of the fundamental underlying mass distribution which can be more cheaply (in terms of telescope time) measured from galaxy light profiles.
 We wish to thank Matthew Bershady for imakiug available the linear regression code frou. Αίας Bershady (1996)., We wish to thank Matthew Bershady for making available the linear regression code from Akritas Bershady (1996).
 Based ou archival data obtained with the Isaac Newtou Group of Telescopes operated ou behalf of the UIS Particle Physics aud Astronomy Research Council (PPARC) and the Necderlause Organisatic voor Wetcnschappelijk Ouderzock (NWO) ou the island of La αμα at the Spanish Observatorio del Roque de Los Muchlachos of the Iustituto de Astrofissica de Canarias., Based on archival data obtained with the Isaac Newton Group of Telescopes operated on behalf of the UK Particle Physics and Astronomy Research Council (PPARC) and the Nederlanse Organisatie voor Wetenschappelijk Onderzoek (NWO) on the island of La Palma at the Spanish Observatorio del Roque de Los Muchachos of the Instituto de sica de Canarias.
 Based ou observations made with the NASA/ESA IIubble Space Telescope. obtained from the data archive at the Space Telescope Institute.," Based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Institute."
 STScIis operated by the association of Viiversitics for Research in Astronomi. muucdler the NASA contract NAS 5-26555.," STScI is operated by the association of Universities for Research in Astronomy, under the NASA contract NAS 5-26555."
 This research bas made use of the NASA/TPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronautics and Space Achuimistration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."
n is the number of radial nodes of the mode.,$n$ is the number of radial nodes of the mode.
" Since 1; has a lower frequency and lower n than in 33831, the value of x is larger than for HR 3831."," Since $\nu_1$ has a lower frequency and lower $n$ than in 3831, the value of $\chi$ is larger than for HR 3831."
" From the stellar model and eigenfunctions used in refsec:models,, we find x—0.045."," From the stellar model and eigenfunctions used in \\ref{sec:models}, we find $\chi = 0.045$."
" Determining the mode inclination from light curves depends strongly on the viewing aspect of the mode, i.e. the value of 7."," Determining the mode inclination from light curves depends strongly on the viewing aspect of the mode, i.e. the value of $i$."
" Indeed, we found several solutions (i,3) leading to a fit of the amplitude ratio (A41+A-1)/Ao. as long as à<72? — see reftab:angles.."," Indeed, we found several solutions $i,\beta$) leading to a fit of the amplitude ratio $(A_{+1}+A_{-1})/A_0$, as long as $i< 72^{\circ}$ – see \\ref{tab:angles}. ."
 The values follow roughly the law 100°., The values follow roughly the law $i +\beta \approx 80-100^{\circ}$ .
" While the angles derived in reftab:angles lead to the same goodness of fit to the light curve, they lead to completely different values of the dipole inclination y."," While the angles derived in \\ref{tab:angles} lead to the same goodness of fit to the light curve, they lead to completely different values of the dipole inclination $\gamma$."
" Indeed, low values of { lead to a dipole almost aligned with the magnetic axis, whereas large values lead to a very inclined mode: e.g. y(i=195,880°)285?,4((. 415,865°)77° and y(t=623,037°)64°."," Indeed, low values of $i$ lead to a dipole almost aligned with the magnetic axis, whereas large values lead to a very inclined mode: e.g. $\gamma(i=19^{\circ},\beta=80^{\circ}) =85^{\circ} $, $\gamma(i=41^{\circ},\beta=65^{\circ}) =77^{\circ} $ and $\gamma(i=62^{\circ},\beta=37^{\circ}) = 64^{\circ}$."
" In all= cases, the= polarization= remains small showing= that this= mode is almost linearly polarized."," In all cases, the polarization remains small showing that this mode is almost linearly polarized."
" Due to the uncertainty in 7, it is hard to reach a conclusion about the inclination of the principal mode in 110195926."," Due to the uncertainty in $i$, it is hard to reach a conclusion about the inclination of the principal mode in 10195926."
 The same problem appeared in the case of HR3831., The same problem appeared in the case of HR3831.
 ? found a mode well inclined with respect to the magnetic axis —8e26° based on a value of i—89? available from spectropolarimetry at this time., \citet{bigot02} found a mode well inclined with respect to the magnetic axis $\gamma-\beta\approx 26^{\circ}$ based on a value of $i=89^{\circ}$ available from spectropolarimetry at this time.
 A more recent and secure value of —68° in 33831 led ? to amode almost aligned with the magnetic axis y—3z0., A more recent and secure value of $i=68^{\circ}$ in 3831 led \citet{bigot10} to amode almost aligned with the magnetic axis $\gamma - \beta\approx 0$.
 The alignment between magnetic and pulsation axes in 33831 seems natural regarding the large magnetic field found for the star ~2.5 kkG. In 110195926 the lower value of B;=0.7 kkG derived in refsec:models suggests a more inclined mode to the magnetic field., The alignment between magnetic and pulsation axes in 3831 seems natural regarding the large magnetic field found for the star $\sim 2.5$ kG. In 10195926 the lower value of $B_p = 0.7$ kG derived in \\ref{sec:models} suggests a more inclined mode to the magnetic field.
 We can extract more constraints on the inclination by considering the inequality of the side peaks Ai;σὲ A..., We can extract more constraints on the inclination by considering the inequality of the side peaks $A_{+1}\neq A_{-1}$ .
" The origin of the inequality is due to the Coriolis force which, unlike the magnetic and centrifugal forces, does not act in the same way on the +m components of the modes."," The origin of the inequality is due to the Coriolis force which, unlike the magnetic and centrifugal forces, does not act in the same way on the $\pm m$ components of the modes."
 The ratio (A41—AΑ.1) is therefore very sensitive to the value of x which determines the polarization of the mode (?)..," The ratio $(A_{+1}-A_{-
1})/(A_{+1}+A_{-1})$ is therefore very sensitive to the value of $\chi$ which determines the polarization of the mode \citep{bigot02}."
 It also depends on the magnetic field and centrifugal forces., It also depends on the magnetic field and centrifugal forces.
" Using the constraint on the unequal amplitude ratio, we restrict the allowed values of the rotational inclination and magnetic obliquity to i~63° and 6= 34°."," Using the constraint on the unequal amplitude ratio, we restrict the allowed values of the rotational inclination and magnetic obliquity to $i\approx 63^{\circ}$ and $\beta\approx 34^{\circ}$ ."
 The mode is well inclined to the magnetic axis with y—6& 26°., The mode is well inclined to the magnetic axis with $\gamma-\beta \approx 26^{\circ}$ .
 We used the formalism developed in ? to fit of the light curve of νι., We used the formalism developed in \citet{bigot10} to fit of the light curve of $\nu_1$ .
" Anexample is shown in for (i= 62°, 8= 63°)."," Anexample is shown in \\ref{fig:opm} for $i=62^{\circ}$ , $\beta=63^{\circ}$ )."
These limits can also be found numerically by solving As shown in Figure 9. the derived limits ave not sviuuetrie about the probability peak. prohibiting ranges which exceed the sample size or axe less than zero.,"These limits can also be found numerically by solving As shown in Figure 9, the derived limits are not symmetric about the probability peak, prohibiting ranges which exceed the sample size or are less than zero."
" For large samples GV.z 100) one recovers the standard Poisson uncertaintylimits. fe,εν)έτειendfen=lin 1."," For large samples $N \gtrsim$ 100) one recovers the standard Poisson uncertaintylimits, ${\epsilon}^U_b-{\epsilon}_b)/{\epsilon}_b =
({\epsilon}_b-{\epsilon}^L_b)/{\epsilon}_b = \sqrt{1/n+1/N}$ ."
of real roots of 4 changes from one to three.,of real roots of $\eta$ changes from one to three.
 In physical terms all of this will mean that if A is reduced further. i.e. if the flow becomes more fractal. it will rule out the possibility of multitransonicity completely.," In physical terms all of this will mean that if $\Delta$ is reduced further, i.e. if the flow becomes more fractal, it will rule out the possibility of multitransonicity completely."
 Strongly fractal dise systems. therefore. would be devoid of the multitransonie character usually associated with conserved continuum dise accreting systems.," Strongly fractal disc systems, therefore, would be devoid of the multitransonic character usually associated with conserved continuum disc accreting systems."
 So the general conclusion that one might draw regarding the influence of the fractal features in the flow. is that the flow is made to behave like a more dilute continuum.," So the general conclusion that one might draw regarding the influence of the fractal features in the flow, is that the flow is made to behave like a more dilute continuum."
 While this helps in generating the transonic solution. in a somewhat paradoxical sense. the same fractal features turn out to be inimical to multitransonicity in the flow.," While this helps in generating the transonic solution, in a somewhat paradoxical sense, the same fractal features turn out to be inimical to multitransonicity in the flow."
 These inferences have been made by studying a general polytropic flow. but arguably they will not be violated when the flow is to be considered as isothermal.," These inferences have been made by studying a general polytropic flow, but arguably they will not be violated when the flow is to be considered as isothermal."
 In this limit also it is possible. from equation (269). to derive a quartic polynomial just as in equation (32)). with the coefficients 24. D. Cand D being set down. respectively. as The rest of the mathematical analysis will remain the same. as it has been for the polytropie flow.," In this limit also it is possible, from equation \ref{critconiso}) ), to derive a quartic polynomial just as in equation \ref{quartic}) ), with the coefficients $A$, $B$, $C$ and $D$ being set down, respectively, as The rest of the mathematical analysis will remain the same, as it has been for the polytropic flow."
" With the knowledge that the critical conditions in the flow can be represented entirely in terms of flow parameters like ME (or (D and &, it now becomes possible to find a direct connection between the steady accretion rate and the mass of the accretor whose gravitational force"," With the knowledge that the critical conditions in the flow can be represented entirely in terms of flow parameters like $\dot{\mathcal{M}}$ (or $\dot{m}$ ) and $\mathcal{E}$, it now becomes possible to find a direct connection between the steady accretion rate and the mass of the accretor whose gravitational force"
The attempt to unity all fuudiueutal interactions resulted --i the development of mimlticdimensional theories like y.rueanotivated field theories (?72777j.. related branc-world theories (277?).. aud (related or not) Ialuza-Ileiu ieories (27777).,"The attempt to unify all fundamental interactions resulted in the development of multidimensional theories like string-motivated field theories \citep{Wu86,Maeda88,Barr88,DP94,DPV2002a,DPV2002b}, related brane-world theories \citep{Youm2001a,Youm2001b,branes03a,branes03b}, and (related or not) Kaluza-Klein theories \citep{Kaluza,Klein,Weinberg83,GT85,OW97}."
. Aone these theories. there are some oei which the gauge coupling constauts may vary Over cosinological timescales.," Among these theories, there are some in which the gauge coupling constants may vary over cosmological timescales."
" On the other haud. theoretical ralmeworks based on first principles. were developed by iffereut authors (777777) to study the variation of the fine structure constant (a) or the electron mass (71,.)."," On the other hand, theoretical frameworks based on first principles, were developed by different authors \citep{Bekenstein82,Bekenstein2002,CLV01,BSM02,OP02,BM05} to study the variation of the fine structure constant $\alpha$ ) or the electron mass $m_e$ )."
 Different versions of the theories mentioned above edic ifferent time behaviors of the fundamental coustauts., Different versions of the theories mentioned above predict different time behaviors of the fundamental constants.
 Thus. bounds obtained from astronomical aud ecophysical data are au inportant tool to test the validity of these theories.," Thus, bounds obtained from astronomical and geophysical data are an important tool to test the validity of these theories."
 The experimental research can be grouped into astronomical and local methods., The experimental research can be grouped into astronomical and local methods.
 The latter ones iuclude ecophysical methods such as the natural unclear reactor that operated about l.810? years ago in Oklo. Gabon (27).. the analysis of natural loug-lived. 7 decavers im ecological minerals and meteorites (2) and laboratory mcasurcmients such as comparisous of rates between clocks with different atomic nunmibers (22227??)..," The latter ones include geophysical methods such as the natural nuclear reactor that operated about $1.8\ 10^9$ years ago in Oklo, Gabon \citep{DD96,Fujii00}, the analysis of natural long-lived $\beta$ decayers in geological minerals and meteorites \citep{Olive04b} and laboratory measurements such as comparisons of rates between clocks with different atomic numbers \citep{PTM95,Sortais00,Marion03,Bize03,Fischer04,Peik04}."
 The astronomical methods are based mainly on the analysis of high-redshift quasar absorption svstenis;, The astronomical methods are based mainly on the analysis of high-redshift quasar absorption systems.
 The relative uaeuitude of the fine splitting of resonance lines of alkaline ious is proportional to a?., The relative magnitude of the fine splitting of resonance lines of alkaline ions is proportional to $\alpha^2 $.
 2 aud? have applied his method to SIV doublet absorption lues svsteiis at differcut redshifts., \citet{Murphy01b} and \citet{Chand05} have applied this method to SiIV doublet absorption lines systems at different redshifts.
 An exteusion of this method was xoposed by ?.., An extension of this method was proposed by \citet{Bahcall04}.
 These authors use strong nebular emission ines of O III to coustrain the variation of a., These authors use strong nebular emission lines of O III to constrain the variation of $\alpha$.
 Furthermore. lis method was nuproved by comparing transitious of different species with widely far atomic masses aud led o the first results consistent with a time varviug fine structure constant for a ranee of redshifts (0.5<2< 3.5) (277).," Furthermore, this method was improved by comparing transitions of different species with widely far atomic masses and led to the first results consistent with a time varying fine structure constant for a range of redshifts $0.5 < z < 3.5$ ) \citep{Webb99,Webb01,Murphy03b}."
 This method is known in the literature as the many nultiplet method (MM)., This method is known in the literature as the many multiplet method (MM).
 However. other recent iudepeudeut analyses of similar data (7777) found no variation.," However, other recent independent analyses of similar data \citep{Srianand04,Chand04,Chand06,QRL04} found no variation."
 Ou the other hand. the standard MM techuique can be revised to avoid the deficicucics pointed out earlier in the literature (??)..," On the other hand, the standard MM technique can be revised to avoid the deficiencies pointed out earlier in the literature \citep{Bahcall04,QRL04}."
 This improved method called iu the literature as revised many multiplet (RATAD) method. was applied bv ? to a homogeneous sample of ΕΟΤ lines at redshift 2=1.15.," This improved method called in the literature as revised many multiplet (RMM) method, was applied by \citet{QRL04} to a homogeneous sample of FeII lines at redshift $z=1.15$."
 Another method. to test cosmological variation of o. from pairs of Fe II lines observed iu individual exposures from a high-resolution spectrograph was proposed by? (this iiethod is known im the literature as SIDAAL).," Another method, to test cosmological variation of $\alpha$, from pairs of Fe II lines observed in individual exposures from a high-resolution spectrograph was proposed by \citet{levshakov05} (this method is known in the literature as SIDAM)."
 The authors found no variation of à at Do ιδια 2=1.15 (2).., The authors found no variation of $\alpha$ at $z=1.84$ and $z=1.15$ \citep{Levshakov06}.
 Towever. a recent reanalysis of spectiun of the quasar Q1101-26| found variability withinlo (?)..," However, a recent reanalysis of spectrum of the quasar Q1101-264 found variability within$1\sigma$ \citep{Levshakov07}."
" Besides. by comparing optical aud radio redshifts. a bouud ou ag,Dμα. (where g, isH the proton g .factor) can be obtained (??73."," Besides, by comparing optical and radio redshifts, a bound on $\alpha ^2g_p\frac{me}{mp}$ (where $g_p$ is the proton $g$ factor) can be obtained \citep{CS95,Tzana07}."
". Furthermore. comparing molecular aud radio- lines. providesB a bouud ou g,a7D aud tho most stringent coustraints were obtained by ον,"," Furthermore, comparing molecular and radio lines provides a bound on $g_p \alpha^2$ and the most stringent constraints were obtained by \citet{Murphy02}."
 On the other haud. ? reports bouuds on the variation of a at +=0.2167 from the satellite 18 cm OFF conjugate lines.," On the other hand, \citet{darling04} reports bounds on the variation of $\alpha$ at $z=0.2467$ from the satellite $18$ cm $OH$ conjugate lines."
" Finally. ? compared the ITE and OIT main line absorption redshifts of the different componcuts in the +=0.765 absorber and the :=0.685 leus toward D0218|357 to establish stringento constraints on changeso iu £F—Mgy,(224;."," Finally, \citet{kanekar05} compared the HI and OH main line absorption redshifts of the different components in the $z=0.765$ absorber and the $z=0.685$ lens toward B0218+357 to establish stringent constraints on changes in $F= g_p
\left({\frac{\alpha^2 m_e}{m_p}}\right)^{1.57}$."
 Besides. the time variation ofthe gauge coupling coustants in the carly universe can be constrained. using data from the cosmic microwave backeround (CMD) (27). aud the primordial abuudances of light elemieuts (??)..," Besides, the time variation of the gauge coupling constants in the early universe can be constrained using data from the cosmic microwave background (CMB) \citep{Martins02,Rocha03} and the primordial abundances of light elements \citep{Ichi02,Nollet}."
 Iun this paper. we would like to focus on the discrepancy between the data on time variation of à fro astronomical observations. following a purelv statistical criterion.," In this paper, we would like to focus on the discrepancy between the data on time variation of $\alpha$ from astronomical observations, following a purely statistical criterion."
 As described above. different methods are able to constrain the variation of o.," As described above, different methods are able to constrain the variation of $\alpha$."
 Towever. to achieve statistical consistency for cach fixed redshift iuterval. the reported value should be the same.," However, to achieve statistical consistency for each fixed redshift interval, the reported value should be the same."
 The usual assumption is that if there is any time variation of a. such variation is constant over all observed. redshifts.," The usual assumption is that if there is any time variation of $\alpha$ , such variation is constant over all observed redshifts."
 So. the reported results are lucas over a range of redshifts.," So, the reported results are means over a range of redshifts."
" Ποπονα, theories mncutioned above predict differcut time evolutions of a vieldiug different variations for different times ο}."," However, theories mentioned above predict different time evolutions of $\alpha$ yielding different variations for different times \citep{Okada,Marciano,Bekenstein82}. ."
These analvtic estimates confirm the basic aspects of our model.,These analytic estimates confirm the basic aspects of our model.
" In a gaseous disk with M,8 250 g 7. the gas halts the collisional cascade."," In a gaseous disk with $\Sigma_g \approx$ 250 g $^{-2}$, the gas halts the collisional cascade."
 Collision fragments entrained by the eas rapidly settle to the midplane., Collision fragments entrained by the gas rapidly settle to the midplane.
 Protoplanets with masses ~ 0.01 ccan accrete collision fragments rapidly and grow (to masses ~ 1 bbefore the σας clissipates in 3.10 Myr., Protoplanets with masses $\sim$ 0.01 can accrete collision fragments rapidly and grow to masses $\sim$ 1 before the gas dissipates in 3–10 Myr.
 To explore this picture in more detail. we calculate the formation of cores with our hybrid multiannulus m-body code (Bromley&Kenyon.2006).," To explore this picture in more detail, we calculate the formation of cores with our hybrid multiannulus $n$ -body code \citep{bk06}."
". In previous calculations. we followed the evolution of objects with r2ry: collision fragments with r<r, were removed by the collisional cascade (INDOS)."," In previous calculations, we followed the evolution of objects with $r \gtrsim r_s$; collision fragments with $r \lesssim r_s$ were removed by the collisional cascade (KB08)."
 IHlere. we include the evolution of small fragments entrained bv the gas.," Here, we include the evolution of small fragments entrained by the gas."
" We follow Draueretal.(2008a) and caleulate the scale height of small particles with r«ry as H—o1,/[min(51.0.5)(14S0)). where H, is the scale height ol the gas (INenvon&Hartmann.1987.INDOS).. a is the turbulent viscosity of the gas. and l—rp.Ofcip,."," We follow \citet{bra08a} and calculate the scale height of small particles with $r < r_s$ as $H = \alpha H_g / [{\rm min}(St,0.5)(1 + St)]$, where $H_g$ is the scale height of the gas \citep[][KB08]{kh87}, $\alpha$ is the turbulent viscosity of the gas, and $St = r \rho_s \Omega / c_s \rho_g$."
" In this expression lor the Stokes number (57). ὃς is the sound speed of (he gas. p, is the gas density. and p; is the mass density ofa fragment."," In this expression for the Stokes number $St$ ), $c_s$ is the sound speed of the gas, $\rho_g$ is the gas density, and $\rho_s$ is the mass density ofa fragment."
 We assume small parücles have vertical velocity ο=HO and horizontal velocity f=1.60., We assume small particles have vertical velocity $v = H \Omega$ and horizontal velocity $h = 1.6 v$.
" Protoplanets accrete fragments al a rate novc,,4. where n is (he number density of fragments. σ is the cross-section (including5D gravitational focusing). and 0; is (he relative velocity (e.g..Nenvon&Luu1998.Appencix A.2).."," Protoplanets accrete fragments at a rate $n \sigma v_{rel}$, where $n$ is the number density of fragments, $\sigma$ is the cross-section (including gravitational focusing), and $v_{rel}$ is the relative velocity \citep[e.g.,][Appendix A.2]{kl98}."
 Although this approximation neglects many details of the molion of particles in the gas (Brauerelal.2008a).. il approximates (he dynamics ancl structure of the fragments reasonably well and allows us to ealeulate accretion of fragmentsby much larger oligarchs.," Although this approximation neglects many details of the motion of particles in the gas \citep{bra08a}, it approximates the dynamics and structure of the fragments reasonably well and allows us to calculate accretion of fragmentsby much larger oligarchs."
 Usine (he statistical approach of Salronoy(1969).. we evolve the masses and orbits of planelesimals in à set of concentric annuli with widths de; at distances e; from the central star (IXNBOS).," Using the statistical approach of \citet{saf69}, we evolve the masses and orbits of planetesimals in a set of concentric annuli with widths $\delta a_i$ at distances $a_i$ from the central star (KB08)."
 The ealeulations use realistic cross-sections (including gravitational focusing) to derive collision rates (Spauteetal.1991). and a Fokker-Planck algorithm (o derive gravitational stirring rates (Ohtsuki.Stewart.&Ida| 2002).., The calculations use realistic cross-sections (including gravitational focusing) to derive collision rates \citep{spa91} and a Fokker-Planck algorithm to derive gravitational stirring rates \citep{oht02}. .
 When large objects reach a nass μοι we “promote them into an n-body code (Bromley&Ixenyon.2006).," When large objects reach a mass $M_{pro}$, we `promote' them into an $n$ -body code \citep{bk06}."
. This code follows the trajectories of individual objects and includes algorithms to allow interactions between the massive n-bodies and less massive objects in (he coagulation code., This code follows the trajectories of individual objects and includes algorithms to allow interactions between the massive $n$ -bodies and less massive objects in the coagulation code.
" To assign collision outcomes. we use the ratio of the center of mass collision energy. Q,. and the energv needed (ο eject half the mass of a pair of colliding planetesimals to infinity (Q."," To assign collision outcomes, we use the ratio of the center of mass collision energy $Q_c$ and the energy needed to eject half the mass of a pair of colliding planetesimals to infinity $Q_d^*$ ."
" We adopt Q5=Qr+Q,p,r (Benz&Asphaug 1999).. where Qyr isthe bulk component of the binding energy. Q,pgr is the gravity component of the binding energy."," We adopt $Q_d^* = Q_b r^{\beta_b} + Q_g \rho_g r^{\beta_g}$ \citep{ben99}, , where $Q_b r^{\beta_b}$ isthe bulk component of the binding energy, $Q_g \rho_g r^{\beta_g}$ is the gravity component of the binding energy,"
for the normalization of the flattened component. and for each normalization. we search [ου values of 2. rj. ancl Sy corresponding to the non-flattened (;3~0.5) profile. such that we minimize the total 4? of the fit to the data of the sum of the flattened and non-IHattened profiles.,"for the normalization of the flattened component, and for each normalization, we search for values of $\beta$ , $r_0$ , and $S_0$ corresponding to the non-flattened $\beta \sim 0.5$ ) profile, such that we minimize the total $\chi^2$ of the fit to the data of the sum of the flattened and non-flattened profiles."
 We fit the data out to radii of 500 arcseconds so as to incorporate constraints from bevond the region of visible emission., We fit the data out to radii of 500 arcseconds so as to incorporate constraints from beyond the region of visible emission.
 The resulting minimum 4? as a function of the normalization of the flattened profile component. and the strongest constraint. (ruled ont at 95%)) is à maximum normalization of So=1.5x10.I count ! 7 7.," The resulting minimum $\chi^2$ as a function of the normalization of the flattened profile component, and the strongest constraint (ruled out at ) is a maximum normalization of $S_0 = 1.5\times10^{-10}$ count $^{-1}$ $^{-2}$ $^{-2}$."
 This corresponds to a total count rate out to 500 kpe of 6.5x107 counts |. or an unabsorbed [hix of 5.2x10B eres i ?. ora 0.6-2 keV luninosity of 2.0x10! erg |.," This corresponds to a total count rate out to 500 kpc of $6.5\times10^{-2}$ counts $^{-1}$, or an unabsorbed flux of $5.2 \times 10^{-13}$ erg $^{-1}$ $^{-2}$, or a 0.6-2 keV luminosity of $2.0 \times 10^{41}$ erg $^{-1}$."
 The normalization is 1.1x10.ni7. corresponding to a hot halo mass in the flattened component of T.4xLOM M...," The normalization is $1.1 \times 10^{-3}$, corresponding to a hot halo mass in the flattened component of $7.4 \times 10^{11}$ $M_{\odot}$."
 A full treatment of the implications of this measurement and this unusual galaxy is best reserved [ον future work. so here we comment briefly on a few salient points.," A full treatment of the implications of this measurement and this unusual galaxy is best reserved for future work, so here we comment briefly on a few salient points."
 Given the historical observational difficulties in detecting diffuse emission at large radii around spiral galaxies. and our own experience and dillieulties with Chis observation. we point oul a few lessons learned (hat may be of use for future observers im this field.," Given the historical observational difficulties in detecting diffuse emission at large radii around spiral galaxies, and our own experience and difficulties with this observation, we point out a few lessons learned that may be of use for future observers in this field."
 First. ib is inadvisable to place the galaxy. too close to the aimpoint of the telescope.," First, it is inadvisable to place the galaxy too close to the aimpoint of the telescope."
 There are nunmerous instrumental effects (vignetting. point source detectabilitv. decreasing throughput. etc) that all vary. with distance from (he aimpoint: while corrections can be applied [ον each. it is very difficult to disentangle instrumental effects [rom ciffiise emission at or below the surface brightness of the background.," There are numerous instrumental effects (vignetting, point source detectability, decreasing throughput, etc) that all vary with distance from the aimpoint; while corrections can be applied for each, it is very difficult to disentangle instrumental effects from diffuse emission at or below the surface brightness of the background."
 Second. it is also inadvisable to place the galaxy al the verv edge of the detector (as we did [or observations 10528 and 10529).," Second, it is also inadvisable to place the galaxy at the very edge of the detector (as we did for observations 10528 and 10529)."
 While this configuration allows lor conjugate subtraction to circumvent many of the radially varving instrumental effects. (he throughput. and vignetting effects are so large al the edge of the detector that it becomes difficult to see the galaxy.," While this configuration allows for conjugate subtraction to circumvent many of the radially varying instrumental effects, the throughput and vignetting effects are so large at the edge of the detector that it becomes difficult to see the galaxy."
 The optimal configuration is probably similar to our observation 10531. where the galaxy is placed a lew arcminutes from the edge of the detector.," The optimal configuration is probably similar to our observation 10531, where the galaxy is placed a few arcminutes from the edge of the detector."
 This allows for conjugate subtraction while still retaining enough throughput to detect faint emission., This allows for conjugate subtraction while still retaining enough throughput to detect faint emission.
 The primary shortcoming of this configuration is (hat the conjugateannulibeein to overlap sooner than Chev would if the galaxy is at the edge of the detector., The primary shortcoming of this configuration is that the conjugateannulibegin to overlap sooner than they would if the galaxy is at the edge of the detector.
above the magnetic poles aud hence ou the streneth of the maenetic field.,above the magnetic poles and hence on the strength of the magnetic field.
 However. at field strenethls near or above the quantum critical field. 10% C. the feld at which the evelotron energy is equal to the electron restanass energv. processes such as photon splitting may inhibit pair-produciug cascades.," However, at field strengths near or above the quantum critical field, $B_c \equiv {m_e^2 c^3}/{e \hbar} = 4.4 \times
10^{13}$ G, the field at which the cyclotron energy is equal to the electron rest-mass energy, processes such as photon splitting may inhibit pair-producing cascades."
 It has therefore been argued (Baring Tarding 1998) that a radio-loud/racio-quict boundary can be drawn ou the P. P diagram. with radio pulsars ou one side. aux ANPs and SCRs ou the other (see Fig.," It has therefore been argued (Baring Harding 1998) that a radio-loud/radio-quiet boundary can be drawn on the $P$ $\dot{P}$ diagram, with radio pulsars on one side, and AXPs and SGRs on the other (see Fig."
 1)., 1).
 The existence of PSRs 6127 iux 17LL. however. demonstrates that radio cussion can be produced iu neutron stars with surface magnetic fields equal to or greater than 2...," The existence of PSRs $-$ 6127 and $-$ 1744, however, demonstrates that radio emission can be produced in neutron stars with surface magnetic fields equal to or greater than $B_c$."
 Especially noteworthy is the proximity of PSR 1711 to the cluster of ANPs and SGRs at the upper right corner of Figure L1., Especially noteworthy is the proximity of PSR $-$ 1744 to the cluster of AXPs and SGRs at the upper right corner of Figure 1.
 In particular. this pulsar has a nearly identical P tothe AXP LE 2259|586 (Faliman Gregory 1981. Davkal ο al.," In particular, this pulsar has a nearly identical $\dot{P}$ to the AXP 1E 2259+586 (Fahlman Gregory 1981, Baykal et al."
 1996. Ἱναροὶ et al.," 1996, Kaspi et al."
 1999)., 1999).
 The disparity in their cussion propertics is therefore surprising., The disparity in their emission properties is therefore surprising.
 The radio emission upper init (Coe et al., The radio emission upper limit (Coe et al.
 1991) for LE 2259|586 iuplies a radio luninosity at MAIs of <0.8 kkpe?., 1994) for 1E 2259+586 implies a radio luminosity at MHz of $<$ $^2$.
 This limit is comparable to the lowest values known for the radio pulsar population., This limit is comparable to the lowest values known for the radio pulsar population.
 That the radio pulse iav be unobservable because of beaming cannot of course be ruled out., That the radio pulse may be unobservable because of beaming cannot of course be ruled out.
 The radio-loud/radio-quiet boundary line displaved iu Figure Lis more illustrative than quantitative., The radio-loud/radio-quiet boundary line displayed in Figure 1 is more illustrative than quantitative.
 However. the apparently normal radio cussion frou: PSRs 6127 and τι and the absence of radio cmission from ANP 1E 2259|5a.," However, the apparently normal radio emission from PSRs $-$ 6127 and $-$ 1744, and the absence of radio emission from AXP 1E 2259+586,"
Fie.,Fig.
 2 shows the block schematic of the correction scheme., \ref{f:scheme} shows the block schematic of the correction scheme.
 At MERE. the full declination. range for each sidereal hour range is divided into 4 (referrow in Fig.," At MRT, the full declination range for each sidereal hour range is divided into 4 (refer in Fig."
 laa or l1bb)., \ref{f:sourcecomparison}a a or \ref{f:sourcecomparison}b b).
 Each zone is imaged with different delay settings to keep the bandwidth: decorrelation. to «20., Each zone is imaged with different delay settings to keep the bandwidth decorrelation to $< 20\%$.
 Therefore. the 6 sidercal hours. of images uncer consideration. have 24 images (~15« 15).," Therefore, the 6 sidereal hours of images under consideration, have 24 images $\sim 15^{\circ}\times15^{\circ}$ )."
 Using the population of common sources. there are four possible alternatives to correct NICE images by computing: 1n principle. bright sources in cach image (15°« 157) can »e used. to indepencently estimate a homography matrix.," Using the population of common sources, there are four possible alternatives to correct MRT images by computing: In principle, bright sources in each image $15^{\circ}\times15^{\circ}$ ) can be used to independently estimate a homography matrix."
 Our earlier experiments to correct each image independently showed that the homography matrices were similar., Our earlier experiments to correct each image independently showed that the homography matrices were similar.
 The ots of errors in à and 9 plotted against à and sinze (refer o Fig., The plots of errors in $\alpha$ and $\delta$ plotted against $\alpha$ and $\sin za$ (refer to Fig.
 laa and Ibb) indicate that the errors are independent of the four delay zones and the range of o., \ref{f:sourcecomparison}a a and \ref{f:sourcecomparison}b b) indicate that the errors are independent of the four delay zones and the range of $\alpha$.
 This implies that estimating a single homography matrix for the entire source »opulation should sullice in representing the errors., This implies that estimating a single homography matrix for the entire source population should suffice in representing the errors.
" The homoeraphy matrix estimated using ~—400 common sources (described in Section 2)) is: In the estimated homography matrix. ,,=1.0000 indicates there is no correction required in à as a function of a."," The homography matrix estimated using $\sim 400$ common sources (described in Section \ref{s:poserror}) ) is: In the estimated homography matrix, $h^{}_{11}=1.0000$ indicates there is no correction required in $\alpha$ as a function of $\alpha$."
 his= indicates MICE images should be corrected ina with a sinca dependence., $h^{}_{12}=0.0006$ indicates MRT images should be corrected in $\alpha$ with a $\sin za$ dependence.
 The estimated correction is up to 104 of the beam in a. at the extreme ends of the sinze range.," The estimated correction is up to $\sim 10\%$ of the beam in $\alpha$ , at the extreme ends of the $\sin za$ range."
" Similarly. ha,=0.0000 indicates that there is no correction required in sinze. as a function of a."," Similarly, $h^{}_{21}=0.0000$ indicates that there is no correction required in $\sin za$, as a function of $\alpha$."
 However. fos=0.9990 indicates that MICE images should be compressed in sinze by a factor of 0.9990 (which is I part in 1000).," However, $h^{}_{22}=0.9990$ indicates that MRT images should be compressed in $\sin za$ by a factor of 0.9990 (which is $\sim 1$ part in 1000)."
" The values of fy, and fis,23 indicate that the zero cross-overs of errors in both à and sinze. plotted against sinze are close to the sinσα of the calibration source 11932-464) used for imagine.", The values of $h^{}_{13}$ and $h^{}_{23}$ indicate that the zero cross-overs of errors in both $\alpha$ and $\sin za$ plotted against $\sin za$ are close to the $\sin za$ of the calibration source 1932-464) used for imaging.
 Using Equation 1.. the homography matrix is used to project cach pixel from the images to a new position. ellectively correctingfor positional errors in images.," Using Equation \ref{eq:inhomog}, , the homography matrix is used to project each pixel from the images to a new position, effectively correctingfor positional errors in images."
 Fie., Fig.
 3. shows positional errors in 9 after. homography- correction., \ref{f:sourcecomparisoncorrect} shows positional errors in $\delta$ after homography-based correction.
 A comparison of these plots with Fig., A comparison of these plots with Fig.
 1 demonstrate that homography has removed the svstematies and the residual errors are within of the beanwidth [or sources above 15-0. as expected.," \ref{f:sourcecomparison} demonstrate that homography has removed the systematics and the residual errors are within of the beamwidth for sources above $\sigma$, as expected."
 Fig., Fig.
 daa and Eig., \ref{f:scatterplot}a a and Fig.
 4hbhb show scatter plots of errors in 0 against errors in à before and after correction. respectively.," \ref{f:scatterplot}b b show scatter plots of errors in $\delta$ against errors in $\alpha$ before and after correction, respectively."
 For visualisation. the errors are represented in percentages of respective MICE beanividths.," For visualisation, the errors are represented in percentages of respective MRT beamwidths."
 Notice. after correction (refer Eig.," Notice, after correction (refer Fig."
 4bb) the scatter is almost circular as opposed. to. elliptical before. correction (refer L&., \ref{f:scatterplot}b b) the scatter is almost circular as opposed to elliptical before correction (refer Fig.
 daa)., \ref{f:scatterplot}a a).
 The rms before correction is ~20% of the beanmwicth., The rms before correction is $\sim 20\%$ of the beamwidth.
 After correction. the rmis is reduced to 7% of the οσο and. the svstematic errors have been removed.," After correction, the rms is reduced to $\sim 7\%$ of the beamwidth and, the systematic errors have been removed."
 Fig., Fig.
 baa and 5bb show MEE contours before and alter correction. respectively. overlaid. on SUMSS. (Sydney University Molonglo. Sky Survey) image. (Alauchctal.2003).. for a source around à=67°.," \ref{f:contourplots}a a and \ref{f:contourplots}b b show MRT contours before and after correction, respectively, overlaid on SUMSS (Sydney University Molonglo Sky Survey) image \citep{mnras:mauch03}, for a source around $\delta = -67^\circ$."
 The corrected. MICE image contours in Fig., The corrected MRT image contours in Fig.
 5bb overlap with the source in SUAISS image., \ref{f:contourplots}b b overlap with the source in SUMSS image.
 Figs., Figs.
 bec and 5dd show similar comparison for a source around 6=40., \ref{f:contourplots}c c and \ref{f:contourplots}d d show similar comparison for a source around $\delta=-40^\circ$.
 Notice Fig., Notice Fig.
 144. since the errors around à=407 ave within of the beanmwidth. the contours in both Figs.," \ref{f:sourcecomparison}d d, since the errors around $\delta=-40^\circ$ are within of the beamwidth, the contours in both Figs."
 bec and Selel show a good overlap as expected. ancl homography has not applied: perceivable correction to images at this declination., \ref{f:contourplots}c c and \ref{f:contourplots}d d show a good overlap as expected and homography has not applied perceivable correction to images at this declination.
 We have overlaid ALICE contours on a number of extended sources at S43 MIIz reported by JonesandMeAdam.(1992)., We have overlaid MRT contours on a number of extended sources at 843 MHz reported by \cite{apjss:jones92}.
. Fig., Fig.
 6. shows a typical overlay of MICE. contours on SUMSS. image of a region around the cluster Abell 3667., \ref{f:contourplotsextsources} shows a typical overlay of MRT contours on SUMSS image of a region around the cluster Abell 3667.
 The overlay is perceivably satisfactory., The overlay is perceivably satisfactory.
 The 2-D homography corrected. the positional errors in the image domain., The 2-D homography corrected the positional errors in the image domain.
 For imaging the remaining 3.5 steracians of MICE survey. ~15000 hours. of data has to be reduced.," For imaging the remaining $\sim 3.5$ steradians of MRT survey, $\sim 15000$ hours of data has to be reduced."
 Leeally. for imaging the new regions. one would like to trace the source of these errors and correct. them in the visibilities.," Ideally, for imaging the new regions, one would like to trace the source of these errors and correct them in the visibilities."
 In the following section we discuss how we traced. the source of errors and corrected them in the visibility. domain., In the following section we discuss how we traced the source of errors and corrected them in the visibility domain.
 This section describes our LYpothesis [or the source of errors in our images., This section describes our hypothesis for the source of errors in our images.
 The subsequent corrections we estimated and applied to eliminate the errors are also described., The subsequent corrections we estimated and applied to eliminate the errors are also described.
 For meridian transit imaging. m= sinze.," For meridian transit imaging, $m = \sin za$."
 The brightness distribution in the sky as a function of sinze and the complex. visibilities measured. for dillerent. values of the north-south (NS) baseline vector component e form a Fourier. pair (ChristiansenandHógbom.1985)., The brightness distribution in the sky as a function of $\sin za$ and the complex visibilities measured for different values of the north-south (NS) baseline vector component $v$ form a Fourier pair \citep{book:christiansen}.
. scaling error of & in m will result. in a scaling factor of &+ in the e-component of the baseline vector., A scaling error of $\kappa$ in $m$ will result in a scaling factor of $\kappa^{-1}$ in the $v$ -component of the baseline vector.
 By positional error analysis itis clear that MICE images are stretched (expanded) in declination. i.e. Note. for imagesthe 2-D homography estimated a correction (compression) factor. & 5. of 0.9990.," By positional error analysis it is clear that MRT images are stretched ) in declination, i.e., Note, for imagesthe 2-D homography estimated a correction ) factor, $\kappa^{-1}$ , of 0.9990."
 This cued. to. the hypothesis that we have compressed the north-south baseline vectors., This cued to the hypothesis that we have compressed the north-south baseline vectors.
 Equation Gbb means. a baseline distance of ~ 1000mm in the NS arm was wronglvmeasured as ~ 999mm (1 part in. 1000).," Equation \ref{e:expcomp}b b means, a baseline distance of $\sim 1000$ m in the NS arm was wronglymeasured as $\sim 999$ m (1 part in 1000)."
 Similarly. a sin ze-depencdent correction in à. eued to possible e-component in the," Similarly, a $\sin za$ -dependent correction in $\alpha$ cued to possible $v$ -component in the"
of sources with known object-type. and unidentified sources in each region.,"of sources with known object-type, and unidentified sources in each region."
 Nearby objects in the Galaxy have an advantage that we can make detailed study on them. while they may have a difficulty to correctly estimate the distance and thus to obtain the absolute magnitude.," Nearby objects in the Galaxy have an advantage that we can make detailed study on them, while they may have a difficulty to correctly estimate the distance and thus to obtain the absolute magnitude."
 Objects in nearby galaxies. on the other hand. have similar distances and thus it is rather straightforward to make a color-magnitude diagram (CMD) for them.," Objects in nearby galaxies, on the other hand, have similar distances and thus it is rather straightforward to make a color-magnitude diagram (CMD) for them."
 The Hippareos data have changed the situation drastically and allow us to estimate the distance of nearby objects reliably., The Hipparcos data have changed the situation drastically and allow us to estimate the distance of nearby objects reliably.
 Combining the AKARI All-Sky Survey data with the Hipparcos data we are able to make a mid-infrared CMD for Galactic objects whose nature is well understood., Combining the AKARI All-Sky Survey data with the Hipparcos data we are able to make a mid-infrared CMD for Galactic objects whose nature is well understood.
 Comparing the AKARI CMD with those of the LMC obtained by the Spitzer SAGE program (Meixner et al. 2006)), Comparing the AKARI CMD with those of the LMC obtained by the Spitzer SAGE program (Meixner et al.\cite{meixner2006}) )
 enables us to investigate populations in the LMC CMD. for which little information is available. such as “fainter. redder O-rich giants” (Blum et al. 2006..," enables us to investigate populations in the LMC CMD, for which little information is available, such as ""fainter, redder O-rich giants"" (Blum et al. \cite{blum2006},"
 Srinivasan et al. 2009))., Srinivasan et al. \cite{srinivasan2009}) ).
 Figure 8 shows the (S9W-LI8W) v.s. M]jgw infrared CMD.where Myjsw is the absolute magnitude in LI8W-band.," Figure \ref{S9WL18W-L18W} shows the $(S9W-L18W)$ v.s. $M_{\textrm{L18W}}$ infrared CMD,where $M_{\textrm{L18W}}$ is the absolute magnitude in $L18W$ -band."
 Only sources with σω/ω« 0.4 and S/N > 5 in (S9W-LI8W) color are included in the figure. where @ and ow are the parallax and its error. respectively.," Only sources with $\sigma \omega/\omega <$ 0.4 and S/N $>$ 5 in $(S9W-L18W)$ color are included in the figure, where $\omega$ and $\sigma \omega$ are the parallax and its error, respectively."
 There are 13.252 sources that matches these criteria.," There are 13,252 sources that matches these criteria."
 In our data set. the brightest stars in M||gw are post-AGB stars. followed by M-type supergiants and giants. and carbon stars and S-type stars.," In our data set, the brightest stars in $M_{\textrm{L18W}}$ are post-AGB stars, followed by M-type supergiants and giants, and carbon stars and S-type stars."
 YSOs and PMS stars show large excess in the color 1.5<(SOW—LI8W)« 3., YSOs and PMS stars show large excess in the color $1.5 < (S9W-L18W) < 3$ .
 Be stars tend to have lower My;gyw luminosities with moderate 0.3«(SOW—LI8W)<1.3 excess. and WR stars also have similar magnitudes and colors as Be stars.," Be stars tend to have lower $M_{\textrm{L18W}}$ luminosities with moderate $0.3 < (S9W-L18W) < 1.3$ excess, and WR stars also have similar magnitudes and colors as Be stars."
 M-type giants follow a sequence of (SOW—LI8W)~0.1 from Mj]gw=—3 to -8. and these stars have little emission from the circumstellar envelopes.," M-type giants follow a sequence of $(S9W-L18W) \sim 0.1$ from $M_{\textrm{L18W}} = -3$ to $-8$, and these stars have little emission from the circumstellar envelopes."
 Once circumstellar envelopes are developed. M-type giants become redder in color.," Once circumstellar envelopes are developed, M-type giants become redder in color."
 There may be two sequences in M-type giants., There may be two sequences in M-type giants.
 One sequence follows Mjον=-9 mag up to ($9W—LISW)~L5 and the other follows Mjjgw=—7 mag up to (SOW—LISW)~1.2., One sequence follows $M_{\textrm{L18W}} = -9$ mag up to $(S9W-L18W) \sim 1.5$ and the other follows $M_{\textrm{L18W}} = -7$ mag up to $(S9W-L18W) \sim1.2$.
 It is not clear whether these two sequences actually represent different populations or stars with different dust properties. or a continuous sequence with a large scatter due to complexity of dust and molecular features.," It is not clear whether these two sequences actually represent different populations or stars with different dust properties, or a continuous sequence with a large scatter due to complexity of dust and molecular features."
 Carbon stars tend to follow a similar trend as M-type giants with little excess., Carbon stars tend to follow a similar trend as M-type giants with little excess.
 We have to interpret this CMD cautiously. as there is no parallax available for stars with heavily obscured central stars with circumstellar dust (1.e.. heavily mass-losing infrared AGB stars).," We have to interpret this CMD cautiously, as there is no parallax available for stars with heavily obscured central stars with circumstellar dust (i.e., heavily mass-losing infrared AGB stars)."
 There are six faint (Myjay> -7 mag) sources classified as M-type supergiants in Figure 8.. namely KT Mus. HD 306799. RV Pup. V408 Aur. NSV 25773. and KN Cas.," There are six faint $M_{\textrm{L18W}} >$ -7 mag) sources classified as M-type supergiants in Figure \ref{S9WL18W-L18W}, namely KT Mus, HD 306799, RV Pup, V408 Aur, NSV 25773, and KN Cas."
 Their Myjaw. (V—SOW) and (B—V) values are tabulated in Table 7..," Their $M_{\textrm{L18W}}$, $(V-S9W)$ and $(B-V)$ values are tabulated in Table \ref{supergiants}."
 Even if they are without circumstellar dust. they are still too faint to classify as supergiants.," Even if they are without circumstellar dust, they are still too faint to classify as supergiants."
 They are more likely to be M-type giants. judging from their LI8W luminosities.," They are more likely to be M-type giants, judging from their L18W luminosities."
 Furthermore. all of them have (V-$9W) and (B—V) colors similar to the general colors of M-type giants (see section 3.1.1).," Furthermore, all of them have $(V-S9W)$ and $(B-V)$ colors similar to the general colors of M-type giants (see section 3.1.1)."
 YSOs and PMS candidates can be selected in Figure 8.., YSOs and PMS candidates can be selected in Figure \ref{S9WL18W-L18W}. .
 In that figure. these types of stars are found at (SOW—LISW) >1. although some contaminations of other populations. such as post-AGB stars and PNe are expected.," In that figure, these types of stars are found at $S9W-L18W$ ) $>$ 1, although some contaminations of other populations, such as post-AGB stars and PNe are expected."
 There are 16 YSOs or PMS stars in Figure 8.., There are 16 YSOs or PMS stars in Figure \ref{S9WL18W-L18W}.
 The number is mostly limited by the Hipparcos detection limit and parallax errors. and stars without apparent central stars i1 optical are not found in this diagram.," The number is mostly limited by the Hipparcos detection limit and parallax errors, and stars without apparent central stars in optical are not found in this diagram."
 Their common names. celestial coordinates. (SOW—LI8W) colors. and MjΠενν absolute magnitudes are listed in Table 6..," Their common names, celestial coordinates, $S9W-L18W$ ) colors, and $M_{\rm{L18W}}$ absolute magnitudes are listed in Table \ref{table:yso}."
 A bibliographical survey shows that these stars are T Tauri and Herbig Ae/Be stars., A bibliographical survey shows that these stars are T Tauri and Herbig Ae/Be stars.
 [tis clear that all of them show infrared excess. and the excess should originate from dust emission in their circumstellar disk (e.g.. Whitney et al. 2003..," It is clear that all of them show infrared excess, and the excess should originate from dust emission in their circumstellar disk (e.g., Whitney et al. \cite{whitney2003},"
 Adam et al. 1987))., Adam et al. \cite{adam1987}) ).
 These stars are distributed in a relatively small range in (SOW— LI8W) color (about | mag) while a wider range in Mjyyw luminosity (about 7 mag)., These stars are distributed in a relatively small range in $S9W-L18W$ ) color (about 1 mag) while a wider range in $M_{\textrm{L18W}}$ luminosity (about 7 mag).
 Most of these stars are likely to have disks., Most of these stars are likely to have disks.
 The cause of the spread in luminosities (Mijgw) is not clear from the table. however. we suggest possibilities. such as the differences in the viewing angle of the disk (Adam et al. 1987)).," The cause of the spread in luminosities $M_{\rm{L18W}}$ ) is not clear from the table, however, we suggest possibilities, such as the differences in the viewing angle of the disk (Adam et al. \cite{adam1987}) ),"
 the inner radius of the disk. and the disk mass.," the inner radius of the disk, and the disk mass."
 It appears that luminosities (ML) sy) do not correlate with the stellar mass in our sample., It appears that luminosities $M_{\rm{L18W}}$ ) do not correlate with the stellar mass in our sample.
" AKARUs mid-infrared CMD helps understanding (|8.0]—[24D v.s. M», color-magnitude diagram of Space Telescope photometric data. such as those from Magellanie Clouds catalog (LMC: Meixner et al.. 2006.. "," AKARI's mid-infrared CMD helps understanding $([8.0] - [24])$ v.s. $M_{24}$ color-magnitude diagram of Space Telescope photometric data, such as those from Magellanic Clouds catalog (LMC: Meixner et al., \cite{meixner2006}, ,"
SMC: Gordon et al.. 2010).," SMC: Gordon et al., \cite{gordon2010}) )."
" We compare our (SOW—LI8W) vs. Mjpay diagram of galactic objects with the ([8.0]--|24]) v.s. M», diagram of the LMC sources as shown in Figure 9..", We compare our $(S9W-L18W)$ v.s. $M_{\textrm{L18W}}$ diagram of galactic objects with the $([8.0] - [24])$ v.s. $M_{24}$ diagram of the LMC sources as shown in Figure \ref{i8m24colmag}.
 After considering the offset values given in the Appendix. ($9W—LISW)~| should correspond to ([8.0]-|24])~ 1.7.," After considering the offset values given in the Appendix, $(S9W-L18W) \sim 1$ should correspond to $([8.0]-[24]) \sim 1.7$ ."
 Therefore the galactic M-type giants. carbon stars and S-type stars with infrared excess (0.4<(SOW—LISW)L5 and Mjjgw<-ὂ in absolute magnitude) probably correspond to the LMC fainter. redder sources located below the solid line (1.e.. sources located on orbelow the sequence Ὦ) indicated inthe Figure 9 6... which is marked in Blum et al. (2006))," Therefore the galactic M-type giants, carbon stars and S-type stars with infrared excess $0.4 < (S9W-L18W) < 1.5$ and $M_{\textrm{L18W}} < -6$ in absolute magnitude) probably correspond to the LMC fainter, redder sources located below the solid line (i.e., sources located on orbelow the sequence 'D') indicated inthe Figure \ref{i8m24colmag} , which is marked in Blum et al. \cite{blum2006}) )"
 and Srinivasan et al. (2009))., and Srinivasan et al. \cite{srinivasan2009}) ).
Dwarf novae are cataclysinic binary svstems (Warner 1995) which eo iuto outbursts at amore or less regular intervals.,Dwarf novae are cataclysmic binary systems (Warner 1995) which go into outbursts at more or less regular intervals.
 Iu cataclysinic binaries. a Rochelobe filling OW lnass (secondary) star loses matter that is accreted by a white ciwart (the xiunrv).," In cataclysmic binaries, a Roche–lobe filling low mass (secondary) star loses matter that is accreted by a white dwarf (the primary)."
 Lf the white dwarf is not too strongly maeuctized (BSLa’ C) the accreting inatter forms a disc that extends down to the white dwarf surface., If the white dwarf is not too strongly magnetized $B \lta 10^5$ G) the accreting matter forms a disc that extends down to the white dwarf surface.
 Despite the variety of the observed. properties of dwarf nova outbursts it has con firmly established that they are due to the buehtcening of the accretion disc in this svstenis., Despite the variety of the observed properties of dwarf nova outbursts it has been firmly established that they are due to the brightening of the accretion disc in this systems.
 This does not mean that the plivsical process leadiug to outbursts must be a disc instability., This does not mean that the physical process leading to outbursts must be a disc instability.
 For some time (see Camnizzo 1993. 1997. for he listory of the subject) an iustabilitv in the mass transfer from the secondary was put forward as an alternative possibility.," For some time (see Cannizzo 1993, 1997, for the history of the subject) an instability in the mass transfer from the secondary was put forward as an alternative possibility."
 This model was discarded by the uajoritv of those working in the field when a simple physical reason for disc instability (livdrogen recombination) was found iu the early 80s., This model was discarded by the majority of those working in the field when a simple physical reason for disc instability (hydrogen recombination) was found in the early 80's.
 Tn the standard version of the disc instability model (DIM) it is asstmed that the mass trausfer is constant iu time. but there is growing evidence that variations in the mass," In the standard version of the disc instability model (DIM) it is assumed that the mass transfer is constant in time, but there is growing evidence that variations in the mass"
"where ej.(.0) is (he bremsstrahlung spectrum and ο the absorption [requency 745, in unit of m,c?/h.",where $\epsilon_{br}(x)$ is the bremsstrahlung spectrum and $x_{abs}$ is the absorption frequency $\nu_{abs}$ in unit of $m_ec^2/h$.
" Since j| is smaller by the [actor expGCran/0.) in presence ol absorption. we take (he maximum amplification factor for bremsstrahlung as I! ""exp(—.r/)dlis(theexponential integral."," Since $\Lambda_{br}$ is smaller by the factor $\exp(x_{abs}/\theta_e)$ in presence of absorption, we take the maximum amplification factor for bremsstrahlung as where $E_n \equiv \int_1^\infty t^{-n}\exp(-xt)dt$ is the exponential integral."
 The final Comptonized bremsstrahlung emission is then The energv-weighted mean photon energy for unsaturated Comptonized bremsstrahlung 1s (see e.g. PO?) and that for saturated. Comptonized bremsstralling is simply since the spectrum approaches Wien spectrum which has 7&4=1., The final Comptonized bremsstrahlung emission is then The energy-weighted mean photon energy for unsaturated Comptonized bremsstrahlung is (see e.g. PO2) and that for saturated Comptonized bremsstrahlung is simply since the spectrum approaches Wien spectrum which has $T_X = T_e$.
 Therefore. the radiation temperature of locally racdiated bremsstrahhme emission is The frequency vais is chosen to be the frequency at which the Iree-DIree absorption optical depth is equal to 1. where a; is Che absorption coellicient given by Dermer et al. (," Therefore, the radiation temperature of locally radiated bremsstrahlung emission is The frequency $\nu_{abs}$ is chosen to be the frequency at which the free-free absorption optical depth is equal to 1, where $a_{f\!f}$ is the absorption coefficient given by Dermer et al. ("
1991),1991)
evolutionary stage involves the release of CO by powerful molecular outflows. which leads to the destruction of and forms large holes in the envelope.,"evolutionary stage involves the release of CO by powerful molecular outflows, which leads to the destruction of and forms large holes in the envelope."
 Then. the aabundance ratio raises considerably. like in the central core of 55142.," Then, the abundance ratio raises considerably, like in the central core of 5142."
 Therefore. either molecular outflows and density/temperature effects seem to be key pieces in the determination of the aabundance ratio.," Therefore, either molecular outflows and density/temperature effects seem to be key pieces in the determination of the abundance ratio."
 In order to quantify the importance of the temperature in the rratio. we compared the results obtained in 55142 with the low-mass star-formmg region L483.," In order to quantify the importance of the temperature in the ratio, we compared the results obtained in 5142 with the low-mass star-forming region L483."
 This region seems to be in the same stage of disruption of the envelope as AFGL35142. as the N2H+ shows two clumps on both sides of the YSO (see Jorgensen2004:Fuller&Wootten 2000)). being then in the later evolutionary stage of the scenario proposed above.," This region seems to be in the same stage of disruption of the envelope as AFGL5142, as the N2H+ shows two clumps on both sides of the YSO (see \citealt{jorgenssen2004a,fuller2000}) ), being then in the later evolutionary stage of the scenario proposed above."
 However. the NH3 emission in L483 is also showing a hole close at the position of the YSO. suggesting that possibly the aabundance ratio is much lower than the values found in 55142. around 400-1000.," However, the NH3 emission in L483 is also showing a hole close at the position of the YSO, suggesting that possibly the abundance ratio is much lower than the values found in 5142, around 400–1000."
 This seems to indicate that the effects of molecular outflows alone cannot explain the laree values derived in 55142. although to draw a firm conclusion this should be modeled.," This seems to indicate that the effects of molecular outflows alone cannot explain the large values derived in 5142, although to draw a firm conclusion this should be modeled."
 Thus. the high temperature reached 1n the central core due to the presence of hot cores seems to affect significantly the abundance ratio. indicating that the," Thus, the high temperature reached in the central core due to the presence of hot cores seems to affect significantly the abundance ratio, indicating that the"
present sample. and these are represented. by the various tracks plotted in reffigepacol..,"present sample, and these are represented by the various tracks plotted in \\ref{figepacol}."
 Llere we have used the stellar population synthesis models of Bruzual Charlot (2003)., Here we have used the stellar population synthesis models of Bruzual Charlot (2003).
" Their code outputs at a series of time-steps the 2# colour and L9 line-strength index. computed directly from high-resolution model spectra: we transformed the outputted οὐ colour into a photographic b,rp colour using the equation (Couch 1981): The results are overplotted in relfigepacol for various cases of interest."," Their code outputs at a series of time-steps the $B - R$ colour and $\delta_{\rm \scriptsize A}$ line-strength index, computed directly from high-resolution model spectra; we transformed the outputted $B -
R$ colour into a photographic $\bj - \rf$ colour using the equation (Couch 1981): The results are overplotted in \\ref{figepacol} for various cases of interest."
" In all models we assumed an exponentiallv-decaving ""background! rate of star formation with e-folding time 7=3 Gyr (our results do not depend significantly on the value of 7).", In all models we assumed an exponentially-decaying `background' rate of star formation with e-folding time $\tau = 3$ Gyr (our results do not depend significantly on the value of $\tau$ ).
 At time /—10 Gyr we superimposed a 9-funcetion starburst creating 10 per cent of the total stellar mass of the model galaxy., At time $t = 10$ Gyr we superimposed a $\delta$ -function starburst creating 10 per cent of the total stellar mass of the model galaxy.
 The solid line in relfigepacol tracks the subsequent. evolution of this galaxy from /=10.1 Gyr to f=13 Gyr., The solid line in \\ref{figepacol} tracks the subsequent evolution of this galaxy from $t = 10.1$ Gyr to $t = 13$ Gyr.
 The other two lines plot variations in the model: the dashed line corresponds to the, The other two lines plot variations in the model: the dashed line corresponds to the
The trauster of polarized radiation is performed using the method described by IIughes(2005).. and is briefly recapped here.,"The transfer of polarized radiation is performed using the method described by \citet{hug05}, and is briefly recapped here."
 It is based ou a formulation for the transfer of polarized radiation through a diffuse plasiua. allowing for conmüsson. absorption. the birefriusence effects of Faraday rotation aud mode conversion (which Ci produce imodoest levels of circular polarization). and relativistic aberration aud boost. which has been described. in detail bv a umber of authors. and is compactly stamarized by Jones(1988).," It is based on a formulation for the transfer of polarized radiation through a diffuse plasma, allowing for emission, absorption, the birefringence effects of Faraday rotation and mode conversion (which can produce modest levels of circular polarization), and relativistic aberration and boost, which has been described in detail by a number of authors, and is compactly summarized by \citet{tom88}."
. The observer lies at arbitrary polar angles (0.0). defined in the conventional scuse with respect to the Cartesian system used to describe the kinematic model.," The observer lies at arbitrary polar angles $\theta$ $\phi$ ), defined in the conventional sense with respect to the Cartesian system used to describe the kinematic model."
 An array of lines-of-sight is established. using a preset density of lines along the longest axis of the projection of the computational volume on the plane of the ska. with a connucnsirate nmunber orthogonal to that. to eusure equal resolution iu the two directions.," An array of lines-of-sight is established, using a preset density of lines along the longest axis of the projection of the computational volume on the plane of the sky, with a commensurate number orthogonal to that, to ensure equal resolution in the two directions."
 For the results prescuted below. a resolution of 128 pixels along he longest axis was used.," For the results presented below, a resolution of $128$ pixels along the longest axis was used."
" For each line-of-sight. the gorithin finds the most distant cell. and radiative ranster is performed. cell to cell. until the ""near side : the volume is exited."," For each line-of-sight, the algorithm finds the most distant cell, and radiative transfer is performed, cell to cell, until the `near side' of the volume is exited."
 Within cach cell. au aberrated naenetic feld direction is computed from the rest frame field. velocity. and observer location. and is used with rauster cocfiicicuts modified by the relevant Doppler j)ost.," Within each cell, an aberrated magnetic field direction is computed from the rest frame field, velocity, and observer location, and is used with transfer coefficients modified by the relevant Doppler boost."
 For a given epoch of ‘observation cell values corresponding to the appropriate retarded time should )o used., For a given epoch of `observation' cell values corresponding to the appropriate retarded time should be used.
 However. as this leads to an enormous mcerease in the computational overhead. aud can lead to simulated VLBI maps that are very difficult to interpret. because of he problem of uuaubieuously associating map features with physical flow structures. the radiation trauster is juitially performed without retarded time effects iecluded. aud the latter will be considered ouly when critical to understanding particular features of lieht curves OF laps.," However, as this leads to an enormous increase in the computational overhead, and can lead to simulated VLBI maps that are very difficult to interpret, because of the problem of unambiguously associating map features with physical flow structures, the radiation transfer is initially performed without retarded time effects included, and the latter will be considered only when critical to understanding particular features of light curves or maps."
 Simulations to justify this strateev are presented iu rofdelav.., Simulations to justify this strategy are presented in \\ref{delay}.
 Radiation transfer is performed at dimensionless observing frequencies of 0.6. LO. and 1.5125 correspouding to the UAIRAQ values of L8. 8.0 and 115 Cz.," Radiation transfer is performed at dimensionless observing frequencies of 0.6, 1.0, and 1.8125 corresponding to the UMRAO values of 4.8, 8.0 and 14.5 GHz."
 As deseribed in Huehes.Aller&(19892) a fiducial Lorentz factor (5: ‘thermal’ nuplics the Loreutz factor associated with the random notion of the c1itting particles. as opposed to the bulk How Lorentz factor) is adopted. which is the energv of those particles radiating at the ceutral observing yequency iu the average magnetic field for the jet voluue at the first time step of evolution.," As described in \citet{hug89a} a fiducial Lorentz factor $\gamma_c$; `thermal' implies the Lorentz factor associated with the random motion of the emitting particles, as opposed to the bulk flow Lorentz factor) is adopted, which is the energy of those particles radiating at the central observing frequency in the average magnetic field for the jet volume at the first time step of evolution."
 The value of his fiducial Lorentz factor is not in itself siguificaut. but node! fitting to the data coustrains how far below this he power law electron cucrey distribution exteuds (to ;). because it is the presence of these lower energy. but still relativistic. particles that produce Faraday effects in the absence of a cold particle distribution: adopting a plausible fiducial value thus enables us to estimate the low cnerev cutoff to the power law distribution.," The value of this fiducial Lorentz factor is not in itself significant, but model fitting to the data constrains how far below this the power law electron energy distribution extends (to $\gamma_i$ ), because it is the presence of these lower energy, but still relativistic, particles that produce Faraday effects in the absence of a `cold' particle distribution; adopting a plausible fiducial value thus enables us to estimate the low energy cutoff to the power law distribution."
 Prior to the radiation trausfer. the optical depth for each cell must be kuowu: this is computed from the dimensionless line-of-sight leneth through the cell. cell nagnetic field. and cell particle density.," Prior to the radiation transfer, the optical depth for each cell must be known; this is computed from the dimensionless line-of-sight length through the cell, cell magnetic field, and cell particle density."
 This is scaled with a sinele adjustable parameter chosen to produce sole “target? optical depth through the cutire volume at he central observing frequency. iu the average magnetic field and particle deusitv for the jet volume at the first time step of evolution.," This is scaled with a single adjustable parameter chosen to produce some `target' optical depth through the entire volume at the central observing frequency, in the average magnetic field and particle density for the jet volume at the first time step of evolution."
 Au initial ‘tarect™ optical depth is chosen iu lisht of the spectral characteristics of the data being modeled: the value is then adjusted o fine-tune the model ft., An initial `target' optical depth is chosen in light of the spectral characteristics of the data being modeled; the value is then adjusted to fine-tune the model fit.
" Caven the actual observing requeucies, the choice of fiducial Loreutz factor iuplics a particular magnetic field streneth: eiven that. aud the optical depth needed to reproduce the data. knowledge of the physical scale of the jet implies a value for the particle deusity. or vice versa."," Given the actual observing frequencies, the choice of fiducial Lorentz factor implies a particular magnetic field strength; given that, and the optical depth needed to reproduce the data, knowledge of the physical scale of the jet implies a value for the particle density, or vice versa."
 However. as the concern here is only with learning what such model fitting can sav about the topology and orientation of observer. shock. and maeuetic field. the iniplied field aud particle densities are not explored.," However, as the concern here is only with learning what such model fitting can say about the topology and orientation of observer, shock, and magnetic field, the implied field and particle densities are not explored."
" As discussed in refiutro.. our primary goal is to ""revalidate the ""shock in jet! model. demonstrating that oblique shocks retain the temporal aud spectral characteristics of the total ancl polarized flux density behavior of eii-baud outbursts previously imodeled with transverse structures. while acconunodating more complex behavior of the EVPA."," As discussed in \\ref{intro}, our primary goal is to `revalidate' the `shock in jet' model, demonstrating that oblique shocks retain the temporal and spectral characteristics of the total and polarized flux density behavior of cm-band outbursts previously modeled with transverse structures, while accommodating more complex behavior of the EVPA."
" As ""proof of concept! parameters are chosen similar to those used to model outbursts in BL Lac (Ibughes.Aller& 1989h).. using a bulk flow of Loreutz factor σεξ2.5 aud 'Onpression A=0.7. but with a shock orieuted at 15 o the flow axis. with the shock deflection in the plane of he sky: see Run A in Table 2.."," As `proof of concept' parameters are chosen similar to those used to model outbursts in BL Lac \citep{hug89b}, using a bulk flow of Lorentz factor $\gamma_f=2.5$ and compression $\kappa=0.7$, but with a shock oriented at $45\arcdeg$ to the flow axis, with the shock deflection in the plane of the sky; see Run A in Table \ref{table2}."
" Asstuuing a forward shock (E). implics the shock plane noving over the unuderlviug flow at Loreutz factor 6.7. which when viewed at an angle to the flow axis of 107 would produce an apparent superhuninal motion of he leading edge of Sapp,6.5."," Assuming a forward shock ), implies the shock plane moving over the underlying flow at Lorentz factor $6.7$, which when viewed at an angle to the flow axis of $10\arcdeg$ would produce an apparent superluminal motion of the leading edge of $\beta_{\rm app}\sim 6.5$."
 This is a significantly aster shock speed than adopted im modeling the 1980s outbursts. but the latter adopted a reverse (R) shock nodel with the observer at a larger angle to the flow sense. euided by the low appareut speeds reported iu the iterature at the time.," This is a significantly faster shock speed than adopted in modeling the 1980s outbursts, but the latter adopted a reverse ) shock model with the observer at a larger angle to the flow sense, guided by the low apparent speeds reported in the literature at the time."
 The current choice of parameters is guided by the much higher apparent speeds reported im he more recent literature (Listeretal.2009).. bearing in uind that over decades of activity the jet flow direction can change. either forward or reverse shocks might be evident at different epochs. aud that shock eveuts within a single source could exhibit a rauge of obliquities.," The current choice of parameters is guided by the much higher apparent speeds reported in the more recent literature \citep{lis09}, bearing in mind that over decades of activity the jet flow direction can change, either forward or reverse shocks might be evident at different epochs, and that shock events within a single source could exhibit a range of obliquities."
 As shown in reftrausverse.. it is possible for oblique shocks to eive rise to even higher percentage polarization. aud thus more pronunent. events than a transverse shock with simular paralucters. for flows seen within teus of degrees of the Imc-of-ieht.," As shown in \\ref{transverse}, it is possible for oblique shocks to give rise to even higher percentage polarization, and thus more prominent, events than a transverse shock with similar parameters, for flows seen within tens of degrees of the line-of-sight."
 Of the other piriuueters. optically thin spectral iudex is reasonably well coustrained bv observation aud lias," Of the other parameters, optically thin spectral index is reasonably well constrained by observation and has"
mocleling of telluric lines pose additional problems to extracting RV in the NIB. where the flux of an M dwarf peaks (?)..,modeling of telluric lines pose additional problems to extracting RV in the NIR where the flux of an M dwarf peaks \citep{Bean2010}.
 For solar type stars. Le.. spectral type of ΕΙΝ. ~Lin-s 1 RV precision has been routinely achieved (??)..," For solar type stars, i.e., spectral type of FGK, $\sim$ 1 $\rm{m}\cdot\rm{s}^{-1}$ RV precision has been routinely achieved \citep{Mayor2008, Howard2010}."
 However. stellar activity. stellar granulation aud instrumental uoise are major obstacles to overcome before detection of Earth-like ο (2)...," However, stellar activity, stellar granulation and instrumental noise are major obstacles to overcome before detection of Earth-like planets \citep{Mayor2008}."
 At the high mass end. a precision of 3—6 ms was deimioustrated by 2? aud 6—8 ια:sHL RV RMS scatter for stars with planets is found in the search of planets around evolved A type stars (2)..," At the high mass end, a precision of $-$ 6 $\rm{m}\cdot\rm{s}^{-1}$ was demonstrated by \citet{Johnson2007} and $-$ 8 $\rm{m}\cdot\rm{s}^{-1}$ RV RMS scatter for stars with planets is found in the search of planets around evolved A type stars \citep{Bowler2010}."
 Fast stellar rotation broadeus stellar absorption lines aud limits the RV precision for main sequence massive stars (?).., Fast stellar rotation broadens stellar absorption lines and limits the RV precision for main sequence massive stars \citep{Wright2005}.
 For evolved iuassive stars. similar problems exist as those facing solar type stars.," For evolved massive stars, similar problems exist as those facing solar type stars."
 The fundamental photon-noise RV uncertainties have been discussed in several previous papers (3," The fundamental photon-noise RV uncertainties have been discussed in several previous papers \citep{Butler1996,Bouchy2001}."
 However. ouly iutriusic properties of stellar spectra are ciscussed in their works while uo detailed calculation of RV uncertainties introduced by the calibration sources.," However, only intrinsic properties of stellar spectra are discussed in their works while no detailed calculation of RV uncertainties introduced by the calibration sources."
 In a recent paper. ? considered the uncertainties in the NUR caused by RV calibration sources. i.e.. a Th-Ar lamp aud an Ammonia gas absorption cell.," In a recent paper, \citet{Reiners2010} considered the uncertainties in the NIR caused by RV calibration sources, i.e., a Th-Ar lamp and an Ammonia gas absorption cell."
 However. these two RV calibration sources can not be completely represelitative of the calibration sources used aud proposed i1 Curren auc planied Dopper platel survey iu je NIR.," However, these two RV calibration sources can not be completely representative of the calibration sources used and proposed in current and planned Doppler planet survey in the NIR."
 For example. there are other emission lamps available i1 the NIDt for 1iV calibration such as a U-e lamp as proposed by ?..," For example, there are other emission lamps available in the NIR for RV calibration such as a U-Ne lamp as proposed by \citet{Mahadevan2010}."
 In addition. other gas abso‘ption cels besic he Ammonia cell have been proposed in the NIR (??)..," In addition, other gas absorption cells besides the Ammonia cell have been proposed in the NIR \citep{Mahadevan2009, Valdivielso2010}."
 Futhermore. in 2.. the calculation of I calibration uncertainty of a gas absorption cell assumes a 250 nm baud width iu A baud. a hen the uncertainty was applied to other NIB. bauds. which is purely hypothetical.," Futhermore, in \citet{Reiners2010}, the calculation of RV calibration uncertainty of a gas absorption cell assumes a 50 nm band width in $K$ band, and then the uncertainty was applied to other NIR bands, which is purely hypothetical."
 Therefore. a uore comprehensive aud detailed study of RV calibration uncertainties is necessary at clifferent observational baudpasses in the NIB in the search of plauets aroud cool stars.," Therefore, a more comprehensive and detailed study of RV calibration uncertainties is necessary at different observational bandpasses in the NIR in the search of planets around cool stars."
 Ou the other hand. in the visible. even though the current RV precision is not limited yw the RV calibratiou source sucli asa Th-A ‘lamp or au Iodiue absorption cell. a better tuuderstaieing of their peTormances uuder he photolimited coudition helps us disceru a stage in which tle RV calibratio1 source becomes he bottle ueck as RV precision keeos diproving.," On the other hand, in the visible, even though the current RV precision is not limited by the RV calibration source such as a Th-Ar lamp or an Iodine absorption cell, a better understanding of their performances under the photon-limited condition helps us discern a stage in which the RV calibration source becomes the bottle neck as RV precision keeps improving."
 ? recently investigated RV precision achievable or M aud L dwarfs. but did uot quantitatively. discussed the influence of RV calibration sources and stela “noise ou precision Dopper measurerent.," \citet{Rodler2011} recently investigated RV precision achievable for M and L dwarfs, but did not quantitatively discussed the influence of RV calibration sources and stellar noise on precision Doppler measurement."
 Stelar uoise is a significant contributor to RV uncertainty budget. which falls into three categories: p-moce oscillation. spos and plagues. and granulations.," Stellar noise is a significant contributor to RV uncertainty budget, which falls into three categories: p-mode oscillation, spots and plagues, and granulations."
 P-mode oscillation usually produces an RV signature with a period of several minutes., P-mode oscillation usually produces an RV signature with a period of several minutes.
 The oscillation mode has been relatively well stuclied by previous work (e.g.. ?22)).," The oscillation mode has been relatively well studied by previous work (e.g., \citet{Carrier2003,Kjeldsen2005}) )."
 Exposure time of 10-:|o min is propose in order to s1nootli the RV siguature indiced by p-mode oscillation (?).., Exposure time of 10-15 min is proposed in order to smooth the RV signature induced by p-mode oscillation \citep{Dumusque2011}.
 Spots aux| plagues iuduced RV sigual has been discussed by seve‘al papers (e.@.. ?22?2)).," Spots and plagues induced RV signal has been discussed by several papers (e.g., \citet{Desort2007, Reiners2010, Lagrange2010, Meunier2010}) )."
 ? concluded that t1e photometric coitribution of plages aud spots should Lot srevent detection of Eartli-uiass planets in the HZ given a ‘y cood temporal sampling aud sienal-to-uolse ratio., \citet{Meunier2010} concluded that the photometric contribution of plages and spots should not prevent detection of Earth-mass planets in the HZ given a very good temporal sampling and signal-to-noise ratio.
 Cirauulatiou is considere o be the major oDlacle in cletection ol Earth planets ju tie HZ because it produces aun RV signa with au amplitile of 810 m-s! based on observation ou the Suu (?).., Granulation is considered to be the major obstacle in detection of Earth planets in the HZ because it produces an RV signal with an amplitude of $\sim$ 10 $\rm{m\cdot s}^{-1}$ based on observation on the Sun \citep{Meunier2010}.
 Iu addition. there is by [ar no good metl[9] oL removing the RV noise from this pjenomenon.," In addition, there is by far no good method of removing the RV noise from this phenomenon."
 ? provided a model of noise contribution ir hV measurements based on precisioi RV observation on stars of different spectral type and at cliflerent evolution, \citet{Dumusque2011} provided a model of noise contribution in RV measurements based on precision RV observation on stars of different spectral type and at different evolution
absorption.,absorption.
 Depending on the method of weighting the individual exposures. the velocity offsets between various absorption features in the final spectrum are always <50. ie. less than one half of a resolution element: often the agreementis 201.," Depending on the method of weighting the individual exposures, the velocity offsets between various absorption features in the final spectrum are always $<50$, i.e. less than one half of a resolution element; often the agreementis $<$ 20."
 We measure the EW of the A5780 feature using both a simple integration of optical depth. as well as by a Gaussian de-blend in order to account for the presence of a second (unidentitied) absorption feature offset by ~ 130 tto the red of the DIB.," We measure the EW of the $\lambda$ 5780 feature using both a simple integration of optical depth, as well as by a Gaussian de-blend in order to account for the presence of a second (unidentified) absorption feature offset by $\sim$ 130 to the red of the DIB."
 The unidentified feature does not correspond to any known stellar or interstellar features at 2=0.1556 and we conclude that it is likely to be due to gas at a different redshift., The unidentified feature does not correspond to any known stellar or interstellar features at $z = 0.1556$ and we conclude that it is likely to be due to gas at a different redshift.
 We also repeat the EW measurements in the UVES_ppopler reduction: all EW values are in excellent agreement and lie within the statistical | e error derived from the spectral error array., We also repeat the EW measurements in the popler reduction; all EW values are in excellent agreement and lie within the statistical 1 $\sigma$ error derived from the spectral error array.
 Our tinal quoted EW (see Table 25) adopts an average of the EWs determined from various measurement methods and spectral combinations., Our final quoted EW (see Table \ref{dib_table}) ) adopts an average of the EWs determined from various measurement methods and spectral combinations.
 For all other absorbers with non-detections. the 3c detection limits are given in Table 2..," For all other absorbers with non-detections, the $\sigma$ detection limits are given in Table \ref{dib_table}."
 For the DIBs that we would expect to be resolved in our spectra (the bband in all cases and. e.g.. the bband towards J1009+0529) we assumed that the absorption would have an observed FWHM of 1|z times the typical Galactic value (see above).," For the DIBs that we would expect to be resolved in our spectra (the band in all cases and, e.g., the band towards J1009+0529) we assumed that the absorption would have an observed FWHM of $1+z$ times the typical Galactic value (see above)."
 This allowed us to calculate the number of pixels over which the absorption would be expected to extend., This allowed us to calculate the number of pixels over which the absorption would be expected to extend.
 For the unresolved lines. we assumed that the number of pixels was equal to the FWHM spectral resolution AA.. see Table L3) divided by the dispersion AA//pixel).," For the unresolved lines, we assumed that the number of pixels was equal to the FWHM spectral resolution , see Table \ref{obs_table}) ) divided by the dispersion /pixel)."
can manifest.,can manifest.
 To map out the spectra in this sensitive regime. we repeated the Monte Carlo simulations extracting spectra for a finely spaced grid of twenty inclination angles (with A@=1 deg) centred around the orientation used in the second panel of Figure (48 deg <6« 67 deg).," To map out the spectra in this sensitive regime, we repeated the Monte Carlo simulations extracting spectra for a finely spaced grid of twenty inclination angles (with $\Delta \theta = 1$ deg) centred around the orientation used in the second panel of Figure \ref{fig:specs}
 (48 deg $< \theta <$ 67 deg)."
 A subset of the spectra obtained for this set of inclination angles in the timestep 800 snapshot is shown in Figure 6.. divided into the component of radiation reaching he observer directly from the X-ray source and that formed by scattering/reprocessing in the disk wind structure.," A subset of the spectra obtained for this set of inclination angles in the timestep 800 snapshot is shown in Figure \ref{fig:specs_mu}, divided into the component of radiation reaching the observer directly from the X-ray source and that formed by scattering/reprocessing in the disk wind structure."
 As expected. the direct component of the spectrum (upper yanel in Figure 6)) is a stronger function of inclination han the scattered/reprocessed component.," As expected, the direct component of the spectrum (upper panel in Figure \ref{fig:specs_mu}) ) is a stronger function of inclination than the scattered/reprocessed component."
 This can be readily understood since the scattered/reprocessed spectrum is. formed by an integration over all positions in the flow and is therefore relatively insensitive to a small (~1 deg) change in inclination., This can be readily understood since the scattered/reprocessed spectrum is formed by an integration over all positions in the flow and is therefore relatively insensitive to a small $\sim 1$ deg) change in inclination.
 In contrast. the attenuation of the direct component is determined only by the conditions in the narrow column of gas which obscures he small (assumed ἐν= Gry} X-ray emission region.," In contrast, the attenuation of the direct component is determined only by the conditions in the narrow column of gas which obscures the small (assumed $r_{em} = 6 r_{g}$ ) X-ray emission region."
 Since he properties of the line-of-sight column change rapidly with inclination. this component of the spectrum is strongly dependent on 6.," Since the properties of the line-of-sight column change rapidly with inclination, this component of the spectrum is strongly dependent on $\theta$."
 Our calculations for the direct component of the radiation field are in qualitative agreement with the results of ?:: they demonstrated that strongly orientation-dependent attenuation is expected in the PKO4 simulation for 50deg&067 (see e.g. heir figure1., Our calculations for the direct component of the radiation field are in qualitative agreement with the results of \cite{schurch09}: they demonstrated that strongly orientation-dependent attenuation is expected in the PK04 simulation for $50 \mbox{ deg} \simlt \theta \simlt 67 \mbox{ deg}$ (see e.g. their figure.
.. But since their calculations effectively include the direct component of the radiation field. we argue that heir study overestimates the role of absorption in shaping the X-ray spectrum: in our emergent spectra (composed of the the sum of the two components shown in Figure 6)). scattered/reprocessed ight dominates for many inclinations leading to spectra with less dramatic absorption features and overall weaker dependence on the observer orientation.," But since their calculations effectively include the direct component of the radiation field, we argue that their study overestimates the role of absorption in shaping the X-ray spectrum: in our emergent spectra (composed of the the sum of the two components shown in Figure \ref{fig:specs_mu}) ), scattered/reprocessed light dominates for many inclinations leading to spectra with less dramatic absorption features and overall weaker dependence on the observer orientation."
 The full spectra (direct plus scattered) around the Fe Ka region for intermediate inclination angles are shown for both of our snapshots in Figure 7.., The full spectra (direct plus scattered) around the Fe $\alpha$ region for intermediate inclination angles are shown for both of our snapshots in Figure \ref{fig:specs_zoom}.
 This illustrates the most striking difference between the spectra obtained from the two snapshots. namely the behaviour of the blueshifted absorption lines.," This illustrates the most striking difference between the spectra obtained from the two snapshots, namely the behaviour of the blueshifted absorption lines."
 Owing to the fairly narrow range of polar angles at which a fast wind is present in the model. it is only for a modest fraction of lines-of-sight that clean. sharp absorption lines appear in our computed spectra for either snapshot.," Owing to the fairly narrow range of polar angles at which a fast wind is present in the model, it is only for a modest fraction of lines-of-sight that clean, sharp absorption lines appear in our computed spectra for either snapshot."
 In the timestep 800 snapshot. an Fe Ka absorption line is present for a range of inclinaions A@~12 deg.," In the timestep 800 snapshot, an Fe $\alpha$ absorption line is present for a range of inclinations $\Delta \theta \sim 12$ deg."
 For the later snapshot. the range is even smaler. A@—5 deg.," For the later snapshot, the range is even smaller, $\Delta \theta \sim 5$ deg."
 In our previous work (Papers I and ID. narrow asorption lines also only appeared for only a minority of inclinations although they were generally more common than found here.," In our previous work (Papers I and II), narrow absorption lines also only appeared for only a minority of inclinations although they were generally more common than found here."
 This is likely a consequence of the simplicity of the velocity aw adopted in the parametrized models (Papers I and ID) — by acopting a smooth outflow velocity at all points. those models increase the fraction of lines-of-sig1 which pass through moderately «»paque Material with a signitican component of velocity directed owards the observer.," This is likely a consequence of the simplicity of the velocity law adopted in the parametrized models (Papers I and II) – by adopting a smooth outflow velocity at all points, those models increase the fraction of lines-of-sight which pass through moderately opaque material with a significant component of velocity directed towards the observer."
 In contrast. —ye model considered here has a much more complex velocity tiele leading to a rarer occurrence of clean outflow signatures.," In contrast, the model considered here has a much more complex velocity field leading to a rarer occurrence of clean outflow signatures."
" Most importantly. the blueshifted absorption features are ""ramatically different between the two snapshots."," Most importantly, the blueshifted absorption features are dramatically different between the two snapshots."
 In the timestep 800 snapshot. the Fe Ka absorption line not only manifests for a wider range of inclinations but it is generally significantly sharper. deeper and blueshifted compared to the same inclination in the timestep 955 snapshot.," In the timestep 800 snapshot, the Fe $\alpha$ absorption line not only manifests for a wider range of inclinations but it is generally significantly sharper, deeper and blueshifted compared to the same inclination in the timestep 955 snapshot."
 The maximum Fe Ka blueshift for the first snapshot corresponds to only ~0.015e while it is as large as 0.006 for the later snapshot., The maximum Fe $\alpha$ blueshift for the first snapshot corresponds to only $\sim 0.015$ c while it is as large as $\sim 0.06$ c for the later snapshot.
 The largest Fe Ka absorption EW is similar in both snapshots ~70 eV. although this occurs for different 6-values (9.~66 deg for timestep SOO and 6~60 dez or timestep 955).," The largest Fe $\alpha$ absorption EW is similar in both snapshots $\sim 70$ eV, although this occurs for different $\theta$ -values $\theta
\sim 66$ deg for timestep 800 and $\theta \sim 60$ deg for timestep 955)."
 For fixed inclination angle. the absorption EW changes quite significantly (a factor of two or more) between qe two snapshots for most orientations.," For fixed inclination angle, the absorption EW changes quite significantly (a factor of two or more) between the two snapshots for most orientations."
 Thus the model predicts iat the properties of blueshifted absorption features should not only be a strong function of observer orientation but will also be significantly. variable on timescales comparable to the time difference between our snapshots GM.~ 5 years)., Thus the model predicts that the properties of blueshifted absorption features should not only be a strong function of observer orientation but will also be significantly variable on timescales comparable to the time difference between our snapshots $\Delta t \sim$ 5 years).
 We note that ye calculated. continuum level is also different between the two snapshots. most obviously around 82;65 deg.," We note that the calculated continuum level is also different between the two snapshots, most obviously around $\theta \simlt 65$ deg."
 This is attributable othe larger column densities for these lines-of-sight in the timestep 955 snapshot (see Figure 29)., This is attributable to the larger column densities for these lines-of-sight in the timestep 955 snapshot (see Figure \ref{fig:nh}) ).
 In contrast. the model predicts that emission features (in xurticular. Fe Ka) should be present in the spectrum for all observer orientations and that their character will be less dramatically time-variable (except for @>75 deg. the Fe Ko emission flux typically changes by no more than ~30 per cent between the two snapshots).," In contrast, the model predicts that emission features (in particular, Fe $\alpha$ ) should be present in the spectrum for all observer orientations and that their character will be less dramatically time-variable (except for $\theta > 75$ deg, the Fe $\alpha$ emission flux typically changes by no more than $\sim 30$ per cent between the two snapshots)."
 The relative insensitivity of the emission line flux arises from the ‘act that they are formed over an extended region in the flow and are thus less affected by details of the structure along the observer's ine of sight., The relative insensitivity of the emission line flux arises from the fact that they are formed over an extended region in the flow and are thus less affected by details of the structure along the observer's line of sight.
 As noted above. it is at the same inclination angles or whieh absorption line features form that the emission lines are most intrinsically broad (FWHM ~0.8 keV) and also where hey develop the most noticeably red-skewed wings via Compton scattering in the flow (see Figure 8)).," As noted above, it is at the same inclination angles for which absorption line features form that the emission lines are most intrinsically broad (FWHM $\sim
0.8$ keV) and also where they develop the most noticeably red-skewed wings via Compton scattering in the flow (see Figure \ref{fig:kawing}) )."
 We note that the red line wings ound in the current simulations are somewhat less well-developed han in the simplified models considered in Papers I and II: this is expected since the fast wind component. in which Doppler shifts can most effectively give rise to the red-skewed wing. occupies only a relatively small region of the model.," We note that the red line wings found in the current simulations are somewhat less well-developed than in the simplified models considered in Papers I and II; this is expected since the fast wind component, in which Doppler shifts can most effectively give rise to the red-skewed wing, occupies only a relatively small region of the model."
 We have applied our Monte Carlo radiative transfer code (see Papers I and ID) to compute X-ray spectra for snapshots from a radiation-hydrodynamies simulation of a line-driven AGN disk wind (PKO4)., We have applied our Monte Carlo radiative transfer code (see Papers I and II) to compute X-ray spectra for snapshots from a radiation-hydrodynamics simulation of a line-driven AGN disk wind (PK04).
 In most important respects. we find that the results of these simulations support conclusions drawn from our previous studies of parametrized outflow models.," In most important respects, we find that the results of these simulations support conclusions drawn from our previous studies of parametrized outflow models."
 In particular. (1) we tind that a disk wind should imprint a wide range of spectroscopic features in the X-ray band and (2) the role of the wind in reflecting/scattering/reprocessing radiation in these simulations is as important as the part it plays in imprinting absorption signatures.," In particular, (1) we find that a disk wind should imprint a wide range of spectroscopic features in the X-ray band and (2) the role of the wind in reflecting/scattering/reprocessing radiation in these simulations is as important as the part it plays in imprinting absorption signatures."
 Since we have considered only two snapshots from one model. one should not expect that the simulated spectra. will quantitatively match observations.," Since we have considered only two snapshots from one model, one should not expect that the simulated spectra will quantitatively match observations."
 Rather the synthetic spectral features should be interpreted as broadly indicative of those which a disk wind may cause., Rather the synthetic spectral features should be interpreted as broadly indicative of those which a disk wind may cause.
 This should guide future studies in which the hydrodynamical modelling will be improved and the system parameters explored., This should guide future studies in which the hydrodynamical modelling will be improved and the system parameters explored.
 It should also be borne in mind that the PKO4 simulation was primarily an attempt to build insight to the problem of line-driven AGN winds and is not expected to capture all the, It should also be borne in mind that the PK04 simulation was primarily an attempt to build insight to the problem of line-driven AGN winds and is not expected to capture all the
Fortran subroutines from Arnold I. Boothroyd>)).,Fortran subroutines from Arnold I. ).
" The results are quite satisfactory, but we want to emphasise that, in the carbon-rich case, problems can occur."," The results are quite satisfactory, but we want to emphasise that, in the carbon-rich case, problems can occur."
" At low values of logR and a high carbon enhancement, a cubic spline interpolation in the logT dimension might overshoot and produce spurious results."," At low values of $\log R$ and a high carbon enhancement, a cubic spline interpolation in the $\log T$ dimension might overshoot and produce spurious results."
 We strongly advise always checking separately the quality of the fit for each table (or relevant parts thereof) used., We strongly advise always checking separately the quality of the fit for each table (or relevant parts thereof) used.
 The problem now is how to account for the element enhancements., The problem now is how to account for the element enhancements.
" As outlined in Sect. ??,,"," As outlined in Sect. \ref{sec:results},"
" the special role of the C/O ratio the parameter range at C/O=1 at low temperatures, and xg is not a continuous function of the carbon content at this point (Fig. 8))."," the special role of the C/O ratio the parameter range at $\mbox{C/O}=1$ at low temperatures, and $\kappa_\mathrm{R}$ is not a continuous function of the carbon content at this point (Fig. \ref{fig:kappa-c-logT-logRm1p5}) )."
" To resolve the sharp turnaround in the Rosseland mean, we require some grid points close to C/O-1."," To resolve the sharp turnaround in the Rosseland mean, we require some grid points close to $\mbox{C/O}=1$."
" Overall, the number of enhancement factors is too low and the grid too coarse to apply any other interpolation scheme than a linear one."," Overall, the number of enhancement factors is too low and the grid too coarse to apply any other interpolation scheme than a linear one."
 As shown in Fig., As shown in Fig.
" 8 for the solar case and at low metallicity, linear interpolation in logkg and logX(!?C) delivers quite gratifying results beyond a certain temperature, where molecules cease to play an important role in determining the value of the Rosseland opacity."," \ref{fig:kappa-c-logT-logRm1p5} for the solar case and at low metallicity, linear interpolation in $\log \kappa_\mathrm{R}$ and $\log X(\mbox{\element[][12]{C}})$ delivers quite gratifying results beyond a certain temperature, where molecules cease to play an important role in determining the value of the Rosseland opacity."
" The lower the temperature becomes, the sharper the turnaround in the functional behaviour of xg."," The lower the temperature becomes, the sharper the turnaround in the functional behaviour of $\kappa_\mathrm{R}$."
" Due to the sudden drop in opacity when the amount of carbon and oxygen atoms become approximately equal, linear interpolation misses out a certain fraction of information."," Due to the sudden drop in opacity when the amount of carbon and oxygen atoms become approximately equal, linear interpolation misses out a certain fraction of information."
" At high metallicities the situation is not so serious, although the case shown in the right panel of Fig."," At high metallicities the situation is not so serious, although the case shown in the right panel of Fig."
 8 (Z= 0.00001) reveals this shortcoming clearly., \ref{fig:kappa-c-logT-logRm1p5} $Z=0.00001$ ) reveals this shortcoming clearly.
" Once the element mixture is carbon-rich (logC/O> 0), the opacity first increases sharply but flattens at high carbon enhancement values."," Once the element mixture is carbon-rich $\log \mbox{C/O}>0$ ), the opacity first increases sharply but flattens at high carbon enhancement values."
" Due to the construction of our tables (see Sect. ??)),"," Due to the construction of our tables (see Sect. \ref{sec:tabledesign}) ),"
 the spacing of the enhancement factors in the carbon-rich regime increases at lower metallicities., the spacing of the enhancement factors in the carbon-rich regime increases at lower metallicities.
" Between the X(!C)x2.2 and the successive enhancement factor, an additional grid point would be favourable."," Between the $X(\mbox{\element[][12]{C}})\times2.2$ and the successive enhancement factor, an additional grid point would be favourable."
" For the case of nitrogen enhancement, linear interpolation in both logxg and logX(!N) is a good approximation, because the relation between the nitrogen content and the opacity has a simpler behaviour."," For the case of nitrogen enhancement, linear interpolation in both $\log \kappa_\mathrm{R}$ and $\log X(\mbox{\element[][14]{N}})$ is a good approximation, because the relation between the nitrogen content and the opacity has a simpler behaviour."
 The definition of the Rosseland mean opacity in Eq., The definition of the Rosseland mean opacity in Eq.
 1 leaves only some ambiguity about how to evaluate this quantity in terms of numerical methods., \ref{eq:rosselandmean} leaves only some ambiguity about how to evaluate this quantity in terms of numerical methods.
" However, the considerable uncertainties in published opacity coefficients originate in data entering the calculations."," However, the considerable uncertainties in published opacity coefficients originate in data entering the calculations."
" In the case of low temperature opacities, there is, in particular, a good amount of physical data of different quality that must be combined into one quantity."," In the case of low temperature opacities, there is, in particular, a good amount of physical data of different quality that must be combined into one quantity."
 The summary in the following paragraphs is not exhaustive but discusses the accuracy of the data presented here and elsewhere., The summary in the following paragraphs is not exhaustive but discusses the accuracy of the data presented here and elsewhere.
" Hitherto, it has been emphasised that low temperature Rosseland opacities are to a large extent determined firstly by the total metallicity of the element mixture Z and secondly by the C/O ratio."," Hitherto, it has been emphasised that low temperature Rosseland opacities are to a large extent determined firstly by the total metallicity of the element mixture $Z$ and secondly by the C/O ratio."
 The individual element abundances play a role as well but do not change the opacity on an order-of-magnitude scale when the aforementioned parameters are kept fixed., The individual element abundances play a role as well but do not change the opacity on an order-of-magnitude scale when the aforementioned parameters are kept fixed.
" Concerning the oxygen-rich case, we refer to a discussion of this topic given by Dotteretal. (2007).."," Concerning the oxygen-rich case, we refer to a discussion of this topic given by \citet{2007ApJ...666..403D}. ."
" For the carbon-rich case, we exemplarily calculated opacity coefficients starting from solar element abundances other than Lodders L03),, that is Grevesse&Sauval(1998,GS98) and Grevesseetal.(2007, GASO7).."," For the carbon-rich case, we exemplarily calculated opacity coefficients starting from solar element abundances other than \citet[][L03]{2003ApJ...591.1220L}, that is \citet[][GS98]{1998SSRv...85..161G} and \citet[][GAS07]{2007SSRv..130..105G}."
 The results of our comparison are shown in Fig., The results of our comparison are shown in Fig.
 9 (for Z=0.02 at logR= —3.0)., \ref{fig:coma-abundances-relative-logT} (for $Z=0.02$ at $\log R=-3.0$ ).
" The solar abundances given by GASO7 are very similar to those of L03, and it is therefore unsurprising to uncover virtually identical opacity coefficients for our test case."," The solar abundances given by GAS07 are very similar to those of L03, and it is therefore unsurprising to uncover virtually identical opacity coefficients for our test case."
" The situation is different when we consider the GS98 abundances, which provide higher values for C, N, and O than L03 and GASO7."," The situation is different when we consider the GS98 abundances, which provide higher values for C, N, and O than L03 and GAS07."
 These elements also make up a higher fraction of Z than in the other cases., These elements also make up a higher fraction of $Z$ than in the other cases.
" In turn, when the metals are scaled to obtain Z—0.02, metals apart from C, N, and O, are present in lower amounts than in the L03 case, and thus contribute a smaller fraction to the opacity at high and intermediate temperatures (beyond logT= 3.5)."," In turn, when the metals are scaled to obtain $Z=0.02$, metals apart from C, N, and O, are present in lower amounts than in the L03 case, and thus contribute a smaller fraction to the opacity at high and intermediate temperatures (beyond $\log T=3.5$ )."
" At the lowest temperatures, more carbon-bearing molecules, such as C3 and Ο2Η., are likely to form and produce a higher value of kr, partially compensating for the lower atomic opacity contribution at intermediate temperatures."," At the lowest temperatures, more carbon-bearing molecules, such as $_3$ and $_2$ $_2$, are likely to form and produce a higher value of $\kappa_\mathrm{R}$, partially compensating for the lower atomic opacity contribution at intermediate temperatures."
 The sensitivity of our results to the adopted starting abundances is limited., The sensitivity of our results to the adopted starting abundances is limited.
 The size of the differences with respect to the standard case is similar to other uncertainties discussed here., The size of the differences with respect to the standard case is similar to other uncertainties discussed here.
" Hence, our data can be used to approximate the Rosseland opacity coefficients for a different set of scaled solar abundances, as long asthe"," Hence, our data can be used to approximate the Rosseland opacity coefficients for a different set of scaled solar abundances, as long asthe"
Typically. we use a 256x erid and 255 contours (linearly. or logarithmically spaced) and target an accuracy of λος<107 after ~10° iterations.,"Typically, we use a $256\times 256$ grid and $255$ contours (linearly or logarithmically spaced) and target an accuracy of $|\Delta\psi/\psi|\leq 10^{-2}$ after $\sim 10^3$ iterations."
 We rescale the » and ϐ coordinates logarithmically in (he regions where steep eracients develop. 92w/2 (?)..," We rescale the $r$ and $\theta$ coordinates logarithmically in the regions where steep gradients develop, $\theta\approx \pi/2$ \citep{pay04}."
 The structure of the polar mountain evolves euasistaticallv. over many Alfvénn times. in response to (1) accretion. which builds up the mountain against the confining stress of the compressed equatorial magnetic field. and Gi) Ohnmic diffusion. which enables (he mountain {ο relax equatorward as magnetic field lines slip through (he resistive (aid.," The structure of the polar mountain evolves quasistatically, over many Alfvénn times, in response to (i) accretion, which builds up the mountain against the confining stress of the compressed equatorial magnetic field, and (ii) Ohmic diffusion, which enables the mountain to relax equatorward as magnetic field lines slip through the resistive fluid."
 The competition between accretion and Ohlnmic diffusion has been studied in detail in the context of neutron stars (227). and white clwarls (?)..," The competition between accretion and Ohmic diffusion has been studied in detail in the context of neutron stars \citep{bro98,lit01,cum01}
 and white dwarfs \citep{cum02}."
 In these papers. steady-state. one-dimensional profiles of the magnetic field are computed as functions of depth. from (he ocean down to the ouler crust. and the Ohnmic (/4) and accretion (/4) time-scales are compared. under the assumptions that (he magnetic field is flattened. parallel to the surface by polar magnetic burial. (he accreted material is unmagnetized. aud the accretion is spherical: the complex problem of the subsequent spreading of matter. is not tackled (?)..," In these papers, steady-state, one-dimensional profiles of the magnetic field are computed as functions of depth, from the ocean down to the outer crust, and the Ohmic $t_{\rm d}$ ) and accretion $t_{\rm a}$ ) time-scales are compared, under the assumptions that the magnetic field is flattened parallel to the surface by polar magnetic burial, the accreted material is unmagnetized, and the accretion is spherical; `the complex problem of the subsequent spreading of matter' is not tackled \citep{cum02}."
" The field penetrates the accreted laver if the accretion rate satisfies AL,<Ομ. where Miu is the Eddington rate. but it is screened diamagnetically bburied) if M,zΟμ. such that the surface fielcl is reduced z(4,/0.002Maa Hold relative to the base of the crust (2)..7MEET"," The field penetrates the accreted layer if the accretion rate satisfies $\dot{M}_{\rm a} \lesssim 0.1 \dot{M}_{\rm Edd}$, where $\dot{M}_{\rm Edd}$ is the Eddington rate, but it is screened diamagnetically buried) if $\dot{M}_{\rm a} \gtrsim 0.1 \dot{M}_{\rm Edd}$ , such that the surface field is reduced $\approx (\dot{M}_{\rm a} / 0.002 \dot{M}_{\rm Edd})$ -fold relative to the base of the crust \citep{cum01}."
 In the regime /4οZoh. Ohmic diffusion outpaces accretion.," In the regime $t_{\rm d}\lesssim t_{\rm a}$, Ohmic diffusion outpaces accretion."
 As material is added. it does not compress the equatorial magnetic field farther: instead. it diffuses across field eracdients and distributes itself uniformly over the stellar surface.," As material is added, it does not compress the equatorial magnetic field further; instead, it diffuses across field gradients and distributes itself uniformly over the stellar surface."
 IIence the polar mountain (the asymmetric component of p) stagnales. at the structure attained when /q~{μι , Hence the polar mountain the asymmetric component of $\rho$ ) `stagnates' at the structure attained when $t_{\rm d}\sim t_{\rm a}$.
"The accretion tinie-scale is defined as ἐν=MM, ", The accretion time-scale is defined as $t_{\rm a}=M_{\rm a}/\dot{M}_{\rm a}$.
The Ohmic diffusion time-scale is given bv ly=4x0L?/c. where σ denotes the electrical conductivity and L=(lc/|Nchua is the characteristic length-scale of the steepest field gradients: L reduces to the hydrostatic in the one-dimensional geometry emploved in earlier work (?2??). but is dominated by ]atitudinal gradients here.," The Ohmic diffusion time-scale is given by $t_{\rm d} = 4\pi \sigma L^2/c^2$, where $\sigma$ denotes the electrical conductivity and $L=(|\psi|/|\nabla\psi|)_{\rm min}$ is the characteristic length-scale of the steepest field gradients; $L$ reduces to the hydrostatic scale-height in the one-dimensional geometry employed in earlier work \citep{bro98,cum01,cum02}
 but is dominated by latitudinal gradients here."
" Following ?.. we assume that the electrical resistivity is dominated bv electvon-phonon scattering in the outer crust. (AL,2LO1M. ). as expected if the crustal composition is primordial. although electron-impurity scattering may dominate if the products of hvdrogen/helium burning leach into the crust."," Following \citet{cum01}, we assume that the electrical resistivity is dominated by electron-phonon scattering in the outer crust $M_{\rm a} \gtrsim 10^{-10} M_{\sun}$ ), as expected if the crustal composition is primordial, although electron-impurity scattering may dominate if the products of hydrogen/helium burning leach into the crust."
 Ithe relaxation time approximation.," Inthe relaxation time approximation,"
small atmospheric features in the hot stars used to outline these DIBs.,small atmospheric features in the hot stars used to outline these DIBs.
" We caution that the ""average spectrum"" used as divisor can introduce features which are difficult to trace."," We caution that the ""average spectrum"" used as divisor can introduce features which are difficult to trace."
 It is unfortunate that the blue wing of our band is affected by a He line present in hot stars (see HD 23180 spectra in Fig., It is unfortunate that the blue wing of our band is affected by a He line present in hot stars (see HD 23180 spectra in Fig.
" 2) and certainly in the ""average reference spectrum"" limiting our ability to obtain suitable corrections at a wavelength bluer than 7070À."," 2) and certainly in the ""average reference spectrum"" limiting our ability to obtain suitable corrections at a wavelength bluer than 7070."
. This region is also closer to the edge of the order in the HET echelle data where the S/N decreases quickly., This region is also closer to the edge of the order in the HET echelle data where the S/N decreases quickly.
" In summary, we find in each of the three spectra plotted in Fig."," In summary, we find in each of the three spectra plotted in Fig."
" 4 a broad band with a maximum depth of about of the continuum, and a central wavelength close to 7088 A.Thhe differences between these spectra give an idea of the uncertainties involved in the measurement of this band which is traced in the spectra of both telescopes by more than 40 resolution elements at 30 from the continuum, leading to à very solid overall detection."," 4 a broad band with a maximum depth of about of the continuum, and a central wavelength close to 7088 \\.Thhe differences between these spectra give an idea of the uncertainties involved in the measurement of this band which is traced in the spectra of both telescopes by more than 40 resolution elements at $\sigma$ from the continuum, leading to a very solid overall detection."
 In Fig., In Fig.
 5 we plot overlaid the three spectra of the previous figure., 5 we plot overlaid the three spectra of the previous figure.
 The combined WHT(a) and HET (c) spectrum can be fitted using a Lorentzian of FWHM of 40+5 centred at 7088.8A., The combined WHT(a) and HET (c) spectrum can be fitted using a Lorentzian of FWHM of $\pm$ 5 centred at 7088.8.
. The equivalent width of the interstellar band was measured integrating the combined spectrum and resulted W= 600+200 where the error takes into account the differences in width and strength of the bands resulting from the various corrections applied and is largely dominated by the uncertainty in the location of the continuum., The equivalent width of the interstellar band was measured integrating the combined spectrum and resulted W= $\pm$ 200 where the error takes into account the differences in width and strength of the bands resulting from the various corrections applied and is largely dominated by the uncertainty in the location of the continuum.
 The characteristics of the observed 7088 band agree reasonably well with the laboratory measurements (Sukhorukov et al., The characteristics of the observed 7088 band agree reasonably well with the laboratory measurements (Sukhorukov et al.
 2004) for the strongest band of the anthracene cation which give a central wavelength of 7085.7 + 13 and a FWHM of 47A.., 2004) for the strongest band of the anthracene cation which give a central wavelength of 7085.7 $\pm$ 1.3 and a FWHM of 47.
 The FWHM measured by Sukhorukov et al., The FWHM measured by Sukhorukov et al.
" in their direct absorption cavity ring-down spectroscopy seems to be larger than the observed value of the interstellar band, but this may well be the result of differences between the conditions of their experiment and the conditions of the cations in the interstellar medium towards Perseus."," in their direct absorption cavity ring-down spectroscopy seems to be larger than the observed value of the interstellar band, but this may well be the result of differences between the conditions of their experiment and the conditions of the cations in the interstellar medium towards Perseus."
 The study of the thermal dust emission at millimeter wavelengths indicate temperatures of order 19 K in the region causing the anomalous microwave emission (Watson et al., The study of the thermal dust emission at millimeter wavelengths indicate temperatures of order 19 K in the region causing the anomalous microwave emission (Watson et al.
" 2005, Tibbs et al."," 2005, Tibbs et al."
 2010)., 2010).
" The laboratory band of the anthracene cation was measured when the source temperature was raised to 205 °C. According to Sukhorukov et al.,"," The laboratory band of the anthracene cation was measured when the source temperature was raised to 205 $^{\circ}$ C. According to Sukhorukov et al.,"
 the absorption profile of the anthracene cation depends on the density and this is a function of the temperature., the absorption profile of the anthracene cation depends on the density and this is a function of the temperature.
 In fact at temperatures lower than 120°C the vapor pressure was too low for these authors to observe the absorption., In fact at temperatures lower than $^{\circ}$ C the vapor pressure was too low for these authors to observe the absorption.
 They concluded that in their experimental setup the anthracene cations may not experience enough collisions to cool down the rotational and vibrational degrees of freedom and therefore that the widths of laboratory bands are likely to be larger than those of interstellar bands., They concluded that in their experimental setup the anthracene cations may not experience enough collisions to cool down the rotational and vibrational degrees of freedom and therefore that the widths of laboratory bands are likely to be larger than those of interstellar bands.
 It is interesting to note that with their experimental setup Sukhorukov et al., It is interesting to note that with their experimental setup Sukhorukov et al.
 obtain larger widths by a factor 1.5 for the bands of naphthalene cation than Biennier et al. (, obtain larger widths by a factor 1.5 for the bands of naphthalene cation than Biennier et al. (
2003).,2003).
 The width of the interstellar band of the naphthalene cation in this line of sight is claimed by Iglesias-Groth et al. (, The width of the interstellar band of the naphthalene cation in this line of sight is claimed by Iglesias-Groth et al. (
2008) to agree well with the laboratory measurements by Biennier et al. (,2008) to agree well with the laboratory measurements by Biennier et al. (
2003).,2003).
 This also supports that the interstellar band of the anthracene cation is narrower than the current laboratory band measurements., This also supports that the interstellar band of the anthracene cation is narrower than the current laboratory band measurements.
 The 7088 bband is not only one of the strongest bands from the cation’s ground state but the sole band for which gas-phase spectroscopy has provided an accurate wavelength., The 7088 band is not only one of the strongest bands from the cation's ground state but the sole band for which gas-phase spectroscopy has provided an accurate wavelength.
 Matrix isolation spectroscopy (MIS) (Szczepanski εἰ al., Matrix isolation spectroscopy (MIS) (Szczepanski et al.
 1993) has provided wavelengths for other bands but these measurements differ from wavelengths for free cations by amounts that are too uncertain to provide a basis for secure identification in an astronomical spectrum., 1993) has provided wavelengths for other bands but these measurements differ from wavelengths for free cations by amounts that are too uncertain to provide a basis for secure identification in an astronomical spectrum.
" For example, the matrix isolation spectroscopy wavelength for the 7088 bband is 22 tto the red of the gas phase measurement."," For example, the matrix isolation spectroscopy wavelength for the 7088 band is 22 to the red of the gas phase measurement."
" The 7088 bband is the 0-0 vibrational band of the 172A, — X?B—3g ", The 7088 band is the 0-0 vibrational band of the $^2$ $_u$ $\leftarrow$ $^2$ $-{3g}$ 
stellav winds or à combination of a stellar wind and a sub Iseplerian disk wincl.,stellar winds or a combination of a stellar wind and a sub Keplerian disk wind.
" This combination of a two-component outflow is ""under uunierical investigation (Mattetal... 2003: I&oido.. 2003: Istikeretal... 2003: Matsakoset al... 2008))."," This combination of a two-component outflow is under numerical investigation \citeauthor{Mattetal03}, , \citeyear{Mattetal03}; ; \citeauthor{Koide03}, , \citeyear{Koide03}; ; \citeauthor{Kuekeretal03}, \citeyear{Kuekeretal03}; ; \citeauthor
{Matsakosetal08}, , \citeyear{Matsakosetal08}) )."
 Reecent simulations (Melietal... 2006: Romanovaet al.. 2009: Alatsakoset al... 2009: Foudt.. 2009)) also show the interplay of mixing between the two components.," Recent simulations \citeauthor{Melianietal06}, \citeyear{Melianietal06}; \citeauthor{Romanovaetal09}, \citeyear{Romanovaetal09}; \citeauthor{Matsakosetal09}, \citeyear
{Matsakosetal09}; \citeauthor{Fendt09}, , \citeyear{Fendt09}) ) also show the interplay of mixing between the two components."
 Several authors. c.g. RKükeretal.(2003).. Rouianovaetal.(2009) aud Fendt(2009).. have shown iu their nunerical simulations that the diskanaegnetosphere connection produces stroug intermittent outflows. the ECSUIts of flares aud reconnection.," Several authors, e.g. \cite{Kuekeretal03}, \cite{Romanovaetal09} and \cite{Fendt09}, have shown in their numerical simulations that the disk-magnetosphere connection produces strong intermittent outflows, the results of flares and reconnection."
 This is somewhat sinilay to coronal mass ejections in the solar wind aud im nici'oquasars., This is somewhat similar to coronal mass ejections in the solar wind and in microquasars.
 Thoueh important to model. those outflows are not necessarily inore important on the loue-term duration compared to the continuous underlying steady flaw. as sugeested by Romanovaetal.(2009).," Though important to model, those outflows are not necessarily more important on the long-term duration compared to the continuous underlying steady flow, as suggested by \cite{Romanovaetal09}."
. Moreover. Matsakosetal.(2009). have shown that the variability of tre source does not destrov the contimmous steady jet.," Moreover, \cite{Matsakosetal09} have shown that the variability of the source does not destroy the continuous steady jet."
 Tudeed. they use the first solutiou presented in this xY. nas muitial condition for the iuner spine jet of their sunlations. but use a polvtropic equation of state.," Indeed, they use the first solution presented in this paper, as initial condition for the inner spine jet of their simulations, but use a polytropic equation of state."
 In their oxevious paper (Matszakosotal..2008). they have shown hat changing from uou polvtropic to polvtropic would redce the size of the radius of the jet. without drastically affe‘tine the outflow behavior. however.," In their previous paper \citep{Matsakosetal08} they have shown that changing from non polytropic to polytropic would reduce the size of the radius of the jet, without drastically affecting the outflow behavior, however."
 IIowever. nunerical simulations are usually ιοconsumune to such an extent that they caunot explore a wide ranec of parameters.," However, numerical simulations are usually time-consuming to such an extent that they cannot explore a wide range of parameters."
 Moreover. they do not really start ejecting mass directly frou the star but rather at a oeiven height between the sonic aud the Alfvéónu surfaces.," Moreover, they do not really start ejecting mass directly from the star but rather at a given height between the sonic and the Alfvénn surfaces."
 Therefore. it is of absolute interest to model the stellar jet that originates in the central star.," Therefore, it is of absolute interest to model the stellar jet that originates in the central star."
 All these problems can be overcome by studviug AMID solutious obtained via a nonlinear separation of the variables., All these problems can be overcome by studying MHD solutions obtained via a nonlinear separation of the variables.
 These so-calle self-similar solutions coutain as special cases all known UID outflow solutious (c.e.. Vilawuksis&Tsineanos.. Sautyet abl. 2002.. hereafter STT02).," These so-called self-similar solutions contain as special cases all known MHD outflow solutions (e.g., \citeauthor{VlahakisTsinganos98}, \citeauthor{STT02}, \citeyear{STT02}, , hereafter STT02)."
 As shown in Sautv&Tsineanos(1991). hereafter STOLL. these sclésinulay models can be secu as a colmbination of stellar wind aud N-wind models.," As shown in \cite{ST94}, hereafter ST94, these self-similar models can be seen as a combination of stellar wind and X-wind models."
 Conversely to formal N-winds (Shuetal... 199 Ll: Shaneet al... 2002)). they do not require that all fieldlines clucree from a single point of the disk iu the form of a fan.," Conversely to formal X-winds \citeauthor{Shuetal94}, \citeyear{Shuetal94}; \citeauthor{Shangetal02}, \citeyear{Shangetal02}) ), they do not require that all fieldlines emerge from a single point of the disk in the form of a fan."
 Instead there is a smooth transition between the stellav wind and the disk jet., Instead there is a smooth transition between the stellar wind and the disk jet.
 They are also shown to be structurally stable (Matsakosetal... 2008: 20093).," They are also shown to be structurally stable \citeauthor{Matsakosetal08}, \citeyear{Matsakosetal08}; \citeyear{Matsakosetal09}) )."
 This Was far from obvious because the heating function is not polytropic as usually in most analytical solutions., This was far from obvious because the heating function is not polytropic as usually in most analytical solutions.
 In a series of papers — Sautyetal.(1999). hereafter: STT99. STTU2. aud Sautyctal.(2001)... hereafter STTOL πο have systematically explored the full paraicter space of this problem.," In a series of papers – \cite{STT99} hereafter STT99, STT02, and \cite{STT04}, hereafter STT04 – we have systematically explored the full parameter space of this problem."
 In ST9L we have shown that the double cisk and star component was promising., In ST94 we have shown that the double disk and star component was promising.
 Towever. the solutions presented there had mass loss rates that were oo low.," However, the solutions presented there had mass loss rates that were too low."
 Ποιο we present solutions where the stellar jet is both under-deuse aud uuder-pressured compared to the disk wind iu the launching region., Here we present solutions where the stellar jet is both under-dense and under-pressured compared to the disk wind in the launching region.
 These solutious have he advantage to adapt themselves not ouly to CTTS. which are connected with the surrounding accretion disk. mt also to WITS where there isitself (Walterctal.1988:Bertout.1989).," These solutions have the advantage to adapt themselves not only to CTTS, which are connected with the surrounding accretion disk, but also to WTTS where there is \citep{Walteretl88, Bertout89}."
. Although winds from WITS ire difficult to measure. mass loss rates between 1yi and LOIMAL./sy have Όσοι obtained by Audréetal.(19925.," Although winds from WTTS are difficult to measure, mass loss rates between $10^{-11}$ and $10^{-10}M_\odot/$ yr have been obtained by \cite{Andreetal92}."
. Winds of WITS might be similar to the solar wind in terms of collimation (see Aibóoetal... 2007.. aud references theremj.," Winds of WTTS might be similar to the solar wind in terms of collimation (see \citeauthor{Aibeoetal07}, \citeyear{Aibeoetal07}, and references therein)."
 However. these vouug stars lave higher mass loss rates and rotational speeds than our sun Hid nieht as well have! Strouelv collimated jets.," However, these young stars have higher mass loss rates and rotational speeds than our sun and might as well have strongly collimated jets."
disk. Their rotation periods rauge from 0.6 to 21 davs with peaks near two and eieht davs (Herbstetal..2007) while the solar rotational period is 21.5 dav., Their rotation periods range from 0.6 to 24 days with peaks near two and eight days \citep{Herbstetal07} while the solar rotational period is 24.5 day.
 Thus. WETS may well produce selfcollimated jets that nevertheless are soweak that they cannot be detected.," Thus, WTTS may well produce self-collimated jets that nevertheless are soweak that they cannot be detected."
 We will use the ST91 meridionally self-similar model to exiuuime the coutrilnition of the stellar compoucut to the overall jet aud how efficieutlv it brakes the star., We will use the ST94 meridionally self-similar model to examine the contribution of the stellar component to the overall jet and how efficiently it brakes the star.
 We first explore how the model parameters can be coustrained from the observations of CTTS jets (Sect. 3))., We first explore how the model parameters can be constrained from the observations of CTTS jets (Sect. \ref{sec.3}) ).
 Then. we focus our attention oli two different classes of solutious (Sections L auc 5)) :uid explore the efficiency of these winds to spin down the central object.," Then, we focus our attention on two different classes of solutions (Sections \ref{sec.4} and \ref{sec.5}) ) and explore the efficiency of these winds to spin down the central object."
 Iu the final section (Sect. 6)), In the final section (Sect. \ref{sec.6}) )
 we discuss how these two classes of solutions may explain the clichetomy between CTTS aud WITS and how they can be adapted to also model uultiphases of T Tauri faint jets. 5uch as in RY Tan.," we discuss how these two classes of solutions may explain the dichotomy between CTTS and WTTS and how they can be adapted to also model multiphases of T Tauri faint jets, such as in RY Tau."
 We stmarize the main asstunptions of our moeridiouallv (0 ) selfsimilay treatiueut of the ΑΠΟ equations iu Appendix AppendixA:., We summarize the main assumptions of our meridionally $\theta-$ ) self-similar treatment of the MHD equations in Appendix \ref{A} .
 More details can be found in STT9L. STT99 aud STT2.," More details can be found in STT94, STT99 and STT02."
 Using spherical cooxinates (67.0.47). all quantities. are normalized to the Alfvóun surface along the rotation axis. which is by asstupticon a sphere of radius r=ων," Using spherical coordinates $r, \theta, \varphi$ ), all quantities are normalized to the Alfvénn surface along the rotation axis, which is by assumption a sphere of radius $r=r_*$."
" The dimensionless racial «istance is denoted bv Ro=rjr while D.. V. aud pare the poloidal maguetic field. velocity aud. deusitv aong the polar axis at the Alfvéónu radius r,. with V?=D2/1zp "," The dimensionless radial distance is denoted by $R=r/r_*$, while $B_*$, $V_*$ and $\rho_*$are the poloidal magnetic field, velocity and density along the polar axis at the Alfvénn radius $r_*$ , with $V^2_*= B^2_* / 4 \pi \rho_*$ ."
The original svsteu of ΑΠΟ) equations reducesto twocoupled partialdiffereutial equationsfor thedensityand the magnetic fiux., The original system of MHD equations reducesto twocoupled partialdifferential equationsfor thedensityand the magnetic flux.
 Then. themomentum conservation law provides three ordinary differential equations. whichtoecther with Eq. (A22))," Then, themomentum conservation law provides three ordinary differential equations, whichtogether with Eq. \ref{F}) )"
 can be solved for the four variables AL?(R). FOR). HGCR) aud GOR). which are," can be solved for the four variables $M^2(R)$ , $F(R)$ , $\Pi(R)$ and $G(R)$ , which are"
region. we find that ενc2x10 (see left panel of Figure 2)).,"region, we find that $\epsilon_{\rm UV} \sim 2 \times 10^{-5}$ (see left panel of Figure \ref{fig:epsandtau}) )."
 For a Scalo mass function with metal-enriched stus (1/200h solar metalicitv). the value calculated [rom population svuthesis is ~5xLO? (WivitheandLoeb2002).," For a Scalo mass function with metal-enriched stars (1/20th solar metalicity), the value calculated from population synthesis is $\sim 5 \times 10^{-5}$ \citep{WL02}."
. Given the uncertainties and the relative simplicity of our model. the correspondence is (uite remarkable.," Given the uncertainties and the relative simplicity of our model, the correspondence is quite remarkable."
" The more striking inconsistency is (hat in all cases. (he optical depth (o electron scattering. where op=6.652xLOem? is the Thomson cross-section and n, is the electron density. is loo low."," The more striking inconsistency is that in all cases, the optical depth to electron scattering, where $\sigma_{\rm T} = 6.652 \times 10^{-25} {\rm cm}^2$ is the Thomson cross-section and $n_e$ is the electron density, is too low."
" Our model findsthat πι«0.06 (seeright panel of Figure 2)). whereas Spereel and IXogutοἱal.(2003) report WMAP-only. best fit values οτι =0.172:0.07 and το,=0.17zc0.04. respectively."," Our model findsthat $\tau_{\rm es} \sim 0.06$ (seeright panel of Figure \ref{fig:epsandtau}) ), whereas \citet{Setal03} and \citet{Kogut03} report WMAP-only best fit values of $\tau_{\rm es} = 0.17\pm 0.07$ and $\tau_{\rm es} = 0.17\pm 0.04$, respectively."
 Several articles written in the wake of (hese results (e.g... llaiman and Ilolder 2003: Ciardi. Ferrara. and White 2003: Cen 2003) have discussed this inconsistency and imdicated (hat star formation must begun much earlier (han previously thought.," Several articles written in the wake of these results (e.g., Haiman and Holder 2003; Ciardi, Ferrara, and White 2003; Cen 2003) have discussed this inconsistency and indicated that star formation must begun much earlier than previously thought."
 We consider this issue in the following analvsis., We consider this issue in the following analysis.
 There are good astrophysical reasons to believe that ei max. effectively. increase with redshift., There are good astrophysical reasons to believe that $\epsilon_{\rm UV}$ may effectively increase with redshift.
 For instance. the first generation of stars would have been metal-free. and stellar models predict them (o have an significantly higher UV. output. per barvon (about 4x hieher was reported bv WivitheandLoeb (2002))).," For instance, the first generation of stars would have been metal-free, and stellar models predict them to have an significantly higher UV output per baryon (about $4\times$ higher was reported by \citet{WL02}) )."
 In. addition. the creation of metals and henceforth dust. whieh would obscure ionizing sources. may also lead to lower elliciencies al lower redshift than at higher redshift.," In addition, the creation of metals and henceforth dust, which would obscure ionizing sources, may also lead to lower efficiencies at lower redshift than at higher redshift."
 Thus we now consider constraints on » and the time-depencence of εν from WALAP and SDSS quasars jointly., Thus we now consider constraints on $n$ and the time-dependence of $\epsilon_{\rm UV}$ from WMAP and SDSS quasars jointly.
 To limit the dimensionality of (he parameter space. we keep the barvon abundance and the Lhibble constant at their WALAP best fit values. and in addition fix Ooh?=0.14 to its WMADP best fit value.," To limit the dimensionality of the parameter space, we keep the baryon abundance and the Hubble constant at their WMAP best fit values, and in addition fix $\Omega_0 h^2 = 0.14$ to its WMAP best fit value."
" For each value of n and το, WALAP predicts a unique best-fit value of the normalization ay (based on the code provided by Verde 22003 and the accompanving data files [rom Iinshaw 22003 and IxXogut 22003)."," For each value of $n$ and $\tau_{\rm es}$, WMAP predicts a unique best-fit value of the normalization $\sigma_8$ (based on the code provided by Verde 2003 and the accompanying data files from Hinshaw 2003 and Kogut 2003)."
 The normalization given approximately by (for our fixed values of 5. O4/2. and Ομ)," The normalization given approximately by (for our fixed values of $h$ , $\Omega_0 h^2$ , and $\Omega_b h^2$ )"
would the much smaller Fux dSph.,would the much smaller Fnx dSph.
 On the other Ίνα. our proposed model has the following shortcomings: (1) the lower |n/Fo| is shifted to the uucertaiuties in theoretical uucleosvuthesis ia massive stars. (2) we lack an explanation for what the major driver of à complex star formation/chemical euricliiieut history is iu the Fux dSph. (3) we lack a sufficicut explanation for why aud how the high mass eud of the EME varies inside the Fux dSph in the contest of the IGIME thoery.," On the other hand, our proposed model has the following shortcomings: (1) the lower $\alpha$ /Fe] is shifted to the uncertainties in theoretical nucleosynthesis in massive stars, (2) we lack an explanation for what the major driver of a complex star formation/chemical enrichment history is in the Fnx dSph, (3) we lack a sufficient explanation for why and how the high mass end of the IMF varies inside the Fnx dSph in the context of the IGIMF thoery."
 These issues point to the need for future studies., These issues point to the need for future studies.
 The author wishes to thauk au auonviuous referee for his/her valuable coments aud excellent review. that has considerably improved the paper. aud is assisted im part by Craut-in-Aid for Scicutific Research (21510216) of the Japouese Ministry of Education. Culture. Sports. Science and Technologx.," The author wishes to thank an anonymous referee for his/her valuable comments and excellent review, that has considerably improved the paper, and is assisted in part by Grant-in-Aid for Scientific Research (21540246) of the Japanese Ministry of Education, Culture, Sports, Science and Technology."
"located at 16.7 and 18.8 kpc from the galactic center, respectively.","located at 16.7 and 18.8 kpc from the galactic center, respectively."
" The analysis of these data indicates that in these clusters the velocity dispersion remains constant beyond r— and r=12+2 pc from the center, respectively."," The analysis of these data indicates that in these clusters the velocity dispersion remains constant beyond $r=12.5\pm 2.5$ and $r=12\pm 2$ pc from the center, respectively."
 Values very similar and statistically fully consistent with the radius ro where the acceleration is ag., Values very similar and statistically fully consistent with the radius $r_0$ where the acceleration is $a_0$.
" Moreover, the two clusters are moving in a fast receding orbit."," Moreover, the two clusters are moving in a fast receding orbit."
" Dinescu et al (1999) assuming a logarithmic gravitational potential for the Milky Way, computed the most probable orbit for NGC 1851 and 1904."," Dinescu et al (1999) assuming a logarithmic gravitational potential for the Milky Way, computed the most probable orbit for NGC 1851 and 1904."
" Integration of these orbits shows that they passed perigalacticon about 51 and 86 millions years ago, respectively."," Integration of these orbits shows that they passed perigalacticon about 51 and 86 millions years ago, respectively."
" According to our velocity dispersion measurement, even in the outermost regions of the clusters the star velocity dispersion is 3.4 and 2.3 km/s. With this velocity stars in NGC 1851 and 1904 cover a distance of twice the tidal radius in ~24 and ~32 Myr, shorter than the time since last perigalacticon."," According to our velocity dispersion measurement, even in the outermost regions of the clusters the star velocity dispersion is $3.4$ and $2.3$ km/s. With this velocity stars in NGC 1851 and 1904 cover a distance of twice the tidal radius in $\sim 24$ and $\sim 32$ Myr, shorter than the time since last perigalacticon."
 Hence these clusters had enough time to revirialise., Hence these clusters had enough time to revirialise.
" Moreover, these two clusters experience a tidal action due to the the Milky Way about one order of magnitude smaller than that acting on the clusters previously studied as part of this project, making it unlikely that the flattening of the VDP is the result of tidal heating."," Moreover, these two clusters experience a tidal action due to the the Milky Way about one order of magnitude smaller than that acting on the clusters previously studied as part of this project, making it unlikely that the flattening of the VDP is the result of tidal heating."
" Thus, these new observations bring to 7 out of 7 the number of high concentration globular clusters showing constant velocity dispersion at large radii (Table 6)."," Thus, these new observations bring to 7 out of 7 the number of high concentration globular clusters showing constant velocity dispersion at large radii (Table 6)."
" While differing in many respects (mass, dynamical history, concentration, position in the Milky Way halo, etc.),"," While differing in many respects (mass, dynamical history, concentration, position in the Milky Way halo, etc.),"
" these clusters do share the property of being sufficiently concentrated to have internal accelerations of gravity above ao at the center, and thus are the equivalent and do behave like high surface brightness elliptical galaxies (e.g., Carolloetal.1995,, Mehlertetal. 2000))."," these clusters do share the property of being sufficiently concentrated to have internal accelerations of gravity above $a_0$ at the center, and thus are the equivalent and do behave like high surface brightness elliptical galaxies (e.g., \cite{Carollo95}, \cite{Mehlert00}) )."
" The availablevelocity dispersion data, however, in no case do probe radii larger than 2.579."," The availablevelocity dispersion data, however, in no case do probe radii larger than $r_0$ ."
 At this radius the, At this radius the
affected |X ostar ormatiou on local scales.,affected by star formation on local scales.
 ALeamvhile. the radial variations m the 160-5OO san ratios aud the SED fits sugeest that ~20% of the GO pau enüdssion. ~30% of the 70 nu enuiüssion. andl ~100% of the >100yan enission originates from dus heated by evolved disc aud bulge stars.," Meanwhile, the radial variations in the 160-500 $\mu$ m ratios and the SED fits suggest that $\sim20$ of the 60 $\mu$ m emission, $\sim30$ of the 70 $\mu$ m emission, and $\sim100$ of the $>100~\mu$ m emission originates from dust heated by evolved disc and bulge stars."
 This is consistent with prior results sugeestiug that 5-L00% of the 60 aud 7OO pra emission from nearby ealaxies originates frou dust heated by evolved stars (e.g.Sauvage&Thuan1992:WalcrbosCireenawalt 1996).," This is consistent with prior results suggesting that $\sim 5$ of the 60 and 100 $\mu$ m emission from nearby galaxies originates from dust heated by evolved stars \citep[e.g.][]{st92,wg96}."
. — [this interpretation is correct. we anticipate that dust enmdttine at 160-5OO you in other galaxies with relatively large fractious of old stars (E-Sah ealaxies) will also have 160-5OO san colows that depeud upon radius. but ealaxies with relatively laree fractious of voung stars (Sc-hu galaxies) will have 160-500 μαι colours that may depend more on infrared surface brightuess. as heating by the evolved stellay population becomes insignificant.," If this interpretation is correct, we anticipate that dust emitting at 160-500 $\mu$ m in other galaxies with relatively large fractions of old stars (E-Sab galaxies) will also have 160-500 $\mu$ m colours that depend upon radius, but galaxies with relatively large fractions of young stars (Sc-Im galaxies) will have 160-500 $\mu$ m colours that may depend more on infrared surface brightness, as heating by the evolved stellar population becomes insignificant."
 The results also imply that the couversion of infrared fluxcs integrated over very broad ranges (e.g. 8-1000 jii) to star formation rates. as done bv Zhuetal.(2008).. Rickectal. (2009)... and I&euuicuttctal.(2009).. will be accurate as long as the iutegrals coutain a signif&cant amount of cnussion shortward of 160 jan that traces dust heated by star formation.," The results also imply that the conversion of infrared fluxes integrated over very broad ranges (e.g. 8-1000 $\mu$ m) to star formation rates, as done by \citet{zwcl08}, \citet{retal09}, and \citet{ketal09}, will be accurate as long as the integrals contain a significant amount of emission shortward of 160 $\mu$ m that traces dust heated by star formation."
 However. it iiv not be possible to derive accurate star formation rates from dust enissiou measured solely at 2160 gin. Iu conclusion. these results for M1 demonstrate LOWHerschel 70-500 jan data can be used to not only measure more accurate dust temperatures and masses but also determine the dust heating sources in nearby ealaxics.," However, it may not be possible to derive accurate star formation rates from dust emission measured solely at $>$ 160 $\mu$ m. In conclusion, these results for M81 demonstrate how 70-500 $\mu$ m data can be used to not only measure more accurate dust temperatures and masses but also determine the dust heating sources in nearby galaxies."
 Further work with data from the VNGS aud other surveys will allow us to determine whether dust traced by the160-500 pau bauds im other spiral galaxies is also heated ba evolved stellar populations aud whether variations iu the relative streneth of dust heating by evolved stars varies across the IIubbο sequence., Further work with data from the VNGS and other surveys will allow us to determine whether dust traced by the 160-500 $\mu$ m bands in other spiral galaxies is also heated by evolved stellar populations and whether variations in the relative strength of dust heating by evolved stars varies across the Hubble sequence.
matches the pulsation periods of KIC 8626021.,matches the pulsation periods of KIC 8626021.
" We assume that all of the observed periods correspond to 6=1 modes, to be consistent with the mean period spacing."," We assume that all of the observed periods correspond to $\ell= 1$ modes, to be consistent with the mean period spacing."
" The goodness of the match between the theoretical pulsation periods (IIx) and the observed individual periods (11,5,;) is measured by means of a quality functiondefined as: where N (= 5) is the number of observed periods."," The goodness of the match between the theoretical pulsation periods $\Pi_k$ ) and the observed individual periods $\Pi_{{\rm obs}, i}$ ) is measured by means of a quality functiondefined as: where $N$ (= 5) is the number of observed periods."
 The DB white dwarf model that shows the lowest value of X) is adopted as the “best-fit model” (see Córrsico et al., The DB white dwarf model that shows the lowest value of $\chi^2$ is adopted as the “best-fit model” (see Córrsico et al.
" 2007a,b, Córrsico et al."," 2007a,b, Córrsico et al."
" 2008, 2009, Romero et al."," 2008, 2009, Romero et al."
 2011)., 2011).
" We evaluate the function Y?(M,,T.g) for stellar masses of 0.515,0.530,0.542,0.565,0.584,0.609,0.664,0.741, and 0.870Mo."," We evaluate the function $\chi^2(M_*, T_{\rm eff})$ for stellar masses of $0.515, 0.530, 0.542,
0.565, 0.584, 0.609, 0.664, 0.741$, and $0.870 M_{\odot}$."
 For the effective temperature we employed a much more finer grid (ΔΤΕῃ=10—30 K).," For the effective temperature we employed a much more finer grid $\Delta
T_{\rm eff}= 10-30$ K)."
" The quality of our period fits is assessed by means of the average of the absolute period differences, ó—(Xl0;D/N, where 6;=ους—Hk, and by the root-mean-square residual, c=(>)|6;2)/NVy."," The quality of our period fits is assessed by means of the average of the absolute period differences, $\overline{\delta}= (\sum_{i=1}^N |\delta_i|)/N$, where $\delta_i=
\Pi_{{\rm obs}, i} -\Pi_k$, and by the root-mean-square residual, $\sigma= \sqrt{(\sum |\delta_i|^2)/N}= \sqrt{\chi^2}$."
 The quantity (2)! in terms of the effective temperature for different stellar masses is shown in Fig., The quantity $(\chi^2)^{-1}$ in terms of the effective temperature for different stellar masses is shown in Fig.
 5 together with the spectroscopic effective temperature of KIC 8626021 (red line) and its uncertainties (gray strip)., \ref{chi2} together with the spectroscopic effective temperature of KIC 8626021 (red line) and its uncertainties (gray strip).
" We found one strong maximum for a model with M,=0.664Μο and Teg=27260 K (model 2)."," We found one strong maximum for a model with $M_*= 0.664 M_{\odot}$ and $T_{\rm eff}= 27\, 260$ K (model 2)."
 Such a pronounced maximum in the inverse of y? implies an excellent agreement between the theoretical and observed periods., Such a pronounced maximum in the inverse of $\chi^2$ implies an excellent agreement between the theoretical and observed periods.
" Notably, the effective temperature of this model is much higher (about 2400 K larger) than the spectroscopic effective temperature of KIC 8626021."," Notably, the effective temperature of this model is much higher (about $2400$ K larger) than the spectroscopic effective temperature of KIC 8626021."
" Another maximum, albeit much less pronounced, is encountered for quite hotter and somewhat less massive model with Teg=29440 and M.=0.609Me (model 1)."," Another maximum, albeit much less pronounced, is encountered for quite hotter and somewhat less massive model with $T_{\rm eff}= 29\,440$ and $M_*= 0.609 M_{\odot}$ (model 1)."
" According to its Teg, this model is in excellent agreement with the asteroseismological solution found by BK@11 (Teg=29200 K; see Table 3 below)."," According to its $T_{\rm eff}$, this model is in excellent agreement with the asteroseismological solution found by 11 $T_{\rm eff}= 29\, 200$ K; see Table \ref{table3} below)."
" Finally, a third asteroseismological solution is found at a model with M.=0.741Mo and Teg=24856 (model 3)."," Finally, a third asteroseismological solution is found at a model with $M_*=
0.741 M_{\odot}$ and $T_{\rm eff}= 24\,856$ (model 3)."
" Interestingly, this model has exactly the spectroscopically inferred effective temperature of KIC 8626021, Teg~24900 K. In Table 1 we summarize the main characteristics of the three solutions we found in our analysis, that is, models 1, 2 and 3."," Interestingly, this model has exactly the spectroscopically inferred effective temperature of KIC 8626021, $T_{\rm eff} \approx 24\,900 $ K. In Table \ref{table1} we summarize the main characteristics of the three solutions we found in our analysis, that is, models 1, 2 and 3."
 Models 1 and 3 constitute acceptable asteroseismological solutions., Models 1 and 3 constitute acceptable asteroseismological solutions.
" However, because the agreement between observed and theoretical periods for these models are much poorer than for model 2 (see columns 5 and 6 of Table 1)), we adopt this last model as the best-fit asteroseismological model of KIC 8626021."," However, because the agreement between observed and theoretical periods for these models are much poorer than for model 2 (see columns 5 and 6 of Table \ref{table1}) ), we adopt this last model as the best-fit asteroseismological model of KIC 8626021."
 One should bear in mind that the analysis of the mean period spacing suggests a preferred mass of 0.7Μο. between our 0.664 Μο and 0.741Μο models.," One should bear in mind that the analysis of the mean period spacing suggests a preferred mass of $\sim 0.7 M_{\odot}$, between our 0.664 $M_{\odot}$ and $ 0.741
M_{\odot}$ models."
" Thus a better fit, with a mass between 0.664 Μο and 0.741Mo, might had arisen if a thinner mass grid were available."," Thus a better fit, with a mass between 0.664 $M_{\odot}$ and $ 0.741 M_{\odot}$ , might had arisen if a thinner mass grid were available."
 A detailed comparison of the observed m=0 periods in KIC 8626021 with the theoretical periods of the best-fit asteroseismological model is provided in Table 2.., A detailed comparison of the observed $m= 0$ periods in KIC 8626021 with the theoretical periods of the best-fit asteroseismological model is provided in Table \ref{table2}.
" For this model, we obtain 6=1.582 s and σ=1.934 s. The mean period spacing of our best fit model is ATI=35.10+0.50 s (nonlinear least-squares fit), in excellent agreement with the mean period spacing of KIC 8626021 (Allg,=35.78+ 0.47)."," For this model, we obtain $\overline{\delta}= 1.582$ s and $\sigma= 1.934$ s. The mean period spacing of our best fit model is $\overline{\Delta \Pi}= 35.10 \pm
0.50$ s (nonlinear least-squares fit), in excellent agreement with the mean period spacing of KIC 8626021 $\overline{\Delta \Pi}_{\rm obs}=
35.78 \pm 0.47$ )."
" BK@11 perform detailed period fits to KIC 8626021 by considering six parameters of their DB white dwarf models: Te, Μ., two parameters describing the C-O core composition profiles (Xo,dtm)*s, and two parameters that define the envelope structure (Meny,Mye)°."," 11 perform detailed period fits to KIC 8626021 by considering six parameters of their DB white dwarf models: $T_{\rm eff}$, $M_*$, two parameters describing the C-O core composition profiles $X_{\rm
 O}, q_{\rm fm}$, and two parameters that define the envelope structure $M_{\rm env}, M_{\rm He}$."
. They fix Meny and vary the remainder 5 parameters., They fix $M_{\rm env}$ and vary the remainder 5 parameters.
" In contrast, in our models we have only 2 free parameters: T.g and M., and the chemical structure at the core and envelope is kept fixed according to the predictions of the evolutionary computations."," In contrast, in our models we have only 2 free parameters: $T_{\rm eff}$ and $M_*$ , and the chemical structure at the core and envelope is kept fixed according to the predictions of the evolutionary computations."
" In order to compare the quality of our best fit with the results of BK@11, we compute the Bayes Information Criterion(BIC; Koen"," In order to compare the quality of our best fit with the results of 11, we compute the Bayes Information Criterion(BIC; Koen"
eenerallv find A values of order unity lor migrating planets (hat clear gaps (Ixlev et al.,generally find $K$ values of order unity for migrating planets that clear gaps (Kley et al.
 2004). but Azz10—30 for smaller embedded planets (Artvimowiez 1993).," 2004), but $K\approx10-30$ for smaller embedded planets (Artymowicz 1993)."
 The outcomes thus depend on gap-clearing., The outcomes thus depend on gap-clearing.
 For low-viscosity disks. planets clear gaps when their Lill sphere exceeds (he disk scale height. ry;>££ (Crida et al.," For low-viscosity disks, planets clear gaps when their Hill sphere exceeds the disk scale height, $r_H>H$ (Crida et al."
 2006: Papaloizou Terquem 2006). which requires mpz;21.M. [or the disk parameters used here.," 2006; Papaloizou Terquem 2006), which requires $m_P\gta27\mearth$ for the disk parameters used here."
 The eap doesnt need to be completely open to reduce the A. value below the threshold Ave., The gap doesn't need to be completely open to reduce the $K$ value below the threshold $K_C$ .
 Nonetheless. relatively large rocky planets (npz;10—20M. ) are required [ον partial reduced A values. ancl hence collisions.," Nonetheless, relatively large rocky planets $m_P\gta10-20\mearth$ ) are required for partial gap-clearing, reduced $K$ values, and hence collisions."
" Small planets with ip<10M, are expected to have A>Ae and hence to avoid collision with hish probabili.", Small planets with $m_P\lta10\mearth$ are expected to have $K>K_C$ and hence to avoid collision with high probability.
 In addition. incoming rocky bodies must survive the collision aud reach the core (o increase ils mass: survival is expected when mp21—103. (Ας et al.," In addition, incoming rocky bodies must survive the collision and reach the core to increase its mass; survival is expected when $m_P\gta{1-10}\mearth$ (Anic et al."
 2007)., 2007).
 Both the occurrence of collisions and subsequent survival to reach the core thus require mpz;10.., Both the occurrence of collisions and subsequent survival to reach the core thus require $m_P\gta10\mearth$.
 Although this threshold mass should be determined more rigorously. these results show that larger rocky planets have more influence (per unit mass) than smaller ones.," Although this threshold mass should be determined more rigorously, these results show that larger rocky planets have more influence (per unit mass) than smaller ones."
 In addition to increasing the core mass. accretion of rocky planets can affect the energy budget of eiat. planets.," In addition to increasing the core mass, accretion of rocky planets can affect the energy budget of giant planets."
 Figure 3. shows the distribution of impact speeds for rocky planets that collide with Hot Jupiters.," Figure \ref{fig:vdist}
 shows the distribution of impact speeds for rocky planets that collide with Hot Jupiters."
" This distribution indicates speeds (040—100 km/s. so we consider a benchmark e60 km/s. With this speed. an accretng ""superearth planet with mass mp=10M. deposits οποιον To put this energv increment into perspective. note that the binding energy of the Lot Jupiter ÜU=[GMBp©1.6x10"" erg (using typical values Mp=LAL). Rp=LAA. and [= 3/5)."," This distribution indicates speeds $v\sim40-100$ km/s, so we consider a benchmark $v\sim60$ km/s. With this speed, an accreting “superearth” planet with mass $m_P=10\mearth$ deposits energy To put this energy increment into perspective, note that the binding energy of the Hot Jupiter $U=fGM_P^2/R_P\approx1.6\times10^{43}$ erg (using typical values $M_P=1M_J$, $R_P=1.4M_J$, and $f=3/5$ )."
 A single collision thus accounts lor e7% of the binding energv of a Hot Jupiter., A single collision thus accounts for $\sim7\%$ of the binding energy of a Hot Jupiter.
 If we assume the energv AL is deposited deep within the planet. and slowly leaks out over lime Al~I Gyr. the associated power increment APzz3.5xLOY W. large enough to help inflate the planetary. radius (BLL.BS).," If we assume the energy $\Delta{E}$ is deposited deep within the planet, and slowly leaks out over time $\Delta{t}\sim1$ Gyr, the associated power increment $\Delta{P}\approx3.5\times10^{18}$ W, large enough to help inflate the planetary radius (BLL,BS)."
 On the other haud. if (he energy is deposited in the upper atmosphere of the planet. it quickly radiates away and cannot inflate the radius.," On the other hand, if the energy is deposited in the upper atmosphere of the planet, it quickly radiates away and cannot inflate the radius."
 The results of this paper pose a number of interesting problems for future work., The results of this paper pose a number of interesting problems for future work.
 To determine the number of accretion events (per Hot Jupiter) we need a better understanding of eccentricity damping rates for both migrating rocky planets and Lot Jupiters: we also need estimates for the number (and masses) of rocky planets produced after οι Jupiter migration has occurred., To determine the number of accretion events (per Hot Jupiter) we need a better understanding of eccentricity damping rates for both migrating rocky planets and Hot Jupiters; we also need estimates for the number (and masses) of rocky planets produced after Hot Jupiter migration has occurred.
 When accretion events take place. we need to understaad the energy deposition within the giant planet and the subsequent long-term transfer of heat/energy oul ofthe planetary. body.," When accretion events take place, we need to understand the energy deposition within the giant planet and the subsequent long-term transfer of heat/energy out ofthe planetary body."
 These issues. ancl others. will help explain the observed diversity in the properties of Hot Jupiters.," These issues, and others, will help explain the observed diversity in the properties of Hot Jupiters."
Our dimensionless transport coefficient o is defined as where athe average is taken over the volume of the simulation box.,Our dimensionless transport coefficient $\alpha$ is defined as where the average is taken over the volume of the simulation box.
" Within a factor of order unity, this is analogous to the more common prescription for the turbulent viscosity v,=ac,H if one identifies L, with the disc thickness H."," Within a factor of order unity, this is analogous to the more common prescription for the turbulent viscosity $\nu_t=\alpha c_s H$ if one identifies $L_z$ with the disc thickness $H$."
" As recalled in the introduction, it has been noted in a number of earlier MRI simulations in a shearing box with a mean vertical field that channel modes constitute somewhat recurrent patterns of the turbulent flow, and appear to be more prominent at the maxima in the fluctuations of the turbulent transport."," As recalled in the introduction, it has been noted in a number of earlier MRI simulations in a shearing box with a mean vertical field that channel modes constitute somewhat recurrent patterns of the turbulent flow, and appear to be more prominent at the maxima in the fluctuations of the turbulent transport."
 Channel modes do transport angular momentum with roughly the right order of magnitude if their amplitude is comparable to the rms fluctuation in the field close to a maximum of the transport., Channel modes do transport angular momentum with roughly the right order of magnitude if their amplitude is comparable to the rms fluctuation in the field close to a maximum of the transport.
 This has suggested a picture of turbulent transport in shearing boxes with a mean vertical field that is sketched on Fig. 1.., This has suggested a picture of turbulent transport in shearing boxes with a mean vertical field that is sketched on Fig. \ref{satproc}.
" According to this picture, the channel modes linearly grow from random noise; at some amplitude, their growth is halted by a secondary instability (parasitic mode) which destroys the channel mode."," According to this picture, the channel modes linearly grow from random noise; at some amplitude, their growth is halted by a secondary instability (parasitic mode) which destroys the channel mode."
" Presumably, the parasitic modes themselves decay into small scale turbulence, which may then produce the seed for the random fluctuations out of which the channel mode grows in the first place."," Presumably, the parasitic modes themselves decay into small scale turbulence, which may then produce the seed for the random fluctuations out of which the channel mode grows in the first place."
" In this scenario, the channel mode(s) would be responsible for most of the transport, in particular near maxima of the transport fluctuations."," In this scenario, the channel mode(s) would be responsible for most of the transport, in particular near maxima of the transport fluctuations."
 One of the objectives of this paper is to examine the relevance of this picture of MRI turbulence., One of the objectives of this paper is to examine the relevance of this picture of MRI turbulence.
" Even if such a scenario is not generic (it depends directly on the presence of a mean vertical field), if confirmed, it might provide an interesting lead to analyze different situations."," Even if such a scenario is not generic (it depends directly on the presence of a mean vertical field), if confirmed, it might provide an interesting lead to analyze different situations."
 Another related objective it to assess the relevance of this scenario to the question of the Prandtl number dependence of MRI-driven transport., Another related objective it to assess the relevance of this scenario to the question of the Prandtl number dependence of MRI-driven transport.
" To this effect, we gather here the relevant pieces of information on the physics of channel modes that is required in order to analyze the simulations presented in the next section."," To this effect, we gather here the relevant pieces of information on the physics of channel modes that is required in order to analyze the simulations presented in the next section."
 The physics of viscous and resistive channel modes has been examined in ? and their properties have been characterized in detail in ? (? have also explored the role of resistivity on MRI in the absence of viscosity)., The physics of viscous and resistive channel modes has been examined in \cite{LL07} and their properties have been characterized in detail in \cite{PC08} \citealt{SM99} have also explored the role of resistivity on MRI in the absence of viscosity).
" Since non axisymmetric MRI modes are transiently growing structures in non ideal MHD (?),, the axisymmetric modes give a good grasp of the linear stability properties of the shearing box."," Since non axisymmetric MRI modes are transiently growing structures in non ideal MHD \citep{BH92}, the axisymmetric modes give a good grasp of the linear stability properties of the shearing box."
 We recall here the dispersion relation of theses modes and a number of other features that will be of use in the next section., We recall here the dispersion relation of theses modes and a number of other features that will be of use in the next section.
" Looking for solutions of the linearized equations of motions in the form v=υιεχρίσί—ik,yikz) and b= leads to the following fourth order dispersion relation: with and where x=[2020—5)]'? is the epicyclic frequency, V4= is the Alfvénn speed based on the imposed mean vertical"," Looking for solutions of the linearized equations of motions in the form $\bm{v}=\bm{v_l}\exp(\sigma t - i k_y y - i k z)$ and $\bm{b}=\bm{b_l}\exp(\sigma t - i k z)$ leads to the following fourth order dispersion relation: with and where $\kappa=[2\Omega(2\Omega - S)]^{1/2}$ is the epicyclic frequency, $V_A = B_0$ is the Alfvénn speed based on the imposed mean vertical"
AX 1931-563. and two neigliboriis ealaxies show very close radial velocities (Fig.,AM 1934-563 and two neighboring galaxies show very close radial velocities (Fig.
 1. Table 3) aud very. probably forma physical triplet.," 1, Table 3) and very probably form physical triplet."
" C'onsideriug this group as au individual dvuamical svstem. we computed the following standard quantities (sec Ikaracheuseva Iaracheutsev 2000 for the corresponding formulae): From the comparison of the above characteristics with the correspouding median values of known isoated triplets (Table 3 in I&aracheutseva IRivacheutsev 2000) we cau conclude hat the AM 193-561 system shows about twice sunaller s, value."," Considering this group as an individual dynamical system, we computed the following standard quantities (see Karachentseva Karachentsev 2000 for the corresponding formulae): From the comparison of the above characteristics with the corresponding median values of known isolated triplets (Table 3 in Karachentseva Karachentsev 2000) we can conclude that the AM 1934-564 system shows about twice smaller $s_v$ value."
 The characteristic size of he triplet UH is close to median values for the southern aud uortheru viplets., The characteristic size of the triplet -- $r_H$ – is close to median values for the southern and northern triplets.
 The relaively low value of the observed dispersion leads to a large crossing timc. a1 πα virial lass and imasseto-unünositv ratio dn comparison with typical triplets.," The relatively low value of the observed dispersion leads to a large crossing time, and small virial mass and mass-to-luminosity ratio in comparison with typical triplets."
 The nuclear Wa spectra of galaxies are prescuted in Fig., The nuclear $\alpha$ spectra of galaxies are presented in Fig.
 3., 3.
 The results of our measurements of the uuclear emissiou-line properties within U«37 are «ununarized in Table I., The results of our measurements of the nuclear emission-line properties within $4'' \times 3''$ are summarized in Table 4.
 The NW menber of the triplet shows typical HII resion-lke spectu., The NW member of the triplet shows typical HII region-like spectrum.
 AMO 1931-563 demonstrates relatively large [NITJA6583/Tla ratio and noticeable width of the cunission lines: but the galaxy shows comparatively faint OTJ|AG300 line AG300/TIn.< 0.05)., AM 1934-563 demonstrates relatively large $\lambda$ $\alpha$ ratio and noticeable width of the emission lines; but the galaxy shows comparatively faint $\lambda$ 6300 line $\lambda$ $\alpha \leq 0.05$ ).
 Therefore. we can classify its spectrum as a transition ΑΝΠΠ type (Veilleux Osterbrock 1987).," Therefore, we can classify its spectrum as a transition – AGN/HII – type (Veilleux Osterbrock 1987)."
 LDiuission lues in the uuclear spectiun of POC 399718 (Seaaxyv) are double-peaked and wide (Fie., Emission lines in the nuclear spectrum of PGC 399718 (S galaxy) are double-peaked and wide (Fig.
 3). reflecting very steep rotation curve visible iu the two-dimensional spectrum. (," 3), reflecting very steep rotation curve visible in the two-dimensional spectrum. ("
The atlas by Πο et al. (,The atlas by Ho et al. (
"1995) gives several exinuples of such objects ce. NGC. tsa, NGC. 3215. and NGC 1772.)","1995) gives several examples of such objects – e.g., NGC 488, NGC 3245, and NGC 4772.)"
 The amplitude of splitting determined from the Gauss decomposition of the Πα aud |NIT/AG583 contours is 250.280 kin 1, The amplitude of splitting determined from the Gauss decomposition of the $\alpha$ and $\lambda$ 6583 contours is 250–280 km $^{-1}$ .
analysis of the data 1 the 300 MeV baud with those obtained by addiug the fiue maps or he two narrower baixIs.,analysis of the data in the $>$ 300 MeV band with those obtained by adding the fine maps for the two narrower bands.
 There is a substantial overlap of the confidence regious. and the differeuc be attributed to he displacement of the source localization atenergies 1.000 MeV reall lat at lower euergles. an informatiou that is preserved iu the co-added fine map but 1 available to the likelilood analysis for the euergy baud 300 MeV. We do not note auy systena »xoblem that might arise from a possibly inaccurate PSF iu the analysis of the wide euergy Jal," There is a substantial overlap of the confidence regions, and the differences can be attributed to the displacement of the source localization atenergies $>$ 1.000 MeV relative to that at lower energies, an information that is preserved in the co-added fine map but not available to the likelihood analysis for the energy band $>$ 300 MeV. We do not note any systematic problem that might arise from a possibly inaccurate PSF in the analysis of the wide energy band."
 Agaiu. the position o “Ser Α and the position of the TeV source seem to be exclude. and he GeV source appears to be located a fraction of a degree away [roui the exact Calactic Center.," Again, the position of Sgr $^\ast$ and the position of the TeV source seem to be excluded, and the GeV source appears to be located a fraction of a degree away from the exact Galactic Center."
 The localization accuracy obtained from the analysis of data lor individual viewing periods will be worse than that derived using the combined data set. aud the best-fit. positious of will be scattered over an area much larger than tle confidence regious sllowh in FigM. 3-—25..," The localization accuracy obtained from the analysis of data for individual viewing periods will be worse than that derived using the combined data set, and the best-fit positions of will be scattered over an area much larger than the confidence regions shown in Figs. \ref{f3}- \ref{f5}."
 We can test whether or not the observed scatter iu the best-fit source position is compatible with a COMMOL true positior and the irueasured localization uicertainties., We can test whether or not the observed scatter in the best-fit source position is compatible with a common true position and the measured localization uncertainties.
 The confidence contours can usually be accurately fted with an ellipse that is speciied by a seminmajor axis p. seminmiuor axis q. aud position augle o ‘the major axis © (Thompsonetal.19925..," The confidence contours can usually be accurately fitted with an ellipse that is specified by a semimajor axis $p$, semiminor axis $q$ , and position angle of the major axis $\phi$ \citep{th95}."
 The ellipse is centered ou the centroid of the conficleice location region. which thus serves as a position estiuae.," The ellipse is centered on the centroid of the confidence location region, which thus serves as a position estimate."
 noted that for sroug sotrees the dependence of the logarilun of the lilselirood of EGRET data upon the assune source position closely. follows a paraboloil. indicatiugoO a Catissiall error distribution aud tlu sjstilviug he use of the \7-test.," \citet{mat97} noted that for strong sources the dependence of the logarithm of the likelihood of EGRET data upon the assumed source position closely follows a paraboloid, indicating a Gaussian error distribution and thus justifying the use of the $\chi^2$ -test."
 Lu contrast to TLOMPSo1eal.(1995). and Mattoxetal.(1997 we use a fi to the confidence contour., In contrast to \citet{th95} and \citet{mat97} we use a fit to the confidence contour.
 The cisplacenjent of the assumed (or measured) position rom the true position is described by the distaCO | alic Lue position augle 0., The displacement of the assumed (or measured) position from the true position is described by the distance $r$ and the position angle $\theta$.
 Then the y7-sum is celined by |)?m A certain miuimui in detection sienificancee is necessary to provide a meaninelul[we localization., Then the $\chi^2$ -sum is defined by ^2 = )^2 + ] A certain minimum in detection significance is necessary to provide a meaningful localization.
 Here we only consider data [rom viewing periods for which was detected with at least νTS-- 3., Here we only consider data from viewing periods for which was detected with at least $\sqrt{\TS}=3$ .
 Table lists the results of the location analysis in the euergy rauge > 300MeV [or the 12, Table \ref{t4} lists the results of the location analysis in the energy range $>$ 300MeV for the 12
forlimate to have the opportunity to conduct observations [rom (his mountain.,fortunate to have the opportunity to conduct observations from this mountain.
 The low stellar accretion rate of V836 Tau (o10.M.vr.|: from Hartigan ethwilhanormalizalionappropr. KIN)," The low stellar accretion rate of V836 Tau $\sim 10^{-9}\Msunperyr$; from Hartigan et with a normalization appropriate to a passive reprocessing disk (e.g., Adams, Lada, Shu 1988)."
 and to have negligible optical depth within that radius (<0.017 AAU)., The disk is assumed to be optically thick beyond the dust sublimation radius (where $T_D = 1500$ K) and to have negligible optical depth within that radius $<0.017$ AU).
 While the 3—9jmir excess is well fit and arises. from disk radii within AAU. the excesses at 24 and TOs are underpredicted.," While the $3-9\micron$ excess is well fit and arises from disk radii within AU, the excesses at 24 and $\micron$ are underpredicted."
 A disk that is more strongly flavecl bevond ~0.5 AAU would likely produce a better fit., A disk that is more strongly flared beyond $\sim 0.5$ AU would likely produce a better fit.
 While such a simple model does a reasonable job fitting the short wavelength. SED. it implies that the inner radius of the dust disk (at AAU) is within the inner radius of the CO emission (at ~0.05 AAU: 833.3).," While such a simple model does a reasonable job fitting the short wavelength SED, it implies that the inner radius of the dust disk (at AU) is within the inner radius of the CO emission (at $\sim 0.05$ AU; 3.3)."
 This is in contrast to the situation found for more active T Tauri stars. where the SED is better fit with a frontallv illuminated hot inner dust rim located further from the star (al 20.1 AAU).," This is in contrast to the situation found for more active T Tauri stars, where the SED is better fit with a frontally illuminated hot inner dust rim located further from the star (at $\gtrsim 0.1$ AU)."
 Such structures can account for the magnitude of (he near-infrared excesses of T Tauri stars (Muzerolle et 22003)., Such structures can account for the magnitude of the near-infrared excesses of T Tauri stars (Muzerolle et 2003).
 Thev also agree with the dust inner radii measured using infrared interferometry (e.g.. Eisner et 22005).," They also agree with the dust inner radii measured using infrared interferometry (e.g., Eisner et 2005)."
 To illustrate the latter case. we fit the SED using the public domain version of the CGPLUS modeling program written by DDullemond. DDominik. aud NNatta (http:/www.mpla-hd.mpsg.de/homes/dullemon/radtrans/) to calculate the disk contribution.," To illustrate the latter case, we fit the SED using the public domain version of the CGPLUS modeling program written by Dullemond, Dominik, and Natta (http://www.mpia-hd.mpg.de/homes/dullemon/radtrans/) to calculate the disk contribution."
 The CGPLUS model is based on the models of Chiang Goldreich (1997) and Dullemond. Dominik. Natta (2001).," The CGPLUS model is based on the models of Chiang Goldreich (1997) and Dullemond, Dominik, Natta (2001)."
 The model includes four physical components: a stellar blackbody. a pulfecd-up inner rim. the disk surface. and the disk interior.," The model includes four physical components: a stellar blackbody, a puffed-up inner rim, the disk surface, and the disk interior."
 Figure 9 shows the contribution to the SED of a disk iruncated at an inner rim temperature of NIX. corresponding to a disk radius of AAU.," Figure 9 shows the contribution to the SED of a disk truncated at an inner rim temperature of K, corresponding to a disk radius of AU."
" The inner rim (long dashed line) is moclestly flared (x,44= 1.25). and the rest of the disk is less strongly flarecl (xgisk= 0.6)."," The inner rim (long dashed line) is modestly flared $\chi_{\rm rim}=1.25$ ), and the rest of the disk is less strongly flared $\chi_{\rm disk} = 0.6$ )."
 While the stellar blackbody was used in caleulating the temperature of the other components. in constructing the composite SED we used a Basel stellar atmosphere v2.2 (corrected: Lejeune 2002) of the same effective temperature.," While the stellar blackbody was used in calculating the temperature of the other components, in constructing the composite SED we used a Basel stellar atmosphere v2.2 (corrected; Lejeune 2002) of the same effective temperature."
 Addinga hot blackbody component 7=1500 Wx (short dashed line). representing hot dust located close to the star. produces a reasonable fit to the SED.," Adding a hot blackbody component $T=1500$ K (short dashed line), representing hot dust located close to the star, produces a reasonable fit to the SED."
 There is significant, There is significant
 ..) ~ M..," $_{\odot}$ \citep[e.g.][]{zhang05, cesaroni07}."
 ~ 10° (e.McKee&Tan2003)..," $\sim$ $_{\odot}$ $\sim$ $^5$ \citep[e.g][]{mt03}. \citep{keto02,sollins05}."
 stars) to show classical spectrosocopic signatures of ongoing accretion and excess continuum emission longward of 2 j/m. indicating the presence of circumstellar dust around them. presumably distributed in the surrounding disks (e.gNattaetal.2000:Manoj 2006).," stars) to show classical spectrosocopic signatures of ongoing accretion and excess continuum emission longward of 2 $\mu$ m, indicating the presence of circumstellar dust around them, presumably distributed in the surrounding disks \citep[e.g][]{ngm00, manoj06}."
. Direct imaging studies at high angular resolution with interferometers have so far detected compact continuum emission around two such objects. viz.," Direct imaging studies at high angular resolution with interferometers have so far detected compact continuum emission around two such objects, viz."
 MWC 1080. and R Mon. and evidence for Keplerian rotation in the optically thick CO line emission from R Mon (Fuenteetal.2003. 2006).," MWC 1080, and R Mon, and evidence for Keplerian rotation in the optically thick CO line emission from R Mon \citep{fuente03,fuente06}."
. However. because of the large distances to these stars (77 800 pe). even with the high angular resolutions provided by interferometers. it is not easy to distinguish between flattened structures of a few thousand AU and circumstellar disks.," However, because of the large distances to these stars $\ge$ 800 pc), even with the high angular resolutions provided by interferometers, it is not easy to distinguish between flattened structures of a few thousand AU and circumstellar disks."
 In this letter we present the first interferometric observations of MWC 297. which is a young 10 M. main sequence star of spectral type B1.5 (Drewetal.1997).," In this letter we present the first interferometric observations of MWC 297, which is a young 10 $_{\odot}$ main sequence star of spectral type B1.5 \citep{drew97}."
 Although distances of 450 to 870 pe to MWC 297 have been cited in the literature (cf.Cantoetal. 1984).. the more reliable distance estimate based on a detailed study of the stellar properties and line-of-sight extinction by (1997).. places it at a distance of 250+50 pe.," Although distances of 450 to 870 pc to MWC 297 have been cited in the literature \citep[cf.][]{canto84}, , the more reliable distance estimate based on a detailed study of the stellar properties and line-of-sight extinction by \citet{drew97}, places it at a distance of $\pm$ 50 pc."
 MWC 297. thus. is one of the closest. young massive star to us and is an ideal candidate for high resolution studies.," MWC 297, thus, is one of the closest, young massive star to us and is an ideal candidate for high resolution studies."
 MWC. 297 was observed with the Submillimeter (SMA) (Hoetal.2004) in the continuum at 230 GHz (1.3 mm) on 28 August. 2006.," MWC 297 was observed with the Submillimeter (SMA) \citep{ho04} in the continuum at 230 GHz (1.3 mm) on 28 August, 2006."
 The two sidebands. each of 2 GHz bandwidth. include the rotational transitions (J=2-1) of CO. and C'O and the correlatorwas configured to provide a COvelocity resolution of 0.5 kms?! for the CO (2- line which was centered in the upper sideband.," The two sidebands, each of 2 GHz bandwidth, include the rotational transitions (J=2-1) of $^{12}$ $^{13}$ CO and $^{18}$ O and the correlatorwas configured to provide a velocity resolution of 0.5 $^{-1}$ for the CO (2-1) line which was centered in the upper sideband."
The,The
the functions flux at the same pixel.,the functions flux at the same pixel.
" The term σί,roy) is the Poisson error at cach pixel position."," The term $\sigma(x,y)$ is the Poisson error at each pixel position."
 The airy) value can be estimated internally by based on the gain and reacd-noise values found in the header of each galaxy. image or provided separately as a EIS image.," The $\sigma(x,y)$ value can be estimated internally by based on the gain and read-noise values found in the header of each galaxy image or provided separately as a FITS image."
 Pixels contained in the mask image are not included in the 47 caleulation., Pixels contained in the mask image are not included in the $\chi^2$ calculation.
 The background is kept fixed to the value derived. in section 2.1.., The background is kept fixed to the value derived in Section \ref{sec:2.1}.
 convolves the model with the point-spread Function (PSE. see 2.2)) to account for the results of atmospheric secing.," convolves the model with the point-spread function (PSF, see \ref{sec:2.2}) ) to account for the results of atmospheric seeing."
 The free parameters for cach component are the magnitude. the scalelength (i7)/elfective radius Gr). the concentration index » for the Sérrsic models. (Sérrsic index). the axis ratio. and the position angle.," The free parameters for each component are the magnitude, the scalelength $r_{s}$ )/effective radius $r_{e}$ ), the concentration index $n$ for the Sérrsic models (Sérrsic index), the axis ratio, and the position angle."
 We mocelled the racial light distribution of each galaxy using combinations of the following analvtic functions: a Seérrsic Cunetion (see Equation 2)) to moelel elliptical galaxies. the bulge and/or the bar of lenticular and. spiral galaxies: an Exponential function (Equation 2. where n=1) to model the disk of the galaxy and a Alollat function to mocel/mask the central part of one elliptical galaxy.," We modelled the radial light distribution of each galaxy using combinations of the following analytic functions: a Sérrsic function (see Equation \ref{eq:sersic}) ) to model elliptical galaxies, the bulge and/or the bar of lenticular and spiral galaxies; an Exponential function (Equation \ref{eq:sersic} where n=1) to model the disk of the galaxy and a Moffat function to model/mask the central part of one elliptical galaxy."
 For some bar-less disk galaxies the combination of a Sérrsic plus an exponential component was insullicient to moclel the galaxy., For some bar-less disk galaxies the combination of a Sérrsic plus an exponential component was insufficient to model the galaxy.
 Ln these cases we modelled the galaxies with a combination of two Sérrsic functions., In these cases we modelled the galaxies with a combination of two Sérrsic functions.
" The function is eiven by: where J. is the intensity at the elleetive radius (ο). n is the Sérrsic index and b, is a function of n. The value of b, can be derived from P—25(2».5,) and is used so that the clleetive radius cneloses half of the total luminosity (see 7))."," The function is given by: where $I_{\rm e}$ is the intensity at the effective radius $r_{\rm e}$ ), $n$ is the Sérrsic index and $b_{\rm n}$ is a function of n. The value of $_{\rm n}$ can be derived from $\Gamma ~ = ~ 2 \gamma(2n,b_{n})$ and is used so that the effective radius encloses half of the total luminosity (see )."
 When the Séórrsic index is fixed to p=4.1 or 0.5 the Sérrsic profile is identical to the well known de Vaucouleurs. exponential or Gaussian profile. respectively.," When the Sérrsic index is fixed to $n= 4, 1$ or 0.5 the Sérrsic profile is identical to the well known de Vaucouleurs, exponential or Gaussian profile, respectively."
 For the first run of we performed. a single Séresic model fit for all galaxies assuming that we can describe the distribution of light with a single component., For the first run of we performed a single Sérrsic model fit for all galaxies assuming that we can describe the distribution of light with a single component.
 The first run used. initial values for the free parameters as implied. bySExtractor., The first run used initial values for the free parameters as implied by.
. The magnitudes derived. from the single Sérrsic model were compared. with the 2ALASS magnitudes., The magnitudes derived from the single Sérrsic model were compared with the 2MASS magnitudes.
 Phe 2ALASS magnitudes agreed with our single Component magnitudes cxeept for two galaxies. λές and NGCALSGA (see Figure 3)).," The 2MASS magnitudes agreed with our single component magnitudes except for two galaxies, NGC4343 and NGC4486A (see Figure \ref{fig:2mass}) )."
 For those cases where an additional Component was required. either due to a poor Sérrsic [it or an obvious disk in the images. a second run was conducted.," For those cases where an additional component was required, either due to a poor Sérrsic fit or an obvious disk in the images, a second run was conducted."
 Phe output parameters of the first run were then used. as input parameters for the second. run ofGALFITS., The output parameters of the first run were then used as input parameters for the second run of.
. The second run used. two-component (ic. Sérrsic bulge - exponential disk) for disk galaxies., The second run used two-component (i.e. Sérrsic bulge - exponential disk) for disk galaxies.
 The Sérrsic bulge plus exponential disk model for the lenticular galaxy NCC4564 was still deficient and so a double Sérrsic model was adopted for a third run., The Sérrsic bulge plus exponential disk model for the lenticular galaxy NGC4564 was still deficient and so a double Sérrsic model was adopted for a third run.
 Note that the resulting Séresic index for the disk of this galaxy was found to be 1.3 which is plausibly: close to the value of the exponential function (n= I)., Note that the resulting Sérrsic index for the disk of this galaxy was found to be 1.3 which is plausibly close to the value of the exponential function $n=1$ ).
 In one case. the disk galaxy NCGCJ4459 the Sérrsic plus clisk fit was not sullicient to model the galaxy.," In one case, the disk galaxy NGC4459 the Sérrsic plus disk fit was not sufficient to model the galaxy."
 After trving to model the galaxy by applying a single Sérrsie model or combining extra functions we conclude that διςΡΟ can been modelled better with a combination of a Sérrsic function and a Molfat. function., After trying to model the galaxy by applying a single Sérrsic model or combining extra functions we conclude that NGC4459 can been modelled better with a combination of a Sérrsic function and a Moffat function.
 “Phe Molfat. function. in has five free. parameters: the total magnitude. the ENIM. the beta powerlaw. the axis ratio and the position angle.," The Moffat function in has five free parameters: the total magnitude, the FWHM, the beta powerlaw, the axis ratio and the position angle."
 We fixed the ΟΝΝΕΔ and the beta parameter to values that we derived through the taskIRAF//psfmeasure., We fixed the FWHM and the beta parameter to values that we derived through the task.
. As deseribed above. the outputs of the second run were used. as input for the third run for galaxies whose residuals implied the existence of a bar.," As described above, the outputs of the second run were used as input for the third run for galaxies whose residuals implied the existence of a bar."
 We applied a third run to ealaxies with a bar component by using a three component model. i.e. Sérrsie bulge - IExponential disk - Sérrsic bar.," We applied a third run to galaxies with a bar component by using a three component model, i.e., Sérrsic bulge - Exponential disk - Sérrsic bar."
 An additional run was also applied to active galaxies (as indicated by X-ray. or Radio observations) that have a right nucleus in near-LR. (corresponding to a point. source at our resolution)., An additional run was also applied to active galaxies (as indicated by X-ray or Radio observations) that have a bright nucleus in near-IR (corresponding to a point source at our resolution).
 Phese galaxies are NOGCS63. NGCJ258. C4303 and NOGCHA35.," These galaxies are NGC863, NGC4258, NGC4303 and NGC4435."
 In these cases we model. the nucleus as a PSE., In these cases we model the nucleus as a PSF.
 L is not always clear whether introducing he PSE component improves the model or not and for this reason we provide two models for some active galaxies. one with and one without the PSE.," It is not always clear whether introducing the PSF component improves the model or not and for this reason we provide two models for some active galaxies, one with and one without the PSF."
" Table 4 lists the main xolile for cach galaxy. which is used to derive the Miu, Lon relations while Table 5. shows the alternative profile information."," Table \ref{table:properties} lists the main profile for each galaxy, which is used to derive the $M_{\rm bh}$ $L,n$ relations while Table \ref{table:secproperties} shows the alternative profile information."
 Alassive elliptical. and bulge galaxies often exhibit partially depleted: cores. (ic. deviations of the profile in the inner regions). this phenomena is well known and the innermost regions (1-5 per cent of the elfective radius) often deviate. see for example and.," Massive elliptical and bulge galaxies often exhibit partially depleted cores (i.e. deviations of the profile in the inner regions), this phenomena is well known and the innermost regions (1-5 per cent of the effective radius) often deviate, see for example and."
?.. While there is relatively little flux involved. their. presence. can. cause xuticular οΠουτος in measuring an accurate Sórrsic index., While there is relatively little flux involved their presence can cause particular difficulties in measuring an accurate Sérrsic index.
 In Section 8.2 we present cdillerent methods used by previous studies to fit the core galaxies., In Section \ref{sec:IG} we present different methods used by previous studies to fit the core galaxies.
 does not provide a unction to model the depleted. cores but if we ignore the existence of the core structure and. mocel tb1e core galaxies with a single Sérrsic model we will erroneousy weight the fit o mocel the inner high signal-to-noise core., does not provide a function to model the depleted cores but if we ignore the existence of the core structure and model the core galaxies with a single Sérrsic model we will erroneously weight the fit to model the inner high signal-to-noise core.
 In these galaxies where the original profiles showed distinct. departures in he inner regions we elect to mask., In these galaxies where the original profiles showed distinct departures in the inner regions we elect to mask.
 For these systenis. indicated in Table 3.. we implement a mask ancl re-profile and eracdually increase the mask size until a stable outcome is founcl.," For these systems, indicated in Table \ref{table:mask}, we implement a mask and re-profile and gradually increase the mask size until a stable outcome is found."
 Table 3. Col 3 shows the final mask sizes in units of the elective radius for each of our galaxies and no obvious correlation or rule of thumb is seen., Table \ref{table:mask} Col 3 shows the final mask sizes in units of the effective radius for each of our galaxies and no obvious correlation or rule of thumb is seen.
 We conclude that masking is critical for the recovery of an accurate Sérrsic index but actually alfects the bulge luminosity relatively little as the majority of the Hux lies outside t10 COLE Le@ion., We conclude that masking is critical for the recovery of an accurate Sérrsic index but actually affects the bulge luminosity relatively little as the majority of the flux lies outside the core region.
 Also in the case of some bright galaxies the center of the galaxy has been saturated and as a result an artificial drop of counts appears., Also in the case of some bright galaxies the center of the galaxy has been saturated and as a result an artificial drop of counts appears.
 Here too we overcome |16 problem of the saturated. area by masking the data., Here too we overcome the problem of the saturated area by masking the data.
" TEje galaxies to which a core mask has been applied are NGC1068. NGC221. Ναςο. Ναςτε. NOGC4473. NOCALSG, ΝαςΕΛ. NOC4621. NOC4649. Ναςστο Νας519. σας250 ane εςτου."," The galaxies to which a core mask has been applied are NGC1068, NGC221, NGC4261, NGC4374, NGC4473, NGC4486, NGC4486A, NGC4621, NGC4649, NGC5576, NGC5813, NGC5846 and UGC9799."
 When the minimisation is complete. produces FIPS files for the original image. the model. the residua and the individual images for cach componeri.," When the minimisation is complete, produces FITS files for the original image, the model, the residual and the individual images for each component."
 Το visually examine the goodness of the fit we use to produce a profile of both the input galaxy. the fi and the each sub-component.," To visually examine the goodness of the fit we use to produce a profile of both the input galaxy, the fit and the each sub-component."
 This process ensures tha the data ancl models are inspected. in an identical manner with the position angle and the axis ratio of the ellipses were fixed to the values that has estimated for the bulge/spheroid., This process ensures that the data and models are inspected in an identical manner with the position angle and the axis ratio of the ellipses were fixed to the values that has estimated for the bulge/spheroid.
 We placed. the resulting ellipses onto both the model image and the sub-component images of the, We placed the resulting ellipses onto both the model image and the sub-component images of the
that low mass stars formation appear to run independently of the formation of massive stars.,that low mass stars formation appear to run independently of the formation of massive stars.
 This may be due to the fact that even in a big cloud that is subdivided into smaller sub-units. massive stars can only form inside the larger cells whereas low-mass stars may form readily in smaller cells.," This may be due to the fact that even in a big cloud that is subdivided into smaller sub-units, massive stars can only form inside the larger cells whereas low-mass stars may form readily in smaller cells."
 If the bulk of the mass in the interstellar medium is not in the form of massive clouds. it is possible that the formation of low mass stars be quite active in regions which are not marked by the presence of massive stars.," If the bulk of the mass in the interstellar medium is not in the form of massive clouds, it is possible that the formation of low mass stars be quite active in regions which are not marked by the presence of massive stars."
 It Is also possible that under suitable conditions this separate channel of low mass star formation be the dominant process to form stars., It is also possible that under suitable conditions this separate channel of low mass star formation be the dominant process to form stars.
 Within this scenario. it is clear that measuring the star formation rates of external galaxies. especially in low surface density galaxies. on the basis of massive star diagnostics (be it direct detection of OB. stars. optical and radio emission from HII regions. or their secondary far-infrared radiation for highly opaque clouds). may indeed lead to gross underestimates and to misleading results on the nature and the evolution of galaxies.," Within this scenario, it is clear that measuring the star formation rates of external galaxies, especially in low surface density galaxies, on the basis of massive star diagnostics (be it direct detection of OB stars, optical and radio emission from HII regions, or their secondary far-infrared radiation for highly opaque clouds), may indeed lead to gross underestimates and to misleading results on the nature and the evolution of galaxies."
 In order to clarify these issues one should intensively and systematically study regions of local galaxies. selected in an unbiassed way. where low mass stars can be individually detected and characterized. so as to determine their physical parameters including mass. luminosity. age and evolutionary status.," In order to clarify these issues one should intensively and systematically study regions of local galaxies, selected in an unbiassed way, where low mass stars can be individually detected and characterized, so as to determine their physical parameters including mass, luminosity, age and evolutionary status."
 This can be done not only in our galaxy and. even better. in the Magellanic Clouds in which all stars are approximately at the same distance from us. but also in many other galaxies of the Local Group.," This can be done not only in our galaxy and, even better, in the Magellanic Clouds in which all stars are approximately at the same distance from us, but also in many other galaxies of the Local Group."
 For this purpose. in addition to a number of regions with obvious signs of active star formation. such as the Orion Nebula Cluster (Da Rio et al.," For this purpose, in addition to a number of regions with obvious signs of active star formation, such as the Orion Nebula Cluster (Da Rio et al."
 2010b. and in preparation) and 33603 in our Galaxy (Beccar et al.," 2010b, and in preparation) and 3603 in our Galaxy (Beccari et al."
 2010). DDor (De Marchi et al.," 2010), Dor (De Marchi et al."
" 2011) and other selected fields in the LMC. and 3346 and 6602 in the SMC. we are also analysing a sample of fields selected from the Archival Pure Parallel that were imaged with the HST-WFPC? in four broad-band filters (F300W. F450W. F606W, and FS81I4W) and a narrow Ho filter (F656N) with a total exposure time of at least 3 orbits. 1e. about 160 minutes (Spezzi et al."," 2011) and other selected fields in the LMC, and 346 and 602 in the SMC, we are also analysing a sample of fields selected from the Archival Pure Parallel that were imaged with the HST-WFPC2 in four broad-band filters (F300W, F450W, F606W, and F814W) and a narrow $\alpha$ filter (F656N) with a total exposure time of at least 3 orbits, i.e. about 160 minutes (Spezzi et al."
 2011)., 2011).
" Although these fields are still not completely ""random"" and ""unbiased"". since they were imaged in parallel with long UV spectroscopic. observations of OB stars taken. with. another HST instrument about tto aaway. they still represent a relatively rich. sample (about 20 fields in each LMC and SMC) of regions with generally marginal massive star formation."," Although these fields are still not completely “random” and “unbiased”, since they were imaged in parallel with long UV spectroscopic observations of OB stars taken with another HST instrument about to away, they still represent a relatively rich sample (about 20 fields in each LMC and SMC) of regions with generally marginal massive star formation."
 For the future it would be helpful to obtain complementary Ha observations of HST archival fields with deep exposures in the V and / bands. at least. as well as to target suitably selected new fields in the Milky Way and in the Magellanic Clouds.," For the future it would be helpful to obtain complementary $\alpha$ observations of HST archival fields with deep exposures in the $V$ and $I$ bands, at least, as well as to target suitably selected new fields in the Milky Way and in the Magellanic Clouds."
 We have studied the properties of the stellar populations in the field of the 3346 cluster in the Small Magellanic Cloud. using the results of a novel self-consistent method that provides a reliable identification of PMS objects actively undergoing mass accretion. regardless of their age.," We have studied the properties of the stellar populations in the field of the 346 cluster in the Small Magellanic Cloud, using the results of a novel self-consistent method that provides a reliable identification of PMS objects actively undergoing mass accretion, regardless of their age."
 We have used the age and other physical parameters measured for these PMS stars to study how star formation has proceeded across time and space in 3346 over the past ~30 MMyr.," We have used the age and other physical parameters measured for these PMS stars to study how star formation has proceeded across time and space in 346 over the past $\sim
30$ Myr."
 The main results of this work can be summarised as follows., The main results of this work can be summarised as follows.
1993) have concentrated on the large-scale bends seen in he tails.,1993) have concentrated on the large-scale bends seen in the tails.
 Lt is instructive to ask a rather cilferent question: why are these sources. with well-collimated. strong-Iavour jets. compact hot spots. and high radio luminosities. not classical double radio galaxies?," It is instructive to ask a rather different question: why are these sources, with well-collimated strong-flavour jets, compact hot spots, and high radio luminosities, not classical double radio galaxies?"
 In ΤΠ objects of this radio »ower. radio-emitting plasma is thought to How back from he hot spots into the cocoon' left behind as the hot spot and. associated shocks propagate into the external medium. orming the radio lobes SScheuer 1974: Williams 1991).," In FRII objects of this radio power, radio-emitting plasma is thought to flow back from the hot spots into the `cocoon' left behind as the hot spot and associated shocks propagate into the external medium, forming the radio lobes Scheuer 1974; Williams 1991)."
 In WATS. thejet appears to terminate in a shock in the same wav.," In WATs, the jet appears to terminate in a shock in the same way."
 Norman ((1088) argue that strong shocks are necessary to explain he single-step transition between jets and plumes. anc observations of compact hot spots in these objects. such as that seen in 1130. support this model.," Norman (1988) argue that strong shocks are necessary to explain the single-step transition between jets and plumes, and observations of compact hot spots in these objects, such as that seen in 130, support this model."
 However. the situation after the shock is cüllerent in the two classes of object.," However, the situation after the shock is different in the two classes of object."
 La WATS lobes are not formed., In WATs lobes are not formed.
 Instead. the hot spo is at the base of the tail: by analogy with the standard moce for FRIIS. we may assume that the emitting material in the tail has passed through and been excited in the hot spot. anc this is borne out by the spectral index results in 1130.," Instead, the hot spot is at the base of the tail; by analogy with the standard model for FRIIs, we may assume that the emitting material in the tail has passed through and been excited in the hot spot, and this is borne out by the spectral index results in 130."
 The tails may immediately deviate from the axis defined by the jets Ss3C465)) or appear to continue in a straight line 5853C130)) but in no case does there appear to be lobe emission.significantly closer to. the core than the hot The fact that there is no cocoon may explain the brightness and two-sidedness of the strong-avour jets in WATS compared. to those in. Els: a direct. interaction with the (comparatively dense) external medium might be expected to make the beam more dissipative and. perhaps to slow the regions of the beam responsible for the emission to only weakly relativistic velocities., The tails may immediately deviate from the axis defined by the jets ) or appear to continue in a straight line ) but in no case does there appear to be lobe emission closer to the core than the hot The fact that there is no cocoon may explain the brightness and two-sidedness of the strong-flavour jets in WATs compared to those in FRIIs; a direct interaction with the (comparatively dense) external medium might be expected to make the beam more dissipative and perhaps to slow the regions of the beam responsible for the emission to only weakly relativistic velocities.
 This would explain the low values (0.20) of jet velocity estimated. from. sidedness by O'Donoghue ((1993) compared to the much higher values. 0.7¢) estimated from the sidedness of jets in ΕΠΗ quasars (Bericlle 11994: Wardle Aaron 1997) and their prominence and sidedness in ΕΠΗ radio galaxies (Llarcleastle in. prep.)., This would explain the low values $0.2c$ ) of `jet velocity' estimated from sidedness by O'Donoghue (1993) compared to the much higher values $0.7c$ ) estimated from the sidedness of jets in FRII quasars (Bridle 1994; Wardle Aaron 1997) and their prominence and sidedness in FRII radio galaxies (Hardcastle in prep.).
 Hardcastle ((1997a) proposed a similar explanation for the prominence and. tvo-sidedness of the jets in the peculiar PRIDE 4438., Hardcastle (1997a) proposed a similar explanation for the prominence and two-sidedness of the jets in the peculiar FRII 438.
 However. in the absence of classical double lobes ancl the associated discontinuity between radio-emitting plasma and shocked external medium. why are there jet. termination shocks in WATS?," However, in the absence of classical double lobes and the associated discontinuity between radio-emitting plasma and shocked external medium, why are there jet termination shocks in WATs?"
 ]t is well known that the cilference between WATS aux classical doubles is the local environment: whereas WATS always lie at the centres of clusters. FRIL radio galaxies of comparable powers tend to avoid them PPrestage 'eacock 1988).," It is well known that the difference between WATs and classical doubles is the local environment; whereas WATs always lie at the centres of clusters, FRII radio galaxies of comparable powers tend to avoid them Prestage Peacock 1988)."
 An explanation for the peculiar properties of WATS compared to their classical double counterparts nius urn on this environmental dillerence., An explanation for the peculiar properties of WATs compared to their classical double counterparts must turn on this environmental difference.
 A suggestion along hese lines by Leahy (1984). applied. to465... invokec motion of the galaxy through the cluster. causing it to leave »Dhind a passive wake of radio-emitting material: in this vpe of model the post-hot-spot material is left. behind. by he motion of the galaxy and so never forms a lobe.," A suggestion along these lines by Leahy (1984), applied to, invoked motion of the galaxy through the cluster, causing it to leave behind a passive wake of radio-emitting material; in this type of model the post-hot-spot material is left behind by the motion of the galaxy and so never forms a lobe."
 However. he motions of central cluster galaxies are not expected to x: large (Elek 1984: Pinkney 11993 and references therein) and in any case such a model cannot account. without invoking projection ellects implausibly often. for the large population of WATs in which one or both tails are more or less aligned with the inner jets (as in 1130).," However, the motions of central cluster galaxies are not expected to be large (Eilek 1984; Pinkney 1993 and references therein) and in any case such a model cannot account, without invoking projection effects implausibly often, for the large population of WATs in which one or both tails are more or less aligned with the inner jets (as in 130)."
 Jurns ((1904) suggest à model in which WATS have an origin in the merger of a cluster with a group or subcluster., Burns (1994) suggest a model in which WATs have an origin in the merger of a cluster with a group or subcluster.
 This is motivatecl by the X-ray. substructure which they find in many WAT host clusters., This is motivated by the X-ray substructure which they find in many WAT host clusters.
 Large-scale. high-velocity residual motions of gas could then be responsible for the bending of the radio tails. while the merger would. provide tidallv stripped gas to fuel the AGN.," Large-scale, high-velocity residual motions of gas could then be responsible for the bending of the radio tails, while the merger would provide tidally stripped gas to fuel the AGN."
 In an extension of this work Commez ((1997) show that the majority of WAT hosts in a larger sample show some X-ray substructure. with an alignment tween the direction. of the X-ray elongation. ancl the angle that bisects the tails. consistent with such a model.," In an extension of this work Gómmez (1997) show that the majority of WAT hosts in a larger sample show some X-ray substructure, with an alignment between the direction of the X-ray elongation and the angle that bisects the tails, consistent with such a model."
 1130. however. is clearly a WAT despite the location of its jost at the centre of a smooth. approximately symmetrical istribution. of N-rav. emitting gas and its (apparently) μαraight tails.," 130, however, is clearly a WAT despite the location of its host at the centre of a smooth, approximately symmetrical distribution of X-ray emitting gas and its (apparently) straight tails."
 Lt appears that strong cluster inhomogeneity. rough it may be necessary for bent tail formation. is not necessary for the existence of a WAT: in particular it does not. on its own. explain the jet shock/hot spot behaviour iscussed above.," It appears that strong cluster inhomogeneity, though it may be necessary for bent tail formation, is not necessary for the existence of a WAT; in particular it does not, on its own, explain the jet shock/hot spot behaviour discussed above."
 Loken ((1995) discuss the physies of a jet propagating across the boundary. between the interstellar medium of the host ealaxy and the hotter. less dense intracluster medium. and gsugeest that this may be the reason for the disruption of 1f inner. well-collimated jet at. a hot. spot.," Loken (1995) discuss the physics of a jet propagating across the boundary between the interstellar medium of the host galaxy and the hotter, less dense intracluster medium, and suggest that this may be the reason for the disruption of the inner, well-collimated jet at a hot spot."
 Vhev then postulate velocity shear across the boundary. as described above. to account for jet bending.," They then postulate velocity shear across the boundary, as described above, to account for jet bending."
 The structures seen in numerical simulation when the jet simply crosses a contact discontinuity with crosswind co not resemble WATS strongly. however.," The structures seen in numerical simulation when the jet simply crosses a contact discontinuity with crosswind do not resemble WATs strongly, however."
 I£the jets are taken to cross a shock front instead NNorman 11955) then the simulations of Loken aare more convincing in their resemblance to WATS. but we again face the problem of the smoothness of the large-scale X-ray emission in 1130: there is little evidence in this source for the recent cluster merger that Loken," If the jets are taken to cross a shock front instead Norman 1988), then the simulations of Loken are more convincing in their resemblance to WATs, but we again face the problem of the smoothness of the large-scale X-ray emission in 130; there is little evidence in this source for the recent cluster merger that Loken"
ἂν has first been derived by Schramm (1990). by using the known force field for a homogenous ellipsoid and letting the largest axis go to infinity in order to get the corresponding 2-dimensional equations.,$\vec {\balpha}_0$ has first been derived by Schramm \shortcite {Schramm1990} by using the known force field for a homogenous ellipsoid and letting the largest axis go to infinity in order to get the corresponding 2-dimensional equations.
 To derive the potential co in ternis of real-numboered: coordinates 01.065. we applied Schraumm's method to the results by Plenniger (1984). for the potential and force. fields. of 3-dimensional Ferrers ellipsoids.," To derive the potential $\psi_0$ in terms of real-numbered coordinates $\theta_1,
\theta_2$, we applied Schramm's method to the results by Pfenniger \shortcite {Pfenniger1984} for the potential and force fields of 3-dimensional Ferrers ellipsoids."
 This enables us to calculate deflection potential and. dellection angles for a whole family of Ferrers profiles., This enables us to calculate deflection potential and deflection angles for a whole family of Ferrers profiles.
 Ehe dellection potential for Ferrers surface.density. profiles with integer exponents À is given by The corresponding 3-dimensional expression. was first. (1877).. (D3), The deflection potential for Ferrers surface–density profiles with integer exponents $\lambda$ is given by The corresponding 3-dimensional expression was first \shortcite {Ferrers1877}. \ref {q00})
): (1984) (B6)). (D4)), \shortcite {Pfenniger1984} \ref {psi_mu}) \ref {rho})
and removed the fit on all scales.,and removed the fit on all scales.
" When we carry out the same analysis, we find a Poisson noise ~ 5x10?Jy?/sr, in agreement with them."," When we carry out the same analysis, we find a Poisson noise $\sim$ $\times 10^3$ $^2$ /sr, in agreement with them."
 We conclude that they overestimated the cirrus contribution by removing a power law on all scales applying a fit only at large scales., We conclude that they overestimated the cirrus contribution by removing a power law on all scales applying a fit only at large scales.
 The power-law fit is indeed contaminated by CIB anisotropies., The power-law fit is indeed contaminated by CIB anisotropies.
" Using the same method as in Sect. ??,,"," Using the same method as in Sect. \ref{par:GC_100},"
 we remove the cirrus emission from the ELAIS N1/MIPS map at 160 um. We compute the hybrid power spectrum with a cut at k=0.05 arcmin™!., we remove the cirrus emission from the ELAIS N1/MIPS map at 160 $\mu$ m. We compute the hybrid power spectrum with a cut at $k=0.05$ $^{-1}$.
 Fig., Fig.
 16 shows the total power spectrum (black) and the cirrus-free one (red)., \ref{fig:pk_cib+cirrus} shows the total power spectrum (black) and the cirrus-free one (red).
 We clearly see the difference only on the largest scales available with this map., We clearly see the difference only on the largest scales available with this map.
" We also plot our fit to the clustering power spectrum from ?) in blue, and the shot noise level in black."," We also plot our fit to the clustering power spectrum from \citet{2007ApJ...665L..89L} in blue, and the shot noise level in black."
 The green line shows the sum of the two-component fits., The green line shows the sum of the two-component fits.
 We also compare our resulting power spectrum to that of ?) in Fig. 17.., We also compare our resulting power spectrum to that of \citet{2007ApJ...665L..89L} in Fig. \ref{fig:cib_fin}. .
" These power spectra are in very good agreement for k> 0.03 arcmin!, where they are dominated by the CIB anisotropies (both clustering and Poisson noise)."," These power spectra are in very good agreement for $k>$ 0.03 $^{-1}$, where they are dominated by the CIB anisotropies (both clustering and Poisson noise)."
" On scales « 0.01 arcmin!, there is more power in the ?) power spectrum because it contains the cirrus contribution (the blue dashed line is their estimate of the power spectrum of the cirrus)."," On scales $<$ 0.01 $^{-1}$, there is more power in the \citet{2007ApJ...665L..89L} power spectrum because it contains the cirrus contribution (the blue dashed line is their estimate of the power spectrum of the cirrus)."
" We can see that using data, we are able to extend the measurement of the correlated fluctuations to large scales."," We can see that using data, we are able to extend the measurement of the correlated fluctuations to large scales."
" This shows that making use of data at 21 cm is an efficient way of removing the contamination of the Galactic We can also use our data and emissivity measurements to compute the absolute level of the CIB at 160 µπι. We consider the two TPMs ofSpitzer archival observations (26961920 26962432) of the ELAIS N1 field that were designed to cross-check the calibration of the diffuse emission at 160 um. Even with a cryogenic telescope such asSpitzer, there is a small component of thermal emission at longer wavelengths that contaminates the standard photometric observations."," This shows that making use of data at 21 cm is an efficient way of removing the contamination of the Galactic We can also use our data and emissivity measurements to compute the absolute level of the CIB at 160 $\mu$ m. We consider the two TPMs of archival observations (26961920 26962432) of the ELAIS N1 field that were designed to cross-check the calibration of the diffuse emission at 160 $\mu$ m. Even with a cryogenic telescope such as, there is a small component of thermal emission at longer wavelengths that contaminates the standard photometric observations."
 The TPM mode by-passes the effects of this spurious radiation by comparing the emission of the target (sky) with that of an internal dark to provide an absolute measurement (see MIPS Handbook $ 3.1.12)., The TPM mode by-passes the effects of this spurious radiation by comparing the emission of the target (sky) with that of an internal dark to provide an absolute measurement (see MIPS Handbook $\S$ 3.1.12).
 This mode was designed precisely to observe relatively faint extended emission regions., This mode was designed precisely to observe relatively faint extended emission regions.
 The TPM observations that we used are discussed in Sect. ??.., The TPM observations that we used are discussed in Sect. \ref{par:tpmobs}.
 There is an HVC in TPM 1 and only the local component in TPM 2 as shown on Fig. 18.., There is an HVC in TPM 1 and only the local component in TPM 2 as shown on Fig. \ref{fig: tpm_sur_gbt}.
 We first compare the MIPS scan map values to the TPMs., We first compare the MIPS scan map values to the TPMs.
" By first subtracting the map values from those of the TPMs (see Table 4)), we determine the offset of the scan map from each TPM position."," By first subtracting the map values from those of the TPMs (see Table \ref{tab:tpm}) ), we determine the offset of the scan map from each TPM position."
" They are in good agreement in the two regions with an average offset of -2.05+0.24 MJy/sr, which hasno consequences for the power spectrum estimate as well as on the CIB level determination"," They are in good agreement in the two regions with an average offset of $\pm$ 0.24 MJy/sr, which hasno consequences for the power spectrum estimate as well as on the CIB level determination"
πα aare robust.,and are robust.
 For NGC S21 we see a similar οσοι., For NGC 821 we see a similar effect.
 Our observation that the line strength. eradients. are constant out to laree radii provides constraints for the mereer and star formation history of the galaxy., Our observation that the line strength gradients are constant out to large radii provides constraints for the merger and star formation history of the galaxy.
 After a eas-rich merger. star formation in the central regions of the remnant is expected to steepen the eradients. while at larger radii violent relaxation Hlattens them. though over time (~3 Cyr) the steep. gradients in the central part get weaker (Llopkins et al. 2009a::," After a gas-rich merger, star formation in the central regions of the remnant is expected to steepen the gradients, while at larger radii violent relaxation flattens them, though over time $\sim
3$ Gyr) the steep gradients in the central part get weaker (Hopkins et al. \nocite{2009ApJS..181..135H};"
 Hopkins et al. 2009b))., Hopkins et al. \nocite{2009ApJS..181..486H}) ).
 Using the stellar population models of Thomas. Maraston 3encler and Schiavon (2007).. we explore the single stellar population (SSP) equivalent age and. metallicity in NGC 3379 and. NGC S21 at large. radii.," Using the stellar population models of Thomas, Maraston Bender \nocite{2003MNRAS.339..897T} and Schiavon \nocite{2007ApJS..171..146S}, we explore the single stellar population (SSP) equivalent age and metallicity in NGC 3379 and NGC 821 at large radii."
 Following the aproach of Thomas ct al., Following the aproach of Thomas et al.
 we define an abundance ratio insensitive metallicity index similar to their Mele] index by using the aand Fe5015 indices available from SAURON. , \nocite{2003MNRAS.339..897T} we define an abundance ratio insensitive metallicity index similar to their [MgFe]' index by using the and Fe5015 indices available from SAURON. [
MgEe50] is defined as: The scaling factor for the iindex was optimized such that the mean dillerence between solar ancl non-solar ratio model predictions from Thomas et al.,MgFe50]' is defined as: The scaling factor for the index was optimized such that the mean difference between solar and non-solar ratio model predictions from Thomas et al.
 is zero., \nocite{2003MNRAS.339..897T} is zero.
 In Figure 9. we plot this index versus and compare with the mocdels., In Figure \ref{fig:lick_model} we plot this index versus and compare with the models.
 Even though the models of Thomas οἱ al., Even though the models of Thomas et al.
 and Schiavon are constructed independently. using clilferent stellar libraries ancl fitting functions. they give the same results for our data at large radii.," \nocite{2003MNRAS.339..897T} and Schiavon \nocite{2007ApJS..171..146S} are constructed independently, using different stellar libraries and fitting functions, they give the same results for our data at large radii."
 For NGC 3379 we find that at 3 - 4 Ao. the stellar population is consistent with an old (12 Cyr) population. and metal-poor. with Z/LI] slightly below 20 per cent of the solar metallicitv.," For NGC 3379 we find that at 3 - 4 $R_e$, the stellar population is consistent with an old (12 Gyr) population, and metal-poor, with [Z/H] slightly below 20 per cent of the solar metallicity."
 We note however that the uncertainty in these values is rather large., We note however that the uncertainty in these values is rather large.
 For NGC 821. we find that at 1 I. the stellar population is of the same age and metallicity range as obtained from the outer bins of the SAUION central field (~ 0.6 1).," For NGC 821, we find that at 1 $R_e$ the stellar population is of the same age and metallicity range as obtained from the outer bins of the SAURON central field $\sim$ 0.6 $R_e$ )."
 Stellar population mocels predict a decrease in stellar mass-to-lieht ratio ML if the metallicity of the stellar population decreases. since the stars then become bluer ancl therefore brighter in the optical.," Stellar population models predict a decrease in stellar mass-to-light ratio $M_*/L$ if the metallicity of the stellar population decreases, since the stars then become bluer and therefore brighter in the optical."
" For instance. for a change in metallicity from 0.0 to -0.84 at a constant age of 10 Gyr (consistent with our. observervations). AL,fL decreases by about 23 per cent in the models of Maraston (2005)..."," For instance, for a change in metallicity from 0.0 to -0.84 at a constant age of 10 Gyr (consistent with our observervations), $M_*/L$ decreases by about 23 per cent in the models of Maraston \nocite{2005MNRAS.362..799M}."
 Llowever. for increasing stellar age at constant metallicity. AL./L also increases.," However, for increasing stellar age at constant metallicity, $M_*/L$ also increases."
 Civen this degeneracy ancl uncertainties. we adopt a constant stellar Al/L while constructing the dynamical mass models that we present in the next section.," Given this degeneracy and uncertainties, we adopt a constant stellar $M/L$ while constructing the dynamical mass models that we present in the next section."
 Furthermore. Al./£ depends strongly on ((sec e.g. Cappellari et al. 20062).," Furthermore, $M_*/L$ depends strongly on (see e.g. Cappellari et al. \nocite{2006MNRAS.366.1126C}) )."
 Since the pprofiles in our galaxies are nearly [lat out to large radii variations in M./£ are most likely small.," Since the profiles in our galaxies are nearly flat out to large radii, variations in $M_*/L$ are most likely small."
 To explore whether our data of NGC 3379 and NGC 821 are consistent with a dark matter halo. we mocel these galaxies with the triaxial Schwarzschild code presented. by van den Bosch et al.," To explore whether our data of NGC 3379 and NGC 821 are consistent with a dark matter halo, we model these galaxies with the triaxial Schwarzschild code presented by van den Bosch et al."
 Orbits are caleulatecd within an a priori specified triaxial potential. and. a superposition of," \nocite{2008MNRAS.385..647V} Orbits are calculated within an a priori specified triaxial potential, and a superposition of"
by Petersen et al. (,by Petersen et al. (
2007). (007b).,"2007a), (2007b)."
 In this case compressional waves can eventually lead to. the development of persistent vortical structures of different polarity., In this case compressional waves can eventually lead to the development of persistent vortical structures of different polarity.
 Hence. high frequency oscillations of the P mode can participate in the generation of anticyclonic vortices that further accelerate dust trapping and planetesimal formation in protoplanetary dises with equilibrium entropy decreasing radially outwards.," Hence, high frequency oscillations of the P mode can participate in the generation of anticyclonic vortices that further accelerate dust trapping and planetesimal formation in protoplanetary discs with equilibrium entropy decreasing radially outwards."
 Using the local linear approximation we have shown the possibility of the potential vorticity generation in flows with both. positive and negative radial entropy gradients (Richardson numbers}.," Using the local linear approximation we have shown the possibility of the potential vorticity generation in flows with both, positive and negative radial entropy gradients (Richardson numbers)."
 In fact. the standard alpha description of the accretion discs implies radial stratification of entropy and hence. weak baroclinic decay of existing vortices.," In fact, the standard alpha description of the accretion discs implies radial stratification of entropy and hence, weak baroclinic decay of existing vortices."
 In this case there will be a competition between the “baroclinic viscosity” and potential vorticity generation due to mode conversion., In this case there will be a competition between the “baroclinic viscosity” and potential vorticity generation due to mode conversion.
 Hence. it is not strictly overruled that a significant amount of compressional perturbations can lead to the development of anticyclonic vortices even in flows with positive entropy gradients.," Hence, it is not strictly overruled that a significant amount of compressional perturbations can lead to the development of anticyclonic vortices even in flows with positive entropy gradients."
 In this case. radial stratification opens an additional degree of freedom for velocity shear induced mode conversion to operate.," In this case, radial stratification opens an additional degree of freedom for velocity shear induced mode conversion to operate."
 Although. the viability of this scenario needs further investigation.," Although, the viability of this scenario needs further investigation."
 This paper presents the results obtained within the linear shearing sheet approximation., This paper presents the results obtained within the linear shearing sheet approximation.
 At nonlinear amplitudes. the P mode leads to the development of shock waves.," At nonlinear amplitudes, the P mode leads to the development of shock waves."
 These shocks induce local heating in the flow., These shocks induce local heating in the flow.
 Therefore. a realistic picture of entropy production and vortex. development in radially stratified. disces with significant amount of compressible perturbations needs to be analyzed by direct numerical simulations.," Therefore, a realistic picture of entropy production and vortex development in radially stratified discs with significant amount of compressible perturbations needs to be analyzed by direct numerical simulations."
 A.G.T. was supported by GNSF/PRES-07/153., A.G.T. was supported by GNSF/PRES-07/153.
 A.G.T. would like to acknowledge the hospitality of Osservatorio Astronomico di Torino., A.G.T. would like to acknowledge the hospitality of Osservatorio Astronomico di Torino.
 This work is supported in part by ISTC grant G-1217., This work is supported in part by ISTC grant G-1217.
 Here we present the approximations used to derive the analytic form of the initial conditions corresponding to individual modes in radially stratified. shear flows., Here we present the approximations used to derive the analytic form of the initial conditions corresponding to individual modes in radially stratified shear flows.
 These conditions are used to construct the initial values of perturbations in the numerical integration of the ODEs governing the linear dynamics of perturbations in these flows., These conditions are used to construct the initial values of perturbations in the numerical integration of the ODEs governing the linear dynamics of perturbations in these flows.
 We employ different methods for high and low frequency modes., We employ different methods for high and low frequency modes.
" P-mode perturbations are intrinsically high frequency and well separated from low frequency modes everywhere outside the coupling region Ayfh,«1l.", P-mode perturbations are intrinsically high frequency and well separated from low frequency modes everywhere outside the coupling region $k_x/k_y < 1$.
 In order to construct P-mode perturbations we use convective eigenfunction derived in. the shearless limit and account for shear flow effects only in the adiabatic limit: where Although this form of the eigenfunction is not valid function for describing W and S modes individually in a sheared medium. it has proved to be a good tool for excluding both modes from the initial spectrum: Assuming that we are looking for P-mode perturbations with Wave-numbers satisfying the condition (0)Αν1 we may use the zero potential vorticity condition: Hence. Εως. C," In order to construct P-mode perturbations we use convective eigenfunction derived in the shearless limit and account for shear flow effects only in the adiabatic limit: where Although this form of the eigenfunction is not valid function for describing W and S modes individually in a sheared medium, it has proved to be a good tool for excluding both modes from the initial spectrum: Assuming that we are looking for P-mode perturbations with wave-numbers satisfying the condition $ k_x(0)/k_y \gg 1 $ we may use the zero potential vorticity condition: Hence, Eqs. ("
"A3.A4) yield the full set of initial conditions for the high frequency P-mode SFH of perturbations: where /% and (, are free parameters corresponding to the two P-modes in the system.","A3,A4) yield the full set of initial conditions for the high frequency P-mode SFH of perturbations: where $P_0$ and $U_0$ are free parameters corresponding to the two P-modes in the system."
 Specific values of these two parameters, Specific values of these two parameters
The observation vector is constructed from the eain tables of the array obtained using calibrators 00407-658 51). OO9IS-LIS (83) and L1932-464 (8).,"The observation vector is constructed from the gain tables of the array obtained using calibrators 0407-658 ${\mathcal{S}^{}_{1}}$ ), 0915-118 ${\mathcal{S}^{}_{2}}$ ) and 1932-464 ${\mathcal{S}^{}_{3}}$ )."
 The sensitivity per baseline at NITE is 26 Jv for a 1 .MIIZ bandwidth and an integration time of one second., The sensitivity per baseline at MRT is $\sim 26$ Jy for a 1 MHz bandwidth and an integration time of one second.
 It takes ~LO minutes of time for sources at 6=40 to transit a 2° primary beamwidth of elements in the cast-west array., It takes $\sim 10$ minutes of time for sources at $\delta = -40^\circ$ to transit a $^\circ$ primary beamwidth of elements in the east-west array.
 This leads to a sensitivity per baseline (including the non-uniform weighting due to primary beam) of ~2 Jy., This leads to a sensitivity per baseline (including the non-uniform weighting due to primary beam) of $\sim 2$ Jy.
 Phe flux density of these three calibrators as seen by MEE is ~100 Jv: strong to get reliable calibration., The flux density of these three calibrators as seen by MRT is $\sim 100$ Jy; strong to get reliable calibration.
 Further. the calibrators are unresolved and isolated from confusing sources and have well known measured. positions (Ciolap1998).," Further, the calibrators are unresolved and isolated from confusing sources and have well known measured positions \citep{thesis:golap98}."
 A plot of typical phase cillerences obtained: using the pair of calibrators SsandS4 is shown in Fig. 7..," A plot of typical phase differences obtained using the pair of calibrators ${\mathcal{S}^{}_{2}}\,\,\mbox{and}\,\,{\mathcal{S}^{}_{3}}$ is shown in Fig. \ref{f:phasediff}."
 Fig., Fig.
 Saa shows the estimated: errors in 945 NS antenna positions., \ref{f:error_estimate}a a shows the estimated errors in 945 NS antenna positions.
 The errors show a gradient of 1 part in 1000 along the NS arm., The errors show a gradient of 1 part in 1000 along the NS arm.
 This matches with the linear gradients in the phase differences estimated from the calibrators., This matches with the linear gradients in the phase differences estimated from the calibrators.
 The estimates in Fig., The estimates in Fig.
 Sbb show alignment errors of the 32 antennas in the EW arm along the NS-direction., \ref{f:error_estimate}b b show alignment errors of the 32 antennas in the EW arm along the NS-direction.
 Ehe fit shows a gradient of about 2 part in 10.000.," The fit shows a gradient of about 2 part in 10,000."
" ""his indicates that the EW arm is mis-aligned from the true EM-direction.", This indicates that the EW arm is mis-aligned from the true EW-direction.
" At one extreme end (1 km from the centre of the arrav) of the LEW arm he error is 0.2 m. equivalent to an angular distance of ~40"" from the centre of the array."," At one extreme end (1 km from the centre of the array) of the EW arm the error is $\sim 0.2$ m, equivalent to an angular distance of $\sim 40''$ from the centre of the array."
 This is the source of a small sinze-dependent error in à. that was observed. in xh. positional error analysis and the homoeraphy matrix., This is the source of a small $\sin za$ -dependent error in $\alpha$ that was observed in both positional error analysis and the homography matrix.
 Further. our simulation of the svnthesised beam in à with old. EW antenna positions and the corrected EW antenna »ositions indeed Confirm: this sinzea-dependent error in à.," Further, our simulation of the synthesised beam in $\alpha$ with old EW antenna positions and the corrected EW antenna positions indeed confirm this $\sin za$ -dependent error in $\alpha$."
 Using the new antenna positions we have re-imaged one Your from the steradian and have also imaged a completely new steradian., Using the new antenna positions we have re-imaged one hour from the steradian and have also imaged a completely new steradian.
 We find no systematics in. positional errors hus endorsinge our re-estimated array oOg&cometry., We find no systematics in positional errors thus endorsing our re-estimated array geometry.
 The homography-basecl correction. was able to correct. for systematics in positional errors in the image domain and the errors are within of the beamwidth for sources above 15-0., The homography-based correction was able to correct for systematics in positional errors in the image domain and the errors are within of the beamwidth for sources above $\sigma$.
 The corrected images of one steracdian are available for download atALT., The corrected images of one steradian are available for download at.
 Positional error analysis showed that uncorrected NITE images are stretched. in declination by ~1 part in. 1000., Positional error analysis showed that uncorrected MRT images are stretched in declination by $\sim 1$ part in 1000.
 This translates to à compression of the NS baseline vector. in the visibility domain.," This translates to a compression of the NS baseline vector, in the visibility domain."
 Phe analysis also showed a sinza- dependent error in o., The analysis also showed a $\sin za$ -dependent error in $\alpha$.
 This cued towards possible errors in our estimation of the array gcometry., This cued towards possible errors in our estimation of the array geometry.
 By formulating a linear svstem. using instrumental phases estimated. from three well separated: calibrators whose positions are well known. the array geometry was re-estimated.," By formulating a linear system, using instrumental phases estimated from three well separated calibrators whose positions are well known, the array geometry was re-estimated."
 Phe estimated error in the e-component of the NS baseline vectors is about lmm/m.Inother words. the error is about half wavelength at 150 Mllz (1 m) for a 1 km baseline.," The estimated error in the $v$ -component of the NS baseline vectors is about 1 mm/m. In other words, the error is about half a wavelength at 150 MHz (1 m) for a 1 km baseline."
 The estimatesa also show a small (2 part in 10.000) e-component in the purely IN. baseline vectors.," The estimates also show a small (2 part in 10,000) $v$ -component in the purely EW baseline vectors."
" This indicates that the EN arm is mis-aligned. and. inclined at an angle of ~40"". to the true IN. direction."," This indicates that the EW arm is mis-aligned and inclined at an angle of $\sim 40\arcsec$, to the true EW direction."
 These estimates match with the observed stretching of MIVE images shown by both the positional error analysis and the homography matrix., These estimates match with the observed stretching of MRT images shown by both the positional error analysis and the homography matrix.
 Using the new antenna positions we have re-imaged one hour from the steradian and have also imaged a completely new steradian., Using the new antenna positions we have re-imaged one hour from the steradian and have also imaged a completely new steradian.
 We find no svsteniaties in positional errors., We find no systematics in positional errors.
 This endorses our re-estimated array geometry., This endorses our re-estimated array geometry.
 Re-imaging one steradian starting [rom visibilities would have been a verv time consuming exercise., Re-imaging one steradian starting from visibilities would have been a very time consuming exercise.
 Development of 2-D homoeraphy-basec correction enabled: us to correct. for the positional errors in the image domain., Development of 2-D homography-based correction enabled us to correct for the positional errors in the image domain.
 In our view. this now technique will be of relevance to the new generation racio telescopes where. owing to huge data rates. only images after a certain integration would be recorded. as opposed to raw visibilities.," In our view, this new technique will be of relevance to the new generation radio telescopes where, owing to huge data rates, only images after a certain integration would be recorded as opposed to raw visibilities."
derive the HCOΠΟ ratio towards 44945.,derive the $\rm HCO^+/HCO$ ratio towards 4945.
 We [ind that the three derived πω. /IICO. and abundance ratios in (he (wo starbursts. 2253 and 58382. are equivalent within the measurement errors.," We find that the three derived $^+$ $^+$ , $^+$ /HCO, and $^+$ $^+$ abundance ratios in the two starbursts, 253 and 82, are equivalent within the measurement errors."
 The ratios are also in reasonable good agreement to those found in galactic sources with similar FUV fluxes (see Table 3))., The ratios are also in reasonable good agreement to those found in galactic sources with similar FUV fluxes (see Table \ref{tab:ratios}) ).
 Such high abunclances ratios of . IICO. and relative to have been claimed to be the evidence of 882 being mostly dominated by photodissociation.," Such high abundances ratios of $^+$, HCO, and $^+$ relative to $^+$ have been claimed to be the evidence of 82 being mostly dominated by photodissociation."
 We notice that the average IICOμου ratio in 2253 are even lower than that measured in 8832., We notice that the average $\rm HCO^+/HCO$ ratio in 253 are even lower than that measured in 82.
 In the case of HCO. the interferometric maps of 882 clearly resolve the spatial variations in this ratio across the ealaxv nuclear region.," In the case of HCO, the interferometric maps of 82 clearly resolve the spatial variations in this ratio across the galaxy nuclear region."
 However. towards the region of peak ICO emission in (he 852 maps. we find a ratio of ΠοΠΟ~0.12£0.04. equivalent to the average observed towards 2253.," However, towards the region of peak HCO emission in the 82 maps, we find a ratio of $\rm H^{13}CO^+/HCO\sim0.12\pm0.04$, equivalent to the average observed towards 253."
 Our data show that the ISM in the nuclear region in 2253 must be significantly pervaced by a strong UV radiation flux [rom the massive star clusters [ormecl in the starburst. as also suggested by the study of the abundances of the IENCO/CS ratio (Martinetal.2009).," Our data show that the ISM in the nuclear region in 253 must be significantly pervaded by a strong UV radiation flux from the massive star clusters formed in the starburst, as also suggested by the study of the abundances of the HNCO/CS ratio \citep{Martin09}."
. Moreover. (hese new observations would imply that photodissociation plavs a similar role in (he ISAT heating of both 2253 and 5882.," Moreover, these new observations would imply that photodissociation plays a similar role in the ISM heating of both 253 and 82."
 Both UCO /IICO and HCOος abuudance ratios in 11005 are dillerent by a factor 2—3 from those of 2253 and 882., Both $\rm HCO^+/HCO$ and $\rm HCO^+/HOC^+$ abundance ratios in 1068 are different by a factor $2-3$ from those of 253 and 82.
 Furthermore. HCO—/IICO is also found to be up to a factor of ~2 lower in the ring of star formation than towards the nuclear region.," Furthermore, $\rm HCO^+/HCO$ is also found to be up to a factor of $\sim2$ lower in the ring of star formation than towards the nuclear region."
 Likein 2253. these ratios are consistent with (he decrease in the abundance," Likein 253, these ratios are consistent with the decrease in the abundance"
compares the observed field statistics wilh theoretical predictions (to constrain (he emission mechanism responsible lor giant pulses ancl giant micropulses.,compares the observed field statistics with theoretical predictions to constrain the emission mechanism responsible for giant pulses and giant micropulses.
 Growth of plasma waves and radiation in inhomogeneous plasmas. and its propagation between source and observer. naturally results in bursty. Gme-variable radiation.," Growth of plasma waves and radiation in inhomogeneous plasmas, and its propagation between source and observer, naturally results in bursty, time-variable radiation."
 Multiple theories exist for the associated field. statisties. differing due to varving degrees of sell- interaction belween the waves. driving particles. and background plasma. the detailed emission mechanisms producing the waves. (he importance of scattering. and the number of wave populations contributing.," Multiple theories exist for the associated field statistics, differing due to varying degrees of self-consistent interaction between the waves, driving particles, and background plasma, the detailed emission mechanisms producing the waves, the importance of scattering, and the number of wave populations contributing."
 The eiant aud “normal” components of pulsar radio emissions have been discussed in (terms of several collective. (or coherent). emission mechanisms. including: (i) linear plasma instabilities such as curvature enussion and beam instabilities Je.g.. Melrose(1996):Gedalinetal. (2002)]]. (i1) linear mode conversion (Melrose&Gedalin1999:Cairnsetal. 2001).. and (ii) nonlinear modulational instabilities and collapse of wavepackets (Asseo. Sol. Pelletier 1990. Asseo 1996. Weatherall 1997. 1993. llankins et al.," The giant and “normal” components of pulsar radio emissions have been discussed in terms of several collective (or coherent) emission mechanisms, including: (i) linear plasma instabilities such as curvature emission and beam instabilities [e.g., \citet{melrose1996,gedalinetal2002}] ], (ii) linear mode conversion \citep{melrosegedalin1999,cetal2001}, and (iii) nonlinear modulational instabilities and collapse of wavepackets (Asseo, Sol, Pelletier 1990, Asseo 1996, Weatherall 1997, 1998, Hankins et al."
 2003)., 2003).
" Theoretical frameworks considered include sell-organized. criticality SOC] (Baketal.1987:Bak1996:Young&Wenny1996)... stochastic growth theory [SGT] (Robinson1992:Cairns&Robinson1999:2001: 2003a.b).. and nonlinear structures (Pelletier. Sol. Asseo 1955. Asseo 1906, Weatherall 1997. 1993)."," Theoretical frameworks considered include self-organized criticality [SOC] \citep{baketal1987,bak1996,youngkenny1996}, stochastic growth theory [SGT] \citep{r1992,cr1999,rc2001,cetal2001,cetal2002a,cetal2002b}, and nonlinear structures (Pelletier, Sol, Asseo 1988, Asseo 1996, Weatherall 1997, 1998)."
 Other possibilities include refractive lensing events due to propagation through density inhomogeneities (ALA. Walker. personal communication. 2003) and time-variable relativistic beaming effects.," Other possibilities include refractive lensing events due to propagation through density inhomogeneities (M.A. Walker, personal communication, 2003) and time-variable relativistic beaming effects."
 As summarized below. these emission mechanisms and theoretical frameworks predict different field statistics. so Chat comparisons between theory aud observation perimit the emission mechanism and source plivsies (ο be constrained.," As summarized below, these emission mechanisms and theoretical frameworks predict different field statistics, so that comparisons between theory and observation permit the emission mechanism and source physics to be constrained."
 Recent analyses do (his lor normal pulses of the Vela pulsar ancl pulsars D1641-45 ancl 0050-05 2003a.b.c)..," Recent analyses do this for normal pulses of the Vela pulsar and pulsars B1641-45 and B0950+08 \citep{cetal2001,cetal2002a,cetal2002b,cetal2002c}."
 The goals of this paper are to: (1) show that the distributions of electric fiekl strengths for known sources of giant pulses ancl eiant micropulses are all approximately power-law al hieh fluxes and have sulliciently similar power-law indices lor them (o be regarded as one population. (2) constrain which models for emission processes ancl source physics for giant pulses/micropulses remain viable. bv comparing observations wil theoretical predictions. (3) show that wave collapse is (he most favored interpretation for giant pulses and micropulses. in the absence of detailed calculations for relativistic beaming. while some other interpretations appear viable but less plausible and others are inconsistent with available data. and (4) point out limitations in current theories lor wave collapse.," The goals of this paper are to: (1) show that the distributions of electric field strengths for known sources of giant pulses and giant micropulses are all approximately power-law at high fluxes and have sufficiently similar power-law indices for them to be regarded as one population, (2) constrain which models for emission processes and source physics for giant pulses/micropulses remain viable, by comparing observations with theoretical predictions, (3) show that wave collapse is the most favored interpretation for giant pulses and micropulses, in the absence of detailed calculations for relativistic beaming, while some other interpretations appear viable but less plausible and others are inconsistent with available data, and (4) point out limitations in current theories for wave collapse."
 These goals are addressed by simnmarizing theory lor field statistics (Section 2). analvzing and discussing the field statistics of giant micropulses (Section 3) and giant pulses (Section 4). and comparing the observations with theoretical predictions (Section 5).," These goals are addressed by summarizing theory for field statistics (Section 2), analyzing and discussing the field statistics of giant micropulses (Section 3) and giant pulses (Section 4), and comparing the observations with theoretical predictions (Section 5)."
 The results are summarized and brief conclusions given in Section 6., The results are summarized and brief conclusions given in Section 6.
"a logRy, = 348 which is outside the validity range of the activitv-age relation but in this case it is compatible with the voung age.",a $R^{'}_{HK}$ = -3.48 which is outside the validity range of the activity-age relation but in this case it is compatible with the young age.
 Both echelle and long slit spectra analysecl in this work allowed. us to study the behavior of the different indicators fromthe Ca HIE Ix to the Ca HE lines. which are formed at different atmospheric altituces.," Both echelle and long slit spectra analysed in this work allowed us to study the behavior of the different indicators from the Ca H K to the Ca IRT lines, which are formed at different atmospheric altitudes."
 Lhe chromospheric contribution to these features was determined by using the spectral subtraction technique described in detail by etal.(2000). and Gálvezetal. (2002).., The chromospheric contribution to these features was determined by using the spectral subtraction technique described in detail by \citet{Montes00b} and \citet{Galvez02}. .
 The excess emission. £M of dilferent spectral features were measured in the subtracted spectra., The excess emission $EW$ of different spectral features were measured in the subtracted spectra.
 In. Table 10. we eive the AW for the Ca HE WK. He. H9. H5. 11. Ho. and Ca HUE (AASAO9S. 8542. 8662 A)) lines for the echelle spectra.," In Table \ref{tab:ew} we give the $EW$ for the Ca H K, $\epsilon$, $\delta$, $\gamma$, $\beta$, $\alpha$, and Ca IRT $\lambda$$\lambda$ 8498, 8542, 8662 ) lines for the echelle spectra."
 These Ms were converted to an absolute surface luxes by using the empirical stellar lux scales calibrated by llall(1996) asa function of the star color index., These $EW$ s were converted to an absolute surface fluxes by using the empirical stellar flux scales calibrated by \citet{Hall} as a function of the star color index.
 In our case. we used the BV index and the corresponding coelficients or Ca 11 Ix. Ho and Ca HUE. using for Le the same coellicients as for Ca11 IHE Ix. and derived the H9. 11: and 17 coellicients of lux by carrving out an interpolation »etween the values of Ca 1E Ix and Ho.," In our case, we used the $B-V$ index and the corresponding coefficients for Ca H K, $\alpha$ and Ca IRT, using for $\epsilon$ the same coefficients as for Ca H K, and derived the $\delta$ , $\gamma$ and $\beta$ coefficients of flux by carrying out an interpolation between the values of Ca H K and $\alpha$."
 The logarithm of he obtained absolute Lux at the stellar surface (logs) in ergs em7 + for the dillerent chromospheric activity indicators is given in Table 11.., The logarithm of the obtained absolute flux at the stellar surface $F$$_{\rm S}$ ) in ergs $^{-2}$ $^{-1}$ $^{-1}$ for the different chromospheric activity indicators is given in Table \ref{tab:fl}.
 Fig., Fig.
 12. shows representative observations in the Ha. and Ca IU AASAJ98. 8542 line regions for high resolution spectra.," \ref{fig:hairt} shows representative observations in the $\alpha$, and Ca IRT $\lambda$$\lambda$$8498$, 8542 line regions for high resolution spectra."
 Fig., Fig.
 13. shows representative observations in the La for low resolution spectra., \ref{fig:haindia} shows representative observations in the $\alpha$ for low resolution spectra.
 Fig., Fig.
 14. shows a closer view of one spectrum from Figs., \ref{fig:hairtzoom} shows a closer view of one spectrum from Figs.
 12 and 13 where the emission can be better seen.," \ref{fig:hairt}
 and \ref{fig:haindia} where the emission can be better seen."
 We analysed the Lo line region for all the spectra., We analysed the $\alpha$ line region for all the spectra.
 This line in the obtained spectra is always observed in emission above the continuum (see Figs., This line in the obtained spectra is always observed in emission above the continuum (see Figs.
 12 and. 13))., \ref{fig:hairt} and \ref{fig:haindia}) ).
 Aleasuring the £M of this line. we found that. the LM. average of the Lla emission is quite cilferent in every season. showing significant variability in time-scales of a vear.," Measuring the $EW$ of this line, we found that the $EW$ average of the $\alpha$ emission is quite different in every season, showing significant variability in time-scales of a year."
 EM (lla) = 3.23 for FOCESO4 run while. £ZWM (lla) = 1.67. 1.72 and 1.57 flor οςορ. FOCLESOTa and FOCIESOTh respectively. LW la) = 1.72 for the only value of FILESOS run.," $EW$ $\alpha$ ) = 3.23 for FOCES04 run while, $EW$ $\alpha$ ) = 1.67, 1.72 and 1.87 for FOCES06, FOCES07a and FOCES07b respectively, $EW$ $\alpha$ ) = 1.72 for the only value of FIES08 run."
 For thelow resolution spectra we have anaverage value(in 37 spectra taken duringthree consecutivenights) of EM lea) = 2.14 tin LIEOSCUA run., For thelow resolution spectra we have anaverage value(in 37 spectra taken duringthree consecutivenights) of $EW$ $\alpha$ ) = 2.14 in HFOSC04 run.
 Fig., Fig.
 15 shows the variation of EM vs. phase (calculated with the photometric period) in HIEOSCOA run., \ref{fig:haindiam11} shows the variation of $EW$ vs phase (calculated with the photometric period) in HFOSC04 run.
 Dillerent. svmbols represent cillerent nights., Different symbols represent different nights.
 “Phe second, The second
normal galaxies at hieh redshift.,normal galaxies at high redshift.
 The augular scales of the region where these lighly maguified high-redshift galaxies are found is also well-matched to the SCUBA field-of-view., The angular scales of the region where these highly magnified high-redshift galaxies are found is also well-matched to the SCUBA field-of-view.
 Tn the following sectious we cive details of the observations aud their reduction. and discuss the results within the framework of current theoretical models of ealaxy formation and evolution.," In the following sections we give details of the observations and their reduction, and discuss the results within the framework of current theoretical models of galaxy formation and evolution."
 We adopt I7.= 50kku 51 1 aud q4—0.5., We adopt $H_\circ=50 $ km $^{-1}$ $^{-1}$ and $q_\circ = 0.5$.
 These data were obtained using SCUBA (οποναι Gear 1991) on the James Clerk Maxwell TelescopeGQCNID)., These data were obtained using SCUBA (Cunningham Gear 1994) on the James Clerk Maxwell Telescope.
". SCUBA contains a umber of detectors and detector arrays cooled to IKI& and covering the atmospheric windows from jan to san. Iu our survey. we operated the 91 clement Short-wave (SW) array at 150ynn and the 37 clement Long-wave (LAV) array at S50yon. giving halfpower beam widths of 7.5 and ll.Taaresec respectively,"," SCUBA contains a number of detectors and detector arrays cooled to K and covering the atmospheric windows from $\mu$ m to $\mu$ m. In our survey, we operated the 91 element Short-wave (SW) array at $\mu$ m and the 37 element Long-wave (LW) array at $\mu$ m, giving half-power beam widths of 7.5 and arcsec respectively."
 Both arravs have a aarcuin Instantaneous ficld-ofview aud the design of the optics ensures that. with a suitable jiggle pattern for the secondary mirror. fully sampled maps can be obtained simultaneously at 150 and jan. The iuiltiplexing aud hieh efficiency of the arravs ies that SCUBA offers a eain in mapping speed ofa factor of about 300 as compared with previous detectors.," Both arrays have a arcmin instantaneous field-of-view and the design of the optics ensures that, with a suitable jiggle pattern for the secondary mirror,, fully sampled maps can be obtained simultaneously at 450 and $\mu$ m. The multiplexing and high efficiency of the arrays means that SCUBA offers a gain in mapping speed of a factor of about 300 as compared with previous detectors."
 The observations eiiploved a 61-poiut jigele pattern. fully seanpling both arravs over a period of 128s. The pattern was subdivided so that the target position could be switched between the signal aud refercuce every ss: arepeating signalreference scheme. with sixteen bss jigeles in each.," The observations employed a 64-point jiggle pattern, fully sampling both arrays over a period of s. The pattern was subdivided so that the target position could be switched between the signal and reference every s: a repeating signal–reference–reference–signal scheme, with sixteen s jiggles in each."
 Whilst jiggling. the secoucdary was chopped at £LITIIz by GOaarcsec in azimuth.," Whilst jiggling, the secondary was chopped at Hz by arcsec in azimuth."
 The pointing stability was checked every hour aud regular skvdips were performed to ineasure the atimospheric opacity., The pointing stability was checked every hour and regular skydips were performed to measure the atmospheric opacity.
 The rus poiting errors were below aarcsec. while atinospheric zenith opacities at 150 and jin were very stable during the course of each might. the nieht to uieht variations beime in the range 0.98.2.2 aud 0.180.37 respectively.," The rms pointing errors were below arcsec, while atmospheric zenith opacities at 450 and $\mu$ m were very stable during the course of each night, the night to night variations being in the range 0.98–2.2 and 0.18–0.37 respectively."
 The dedicated SCUBA data reduction software (SURF. Jeuness 1997) was used to reduce the observations.," The dedicated SCUBA data reduction software (SURF, Jenness 1997) was used to reduce the observations."
 The reduction consisted. of subtracting the reference from the sienal after carefully rejecting spikes aud data from noisy bolometers., The reduction consisted of subtracting the reference from the signal after carefully rejecting spikes and data from noisy bolometers.
 Six quiet bolometers at the edge of cach array were used to compensate for spatiallv-correlated kv enüssion., Six quiet bolometers at the edge of each array were used to compensate for spatially-correlated sky emission.
 This reduced the effective noise-equivaleut fiux deusitv from 100.350 to [7 at pau Ivison 1995)., This reduced the effective noise-equivalent flux density from 100–350 to $^{-1/2}$ at $\mu$ m Ivison 1998).
 The resulting maps were gatfielded. corrected for atinospheric attenuation. aud calibrated using wiehtly bean maps of Uranus.," The resulting maps were flatfielded, corrected for atmospheric attenuation, and calibrated using nightly beam maps of Uranus."
" The calibrated maps from each weht were coadded and then linearly interpolated onto an astrometric erid usine an approximately Nyquist sampling. of 2 aud Laaresecppixel+ at L50 and pan respectively, to produce the maps presented in Fie."," The calibrated maps from each night were coadded and then linearly interpolated onto an astrometric grid using an approximately Nyquist sampling, of 2 and $^{-1}$ at 450 and $\mu$ m respectively, to produce the maps presented in Fig."
 1 (Plate 1)., 1 (Plate 1).
 The final ou-source inteeration times are listed in Table 1. along with feld positious aud sensitivity linüts.," The final on-source integration times are listed in Table 1, along with field positions and sensitivity limits."
 The beams have moderate error lobes. especially at gan. ancl so we correct our aperture measurements for flux outside the aperture using the measured values frou our calibration sources.," The beams have moderate error lobes, especially at $\mu$ m, and so we correct our aperture measurements for flux outside the aperture using the measured values from our calibration sources."
 Even without including a factor to account for the lensing amplification. the data shown iu Fig.," Even without including a factor to account for the lensing amplification, the data shown in Fig."
 l are the deepest sub-uni maps ever published. aud illustrate the cosineticallv clean aud flat maps achievable with SCUBA iu lone inteeratious.," 1 are the deepest sub-mm maps ever published, and illustrate the cosmetically clean and flat maps achievable with SCUBA in long integrations."
 Source catalogs from our fields were constructed using the Sextractor package (Bertin Arnouts 1996)., Source catalogs from our fields were constructed using the Sextractor package (Bertin Arnouts 1996).
 The detection algorithià requires that the surface briehtuess in | contiguous pixels exceeds a threshold (clioscu as ~1o of the skv noise. Table 2). after subtracting a simooth backeround signal aud convolving the map witha ἐν1 pixel top-hat filter.," The detection algorithm requires that the surface brightness in 4 contiguous pixels exceeds a threshold (chosen as $\sim 1\sigma$ of the sky noise, Table 2), after subtracting a smooth background signal and convolving the map with a $4\times 4$ pixel top-hat filter."
 The umubers of objects (N) detected in each field are eiven in Table 2. indicating that our observations are far from being Imited by confusion: there are ~60 beams per source.," The numbers of objects (N) detected in each field are given in Table 2, indicating that our observations are far from being limited by confusion: there are $\sim 60$ beams per source."
 To assess the contribution of noise to our catalogs we re-van the detection algorithm ou the negative fluctuations in the map., To assess the contribution of noise to our catalogs we re-ran the detection algorithm on the negative fluctuations in the map.
 This eave a simple estimate of the umber of falsepositive detectious that may arise from the noise. asstunine that the noise properties of the map are Gaussian.," This gave a simple estimate of the number of false–positive detections that may arise from the noise, assuming that the noise properties of the map are Gaussian."
 We estimate that there are no false detections in our catalogs 4. Table 2). aud so all the detections are real.," We estimate that there are no false detections in our catalogs $_{-ve}$, Table 2), and so all the detections are real."
 The presence of the brightest source in the reference beans aaresee to the East and West iu the pau map of A370) was disregarded., The presence of the brightest source in the reference beams arcsec to the East and West in the $\mu$ m map of A370) was disregarded.
 This detection does. confir. however. the reality of positive features at this faint level. while the abseuce of auy other negative detections linüts the uuuber of luminous sources which cau le in the regions covered by the reference beams.," This detection does confirm, however, the reality of positive features at this faint level, while the absence of any other negative detections limits the number of luminous sources which can lie in the regions covered by the reference beams."
 Secondly. to determine the completeness of our sample we added a faint source to the maps repeatedly. re-ran our detection algorithi auc estimated the efficicney of detecting this source as a function of its flux deusity.," Secondly, to determine the completeness of our sample we added a faint source to the maps repeatedly, re-ran our detection algorithm and estimated the efficiency of detecting this source as a function of its flux density."
 This provides a reliable estimate of the visibility of a faint conrpact source in the maps., This provides a reliable estimate of the visibility of a faint compact source in the maps.
 The template source was a scaled version of our calibration source. Uranus.," The template source was a scaled version of our calibration source, Uranus."
 The estimated and coiipleteness lauits of the catalogs derived from these simulatious are listed in Table 2 as Suy and $395., The estimated and completeness limits of the catalogs derived from these simulations are listed in Table 2 as $_{80\%}$ and $_{50\%}$.
 The incompleteness limits are relatively bright for the ju maps because a large proportion of the flux deusity (about 105€) is found iu the low surface brightucss wines of the beam., The incompleteness limits are relatively bright for the $\mu$ m maps because a large proportion of the flux density (about ) is found in the low surface brightness wings of the beam.
 The simulatious also indicate that the measured 21 flux deusitics are unbiased aud are typically accurate to at 1iuuJy aud at παν., The simulations also indicate that the measured $\mu$ m flux densities are unbiased and are typically accurate to at mJy and at mJy.
 We discuss the detailed properties of the sources in, We discuss the detailed properties of the sources in
oonly in three of the IRAC channels (4.5. 5.8. and 8.0 jam). so the source could not be classified.,"only in three of the IRAC channels (4.5, 5.8, and 8.0 $\mu$ m), so the source could not be classified."
 Its X-ray spectrum is very hard., Its X-ray spectrum is very hard.
 A fit with a thermal spectrum gives a temperature of 60 keV. but it is badly constrained.," A fit with a thermal spectrum gives a temperature of 60 keV, but it is badly constrained."
 A a=1.2 power law provides as good a fit as the thermal model., A $\alpha = 1.2$ power law provides as good a fit as the thermal model.
 Such a spectrum is unlikely to originate in a stellar source. and therefore we consider this nost likely an X-ray bright background extragalactic object.," Such a spectrum is unlikely to originate in a stellar source, and therefore we consider this most likely an X-ray bright background extragalactic object."
 The source is present in the oobservation of Preibisch(2003).. who also does not detect any near IR counterpart.," The source is present in the observation of \cite{pre2003}, who also does not detect any near IR counterpart."
 During our observation. this Class II object. identified both 1αυ] the ISO and ddata. undergoes a strong. long-duration. flare: the intensity of the source increases by a factor of 10. impulsively. and then slowly decays over a period of more than 50 ks.," During our observation, this Class II object, identified both in the ISO and data, undergoes a strong, long-duration, flare: the intensity of the source increases by a factor of 10, impulsively, and then slowly decays over a period of more than 50 ks."
 To determine the spectral parameters of the flaring emission we subdivided the data for this source in four time intervals: the quiescent phase. the rise phase of the flare. its peak. and the flare decay.," To determine the spectral parameters of the flaring emission we subdivided the data for this source in four time intervals: the quiescent phase, the rise phase of the flare, its peak, and the flare decay."
 The parameters of the spectral fits derived for these four time intervals are summarised in reftab:flare.., The parameters of the spectral fits derived for these four time intervals are summarised in \\ref{tab:flare}.
 To derive the flare’s physical parameters we used the approach initially discussed by Realeetal.(1997) and since then applied to a variety of stellar fares., To derive the flare's physical parameters we used the approach initially discussed by \citet{rbp+97} and since then applied to a variety of stellar flares.
 This approach uses the slope ¢ of the flare decay in the logT versus logVEM diagram to account properly for the presence of sustained heating during the flare decay., This approach uses the slope $\zeta$ of the flare decay in the $\log T$ versus $\log \sqrt{E\!M}$ diagram to account properly for the presence of sustained heating during the flare decay.
 The calibration of the method for AACIS. and a detailed explanation of the physics behind it. can be found in Favataetal.(200Sa).. to which the reader ts referred.," The calibration of the method for ACIS, and a detailed explanation of the physics behind it, can be found in \citet{ffr+2005}, to which the reader is referred."
" In this formulation. the semi-length of the flaring loop is given by where «=3.7xI0emεκ KZ, nc is the H/e folding time of the light curve decay. and 74, Is the peak temperature of the plasma in the flaring loop."," In this formulation, the semi-length of the flaring loop is given by where $\alpha = 3.7 \times 10^{-4} {\rm cm^{-1} s^{-1} K^{1/2}}$ , $\tau_{\rm LC}$ is the $1/e$ folding time of the light curve decay, and $T_{\rm max}$ is the peak temperature of the plasma in the flaring loop."
 The limits of applicability of refeq:loop correspond.on one side (Z= 1.5). to a freely decaying loop. with no sustained heating. on the other 0.32). to a sequence of quasi-statie states for the loop. in which the heating timescale is so long as to mask the loop's intrinsic decay.," The limits of applicability of \\ref{eq:loop} correspond,on one side $\zeta \simeq 1.5$ ), to a freely decaying loop, with no sustained heating, on the other $\zeta=0.32$ ), to a sequence of quasi-static states for the loop, in which the heating timescale is so long as to mask the loop's intrinsic decay."
" F(Z) and the relationship between 7,4, and the best-fit peak temperature 7,4, are both functions that need to be separately determined for each. X-ray detector. depending on its spectral response."," $F(\zeta)$ and the relationship between $T_{\rm max}$ and the best-fit peak temperature $T_{\rm obs}$ are both functions that need to be separately determined for each X-ray detector, depending on its spectral response."
 For ACIS. and The log7 versus logVEM diagram for the flare of source 79 is shown in Fig. 12..," For ACIS, and The $\log T$ versus $\log \sqrt{E\!M}$ diagram for the flare of source 79 is shown in Fig. \ref{fig:zeta}."
 The lowest point refers to the quiescent phase. the highest point corresponds to the rise phase of the flare. and the line joins the points relatives to the flare peak and its decay.," The lowest point refers to the quiescent phase, the highest point corresponds to the rise phase of the flare, and the line joins the points relatives to the flare peak and its decay."
 The slope of this line is Z=1.67. which ts outside the limit of applicabilityof refeq:loop.. however the error bars of the points are compatible with €=1.0—1.5.," The slope of this line is $\zeta = 1.67$, which is outside the limit of applicabilityof \\ref{eq:loop}, however the error bars of the points are compatible with $\zeta = 1.0 - 1.5$."
 Given a flare decay |/e-folding time S53 ks. Eqs.," Given a flare decay $1/e$ -folding time $\tau_{\rm LC} = 53$ ks, Eqs."
 2 and ] result in a loop semi-length of L=10--12 Re»., \ref{eq:fchi} and \ref{eq:loop} result in a loop semi-length of $L = 10-12$ $R_\odot$.
 Source 79 appears to be a very-low-mass star: its position in the color-magnitude diagram of reffig:omdsmnyrimplviesamassM ;0.1Mo.," Source 79 appears to be a very-low-mass star; its position in the color-magnitude diagram of \\ref{fig:cmd_2myr} implyies a mass $M
< 0.1~M_{\sun}$."
 According to the evolutionary model of Siessetal.(2000).. at 2 Myr of age. such a star would have a radius R<Re. hence. the flaring loop of source 79 extends to a dinstance of more than 10 times the stellar radius.," According to the evolutionary model of \citet{sdf00}, at 2 Myr of age, such a star would have a radius $R < R_{\sun}$, hence, the flaring loop of source 79 extends to a dinstance of more than 10 times the stellar radius."
" Assuming for the loop a radius r=0.1L. typical of solar events. from the emission measure at the flare maximum. one derives an electron density 11,~3.6x10? em™ and a corresponding equipartition magnetic field strength B=60 G. Very long flaring structures in YSOs have been recently reported for half a dozen sources in the ONC by Favataetal.(2005a) and. more tentatively. for HL Tau in L1551 by Giardinoetal.(2006)."," Assuming for the loop a radius $r =
0.1~L$, typical of solar events, from the emission measure at the flare maximum, one derives an electron density $n_e \simeq 3.6 \times
10^{9}$ $^{-3}$ and a corresponding equipartition magnetic field strength $B \simeq 60$ G. Very long flaring structures in YSOs have been recently reported for half a dozen sources in the ONC by \citet{ffr+2005} and, more tentatively, for HL Tau in L1551 by \citet{gfs+06}."
. The flare in source 79 is similar. even though the star is significantly less massive than HL Tau and the objects in the ONC that exhibited evidence of very long flaring structures.," The flare in source 79 is similar, even though the star is significantly less massive than HL Tau and the objects in the ONC that exhibited evidence of very long flaring structures."
" This indicates that these long flaring structures develop in stars across a wide mass range (from M, apparently well below 0.1 Mea to M,~2.4Mo. the most massive object in the COUP flaring sample)."," This indicates that these long flaring structures develop in stars across a wide mass range (from $M_{\star}$ apparently well below 0.1 $M_{\sun}$ to $M_{\star} \sim
2.4~M_{\sun}$, the most massive object in the COUP flaring sample)."
 As the majority of YSOs is surrounded by disks. Favataal.(2005a) speculated that the large magnetic structures that confine the flaring plasma are actually the same type of structures that connect the star to the circumstellar disk. in the magnetospheric accretion paradigm.," As the majority of YSOs is surrounded by disks, \citet{ffr+2005}
 speculated that the large magnetic structures that confine the flaring plasma are actually the same type of structures that connect the star to the circumstellar disk, in the magnetospheric accretion paradigm."
 As described below. we detect. in the spectrum of this star. 64 keV Fe fluorescent emission with a large equivalent width. compatible with it being due to fluorescence from a centrally irradiated circumstellar disk.," As described below, we detect, in the spectrum of this star, 6.4 keV Fe fluorescent emission with a large equivalent width, compatible with it being due to fluorescence from a centrally irradiated circumstellar disk."
 The spectrum (integrated over the entire observation) of source 79 is shown in reffig:le together with its spectral fit with an absorbed 1T plasma model., The spectrum (integrated over the entire observation) of source 79 is shown in \\ref{fig:lc} together with its spectral fit with an absorbed 1T plasma model.
 There appears to be an excess of emission redward of the Fe K complex at =6.7 keV. at the expected energy of the 6.4 keV Fe fluorescent line.," There appears to be an excess of emission redward of the Fe K complex at $\simeq 6.7$ keV, at the expected energy of the 6.4 keV Fe fluorescent line."
 To determine the significance of this excess. we fitted the spectrum of source 79 again with an additional Gaussian line component at 6.4 keV. which was constrained to be narrow (10 eV). while its normalisation was unconstrained.," To determine the significance of this excess, we fitted the spectrum of source 79 again with an additional Gaussian line component at 6.4 keV, which was constrained to be narrow (10 eV), while its normalisation was unconstrained."
 The other parameters of the absorbed IT plasma model (absorbing column density. temperature anc normalisation of the thermal spectrum) were also unconstrained.," The other parameters of the absorbed 1T plasma model (absorbing column density, temperature and normalisation of the thermal spectrum) were also unconstrained."
 The result of this new fit canbe compared with the original fit in reffig:fluo:: the excess at 6.4 keV is well accounted for by a narrow Gaussian line with fitted intensity /=(3.79€5.78) photons οη s7!., The result of this new fit canbe compared with the original fit in \\ref{fig:fluo}: : the excess at 6.4 keV is well accounted for by a narrow Gaussian line with fitted intensity $I = (3.79 \pm 5.78) \times 10^{-7}$ photons $^{-2}$ $^{-1}$ .
 The fitted values of the absorbed IT plasma model do not change significantly with the addition of the Gaussian line at 6.4 keV, The fitted values of the absorbed 1T plasma model do not change significantly with the addition of the Gaussian line at 6.4 keV
The details of the derivation of the basic governing equations for a non-adiabatic. partially ionized. one-fluid plasma can be followed in. e.g..Braginski(1965):FortezaPintoetal. (2008).,"The details of the derivation of the basic governing equations for a non-adiabatic, partially ionized, one-fluid plasma can be followed in, e.g.,\citet{brag,forteza07,forteza08,pinto}."
. Here. we follow the same procedure but generalize the analysis of by including additional species.," Here, we follow the same procedure but generalize the analysis of \citet{forteza07} by including additional species."
 In brief. the separate governing equations for the five species are added and a generalized Ohm's law ts obtained.," In brief, the separate governing equations for the five species are added and a generalized Ohm's law is obtained."
 These basic equations correspond to Eqs. (, These basic equations correspond to Eqs. (
1)-(6) of Fortezaetal.(2008).. which are formally identical in our case.,"1)–(6) of \citet{forteza08}, which are formally identical in our case."
" A key step 1n the present derivation is to compute the density current. J. às along with the condition rg=np+ng,,. Where fy. Ap. and yo), are the electron. proton. and number densities. respectively. and e is the electron charge."," A key step in the present derivation is to compute the density current, $\vec{j}$ as along with the condition $n_{\rm e} = n_{\rm p} + n_\ion{He}{ii}$, where $n_{\rm e}$, $n_{\rm p}$, and $n_\ion{He}{ii}$ are the electron, proton, and number densities, respectively, and $e$ is the electron charge."
 The resulting induction equation (see Eq. [, The resulting induction equation (see Eq. [
14] of Fortezaetal. 2007)) contains several diffusion terms whose coefficients depend on the collisional frequencies between species.,14] of \citealt{forteza07}) ) contains several diffusion terms whose coefficients depend on the collisional frequencies between species.
 The physical meaning of these nonideal terms is explained in detail in Pintoetal.(2008)., The physical meaning of these nonideal terms is explained in detail in \citet{pinto}.
. In particular. 10n-neutral collisions are responsible for the so-called Cowling’s diffusion. which is much more efficient than Ohm’s diffusion in a partially ionized plasma.," In particular, ion-neutral collisions are responsible for the so-called Cowling's diffusion, which is much more efficient than Ohm's diffusion in a partially ionized plasma."
 However. some terms are not relevant for our present application.," However, some terms are not relevant for our present application."
" Hall's effect is negligible in prominence conditions (Soleretal.2009c).. and the so-called ""Biermann's battery"" term is identically zero in a homogeneous medium."," Hall's effect is negligible in prominence conditions \citep{soler09INRA}, and the so-called “Biermann's battery” term is identically zero in a homogeneous medium."
 For this reason. our final form of the induction equation (Eq. [," For this reason, our final form of the induction equation (Eq. ["
21] of Fortezaetal. 2007)) only contains the terms corresponding to Ohm's and ambipolar (Cowling’s) diffusion. along with the diamagnetic current term.,"21] of \citealt{forteza07}) ) only contains the terms corresponding to Ohm's and ambipolar (Cowling's) diffusion, along with the diamagnetic current term."
 Ohim’s. 77. and Cowling’s. jc. coefficients of magnetic diffusion can be expressed in terms of their corresponding conduetivities. with jp2cx107 N A7.," Ohm's, $\eta$, and Cowling's, $\eta_{\rm C}$, coefficients of magnetic diffusion can be expressed in terms of their corresponding conductivities, with $\mu = 4\pi \times 10^{-7}$ N $^{-2}$."
" So. Ohm's and Cowling's conductivities. as well as the diamagnetic current coefficient. =. which applies in our case when helium is included are: In addition. ay. o3. and a, are the electron. electron-neutral. and neutral friction coethcients. respectively.whose expressions depend on the sum of the friction coefficients between particular species. Each particular friction coefficient. ayy. is computed as"," So, Ohm's and Cowling's conductivities, as well as the diamagnetic current coefficient, $\Xi$, which applies in our case when helium is included are: In addition, $\alpha_{\rm e}$, $\alpha_{\rm en}$, and $\alpha_{\rm n}$ are the electron, electron-neutral, and neutral friction coefficients, respectively,whose expressions depend on the sum of the friction coefficients between particular species, Each particular friction coefficient, $\alpha_{\beta \beta'}$ is computed as"
Formation Rate (SFR) is 4.3. 31.0 and 4.5 ! in Lupus 1. 3 and 4. respectively. inclicating that Lupus 3 has a higher star lormation activity (hen Lupus 1 ancl 4.,"Formation Rate (SFR) is 4.3, 31.0 and 4.5 $^{-1}$ in Lupus 1, 3 and 4, respectively, indicating that Lupus 3 has a higher star formation activity then Lupus 1 and 4."
 The Lupus clouds are included in (he extended survevs of nearby molecular clouds that are being carried out. with both ground ancl space facilities. namely: 70. 100. 160. 250. 350 and 500 Gould Belt Herschel survey. (Andréetal.2010): JCNITE Gould's Belt Legacy Survey. with SCUBA? and ILARP-D (Atchelletal.2005: Johnstone.DiFrancesco&Nirk 2004)).," The Lupus clouds are included in the extended surveys of nearby molecular clouds that are being carried out with both ground and space facilities, namely: 70, 100, 160, 250, 350 and 500 Gould Belt Herschel survey \cite[]{andre10}; JCMT Gould's Belt Legacy Survey with SCUBA2 and HARP-B \citealt{atchell05}; \citealt{johnstone04}) )."
 In order to identify the population of pre- and proto-stellar cores. we carried oul a molecular survey of the three Lupus subgroups where there is evidence of star. [ormation aclivitv. Le. Lupus 1. 3 and 4. at millimetre wavelengths in several molecular species (hat are good (racers of dense gas.," In order to identify the population of pre- and proto-stellar cores, we carried out a molecular survey of the three Lupus subgroups where there is evidence of star formation activity, i.e. Lupus 1, 3 and 4, at millimetre wavelengths in several molecular species that are good tracers of dense gas."
 The millimetre data are complementary (to the otlier surveys of the region and will facilitate their interpretation., The millimetre data are complementary to the other surveys of the region and will facilitate their interpretation.
 The complete set of data will allow to understand the star formation activity in the Lupus region and more in general the low-mass star formation process from the cores condensation to the protostellar phase., The complete set of data will allow to understand the star formation activity in the Lupus region and more in general the low-mass star formation process from the cores condensation to the protostellar phase.
 Molecular line survevs of the Lupus 1 ancl 3 molecular clouds at 3 and 12 mm were carried oul with the Mopra telescope., Molecular line surveys of the Lupus 1 and 3 molecular clouds at 3 and 12 mm were carried out with the Mopra telescope.
 Moreover. the Lupus 4 cloud were also mapped at 12 mun.," Moreover, the Lupus 4 cloud were also mapped at 12 mm."
 The observations were executed in (wo periods: fom 17 to 19 July 2008 and from 20 to 26 October 2003., The observations were executed in two periods: from 17 to 19 July 2008 and from 20 to 26 October 2008.
 The observations were carried out in the On The Fly observing mode with the narrow hand mode of the UNSW-Mopra Spectrometer(UNSW-MOPS) digital fillerbank back-end. and the Monolithie Microwave Integrated Circuit (MMICO 77 to 116 GlIz receiver.," The observations were carried out in the On The Fly observing mode with the narrow band mode of the UNSW-Mopra Spectrometer(UNSW-MOPS) digital filterbank back-end, and the Monolithic Microwave Integrated Circuit (MMIC) 77 to 116 GHz receiver."
 has a 8-Gllz bandwidth with four overlapping 2.2-Gllz subbands. each subbanud having four dual-polarization 137.5-MlIITz-wide windows giving a total of sixteen dual-polarization windows.," UNSW-MOPS has a 8-GHz bandwidth with four overlapping 2.2-GHz subbands, each subband having four dual-polarization 137.5-MHz-wide windows giving a total of sixteen dual-polarization windows."
 Each window has 4096 channels providing a velocity resolution of 0.11 al 94 GH and 0.41 ad 22 GlIIz., Each window has 4096 channels providing a velocity resolution of 0.11 at 94 GHz and 0.41 at 22 GHz.
 We selected the 16 zoom bands in (he range between 19.5 and 27.5 Gllz and al 12 mm and between 90 and 93 GIIz αἱ 3 mm., We selected the 16 zoom bands in the range between 19.5 and 27.5 GHz and at 12 mm and between 90 and 98 GHz at 3 mm.
 The selected frequencies are listed in Table l.., The selected frequencies are listed in Table \ref{obs}.
 Since the beam of the telescope at 12 nun is2.5... at this [requeney. we were able to map all the zones of the Lupus 1. 3 and 4 clouds with visual extinction larger than 2 mag (see," Since the beam of the telescope at 12 mm is, at this frequency we were able to map all the zones of the Lupus 1, 3 and 4 clouds with visual extinction larger than 3 mag (see"
larger {ρωLead ratio observed in our reference sample of Sevlert 1 when compared to DLRG. are in agreement with the presence of a different accretion flow configuration al least in (he inner regions of radio galaxies.,"larger $L_{\rm Bol}/L_{\rm Edd}$ ratio observed in our reference sample of Seyfert 1 when compared to BLRG, are in agreement with the presence of a different accretion flow configuration at least in the inner regions of radio galaxies."
 However. (his hypothesis is clislavorecl by and observations showing (hat eravitationallv redshifted iron lines. supposed to be produced very close to the black hole. are not so easily detectable in Sevlert 1: as previously thought.," However, this hypothesis is disfavored by and observations showing that gravitationally redshifted iron lines, supposed to be produced very close to the black hole, are not so easily detectable in Seyfert 1 as previously thought."
 The Sevler(-BLRG different accretion rates also question the possibility Chat a strong ionization of (he upper lavers of (he geometrically (hin disk inhibits the Fe line production in BLRG., The Seyfert-BLRG different accretion rates also question the possibility that a strong ionization of the upper layers of the geometrically thin disk inhibits the Fe line production in BLRG.
 In a reasonable Sevlert-like configuration with a flaring corona above a thin disk. the EW is in fact expected to decrease will the accretion rate. in contrast wilh our results.," In a reasonable Seyfert-like configuration with a flaring corona above a thin disk, the EW is in fact expected to decrease with the accretion rate, in contrast with our results."
 BLRG have smaller accretion rates but smaller EW Chan Sevfert galaxies., BLRG have smaller accretion rates but smaller EW than Seyfert galaxies.
" This contracdicts also a model recently proposed (Zhou&Wang2005).. which shows that higher accretion rates imply [latter tori (ancl. as a consequence. smaller EW),"," This contradicts also a model recently proposed \citep{zho05}, which shows that higher accretion rates imply flatter torii (and, as a consequence, smaller EW)."
 In spite of this. the role of (he circumnmiclear matter (as the main reprocessing medium in adcdition/alternative to the accretion disk) deserves a deeper investigation.," In spite of this, the role of the circumnuclear matter (as the main reprocessing medium in addition/alternative to the accretion disk) deserves a deeper investigation."
 Physical/geometrical differences as well as metal abundances of the gas environment should be investigated in and. AGN., Physical/geometrical differences as well as metal abundances of the gas environment should be investigated in and AGN.
 This point could be better tested by comparing NLRG and Sevlert 2 galaxies. which are both strongly affected bv the gas environment.," This point could be better tested by comparing NLRG and Seyfert 2 galaxies, which are both strongly affected by the gas environment."
 This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronauties and Space Acministration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."
 We thank DP. Giommi for valuable discussions and E. Palazzi for help on a statistical problem., We thank P. Giommi for valuable discussions and E. Palazzi for help on a statistical problem.
centering errors (see below).,centering errors (see below).
 Because our expansion center differs from those of previous estimates (see below). we estinated our measuremeut uucertainties in several wavs.," Because our expansion center differs from those of previous estimates (see below), we estimated our measurement uncertainties in several ways."
 Since we have computed a likelihood function. the likelihood-ratio test described by Cash(1979) can be used to formi confidence contours.," Since we have computed a likelihood function, the likelihood-ratio test described by \citet{cash79} can be used to form confidence contours."
 Such contours. however. assume that the positional errors we estimated by eve are truly oue standard deviation.," Such contours, however, assume that the positional errors we estimated by eye are truly one standard deviation."
 The resulting confidence contour is an oval slightly elongated uortlwest-southeast. with a radius ~173.," The resulting confidence contour is an oval slightly elongated northwest-southeast, with a radius $\sim 1 \farcs 3$."
 Figure 3 is a maguified view of the center region. showing the lies of position together with the to confidence contours from this procedure.," Figure 3 is a magnified view of the center region, showing the lines of position together with the to confidence contours from this procedure."
 We also used a Monte Carlo simmlation of the proper motion measurements to check our uucertaiuties aud to normalize our error estimates., We also used a Monte Carlo simulation of the proper motion measurements to check our uncertainties and to normalize our error estimates.
 We beean by απλαιο that the explosion occurred at the observed. maxiuun-lkelihood position., We began by assuming that the explosion occurred at the observed maximum-likelihood position.
 Thou. aking each knots present position as shown and fixed (because the proper imotious ουια» the errors). we computed an idealized oxoper motion for cach knot. which extrapolated ck exactly to the observed maximmuu-kelihood »ositiou.," Then, taking each knot's present position as known and fixed (because the proper motions dominate the errors), we computed an idealized proper motion for each knot, which extrapolated back exactly to the observed maximum-likelihood position."
 We next created 1000 artificial data sets x addiug Gaussian random noise to the idealized oxoper motions., We next created 1000 artificial data sets by adding Gaussian random noise to the idealized proper motions.
 For each artificial data set. we computed the maximuimnm-likelibood ceuter aud its associated Wasi A.," For each artificial data set, we computed the maximum-likelihood center and its associated maximum $\lambda$."
 Tn the first trials. the standard deviation usec for the Gaussian noise was simply the estimated proper motion uncertainty of cach knot in effect. we took our estimated position errors to be realistic.," In the first trials, the standard deviation used for the Gaussian noise was simply the estimated proper motion uncertainty of each knot – in effect, we took our estimated position errors to be realistic."
 For nearly all the trials. this choice led to maximum values of A larger than observed. indicating that the errors iu the proper motions were overestimated (as expected since our error estimates were believed couservative).," For nearly all the trials, this choice led to maximum values of $\lambda$ larger than observed, indicating that the errors in the proper motions were overestimated (as expected since our error estimates were believed conservative)."
 In the final Monte Carlo calculation. we multiplied the proper motion standard deviations by a global fudee factor f~0.7.," In the final Monte Carlo calculation, we multiplied the proper motion standard deviations by a global `fudge factor' $f \sim 0.7$."
 These simulated data sets vielded maxima values of ACN.37) very simular to tha of the real data.," These simulated data sets yielded maximum values of $\lambda(X,Y)$ very similar to that of the real data."
 The spread in the positions generated by this procedure should be a realistic indicator of the uucertaintv in the ceutroid., The spread in the positions generated by this procedure should be a realistic indicator of the uncertainty in the centroid.
 The cloud of Moute Carlo positions is also shown in Figure 3 aud has standard deviatious in WY aud Y of 398 aud 366 nas. respectively.," The cloud of Monte Carlo positions is also shown in Figure 3 and has standard deviations in $X$ and $Y$ of 398 and 366 mas, respectively."
 Talf of the poiuts lie within [Ls nas of the mean position and within 916 nas., Half of the points lie within 448 mas of the mean position and within 946 mas.
" This agrees well with the likelihood-ratio test described above once the scaling factor of 0,7 is aken mto account and provides a cross-check ou he likelibood-ratio procedure.", This agrees well with the likelihood-ratio test described above once the scaling factor of 0.7 is taken into account and provides a cross-check on the likelihood-ratio procedure.
 As an additional check. we divided our data into WO sli]es sllJl knots aud outer knots.," As an additional check, we divided our data into two samples – shell knots and outer knots."
 The outer knots gave Vo=599 mas. Y—2809 mas with half the Monte Carlo poiuts within 508 mas of the mean: the shell knots gave Vo=SSS las and Y—2810 imas. with half within 783 mas.," The outer knots gave $X = 599$ mas, $Y = 2809$ mas with half the Monte Carlo points within 508 mas of the mean; the shell knots gave $X = -388$ mas and $Y = 2840$ mas, with half within 783 mas."
 The disagreements between these aud the combined data are about as expected eiven the estimated, The disagreements between these and the combined data are about as expected given the estimated
similar laminar viscous disc.,similar laminar viscous disc.
 This seems to be in agreement with the numerical simulations of a giant planet in a turbulent disc performed by Nelson Papaloizou (2002)., This seems to be in agreement with the numerical simulations of a giant planet in a turbulent disc performed by Nelson Papaloizou (2002).
 Once the gap is completely cleared out. the ellect of the magnetic resonances disappear as they are inside the edges of the gap (Gwhich comncide with the Lindblad resonances corresponding to m~r/41).," Once the gap is completely cleared out, the effect of the magnetic resonances disappear as they are inside the edges of the gap (which ncide with the Lindblad resonances corresponding to $m \sim
r/H$ )."
 The magnetic field may. however still have an effect on the dise.planet interaction because of the turbulence it produces (Nelson Papaloizou 2002)., The magnetic field may however still have an effect on the disc–planet interaction because of the turbulence it produces (Nelson Papaloizou 2002).
 We have focused here on a planet with a circular orbit., We have focused here on a planet with a circular orbit.
 A planet on an eccentric orbit in a nonmagnetic disce usually sullers eccentricitv damping. as in that case the corotation resonances. which damp the eccentricity. dominate over the Lindblad resonances. which excite it (Goldreich Tremaine 1980: Papaloizou. Nelson Masset 2001).," A planet on an eccentric orbit in a nonmagnetic disc usually suffers eccentricity damping, as in that case the corotation resonances, which damp the eccentricity, dominate over the Lindblad resonances, which excite it (Goldreich Tremaine 1980; Papaloizou, Nelson Masset 2001)."
 Ες picture may change once a magnetic field is introduced., This picture may change once a magnetic field is introduced.
 The ellect of à magnetic field on the eccentricity of a planet will be studied in another paper., The effect of a magnetic field on the eccentricity of a planet will be studied in another paper.
 ]t is a pleasure to thank Steven Balbus and John Papaloizou for their advice. encouragement. and many valuable suggestions ancl discussions.," It is a pleasure to thank Steven Balbus and John Papaloizou for their advice, encouragement, and many valuable suggestions and discussions."
 Lam grateful to John Papaloizou for his comments on an carly draft of this paper which led to significant improvements., I am grateful to John Papaloizou for his comments on an early draft of this paper which led to significant improvements.
The radiation emitted by the quark laver al (he surface of the quark star must also cross the thin electron laver extending bevond the stars surface.,The radiation emitted by the quark layer at the surface of the quark star must also cross the thin electron layer extending beyond the star's surface.
 We also consider the effect of this laver on the outgoing radiation and show that it can significantly reduce the intensity of the radiation coming from the quark star., We also consider the effect of this layer on the outgoing radiation and show that it can significantly reduce the intensity of the radiation coming from the quark star.
 The present paper is organized as follows., The present paper is organized as follows.
 In Section IL we discuss the Landau-Pomeranchuk- effect for quark matter., In Section II we discuss the Landau-Pomeranchuk-Migdal effect for quark matter.
 The bremsstrahlung emissivity of quark matter is considered in Section III., The bremsstrahlung emissivity of quark matter is considered in Section III.
 The effect of the electron laver on the radiation outgoing from the quark star surface is analvzed in Section IV., The effect of the electron layer on the radiation outgoing from the quark star surface is analyzed in Section IV.
 In Section V. we discuss and conclude our results., In Section V we discuss and conclude our results.
 Throughout this paper we use unitis so thal c=fhbgl1. with Ap the Bolizimann constant.," Throughout this paper we use units so that $c=\hbar =k_{B}=1$, with $k_{B}$ the Boltzmann constant."
 The dispersion relation shows that only photons with frequency w>«y can propagate inside strange matter.," The dispersion relation shows that only photons with frequency $\omega
>\omega _{p}$ can propagate inside strange matter."
 Propagation of electromagnetic waves of [requencies lower than oy is exponentially damped. with the damping coellicient 7 depending on w and wy).," Propagation of electromagnetic waves of frequencies lower than $\omega _{p}$ is exponentially damped, with the damping coefficient $\beta $ depending on $\omega $ and $\omega _{p}$."
" Fore <<wy, the value of 9 is given by 92:2o,(1999)..", For $\omega <<\omega _{p}$ the value of $\beta $ is given by $\beta \approx 2\omega _{p}$.
 This means that photons with vw<wy emitted in various processes inside strange matter are absorbed., This means that photons with $\omega <\omega _{p}$ emitted in various processes inside strange matter are absorbed.
" The mean free path of such a photon is of the order of Àzzο)2οδω,%5 Im1991)..", The mean free path of such a photon is of the order of $\lambda \approx c/\beta \approx c/2\omega _{p}\approx 5$ fm.
 Therefore. only photons produced just below the surface with momenta pointing outwards can leave strange matter.," Therefore, only photons produced just below the surface with momenta pointing outwards can leave strange matter."
 In the following we shall consider (he photon emissivity of quark matter. by also taking into account the effect of multiple scatterings on the emitted radiation.," In the following we shall consider the photon emissivity of quark matter, by also taking into account the effect of multiple scatterings on the emitted radiation."
 This ellect is called the Landau-Pomeranchuk-Migdal (LPM) effect. and was considered initially by(1953).. who used classical electrodynamies to demonstrate bremsstrahlilung suppression due to multiple scattering: the suppression comes from the interlerence between photons emitted by different. elements of the charged. particle trajectory.," This effect is called the Landau-Pomeranchuk-Migdal (LPM) effect, and was considered initially by, who used classical electrodynamics to demonstrate bremsstrahlung suppression due to multiple scattering: the suppression comes from the interference between photons emitted by different elements of the charged particle trajectory."
 To study. the astrophysical implications of this effect on quark matter we shall take into account. the bremsstrahlung photons produced in the quark-quark interactions. (hat is in the process qiqoagy+qac.," To study the astrophysical implications of this effect on quark matter we shall take into account the bremsstrahlung photons produced in the quark-quark interactions, that is in the process $q_{1}+q_{2}\rightarrow q_{1^{\prime
}}+q_{2^{\prime }}+\gamma $."
 The LPAI effect can be discussed in a simple qualitative wav as follows., The LPM effect can be discussed in a simple qualitative way as follows.
" Let's consider a bremsstrahlung photon of energy v» produced by an ulirarelativistic quark of enerev Z and niass m,py. Where <<E."," Let's consider a bremsstrahlung photon of energy $\omega $ produced by an ultrarelativistic quark of energy $E$ and mass $m_{eff}$, where $\omega <<E$."
" In this kinematic regime the average angle 4, between the incident quark and the produced photon is small. 6,2r/mi;E."," In this kinematic regime the average angle $\theta _{\gamma }$ between the incident quark and the produced photon is small, $\theta _{\gamma }\approx
m_{eff}/E$."
 We assume that the angle between the incident. ancl scattered quark is also small., We assume that the angle between the incident and scattered quark is also small.
 Moreover. we shall assume that all quarks," Moreover, we shall assume that all quarks"
is an accreting neutron star with a ~25 min spin period. the longest known period of any X-ray pulsar in a Be-star system.,"is an accreting neutron star with a $\sim$ 25 min spin period, the longest known period of any X-ray pulsar in a Be-star system."
 This fact was realized (Mereghetti. Stella De Nile 1993) only after the re-discovery of this source in the ROSAT All Sky Survey and its identification with the 11 magnitude Be star LS I +61° 235 (Motch et al.," This fact was realized (Mereghetti, Stella De Nile 1993) only after the re–discovery of this source in the ROSAT All Sky Survey and its identification with the $^{th}$ magnitude Be star LS I $^{\rm o}$ 235 (Motch et al."
 1991)., 1991).
 Indeed the 25 min periodicity had already been discovered with EXOSAT (White et al., Indeed the 25 min periodicity had already been discovered with EXOSAT (White et al.
 1987). but it was attributed to a nearby source (4U 01424614; see also Israel. Mereghetti Stella 1994. Hellier 1994).," 1987), but it was attributed to a nearby source (4U 0142+614; see also Israel, Mereghetti Stella 1994, Hellier 1994)."
 The optical companion of was classified as B5lllIe (Slettebak 1985). but Coe et al. (," The optical companion of was classified as B5IIIe (Slettebak 1985), but Coe et al. ("
1993) derived a somewhat earlier spectral type of O9-BO.,1993) derived a somewhat earlier spectral type of O9–B0.
 This star is probably a member of the open cluster NGC 663 at a distance of about 2.5 kpe (Tapia et al., This star is probably a member of the open cluster NGC 663 at a distance of about 2.5 kpc (Tapia et al.
 1991)., 1991).
 For this distance. the 1— keV luminosity during the EXOSAT detection in 1984 was ~10° eres. + (Mereghetti. Stella De Nile 1993).," For this distance, the 1--20 keV luminosity during the EXOSAT detection in 1984 was $\sim 10^{36}$ erg $^{-1}$ (Mereghetti, Stella De Nile 1993)."
 All the observations of carried out after its re-discovery yielded lower luminosities. of the order of a few 10°! ere ! (Hellier 1994. Haberl et al.," All the observations of carried out after its re-discovery yielded lower luminosities, of the order of a few $10^{34}$ erg $^{-1}$ (Hellier 1994, Haberl et al."
 1998). until an observation with the ssatellite showed that in July 1997 the flux started to rise again (Haberl. Angelini Motch 1998). though not up to the level of the first EXOSAT observation.," 1998), until an observation with the satellite showed that in July 1997 the flux started to rise again (Haberl, Angelini Motch 1998), though not up to the level of the first EXOSAT observation."
 Here we report on observations performed with the ((Bradt et al., Here we report on observations performed with the (Bradt et al.
 1993) and ((Boella et al., 1993) and (Boella et al.
 19972) satellites from 1996 to 1998., 1997a) satellites from 1996 to 1998.
 was observed with the ssatellite on March 28. 1996 from 11:17 UT to 22:11 UT.," was observed with the satellite on March 28, 1996 from 11:17 UT to 22:11 UT."
 The results presented here are based on data collected with the Proportional Counter Array (PCA. Jahoda et al.," The results presented here are based on data collected with the Proportional Counter Array (PCA, Jahoda et al."
 1996)., 1996).
 The PCA instrument consists of an array of 5 proportional counters operating in the 2-60 keV energy range. with a total effective area of approximately 7000 em? and a field of view. defined by passive collimators. of ~1° FWHM.," The PCA instrument consists of an array of 5 proportional counters operating in the 2–60 keV energy range, with a total effective area of approximately 7000 $^{2}$ and a field of view, defined by passive collimators, of $\sim1\deg$ FWHM."
 For the analysis of the PCA data. time intervals with a source elevation angle greater than 10° were selected. resulting in a net exposure time of about 18.5 Ks.," For the analysis of the PCA data, time intervals with a source elevation angle greater than $\deg$ were selected, resulting in a net exposure time of about 18.5 ks."
 Only the top layer anodes of the five proportional counters were used to accumulate spectra and light curves of., Only the top layer anodes of the five proportional counters were used to accumulate spectra and light curves of.
 The background was estimated using the latest version of the program PCABACKEST applicable to the time period of our observation (version 1.5)., The background was estimated using the latest version of the program PCABACKEST applicable to the time period of our observation (version 1.5).
 To account for the uncertainties in the response matrix (version 2.2.1). we added a systematic error to the PHA data.," To account for the uncertainties in the response matrix (version 2.2.1), we added a systematic error to the PHA data."
 Attempts to fit the PCA spectrum with single component models gave unacceptable results. due to the presence of some contamination from the nearby source 4U 0142+61," Attempts to fit the PCA spectrum with single component models gave unacceptable results, due to the presence of some contamination from the nearby source 4U 0142+614."
 In fact the PCA collimator (Strohmayer Jahoda 1998) has a transmission of about at the off-axis angle of this pulsar (~24°)., In fact the PCA collimator (Strohmayer Jahoda 1998) has a transmission of about at the off-axis angle of this pulsar $\sim$ 24').
 Since the luminosity of 4U 0142+614 shows little or no variability on long timescales (Israel 19993) we can estimate its contribution and model it in the spectral analysis., Since the luminosity of 4U 0142+614 shows little or no variability on long timescales (Israel 1999a) we can estimate its contribution and model it in the spectral analysis.
 Assuming the spectral parameters measured with ASCA (White et al., Assuming the spectral parameters measured with ASCA (White et al.
 1996: Nyy=0.95«107 7. power law photon index & = 3.67. blackbody temperature KT = 0.386 keV) and reducing the normalization according. to the collimator response. we expect from 4U 01424614 ~10 counts + in the 2-20 keV range.," 1996; $_H= 0.95\times 10^{22}$ $^{-2}$, power law photon index $\alpha$ = 3.67, blackbody temperature kT = 0.386 keV) and reducing the normalization according to the collimator response, we expect from 4U 0142+614 $\sim$ 10 counts $^{-1}$ in the 2-20 keV range."
 This corresponds to about, This corresponds to about
accurate coordinates for the 6 7D galaxies catched by the spectrograph A graphical displav of the SED for the 11. member ealaxies is given in the series of Fig.,accurate coordinates for the 6 “B” galaxies catched by the spectrograph A graphical display of the SED for the 11 member galaxies is given in the series of Fig.
 11 to 13.., \ref{f11} to \ref{f13}.
" The observations. obtained with a ""μου setup are reported irst in Fig. Τι."," The observations, obtained with a “bluer” setup are reported first in Fig. \ref{f11},"
 while the spectra are collected in he other two figures., while the spectra are collected in the other two figures.
" For a closer ""quick-Iook analysis of he two data sets. and. to increase S/N in the plots. all he clisplaved spectra have been homogeneously degraded o a EFWILAL resolution of 19Α."," For a closer “quick-look” analysis of the two data sets, and to increase S/N in the plots, all the displayed spectra have been homogeneously degraded to a FWHM resolution of 12."
. Once comparing the hree objects in common between and (namely ealaxies N30. N42. and N50. asin Fig.," Once comparing the three objects in common between and (namely galaxies N30, N42, and N50, asin Fig."
 11. and 12)) one sees hat along the wavelength. region in common the spectral xutern of absorption features is consistentIy reproduced in roth data sets., \ref{f11} and \ref{f12}) ) one sees that along the wavelength region in common the spectral pattern of absorption features is consistently reproduced in both data sets.
 Some dillerence can be noticed. on the contrary. for the overall slope of the continuum emission.," Some difference can be noticed, on the contrary, for the overall slope of the continuum emission."
 One has to consider. in this regard. that spectra have all been taken at fixed. (E/W) slit position angle: this is not the case for the spectra for which a range of slit inclinations led in some cases to a larger departure from the parallactic angle. and therefore to a slightly. poorer flux. calibration.," One has to consider, in this regard, that spectra have all been taken at fixed (E/W) slit position angle; this is not the case for the spectra for which a range of slit inclinations led in some cases to a larger departure from the parallactic angle, and therefore to a slightly poorer flux calibration."
 Phis effect has been explored by means of repeated spectra for the dl ealaxy N34 taken in dillerent nights., This effect has been explored by means of repeated spectra for the dE galaxy N34 taken in different nights.
 On the basis of the observed drift in the continuum shape we estimate that the induced. internal uncertainty of our [ux calibration can be quantified in  LOM..., On the basis of the observed drift in the continuum shape we estimate that the induced internal uncertainty of our flux calibration can be quantified in $\sim10$ .
of an adwvection-donminated: accretion mode in the inner porGous of (he accretion flow. is triggered by a decreasing Edcington ratio.,"of an advection-dominated accretion mode in the inner portions of the accretion flow, is triggered by a decreasing Eddington ratio."
 The decline of / might be due to a combination of a decreasing accretion rate and an increasing black-hole mass., The decline of $l$ might be due to a combination of a decreasing accretion rate and an increasing black-hole mass.
 An implication of (his scenario is that the masses of (he central black holes in galaxies which host BL Laes should. on average. be greater than the masses of black holes in galaxies which host FSRQs or optical QSOs.," An implication of this scenario is that the masses of the central black holes in galaxies which host BL Lacs should, on average, be greater than the masses of black holes in galaxies which host FSRQs or optical QSOs."
 Moreover. subclasses at earlier stages in (he blazar sequence should exhibit increasinely stronger cosmological evolution.," Moreover, subclasses at earlier stages in the blazar sequence should exhibit increasingly stronger cosmological evolution."
 Dadeetal.(1998) [ind evidence for negative cosmological evolution of X-ray selected BL Lac objects. and Stickeletal.(1991) [find evidence lor positive cosmological evolution in a radio-selected BL Lac sample. in accord with this picture.," \cite{bad98} find evidence for negative cosmological evolution of X-ray selected BL Lac objects, and \cite{sti91} find evidence for positive cosmological evolution in a radio-selected BL Lac sample, in accord with this picture."
 Our work provides strong support lor the suggestion bx DElia&Cavaliere(2000) aid. &D'Elia(2001). along parallel lines. but on the basis of general energy considerations and a generic cosmological evolution scenario lor quasars evolving into BL Lac objects.," Our work provides strong support for the suggestion by \cite{delia00} and \cite{cavaliere01} along parallel lines, but on the basis of general energy considerations and a generic cosmological evolution scenario for quasars evolving into BL Lac objects."
 We have combined the basic idea of such a cosmological evolution wilh a sell-consistent spectral blazar model aud demonstrated Chat (he spectral properties of the different blazar subclasses can be consistently explained by such an evolutionary sequence., We have combined the basic idea of such a cosmological evolution with a self-consistent spectral blazar model and demonstrated that the spectral properties of the different blazar subclasses can be consistently explained by such an evolutionary sequence.
 The blazar model adopted here is similar to the one previously used by Ghiselliniοἱal.(1998) but with the important addition of particle escape and adiabatic losses who had argued that the different blazar subelasses could be unified by an increasing level of external radiation to the soft radiation field in the emitting region., The blazar model adopted here is similar to the one previously used by \cite{ghisellini98} — but with the important addition of particle escape and adiabatic losses — who had argued that the different blazar subclasses could be unified by an increasing level of external radiation to the soft radiation field in the emitting region.
 To summniarize. we have proposed an evolutionary scenario linking FSRQs. LDLs. aud 1IBLs through gradual depletion of (he cireumnuclear environment of a supermassive black hole.," To summarize, we have proposed an evolutionary scenario linking FSRQs, LBLs, and HBLs through gradual depletion of the circumnuclear environment of a supermassive black hole."
 As the accretion power declines with time. less gas and dust is available to reprocess accretion-disk radiation and produce an external Conmpton-scattered component in the blazar jel.," As the accretion power declines with time, less gas and dust is available to reprocess accretion-disk radiation and produce an external Compton-scattered component in the blazar jet."
 Analvtic formulae are given to estimate the relevant model parameters lor FSRQs., Analytic formulae are given to estimate the relevant model parameters for FSRQs.
 We have calculated a spectral sequence for different blazar subclasses that are related. (hrough a one-parameter model defined bv the optical depth of the circumnuclear matter., We have calculated a spectral sequence for different blazar subclasses that are related through a one-parameter model defined by the optical depth of the circumnuclear matter.
 This scenario links radio-loud AGNs with progenitor merger galaxies and QSOs that constitute the high Eddington-ratio limit of the evolutionary sequence., This scenario links radio-loud AGNs with progenitor merger galaxies and QSOs that constitute the high Eddington-ratio limit of the evolutionary sequence.
 In analogv. wilh the observed anti-correlation between radio and soft X-ray activity in some Galactic black-hole σαι]αἱes. these progenitor sources would accrete with large Edcdington ratios. resulting in an accretion disk that quenches relativistic jet productioΕν," In analogy with the observed anti-correlation between radio and soft X-ray activity in some Galactic black-hole candidates, these progenitor sources would accrete with large Eddington ratios, resulting in an optically-thick accretion disk that quenches relativistic jet production."
 We (hank the anonvinous referee lor a very careful review ancl helpful and constructive comments., We thank the anonymous referee for a very careful review and helpful and constructive comments.
 The work of MD is supported by NASA through Chandra Postdoctoral Fellowship erant PF 9-LOQOT awarded by (he Chandra N-ray Center. which is operated by (he Smithsonian Astrophysical Observatory for NASA under contract NAS 8-39073.," The work of MB is supported by NASA through Chandra Postdoctoral Fellowship grant PF 9-10007 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS 8-39073."
 The work of CD is supported by the Office of Naval Research., The work of CD is supported by the Office of Naval Research.
a/é47~10° marking the cross-over between the two regimes.,$n/\zeta_{-17} \sim 10^3$ marking the cross-over between the two regimes.
 The HCN/CO abundance ratio can become large z107° in the high-ionisation phase even at low gas temperatures. due to the large densities of atomic and tonic carbon.," The HCN/CO abundance ratio can become large $\gtrsim 10^{-3}$ in the high-ionisation phase even at low gas temperatures, due to the large densities of atomic and ionic carbon."
 Here we have re-run these calculations using the same elemental gas-phase abundances. and with a slightly updated reaction set.," Here we have re-run these calculations using the same elemental gas-phase abundances, and with a slightly updated reaction set."
 Fig., Fig.
 4 shows the resulting abundance ratios as a function of /é_)7 for KK gas., \ref{fig:ratio} shows the resulting abundance ratios as a function of $n/\zeta_{-17}$ for K gas.
 At very low n/Zj;<100 corresponding to that in the nuclear region of 33227 the HCN/CO abundance ratio approaches ~107., At very low $n/\zeta_{-17} \lesssim 100$ corresponding to that in the nuclear region of 3227 the HCN/CO abundance ratio approaches $\sim 10^{-3}$.
 For comparison. Lepp&Dalgarno(1996) find a peak value of 5x1074 in their calculation.," For comparison, \cite{lep96} find a peak value of $5\times 10^{-4}$ in their calculation."
 These models track the abundances of numerous molecules across many orders of magnitude and shcww that at low //Z-457. the HCN/CO abundance ratio Is raised several orders of magnitude above that typically expected. to a level at which it approaches — and. given the uncertainties in such models. is commensurate with — that implied by the LVG mocels.," These models track the abundances of numerous molecules across many orders of magnitude and show that at low $n/\zeta_{-17}$, the HCN/CO abundance ratio is raised several orders of magnitude above that typically expected, to a level at which it approaches – and, given the uncertainties in such models, is commensurate with – that implied by the LVG models."
 Haradaetal.(2010) have shown that at elevated temperatures > 300 K. rapid hydrogenation of CN to HCN can increase the HCN/CO abundaices further still. and they comment that such warm gas may! be present in the X-ray heated gas near AGN.," \cite{har10} have shown that at elevated temperatures $\gtrsim$ 300 K, rapid hydrogenation of CN to HCN can increase the HCN/CO abundances further still, and they comment that such warm gas may be present in the X-ray heated gas near AGN."
 We caution however. that their higher temperature models for which HC/CO ts largest. correspond to n/Z4;107? which is significantly larger than the value we are invoking as characteristic for the nucleus of 33227.," We caution however, that their higher temperature models for which HCN/CO is largest, correspond to $n/\zeta_{-17} = 10^{4.5}$ which is significantly larger than the value we are invoking as characteristic for the nucleus of 3227."
 The models show that a combination of X-ray 1onisation and heating do yield high HCN abundances. although not yet quite as high as HCN/CO~107 as implied by the LVG analysis in Sec.," The models show that a combination of X-ray ionisation and heating do yield high HCN abundances, although not yet quite as high as $\sim10^{-2}$ as implied by the LVG analysis in Sec."
 3.3 for the nucleus., \ref{sec:others} for the nucleus.
" Further chemical modeling is required, but a high HCN/CO intensity ratio in the nucleus due to elevated X-ray ionisation rates appears plausible."," Further chemical modeling is required, but a high HCN/CO intensity ratio in the nucleus due to elevated X-ray ionisation rates appears plausible."
 In this picture. the lower HCN/CO intensity ratio in the ring may simply reflect the lower tonisation rate there. and not just a lower gas density m this circumgalactie environment.," In this picture, the lower HCN/CO intensity ratio in the ring may simply reflect the lower ionisation rate there, and not just a lower gas density in this circumgalactic environment."
 We present an LVG analysis of high-resolution observations of CO (2-1) and HCN (1-0) line emissions in the central regions of the Seyfert galaxy NGC 3227., We present an LVG analysis of high-resolution observations of CO (2-1) and HCN (1-0) line emissions in the central regions of the Seyfert galaxy NGC 3227.
 We find that, We find that
me of around 10.000 QSOs.,"sample of around 10,000 QSOs."
 Our resIts are thus conservative and will TOI uproved sienificautlv in the future. assuniug that ποιατίς errors cani x0 kept under control.," Our results are thus conservative and will be improved significantly in the future, assuming that systematic errors can be kept under control."
" We assume the spcοσα have signal to noise of 5 and rosOution of τοις, which is tvpical of t16 SDSS spectra."," We assume the spectra have signal to noise of 5 and resolution of 70km/s, which is typical of the SDSS spectra."
 Neither signal to roise nor resolution are particularly critical in this application. since one is LOSIv interested in huge scale correlationis where other parameters such as he cluperature of the eas or the density eniperature relation do uot plav a uajor role.," Neither signal to noise nor resolution are particularly critical in this application, since one is mostly interested in large scale correlations where other parameters such as the temperature of the gas or the density temperature relation do not play a major role."
 To sudyv the dark energy parameters we project the Fisher matrix to fewer paraueters. pariunetrizius the erowth factor evolution m terms of ¢)ele aud ws}.," To study the dark energy parameters we project the Fisher matrix to fewer parameters, parametrizing the growth factor evolution in terms of $\Omega_{\rm de}$ and $w(z)$."
 For the redshit evolution we lait ourselves to constant aud linear evolition models. uy=d)|Uxta1).," For the redshift evolution we limit ourselves to constant and linear evolution models, $w_q = w_0 + w_1 (a-1)$."
 The density iu dark energy aixd equation of st:ite are degencrate if one only uses iuforiiatiol1 from Ίσα forest., The density in dark energy and equation of state are degenerate if one only uses information from $\alpha$ forest.
 This is not surprisnug. sniee he redshift range probed is too simall to determine two paraucters frou the &yowth factor evolution (as mentioned above. we fiud that IT(+) information does not provide any additional coustraimts).," This is not surprising, since the redshift range probed is too small to determine two parameters from the growth factor evolution (as mentioned above, we find that $H(z)$ information does not provide any additional constraints)."
 Iu the ‘ollowing we fix Oqc aud present eirOrs on equatio1r of state only., In the following we fix $\Omega_{\rm de}$ and present errors on equation of state only.
 The motivatio1 for this is that other tests. most notably CMD combined witi large scale structure tests (ee. cluster counts. HHOrdaxy clustering. weak leusine). will be able to deter1C Qu. at +=0 verv accuratedv.," The motivation for this is that other tests, most notably CMB combined with large scale structure tests (e.g. cluster counts, galaxy clustering, weak lensing), will be able to determine $\Omega_{\rm de}$ at $z=0$ very accurately."
 If these tess also provide independent costraints on cy then for the tine «ependent v οἱ1ο can use our results to consral d., If these tests also provide independent constraints on $w_0$ then for the time dependent $w$ one can use our results to constrain $w_1$.
 Since the seusitivitv to the dark energy depeucds strongly ou the aout of dark energy at : »21 is clear tha je errors will depend strong VOithe assunied values of Og. and wt)., Since the sensitivity to the dark energy depends strongly on the amount of dark energy at $z>2$ it is clear that the errors will depend strongly on the assumed values of $\Omega_{\rm de}$ and $w(z)$.
 For 5 models studied here their value sare eiven in table 3.., For the models studied here their values are given in table \ref{T:qmodels}.
 The tadle also show: 10 CYTOTS OLL Wy ASSTe fixe 0deo (and wy in time dependeif mmodels} a απους OL Wy assuniue fixed O4. aud wy., The table also shows the errors on $w_0$ assuming fixed $\Omega_{\rm de}$ (and $w_1$ in time dependent models) and errors on $w_1$ assuming fixed $\Omega_{\rm de}$ and $w_0$.
 The errors are mareinalized over al the other piuzuueters., The errors are marginalized over all the other parameters.
 One ca1 see that the limuts improve if Wy Is nore ]YONIive or if wy is significantv negative. since the dark energy is t1011 more nu)OYant at higher redshitt.," One can see that the limits improve if $w_0$ is more positive or if $w_1$ is significantly negative, since the dark energy is then more important at higher redshift."
 Of particular interest are the limits on time depende ito., Of particular interest are the limits on time dependent $w$.
" For example. in uxxlels 7 aud Swe assune today iy0.5. which ijicreases tow=OL ane a=0.2 at z=2.6. respectively,"," For example, in models 7 and 8 we assume today $w_0=-0.8$, which increases to $w=-0.4$ and $w=-0.2$ at z=2.6, respectively."
 In such modeS le Crror on wy ds 0.2. which makes them distiuguishable at 1.56 with the current sample aud 26 with the full saluple. assunniug that both Qa. aud wy cau be accurately determined with the other methods.," In such models the error on $w_1$ is 0.2, which makes them distinguishable at $\sigma$ with the current sample and $\sigma$ with the full sample, assuming that both $\Omega_{\rm de}$ and $w_0$ can be accurately determined with the other methods."
" These errors improve further if we live iu à universe with lower matter density than @,,.=0.33 assumed here.", These errors improve further if we live in a universe with lower matter density than $\Omega_m=0.33$ assumed here.
 While there is no simple single parameter combination that describes the sensitivity to dark energy it is clear that the precision is correlated with Qua. at 2=2.6., While there is no simple single parameter combination that describes the sensitivity to dark energy it is clear that the precision is correlated with $\Omega_{\rm de}$ at $z=2.6$.
 Our results show that if Qa.=2.6)>0.2 then the deviations in the erowth factor are sufficientlv large to be detected in Ly-a forest spectra using the current SDSS sample., Our results show that if $\Omega_{\rm de}(z=2.6)>0.2$ then the deviations in the growth factor are sufficiently large to be detected in $\alpha$ forest spectra using the current SDSS sample.
 With the full SDSS sample this limit can be, With the full SDSS sample this limit can be
In this section. we analyze the validity of the assumption of constant (2.,"In this section, we analyze the validity of the assumption of constant $Q$."
 With a radius-dependent aceretion rate described. in equation (10)). we have then equation (4)) can be expressed as We assume. that the specific angularmomentum corresponding to «P is proportional to that of the gas in the disc. Le. ‘This is the case for thermal energy. driving outllows. magnetic field. centrifugal accelerating wind Pringle 2006)) and disc evaporation moclel.," With a radius-dependent accretion rate described in equation \ref{AccretionRate}) ), we have then equation \ref{Q}) ) can be expressed as We assume that the specific angularmomentum corresponding to $\Phi$ is proportional to that of the gas in the disc, i.e. This is the case for thermal energy driving outflows, magnetic field centrifugal accelerating wind \citealp{Mayer06}) ) and disc evaporation model."
 For the general situation (sz 1/2). we have and therefore where fgin is the angular momentum of e at the inner radius rin.," For the general situation ${s} \neq -1/2$ ), we have and therefore where $l_{\Phi,{\rm in}}$ is the angular momentum of $\Phi$ at the inner radius $r_{\rm in}$ ."
 Thus. the analysis presented in this paper holds [or sz—1/2.," Thus, the analysis presented in this paper holds for ${s} > -1/2$."
 For s<1/2. our analvsis may present a qualitative result.," For ${s} < -1/2$, our analysis may present a qualitative result."
" The dynamic equations of ΑΟΛΙ read as follows &Vi1904: Ixatoetal.2008: Li&Cao2009)). where 5, and 5» are the usual generalized. ratios of the specific heat τος=ap. Εν=const. and o. Af=fyros maintain the value of the stationary state."," The dynamic equations of ADAFs read as follows \citealp{Narayan94}; \citealp{Kato08}; ; \citealp{Li09}) ), where $\gamma_1$ and $\gamma_2$ are the usual generalized ratios of the specific heat, $\tau_{r\varphi}=-{\alpha}p$, $H/r=\rm const.$, and ${\Phi}$, ${\Delta}l= {{l_{{\mathop{\Phi}} }} - r\upsilon_\varphi}$ maintain the value of the stationary state."
 The self-similar solution of the above equations is We introduce small deviations of the clise parameters [rom the stationary. parameters as follows. where aj. 2. a3. and αι are constant.," The self-similar solution of the above equations is We introduce small deviations of the disc parameters from the stationary parameters as follows, where $a_1$, $a_2$, $a_3$ , and $a_4$ are constant."
 Withthe above equations. the evolutionequations of the perturbed variables are ‘The accretion rate is and its Fluctuating component is," Withthe above equations, the evolutionequations of the perturbed variables are The accretion rate is and its fluctuating component is"
Spectral fitting on its own cannot distinguish. between these possibilities and. indeed. gives Little information on the geometry of the emitting regions.,"Spectral fitting on its own cannot distinguish between these possibilities and indeed, gives little information on the geometry of the emitting regions."
 Combining spectral fitting with a study. of the variability properties. of the dillerent energy. bands gives information on the connection between the spectral components and their possible emission mechanisms., Combining spectral fitting with a study of the variability properties of the different energy bands gives information on the connection between the spectral components and their possible emission mechanisms.
 The fractional variability of the X-ray light. curves is encrey dependent., The fractional variability of the X-ray light curves is energy dependent.
 In the case of Narrow Line Sevíert 15. such as766. the variability appears strongest in the middle of the bband. around 12 keV decreasing noticeably towards lower and higher energies.," In the case of Narrow Line Seyfert 1s, such as, the variability appears strongest in the middle of the band, around 1–2 keV decreasing noticeably towards lower and higher energies."
 This behaviour suggests that the variability is produced mainly by the power law component while the soft excess anc Compton reflection components remain constant (e.gFabianetal..2002)., This behaviour suggests that the variability is produced mainly by the power law component while the soft excess and Compton reflection components remain constant \citep[e.g][]{fabian02}.
 In this scenario. the constant components add to the Dux of the variable component but. not to the variability. thus diluting the fractional variability in the energy bands where they dominate the spectrum.," In this scenario, the constant components add to the flux of the variable component but not to the variability, thus diluting the fractional variability in the energy bands where they dominate the spectrum."
 This two-component (constant plus variable) model can broadly. reproduce the Iux-dependent spectral changes observed in several AGN (Lavlor2003:Vaughan&Fabian.2004) .," This two-component (constant plus variable) model can broadly reproduce the flux-dependent spectral changes observed in several AGN \citep{taylor,
 vaughan04} ."
 In particular. have used the available ~600 ks of deata of tto show that the spectral variability of this AGN on time-scales longer than 20 ks. can be largely explained through two distinct spectral components that vary in relative normalisation.," In particular, \citet{miller} have used the available $\sim 600$ ks of data of to show that the spectral variability of this AGN on time-scales longer than 20 ks, can be largely explained through two distinct spectral components that vary in relative normalisation."
 In its simplest form. however. the two-component model cannot reproduce the dependence of the spectral variabilitv. ie. if only one of the spectral components varies in normalisation. the spectral changes would. depend only on the relative [luxes regardless of the time-scale of heir Huctuations.," In its simplest form, however, the two-component model cannot reproduce the dependence of the spectral variability, i.e. if only one of the spectral components varies in normalisation, the spectral changes would depend only on the relative fluxes regardless of the time-scale of their fluctuations."
 The fact that the energy. bands behave differently on. different time-scales can be readily seen hrough the power density spectrum (PDS). which measures he variability power as a function of Fourier. frequency.," The fact that the energy bands behave differently on different time-scales can be readily seen through the power density spectrum (PDS), which measures the variability power as a function of Fourier frequency."
 1n most cases. the PDS of AGN are well described. by a woken power law model. with a slope of ~1. below the oeak and ~2 or steeper. at. higher frequencies.," In most cases, the PDS of AGN are well described by a broken power law model, with a slope of $\sim -1$ below the break and $\sim -2$ or steeper, at higher frequencies."
 Energy dependence of the PDS shape is normally observable around he break frequency. and implies that higher energy. bands are more rapidly. varving., Energy dependence of the PDS shape is normally observable around the break frequency and implies that higher energy bands are more rapidly varying.
 This additional variability power can appear as a Latter high-frequency PDS slope for higher energies. as in NGC 4051 (Mellardyetab.2004)... as a shift of the break to higher frequencies. as observed. for the first time in bhy Markowitzetal.(2007) or as a high-frequeney Lorentzian component that appears stronger in the energy PDS of Ark 564 (Mellardyctal..2007).," This additional variability power can appear as a flatter high-frequency PDS slope for higher energies, as in NGC 4051 \citep{McHardy4051}, as a shift of the break to higher frequencies, as observed for the first time in by \citet{markowitz} or as a high-frequency Lorentzian component that appears stronger in the high-energy PDS of Ark 564 \citep{mchardy07}."
. This simple two-component model can explain. the enerev dependence of the PDS normalisation but not energv-dependent PDS shapes., This simple two-component model can explain the energy dependence of the PDS normalisation but not energy-dependent PDS shapes.
 The fact that many AGN co clisplay more short time-scale variability at higher energies does not rule out. two-component models. but it. implies that the variability is more complex than simple changes in normalisation of one of the components.," The fact that many AGN do display more short time-scale variability at higher energies does not rule out two-component models, but it implies that the variability is more complex than simple changes in normalisation of one of the components."
 One possibility is that the variable component changes its spectral shape when viewed on different time-scales., One possibility is that the variable component changes its spectral shape when viewed on different time-scales.
 This can happen. for example. if softer energies are emitted by a more extended region. then their short time-scale variability can be suppressed and. therefore. the high-frequency spectrum appears harder.," This can happen, for example, if softer energies are emitted by a more extended region, then their short time-scale variability can be suppressed and, therefore, the high-frequency spectrum appears harder."
 Alternatively. both spectral components might be variable but with ciffercnt timing-properties. cach one defining the behaviour of the energy bands where they ominate the spectrum.," Alternatively, both spectral components might be variable but with different timing-properties, each one defining the behaviour of the energy bands where they dominate the spectrum."
 Markowitzetal.(2007). studied in detail the energy ependence of the PDS of ΠΠΠΕ data., \citet{markowitz} studied in detail the energy dependence of the PDS of using data.
 Vheyv lind that the 1.112 keV energv band has 4oienificantly more variability power than lower energy bands. on time-scales around the break in the PDS.," They find that the 1.1–12 keV energy band has significantly more variability power than lower energy bands, on time-scales around the break in the PDS."
 This energv-ependent shape can be either interpreted as a shift. of 10 break frequency to higher values for higher energies or is an additional variability component with a hard energy μα»ectrum and a band-limited PDS., This energy-dependent shape can be either interpreted as a shift of the break frequency to higher values for higher energies or as an additional variability component with a hard energy spectrum and a band-limited PDS.
 In this paper. we analyze rw same data set to determine the dependence of the amplitude X the variability on energy. ancl time-scale by calculating 16 F'ourier-resolved. spectra (Revnivtiseyetal.," In this paper, we analyze the same data set to determine the dependence of the amplitude of the variability on energy and time-scale by calculating the Fourier-resolved spectra \citep{Revnivtsev}."
..1999)... In short. this. technique produces the absolute root-mean-square (rms) amplitude of variability and also the fractional rms variability (rms civided by count rate) as a function of energy and time-scale.," In short, this technique produces the absolute root-mean-square (rms) amplitude of variability and also the fractional rms variability (rms divided by count rate) as a function of energy and time-scale."
 H£ the variability is produced. by a spectral component varving in normalisation. the Fouricr-resolved. spectrum will have the same shape as the variable spectral component.," If the variability is produced by a spectral component varying in normalisation, the Fourier-resolved spectrum will have the same shape as the variable spectral component."
 IE there are additional constant spectral components. these will dilute the variability in the energy bands where this constant component dominates.," If there are additional constant spectral components, these will dilute the variability in the energy bands where this constant component dominates."
 Vhe dilution of the fractional variability is evidenced in the variance spectra., The dilution of the fractional variability is evidenced in the variance spectra.
 The paper is organized as Follows: we describe the data reduction in Sec. 2..," The paper is organized as follows: we describe the data reduction in Sec. \ref{data},"
 and the LFourier-resolved. spectrum technique in Sec. 3., and the Fourier-resolved spectrum technique in Sec. \ref{technique}.
 The resulting normalisecl excess variance (m&gx4) spectra. discussed in Sec.," The resulting normalised excess variance ) spectra, discussed in Sec."
 4 show the characteristic shape found in other NLSIs where the ppeaks around 12 keV. at low frequencies.," \ref{nxs} show the characteristic shape found in other NLS1s where the peaks around 1–2 keV, at low frequencies."
 At high [requencies however. the sspectra becomes harder.," At high frequencies however, the spectra becomes harder."
 Εις frequency dependence: is studied in more detail in Sec., This frequency dependence is studied in more detail in Sec.
 5. where we examine the spectral shape of the variable components only. through the unnormalised sspectra.," \ref{rms} where we examine the spectral shape of the variable components only, through the unnormalised spectra."
 We discuss the possible contribution of an aclelitional spectral component to the sspectra in Sec. 6.., We discuss the possible contribution of an additional spectral component to the spectra in Sec. \ref{constant}.
 In Sec., In Sec.
 7. we discuss the origin of the variability and frequency dependence of the sspectra in cdilferent possible scenarios.," \ref{discussion}
 we discuss the origin of the variability and frequency dependence of the spectra in different possible scenarios."
 wavas recently observed by [for ~500 ks [rom 2005-05-23 to 2005-05-31 cluring revolutions 999.1004 (observation LD in the range 0304031-1]01)., was recently observed by for $\sim 500$ ks from 2005-05-23 to 2005-05-31 during revolutions 999–1004 (observation ID in the range 030403[1-7]01).
 llere we combine this data set with. earlier observations made on 2000-05-20 (obs LD 00906020101) and 2001-05-2021 (obs LD 0100141301) during orbits S2 and 265. respectively.," Here we combine this data set with earlier observations made on 2000-05-20 (obs ID 0096020101) and 2001-05-20–21 (obs ID 0109141301) during orbits 82 and 265, respectively."
 Spectral fitting ancl spectral variability analvses of these data have been published by 2006)..," Spectral fitting and spectral variability analyses of these data have been published by\citet{miller06, miller,turner,turner06}. ."
fice. the mericiaus of longitude).,(i.e. the meridians of longitude).
 Thus by the argument given above. the average flexion integrated around a random great circle must be (f)=1. because the trucks velocity vector on a random ereat circle must rotate by 3607 as it circles the 360° of are completing that great. circle ou the elobe.," Thus by the argument given above, the average flexion integrated around a random great circle must be $\langle f\rangle = 1$, because the truck's velocity vector on a random great circle must rotate by $360^\circ$ as it circles the $360^\circ$ of arc completing that great circle on the globe."
 The magnitude of the velocity vector of the truck ou the map is larger the further from the north pole it is aud so its rotation per augle of are of truck travel ou the globe is larger there as well. and so the flexion along that rauclom geodesic is larger the further away [rom the pole one 1s. with the integrated average value along the whole great circle being €.d;-1.," The magnitude of the velocity vector of the truck on the map is larger the further from the north pole it is and so its rotation per angle of arc of truck travel on the globe is larger there as well, and so the flexion along that random geodesic is larger the further away from the pole one is, with the integrated average value along the whole great circle being $\langle f \rangle =1$."
" The Mercator projection (see Fig 2)) is conformal aud so ouly the scale factor ehauges as a fuuctiou of position on the map (Le. ger=gyy. aud gry=0 and the Tissot ellipses are all circles with radii proportional to 1/9,,)."," The Mercator projection (see Fig \ref{fg:mercator}) ) is conformal and so only the scale factor changes as a function of position on the map (i.e. $g_{xx} = g_{yy}$, and $g_{xy} = 0$ and the Tissot ellipses are all circles with radii proportional to $g_{xx}$ )."
 But there is bending., But there is bending.
 The northern boundary between the continental United States and Canada at the LO! parallel of latitude is shown as a straight line in the Mercator Map. but really it is a small circle that is concave to the north.," The northern boundary between the continental United States and Canada at the $49^{th}$ parallel of latitude is shown as a straight line in the Mercator Map, but really it is a small circle that is concave to the north."
 If oue drove a truck down tliat border [rom west to east. one would have to turn tlie steering wheel slightly to the left so that one was coutinually changiug direction.," If one drove a truck down that border from west to east, one would have to turn the steering wheel slightly to the left so that one was continually changing direction."
 The great circle route (the straightest route) connecting the Washiugtou State aud Minnesota (both at the [9th parallel) is a straielt liue which goes entirely through Canada., The great circle route (the straightest route) connecting the Washington State and Minnesota (both at the 49th parallel) is a straight line which goes entirely through Canada.
 This straight line ou the globe when extended. passes south of the northern part ol Maine. so the continental United States is bend downward like a frown iu tle Mercator Map. (," This straight line on the globe when extended, passes south of the northern part of Maine, so the continental United States is bend downward like a frown in the Mercator Map. ("
See Figure 3 sul 1)).,See Figure \ref{fg:us_mercator} and \ref{fg:us_oblique_mercator}) ).
 Likewise. Maine on a Mercator map Maine sags below the line connecting Washiugtou State and Minnesota. while ou the globe this is not true.," Likewise, Maine on a Mercator map Maine sags below the line connecting Washington State and Minnesota, while on the globe this is not true."
 Iu the Mercator projection. the flexion along the equator is zero. also along all merkliaus of ongitude. but these are a set of measure zero.," In the Mercator projection, the flexion along the equator is zero, also along all meridians of longitude, but these are a set of measure zero."
 A random geodesic is a great circle that is inclined at soie angle between 07 aud 907 with respect to the equator., A random geodesic is a great circle that is inclined at some angle between $0^\circ$ and $90^\circ$ with respect to the equator.
 Ou the Mercator map this is à wavy ine that bends downward iu the northern—— hemisphere. aud by syiuuetry. upward in the southern.," On the Mercator map this is a wavy line that bends downward in the northern hemisphere, and by symmetry, upward in the southern."
 Since the eurvatiures are equal aud opposite in the two hemispheres. the average flexion (f)=0. jut this is misleadiug because the flexion at each point off the equator is not zero.," Since the curvatures are equal and opposite in the two hemispheres, the average flexion $\langle f\rangle =0$, but this is misleading because the flexion at each point off the equator is not zero."
 So i we are alius map projections by the amount of flexion they coutain we should use the absolute value of he flexion iustead: |/|., So if we are rating map projections by the amount of flexion they contain we should use the absolute value of the flexion instead: $|f|$.
 In a region where the flexion does not change sign (such as the northern iemisphere iu the Mercator projection or the entire stereographic map)VY the total bencing of a eeodesic segment will be the integral of the flexion |/| over that segment., In a region where the flexion does not change sign (such as the northern hemisphere in the Mercator projection or the entire stereographic map) the total bending of a geodesic segment will be the integral of the flexion $|f|$ over that segment.
 In fact. iu Section 6.1 we will evaluate the overall flexion on a map by simply pickiug random poiuts on the sphere and random cdirectious for geodesics going through them. and then calculating the absolute value Lor the flexion for all raudom points ou the globe ancl raucom directions through them.," In fact, in Section \ref{sec:numerical} we will evaluate the overall flexion on a map by simply picking random points on the sphere and random directions for geodesics going through them, and then calculating the absolute value for the flexion for all random points on the globe and random directions through them."
 We can calculate the flexion for any point in the Mercator (or any other) projection through any ceodesic using spherical trigonometry., We can calculate the flexion for any point in the Mercator (or any other) projection through any geodesic using spherical trigonometry.
 As a remiuder to the reader. the Mercator projection uses the mappine: where here and throughout. A is the lougitude expressed iu radians. and © is the latitude expressed in radians.," As a reminder to the reader, the Mercator projection uses the mapping: where here and throughout, $\lambda$ is the longitude expressed in radians, and $\phi$ is the latitude expressed in radians."
"Llere J,=J,(2) and Ji=iz).",Here $J_n=J_n(z)$ and $J_l=J_l(z^\prime)$.
 Equations (11)-(12) give the scattering cross-sections in case of a gvrating electron., Equations (11)-(12) give the scattering cross-sections in case of a gyrating electron.
 In astrophysical applications. the particles generally perform helical motion. and the corresponding cross-sections can be obtained from equations (11)-(12) by means of relativistic transformations.," In astrophysical applications, the particles generally perform helical motion, and the corresponding cross-sections can be obtained from equations (11)-(12) by means of relativistic transformations."
" In case of relativistic longitudinal motion of the electron. 5|=(1"")DTox ]oitds convenient to involve the cross-section X defined as the ratio of the number of the scattered photons to the flux density of the photons Ilving against the electron."," In case of relativistic longitudinal motion of the electron, $\gamma_\Vert=(1-\beta_\Vert^2)^{-1/2}\gg 1$, it is convenient to involve the cross-section $\Sigma$ defined as the ratio of the number of the scattered photons to the flux density of the photons flying against the electron."
 Vhis quantity is a relativistic invariant and isrelated to the cross-section m as (w/w')mdO'=(1j|cosAddO”.," This quantity is a relativistic invariant and isrelated to the cross-section $\sigma$ as $(\omega/\omega^\prime){\rm d}\sigma/{\rm
d}O^\prime=(1-\beta_\Vert\cos\theta){\rm d}\Sigma/{\rm
d}O^\prime$."
" Then making use of the transformations w,=wTR aySasyay and dO.=dO'/-Tu (where pol(6088. ij!SLdqcos. and the quantities of the guiding centre [rame are denoted by the subscript c). one can obtain that where the quantities entering (deο], should be expressed via the quantities of the laboratory frame."," Then making use of the transformations $\omega_c=\omega\gamma_\Vert\eta$, $\omega_c^\prime=\omega^\prime\gamma_\Vert\eta^\prime$, and ${\rm
d }O_c^\prime={\rm d}O^\prime/\gamma_\Vert^2\eta^{\prime^2}$ (where $\eta\equiv 1-\beta_\Vert\cos\theta$, $\eta^\prime\equiv
1-\beta_\Vert\cos\theta^\prime$, and the quantities of the guiding centre frame are denoted by the subscript 'c'), one can obtain that where the quantities entering $({\rm d}\sigma/{\rm d}O^\prime)_c$ should be expressed via the quantities of the laboratory frame."
 Lt is worthy to examine the symmetry properties of the cross-sections (11)-(12)., It is worthy to examine the symmetry properties of the cross-sections (11)-(12).
 Weeping in mind that η.dwS/Oa. ∪⊔⋖⋅≼⇍⋜⋯⊳∖∢⊾⋖⋅↿↓↥⋜⊔⊢∣⋤∣∕∣↴⋜⊔⋅⋖⋅⊳∖∙∖⇁⊔↓⊔↓∢⊾↿↓⋅⊔∼⋜↧↓∖∖⋎↓↿↓↥↓⋅⋖⋅⊳∖↓≻⋖⊾≼⇍↿⋯↿↓↕⋖⋅⊳∖↓⊔↓⊔∐⋜⋯⋖⋅∪⊔⊳∖≼∼↓↥⋜⋯⋏∙≟∢⊾∣∽↙⋎∶∣∽↙⋎⊳⊔∶∣⊳⋜⋯∠⇂∣∶⋅∣⊳⋜⋯∠⊔↥∢⊾⊔⊓⊾. . . ; .⋅ the cross-sections. can be written. in. the form⋅ deο∕=Y.1svar. where s;7 are svmmoetrical ⋠⋠in the above mentioned. sense.," Keeping in mind that $n\Omega
-\omega\equiv l\Omega-\omega^\prime$ , one can see that $\vert
a_{nl}^{ij}\vert$ are symmetrical with respect to the simultaneous change $\omega{\iff}\omega^\prime$, $n{\iff}l$, and $i{\iff} j$, and hence the cross-sections can be written in the form ${\rm
d}\sigma^{ij}/{\rm d
}O^\prime=\sum_{\nu}s_\nu^{ij}\omega^{\prime^4}$, where $s_\nu^{ij}$ are symmetrical in the above mentioned sense."
 This corresponds to the symmetry of each harmonic of the scattering probability with respect to the initial and final photon states., This corresponds to the symmetry of each harmonic of the scattering probability with respect to the initial and final photon states.
 Indeed. the power supplied by the scattering electron can be presented. as where N(A) is the occupation number of the incident photons and iw is the scattering probability.," Indeed, the power supplied by the scattering electron can be presented as where $N({\bmath k})$ is the occupation number of the incident photons and $w$ is the scattering probability."
 With equations (13)-(14) it is obvious that wy.xscepp.," With equations (13)-(14) it is obvious that $w_\nu\propto
s_\nu\omega\omega^\prime\eta\eta^\prime$."
 The general form of the scattering cross-section given by equations (11)-(12) is so complicated that it can hardly be involved directly in concrete applications., The general form of the scattering cross-section given by equations (11)-(12) is so complicated that it can hardly be involved directly in concrete applications.
 To analyze the basic features of the scattering oll a evrating electron we turn to reasonable approximations. (, To analyze the basic features of the scattering off a gyrating electron we turn to reasonable approximations. (
Note that the approximate cross-sections obtained below refer to the guiding-centre frame and it is necessary to apply the Lorentz transformation (13) in order to use them in any realistic caleulations.),Note that the approximate cross-sections obtained below refer to the guiding-centre frame and it is necessary to apply the Lorentz transformation (13) in order to use them in any realistic calculations.)
 First of all. we consider the limiting case when Jj20.," First of all, we consider the limiting case when $\beta_0\to 0$."
" Xs coz$0. one can use the approximation of the Bessel function at small arguments. taking into account that Jνο)=(1)"" 4,(C0)."," As $z,z^\prime \to
0$, one can use the approximation of the Bessel function at small arguments, taking into account that $J_{-n}(\zeta)=(-1)^nJ_n(\zeta)$ ."
 Phen only the zeroth harmonic. v=0 (u tw). vields anon-zero contribution to the cross-sections. and they are reduced to the form," Then only the zeroth harmonic, $\nu=0$ $\omega^\prime=\omega$ ), yields anon-zero contribution to the cross-sections, and they are reduced to the form"
"Compton thick Sv2s are hosted in strongly barred «μέσα», to be compared with ~ of the general population.","Compton thick Sy2s are hosted in strongly barred systems, to be compared with $\sim$ of the general population."
 Maioling ot al. (, Maiolino et al. (
1997) found that Syv2s are characterized by a rate of non-axisviunietrie potentials Gucluding interactions and peculiar miorphlologies) about Ineher than Svls. this difference appears sieuificant.,"1997) found that Sy2s are characterized by a rate of non-axisymmetric potentials (including interactions and peculiar morphologies) about higher than Sy1s, this difference appears significant."
 Tut Malkau (1998) πα the occurence of bars in Sv2s not sienificautly higher than in Svls within the CEA aud the 12:0. samples., Hunt Malkan (1998) find the occurence of bars in Sy2s not significantly higher than in Sy1s within the CfA and the $\mu m$ samples.
 Tn the samples of Πο et al. (, In the samples of Ho et al. (
1997a) aud Mulchaey Reean (1997) the occurrence of bars iu type 2 Sevferts is higher than type 1 Sevferts.,1997a) and Mulchaey Regan (1997) the occurrence of bars in type 2 Seyferts is higher than type 1 Seyferts.
 These results indicate that even if bars drive gas into the ciretunnuclear region. such gas does not reduce much the opening angle of the light. cones.," These results indicate that even if bars drive gas into the circumnuclear region, such gas does not reduce much the opening angle of the light cones."
 Yet. if the correlation between bar streneth and amount of ciremuuclear gas obtained for Sv2s applies also to Svls. we would expect a large amount of eas in the Οτοιοσα region of barred Svls as well.," Yet, if the correlation between bar strength and amount of circumnuclear gas obtained for Sy2s applies also to Sy1s, we would expect a large amount of gas in the circumnuclear region of barred Sy1s as well."
 The cireumuiuclear (cold) gas is expected to reflect the uuclear N-vav radiation., The circumnuclear (cold) gas is expected to Compton-reflect the nuclear X-ray radiation.
 This Conmptou-reflected component should flatten the X-ray spectruu imn the 1030 keV spectral range., This Compton-reflected component should flatten the X-ray spectrum in the 10–30 keV spectral range.
 Therefore. within the barcireunmuclear gas connection scenario depicted above. we would expect barred Sy1s to have a flatter spectrum in the 1030 keV baud.," Therefore, within the bar--circumnuclear gas connection scenario depicted above, we would expect barred Sy1s to have a flatter spectrum in the 10–30 keV band."
" However. this test is subject ο vallous caveats,"," However, this test is subject to various caveats."
 First. variability affects he slope of the observed spectrum because of the tine-lag between the primary anc reprocessed radiation.," First, variability affects the slope of the observed spectrum because of the time-lag between the primary and reprocessed radiation."
 Second. a fraction of he “cold” reflection is expected to come from the accretion disk.," Second, a fraction of the “cold” reflection is expected to come from the accretion disk."
 Third. the effect is expected to be small: the reflected conrponeut should coutribute no nore han ~30% in this spectral region.," Third, the effect is expected to be small: the reflected component should contribute no more than $\sim$ in this spectral region."
 Fourth. to date spectra in this N-rav baud are sparse and with low scusitivity.," Fourth, to date spectra in this X-ray band are sparse and with low sensitivity."
 So far. the ouly (stall) siuuple of Sv1s observed at energies higher than 10 keV is the one presented m Naudra Pouuds (1991). that use CGinea data.," So far, the only (small) sample of Sy1s observed at energies higher than 10 keV is the one presented in Nandra Pounds (1994), that use Ginga data."
 Their sample coutaius nine Svls whose host ealaxy have a bar classification., Their sample contains nine Sy1s whose host galaxy have a bar classification.
 As shown iu Tab., As shown in Tab.
 3 the PAxead of the photon index measured between 10 and 18 seV ds laree., 3 the spread of the photon index measured between 10 and 18 keV is large.
 Nonetheless. Tab.," Nonetheless, Tab."
 3 shows a tendeney for the jud Xaay spectra of barred Sy1s to be fatter than the uubared Svls., 3 shows a tendency for the hard X-ray spectra of barred Sy1s to be flatter than the unbarred Sy1s.
 Large amounts of cireunummcelear gas iu Svis could © detected via dust-reprocessed light iu the iufrared., Large amounts of circumnuclear gas in Sy1s could be detected via dust-reprocessed light in the infrared.
 More ciremmauclear gas would imply mere wan CAGN-leatcc) dust. hence more infrared emission relative to the intrinsic Iuniinositv of the AGN (traced by the hard ταν uuimnositv).," More circumnuclear gas would imply more warm (AGN-heated) dust, hence more infrared emission relative to the intrinsic luminosity of the AGN (traced by the hard X-ray luminosity)."
 The midIR (~10j00) is an excellent baud o look for this excess. since the AGN IR cunission peaks here CMaioliuo et al.," The mid–IR $\sim 10\mu m$ ) is an excellent band to look for this excess, since the AGN IR emission peaks there (Maiolino et al."
 1995)., 1995).
 Also. bv using narrow beam photometry it is possible to isolate the coutribution of the AGN from the host ealaxy.," Also, by using narrow beam photometry it is possible to isolate the contribution of the AGN from the host galaxy."
 Witlin the scenario ofthe barcircunmnuclear eas connection. barred Svls are expected o show a mnid-IR to N-rav flux ratio higher had non-xured Sx]s.," Within the scenario of the bar--circumnuclear gas connection, barred Sy1s are expected to show a mid-IR to X-ray flux ratio higher than non-barred Sy1s."
 Yot. several caveats affect this tes as well.," Yet, several caveats affect this test as well."
 Both short iux long terii variability plague the reliabilitv of the N-rav flux as a calibrator of the ACN Buuinosity., Both short and long term variability plague the reliability of the X-ray flux as a calibrator of the AGN luminosity.
 Equilibrium temperature arguments indicate that the dust cuuitting sienificantlv at 105/45 should be located within the centra l10 pe: therefore. excess of cireiunmmclear gas distributed over the 100 pe scale woule not be probed by this indicator.," Equilibrium temperature arguments indicate that the dust emitting significantly at $\mu m$ should be located within the central 1–10 pc; therefore, excess of circumnuclear gas distributed over the 100 pc scale would not be probed by this indicator."
 Finally. even the snall aperture (5) used in niost of the groundbased mid-IR observations mig1 oeclude the coutribution from a central compact starburst.," Finally, even the small aperture $''$ ) used in most of the groundbased mid-IR observations might include the contribution from a central compact starburst."
 Tab., Tab.
 3 reports the mean of the μη 5LokeV luminosity ratio as a function of the bar strength for a sample of 19 Syls., 3 reports the mean of the $\mu m$ /2–10keV luminosity ratio as a function of the bar strength for a sample of 19 Sy1s.
 The 1ü4050 data are from Maiolino et al. (, The $\mu m$ data are from Maiolino et al. (
1995) aud from Cauricin et al. (,1995) and from Giuricin et al. (
1995): the N-vay data are frou Malaguti et al. (,1995); the X-ray data are from Malaguti et al. (
199D. where we choose the datu closes in time to the mid-IR observation. to minuinize long term. variability effects.,"1994), where we choose the datum closest in time to the mid-IR observation, to minimize long term variability effects."
" There is a tendency for barred svsteuis to have a ugher Lio,,,/L ratio. though. the spread is large and the statistics are xpoor."," There is a tendency for barred systems to have a higher $_{10\mu m}$ $_X$ ratio, though the spread is large and the statistics are poor."
 The important result of our study is that the absorbing column deusitv of type 2 Sevterts strouegly correlates with the presence of a stellar bar iu their host galaxies., The important result of our study is that the absorbing column density of type 2 Seyferts strongly correlates with the presence of a stellar bar in their host galaxies.
 As discussed. in the Iutroductiou. this result is uot colpletely unexpected: stellar bars are very effective iu daivingo gas iuto the central region. thus contributing to the obscurationOo of ACNs.," As discussed in the Introduction, this result is not completely unexpected: stellar bars are very effective in driving gas into the central region, thus contributing to the obscuration of AGNs."
 On the other hand this gas, On the other hand this gas
"frequency), and only the (Nmem) highest ranked stars are considered cluster members and transposed to the respective decontaminated CMD (e.g. Figs.","frequency), and only the $\left<N_{mem}\right>$ highest ranked stars are considered cluster members and transposed to the respective decontaminated CMD (e.g. Figs."
 5 and 6))., \ref{fig5} and \ref{fig6}) ).
" 'The subtraction efficiency, i.e. the difference between the expected number of field stars (which may be fractional) and the number of stars effectively subtracted (which is integer) from each cell, summed over all cells, is for 992 and for 1197."," The subtraction efficiency, i.e. the difference between the expected number of field stars (which may be fractional) and the number of stars effectively subtracted (which is integer) from each cell, summed over all cells, is for 92 and for 197."
 As a caveat we note that the present decontamination approach implicitly assumes that the field colour-magnitude distribution somewhat matches that of the cluster., As a caveat we note that the present decontamination approach implicitly assumes that the field colour-magnitude distribution somewhat matches that of the cluster.
" Figure 1 shows some gas and dust around both clusters, which might lead to appreciable reddening and differential reddening."," Figure \ref{fig1}
 shows some gas and dust around both clusters, which might lead to appreciable reddening and differential reddening."
" While the effect in the foreground contamination may be small, it should be more important in the background."," While the effect in the foreground contamination may be small, it should be more important in the background."
" However, the 374 Galactic quadrant location of 1197 and 992 is expected to minimise the background contamination."," However, the $3^{rd}$ Galactic quadrant location of 197 and 92 is expected to minimise the background contamination."
 The number-density of the probable member stars (mem) are shown in the Jx(J—Κε) CMDs in Figure 2 (top panels)., The number-density of the probable member stars $\eta_{mem}$ ) are shown in the $\jj\times\jk$ CMDs in Figure \ref{fig2} (top panels).
" In both cases, most of the stars are relatively faint and red, covering a wide range in colour, which is expected of PMS stars somewhat affected by differential reddening."," In both cases, most of the stars are relatively faint and red, covering a wide range in colour, which is expected of PMS stars somewhat affected by differential reddening."
 Also shown in Figure 2 (bottom panels) is the survival frequency of the decontaminated stars., Also shown in Figure \ref{fig2} (bottom panels) is the survival frequency of the decontaminated stars.
" Again, the highest membership probabilities occur among the PMS stars."," Again, the highest membership probabilities occur among the PMS stars."
 Our decontamination approach relies upon differences in the colour and magnitude distribution of stars located in separate spatial regions., Our decontamination approach relies upon differences in the colour and magnitude distribution of stars located in separate spatial regions.
" For a star cluster, which can be characterised by a single-stellar population projected against a Galactic stellar field, the decontaminated surface-density is expected to present a marked excess at the assumed cluster position."," For a star cluster, which can be characterised by a single-stellar population projected against a Galactic stellar field, the decontaminated surface-density is expected to present a marked excess at the assumed cluster position."
" Maps of the spatial distribution of the stellar surface-density (c, in units of starsarcmin2), built with field-star decontaminated photometry to maximise the cluster/background contrast, are shown in Figs."," Maps of the spatial distribution of the stellar surface-density $\sigma$, in units of $\rm stars\,arcmin^{-2}$ ), built with field-star decontaminated photometry to maximise the cluster/background contrast, are shown in Figs."
 3 (Cr1197) and 4 992)., \ref{fig3} 197) and \ref{fig4} 92).
" Also shown are the isopleths, in which cluster size and geometry can be observed."," Also shown are the isopleths, in which cluster size and geometry can be observed."
 The surface density is computed in a rectangular mesh with, The surface density is computed in a rectangular mesh with
are horn intrinsically fainter. they are visible oulv at more recent epochs. however. their production is also assumed to have been coutinuous since the Big Bane.,"are born intrinsically fainter, they are visible only at more recent epochs, however, their production is also assumed to have been continuous since the Big Bang."
" If it is assumed that these objects don't just disappear. they must still exist in some form. and in both models they aest then also Οδ as objects whose ayes are continous from LOS £o 1.3«1071"" yes,"," If it is assumed that these objects don't just disappear, they must still exist in some form, and in both models they must then also exist as objects whose ages are continuous from $10^{8}$ to $1.3\times10^{10}$ yrs."
 Most ποια]. galaxies are assuned to have ages ereater than LO Car., Most normal galaxies are assumed to have ages greater than 10 Gyr.
 Have the galaxies with ages near 1 Gyr been somehow overlooked?, Have the galaxies with ages near 1 Gyr been somehow overlooked?
 Are they vet to be discovered?, Are they yet to be discovered?
 Tow accurate are the ages that have been determined?, How accurate are the ages that have been determined?
 These are ouly some of the questions that need to be asked if QSOs are a short-lived) phenomenon. and they need to be asked regardless of whetler the cosinological model or the feed? 1odel is the correct ono.," These are only some of the questions that need to be asked if QSOs are a short-lived phenomenon, and they need to be asked regardless of whether the cosmological model or the $local$ model is the correct one."
 Using the results found previously for the QSOs rear NCC 1068 (Bell2002) it is shown that. iu] his foea? model. Changes in their πασάος aud redshifts with time during the QSO stage can he fitted best to a model similar to that proposed by NarlikarandDas(1980)..," Using the results found previously for the QSOs near NGC 1068 \citep{bel02} it is shown that, in this $local$ model, changes in their magnitudes and redshifts with time during the QSO stage can be fitted best to a model similar to that proposed by \citet{nar80b}."
". The compact objects Lear NGC 1068 (z, = U.0088) are born with apparent magnitudes near 19.5 (or fainter} aud a arge intrinsic redshift componcut that decreases as thei huuinositv ducreases.", The compact objects near NGC 1068 $_{\rm c}$ = 0.0038) are born with apparent magnitudes near 19.5 (or fainter) and a large intrinsic redshift component that decreases as their luminosity increases.
 After ~105 ves lis intrinsic redshift component will have largely disappeared aud they are assumed. to evolve into ealaxies., After $\sim10^{8}$ yrs this intrinsic redshift component will have largely disappeared and they are assumed to evolve into galaxies.
 In this scenario. the formation of QSOs (and therefore also galaxies) is continous aud uniform throughout the eutire age of the Universe.," In this scenario, the formation of QSOs (and therefore also galaxies) is continuous and uniform throughout the entire age of the Universe."
 These results (varvine luninesityv. redshift andl nass) differ from the model of Narlikar aud Das iu hat they secu to apply only duiug the objects arth aud the first brief period thereafter (the QSO stage).," These results (varying luminosity, redshift and mass) differ from the model of Narlikar and Das in that they seem to apply only during the object's birth and the first brief period thereafter (the QSO stage)."
 Because he QSO stage is so short. an initial Bie Bane still appears to be required o explain the existence of high-redshift ealaxies whose intrinsic redshift component should have oug ago fallen to near-zero values.," Because the QSO stage is so short, an initial Big Bang still appears to be required to explain the existence of high-redshift galaxies whose intrinsic redshift component should have long ago fallen to near-zero values."
 It has been shown that in this model it is no longer necessary o hypothesize a period of high-huninosity QSO oxoduction near z = 2. as is required for the cosmological redshift nodel.," It has been shown that in this model it is no longer necessary to hypothesize a period of high-luminosity QSO production near z = 2, as is required for the cosmological redshift model."
 In the QSO stage. he change of huuinositv with intrinsic redshift and the change of mass with time are both found o agree well with the predictions of the Narlikar and Das theory;," In the QSO stage, the change of luminosity with intrinsic redshift and the change of mass with time are both found to agree well with the predictions of the Narlikar and Das theory."
" The amount of time spent in the QSO stage (~105 vis) compared to the lite of a ealaxy. results in a galaxv/OQSO umuber ratio of ~1031,"," The amount of time spent in the QSO stage $\sim10^{8}$ yrs) compared to the life of a galaxy, results in a galaxy/QSO number ratio of $\sim10^{2} - \sim10^{3}$."
 Finally. it is suggested that. in the future. if this local model is ever to be convincingly confined. or proven to be incorrect. if is very important to continue to measure the redshifts aud magnitudes of those QSOs that appear o have been ejected from nearby active galaxies.," Finally, it is suggested that, in the future, if this $local$ model is ever to be convincingly confirmed, or proven to be incorrect, it is very important to continue to measure the redshifts and magnitudes of those QSOs that appear to have been ejected from nearby active galaxies."
 This is especially true for those cases where a huge umber of objects have been reported., This is especially true for those cases where a large number of objects have been reported.
"(DaCostaetal.2009),, and (Leeetal. were added to the sample.","\citep{dacosta}, and \citep{lee05} were added to the sample."
 McLaughlin&vanderMarel(2005) estimated cluster masses for all objects using population-synthesis models to define a V-band mass-to-light ratio for every cluster., \cite{mvdm} estimated cluster masses for all objects using population-synthesis models to define a V-band mass-to-light ratio for every cluster.
" We use a typical mass-to-light ratio of M/Ly=2, which is consistent with the results of McLaughlin&vanderMarel(2005),, to estimate masses for the remaining objects of this section."," We use a typical mass-to-light ratio of $M/L_{V} = 2$, which is consistent with the results of \cite{mvdm}, to estimate masses for the remaining objects of this section."
 Rejkubaetal.(2007) and Tayloretal.(2010) analyzed a sample of massive GCs in the nearby giant elliptical galaxy (Centaurus A)., \cite{rejkuba} and \cite{taylor} analyzed a sample of massive GCs in the nearby giant elliptical galaxy (Centaurus A).
 Their sample contains 22 massive GCs with masses larger than 10° Mo., Their sample contains 22 massive GCs with masses larger than $10^{6}$ $_{\sun}$.
" The parameters of UCDs were compiled for the Fornax Cluster (Mieskeetal.2008;Richtler2005;Evstigneevaal. 2008),, the Virgo Cluster (Haseganetal.2005;Evstigneevaetal.2007, 2008),, the Centaurus Cluster (Mieskeetal.2007),, and the Coma Cluster (Madridetal.2010)."," The parameters of UCDs were compiled for the Fornax Cluster \citep{mieske08,richtler,evstigneeva08}, the Virgo Cluster \citep{hasegan,evstigneeva07,evstigneeva08}, the Centaurus Cluster \citep{mieske07}, and the Coma Cluster \citep{madrid}."
". In addition, the UCD found in the Sombrero galaxy (M104) by Hauetal.(2009) was considered."," In addition, the UCD found in the Sombrero galaxy (M104) by \cite{hau} was considered."
" Blakeslee&Barber(2008) identified 15 UCD candidates in the ABELL S0740 cluster, which have rather large effective radii."," \cite{blakeslee} identified 15 UCD candidates in the ABELL S0740 cluster, which have rather large effective radii."
" We added these UCD candidates to our list, but it should be noted that these UCDs are not yet confirmed members of the ABELL S0740 cluster and might therefore be background objects."," We added these UCD candidates to our list, but it should be noted that these UCDs are not yet confirmed members of the ABELL S0740 cluster and might therefore be background objects."
 A large fraction of UCDs has reliable mass estimates., A large fraction of UCDs has reliable mass estimates.
" We used a typical mass-to-light ratio for UCDs of M/Ly=4 (Mieskeetal.2008) to derive mass estimates for those UCDs, where no mass estimate was published so far."," We used a typical mass-to-light ratio for UCDs of $M/L_{V} = 4$ \citep{mieske08} to derive mass estimates for those UCDs, where no mass estimate was published so far."
" Figure | shows the effective radii of the GCs, ECs, and UCDs as a function of their estimated masses."," Figure \ref{fig_ucdgc} shows the effective radii of the GCs, ECs, and UCDs as a function of their estimated masses."
" Below masses of 10° Mo, the vast majority of clusters have effective radii of a few pc."," Below masses of $10^{6}$ $_{\sun}$, the vast majority of clusters have effective radii of a few pc."
" Nevertheless, a few dozens of objects have effective radii larger than 10 pc."," Nevertheless, a few dozens of objects have effective radii larger than 10 pc."
 Most of them have masses of the order 10? Mo., Most of them have masses of the order $10^{5}$ $_{\sun}$.
" In contrast, only very few ECs are found at masses of the order 10$ Mo."," In contrast, only very few ECs are found at masses of the order $10^{6}$ $_{\sun}$."
" For masses above 10° Mo, there is no clear concentration at low effective radii."," For masses above $10^{6}$ $_{\sun}$, there is no clear concentration at low effective radii."
 The radii are more evenly distributed with a clear trend of increasing reg with increasing masses., The radii are more evenly distributed with a clear trend of increasing $r_{\rm eff}$ with increasing masses.
 Above 107? Μο all objects have effective radii above 10 pc., Above $10^{7.5}$ $_{\sun}$ all objects have effective radii above 10 pc.
" The general trend of increasing reg, which is added as a grey curve in Fig. 1,,"," The general trend of increasing $r_{\rm eff}$, which is added as a grey curve in Fig. \ref{fig_ucdgc},"
 was parameterized by Dabringhausenet (2008)., was parameterized by \cite{dabringhausen08}.
". While this line provides a trend for the majority of massive GCs and UCDs, the scatter is quite large and a number of objects are located far from this line."," While this line provides a trend for the majority of massive GCs and UCDs, the scatter is quite large and a number of objects are located far from this line."
 Most UCDs show reg smaller than 35 pc., Most UCDs show $r_{\rm eff}$ smaller than 35 pc.
" However, one UCD in the Fornax Cluster and one in the Virgo Cluster have effective radii larger than 90 pc."," However, one UCD in the Fornax Cluster and one in the Virgo Cluster have effective radii larger than 90 pc."
" These two UCDs show a core-halo structure, where the cores have an effective radius of about 10 pc (Evstigneevaetal.2007)."," These two UCDs show a core-halo structure, where the cores have an effective radius of about 10 pc \citep{evstigneeva07}."
". In addition, four UCD candidates in the Coma cluster (Madridetal.2010) and the majority of the UCD candidates in Abell 80740 (Blakeslee&Barber2008) are considerably larger than 35 pc."," In addition, four UCD candidates in the Coma cluster \citep{madrid} and the majority of the UCD candidates in Abell S0740 \citep{blakeslee} are considerably larger than 35 pc."
" As most of these objects are not yet confirmed as cluster members, they might also be background galaxies."," As most of these objects are not yet confirmed as cluster members, they might also be background galaxies."
 The formation scenario described in this paper starts with newly born complexes of star clusters covering a large range in masses and sizes., The formation scenario described in this paper starts with newly born complexes of star clusters covering a large range in masses and sizes.
 We model the dynamical evolution of various CCs leading to merger objects., We model the dynamical evolution of various CCs leading to merger objects.
" We do not, however, consider the galaxy-galaxy interaction, which formed the CCs in the first place."," We do not, however, consider the galaxy-galaxy interaction, which formed the CCs in the first place."
" Individual young massive star clusters were analyzed in detail by Mengeletal.(2008) and Bastianetal.(2009),, leading to a combined sample of 25 objects."," Individual young massive star clusters were analyzed in detail by \citet{mengel08} and \citet{bastian09}, leading to a combined sample of 25 objects."
 The median effective radius of these 25 young massive star clusters is 4 pc., The median effective radius of these 25 young massive star clusters is 4 pc.
" We use this value for our individual star clusters, which are the building blocks of the CC models."," We use this value for our individual star clusters, which are the building blocks of the CC models."
 All CC models in this paper consist of NGC = 32 star clusters., All CC models in this paper consist of $N_{\rm 0}^{\rm CC}$ = 32 star clusters.
 The individual star clusters are represented by Plummer spheres (Plummer1911;Kroupa2008) with NSC = 0000 particles.," The individual star clusters are represented by Plummer spheres \citep{plum1911, krou08} with $N_{\rm 0}^{\rm SC}$ = 000 particles."
" The Plummer radius, which corresponds to the effective radius, is chosen to be 4 pc for all models."," The Plummer radius, which corresponds to the effective radius, is chosen to be 4 pc for all models."
 We select a cutoff radius of RSC=SRS20 pc., We select a cutoff radius of $R_{\rm cut}^{\rm SC}= 5 R_{\rm pl}^{\rm SC} = 20$ pc.
" For each CC, the 32 star clusters have the same mass, which is 1/32 of the corresponding CC mass."," For each CC, the 32 star clusters have the same mass, which is 1/32 of the corresponding CC mass."
 The initial velocity distribution of the star clusters is chosen such that they are in virial equilibrium., The initial velocity distribution of the star clusters is chosen such that they are in virial equilibrium.
"Kravtsovetal.(2010) found signs of multiple sequences among subgiant branch stars in this GC, with stars at different magnitude levels preferentially lying at different radial distances, with a high level of statistical significance.","\cite{kravtsov10} found signs of multiple sequences among subgiant branch stars in this GC, with stars at different magnitude levels preferentially lying at different radial distances, with a high level of statistical significance."
" Additionally, a similar dependence on the radial distances is observed among RGB stars, with the bluer stars in B systematically located towards outer cluster regions Kravtsovetal.,2010,their Fig.3).."," Additionally, a similar dependence on the radial distances is observed among RGB stars, with the bluer stars in $U-B$ systematically located towards outer cluster regions \citep[see][their Fig.3]{kravtsov10}. ."
 We show in Fig., We show in Fig.
" 3 (left panel) the U,U—B CMD for all the 138 stars of our sample in NGC 3201 in common with Kratsov et al."," \ref{f:rgbPIE} (left panel) the $U,U-B$ CMD for all the 138 stars of our sample in NGC 3201 in common with Kratsov et al."
 The colour coding identifies the same two intervals in radial distances used by them and reflects the trend noted in the radial distribution., The colour coding identifies the same two intervals in radial distances used by them and reflects the trend noted in the radial distribution.
" In the right panel, however, the stars in are simply colour-coded according to their status of P, I, or E. The comparison between the two plots immediately tells us that second-generations stars in NGC 3201 must also be those more concentrated toward the cluster centre, according to their location on the CMD."," In the right panel, however, the stars in are simply colour-coded according to their status of P, I, or E. The comparison between the two plots immediately tells us that second-generations stars in NGC 3201 must also be those more concentrated toward the cluster centre, according to their location on the CMD."
" This result supports what we find from our sample only (see Fig. 1)),"," This result supports what we find from our sample only (see Fig. \ref{f:distrPIE}) ),"
" but is now more robust, being anchored to a much larger sample (almost 500 stars with UBVI photometry with respect to about 100 RGB stars with Na,O abundances)."," but is now more robust, being anchored to a much larger sample (almost 500 stars with $UBVI$ photometry with respect to about 100 RGB stars with Na,O abundances)."
 In conclusio. wel find that second-generation stars are most likely more concentrated toward the inner cluster regions in NGC 3201.," In conclusion, we find that second-generation stars are most likely more concentrated toward the inner cluster regions in NGC 3201."
" Apparently, it seems that even if the relaxation time of NGC 3201 is much shorter than its lifetime, some trace of the initial formation process might be still recognizable."," Apparently, it seems that even if the relaxation time of NGC 3201 is much shorter than its lifetime, some trace of the initial formation process might be still recognizable."
" Interestingly, Norris&Freeman(1979) found evidence of the same effect in another cluster, 47 Tucane: they determined that the CN-strong stars, i.e., the ones that we now attribute to the second generation, are more centrally located."," Interestingly, \cite{norris79} found evidence of the same effect in another cluster, 47 Tucane: they determined that the CN-strong stars, i.e., the ones that we now attribute to the second generation, are more centrally located."
" While our finding does not help to discriminate between scenarios where the pollution comes either from AGB or FRMS, it offers another piece of evidence, useful to reconstruct the complexpuzzle of multiple stellar populations in GCs."," While our finding does not help to discriminate between scenarios where the pollution comes either from AGB or FRMS, it offers another piece of evidence, useful to reconstruct the complexpuzzle of multiple stellar populations in GCs."
effect on the nucleosvnthesis in the partial mixing zone due to stellar rotation also did not seen (o improve (he match with observations (Ilerwig.Langer&Lugaro2003).,effect on the nucleosynthesis in the partial mixing zone due to stellar rotation also did not seem to improve the match with observations \citep*{herwig:03}.
. The aims of this paper are to update the study of the production of in AGB stars and to explore the impact of the uncertainties of nuclear reaction rales on the abundance of fluorine produced in the framework of the current. AGB star models., The aims of this paper are to update the study of the production of in AGB stars and to explore the impact of the uncertainties of nuclear reaction rates on the abundance of fluorine produced in the framework of the current AGB star models.
 First we introduce the production of iin AGB models of a large range of masses and metallicities., First we introduce the production of in AGB models of a large range of masses and metallicities.
 We caleulate the stellar structure and (hen follow the incleosvnthesis bv making use of a postprocessing code., We calculate the stellar structure and then follow the nucleosynthesis by making use of a postprocessing code.
 Our computations represent an improvement with respect to previous computations lor several reasons., Our computations represent an improvement with respect to previous computations for several reasons.
 First. we find the TDU to occur sell-consistentlv. after a certain number of thermal pulses. hence we do not paranmetrize this process as done in all the previous studies.," First, we find the TDU to occur self-consistently after a certain number of thermal pulses, hence we do not parametrize this process as done in all the previous studies."
 If itis (ue that the amount of EDU is still uncertain (seee.g.Frost&Lattanzio1996:\lowlavi1999) and hence can be parametrized. our approach is more consistent in (the fact we not only deal with ΤΕΙ: as à way of mixing fIuorine (o the stellar surface but also take into account the feedback effect of TDU on the nucleosvnthesis of iin the Ile intershell.," If it is true that the amount of TDU is still uncertain \citep[see 
e.g.][]{frost:96,mowlavi:99} and hence can be parametrized, our approach is more consistent in the fact we not only deal with TDU as a way of mixing fluorine to the stellar surface but also take into account the feedback effect of TDU on the nucleosynthesis of in the He intershell."
 As we will show. this feedback has a large impact on the production ofPF.," As we will show, this feedback has a large impact on the production of."
. Secondly. our postprocessing code follows the nucleosvuthesis throughout all the different thermal pulses previously computed by the evolutionary code.," Secondly, our postprocessing code follows the nucleosynthesis throughout all the different thermal pulses previously computed by the evolutionary code."
 This was done by Alowlavietal.(1996) for three stellar models with a limited number of pulses. but without including a partial mixing zone.," This was done by \citet{mowlavi:96} for three stellar models with a limited number of pulses, but without including a partial mixing zone."
 Goriely&Mowlavi(2000) included a partial mixing zone in (heir calculations but only followed the nucleosvnthesis “during one representative interpulse and pulse phase” hence missing the possible effects due to variations of the thermodynamic features of each thermal pulse., \citet{goriely:00} included a partial mixing zone in their calculations but only followed the nucleosynthesis “during one representative interpulse and pulse phase” hence missing the possible effects due to variations of the thermodynamic features of each thermal pulse.
 Finally. our postprocessing code computes abundances of nuclei up to iron solving simullaneously the changes due to nuclear reactions ancl (hose due to mixing. when convection is present.," Finally, our postprocessing code computes abundances of nuclei up to iron solving simultaneously the changes due to nuclear reactions and those due to mixing, when convection is present."
 This allows us. for example. to properly model the nucleosvnthesis that occurs al the delicate moment when the II-burning ashes are progressively ingested in the convective pulse and the ppresent in (he ashes burns via (he (0.2) reaction while the ingestion is occurring.," This allows us, for example, to properly model the nucleosynthesis that occurs at the delicate moment when the H-burning ashes are progressively ingested in the convective pulse and the present in the ashes burns via the $\alpha,n)$ reaction while the ingestion is occurring."
 We discuss and compare results [rom a laree set of stellar models. analvze in detail the impact of the introduction of the partial mixing zone and of the reaction rate uncertainties on the 3. Z=0.02 modelandthenpresentupperandloiwerlimils forlheproduclionof [lTuorineinseveralselected," We discuss and compare results from a large set of stellar models, analyze in detail the impact of the introduction of the partial mixing zone and of the reaction rate uncertainties on the 3 $Z=0.02$ model and then present upper and lower limits for the production of fluorine in several selected models."
imodel," On top of the comparison with spectroscopic observations of AGB stars, our results are of relevance when studying the Galactic chemical evolution of fluorine, as done recently by \citet{renda:04}."
s., The evolutionary and nucleosynthesis codes are presented in 2.
 aarediscussedin, The production of fluorine in a large range of stellar models is discussed in 3.
ts, The effect of introducing a partial mixing zone is discussed in 4.
bblogetherwilhtheef [ectloflheiruncertaintiesontheproducliono[, The nuclear reactions contributing to the production of are discussed in 5 together with the effect of their uncertainties on the production of.
 E. EntioGwepresenta., In 6 we present a final discussion and possible directions for future work.
definition not. be altered. here.,definition not be altered here.
 Instead. we concentrate here on the relationship between the size of the centra component and disk of cach galaxy. ancl compare this with observations.," Instead, we concentrate here on the relationship between the size of the central component and disk of each galaxy, and compare this with observations."
 Another ciscrepancy between observed. and. simulate ealaxies is their noise content as noise does not overlay the simulated: galaxies., Another discrepancy between observed and simulated galaxies is their noise content as noise does not overlay the simulated galaxies.
 Unlike the other CAS parameters. the measure of concentration does not include a backgrouim subtraction stage.," Unlike the other CAS parameters, the measure of concentration does not include a background subtraction stage."
 This is due to the negligible effects of noise on the measure of concentration., This is due to the negligible effects of noise on the measure of concentration.
 For this reason. no adjustments were mace to the concentration parameter regarding background. noise.," For this reason, no adjustments were made to the concentration parameter regarding background noise."
 The measure of asymmetry considers the residuals produced when a galaxy image is subtracted [rom the same image hat has been rotated by 1807., The measure of asymmetry considers the residuals produced when a galaxy image is subtracted from the same image that has been rotated by $^\circ$.
 Ehe central bulge component of a galaxy is generally. symmetric. and for this reason no acaptation was required to account for the excessive central xilee component of the simulated galaxies.," The central bulge component of a galaxy is generally symmetric, and for this reason no adaptation was required to account for the excessive central bulge component of the simulated galaxies."
 However. it was discovered. that the elfects. of noise were critical. as the vackeround Component was comparable in magnitude to he component due to the galaxy itself.," However, it was discovered that the effects of noise were critical, as the background component was comparable in magnitude to the component due to the galaxy itself."
 H0 was imperative o ensure that this aspect of the algorithm was correct. as simulated galaxies contain essentially zero background noise compared to their observed counterparts. the latter of which contain varving amounts of noise depending upon exposure time. sky background. and distance.," It was imperative to ensure that this aspect of the algorithm was correct, as simulated galaxies contain essentially zero background noise compared to their observed counterparts, the latter of which contain varying amounts of noise depending upon exposure time, sky background, and distance."
 For this reason. any discrepancies concerning the computation of the background would Lead to an inaccurate Comparison.," For this reason, any discrepancies concerning the computation of the background would lead to an inaccurate comparison."
 In order to test this hypothesis. an artificial array of noise was created. and the galaxies were analysed both before and after the application of this noise array.," In order to test this hypothesis, an artificial array of noise was created, and the galaxies were analysed both before and after the application of this noise array."
 We replicate the signal-to-noise values of the Frei et al. (, We replicate the signal-to-noise values of the Frei et al. (
1996) sample by first pixelating the simulated images to the same resolution. then scaling the flux to be comparable to that in the images of the real galaxies. and finally adding a normally-clistributec noise array of sullicient. amplitude to reproduce the signal-to-noise of the observed galaxies in Frei at al. (,"1996) sample by first pixelating the simulated images to the same resolution, then scaling the flux to be comparable to that in the images of the real galaxies, and finally adding a normally-distributed noise array of sufficient amplitude to reproduce the signal-to-noise of the observed galaxies in Frei at al. ("
1996).,1996).
 Furthermore. ?. demonstrated that accurate asvmmetry. calculations can only be performed. without corrections. on galaxies with signal-to-noise greater than 100.," Furthermore, \citet{Conselice2000b} demonstrated that accurate asymmetry calculations can only be performed, without corrections, on galaxies with signal-to-noise greater than 100."
 For this reason. each galaxy was tested. individually o ensure that the application of these characteristic noise values led to signal-to-noise ratios in excess of 100.," For this reason, each galaxy was tested individually to ensure that the application of these characteristic noise values led to signal-to-noise ratios in excess of 100."
 A comparison of the asymmetry results derived [rom he simulated galaxies. both before and after the application of noise. can be seen in Figure 5.," A comparison of the asymmetry results derived from the simulated galaxies, both before and after the application of noise, can be seen in Figure \ref{AsymN}."
 |t was found that he inferred asvometry values cillered only marginally after the application of noise (in large part because of he stringent. signal-to-noise limit imposed). although the impact varied for each galaxy and appeared. to be more substantial for more asymmetric galaxies.," It was found that the inferred asymmetry values differed only marginally after the application of noise (in large part because of the stringent signal-to-noise limit imposed), although the impact varied for each galaxy and appeared to be more substantial for more asymmetric galaxies."
 Whilst there is some variation visible in Figure 5 due to the application of noise. it is not significant.," Whilst there is some variation visible in Figure \ref{AsymN} due to the application of noise, it is not significant."
 Llowever. to ensure that a fair comparison was made between observed and simulated galaxies. i was decided that noise would be applied. to the simulated. galaxies prior to the computation. of the asvmnmeltry parameter.," However, to ensure that a fair comparison was made between observed and simulated galaxies, it was decided that noise would be applied to the simulated galaxies prior to the computation of the asymmetry parameter."
"the presence of the non-thermal component: indeed the bias changes with r,,=0. but is still present.","the presence of the non-thermal component: indeed the bias changes with $\tau_{nt}=0$, but is still present."
 If a 4-parameter fit is used. the bias is significantly reduced. and does not depend anymore on the presence of the non-thermal component.," If a 4-parameter fit is used, the bias is significantly reduced, and does not depend anymore on the presence of the non-thermal component."
 However. this comes at the cost of wider confidence areas. as evident from figure 6..," However, this comes at the cost of wider confidence areas, as evident from figure \ref{fig4}."
" The contamination of dust is significant and degenerates to some extent also with ATc5: in the 3-parameter fit. where ATcare is not fitted. the best-fit for AZ, is far from the input value. and this probably contributes to the tension between the best-fit value of 7, and its input value."," The contamination of dust is significant and degenerates to some extent also with $\Delta T_{CMB}$: in the 3-parameter fit, where $\Delta T_{CMB}$ is not fitted, the best-fit for $\Delta I_d$ is far from the input value, and this probably contributes to the tension between the best-fit value of $T_e$ and its input value."
 We believe that this 15 the result of a degeneracy of parameters combined with the poor coverage of high frequencies in ground-based experiments., We believe that this is the result of a degeneracy of parameters combined with the poor coverage of high frequencies in ground-based experiments.
 In the 4-parameter fits the y improves. but the best fits are still biased. and only with the 3 keV prior the estimates of all parameters are consistent with the input values (see fig. 6)).," In the 4-parameter fits the $\chi^2$ improves, but the best fits are still biased, and only with the 3 keV prior the estimates of all parameters are consistent with the input values (see fig. \ref{fig4}) )."
 For ECI (4-bands balloon-borne photometer) the coverage of frequencies higher than 300 GHz helps in removing the degeneracy (see fig. 7))., For EC1 (4-bands balloon-borne photometer) the coverage of frequencies higher than 300 GHz helps in removing the degeneracy (see fig. \ref{fig5}) ).
" If we use the very weak prior on 7, (Gaussian with standard deviation 8 keV). the best-fit cluster parameters are already close to the input values. even if the error (completely dominated by the degeneracy) is relatively large."," If we use the very weak prior on $T_e$ (Gaussian with standard deviation 8 keV), the best-fit cluster parameters are already close to the input values, even if the error (completely dominated by the degeneracy) is relatively large."
 The situation improves. of course. if the standard deviation on the prior is reduced to 3 keV. ΑΤΟΜΑ 1s better constrained. but is biased low.," The situation improves, of course, if the standard deviation on the prior is reduced to 3 keV. $\Delta T_{CMB}$ is better constrained, but is biased low."
 While performing significantly better than ECO. this configuration is limited by radiation noise in the high-frequency bands. which can be removed only by cooling the telescope or/and adding spectroscopic capabilities (see below).," While performing significantly better than EC0, this configuration is limited by radiation noise in the high-frequency bands, which can be removed only by cooling the telescope or/and adding spectroscopic capabilities (see below)."
 In fig., In fig.
 8 we plot the histograms of the best-fit 7;xτι normalized to the input of the simulation.," \ref{bias} we plot the histograms of the best-fit $T_e
\times \tau_t$ normalized to the input of the simulation."
 [t is evident how the bias is reduced passing from ECO with three parameters to ECO with four parameters to ECI. which shows how important the coverage of high frequencies ts. which are difficult to observe from the ground.," It is evident how the bias is reduced passing from EC0 with three parameters to EC0 with four parameters to EC1, which shows how important the coverage of high frequencies is, which are difficult to observe from the ground."
" For EC4. where six independent data-sets are available for each measurement. we tried to fit four parameters (τι T,. Aly and ATeayg. see fig."," For EC4, where six independent data-sets are available for each measurement, we tried to fit four parameters $\tau_t$ , $T_e$, $\Delta I_d$ and $\Delta T_{CMB}$, see fig."
" 9 ) and also six parameters (including τη, and pj. see fig. 10)."," \ref{fig6} ) and also six parameters (including $\tau_{nt}$ and $p_1$, see fig. \ref{fig7}) ),"
 always adding the fictitious zero frequency zero brightness data point., always adding the fictitious zero frequency zero brightness data point.
 The good coverage of high frequencies and low photon noise owing to the low radiative background results in very good performance in terms of statistical errors., The good coverage of high frequencies and low photon noise owing to the low radiative background results in very good performance in terms of statistical errors.
 Again. the presence of the non-thermal component produces a bias in the determination of the other parameters for the 4-parameter fit.," Again, the presence of the non-thermal component produces a bias in the determination of the other parameters for the 4-parameter fit."
 In the 6-parameter fits. the non thermal parameters are basically not constrained (with a bimodal distribution of the best fit p; ). but the other parameters are well constrained and unbiased.," In the 6-parameter fits, the non thermal parameters are basically not constrained (with a bimodal distribution of the best fit $p_1$ ), but the other parameters are well constrained and unbiased."
 The effects of parameters degeneracies are still evident. however. and it is difficult to estimate AZc3;5 because it tends to be biased low in the 4-parameter fit. while is not well constrained in the 6-parameter fits (see also table 1)).," The effects of parameters degeneracies are still evident, however, and it is difficult to estimate $\Delta T_{CMB}$ because it tends to be biased low in the 4-parameter fit, while is not well constrained in the 6-parameter fits (see also table \ref{tab1}) )."
 The space spectrometers EC2. EC3. and ECS. featuring wide frequency coverage and low radiative background noise. perform better. and allow an unbiased recovery of SIX parameters withincreasing accuracy.," The space spectrometers EC2, EC3, and EC5, featuring wide frequency coverage and low radiative background noise, perform better, and allow an unbiased recovery of six parameters withincreasing accuracy."
 If we compare, If we compare
PSR B1509-58 was discovered as a 150 ms X-ray pulsar in the HRI and. IPC. (0.2-4 keV) data from observations performed in 1979 and 1980 of supernova remnant (SNR) MSH 15-52 (Seward&Harnden 1982)).,PSR B1509-58 was discovered as a 150 ms X-ray pulsar in the HRI and IPC (0.2-4 keV) data from observations performed in 1979 and 1980 of supernova remnant (SNR) MSH 15-52 \cite{seward}) ).
 The pulsations and the large period derivative indicated in the X-ray data were soon confirmed at radio-wavelengths (Manchesteretal. 1982)). while the derived dispersion measure supports its association with the SNR.," The pulsations and the large period derivative indicated in the X-ray data were soon confirmed at radio-wavelengths \cite{manchester}) ), while the derived dispersion measure supports its association with the SNR."
 The inferred characteristic age is 1570 year and the component of the surface magnetic field perpendicular to the spin axis at the magnetic pole is 3.1«10°Gaub.. one of the highest among the steadily growing sample of radio-pulsars.," The inferred characteristic age is 1570 year and the component of the surface magnetic field perpendicular to the spin axis at the magnetic pole is $3.1\times 10^{13}$, one of the highest among the steadily growing sample of radio-pulsars."
 Radio-data collected during an 11 yr time span showed that the pulsar did not glitch and made a detailed. study of its slow-down possible (Kaspietal. 1994))., Radio-data collected during an 11 yr time span showed that the pulsar did not glitch and made a detailed study of its slow-down possible \cite{kaspi}) ).
 The measured braking index was n—2.837(1). close to =3 expected for a dipole.," The measured braking index was $n = 2.837(1)$, close to $n = 3$ expected for a dipole."
 Extensive X-ray studies of PSR BIS09-58 and Its environment have been performed in the early eighties at soft. and medium X-ray energies using the HRI. IPC and SSS (Sewardetal. 1983..1984) and MPC," Extensive X-ray studies of PSR B1509-58 and its environment have been performed in the early eighties at soft- and medium X-ray energies using the HRI, IPC and SSS \cite{seward2}, ,1984) and MPC"
"The value of the orbital velocity for a particle ou an elliptical orbit originating from Ay, witha certain) value at Rour radius (where it will collide with a particle ona circular orbit) is The angle between the orbital velocities cam be expressed as where The collisional velocity is then where es is the orbital velocity for the particle ou a circular orbit at Rout.",The value of the orbital velocity for a particle on an elliptical orbit originating from $R_{\rm in}$ with a certain $\beta$value at $R_{\rm out}$ radius (where it will collide with a particle on a circular orbit) is The angle between the orbital velocities can be expressed as where The collisional velocity is then where $v_{\rm o}$ is the orbital velocity for the particle on a circular orbit at $R_{\rm out}$.
" We plot the values of this collisional velocity for particles originating from Rp,=10AU aud 50AU in svstenis around a solar- and carly-type star in Figure 10..", We plot the values of this collisional velocity for particles originating from $R_{\rm in}=10~{\rm AU}$ and $50~{\rm AU}$ in systems around a solar- and early-type star in Figure \ref{fig:vcol}.
 We shade the collisional velocity region above our 3knis init. where waves start to appear.," We shade the collisional velocity region above our $3~{\rm km~s}^{-1}$ limit, where waves start to appear."
 As we cal sees nearby vines at AR=1AU have low collisional velocitics. reassuring that our prescription for a constant collisional velocity value in narrow debris tines is reasonable.," As we can see, nearby rings at $\Delta R=1~{\rm AU}$ have low collisional velocities, reassuring that our prescription for a constant collisional velocity value in narrow debris rings is reasonable."
 We can also see that once we depart from the narrow ring assunptioun (AR>Lo AU). the collisional velocitics do increase.," We can also see that once we depart from the narrow ring assumption $\Delta R > 10~{\rm AU}$ ), the collisional velocities do increase."
 Around a sobu-tvpe stir. particles originating frou an inner radius of LOAU are able to achieve collisional velocities of ~3ns rowever. the particle size range that is able to achieve this linüt is τον narrow. between 0. band 0.6jan.," Around a solar-type star, particles originating from an inner radius of $10~{\rm AU}$ are able to achieve collisional velocities of $\sim 3~{\rm km~s}^{-1}$; however, the particle size range that is able to achieve this limit is very narrow, between 0.4 and $0.6~\micron$."
 Taking into account the dilution of these simnall particles within a limited narrow size range. we conclude that extended debris disks with inner boundaries outside of LO - 15AU around solar ype stars should be well approximated by a simple vower-law iaass (size) distribution function.," Taking into account the dilution of these small particles within a limited narrow size range, we conclude that extended debris disks with inner boundaries outside of 10 - $15~{\rm AU}$ around solar type stars should be well approximated by a simple power-law mass (size) distribution function."
 In Paper L we show a comparison run to Lolineetal.(2008) and Wyattctal. (2011).. asstuning an extended disk votween radii of 7.5 and 15AU around a solar-type star.," In Paper I, we show a comparison run to \cite{lohne08} and \cite{wyatt11}, , assuming an extended disk between radii of 7.5 and $15~{\rm AU}$ around a solar-type star."
 The runs by Wyattetal.(2011). aud our code show weheible/simmall amplitude waves. while Lóhneetal.(2008). show moderate amplitude waves. likelv duc to hei full three dimensional modeling of the svsteu. aking mto account smaller particles originating from regions jmward of 10 AU.," The runs by \cite{wyatt11} and our code show negligible/small amplitude waves, while \cite{lohne08} show moderate amplitude waves, likely due to their full three dimensional modeling of the system, taking into account smaller particles originating from regions inward of 10 AU."
 These results confnriu our analytic analvsis on the conditions required to iuitiate waves in the dust particle nass-distributiou., These results confirm our analytic analysis on the conditions required to initiate waves in the dust particle mass-distribution.
 We show the same analysis for earlv-tvpoe stars du the right panels of Figure 10.., We show the same analysis for early-type stars in the right panels of Figure \ref{fig:vcol}.
 The collisional velocities of particles originating from 10AU with particles on external circular orbits around an AQ spectral-tvpe star will be significantly larecr than our lanit for a larger range of particle sizes (5 - 10 san)., The collisional velocities of particles originating from $10~{\rm AU}$ with particles on external circular orbits around an A0 spectral-type star will be significantly larger than our limit for a larger range of particle sizes (5 - $10~\micron$ ).
 Particles originating from orbits inside of LOAU will definitely initiate waves in extended disks or external rings., Particles originating from orbits inside of $10~{\rm AU}$ will definitely initiate waves in extended disks or external rings.
 Towever. particles originating from 50AU will barely reach collisional velocities at or above our limit aud for a limited range of yarticle sizes.," However, particles originating from $50~{\rm AU}$ will barely reach collisional velocities at or above our limit and for a limited range of particle sizes."
 We conclude that extended debris disks with inner boundaries outside of 50 - 60AU around earlv-tvpe stars shouldbe well approximated by a simple yower-law nass (size) distribution fuuction Ow ID ~particle-in-a-box” ummerical code adjusts he collisional velocities through the ring thickness aud vcieht (AR aud D). aud the resulting orbital inclinations or the particles.," We conclude that extended debris disks with inner boundaries outside of 50 - $60~{\rm AU}$ around early-type stars shouldbe well approximated by a simple power-law mass (size) distribution function Our 1D “particle-in-a-box” numerical code adjusts the collisional velocities through the ring thickness and height $\Delta R$ and $h$ ), and the resulting orbital inclinations for the particles."
 Our results are only moderately affected over the relatively narrow range of velocities obtained o» varvius them (see Figure 7))., Our results are only moderately affected over the relatively narrow range of velocities obtained by varying them (see Figure \ref{fig:errs}) ).
 We modified the code (see above) to simulate the higher-velocity collisions with particles ou elliptical orbits to determine a threshold for eeneration of waves in the particle distribution., We modified the code (see above) to simulate the higher-velocity collisions with particles on elliptical orbits to determine a threshold for generation of waves in the particle distribution.
 However. our model cannot explore the nuauces resulting from varving collisional velocities iu extended svstenis. (ucl as varvine collisional rates aud collisional outcomes). which could also play a role in the possible formation of substructures superposed on the generally steeper particle size-distributious (seee.g.Iivovetal.2010).," However, our model cannot explore the nuances resulting from varying collisional velocities in extended systems (such as varying collisional rates and collisional outcomes), which could also play a role in the possible formation of substructures superposed on the generally steeper particle size-distributions \citep[see e.g.,][]{krivov05,thebault07,lohne08,muller10}."
. As stated at the cud of Section 3.1. our generalization asstuned a specific xvsteui (with sae material properties and inininuuna particle mass).," As stated at the end of Section 3.1, our generalization assumed a specific system (with same material properties and minimum particle mass)."
 Although we explored varving the udm particle mass when introducing different spectral type central stars. both the tensile streneth aud the uid mass may vary with material properties as well," Although we explored varying the minimum particle mass when introducing different spectral type central stars, both the tensile strength and the minimum mass may vary with material properties as well."
 Iu addition to minerals such as basalt. it is likely that eraims in the outer zoucs of debris disks contain siguificaut amounts of icc.," In addition to minerals such as basalt, it is likely that grains in the outer zones of debris disks contain significant amounts of ice."
 The mechanical properties of icy eraius are explored by Benz and Leinhardt&Stewart (2009). vielding roughly a factor of 3 in difference between the tensile streneth of basalt and ice.," The mechanical properties of icy grains are explored by \cite{benz99} and \cite{leinhardt09}, , yielding roughly a factor of 3 in difference between the tensile strength of basalt and ice."
 Civen the relative iusensitivitv of our results to the scaling of the erain streneth curve (Q.. - see Figure 7)). these properties are simular enough that our basic conclusions about the erai size distribution aud region of applicability of the power law approximation to it are essentially unchanged even outside ofthe iccline.," Given the relative insensitivity of our results to the scaling of the grain strength curve $Q_{\rm sc}$ - see Figure \ref{fig:errs}) ), these properties are similar enough that our basic conclusions about the grain size distribution and region of applicability of the power law approximation to it are essentially unchanged even outside of the iceline."
 The slope of the size distribution slope iu collisional cascades has been investigated with analytic approaches with increasing complexity since the piouccriug work of Dolnanvi(1969)., The slope of the size distribution slope in collisional cascades has been investigated with analytic approaches with increasing complexity since the pioneering work of \cite{dohnanyi69}.
". Tis assumptions of sclfsimular fraeieutation. constant material streneth. aud collision rates proportional to the ecometric cross section lead to the well known aud now widely used steady state size-distribution slope of +,=11/6 (jj,= 3.5)."," His assumptions of self-similar fragmentation, constant material strength, and collision rates proportional to the geometric cross section lead to the well known and now widely used steady state size-distribution slope of $\eta_m = 11/6$ $\eta_a = 3.5$ )."
 The validity of his assunptious has been investigated m a number of analytic studies., The validity of his assumptions has been investigated in a number of analytic studies.
" Tanakaetal.(1996) fouud that varving the power of the colliional cross section (17. where vy=2/3 for a siuple ecometric cross section) will set the steady state distribution slope as jp, 3)/2."," \cite{tanaka96} found that varying the power of the collisional cross section $m^{\nu}$ , where $\nu=2/3$ for a simple geometric cross section) will set the steady state distribution slope as $\eta_m = (\nu+3)/2$ ."
 Such nou-geonietrie cross sections (collision rates) can be theresults of massweighted collision probabilities. varving amounts of erai porosity. mass dependent collisional velocities. ete.," Such non-geometric cross sections (collision rates) can be theresults of massweighted collision probabilities, varying amounts of grain porosity, mass dependent collisional velocities, etc."
particularly to the molecular cloud data 33.1). for which we have used a single catalogue.,"particularly to the molecular cloud data 3.1), for which we have used a single catalogue."
 However. since we obtained very nearly the same result using a variety of tracers for the sinaller cloud. cores. Bok globules. and coudeusatious. the results in these cases secu robust.," However, since we obtained very nearly the same result using a variety of tracers for the smaller cloud cores, Bok globules, and condensations, the results in these cases seem robust."
 This investigationOo shows that iutriusic triaxial objects produce distributions which reasonably iateh observations of projected axis ratios for molecular clouds. molecular cloud cores. Dok elobules. and protostellar condensatious.," This investigation shows that intrinsic triaxial objects produce distributions which reasonably match observations of projected axis ratios for molecular clouds, molecular cloud cores, Bok globules, and protostellar condensations."
 The results clearly fall iuto two categories: (1) on scales >L pe. mapped in CO. molecular clouds. including GALC’s. have triaxial shapes which are nore closclv. prolate than oblate: (2) dense cores. Bok globules. auc coudeusatious. mapped im a varietv of tracers. on scales from few <0.1 pe down to 0.01 pe. lave triaxial shapes which are nore closeke oblate than prolate.," The results clearly fall into two categories: (1) on scales $\gtrsim 1$ pc, mapped in $^{12}$ CO, molecular clouds, including GMC's, have triaxial shapes which are more closely prolate than oblate; (2) dense cores, Bok globules, and condensations, mapped in a variety of tracers, on scales from few $\times \,\, 0.1$ pc down to $0.01$ pc, have triaxial shapes which are more closely oblate than prolate."
 The results about the latter objects reinforce our carlicr Ποιο (Paper I) from two other catalogues of dense core shapes., The results about the latter objects reinforce our earlier finding (Paper I) from two other catalogues of dense core shapes.
 See Table d. for a sunu of the best fit axis ratios. (£g. Q9). for each of the data sets we investigated.," See Table \ref{summary} for a summary of the best fit axis ratios, $\xi_0, \zeta_0$ ), for each of the data sets we investigated."
 The results frou Paper I are included for comparison., The results from Paper I are included for comparison.
 The robust teudenev for cores. Dok globules. and smaller condensations to have triaxial fits with £y=0.30.5. and (y=0.9 implics that they are all prefercutially flattened inone direction.," The robust tendency for cores, Bok globules, and smaller condensations to have triaxial fits with $\xi_0 = 0.3-0.5$, and $\zeta_0 = 0.9$ implies that they are all preferentially flattened in direction."
 This could be due to flattening along the direction of a incan magnetic field. or due to significant rotational support in the smallest objects.," This could be due to flattening along the direction of a mean magnetic field, or due to significant rotational support in the smallest objects."
 The maencetic field explanation for cores is attractive as it implies that the observed ucar-aliguinent of core nünor axes and maeuetic field direction iu Taurus (see Onishi et al., The magnetic field explanation for cores is attractive as it implies that the observed near-alignment of core minor axes and magnetic field direction in Taurus (see Onishi et al.
 1996) may be indicative of à amore universal phenomenon., 1996) may be indicative of a more universal phenomenon.
 We also note that carly subuullimeter polariuctry of a few dense cores (Ward-Thoipson et al., We also note that early submillimeter polarimetry of a few dense cores (Ward-Thompson et al.
 2000) reveals a tendency toward aliguiment. but also a noticeable aneular offset.," 2000) reveals a tendency toward alignment, but also a noticeable angular offset."
 This is interpreted as evidence for traxialitv of the cores (Basu 2000). which max still be prefercutially flattened along the direction of the magnetic field.," This is interpreted as evidence for triaxiality of the cores (Basu 2000), which may still be preferentially flattened along the direction of the magnetic field."
 While txiaxialitv is consistent with a nonequilibrimu state. evolviug due to external turbulence or internal gravity. the near-oblate shape also meas that the objects may not be particularly far roni equilibrium. and that oblate equilibrimm uodels may act as a reasonable approximation o these objects.," While triaxiality is consistent with a nonequilibrium state, evolving due to external turbulence or internal gravity, the near-oblate shape also means that the objects may not be particularly far from equilibrium, and that oblate equilibrium models may act as a reasonable approximation to these objects."
 This cau explain why the internal structure of some Dok globules aud pre-stellar cores can be closely or approximately fit w spherical equilibrium Bounor-Ebert or nem-equilibrimm oblate magnetic models (Alves; Lada. Lada 2001: Dacinauu et al.," This can explain why the internal structure of some Bok globules and pre-stellar cores can be closely or approximately fit by spherical equilibrium Bonnor-Ebert or near-equilibrium oblate magnetic models (Alves, Lada, Lada 2001; Bacmann et al."
 2000: οποίος Dasu 2000: Zucconi Waluslev. Calli 2001).," 2000; Ciolek Basu 2000; Zucconi, Walmsley, Galli 2001)."
 It isB also consistentB withB the observed near-virial-ο.equilibrimui∙∙∙ of. most cores (Myers. Goodman. 88)., It is also consistent with the observed near-virial-equilibrium of most cores (Myers Goodman 1988).
 We also note that the Bok elobules. which are by defiuition isolated sites of star formation. have shapes that are not significantly different frou that of molecular cloud cores aud condeusations embedded within larger clouds.," We also note that the Bok globules, which are by definition isolated sites of star formation, have shapes that are not significantly different from that of molecular cloud cores and condensations embedded within larger clouds."
 This suggests that the cuviromment iu which the cores and condeusatious are embedded plays a relatively insignificant role m thei dynamics. Le. the external pressure frout the parental cloud docs uot scem to be important at this stage.," This suggests that the environment in which the cores and condensations are embedded plays a relatively insignificant role in their dynamics, i.e., the external pressure from the parental cloud does not seem to be important at this stage."
 The smallest objects in our study the condensatious mapped in millimeter aud subiillimeter continua Cluission. may be the precursors to individual stars since the mass spectrum appears to match the Iuitial Mass Function (AIF) compiled by Salpeter (1955) over a certain mass range (Motte ef al.," The smallest objects in our study, the condensations mapped in millimeter and submillimeter continuum emission, may be the precursors to individual stars since the mass spectrum appears to match the Initial Mass Function (IMF) compiled by Salpeter (1955) over a certain mass range (Motte et al."
 1998)., 1998).
 The estimated triaxial but neu-oblate shape of these objects are an nuportaut lak in understaudius the collapse process that leads to star formation., The estimated triaxial but near-oblate shape of these objects are an important link in understanding the collapse process that leads to star formation.
 For the larger molecular cloud scale. we have utilized au exhaustive catalogue of the shapes of clouds in the outer Galaxy (Dever et al.," For the larger molecular cloud scale, we have utilized an exhaustive catalogue of the shapes of clouds in the outer Galaxy (Heyer et al."
 2001)., 2001).
 Although our study of molecular cloud shapes is based ou this single available sample of projected axis ratios. aud the result should be confirmed when other shape data become available. the sheer size of this catalogue is a strong point.," Although our study of molecular cloud shapes is based on this single available sample of projected axis ratios, and the result should be confirmed when other shape data become available, the sheer size of this catalogue is a strong point."
 The listoeram of observed axis ratios (Fie. 3)), The histogram of observed axis ratios (Fig. \ref{heyertotalbest}) )
 is very distinct from anv of the other samples., is very distinct from any of the other samples.
 It has a very sharp peak and a severe lack of objects with p20.5., It has a very sharp peak and a severe lack of objects with $p\gtrsim 0.5$.
" While there may be some ""uknown selection effect which biases against the observation of near-circular objects we note that the the orientations of the projected shapes in the pluie of the sky do appear to be truly randoni."," While there may be some unknown selection effect which biases against the observation of near-circular objects, we note that the the orientations of the projected shapes in the plane of the sky do appear to be truly random."
 Furthermore. we note that the earlier a 15C0 catalogue of only 23 clouds in Ophiuchus by," Furthermore, we note that the earlier $^{13}$ CO catalogue of only 23 clouds in Ophiuchus by"
value of ely=45 mag based on the mid-infrared. hydrogen recombination lines A 2.17 pm. Bra A 4.05pm and Pla À 1.46 pim). the mid-infrared. sources observed by Soifer et al. (,"value of $A_V=45$ mag based on the mid-infrared hydrogen recombination lines $\beta$ $\lambda$ 2.17 $\mu$ m, $\alpha$ $\lambda$ $\mu$ m and $\alpha$ $\lambda$ 7.46 $\mu$ m), the mid-infrared sources observed by Soifer et al. ("
1999) must be highly. obscured objects.,1999) must be highly obscured objects.
 This suggests that what Surace et al. (, This suggests that what Surace et al. (
1998) found to be true in the warm. ULICGs. specifically that the contribution of the observed clusters to the bolometric luminosity is small. is also true in Arp 220.,"1998) found to be true in the warm ULIGs, specifically that the contribution of the observed clusters to the bolometric luminosity is small, is also true in Arp 220."
 We now investigate this in detail by studying the energy outputs of the SSCs themselves., We now investigate this in detail by studying the energy outputs of the SSCs themselves.
 The images of the core of Arp 220 show eleven SSCs at optical (V-.. Re. and. f-hancl) wavelengths (Shava et al.," The images of the core of Arp 220 show eleven SSCs at optical $V$ -, $R$ -, and $I$ -band) wavelengths (Shaya et al."
 1994) and twelve SSCs at near-infrared (J-.. H-.. ancl A-band) wavelengths (Scoville et al.," 1994) and twelve SSCs at near-infrared $J$ -, $H$ -, and $K$ -band) wavelengths (Scoville et al."
 1998)., 1998).
 In this paper. we call the FLIOW filter (1.1 jum) as J filter. though the standard. ο filter is at 1.25542. We combine these datasets in order to obtain a set of SSC's that are detected at all wavelengths.," In this paper, we call the F110W filter (1.1 $\mu$ m) as $J$ filter, though the standard $J$ filter is at $\mu$ m. We combine these datasets in order to obtain a set of SSCs that are detected at all wavelengths."
 This allows us to sample the SEDs over as wide a range in wavelength as possible., This allows us to sample the SEDs over as wide a range in wavelength as possible.
 Three SSC's are located in the outer regions of the core we expect dust extinction to be smallest. here. so that these SSCs should be seen at all wavelengths.," Three SSCs are located in the outer regions of the core – we expect dust extinction to be smallest here, so that these SSCs should be seen at all wavelengths."
 Given the published coordinates. there is a slight ollset between the and near-infraredoptical of positionsthese SSC's (see the Ieft panel of Figure 1).," Given the published coordinates, there is a slight offset between the near-infrared and optical positions of these SSCs (see the left panel of Figure 1)."
 However. if we rotate the near-infrared images by 4 around the nuclear SSC associated with the western nucleus. the positions of the star clusters in the two images are almost coincident (see the right panel of Figure 1).," However, if we rotate the near-infrared images by $-4^{\circ}$ around the nuclear SSC associated with the western nucleus, the positions of the star clusters in the two images are almost coincident (see the right panel of Figure 1)."
 Given the probable low extinction along these lines of sight. we regard. this astrometrical solution as likely to be the correct one.," Given the probable low extinction along these lines of sight, we regard this astrometrical solution as likely to be the correct one."
 In addition. given this astrometry. we then find that three nuclear SSCs (hereafter NI. N2. and N3) are coincident in the optical ancl near-infrared. images. in addition to the three eireumnuclear ones (hereafter CL. C2. and C3).," In addition, given this astrometry, we then find that three nuclear SSCs (hereafter N1, N2, and N3) are coincident in the optical and near-infrared images, in addition to the three circumnuclear ones (hereafter C1, C2, and C3)."
 ln Figure 2. we show the observed SEDs of the six SSCs.," In Figure 2, we show the observed SEDs of the six SSCs."
 We use the photometric data published by Shava ct al. (, We use the photometric data published by Shaya et al. (
1994: VRE bands) and by Scoville ct al. (,1994; $VRI$ bands) and by Scoville et al. (
LOOS: 74A. bands) for SSC N2 N3 and ο €3.,1998; $JHK$ bands) for SSC N2 – N3 and C1 – C3.
 In the case of SSC NI. we have used 457 archival data to measure the optical Dluxes using the same 0.92 aresee 0.58 aresee aperture used. by Scoville et al. (," In the case of SSC N1, we have used $HST$ archival data to measure the optical fluxes using the same 0.92 arcsec $\times$ 0.58 arcsec aperture used by Scoville et al. ("
1998) for the near-infrared measurements (Shava et al.,1998) for the near-infrared measurements (Shaya et al.
 used à smaller aperture in their analysis)., used a smaller aperture in their analysis).
 The magnitudes of SSC NI are 21.96 mag and 19.36 for H-band (1702) and /-band (ET85LP) respectively., The magnitudes of SSC N1 are 21.96 mag and 19.36 for $R$ -band (F702W) and $I$ -band (F785LP) respectively.
 This SSC was not detected in the VY -band (P555W)., This SSC was not detected in the $V$ -band (F555W).
 All three nuclear SSC's show a peak at 1.6 jin. whereas all three cireumnuclear SSCs have SEDs that rise towards bluer wavelengths.," All three nuclear SSCs show a peak at 1.6 $\mu$ m, whereas all three circumnuclear SSCs have SEDs that rise towards bluer wavelengths."
 This is à very important difference and is immediately sugeestive of far more dust extinction along the lines of sight to the nuclear SSC's than along the lines of sight to the cireumnuclear ones., This is a very important difference and is immediately suggestive of far more dust extinction along the lines of sight to the nuclear SSCs than along the lines of sight to the circumnuclear ones.
 We now compare the SEDs with the Starburst90 spectral synthesis models of Leitherer et al. (, We now compare the SEDs with the Starburst99 spectral synthesis models of Leitherer et al. (
1999).,1999).
 One of the advantages of the Starburst99 is that it tell us the evolution of the strength. of CO index whieh is useful to constrain the range of ages., One of the advantages of the Starburst99 is that it tell us the evolution of the strength of CO index which is useful to constrain the range of ages.
 When fitting model SEDs to observed ones in the presence of internal extinction. there are several parameters that we need to consider: Ipt 1) the mode of star. formation.," When fitting model SEDs to observed ones in the presence of internal extinction, there are several parameters that we need to consider: 1pt 1) the mode of star formation."
 For example. the star formation mav occur continuously (the constant star formation. or CSE model). may occur in a short. almost instantaneous. burst (the instantaneous starburst. or ISB model). or may occur in a way that varies with time in a complex manner.," For example, the star formation may occur continuously (the constant star formation, or CSF model), may occur in a short, almost instantaneous, burst (the instantaneous starburst, or ISB model), or may occur in a way that varies with time in a complex manner."
 For the blue circummuclear SSCs. there is no evidence that star formation has been ongoing in these isolated clusters for any considerable time. and we adopt an ISB model for describing star formation in these svstenis.," For the blue circumnuclear SSCs, there is no evidence that star formation has been ongoing in these isolated clusters for any considerable time, and we adopt an ISB model for describing star formation in these systems."
 On the other hand. the nuclear star-forming regions of Arp 220 are probably at least LO” wears old (Mouri Taniguchi 1992: Prestwich. Joseph. Wright 1904: Armius ct al.," On the other hand, the nuclear star-forming regions of Arp 220 are probably at least $^{8}$ years old (Mouri Taniguchi 1992; Prestwich, Joseph, Wright 1994; Armus et al."
 1995: Larkin et al., 1995; Larkin et al.
 1995)., 1995).
 Yet there still appear to be ionizing sources in the nuclear region (Larkin et al., Yet there still appear to be ionizing sources in the nuclear region (Larkin et al.
 1995. lim οἱ al.," 1995, Kim et al."
 1995. and Goldacder et al.," 1995, and Goldader et al."
 1995)., 1995).
 Therefore an ISB mocel will not work here. and we approximate star formation in rw nuclear SSCs by a CSE model.," Therefore an ISB model will not work here, and we approximate star formation in the nuclear SSCs by a CSF model."
 On the other hand. there is a possibility that the nuclear SSCs are not the ongoing starburst discussed in the above papers but post-starburst and we also consider an ISB model for the nuclear SSCs. although we regard the CSE one as the more likely: Ipt 2) the stellar IEME.," On the other hand, there is a possibility that the nuclear SSCs are not the ongoing starburst discussed in the above papers but post-starburst and we also consider an ISB model for the nuclear SSCs, although we regard the CSF one as the more likely; 1pt 2) the stellar IMF."
" We adopt a Salpeter IME with an upper mass cutoll of AZ,=100M. and a lower mass cutoll of A=IAL..."," We adopt a Salpeter IMF with an upper mass cutoff of $M_{\rm u} = 100 \, {\rm M}_\odot$ and a lower mass cutoff of $M_{\rm l} = 1 \, {\rm M}_\odot$."
 We note that AZ; might be larger in a violent. star-forming region (see e.g. Goldacder ct al., We note that $M_{\rm l}$ might be larger in a violent star-forming region (see e.g. Goldader et al.
 1997) and investigate the elfect of the IME on our results in the next section: Ipt 3) the initial eas metallicity., 1997) and investigate the effect of the IMF on our results in the next section; 1pt 3) the initial gas metallicity.
 We assume solar metallicity (Z= 0.02)., We assume solar metallicity $Z=0.02$ ).
 Since the metallicity of galactic centre may be larger than the solar value. we also study the case of (see the next section): Ipt 4) the age at which we observe the star clusters.," Since the metallicity of galactic centre may be larger than the solar value, we also study the case of $Z=0.04$ (see the next section); 1pt 4) the age at which we observe the star clusters."
" We leave this as a free parameter in the range of 2.107 vr to 1.10"" ve: Ipt 5) the ellect of extinction.", We leave this as a free parameter in the range of $2 \times 10^5$ yr to $1 \times 10^9$ yr; 1pt 5) the effect of extinction.
 The total extinction can be regarded as the sum of two parts: 1) extinction from dust in Arp 220 along our line of sight to the SSCs. and 2) extinction from dust the SSCs.," The total extinction can be regarded as the sum of two parts: 1) extinction from dust in Arp 220 along our line of sight to the SSCs, and 2) extinction from dust the SSCs."
 Ehe relative importance of these two regimes can be tested as follows., The relative importance of these two regimes can be tested as follows.
" A screen model may be used to describe extinction along our line of sight to the SSCs. and the ""onion-skin model of Surace ancl Sanders (1999) may be used to quantify the extinction from cust within the SSC's."," A screen model may be used to describe extinction along our line of sight to the SSCs, and the “onion-skin"" model of Surace and Sanders (1999) may be used to quantify the extinction from dust within the SSCs."
 This comparison is made in Appenclix A.," This comparison is made in Appendix A,"
detailed analysis of their effects on void properties by revising the void-finding algorithm.,detailed analysis of their effects on void properties by revising the void-finding algorithm.
 Our Fig., Our Fig.
" 1 shows that in the coupled scalar field models matter is more concentrated in some regions, leaving the remaining of the space more evacuated, in line with the expectations."," \ref{densprob} shows that in the coupled scalar field models matter is more concentrated in some regions, leaving the remaining of the space more evacuated, in line with the expectations."
" Here we note that the N and C models behave differently: for the former, the fifth force is never suppressed, and the migration of matter from low density regions to high density regions starts earlier thanks to it; for the latter, the chameleon effect suppresses the fifth force at the early times, the effect of which in boosting the clustering of matter only becomes significant recently (after redshift 1)."," Here we note that the N and C models behave differently: for the former, the fifth force is never suppressed, and the migration of matter from low density regions to high density regions starts earlier thanks to it; for the latter, the chameleon effect suppresses the fifth force at the early times, the effect of which in boosting the clustering of matter only becomes significant recently (after redshift 1)."
" In both models, larger portion of space is under-dense today than in the L model."," In both models, larger portion of space is under-dense today than in the L model."
" We apply our void-finding algorithm to the N and C models, and find that both models predict a bigger number of larger voids than the L model does (Fig. 2))."," We apply our void-finding algorithm to the N and C models, and find that both models predict a bigger number of larger voids than the L model does (Fig. \ref{vvf}) )."
" Once again, the N and C models behave quite differently, in particular at early times: by redshift 1.0 the N4 model produces several times more voids than the L model (and also the biggest voids are several times bigger), while the C models are only slightly different from the L model, though the fifth force in them, if unsuppressed, is much stronger than in the N models."," Once again, the N and C models behave quite differently, in particular at early times: by redshift $1.0$ the N4 model produces several times more voids than the L model (and also the biggest voids are several times bigger), while the C models are only slightly different from the L model, though the fifth force in them, if unsuppressed, is much stronger than in the N models."
 The result seems to be contradictory to the expectation that in the void regions the fifth force gets less suppressed and therefore we should have seen greater difference from the L model., The result seems to be contradictory to the expectation that in the void regions the fifth force gets less suppressed and therefore we should have seen greater difference from the L model.
" The reason is as follows: firstly, the scalar field equation of motion is dynamical and the solution in the void regions depends on the overall environment in the simulation box, so it is untrue that the fifth force in void regions is unsuppressed; secondly, the formation rate of voids is more dependent on how fast high density regions could pull matter out of them, but as the fifth force is suppressed this pull is not much stronger than in the L model."," The reason is as follows: firstly, the scalar field equation of motion is dynamical and the solution in the void regions depends on the overall environment in the simulation box, so it is untrue that the fifth force in void regions is unsuppressed; secondly, the formation rate of voids is more dependent on how fast high density regions could pull matter out of them, but as the fifth force is suppressed this pull is not much stronger than in the L model."
" It is worth noting that the difference between the void volume functions in N and L models is bigger at earlier times (Fig. 2)),"," It is worth noting that the difference between the void volume functions in N and L models is bigger at earlier times (Fig. \ref{vvf}) ),"
" because at later times most potential void regions have already been developed: since there are not many more new voids yet to be produced in the N models, the L model gradually catches up."," because at later times most potential void regions have already been developed: since there are not many more new voids yet to be produced in the N models, the L model gradually catches up."
" For the C models, the trend is quite opposite, and more voids are produced recently than in the L model, because finally the fifth force is freed and starts to take effect."," For the C models, the trend is quite opposite, and more voids are produced recently than in the L model, because finally the fifth force is freed and starts to take effect."
 We also show in Fig., We also show in Fig.
 3 the fraction of space which is filled by voids exceeding a certain threshold in volume., \ref{ff} the fraction of space which is filled by voids exceeding a certain threshold in volume.
" Here the qualitative features could be explained by the same argument used for Fig. 2,,"," Here the qualitative features could be explained by the same argument used for Fig. \ref{vvf},"
 and what is more impressive is the quantitative result it illustrates., and what is more impressive is the quantitative result it illustrates.
" For example, at redshift 1.0 the N4 model, which is the most extreme in the N models, predicts almost 4 times as much space filled by voids larger than 35h-?Mpc? as does the L model."," For example, at redshift $1.0$ the N4 model, which is the most extreme in the N models, predicts almost 4 times as much space filled by voids larger than $35~h^{-3}{\rm Mpc}^3$ as does the L model."
 Even at present the number is almost 2 (the same also applies for the C models)., Even at present the number is almost 2 (the same also applies for the C models).
 Voids prove to be a promising tool to constrain the scalar field couplings., Voids prove to be a promising tool to constrain the scalar field couplings.
" Finally, we have studied the density profiles of the voids (Figs. 4,, 5))."," Finally, we have studied the density profiles of the voids (Figs. \ref{vprofile_l}, \ref{vprofile_s}) )."
" We find that in general the voids in the coupled scalar field models are featured by a sharper transition from low density to high density around their edges, similar as the result for the ReBEL model (Keselman,Nusser&Peebles 2010)."," We find that in general the voids in the coupled scalar field models are featured by a sharper transition from low density to high density around their edges, similar as the result for the ReBEL model \citep{knp2010}."
. At earlier times the large voids in coupled scalar field models also have lower overdensities in the inner part due to the more effective evacuation of the region., At earlier times the large voids in coupled scalar field models also have lower overdensities in the inner part due to the more effective evacuation of the region.
" Due to the limitation of the simulation box and resolution, we have not studied other interesting void properties such as the halos in voids."," Due to the limitation of the simulation box and resolution, we have not studied other interesting void properties such as the halos in voids."
" And because we have only dark matter in the simulations, we have not touched the formations and properties of the void galaxies."," And because we have only dark matter in the simulations, we have not touched the formations and properties of the void galaxies."
 These shall be left to future works., These shall be left to future works.
" The existing results, however, already indicate that the void properties could be largely influenced by a coupled scalar field, being it chameleon or not, and therefore voids could provide a useful tool to study and constrain such alternative scenarios for structure formation."," The existing results, however, already indicate that the void properties could be largely influenced by a coupled scalar field, being it chameleon or not, and therefore voids could provide a useful tool to study and constrain such alternative scenarios for structure formation."
" The simulations and processing of data for this work are performed on theSARA supercomputer in the Netherlands, under the project, with the support of the European Community Research Infrastructure Action under the ""Structuring the European Research Area? program, using a modified version of the publicly available code (Knebe,Green&Binney2001)."," The simulations and processing of data for this work are performed on the supercomputer in the Netherlands, under the project, with the support of the European Community Research Infrastructure Action under the ""Structuring the European Research Area"" program, using a modified version of the publicly available code \citep{kgb2001}."
 The author is grateful to Lin Jia for helpful discussions and aid in the implementation of the void-finding algorithm., The author is grateful to Lin Jia for helpful discussions and aid in the implementation of the void-finding algorithm.
" The author is supported by the Research Fellowship in Applied Mathematics at Queens! College, University of Cambridge, and the Science and Technology Facility Council (STFC) of the United Kingdom."," The author is supported by the Research Fellowship in Applied Mathematics at Queens' College, University of Cambridge, and the Science and Technology Facility Council ) of the United Kingdom."
Galaxy clises are. Κον structural components in. the understanding of ealaxy formation.,Galaxy discs are key structural components in the understanding of galaxy formation.
 They contain approximately of the stellar mass —in. the —Universe (7) and are one of the main sites of current star formation activity (7).., They contain approximately of the stellar mass in the Universe \citep{Driver2007} and are one of the main sites of current star formation activity \citep{Kennicutt1998}.
 Moreover. their prominence and appearance form the basis of the ? morphological sequence.," Moreover, their prominence and appearance form the basis of the \citet{Hubble1926} morphological sequence."
 Despite this enormous importance. understanding the details of disc formation remains extremely challenging.," Despite this enormous importance, understanding the details of disc formation remains extremely challenging."
 The basic scenario considers that barvons cool and. collapse within hierarchically assembled clark matter haloes., The basic scenario considers that baryons cool and collapse within hierarchically assembled dark matter haloes.
 A certain amount of their torquc-acquired angular momentum is transferred. to the barvonic component leading to the formation of a rotationally supported. thin disc (2).., A certain amount of their torque-acquired angular momentum is transferred to the baryonic component leading to the formation of a rotationally supported thin disc \citep{Fall1980}.
" ""Ehis relatively simple picture has been able to reproduce many observational properties of dise galaxies flat rotation curves. Tullv-Fisher relation. gas content (e.g. 22?27)). but sullers from several shortcomings."," This relatively simple picture has been able to reproduce many observational properties of disc galaxies –flat rotation curves, Tully-Fisher relation, gas content (e.g., \citealt{Dalcanton1997,Mo1998,vandenBosch1998,vandenBosch2000}) )– but suffers from several shortcomings."
 On the one hand. detailed N-body simulations showed that when the dissipative effects of gas are not considered. the hierarchical nature of structure formation unavoidably results in cise cestruction (?)..," On the one hand, detailed N-body simulations showed that when the dissipative effects of gas are not considered, the hierarchical nature of structure formation unavoidably results in disc destruction \citep{Toth1992}."
 On the other hand. hycrodynamical simulations of this process systematically produced. dises that were too small ancl too centrally concentratoc due to excessive angular momentunm. exchange between the eas and the dark matter haloes (?)..," On the other hand, hydrodynamical simulations of this process systematically produced discs that were too small and too centrally concentrated due to excessive angular momentum exchange between the gas and the dark matter haloes \citep{Navarro1997}."
 A physically-moivated solution for. these problems is the inclusion of srong [feedback ellects from. dilferent sources but specially [rom star formation and supernovac explosions which. when coupled with a cosmic UV field. are able not onlv to produce realistic dises (e.g. 2)). but also o provide one possible explanation for the missing satellite xoblem (?)..," A physically-motivated solution for these problems is the inclusion of strong feedback effects from different sources –but specially from star formation and supernovae explosions– which, when coupled with a cosmic UV field, are able not only to produce realistic discs (e.g., \citealt{Governato2010}) ), but also to provide one possible explanation for the missing satellite problem \citep{Klypin1999}."
 This approach. in turn. raises the question of which role does mass play in shaping the properties of disces. as hese strong heating mechanisms are expected to. produce a greater inlluence in lower-mass galaxies (τι INWDOT iereafter).," This approach, in turn, raises the question of which role does mass play in shaping the properties of discs, as these strong heating mechanisms are expected to produce a greater influence in lower-mass galaxies \citealt{Kaufmann2007}, KWB07 hereafter)."
 bLndeed. it is well known that. galaxies have ügher gas mass fractions (c.g. 2)) and more extended star ormation time scales (7). as they are less massive. and it ws been proposed that chwarl and dise galaxies are probably wo dillerent structural entities (?)..," Indeed, it is well known that galaxies have higher gas mass fractions (e.g., \citealt{Schombert2001}) ) and more extended star formation time scales \citep{Hunter1985} as they are less massive, and it has been proposed that dwarf and disc galaxies are probably two different structural entities \citep{Schombert2006}."
 From an observational point of view. galaxy cliscs are best. described. as Qattenecl triaxial ellipsoids with exponential surface brightness profiles (2)..," From an observational point of view, galaxy discs are best described as flattened triaxial ellipsoids with exponential surface brightness profiles \citep{Freeman1970}."
 Though they are traditionally. considered. to be perfectly. circular. dt is well known that disces are indeed sliehth elliptical. with bia0.9 (??)..," Though they are traditionally considered to be perfectly circular, it is well known that discs are indeed slightly elliptical, with $b/a \gtrsim 0.9$ \citep{Lambas1992,Ryden2004}."
 Thev are said to be because their vertical toradial axis ratios have long been known to lie in à narrow range O15qoO.25 (?77)..," They are said to be because their vertical toradial axis ratios have long been known to lie in a narrow range $0.15 \lesssim q_{0} \lesssim 0.25$ \citep{Holmberg1950,Sandage1970,Heidmann1972}. ."
 llowever.," However,"
Tt wielt be argued that the application of these relations is wrong because the IGIME will affect the stellarauass-to-light-ratiocolour relations.,It might be argued that the application of these relations is wrong because the IGIMF will affect the stellar-mass-to-light-ratio–colour relations.
 Iu 2 df has been shown that for sinall SFRs the IGIME effect for the FUV-fux is less than one dex if the IGIME effect for Ta is two dex., In \citet{pflamm-altenburg2009a} it has been shown that for small SFRs the IGIMF effect for the FUV-flux is less than one dex if the IGIMF effect for $\alpha$ is two dex.
 The B-baud aud louger waveleneth bauds are expected to show an even simaller IGIME effect than the FUV-fiux., The B-band and longer wavelength bands are expected to show an even smaller IGIMF effect than the FUV-flux.
 The dominating influence ou the stellar mass builliup time scale is by far the IGIME- for the Ha based SERs (eq. 10))., The dominating influence on the stellar mass buildup time scale is by far the IGIMF-effect for the $\alpha$ based SFRs (eq. \ref{eq_tau_star}) ).
 Thus. the 7O stellay-mass-to-lhelt-ratiocolour relations are applicable for an order-ofanaguitude estimate of the stellar nass buildup times.," Thus, the \citet{bell2001a} stellar-mass-to-light-ratio–colour relations are applicable for an order-of-magnitude estimate of the stellar mass buildup times."
 However. precisiou ealaxv evolution modoeliug would require revised niass-to-lielit ratios. which we will adress in future projects.," However, precision galaxy evolution modeling would require revised mass-to-light ratios, which we will adress in future projects."
 The two stcllaranass-to-light-vatiocolour relations aud tabulated iu ?7— can be used to construct a stellaxnass-to-light-ratiocolour relation between the B-hand magnitude aud the D-IT--colour. where the two cocfiicicuts are given by aud The required colour is obtained using the abulated bluc-baud magnitude. aud the IT-baud uaenitude. Ag.," The two stellar-mass-to-light-ratio–colour relations and tabulated in \citet{bell2001a} can be used to construct a stellar-mass-to-light-ratio–colour relation between the B-band magnitude and the -colour, where the two coefficients are given by and The required colour is obtained using the tabulated blue-band magnitude, and the H-band magnitude, $M_\mathrm{H}$."
" To assign au IH-baud maguitude ο cach galaxy we use the observed extremely tight correlation between the B- aud IT-baud magnitude of galaxies (2.eq.9) ranging from Mp=8 ο Af,=22.", To assign an H-band magnitude to each galaxy we use the observed extremely tight correlation between the B- and H-band magnitude of galaxies \citep[eq.~9]{kirby2008a} ranging from $M_\mathrm{B}=-8$ to $M_\mathrm{B}=-22$.
 The resulting empirical relation vetween the D-IT colour aud the D-baud is then eiven bv In ? the stellar-nass-to-light-ratiocolour relafious are given for seven different ealaxy evolution models. which lead to slightly different values for appv. pvi Sepve and bpqr.," The resulting empirical relation between the B-H colour and the B-band is then given by In \citet{bell2001a} the stellar-mass-to-light-ratio–colour relations are given for seven different galaxy evolution models, which lead to slightly different values for $a_\mathrm{B,B-V}$, $a_\mathrm{B,V-H}$, $b_\mathrm{B,B-V}$, and $b_\mathrm{B,V-H}$."
 The resulting coefficients. eppqp and bpppp. are listed in Tab. 3..," The resulting coefficients, $a_\mathrm{B,B-H}$ and $b_\mathrm{B,B-H}$, are listed in Tab. \ref{tab_M_L}. ."
 In the following analysis we use their mean values for the logALἐν (MpAdy) relation. We now have for each of our galaxies Mg (Tab. νι," In the following analysis we use their mean values for the $\log M_\mathrm{*}/L_\mathrm{B}$ $M_\mathrm{B}-M_\mathrm{H}$ ) relation, We now have for each of our galaxies $M_\mathrm{B}$ (Tab. \ref{tab_data},"
 Col D. Ady Grom eq. 16))," Col 4), $M_\mathrm{H}$ (from eq. \ref{eq_B_H}) )"
 aud. thus AL./£y Grom eq. 13))., and thus $M_\mathrm{*}/L_\mathrm{B}$ (from eq. \ref{eq_B_B-H}) ).
" Each of the Mp values can therewith be couverted to he total stellar mass AL. allowing the computatioLot 7. for each galaxy,", Each of the $M_\mathrm{B}$ values can therewith be converted to the total stellar mass $M_\mathrm{*}$ allowing the computation of $\tau_\mathrm{*}$ for each galaxy.
 For a few galaxies of our sample absolute II-baud maguitudes are listed i1 7.., For a few galaxies of our sample absolute H-band magnitudes are listed in \citet{kirby2008a}.
 For these galaxies we use the observed absolue II-baud magnitude. for all the others we usethe calculated D-II colour according to the procccure described above.," For these galaxies we use the observed absolute H-band magnitude, for all the others we usethe calculated B-H colour according to the procedure described above."
 Table Lt lists those galaxies which have observed absolute IT-baud magnitudes bv 7., Table \ref{tab_H_obs_cal} lists those galaxies which have observed absolute H-band magnitudes by \citet{kirby2008a}. .
consist mostly of the field stars.,consist mostly of the field stars.
 Phe N-region is intermediate between the C-region and the F-region., The N-region is intermediate between the C-region and the F-region.
 The distinguishable features seen in the color-magnitude diagrams of the C-region are: (a) Phere is a well-defined main sequence the top of which is located at V216 mag: (b) There is seen a distinct gap at Vz16.2 mag in the main sequence. which is often seen in other old open clusters (e.g. M67): (0) There is a poorly defined red giant branch andl these is seen some excess of stars around (13Vy=13 and Vo=15.6 mag on this giant. branch. which is remarked by the small box in the figures.," The distinguishable features seen in the color-magnitude diagrams of the C-region are: (a) There is a well-defined main sequence the top of which is located at $V \approx 16$ mag; (b) There is seen a distinct gap at $V \approx 16.2$ mag in the main sequence, which is often seen in other old open clusters (e.g. M67); (c) There is a poorly defined red giant branch and these is seen some excess of stars around $(B-V)=1.3$ and $V=15.6$ mag on this giant branch, which is remarked by the small box in the figures."
 This may bea random excess of stars., This may be a random excess of stars.
 Llowever. the positions of the stars in the CMDs are consistent with the positions of known red giant clump in other old open clusters.," However, the positions of the stars in the CMDs are consistent with the positions of known red giant clump in other old open clusters."
 Therefore most of these stars are probably red. giant clump stars: ancl (cl) There are a small number of stars along the locus of the red giant branch., Therefore most of these stars are probably red giant clump stars; and (d) There are a small number of stars along the locus of the red giant branch.
 NGC 1798 is located close to the galactic plane in the anti-ealactic centre direction. (b.=4°.S5 and /= 160°.76) so that it is expected that the reddening toward this cluster is significant., NGC 1798 is located close to the galactic plane in the anti-galactic centre direction $b=4^\circ.85$ and $l=160^\circ.76$ ) so that it is expected that the reddening toward this cluster is significant.
 We have estimated the reddening for NGC 1798 using two methods as follows., We have estimated the reddening for NGC 1798 using two methods as follows.
 First we have used the mean color of the red. giant clump., First we have used the mean color of the red giant clump.
 Janes Phelps (1994) estimated the mean color and magnitude of the red giant clump in old open clusters to be (D.V)pee=OSTEO? ancl Adyper=0.5920.09. when the dillerence between the red. giant clump ancl the main sequence turn-olf of the clusters. OV. is smaller than one.," Janes Phelps (1994) estimated the mean color and magnitude of the red giant clump in old open clusters to be $(B-V)_{RGC}=0.87 \pm 0.02$ and $M_{V, RGC} = 0.59 \pm 0.09$, when the difference between the red giant clump and the main sequence turn-off of the clusters, $\delta V$, is smaller than one."
 The mean color of the red. giant. clump in the C-region is estimated to be CDΕο—1.34E0.01 (Vμοι=1.474 0.01. and (€Bypee=1.62+ 0.04). and the corresponding mean magnitude is Έρως=15.57EOOS.," The mean color of the red giant clump in the C-region is estimated to be $(B-V)_{RGC}=1.34 \pm 0.01$ $(V-I)_{RGC}=1.47 \pm 0.01$ , and $(U-B)_{RGC}=1.62 \pm 0.04$ ), and the corresponding mean magnitude is $V_{RGC} = 15.57 \pm 0.05$."
" AV"" is estimated to be 0.82E 0.2. which is the same value derived by Phelps et ((1994)."," $\delta V$ is estimated to be $0.8\pm 0.2$ , which is the same value derived by Phelps et (1994)."
 From these data we have derived a value of the reddening. {04Vo)=0.47£0.02.," From these data we have derived a value of the reddening, $E(B-V) = 0.47 \pm 0.02$."
 Secondly we have used the color-color lagram to estimate the reddening and the metallicity simultaneously., Secondly we have used the color-color diagram to estimate the reddening and the metallicity simultaneously.
κ We have fitted. the mean colors of the stars in the C-region with the color-color relation used. in the Padova isochrones ortellictal.1994)., We have fitted the mean colors of the stars in the C-region with the color-color relation used in the Padova isochrones \cite{ber94}.
 This process requires iteration. because we need to know the age of the cluster as well as the reddening and metallicity.," This process requires iteration, because we need to know the age of the cluster as well as the reddening and metallicity."
 We have iterated this process until all three parameters are stabilized., We have iterated this process until all three parameters are stabilized.
 Fig., Fig.
 6 illustrates the results of fitting in the (2B)(BV) color-color diagram., 6 illustrates the results of fitting in the $(U-B)-(B-V)$ color-color diagram.
 IH is shown in this figure that the stars in NGC 1798 are reasonably fitted by the color-color relation of the isochrones for ο) =0-4( with a reddening value of £(BV)=0.550.05., It is shown in this figure that the stars in NGC 1798 are reasonably fitted by the color-color relation of the isochrones for [Fe/H] $= -0.47 \pm 0.15$ with a reddening value of $E(B-V)=0.55 \pm 0.05$.
 The error for the metallicity. 0.15. was estimated by comparing isochrones with clilferent metallicities.," The error for the metallicity, 0.15, was estimated by comparing isochrones with different metallicities."
 As a reference the mean locus of the giants for solar abundance given by Schmicdt-Ixaler. (1982) is also plotted in Fig., As a reference the mean locus of the giants for solar abundance given by Schmidt-Kaler (1982) is also plotted in Fig.
 6., 6.
 Finally we derive a mean value of the two estimates for the reddening. £(BV)z051I£0.04.," Finally we derive a mean value of the two estimates for the reddening, $E(B-V) = 0.51 \pm 0.04$."
 We have estimated the distance to NGC 1798 using two methocls as follows., We have estimated the distance to NGC 1798 using two methods as follows.
 First we have used the mean magnitude of the red. giant clump., First we have used the mean magnitude of the red giant clump.
 We have derived. a value of the apparent distance modulus (01.A4)=14.980.10 from the values for the mean magnitudes of the rec giant clump stars described above., We have derived a value of the apparent distance modulus $(m-M)_V = 14.98 \pm 0.10$ from the values for the mean magnitudes of the red giant clump stars described above.
 Secondly wei have. usec the the zero-age main sequence (ZAAIS) fitting. following the method. described in VandenDerg Poll (1989).," Secondly we have used the the zero-age main sequence (ZAMS) fitting, following the method described in VandenBerg Poll (1989)."
 VandenDerg Poll (1989) presented the semi-empirical ZAAIS as a function of the metallicity Fe/LU] and the helium abundance Y: where OALOY)=2.600.27) and SAL(Fel)= Μο]. 3e, VandenBerg Poll (1989) presented the semi-empirical ZAMS as a function of the metallicity [Fe/H] and the helium abundance Y: where $\delta M_V (Y) = 2.6 (Y -0.27)$ and $\delta M_V({\rm [Fe/H]}) = - {\rm [Fe/H]} (1.444 + 0.362 {\rm [Fe/H]})$ .
fore the ZAMS fitting. we subtracted statistically the contribution due to the field stars in the CMDs of the C- using the CMDs of the Eb-region for DV photometry and the CAIDs of the FilFir region for V7 photometry.," Before the ZAMS fitting, we subtracted statistically the contribution due to the field stars in the CMDs of the C-region using the CMDs of the Fb-region for $BV$ photometry and the CMDs of the Fi+Fir region for $VI$ photometry."
 The size of the bin used for the subtraction is AV=0.25 and (D.V)=0.1., The size of the bin used for the subtraction is $\Delta V = 0.25$ and $\Delta (B-V) = 0.1$.
 The resulting CALDs are displaved in Fig., The resulting CMDs are displayed in Fig.
 7., 7.
 We used the metallicity of. ο] = 0.47 as derive above and adopted Y=0.28 which is the mean value for ol open clusters (Ciratton.1982)., We used the metallicity of [Fe/H] = –0.47 as derived above and adopted $Y=0.28$ which is the mean value for old open clusters \cite{gra82}.
. Using this method we have obtained a value of the apparent distance modulus. (2Αι=1454022., Using this method we have obtained a value of the apparent distance modulus $(m-M)_V = 14.5 \pm 0.2$ .
 Finally we calculate a mean value of the two estimates. GaAZ=14.7+0.2.," Finally we calculate a mean value of the two estimates, $(m-M)_V = 14.7 \pm 0.2$."
 Adopting the extinction law of ely=οV). we derive a value of the intrinsic distance moclulus (nAl)y=13.1 40.2.," Adopting the extinction law of $A_V = 3.2 E(B-V)$, we derive a value of the intrinsic distance modulus $(m-M)_0 = 13.1 \pm 0.2$ ."
 This corresponds to a clistance of d—4.2£0.3 kpc., This corresponds to a distance of $d=4.2\pm 0.3$ kpc.
 We have estimated the age of NCC 1798 using two methods as follows., We have estimated the age of NGC 1798 using two methods as follows.
 First we have used the morphological age index (ALAL) as described in Phelps et (1994)., First we have used the morphological age index (MAI) as described in Phelps et (1994).
 Phelps ct ((1994) and Janes Phelps (1994) presented the oV. relation. From the value of 98V. derived above. 0.8c0.2 mag. we obtain a value for the age. ALAL =1.340.2 Gyes.," Phelps et (1994) and Janes Phelps (1994) presented the $\delta V$ relation, From the value of $\delta V$ derived above, $0.8\pm0.2$ mag, we obtain a value for the age, MAI $= 1.3\pm0.2$ Gyrs."
 Secondly we have estimated. the age of the cluster using the theoretical isochrones given by the Padova group (Bertellietal.1994)., Secondly we have estimated the age of the cluster using the theoretical isochrones given by the Padova group \cite{ber94}.
.. Fitting the isochrones for οΗ] = 0.47 to the CMDs of NGC 1798. as shown in Fig.," Fitting the isochrones for [Fe/H] = –0.47 to the CMDs of NGC 1798, as shown in Fig."
 S. we estimate the age to be 14+0.2 Civrs.," 8, we estimate the age to be $1.4\pm0.2$ Gyrs."
 Both resultsagree very well., Both resultsagree very well.
 We have derived the V. luminosity functions of the main sequence stars inNGC 1798. which are displaved in Fig.," We have derived the $V$ luminosity functions of the main sequence stars inNGC 1798, which are displayed in Fig."
 9., 9.
" ""Phe Fh-region was used for subtraction of the field star contribution from the C-region and the magnitude bin size", The Fb-region was used for subtraction of the field star contribution from the C-region and the magnitude bin size
For simulations that end in planetary. collisions. the effect on the Jovian planet depends on the impact velocity of the rocky planet.,"For simulations that end in planetary collisions, the effect on the Jovian planet depends on the impact velocity of the rocky planet."
 Distributions of these impact velocities are depicted in Figure 3. (for eccentricity damping parameter A=1)., Distributions of these impact velocities are depicted in Figure \ref{fig:vdist} (for eccentricity damping parameter $K=1$ ).
 The top panel shows clistvibutions of the angele at which the incoming planet strikes the giant planet surface., The top panel shows distributions of the angle at which the incoming planet strikes the giant planet surface.
 This distribution is equivalent to the distribution of impact parameter c=Apsind., This distribution is equivalent to the distribution of impact parameter $\varpi=R_P\sin\theta$.
" Collision dvnamies depend on the impact speed 0,4. shown in the bottom panel of Figure 3.. and the escape speed to=(CAMp/Bp)?zz37 km/s (lor Mp=LM, and Rp=LAR)."," Collision dynamics depend on the impact speed $v_{rel}$, shown in the bottom panel of Figure \ref{fig:vdist}, , and the escape speed $v_{esc}=(GM_P/R_P)^{1/2}\approx37$ km/s (for $M_P=1M_J$ and $R_P=1.4R_J$ )."
 In the limit ey2v. the giant planet presents a circular tareet and (he probability P(z)xP(sn0) increases with impact parameter a.," In the limit $v_{rel}\gg{v_{esc}}$, the giant planet presents a circular target and the probability $P(\varpi)\propto{P}(\sin\theta)$ increases with impact parameter $\varpi$."
 In the limit (44«Όρο. gravity focuses Incoming (trajectories into nearly racial paths aud the distribution peaks near a=0.," In the limit $v_{rel}\ll{v_{esc}}$, gravity focuses incoming trajectories into nearly radial paths and the distribution peaks near $\varpi=0$."
 The ealeulated. distribution is relatively flat. but [alls with ze. which suggests significant eravitational focusing.," The calculated distribution is relatively flat, but falls with $\varpi$, which suggests significant gravitational focusing."
 This expectation is validated in the bottom panel. which shows that (he impact speeds [all in the range e40—100 km/s. ie. c/c.~1—3.," This expectation is validated in the bottom panel, which shows that the impact speeds fall in the range $v\sim40-100$ km/s, i.e., $v/v_{esc}\sim1-3$ ."
 When the Jovian planet has nonzero eccentricity. the velocity distribution shows a broad peak near ve=50 km/s. For svstems with e=0. however. the distribution has a narrower peak near ¢=65 km/s. One reason for this difference is (hat (he rocky planets migrate further inwarel (before colliding) when e=0. so thev are deeper in the gravitational potential well of the star.," When the Jovian planet has nonzero eccentricity, the velocity distribution shows a broad peak near $v=50$ km/s. For systems with $e=0$, however, the distribution has a narrower peak near $v=65$ km/s. One reason for this difference is that the rocky planets migrate further inward (before colliding) when $e=0$, so they are deeper in the gravitational potential well of the star."
 Obtaining a greater dynamical understauding of this trend provides an interesting problem for Piture investigation., Obtaining a greater dynamical understanding of this trend provides an interesting problem for future investigation.
 This paper explores the accretion of rocky planetary bodies by Hot Jupiters after they reach close-in orbits., This paper explores the accretion of rocky planetary bodies by Hot Jupiters after they reach close-in orbits.
 The results show that collisions between planets are common when (he eccentricity damping rate is sufficiently small. and rare otherwise.," The results show that collisions between planets are common when the eccentricity damping rate is sufficiently small, and rare otherwise."
 In approximate terms. collisions require (he eccentricity damping parameter A.νο210. where the threshold Ac depends on the eccentricity and mass of (he Jovian planet (Figures 1.. 2)).," In approximate terms, collisions require the eccentricity damping parameter $K\le{K_C}\approx{10}$, where the threshold $K_C$ depends on the eccentricity and mass of the Jovian planet (Figures \ref{fig:efraction}, \ref{fig:mfraction}) )."
 The corresponding distributions of impact velocities for the collisions are shown in Figure 3.., The corresponding distributions of impact velocities for the collisions are shown in Figure \ref{fig:vdist}.
 These results have important implications for the diversity seen in the observational sample of Lot Jupiters: For laree A. values. both planets usually survive. in resonance. ancl such svstems can exhibit observable transit timing variations (ASSC).," These results have important implications for the diversity seen in the observational sample of Hot Jupiters: For large $K$ values, both planets usually survive, in resonance, and such systems can exhibit observable transit timing variations (ASSC)."
 For small A. values. collisions are common whenever disks produce rocky bodies alter a Lot Jupiter has migrated io its inner orbit.," For small $K$ values, collisions are common whenever disks produce rocky bodies after a Hot Jupiter has migrated to its inner orbit."
 These collisions. in (turn. can inerease the core mass and the metallicity of the Jovian planet.," These collisions, in turn, can increase the core mass and the metallicity of the Jovian planet."
 Accretion onto the star and ejection are almost alwavs rare., Accretion onto the star and ejection are almost always rare.
 The lrequency of collisions isgoverned by the A value. which depends on disk structure. viscosity.and (he mass of (he mierating rocky planet.," The frequency of collisions isgoverned by the $K$ value, which depends on disk structure, viscosity,and the mass of the migrating rocky planet."
 Previous studies of planet-disk interactions, Previous studies of planet-disk interactions
"within 0.5"" exeludius sources within 5"" of the micleus.",within $0.5\arcsec$ excluding sources within $5\arcsec$ of the nucleus.
 There are 107 Chandra sources aud 110 2inass sources in this same region., There are 107 Chandra sources and 110 2mass sources in this same region.
" The expected number of chauce coincidences within 0.5"" is 0.02.", The expected number of chance coincidences within $0.5\arcsec$ is 0.02.
 Therefore it is unlikely that more than one of the 6 coincidences is due to chance., Therefore it is unlikely that more than one of the 6 coincidences is due to chance.
 We calculated he average coordinate shift for the 6 sources aud used this to correct the Chandra position., We calculated the average coordinate shift for the 6 sources and used this to correct the Chandra position.
" The uaenitude of the shift was 0.2"".", The magnitude of the shift was $0.2\arcsec$.
 The positions iu Table P. include this correction., The positions in Table \ref{table:src} include this correction.
" After the shift. all 6 sources ave colucideut within 0.17 with an average Inaenitude of cisplaccment of 0.1rifdo,"," After the shift, all 6 sources are coincident within $0.4\arcsec$ with an average magnitude of displacement of $0.15\arcsec$."
 We searched for variability ou long time scales (o10 veas) by comparing the Chandra fluxes with fluxes measured iu a ROSAT observation iade duiue 1990 (Primietal.1993) and on short times scales (~ 10/5) by looking at light curves extracted from our Chandra data., We searched for variability on long time scales $\sim 10$ years) by comparing the Chandra fluxes with fluxes measured in a ROSAT observation made during 1990 \citep{primini93} and on short times scales $\sim 10^4 \rm s$ ) by looking at light curves extracted from our Chandra data.
 We also searched for periodic signals., We also searched for periodic signals.
 Primioetal.(1993) derived a source list from a ROSAT Wieh-Resolution Tnager (1141) observation of the central region of M31 made ou 25-28 July 1990., \citet{primini93} derived a source list from a ROSAT High-Resolution Imager (HRI) observation of the central region of M31 made on 25-28 July 1990.
 Because the scusitivity aud poiut spread function of both ROSAT and Chandra decrease as one goes off-axis. we restricted our comparison to sources with 7.5 of the uucleus of M31 (which was close to the aimpoint for both observations).," Because the sensitivity and point spread function of both ROSAT and Chandra decrease as one goes off-axis, we restricted our comparison to sources with $7.5 \arcmin$ of the nucleus of M31 (which was close to the aimpoint for both observations)."
 Comparing the source lists. we searched for matches aud found an average offset of 0.37 in RA aud |0.897 in DEC.," Comparing the source lists, we searched for matches and found an average offset of $-0.37\arcsec$ in RA and $+0.89\arcsec$ in DEC."
 After adding these offsets to the ROSAT positions. we found 53 coincidences within 3”.," After adding these offsets to the ROSAT positions, we found 53 coincidences within $3\arcsec$."
 To compare with our Chandra results. we iuultiplied. the ROSAT lhuuiosities Iuuinosities bv a factor of 1.91 to correct for the different distance. spectral uodel. aud spectral range assumed.," To compare with our Chandra results, we multiplied the ROSAT luminosities luminosities by a factor of 1.31 to correct for the different distance, spectral model, and spectral range assumed."
 To allow for calibration errors and uncertainties Induced by the ack of spectral information in either observation. we assign a systematic error of on cach unmdnositv.," To allow for calibration errors and uncertainties induced by the lack of spectral information in either observation, we assign a systematic error of on each luminosity."
 Fie., Fig.
 3. shows a comparison of the ROSAT and Chandra source Iuniuosities., \ref{vrosat} shows a comparison of the ROSAT and Chandra source luminosities.
 There are many nore Chandra sources below a Dunünositv of 5«108eresto owhich lack a counterpart than here are ROSAT sources.," There are many more Chandra sources below a luminosity of $5\times 10^{36} \rm \, erg \, s^{-1}$ which lack a counterpart than there are ROSAT sources."
 This likely iudicates, This likely indicates
the syminetry axis is 90°.,the symmetry axis is $90^o$.
 However. the «eeree of polarization falls steeply with the decrease in 0.," However, the degree of polarization falls steeply with the decrease in $\theta$ ."
" Ai 0=90"". significant polarization is found even up to a wavelength of 1.5 gan for the coolest Todwarf (Tog sOO/.)."," At $\theta=90^0$, significant polarization is found even up to a wavelength of 1.5 ${\rm \mu m}$ for the coolest T dwarf $T_{\rm eff}=800K$ )."
 But at a slightly smaller vale of 0. polarization becomes iusignilicaut at wavelenet1 loieer (han even 0.6 jin.," But at a slightly smaller value of $\theta$, polarization becomes insignificant at wavelength longer than even 0.6 ${\rm \mu m}$."
 The angular «ependeney of the polarization for different effective tem»eraure ]s preseuled in figure 3., The angular dependency of the polarization for different effective temperature is presented in figure 3.
 As the aele between the direction of the radiation fielcl aud the SVLimeiry axis decreases. he anisotropy in the adiatiou field reduces drastically because of tle [act that at sijaller angles. mostly the scattered photous emerged out aud that the probabiliy ( “scattering 11Creases as 0 Increases.," As the angle between the direction of the radiation field and the symmetry axis decreases, the anisotropy in the radiation field reduces drastically because of the fact that at smaller angles, mostly the unscattered photons emerged out and that the probability of scattering increases as $\theta$ increases."
 Te probajlity of scattering is maximum at ()—90., The probability of scattering is maximum at $\theta=90^o$.
 Figure 2(a-d) also slows hat the deereee of polarization dec'eases as the effective temperature oLthe object increases., Figure 2(a-d) also shows that the degree of polarization decreases as the effective temperature of the object increases.
 In fact. thus is true. not ouly at the outermost bouudary but also at αν depth iuside the atinosphere.," In fact, this is true, not only at the outermost boundary but also at any depth inside the atmosphere."
 In figure | we present the atmospheric derth dependence of the polarization al a particular wavelength: (A= 0.6510) and at a direction jj=0.02., In figure 4 we present the atmospheric depth dependence of the polarization at a particular wavelength $\lambda=0.6\mu$ m) and at a direction $\mu=0.02$.
 The degree of polarization for Tap=8004y remains almost constant ip to 1 bar of pressu'e level aid then falls rapidly to zero., The degree of polarization for $T_{\rm eff}=800K$ remains almost constant up to 1 bar of pressure level and then falls rapidly to zero.
 As the ellective temperature increases. the degree of polarization falls rapidly to zero at a higher altitude or at a lower pressure level.," As the effective temperature increases, the degree of polarization falls rapidly to zero at a higher altitude or at a lower pressure level."
 Tie plivsical explanation oL this feature becomes clear from igure 5 wherein the variation of the siigle scattering albeο cu with respect to the atmospheric sresstre P ancl temperature T is presenecd., The physical explanation of this feature becomes clear from figure 5 wherein the variation of the single scattering albedo $\omega_0$ with respect to the atmospheric pressure P and temperature T is presented.
 For an object wilth Tey—1:L200/.. the scattering albe) is almost coustaut and its value is abou one above a pi“ESSUL'e level of 10! bar.," For an object with $T_{\rm eff}=1200K$, the scattering albedo is almost constant and its value is about one above a pressure level of $10^{-1}$ bar."
 Below this dept[un it asyinptotically falls to zero.," Bellow this depth, it asymptotically falls to zero."
 wy becoiles zero al dee261 region as ole goes [rom jotter to cooler objects., $\omega_0$ becomes zero at deeper region as one goes from hotter to cooler objects.
 This meaus. the scattering albelo reais Doi zero up to ucl deeper region as the objects )ecome cooler and hence contribution o the polarizaio originates rom deeper region in cooler objects.," This means, the scattering albedo remains non zero up to much deeper region as the objects become cooler and hence contribution to the polarization originates from deeper region in cooler objects."
 As a consequence. the degree of polarization is higher in cooler objects as slown lu figure [.," As a consequence, the degree of polarization is higher in cooler objects as shown in figure 4."
 The polarization profile discussed above is calcuated at a loca point of the surface of the atmosphere stratified into plane-parallel geometry., The polarization profile discussed above is calculated at a local point of the surface of the atmosphere stratified into plane-parallel geometry.
 This cau be observable ouly if tle object cau be spatially resolved., This can be observable only if the object can be spatially resolved.
 However. a distau stellar object cauiot be spatialy resolved aud it appears to be a point source of light to an eart1 based observer.," However, a distant stellar object cannot be spatially resolved and it appears to be a point source of light to an earth based observer."
 Therefore ouly tie clisk averaged polarization is tlie observable quantity., Therefore only the disk averaged polarization is the observable quantity.
 However. if the apj»areut disk of a stellar object is perfectly spherical. because of svuunetry. the net polariZallon aveaged over the spjerical disk would cancelled out.," However, if the apparent disk of a stellar object is perfectly spherical, because of symmetry, the net polarization averaged over the spherical disk would cancelled out."
 High resolution spectroscopic aialysis of T dwarls |w Zapaleroal.(2009) shows that just like L dwarfs. 11ese objeüs areaso [as rotators.," High resolution spectroscopic analysis of T dwarfs by \cite{osorio06,
del09} shows that just like L dwarfs, these objects are also fast rotators."
 As a consequece. het non-zero yolarization should a‘ise when integrate| over tie apparent disk because rotation induces distortion in the stellar clisk.," As a consequence, net non-zero polarization should arise when integrated over the apparent disk because rotation induces distortion in the stellar disk."
 In. figure 6 ane figure 7. we present Ithe disk iutegrate polarization «) E dwarls at an edge ou view. Le. at al inclinaion of90° withh rotational velocity V=90 and 6t) respectively.," In figure 6 and figure 7, we present the disk integrated polarization of T dwarfs at an edge on view, i.e., at an inclination of$90^o$ with rotational velocity V=90 and 60 $^{-1}$ respectively."
 The degree of podzatlon is Iniixiinuin en the tnelinatidL augle is 907. L.e.. at au edge on view to an observe and it decreases. witl the decrease in the inclination angle as can be seen [roin figure 8.," The degree of polarization is maximum when the inclination angle is $90^o$, i.e., at an edge on view to an observer and it decreases with the decrease in the inclination angle as can be seen from figure 8."
 HarJjigtouὡςCollinsI(1965) also reporte the same featue., \cite{harrington68} also reported the same feature.
 Figure 6 and Figure 7 shows that the degree of polariza10 ofT dwarf witl auy spectral type is non-zero ouly at wavelengths shorer than 0.6 gan., Figure 6 and Figure 7 shows that the degree of polarization ofT dwarf with any spectral type is non-zero only at wavelengths shorter than 0.6 ${\rm \mu m}$ .
 As 1le 'otational velocity, As the rotational velocity
 ∺∏↴⋝∐∐∐∐⊔↸∖↑↸∖↥⋅≼⊲∪∐∐⊔∪∐↕↴↴∖↴↸∖↥⋅↕≧∪↕∪⊔↸∖↑↸∖↥⋅⊀≚∐⋅⋜↧⋅↖↽⋖∺≼⊲↕↴↕≧⋎⋝ ⋯⋯↸∖⋯≺∐∪∐⋜⋯≼⊓∖↑⋜↧↕⋅↓⋂∩≝⊔∪∐↑∐↸∖⋅↧⋜∐⊔↸∖↴∖↴≼⊲↕↸∖↥⋅↨↘↽⋀∖↕⋜⋯↖↖↽↸∖∐ CL>l21022£: (~70 ⋅⋅⋅⋅ ≻≺∪∏⋪↧↕∪∐↴∖↴∪∩⊾⋪↧⋪↧⊼↕↸∖↴∖↴↖∏⋪↧ ∪↥⋅∐⊔↕∪∐∐↴∖↴∪↕⋅↖↽∪∐∖⋯∐↖↽↸∖↕⋅↴∖↴↸∖↸∖⋯↸∖↕⋅∩⊾↸∖∙ 15” a. , $L>10^{12}L_{\sun}$ $\sim 70$ $''$ 
The NS enters the propeller phase as soon as the dynamical pressure exerted by the incoming material overwhelms the pulsar momentum flux at the gravitational radius. as discussed above.,"The NS enters the propeller phase as soon as the dynamical pressure exerted by the incoming material overwhelms the pulsar momentum flux at the gravitational radius, as discussed above."
" If no stable equilibrium exists. matter will reach the light cylinder radius on a free-fall timescale. and proceed inwards if the ram pressure overcomes the magnetic pressure of the dipole field. /5,,,= J/8z."," If no stable equilibrium exists, matter will reach the light cylinder radius on a free-fall timescale, and proceed inwards if the ram pressure overcomes the magnetic pressure of the dipole field, $P_{mag}=B^2/8\pi$ ."
 have shown that stable matter configurations can be present even if the inner boundary ofthe flow. Is. ds outside £2).," have shown that stable matter configurations can be present even if the inner boundary of the flow, $R_{in}$ , is outside $R_l$ ."
" This occurs when Z4,<Loi=(αν. with (0)z La function of the magnetic tilt angle Hao=(0j/23)BtRTLSS."," This occurs when $R_{in}<R_{crit}=F(\alpha) R_A$, with $F(\alpha)\geq 1$ a function of the magnetic tilt angle $R_A=(1/2)B^{4/7}R_{NS}^{12/7}/(8GM_{NS}\dot M^2)^{1/7}$."
 For < ην the pulsar is still activeSCAM and the star is spun down by magneto-dipole torque.," For $R_l<R_{in}<R_{crit}$ , the pulsar is still active and the star is spun down by magneto-dipole torque."
" Under these conditions provide an expression for /?;,, in terms of a and //4.", Under these conditions provide an expression for $R_{in}$ in terms of $\alpha$ and $R_A$.
" When Ri,<Ky. instead. the flow is truncated at the Alfvénn radius. where Pay.=1,44. the pulsar is turned off and only propeller torques act."," When $R_{in}<R_l$, instead, the flow is truncated at the Alfvénn radius, where $P_{dyn}=P_{mag}$, the pulsar is turned off and only propeller torques act."
 The propeller physies is very complicated and no unanimous consensus exists about the form of the torque., The propeller physics is very complicated and no unanimous consensus exists about the form of the torque.
 However. since spin-down is expected to be very efficient in the propeller phase. its duration is quite short.," However, since spin-down is expected to be very efficient in the propeller phase, its duration is quite short."
" The period rapidly increases and the corotation radius. /?,,,=GAINαπ”j|BPP moves quickly outwards until it matches the Alfvénn radius. at which point accretion begins and the period freezes at the equilibrium value."," The period rapidly increases and the corotation radius, $R_{co}=[GM_{NS}/(4\pi^2)]^{1/3}P^{2/3}$, moves quickly outwards until it matches the Alfvénn radius, at which point accretion begins and the period freezes at the equilibrium value."
 While the latter depends on the propeller/accretion mechanisms. and several options have been discussed (see Sec. 1}).," While the latter depends on the propeller/accretion mechanisms, and several options have been discussed (see Sec. \ref{intro}) ),"
 the duration of the ejector phase does not., the duration of the ejector phase does not.
" For this reason we consider here only the “maximally efficient torque""2002).. as an illustrative example: where Oy is the keplerian angular velocity."," For this reason we consider here only the “maximally efficient torque”, as an illustrative example: where $\Omega_K$ is the keplerian angular velocity."
" Finally. to. follow the period evolution in the accretor stage. ἐκRoo. we assume the settling accretion regime recently proposed by Here4—2:2ION(Bisu)PVP aC75.1107AY(BeResu)PHop (both in egs units): the constant Av, and the index » were fixed to 40 and 2. respectively."," Finally, to follow the period evolution in the accretor stage, $R_{in}< R_{co}$, we assume the settling accretion regime recently proposed by Here $A\sim 2.2\times 10^{32}K_1(B_{12}R_{NS\,
6})^{1/11}V_{300}^{-4}P_{orb\, 300}^{-1}$, $C\sim 5.4\times
10^{31} K_1(B_{12}R_{NS\, 6})^{13/11}P_{1000}^{-1}$ (both in cgs units); the constant $K_1$ and the index $n$ were fixed to 40 and 2, respectively."
" The accretion torque can produce either spin-up or spin-down and it is interesting to note that in the spin-down phase /? increases exponentially. with a typical timescale =1002.77MALSMy, "," The accretion torque can produce either spin-up or spin-down and it is interesting to note that in the spin-down phase $P$ increases exponentially, with a typical timescale $\approx 100B_{12}^{-13/11}\dot M_{16}^{-3/11}\, {\rm yr}$."
We solved numerically the equation for the period evolution in the three stages (Eqs. [5]]- [6]]- [7] ," We solved numerically the equation for the period evolution in the three stages (Eqs. \ref{ejtorque}] ], \ref{maxtorque}] ], \ref{shaktorque}] ])"
"starting from fy=0.01vr with an initial period /1,=0.01 s."," starting from $t_0=0.01\, {\rm yr}$ with an initial period $P_0=0.01 \, {\rm s}$ ."
" The accretion rate was fixed to the value derived from current observations. AJ=61017gs. together with Po,= 300d. V=300kms . zo=10vr and By,=8.1077 G."," The accretion rate was fixed to the value derived from current observations, $\dot M =6\times
10^{15}\, {\rm g/s}$, together with $\po=300\, {\rm d}$ , $V=300\,
{\rm km\,s}^{-1}$ , $\tau_O=10^6\, {\rm yr}$ and $B_{fin}=8\times
10^{12}\, {\rm G}$ ."
 Several cases were then computed varying the magnetic dipole angle o. the Hall timescale 74 and especially the initial field By.," Several cases were then computed varying the magnetic dipole angle $\alpha$, the Hall timescale $\tau_H$ and especially the initial field $B_0$."
 Figure |. illustrates the results fora =107. ry=10vr and By—4107. 108. 7.1077.4. 1077. 1077C.," Figure \ref{perplot}
 illustrates the results for $\alpha=10^\circ$, $\tau_H=10^3\, {\rm
yr}$ and $B_0=4\times 10^{14}$, $10^{14}$, $7\times 10^{13}$, $4\times 10^{13}$, $10^{13}\, {\rm G}$."
 A common feature to all evolutionary tracks is a very rapid propeller stage which is followed by an even more rapid spin-down phase as the NS enters the accretion regime., A common feature to all evolutionary tracks is a very rapid propeller stage which is followed by an even more rapid spin-down phase as the NS enters the accretion regime.
 The period then saturates at its equilibrium value., The period then saturates at its equilibrium value.
" The decrease in /? seen at later times for the larger fields is due to the dependence of /7., on £3 and to the fact that the Ποιά is still decaying (see. SSec. 2.19).", The decrease in $P$ seen at later times for the larger fields is due to the dependence of $P_{eq}$ on $B$ and to the fact that the field is still decaying (see Sec. \ref{spindowntorq}) ).
 The time variation of £2 is also responsible for the deviations of ?(/) from a power-law in the later ejector phase. which are. again. more prominent for large ο.," The time variation of $B$ is also responsible for the deviations of $P(t)$ from a power-law in the later ejector phase, which are, again, more prominent for large $B$."
 The main information Figure |. conveys is that a quite large initial field is required in order for tto enter the propeller phase (and quickly start accreting) in a time as short as a τον 107vr.," The main information Figure \ref{perplot} conveys is that a quite large initial field is required in order for to enter the propeller phase (and quickly start accreting) in a time as short as a few $\times 10^4 \, {\rm yr}$."
 For the case shown here it has to be Bo&10+!C for this to occur.," For the case shown here it has to be $B_0\ga 10^{14}\, {\rm G}$ for this to occur."
 This result is not very sensitive to the actual choice of à and 74., This result is not very sensitive to the actual choice of $\alpha$ and $\tau_H$.
" Both increasing @ and decreasing TH results in a somehow higher value of the minimum initial field. which is however in all cases in the range ~LOM —4010, "," Both increasing $\alpha$ and decreasing $\tau_H$ results in a somehow higher value of the minimum initial field, which is however in all cases in the range $\sim 10^{14}\,$ $\,4\times
10^{14}\, {\rm G}$."
The conclusion that hharbours an initially strongly magnetized NS seems therefore que robust., The conclusion that harbours an initially strongly magnetized NS seems therefore quite robust.
 We stress that our main goal is not to reproduce within the current model the observed value of /? at the present age., We stress that our main goal is not to reproduce within the current model the observed value of $P$ at the present age.
 Although. for completeness. we followed the spin evolution also in thepropellerand accretor stages. the treatment we employed is necessary approximated and contains some degrees of arbitrariness in the choice of the propeller/accretortorques.," Although, for completeness, we followed the spin evolution also in thepropellerand accretor stages, the treatment we employed is necessary approximated and contains some degrees of arbitrariness in the choice of the propeller/accretortorques."
 Our computed evolution past theejector phasehas mainly an illustrative purpose and has to be taken with caution., Our computed evolution past theejector phasehas mainly an illustrative purpose and has to be taken with caution.
 The quite short age implied by the association. of the newly discovered BeXB in the SMC wwith a SNR, The quite short age implied by the association of the newly discovered BeXB in the SMC with a SNR
"absorbers are completely opaque to the X-ray spectrum of USSco, and the lower limit represents the value above which only the constant additional emission remains.","absorbers are completely opaque to the X-ray spectrum of Sco, and the lower limit represents the value above which only the constant additional emission remains."
 This can be compared to predictions from the expected density of the accretion disk material and the path length through it., This can be compared to predictions from the expected density of the accretion disk material and the path length through it.
" The volume of flared disk rim is of the order of 1054 cm?, e.g., ?.."," The volume of a flared disk rim is of the order of $10^{34}$ $^3$ , e.g., \cite{drake10}."
" For a amass loss rate of ~107’ MM yr? and a build-up time of ~5 days, the accretion (e.g.,disk ?)),rim density is of order 3x1014 ccm?."," For a mass loss rate of $\sim 10^{-7}$ $_\odot$ $^{-1}$ (e.g., \citealt{hachisu_usco}) ), and a build-up time of $\sim 5$ days, the accretion disk rim density is of order $3\times10^{14}$ $^{-3}$."
" For a path length through the gas of ~0.1 Ro, the column density is of order 1034 ccm?."," For a path length through the gas of $\sim 0.1$ $_\odot$, the column density is of order $^{24}$ $^{-2}$."
" While this is higher than the number derived from the eclipse model, a fraction of all hydrogen can be ionized, requiring a higher column density for the same opacity, or the build-up time may be shorter."," While this is higher than the number derived from the eclipse model, a fraction of all hydrogen can be ionized, requiring a higher column density for the same opacity, or the build-up time may be shorter."
" Moreover, the disk may not have fully reformed at the time of observation, and during the reformation process, the density should be lower."," Moreover, the disk may not have fully reformed at the time of observation, and during the reformation process, the density should be lower."
 'The vertical dotted line in the bottom two panels of Fig., The vertical dotted line in the bottom two panels of Fig.
" 4 indicates phase 1.0, where the center of eclipse by the companion should be."," \ref{emap22} indicates phase 1.0, where the center of eclipse by the companion should be."
" A dip of the expected width is present, however, it is clearly shifted."," A dip of the expected width is present, however, it is clearly shifted."
" For better reproduction of the data, we had to include a phase shift parameter with a value of -0.026 in the model."," For better reproduction of the data, we had to include a phase shift parameter with a value of -0.026 in the model."
 Such an artificial shift could be avoided if a non spherical symmetry of the central X-ray source is allowed., Such an artificial shift could be avoided if a non spherical symmetry of the central X-ray source is allowed.
" For example, we tested a model with a crescent shaped source and were able to reproduce the second dip without a phase shift."," For example, we tested a model with a crescent shaped source and were able to reproduce the second dip without a phase shift."
" There is, however, no physical explanation for a crescent shaped central source."," There is, however, no physical explanation for a crescent shaped central source."
 'The same procedure was applied to the 27 OM grism exposures of day 22.9., The same procedure was applied to the 27 OM grism exposures of day 22.9.
 We constructed two separate UV light curves by integrating each grism spectrum over the two wavelength bands aandAA., We constructed two separate UV light curves by integrating each grism spectrum over the two wavelength bands and.
". Combined with the light curve from the non-dispersed photons, we have three light curves representing different spectral colors, all containing clear eclipses."," Combined with the light curve from the non-dispersed photons, we have three light curves representing different spectral colors, all containing clear eclipses."
" In Fig. 6,"," In Fig. \ref{emap_uv},"
" the results are illustrated, where the red circles represent the location and relative size of the companion during each of the 27 exposures and the shaded circles in the center represent the primary with the best-fit radii for each band, following the color scheme given in the top right legend."," the results are illustrated, where the red circles represent the location and relative size of the companion during each of the 27 exposures and the shaded circles in the center represent the primary with the best-fit radii for each band, following the color scheme given in the top right legend."
 The fit radii are given in the top left legend., The best-fit radii are given in the top left legend.
" The short-wavelength UV band yields the smallest radius, while the longest-wavelength optical band (zero order) yields the largest radius, close to the inner Lagrangian point."," The short-wavelength UV band yields the smallest radius, while the longest-wavelength optical band (zero order) yields the largest radius, close to the inner Lagrangian point."
" 'The significance of the light curve fit is illustrated in Fig. 7,,"," The significance of the light curve fit is illustrated in Fig. \ref{chi},"
 where a range of primary radii is plotted against changes in x? relative to the best fit for each wavelength band., where a range of primary radii is plotted against changes in $\chi^2$ relative to the best fit for each wavelength band.
" The boundaries around the 1-o uncertainties are marked by the vertical colored lines, based on an increase of x? by 1 (horizontal black line)."," The boundaries around the $\sigma$ uncertainties are marked by the vertical colored lines, based on an increase of $\chi^2$ by 1 (horizontal black line)."
 The best-fit light curve models are shown in comparison to the data (in normalized units) in the bottom panel of Fig. 6.., The best-fit light curve models are shown in comparison to the data (in normalized units) in the bottom panel of Fig. \ref{emap_uv}.
" While the models connected by lines, see bottom right legend) give no (pointsperfect reproduction of the data (shaded areas and gray line, see top leftlegend), the width of the"," While the models (points connected by lines, see bottom right legend) give no perfect reproduction of the data (shaded areas and gray line, see top leftlegend), the width of the"
This research has made use of data obtained through the HEASARC Ouline Service. provided by the NASA/CSEC. aud the Cween Bau Interferometer. a facility of the National Science. Foundation operated bv the NRAQO in support of NASA Teh Encrey Astroplysics Programs.,"This research has made use of data obtained through the HEASARC Online Service, provided by the NASA/GSFC, and the Green Bank Interferometer, a facility of the National Science Foundation operated by the NRAO in support of NASA High Energy Astrophysics Programs."
 The authors thank the anouvmous referee for the oxtcusive and insightful comments., The authors thank the anonymous referee for the extensive and insightful comments.
 MC aud SVV have been partially supported by the Iauwal Rekhi Scholarship for Career Development., MC and SVV have been partially supported by the Kanwal Rekhi Scholarship for Career Development.
 AIKJ is grateful to P. S. Goel. Director. ISAC and Is. Nasturirangan. Chairman. ISRO. for their constant eucouragement and support durus the course of this work.," AKJ is grateful to P. S. Goel, Director, ISAC and K. Kasturirangan, Chairman, ISRO, for their constant encouragement and support during the course of this work."
3oth the present sumple and the ssample of Paper I were confined to stars that happen to lic near the Sun at present.,Both the present sample and the sample of Paper I were confined to stars that happen to lie near the Sun at present.
 Since stars move on eccentric orbits. most stars in the sample are merely visiting the solar Vicinity from farther afield.," Since stars move on eccentric orbits, most stars in the sample are merely visiting the solar vicinity from farther afield."
 Fig., Fig.
 Al shows four possible orbits of stars near the Sun that all happen to pass through the (shaded) survey volume., \ref{draw} shows four possible orbits of stars near the Sun that all happen to pass through the (shaded) survey volume.
 The orbits are drawn in the frame of the aand have sullicientIy small racial excursions to approximate Lindblad. epicyeles., The orbits are drawn in the frame of the and have sufficiently small radial excursions to approximate Lindblad epicycles.
" ALL four orbits have the same ο (epievele size): those labelled 2 4. with guiding centres (plus svmbols) tving on the solar circle. have the same Jd,(=Li) as does the Sun. while orbits 1 3 have. respectively. greater and smaller. values ο, "," All four orbits have the same $J_R$ (epicycle size); those labelled 2 4, with guiding centres (plus symbols) lying on the solar circle, have the same $J_\phi \;(=L_z)$ as does the Sun, while orbits 1 3 have, respectively, greater and smaller values of $J_\phi$."
Orbits 2 4 are closed. ellipses. because their guiding centres move at the same angular rate as the lrame. but the guiding centres of the other two ellipses. which are marked at the point of the star's closest approach to the Sun. drift relative to theL8BR.," Orbits 2 4 are closed ellipses, because their guiding centres move at the same angular rate as the frame, but the guiding centres of the other two ellipses, which are marked at the point of the star's closest approach to the Sun, drift relative to the."
. For clarity. the orbits shown do not loop around the Sun so that the vectors. which show peculiar velocities relative to theLAR. appear to correlate with the direction of the star from the solar position.," For clarity, the orbits shown do not loop around the Sun so that the vectors, which show peculiar velocities relative to the, appear to correlate with the direction of the star from the solar position."
 In reality. stars anywhere in the survey region can have peculiar velocities in any direction.," In reality, stars anywhere in the survey region can have peculiar velocities in any direction."
" The value of «s, is the instantaneous Galactic azimuth of the guiding centre. which Sellwood(2010.PaperD). chose to be zero on the line connecting the Sun to the Galactic centre."," The value of $w_\phi$ is the instantaneous Galactic azimuth of the guiding centre, which \citet[][Paper I]{Sell10} chose to be zero on the line connecting the Sun to the Galactic centre."
" Thus e,z0 for stars ahead of the Sun.", Thus $w_\phi>0$ for stars ahead of the Sun.
 The wy variable is the phase of the star around its epievcle. which increases with time in the sense shown by the arrows.," The $w_R$ variable is the phase of the star around its epicycle, which increases with time in the sense shown by the arrows."
 Again, Again
-O.4truein,-0.4truein
input values for the sonic aud Alfvéónnie Mach umuber.,input values for the sonic and Alfvénnic Mach number.
 The sonic Mach nmubers are defined as My.=(v|/C.. where is v ds the local velocity. Cy is the sound speed. and the averaging is doue over the whole box.," The sonic Mach numbers are defined as ${\cal M}_s \equiv \langle |{\bf v}|/C_s \rangle$, where is ${\bf v}$ is the local velocity, $C_s$ is the sound speed, and the averaging is done over the whole box."
 Similarly. the Alfvéunic Mach umuber is May=Ovifey). where c= is the Alfvenuic velocity. B is maguetic ficld and pis|B density.," Similarly, the Alfvénnic Mach number is ${\cal M}_A\equiv \langle |{\bf v}|/v_A \rangle$, where $v_A = |{\bf B}|/\sqrt{\rho}$ is the Alfvénnic velocity, ${\bf B}$ is magnetic field and $\rho$ is density."
Vp We briefly outline the major poiuts of the mmuerical setup (for more details see Cho Lazarian (2003)., We briefly outline the major points of the numerical setup (for more details see Cho Lazarian (2003).
 The code is a secouc-order-accurate hvbrid esseutiallv uonoscillatorv (ENO) scheme (Cho Lazarian 2003) which solves the ideal MITID equations in a periodic box: with zero-diversence condition V:B.=0. aud an isothermal equation of state p=CZp. where p is the eas pressure.," The code is a second-order-accurate hybrid essentially nonoscillatory (ENO) scheme (Cho Lazarian 2003) which solves the ideal MHD equations in a periodic box: with zero-divergence condition $\nabla \cdot {\bf B} = 0$, and an isothermal equation of state $p = C_s^2 \rho$, where $p$ is the gas pressure."
 Ou the right-hand side. the source term £ is a random large-scale solenoidal drivingforce.," On the right-hand side, the source term $\bf{f}$ is a random large-scale solenoidal driving."
 The magnetic field consists of the uniformi background Ποια aud a fluctuating field: B—|b., The magnetic field consists of the uniform background field and a fluctuating field: ${\bf B}= {\bf B}_\mathrm{ext} + {\bf b}$.
 Initially b=0., Initially ${\bf b}=0$.
 We scale the simulations to physical units. adopting vpical paraiueters for wari ionized gas.," We scale the simulations to physical units, adopting typical parameters for warm ionized gas."
 We assunuea jxel size of 0.15 parsees and deusity of 0.1 cur7., We assume a pixel size of 0.15 parsecs and density of 0.1 $^{-3}$.
 The siuulatiouns are assumed to be fully ionized aud we do rot include the effects of partial ionization., The simulations are assumed to be fully ionized and we do not include the effects of partial ionization.
 To make the maps of [VP| we first calculate the LOS rotation measure at each pixel then we take the take he eradieut of this rotation measure map and convert it to via Equation 5.., To make the maps of $|\nabla \textbf{P}|$ we first calculate the LOS rotation measure at each pixel then we take the take the gradient of this rotation measure map and convert it to $|\nabla \textbf{P}|$ via Equation \ref{eq:1}.
 An equally valid wav is to calculate [VP]the rotation measure at cach pixel. then shine a polarized signal through the cube with our asstued backeround values of Q = 1 U = 0.," An equally valid way is to calculate the rotation measure at each pixel, then shine a polarized signal through the cube with our assumed background values of Q = 1, U = 0."
 Then one can calculate the emergent values of Q and U by applying the simulated rotation measure map and then calculate the resulting [WP]., Then one can calculate the emergent values of Q and U by applying the simulated rotation measure map and then calculate the resulting $|\nabla \textbf{P}|$.
 Both iiethods will produce ideutical maps of |VP|., Both methods will produce identical maps of $|\nabla \textbf{P}|$.
 Additional smoothing of the maps of Q and U uxiug a Gaussian kernel can also be performed to ninic the telescope beam., Additional smoothing of the maps of Q and U using a Gaussian kernel can also be performed to mimic the telescope beam.
 A fibuneut traced by or will form as a result of a localized |VP]change im [WRAL|either density or uaenetic field as a fiction of position ou the skv as xx Equation 1.., A filament traced by $|\nabla \textbf{P}|$ or $|\nabla RM|$ will form as a result of a localized change in either density or magnetic field as a function of position on the sky as per Equation \ref{RM}.
 There are many pliysical processes hat can result in sharp changes iu these quantities iu he ISAL includius eravitatioual collapse aud outflows.," There are many physical processes that can result in sharp changes in these quantities in the ISM, including gravitational collapse and outflows."
 However. high Revuolds fluids iu the ISAL are expected o be turbuleut (see Cho. Laziriu Vishuiac 2003. LEhuegreeun Scalo 20014. Lazarian ct al.," However, high Reynolds fluids in the ISM are expected to be turbulent (see Cho, Lazarian Vishniac 2003, Elmegreen Scalo 2004, Lazarian et al."
" 2009) and a uore ubiquitous process responsible for fiuctuations in n, or D is due to MIID turbuleuce. precisely because it expected everywhere in theISAD'.. although the type of urbuleut cuviroument can vary (6.8. the compressibility. naenctization. equation of state. etc.)."," 2009) and a more ubiquitous process responsible for fluctuations in $n_e$ or B is due to MHD turbulence, precisely because it expected everywhere in the, although the type of turbulent environment can vary (e.g. the compressibility, magnetization, equation of state, etc.)."
 Iu the ISAL fluctuations in density aud magnetic field will occur as a result of MIID turbulence. which will ve Visible in polarimetric maps.," In the ISM, fluctuations in density and magnetic field will occur as a result of MHD turbulence, which will be visible in polarimetric maps."
 In the case of talking eracieuts of a turbulent field. oue would expect to fud Blunueutarv structure created by shock frouts. Jumps aud discontinuities.," In the case of taking gradients of a turbulent field, one would expect to find filamentary structure created by shock fronts, jumps and discontinuities."
 Figure bo shows a cartoon illustrating hese three separate cases of a possible profile aud its respective derivative., Figure \ref{fig:jumps} shows a cartoon illustrating these three separate cases of a possible profile and its respective derivative.
 The cases are: Iu respect to case one. it is known that the turbuleut velocity field in a Noluogorov-type inertial range both iu lhivdro and MIID are not differentiable. but ouly Wollder continuous (Bernard et al.," The cases are: In respect to case one, it is known that the turbulent velocity field in a Kolmogorov-type inertial range both in hydro and MHD are not differentiable, but only Höllder continuous (Bernard et al."
 1998. Evink 2009).," 1998, Eyink 2009)."
 Another exanirple is that of anv fractal function that displays selfsinularity but is not differeutiable everywhere., Another example is that of any fractal function that displays self-similarity but is not differentiable everywhere.
 This profile will naturallv create discoutinuitics when oue takes its derivative., This profile will naturally create discontinuities when one takes its derivative.
 Therefore. case one cau be fouud in both subsonic and supersonic type turbulence.," Therefore, case one can be found in both subsonic and supersonic type turbulence."
 Case oue type filaments can be seen iu Figure 2 for N. D. aud P iu the right coluun.," Case one type filaments can be seen in Figure \ref{fig:RM1} for N, B, and $\textbf{P}$ in the right column."
 Case two creates a structure iu the eradieut by a shock juup or a larec fluctuation iu either ο or D. Here again. this type of cuhancemeit ii. [VP] could be foun n supersonic and subsonic ype turbulence aud is due either to large random spatiid iuereases or decreases die to turbuleut fluctuations aong the LOS or weak shocks.," Case two creates a structure in the gradient by a shock jump or a large fluctuation in either $n_e$ or B. Here again, this type of enhancement in $|\nabla \textbf{P}|$ could be found in supersonic and subsonic type turbulence and is due either to large random spatial increases or decreases due to turbulent fluctuations along the LOS or weak shocks."
 We expect weak shock turbuleuce to show a lager amplitude in, We expect weak shock turbulence to show a lager amplitude in
NGC 362. which has the same metallicity. but very different HB morphology: they represent one of the classical second parameter pairs.,"NGC 362, which has the same metallicity, but very different HB morphology: they represent one of the classical second parameter pairs."
 was one of the first to propose helium. CNO. or age differences as possible explanations for the seconc parameter problem.," was one of the first to propose helium, CNO, or age differences as possible explanations for the second parameter problem."
 made a comparative spectroscopic study of red giants m the second-parameter GC pair NGC 288 and NGC 362., made a comparative spectroscopic study of red giants in the second-parameter GC pair NGC 288 and NGC 362.
 The [Fe/H] they derived for NGC 288 is —1.39+0.01 dex., The [Fe/H] they derived for NGC 288 is $-1.39 \pm 0.01$ dex.
 These authors also remark on the Na-O and AI-O anti-correlations. which were found in both clusters.," These authors also remark on the Na-O and Al-O anti-correlations, which were found in both clusters."
 Fig., Fig.
 7 by shows even a hint of bimodality in the Na-O anti-correlation., 7 by shows even a hint of bimodality in the Na-O anti-correlation.
 A clear bimodality in the CH and CN index strength has been detected among red giants by and)., A clear bimodality in the CH and CN index strength has been detected among red giants by and.
. Our data are the ones by(2008).. of which we selected only unevolved stars. and we do not see any clear anti-correlation.," Our data are the ones by, of which we selected only unevolved stars, and we do not see any clear anti-correlation."
 There is no reason why unevolved stars in a GGC should have a uniform composition while the evolved ones show a bimodality. because no known mixing mechanism would be able to create à bimodality from à homogeneous population.," There is no reason why unevolved stars in a GGC should have a uniform composition while the evolved ones show a bimodality, because no known mixing mechanism would be able to create a bimodality from a homogeneous population."
 Therefore we must conclude that our data do not have a sufficient S/N to reveal a bimodality in these metal-poor MS stars., Therefore we must conclude that our data do not have a sufficient S/N to reveal a bimodality in these metal-poor MS stars.
 Spectral synthesis calculation will be able to quantify the sensitivity of our spectra to C and N abundances. while more higher quality data are most probably needed anyway to settle the question.," Spectral synthesis calculation will be able to quantify the sensitivity of our spectra to C and N abundances, while more higher quality data are most probably needed anyway to settle the question."
 We note here that as we will see in Sect. 6..," We note here that as we will see in Sect. \ref{sec-trends},"
 NGC 288 falls perfectly in line with other clusters in all correlations with cluster parameters., NGC 288 falls perfectly in line with other clusters in all correlations with cluster parameters.
 As mentioned before. NGC 288 and NGC 362 are one of the second-parameters pairs. with similar metallicity and different HB morphology.," As mentioned before, NGC 288 and NGC 362 are one of the second-parameters pairs, with similar metallicity and different HB morphology."
 proposed CNO. among others. as one of the second parameters.," proposed CNO, among others, as one of the second parameters."
 NGC 362 has a metallicity of -1.33+40.01 dex2000).. it is more concentrated than NGC 288 (Table 3)) and slightly closer to the Galactic centre.," NGC 362 has a metallicity of $\pm$ 0.01 dex, it is more concentrated than NGC 288 (Table \ref{int_params}) ) and slightly closer to the Galactic centre."
 The anomalies in the CH and CN band strengths among its giants were studied more than in NGC 2881984)., The anomalies in the CH and CN band strengths among its giants were studied more than in NGC 288.
.. extensively studied both NGC 288 and NGC 362. finding a clear anti-correlation among RGB and SGB stars in both clusters. and a clear bimodality among red giantsclusters.," extensively studied both NGC 288 and NGC 362, finding a clear anti-correlation among RGB and SGB stars in both clusters, and a clear bimodality among red giants."
 This suggests that anti-correlations or chemical anomalies cannot be the predominant source of the different HB morphology in these two clusters., This suggests that anti-correlations or chemical anomalies cannot be the predominant source of the different HB morphology in these two clusters.
 As for NGC 288. bimodalities and an anti-correlation were found in the CH and CN band strengths of RGB stars. while our data for the MS stars reveal none.," As for NGC 288, bimodalities and an anti-correlation were found in the CH and CN band strengths of RGB stars, while our data for the MS stars reveal none."
 We suspect that here also this is simply owing to the low S/N of the spectra (lower than for NGC 288). and it must be worsened by the smaller sample.," We suspect that here also this is simply owing to the low S/N of the spectra (lower than for NGC 288), and it must be worsened by the smaller sample."
 A study with higher quality spectra would be even more interesting than for NGC 288. because NGC 362 does not behave like the other GGC in the correlations with cluster parameters (Sect. 6))," A study with higher quality spectra would be even more interesting than for NGC 288, because NGC 362 does not behave like the other GGC in the correlations with cluster parameters (Sect. \ref{sec-trends}) )"
 and it is not clear whether NGC 362 ts à real outlier or 1f the present data are simply inconclusive., and it is not clear whether NGC 362 is a real outlier or if the present data are simply inconclusive.
These results all strongly suggest that minor mergers act as a trigger for AGN activity in dust lane earlv-tvpe galaxies.,These results all strongly suggest that minor mergers act as a trigger for AGN activity in dust lane early-type galaxies.
 These results indicate that the minor mergers are both gas rich and recent., These results indicate that the minor mergers are both gas rich and recent.
 The mergers act as a trigger for roth the starburst and AGN activity., The mergers act as a trigger for both the starburst and AGN activity.
" The dust lane. phase is associated with starburst) galaxies in which the ACN ias already been triggered. but has not vet shut olf star ormation Completely,"," The dust lane phase is associated with starburst galaxies in which the AGN has already been triggered, but has not yet shut off star formation completely."
 SSS thanks the Australian Research Council ancl New College. Oxford for research fellowships.," SSS thanks the Australian Research Council and New College, Oxford for research fellowships."
 YST is grateful to the French Ministry. of Foreign and. European Allairs for an lIgide-IEillel. scholarship. and Ecole Polytechnique.," YST is grateful to the French Ministry of Foreign and European Affairs for an Egide-Eiffel scholarship, and Ecole Polytechnique."
 SI acknowledges a Researeh Fellowship from the oval Commission for the Exhibition of 1851. an Imperial College Junior Research Fellowship anc a Senior Research Fellowship from Worcester College. Oxford.," SK acknowledges a Research Fellowship from the Royal Commission for the Exhibition of 1851, an Imperial College Junior Research Fellowship and a Senior Research Fellowship from Worcester College, Oxford."
 We are grateful to Martin. Bureau. Christophe Pichon ancl Acdrianne Slvz for illuminating cliscussions. the referee for useful comments. and. Sally Hales for assistance with FIRST and NVSS data.," We are grateful to Martin Bureau, Christophe Pichon and Adrianne Slyz for illuminating discussions, the referee for useful comments, and Sally Hales for assistance with FIRST and NVSS data."
 This work would not have been possible without the contributions of citizen scientists as part of the Galaxy. Zoo 2 project., This work would not have been possible without the contributions of citizen scientists as part of the Galaxy Zoo 2 project.
 Funding for the SDSS and SDSS-LE has been provided bv the Alfred PL Sloan Foundation. the Participating Institutions. the National Science. Foundation. the US Department of Energy. the National Acronautics and Space Administration. the Japanese Monbukagakusho. the Max Planck Society ancl the Llieher Education Funding Council for England.," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the US Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society and the Higher Education Funding Council for England."
 The SDSS web site is http://www.sdss.org., The SDSS web site is http://www.sdss.org.
 The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions., The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions.
 “Lhe Participating Institutions are the American— Museum of Natural History. Astrophysical Institute — Potsclam. University of Basel. University of Cambridge. Case Western Reserve University. University of Chicago. Drexel University. Fermilab. the Institute. for Advancecl Study. the Japan Participation Group. Johns Llopkins University. the Joint Institute for Nuclear Astrophysics. the ]xavli Institute for Particle Astrophysics and Cosmology. the Jxorean. Scientist Group. the Chinese Academy of Sciences (LAAMOST). Los Alamos National Laboratory. the Max-Planck-lnstitute for Astronomy (MPLX). the Max-Planck-Institute for Astrophysics (AIPA). New Mexico State University. Ohio State University. University of Pittsburgh. University of Portsmouth. Princeton University. the United States Naval Observatory and the University of Washington.," The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory and the University of Washington."
 The NVSS and FIRST surveys were carried out. using the National Racio Astronomy Observatory VLA., The NVSS and FIRST surveys were carried out using the National Radio Astronomy Observatory VLA.
 The National Radio Astronomy Observatory is a facility of the National Science. Foundation. operated under cooperative agreement by Associated Universities. Inc.," The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc."
 w. O4; dy citealtEvrard93.Smith03.Mantz07)). citealtNatarajanO2b)). 2007)) (Kneibetal.1996).," $w$ $\Omega_M$ $\sigma_8$ \\citealt{Evrard93,Smith03,Mantz07}) \\citealt{Natarajan02b}) \\citeauthor{Moran07}
 \citeyear{Moran07}) \\citealt{Poole08}) \citep{Pello91,Kneib93,Kneib95} \citep{Kneib96}."
. Smithetal. (2005. refsec:obs)) 10. clusters at zc0.2., \citeauthor{Smith05a} \citeyear{Smith05a} \\ref{sec:obs}) 10 clusters at $z{\simeq}0.2$.
" In this article we use Taylor&Babul""s (2004 — hereafter TBO4) semi-analytical models of structure formation to interpret SmO5's cluster substructure measurements. as a means of exploring lensing-based substructure measurements as a quantitative probe of cluster age and assembly history."," In this article we use \citeauthor{Taylor04}' 's \citeyear{Taylor04} – hereafter TB04) semi-analytical models of structure formation to interpret Sm05's cluster substructure measurements, as a means of exploring lensing-based substructure measurements as a quantitative probe of cluster age and assembly history."
 We summarize Sm05 and TBO4 in refsec:obs and respectively. and then synthesize observations and theory in refsec:results..," We summarize Sm05 and TB04 in \\ref{sec:obs} and \\ref{sec:theory}
 respectively, and then synthesize observations and theory in \\ref{sec:results}."
 We discuss caveats in refsee:discuss and summarize our conclusions and discuss future prospects in refsee:cone.., We discuss caveats in \\ref{sec:discuss} and summarize our conclusions and discuss future prospects in \\ref{sec:conc}. .
 We assume Hoz70kms|Mpe|. Oy=0.3. O420.7 and oy=0.9 throughout.," We assume $H_0{=}70{\rm km\,s^{-1}Mpc^{-1}}$, ${\Omega}_{\rm M}{=}0.3$, ${\Omega}_{\rm \Lambda}{=}0.7$ and $\sigma_8=0.9$ throughout."
 The lookback time from τξθίοςΞ0.2 Ιδ 299=2.44Gyr in this cosmology.," The lookback time from $z=0$ to $z=0.2$ is $t_{z=0.2}=2.44\,{\rm Gyr}$ in this cosmology."
 Sm05 investigated the projected mass and structure of ten X-ray luminous (Ly24«IOergs7!. 0.1—2.4 keV) cluster cores at 0.17xz<0.25 (Table 1). (HST)," Sm05 investigated the projected mass and structure of ten X-ray luminous $L_X\ge4\times10^{44}\,{\rm erg\,s^{-1}}$, $0.1-2.4\,{\rm
keV}$ ) cluster cores at $0.17\le z\le0.25$ (Table \ref{tab:sample}) )."
//WFPC2 imaging and ground-based spectroscopy. ofgravitational ares (Smithetal.2001.2002:Sand2005:Richardetal. 2007).. were used to characterize the strong and weak gravitational lensing signal of each cluster core.," /WFPC2 imaging and ground-based spectroscopy ofgravitational arcs \citep{Smith01a,Smith02b,Sand05,Richard07}, were used to characterize the strong and weak gravitational lensing signal of each cluster core."
 The lensing signals were then used to constrain a detailed parametrized model of the projected mass distribution in each cluster core following Kneib. (1993. — see also Kneibetal.1996 and Smith 2002)., The lensing signals were then used to constrain a detailed parametrized model of the projected mass distribution in each cluster core following \citeauthor{Kneib93Th} \citeyear{Kneib93Th} – see also \citealt{Kneib96} and \citealt{Smith02Th}) ).
 Each lens model includes mass components that account for both the underlying dark matter distribution in the cluster (cluster/group-scale mass components)and the cluster galaxies downto Ly , Each lens model includes mass components that account for both the underlying dark matter distribution in the cluster (cluster/group-scale mass components)and the cluster galaxies downto $L_K{\ge}0.1L^\star_K$ .
For clarity. we refer to the main central cluster dark matter 0.1L}.halo as the cluster-scale mass component. and all other massive substructures associated with infallen clusters and/or groups," For clarity, we refer to the main central cluster dark matter halo as the cluster-scale mass component, and all other massive substructures associated with infallen clusters and/or groups"
well-described by models of either flat or flared accretion disks (Nattaοἱal.2002:Pascuccietal.2003:Mohanty2004:Allers 2006).,"well-described by models of either flat or flared accretion disks \citep{ntc02,pah03,mjn04,akc06}."
. Additional evidence for the existence of substellar disks comes from spectroscopic accretion studies: A significant. [raction of voung brown dwarls shows spectroscopic signatures of ongoing accretion and mass outflow. tvpical for classical T Tauri stars (Fernández&Comerón2001:Javawardhana.Mohanty.Dasri2003:Muzerolleetal.Mohanty.Javawardhana.&Basri 2005).," Additional evidence for the existence of substellar disks comes from spectroscopic accretion studies: A significant fraction of young brown dwarfs shows spectroscopic signatures of ongoing accretion and mass outflow, typical for classical T Tauri stars \citep{fc01,jmb03,mhc03,mjb05}."
. The main conclusion so far is (hat accretion disks around brown dwarls are comparable (ο or at least not. vastly different. [rom stellar disks. in terms of their geometry. their accretion behaviour. and {heir lifetime (e.g.Javawardhana.Mohanty.&Basri2002:Barracloy.Scholz&Javawarcdhana 2006).," The main conclusion so far is that accretion disks around brown dwarfs are comparable to or at least not vastly different from stellar disks, in terms of their geometry, their accretion behaviour, and their lifetime \citep[e.g.][]{jmb02,bm03,sj06}."
. This finding alone is not sullicient (o distinguish between the competing formation models: The pure existence of circeum-sub-stellar disks does not rule out an ejection. because simulations show (hat a substantial fraction of material can survive the ejection process (Date.Bonnell.&Bromm2002).," This finding alone is not sufficient to distinguish between the competing formation models: The pure existence of circum-sub-stellar disks does not rule out an ejection, because simulations show that a substantial fraction of material can survive the ejection process \citep{bbb02}."
. Unfortunately. quantitative testable predictions for the amount of dust and gas remaining after a (vpical encounter in a multiple svstem. which leads to the ejection of the lower mass body. are rare in the literature.," Unfortunately, quantitative testable predictions for the amount of dust and gas remaining after a typical encounter in a multiple system, which leads to the ejection of the lower mass body, are rare in the literature."
 Heller(1995). estimates the average mass loss through an encounter to be less than ~50% of the initial disk nass. where most of the lost material may be captured by (he perturber.," \citet{h95} estimates the average mass loss through an encounter to be less than $\sim 50$ of the initial disk mass, where most of the lost material may be captured by the perturber."
 Is has also been predicted that brown dwarls with disk radii larger than AAU are rare (~5%.Dromumn2002. 2003).," Is has also been predicted that brown dwarfs with disk radii larger than AU are rare \citep[$\sim 5$\%,][]{bbb02,bbb03}."
. Generally. it is believed (hat in a statistical sense an ejection process will significantly reduce the disk mass and the disk radius of the ejected body 2001).. and thus leads to àuncated disks.," Generally, it is believed that in a statistical sense an ejection process will significantly reduce the disk mass and the disk radius of the ejected body \citep{rc01}, and thus leads to truncated disks."
 This provides motivation lor studies of disk properties for brown cwarls., This provides motivation for studies of disk properties for brown dwarfs.
 A further reason (o explore disk masses in the substellar regime is the unsettled issue of a possible trend of disk mass. absolute or relative. with object mass.," A further reason to explore disk masses in the substellar regime is the unsettled issue of a possible trend of disk mass, absolute or relative, with object mass."
 Intuitively. one expects lower-mass stars (ο have lower absolute disk masses. resulting in a constant disk massto object mass ratio. and indeed this has been found by some authors (seethereviewbyNatta.Alannines 2000).," Intuitively, one expects lower-mass stars to have lower absolute disk masses, resulting in a constant disk massto object mass ratio, and indeed this has been found by some authors \citep[see the review by][]{ngm00}."
". Other exoups claim to find constant absolute disk masses and. as a consequence, hieher relative disk masses for lower mass stars (e.g.Nuernberger.Chini.Zinnecker1997;Mannines&Sargent 2000)."," Other groups claim to find constant absolute disk masses and, as a consequence, higher relative disk masses for lower mass stars \citep[e.g.][]{ncz97,ms00}."
. The main problem. which might prevent the detection of a clear trend. is the large scatter of 2-3 orders of magnitude in the measured disk masses at any given stellar mass.," The main problem, which might prevent the detection of a clear trend, is the large scatter of 2-3 orders of magnitude in the measured disk masses at any given stellar mass."
 Extending the mass range to substellar objects might help to determine whether (here is a correlation of disk with object mass or not., Extending the mass range to substellar objects might help to determine whether there is a correlation of disk with object mass or not.
 The best wav to determine disk masses and outer radii is to analvse SEDs with coverage from near-infrared to the submillimeter or millimeter regime., The best way to determine disk masses and outer radii is to analyse SEDs with coverage from near-infrared to the submillimeter or millimeter regime.
 Infrared SEDs alone are not sensilive to constrain these parameters (seeAllersοἱal. 2006).., Infrared SEDs alone are not sensitive to constrain these parameters \citep[see][]{akc06}. .
 Moreover. the submm/mm," Moreover, the submm/mm"
accretion luminosity should be up to 10 times higher owing to he gas being much denser and cooler.,accretion luminosity should be up to $10^3$ times higher owing to the gas being much denser and cooler.
 If these galaxies do contain mini haloes then they are further extreme examples of the general oroblem founc for the supermassive black holes in early-type galaxies (Fabi:in Canizares 1988: Pellegrini 2005)., If these galaxies do contain mini haloes then they are further extreme examples of the general problem found for the supermassive black holes in early-type galaxies (Fabian Canizares 1988; Pellegrini 2005).
 On simple grounds they s10uld all be much more luminous than observed if he black hole accretes in a radiatively-efticient manner., On simple grounds they should all be much more luminous than observed if the black hole accretes in a radiatively-efficient manner.
 None are as faint as our own Galactic Centre. Ser A*. but there is the fuel at qand for them o be much brighter.," None are as faint as our own Galactic Centre, Sgr A*, but there is the fuel at hand for them to be much brighter."
 The solution may lie in ADAFs (Narayan Yi 1995) or other radiatively ine‘ficient flows or with outflows so that little matter reaches the centre (Blandford Begelman 1999)., The solution may lie in ADAFs (Narayan Yi 1995) or other radiatively inefficient flows or with outflows so that little matter reaches the centre (Blandford Begelman 1999).
 The luminosity of the sources may also aet back on the accreting gas COstriker et al., The luminosity of the sources may also act back on the accreting gas (Ostriker et al.
 1976: Di Matteo et al 2003)., 1976; Di Matteo et al 2003).
 Alternatively the matter may üccrete to the centre and power relativistic jets (e.g. Allen et al 2006). which can be very radiatively inefficient.," Alternatively the matter may accrete to the centre and power relativistic jets (e.g. Allen et al 2006), which can be very radiatively inefficient."
 We do no however see any disturbance in the surrounding hot gas. nor radio emission. which would be expected to accompany such powerful jets.," We do not however see any disturbance in the surrounding hot gas, nor radio emission, which would be expected to accompany such powerful jets."
 Our results do not distinguish which solution is he more correct. but underscore the widespread nature of the problem.," Our results do not distinguish which solution is the more correct, but underscore the widespread nature of the problem."
inclined less than the critic:U angle of 60° with respect to the radial direction.,inclined less than the critical angle of $^\circ$ with respect to the radial direction.
 The space near the inner region of the dise is a dead zone’. where the magnetic field line is too steep. the flow not being able to overcome a barrier of gravitational potential.," The space near the inner region of the disc is a 'dead zone', where the magnetic field line is too steep, the flow not being able to overcome a barrier of gravitational potential."
 We investigate the dynamical properties of the bead on the magnetic fields threading the rotating dise around a Kerr black hole., We investigate the dynamical properties of the bead on the magnetic fields threading the rotating disc around a Kerr black hole.
 We have the same critical angle 60° for the non-rotating black hole ¢@=0) as Newtonian case., We have the same critical angle $^\circ$ for the non-rotating black hole $a=0$ ) as Newtonian case.
 Even if in the region very close to a Schwarzschild black hole. the flow could not be centrifugally flung out if the field lines inclined greater than the critical angle 60° with respect to the radial direction.," Even if in the region very close to a Schwarzschild black hole, the flow could not be centrifugally flung out if the field lines inclined greater than the critical angle $^\circ$ with respect to the radial direction."
 Abramowicz(l990) point out that the centrifugal force reverses sign at kr.=3A., Abramowicz(1990) point out that the centrifugal force reverses sign at $r=3M$.
 For the free particle in circular motion. the minimum radius is 4A/ (unstable).," For the free particle in circular motion, the minimum radius is $4M$ (unstable)."
" The results obtained here could not be extended to the region r=3,U.", The results obtained here could not be extended to the region $r=3M$.
 (πο1905) study the same problem by using a pseudo-Newtonian potential to simulate general relativistic effects., Cao(1995) study the same problem by using a pseudo-Newtonian potential to simulate general relativistic effects.
 They find that the critical angle becomes larger in the region close to a non-rotating black hole., They find that the critical angle becomes larger in the region close to a non-rotating black hole.
" The reason is that the angular velocity derived from the pseudo-Newtonian potential simulates ""n T. not des>."," The reason is that the angular velocity derived from the pseudo-Newtonian potential simulates ${{d\phi}\over {d\tau}}$ , not ${{d\phi}\over {dt}}$."
" In general relativisticnH frame. 77""n and 77""n have differentCD values."," In general relativistic frame, ${{d\phi}
\over {d\tau}}$ and ${{d\phi}\over {dt}}$ have different values."
 The beads move along a rigidm magnetic. field. line. have a constant angular velocity —di measured by a distant observer., The beads move along a rigid magnetic field line have a constant angular velocity ${{d\phi}\over {dt}}$ measured by a distant observer.
 The results areshown in Fig., The results areshown in Fig.
 | for the rotating black holes., 1 for the rotating black holes.
" The critical angle 06,,;; increases with the reduction of the radius of the magnetic field line footpoint.", The critical angle $\theta_{crit}$ increases with the reduction of the radius of the magnetic field line footpoint.
" For the beads at the minimum stable radius of an extreme Kerr black hole. the critical angle @...;, could be as large as 907. whieh may imdy that the flows could be centrifugally accelerated to high velocities even by the magnetic field lines with low inclination angles very close to the black hole."," For the beads at the minimum stable radius of an extreme Kerr black hole, the critical angle $\theta_{crit}$ could be as large as $90^\circ$, which may imply that the flows could be centrifugally accelerated to high velocities even by the magnetic field lines with low inclination angles very close to the black hole."
" We note that the critical angle falls rapidly in the cases of relative slowly rotating black hole. for example. 6,,;;~10 at ye inner edge of the dise for @=0.9."," We note that the critical angle falls rapidly in the cases of relative slowly rotating black hole, for example, $\theta_{crit} \sim 70^{\circ}$ at the inner edge of the disc for $a=0.9$."
 The results obtained here strongly imply that the rotating black hole will be helpful on the centrifugay acceleration of flows very close to the black hole., The results obtained here strongly imply that the rotating black hole will be helpful on the centrifugally acceleration of flows very close to the black hole.
 The “dead zone’ for accelerating over the the inner region of the dise will disappear for the rapidly rotating black hole with an appropriate dise magnetic field configuration., The 'dead zone' for accelerating over the the inner region of the disc will disappear for the rapidly rotating black hole with an appropriate disc magnetic field configuration.
 The further investigation on this problem using the fu relativistic MHD approach is necessary., The further investigation on this problem using the full relativistic MHD approach is necessary.
 We also study the case that the matter in the dise is in the retrograde orbit around the black hole. though it is not sure whether such disce exists in reality.," We also study the case that the matter in the disc is in the retrograde orbit around the black hole, though it is not sure whether such disc exists in reality."
 The results show that the critical angle is slightly influenced by the rotating black hole. the critical angle is always less than. but very close to 60.," The results show that the critical angle is slightly influenced by the rotating black hole, the critical angle is always less than, but very close to $^\circ$."
 The critical angle at the minimum stable radius for the extreme Kerr black hole is about57. almost same as the non-rotating case.," The critical angle at the minimum stable radius for the extreme Kerr black hole is about$^\circ$ , almost same as the non-rotating case."
the cE?5 scaling. in1 the logarithmic potential.,the $r^{-1/2}$ scaling in the logarithmic potential.
 One might worry that this would change the results of the previous section by forcing the cooling flow to have its sonic poit outside of ry., One might worry that this would change the results of the previous section by forcing the cooling flow to have its sonic point outside of $\rt$.
 Our calculations show. however. that this docs not happen.," Our calculations show, however, that this does not happen."
 Figure 3 shows tje temperature. density. Mach unuber and ratio of cooling time to inflow time for three models of AIST with 4=0.6. and Fieure | shows the correspouding predicted N-vav surface brightness profiles.," Figure 3 shows the temperature, density, Mach number and ratio of cooling time to inflow time for three models of M87 with $q = 0.6$, and Figure 4 shows the corresponding predicted X-ray surface brightness profiles."
 The models in Fieures 3 and { assunie three different forms for the potential of the host eailaxy: oue purely logarithiic (solid line: the same niodel is also shown by a solid line in Figs., The models in Figures 3 and 4 assume three different forms for the potential of the host galaxy: one purely logarithmic (solid line; the same model is also shown by a solid line in Figs.
" 1 2) and two with Hattenimg mass profiles: 3zz0.25 inside ,7OF kpe (dotted line) or ej2:3 χωρο (dashed-dot As illustrated by Figures 3 and LE the quantitative details of the flow structure depeud (uot surprisingly) ou the form of the potential on kilo-parsec scales."," 1 2) and two with flattening mass profiles; $\beta \approx
0.25$ inside $r_b \approx 0.7$ kpc (dotted line) or $r_b \approx 3$ kpc (dashed-dot As illustrated by Figures 3 and 4, the quantitative details of the flow structure depend (not surprisingly) on the form of the potential on kilo-parsec scales."
" The most iuportant result of this subsection. however. is that even when the mass profile flattens. the cooling flow still has its sonic poiut well inside r4, and therefore still makes a smooth transition to a nearly adiabatic accretion flow."," The most important result of this subsection, however, is that even when the mass profile flattens, the cooling flow still has its sonic point well inside $\rt$ and therefore still makes a smooth transition to a nearly adiabatic accretion flow."
 The qualitative picture outlined iu the previous section 1s therefore unchanged., The qualitative picture outlined in the previous section is therefore unchanged.
 This is partially because the interred Mach uuuber in MST at a few kilo-parsec is sufficicuthy: sanall (220.01: see Fie., This is partially because the inferred Mach number in M87 at a few kilo-parsec is sufficiently small $\approx 0.04$; see Fig.
 1ο) that even if the Mach umber lnereascs linearly at small radii the black hole still becomes iuportaut before the cooling flow has its sonic poiut., 1c) that even if the Mach number increases linearly at small radii the black hole still becomes important before the cooling flow has its sonic point.
" Iu addition. because the teniperature of the gas decreases somewhat if the galaxv's poteutial flatteus. the black hole becomes miportaut for the dynamics of the gas at larger radii (the transition radius. rg. is effectively X0,7 when €, 0)."," In addition, because the temperature of the gas decreases somewhat if the galaxy's potential flattens, the black hole becomes important for the dynamics of the gas at larger radii (the transition radius, $\rt$ , is effectively $\propto c_s^{-2}$ when $c_s
< \sigma$ )."
" Note. for exauuple. that ρωμε Is actually larger at smaller radii iu the model with rj,=3 kpe."," Note, for example, that $t_{\rm cool}/t_{\rm inf}$ is actually larger at smaller radii in the model with $r_b = 3$ kpc."
 This is because the decreasing temperature due to the flat mass profile implies that the flow undergoes its transition frou a cooling flow to an accretion flow at a larger radius., This is because the decreasing temperature due to the flat mass profile implies that the flow undergoes its transition from a cooling flow to an accretion flow at a larger radius.
 The theoretical picture which emerges from the above analysis is a very intuitive one: cooling flows in elliptical ealaxies remain subsonic down to roughly kilo-pxusec scales at which point they are gravitationally “captured” by the central supermassive black hole., The theoretical picture which emerges from the above analysis is a very intuitive one: cooling flows in elliptical galaxies remain subsonic down to roughly kilo-parsec scales at which point they are gravitationally “captured” by the central supermassive black hole.
 They then uudergo a transition to a nearly adiabatie Bondi flow ancl accrete outo the black hole., They then undergo a transition to a nearly adiabatic Bondi flow and accrete onto the black hole.
" There is cousequeutlv a direct and simple dvuanical transition frou, a cooling flow to an accretion flow.", There is consequently a direct and simple dynamical transition from a cooling flow to an accretion flow.
" Our calculations indicate that only if the cooling flow accretion rate onu scales of a few kilo-parsecs ix 210100AL.v twill the cooling flow have its sonic transition fore. being captured by the black hole A depends ou the black hole mass assumed(the2preciseLO?AL, and the galaxy potential. Le. 3. σι and rg: less massive dack holes. larger σ. aud flatter galaxy mass profiles arecr ry, and snialler require snmiadler AY)."," Our calculations indicate that only if the cooling flow accretion rate on scales of a few kilo-parsecs is $\gsim \ 10-100 \ \mpy$ will the cooling flow have its sonic transition before being captured by the black hole (the precise $\dot M$ depends on the black hole mass – assumed $\gsim 10^9 M_\odot$ – and the galaxy potential, i.e., $\beta$, $\sigma$, and $r_b$; less massive black holes, larger $\sigma$, and flatter galaxy mass profiles – larger $r_b$ and smaller $\beta$ – require smaller $\dot M$ )."
 Iu this case. he eas cools rapidly just inside its sonic poiut. which lies outside the region where the gravitational influence of the lack hole is inportaut.," In this case, the gas cools rapidly just inside its sonic point, which lies outside the region where the gravitational influence of the black hole is important."
 Although Ρα”. is readily achieved ou ~100 kpc scales. mass drop out due to thermal iustability. and the cousequeut decrease of Af with decreasingOo radius. πράος that observed coolineC» flows typically lic iu the parameter reedne where a smooth transition from a cooling flow to a nearly adiabatic accretion flow is the viable trausouic solution.," Although $\dot M \gsim 10-100 \ \mpy$ is readily achieved on $\sim
100$ kpc scales, mass drop out due to thermal instability, and the consequent decrease of $\dot M$ with decreasing radius, implies that observed cooling flows typically lie in the parameter regime where a smooth transition from a cooling flow to a nearly adiabatic accretion flow is the viable transonic solution."
 We find that this conchision is valid even given uucerainties in the nass profile of the host ealaxy ou kilo-parsec scales (83.1)., We find that this conclusion is valid even given uncertainties in the mass profile of the host galaxy on kilo-parsec scales 3.1).
 It is interesting to note that all of t16 solutions shown in Figures 1-5 have ες&rg: that is. the sonic poiut lies well inside the radius where the poteitial changes. from that of the galaxy to that of the black hole.," It is interesting to note that all of the solutions shown in Figures 1-5 have $r_s \ll \rt$; that is, the sonic point lies well inside the radius where the potential changes from that of the galaxy to that of the black hole."
 Nonetheless. the dynamics of the accreting gas changes from that of a cooling flow to that of a Bondi flow at. or even outsicle of. ru.," Nonetheless, the dynamics of the accreting gas changes from that of a cooling flow to that of a Bondi flow at, or even outside of, $\rt$."
 The requirement that the flow undergo a smooth sonic transition influences its structure out to rac ZrgDry," The requirement that the flow undergo a smooth sonic transition influences its structure out to radii $\gsim
\rt \gg r_s$."
 The primary assumption of our analysis is that there is negligible augular momentum in the inflowing material., The primary assumption of our analysis is that there is negligible angular momentum in the inflowing material.
 Aneular momentum mav. however. become iuaportant ou the small scales of interest here: if so. a transition to a Bondi flow will not be viable.," Angular momentum may, however, become important on the small scales of interest here; if so, a transition to a Bondi flow will not be viable."
 Iu this case. we believe that the cooling flow will eenerally undergo a trausition to an advection-doiminated: accretion flow (ADAF). the hot accretion flow analogue of Bondis solution for flows with angular momentum (Naravan Yi 1991. 1995: Abramowiez et al.," In this case, we believe that the cooling flow will generally undergo a transition to an advection-dominated accretion flow (ADAF), the hot accretion flow analogue of Bondi's solution for flows with angular momentum (Narayan Yi 1994, 1995; Abramowicz et al."
 1995)., 1995).
 Tt is well known that ADAFs can only exist below a critical accretion rate. AL.," It is well known that ADAFs can only exist below a critical accretion rate, $\dot M_c$."
 Tu the present context. this can be estimated by requiring the cooling time at rg to be greater than the inflow time. which vields ALI. L0alpha LOPE umet ," In the present context, this can be estimated by requiring the cooling time at $\rt$ to be greater than the inflow time, which yields M_c 10 ^2 (M 10^9 ) 300 )."
Iu equation (£3). à is the ratio of the inflow velocity to the local I&epleriau speed. aud is roughly the Shakura Suuvaev (1973) viscosity parameter.," In equation \ref{mdc}) ), $\alpha$ is the ratio of the inflow velocity to the local Keplerian speed, and is roughly the Shakura Sunyaev (1973) viscosity parameter."
 The properties of the transition from a cooling flow to a Dondi flow described iu 833 are determined primarily bv the low radiative efficiency of the Bondi solution., The properties of the transition from a cooling flow to a Bondi flow described in 3 are determined primarily by the low radiative efficiency of the Bondi solution.
 Consequently. the qualitative picture outlined. im this paper should apply equally well to the transition from a cooling flow to an ADAF. since the latter is also radiatively incfficieut (the quantitative details may. of course. change).," Consequently, the qualitative picture outlined in this paper should apply equally well to the transition from a cooling flow to an ADAF, since the latter is also radiatively inefficient (the quantitative details may, of course, change)."
 If. however. the accretion rate supplied by the cooling tow to ry Is zmAL.. the cooling flow may not be able to evolve into an ADAF: it will instead likely collapse to a thin disk.," If, however, the accretion rate supplied by the cooling flow to $\rt$ is $\gsim \dot M_c$, the cooling flow may not be able to evolve into an ADAF; it will instead likely collapse to a thin disk."
 We plan to explore this question in a subsequent paper., We plan to explore this question in a subsequent paper.
 To conclude. we discuss the observational prospects for observing the transition from a cooling flow to an accretion How with the excellent (51 arcsec) aneular resolution of heCNO.," To conclude, we discuss the observational prospects for observing the transition from a cooling flow to an accretion flow with the excellent $\lsim 1$ arcsec) angular resolution of the."
. We focus our discussion on AIST in the Vireo cluster. as it is the closest large cooling flow.," We focus our discussion on M87 in the Virgo cluster, as it is the closest large cooling flow."
 For a distance ο ALS? of &18 Mpc. one aresee is z0.1 kpe.," For a distance to M87 of $\approx 18$ Mpc, one arcsec is $\approx 0.1$ kpc."
 The basic inference from Figures 1 23 is that ou scales of 0.1 spc. he dyvuiuuices of accreting eas in ΔΙΟΥ ds far from that of a cooling flow.," The basic inference from Figures 1 3 is that on scales of $0.1$ kpc, the dynamics of accreting gas in M87 is far from that of a cooling flow."
 The ratio of the cooling time to the inflow nue is likelyz10 or larger., The ratio of the cooling time to the inflow time is likely$\approx 10$ or larger.
 One prediction of our model is that the inferred gas cluperature iu. ALS? should inerease with decreasing radius ou sufficiently small scales (when the black holes, One prediction of our model is that the inferred gas temperature in M87 should increase with decreasing radius on sufficiently small scales (when the black hole's
available and with a recent weak lensing analysis of the cluster based on UST/ACS data (Jee ct al.,available and with a recent weak lensing analysis of the cluster based on HST/ACS data (Jee et al.
 2001). and we diseuss the ανασα. state of the cluster.," 2004), and we discuss the dynamical state of the cluster."
 Crouud-based anulti-band photometry is also used το stucly the distribution of cluster galaxies iu colourauasnitude and colour-colour space., Ground-based multi-band photometry is also used to study the distribution of cluster galaxies in colour-magnitude and colour-colour space.
 Iu forthcoming papers. we will conibine the spectroscopic information presented here with UST/ACS data in a detailed study of the ealaxies iuJ0152.," In forthcoming papers, we will combine the spectroscopic information presented here with HST/ACS data in a detailed study of the galaxies in."
7-1357.. Wo used παας optical and ucar-IR nuaenie observations of tto select targets for spectroscopy., We used multi-band optical and near-IR imaging observations of to select targets for spectroscopy.
 Optical images in the B-. V-. R- aud Lbanuds were obtained with the Low Resolution Imaging Spectrometer (LRIS: Oke et al.," Optical images in the B-, V-, R- and I-bands were obtained with the Low Resolution Imaging Spectrometer (LRIS; Oke et al."
 1995) at the W. AL Keck Observatory., 1995) at the W. M. Keck Observatory.
 The LRIS images cover a region of 99 ς 61551 (see Fie. 1)), The LRIS images cover a region of 9 $\times$ 54 (see Fig. \ref{lrisonfors}) )
 with a pixel scale of (7221 !., with a pixel scale of 21 $^{-1}$.
" The seeiug. as measured by the FWIIM of poiuts sources. was OVS86 in V. 17119 in D. 1700 in R and 07773 in 1. Near-IR images in the J- and. I,-bauds were obtained with Sofl (Moorwood. Cuby Liduiui 1998) on the ESO NTT telescope at the Cerro La Silla Observatory."," The seeing, as measured by the FWHM of points sources, was 86 in V, 19 in B, 0 in R and 73 in I. Near-IR images in the J- and $\mathrm{K_s}$ -bands were obtained with SofI (Moorwood, Cuby Lidman 1998) on the ESO NTT telescope at the Cerro La Silla Observatory."
 The seeing was 07995 in J ai 0/991 in Ik., The seeing was 95 in J and 94 in $\mathrm{K_s}$.
 The Soff images cover a region of 1799 1/99. (μος Fig. 1)), The SofI images cover a region of 9 $\times$ 9 (see Fig. \ref{lrisonfors}) )
 with a pixel scale of 072209. 1, with a pixel scale of 29 $^{-1}$.
 The LRIS and Sofl images provided the basis for the photometric catalog used to select target for spectroscopy., The LRIS and SofI images provided the basis for the photometric catalog used to select target for spectroscopy.
 The catalog was created with SExtractor (Bertin Arnouts. 1996). vielding aperture photometry aud colours for 1191 sources in the LRIS field of view (Fig. 1)).," The catalog was created with SExtractor (Bertin Arnouts, 1996), yielding aperture photometry and colours for 1494 sources in the LRIS field of view (Fig. \ref{lrisonfors}) )."
 Additional V-. R-. aud I-baud tages ceutered on wwere obtained with the FORSL (FOcal Reducer aud low dispersion Spectrograph: Appenzeller Bupprecht 1992) at the ESO VLT aud cover a field of view of 0155 9 G/88 centered.," Additional V-, R-, and I-band images centered on were obtained with the FORS1 (FOcal Reducer and low dispersion Spectrograph; Appenzeller Rupprecht 1992) at the ESO VLT and cover a field of view of 8 $\times$ 8 centered."
 Veea magnitudes are used throughout this paper., Vega magnitudes are used throughout this paper.
 The spectroscopic observations of wiwere conducted im visitor and service modes (VM and SAD) from: December 1999 to December 2003. as summarized in Table l..," The spectroscopic observations of were conducted in visitor and service modes (VM and SM) from December 1999 to December 2003, as summarized in Table \ref{tab_survey}. ."
" Bavesian photometric redshifts (Beuittez 2000) were computed for each source using our DVRIJIS, catalog.", Bayesian photometric redshifts tez 2000) were computed for each source using our $_s$ catalog.
Candidates for spectroscopy were selected according to their R-baud magnitudes (BR. 21) and photometric redshifts (0.7τρως«X 0.95).,"Candidates for spectroscopy were selected according to their R-band magnitudes $\mathrm{R} < 24$ ) and photometric redshifts $ 0.7
< z_\mathrm{phot} < 0.95 $ )."
 This photometric redshift interval was chosen to match the dispersion i puo tapee OF the ~20 redshifts obtained from the first few masks. which were designed to target ealaxies in the cluster red sequence (CRS).," This photometric redshift interval was chosen to match the dispersion in $z_\mathrm{phot}-z_\mathrm{spec}$ of the $\sim 20$ redshifts obtained from the first few masks, which were designed to target galaxies in the cluster red sequence (CRS)."
 Because of the larger FOV of FORS1 compared to the LRIS aud Sofl fields of view (see Fie. 1)).," Because of the larger FOV of FORS1 compared to the LRIS and SofI fields of view (see Fig. \ref{lrisonfors}) ),"
 uo multibaud plotometric information was available for a nuuber of sources outside thedashed rectangle in Fig. 1.," no multi-band photometric information was available for a number of sources outside thedashed rectangle in Fig. \ref{lrisonfors},"
 and selections iu this region were carried out using only the FORS] nacen., and selections in this region were carried out using only the FORS1 imaging.
 Atl OS. spectral features such as the [OIT|CA3727) enission line. he Call IT aud I& absorption lines aud the 1000. bbreak. which are normally used to measure the redshitt of a galaxy. are between 6500 and 850A.," At $z \sim 0.8$, spectral features such as the $\lambda$ 3727) emission line, the $\mathrm{Ca II}$ H and K absorption lines and the 4000 break, which are normally used to measure the redshift of a galaxy, are between 6500 and 8500."
. An adequate coverage of this range is provided with he 300I eri ofFORS?., An adequate coverage of this range is provided with the 300I grism of.
. During poor seciug conditions. we used the 150I exin. which provides additional coverage below 5000.A.. to observe relatively bright field galaxies with a lower resolution.," During poor seeing conditions, we used the 150I grism, which provides additional coverage below 5000, to observe relatively bright field galaxies with a lower resolution."
 No order-separation filters were used iu order to obtain extended coverage in the blue part of the spectrum., No order-separation filters were used in order to obtain extended coverage in the blue part of the spectrum.
 A total of L1 masks for iuulti-object spectroscopy were prepared with FIMS. the FORS imask preparation tool.," A total of 11 masks for multi-object spectroscopy were prepared with FIMS, the FORS mask preparation tool."
 Seven masks were designed for use with the MOS (Multi Object Spectroscopy) mode and the other four masks were designed for use with the MXU (Mask Exchange Unit) mode., Seven masks were designed for use with the MOS (Multi Object Spectroscopy) mode and the other four masks were designed for use with the MXU (Mask Exchange Unit) mode.
 The MOS mode allows the positioning of up to 19 slits per ask. each of which is 22755 ong aud formed by ⋜↧↻⋜↧∐⋅∪↕≯⋯∪↖⇁⋜∏⋝↕↸∖↴⋝↕⋜⊔," The MOS mode allows the positioning of up to 19 slits per mask, each of which is 5 long and formed by a pair of movable blades."
∐∖↴∖↴∙↕∐↑∐↸∖⋀∖∟∖⊽↕↸⋯∪≼∐∖∙↸∖⋜↧↸⊳∐⋯⋜↧↴∖↴↨↘↽ ↸⊳∪∐↑⋜↧↕∐↴∖↴⋜↧↕⋜∐⋅∶↴∙⊾↸∖↥⋅∐↿∐∐⋝↸∖↥⋅∪↕⋡↴∖↴∐↑↴∖↴∙↖↖↽↕∐↸⊳↕⊔⊳⋜⋯↴⋝↸," In the MXU mode, each mask contains a larger number of slits, which can be chosen to vary in length."
∖↸⊳↕⋯↴∖↴↸∖∐∪ ↖⇁⋜∐⋅⋅↖↽↕∐↕↸∖∐∶↴⋁↑∐∙↕∐∪↥⋅≼∐∖↥⋅↑∪↥⋅↸∖↕⊔∪↖⇁↸∖↕⋟↥⋅↕∐∶↴⋁↸∖↴∖↴⋜↧↸⊳↸⊳↿∐⋅⋜↧↑↸∖↕⋅↖↽≺↴∖↴↸∖↸∖ below). we chose a ⊔↕∐↕∐∐∐⊔↴∖↴∐↑≓↕↸∖∐∶↴∙⊾↑∐∪↕≯∐∣⊔ allowing us to place up to  10 slits per mask.," In order to remove fringes accurately (see below), we chose a minimum slit-length of allowing us to place up to $\sim$ 40 slits per mask."
 MOS observatious were carried out with both FORSI aud FORS2 (see Table 1). while the MINT mace was ouly available with FORS2.," MOS observations were carried out with both FORS1 and FORS2 (see Table \ref{tab_survey}) ), while the MXU mode was only available with FORS2."
 Before Michi 2002. both FORSI and FORS2 were equipped with Tektronix CCD detectors with 2080 2015 pixels.," Before March 2002, both FORS1 and FORS2 were equipped with Tektronix CCD detectors with 2080 $\times$ 2048 pixels."
 During March 2002. FORS2 was uperaced with a mosaic of two 2k. « k MIT CCDs with a eap of bhetween them.," During March 2002, FORS2 was upgraded with a mosaic of two 2k $\times$ 4k MIT CCDs with a gap of between them."
 As a result the sensitivity in the rec increased by . allowing us to obtain about more redshifts per mask.," As a result the sensitivity in the red increased by , allowing us to obtain about more redshifts per mask."
" Our data were taken in the staudux resolution mode. which provides a field of view of G88 « οἱδδ, "," Our data were taken in the standard resolution mode, which provides a field of view of 8 $\times$ 8."
Slit widths of 1.0. 1.2. and 1.1 arcseconds were use iu MOS observations ou both FORSI aud FORS2. which resulted in spectral resolutions of ~ 13À..  16AL. iux 9 8À ivespectivelv for the 3001 eris. aud resolutions of ~27 A.. ~ 32 Anand ~ 38 irespectively for theL500 exi.," Slit widths of 1.0, 1.2, and 1.4 arcseconds were used in MOS observations on both FORS1 and FORS2, which resulted in spectral resolutions of $\sim$ 13, $\sim$ 16, and $\sim$ 18 respectively for the 300I grism, and resolutions of $\sim$27 , $\sim$ 32 , and $\sim$ 38 respectively for the150I grism."
 For AINU observations. all slits were wwide. which corresponds to resolutions of ~28 aand ~13 ," For MXU observations, all slits were wide, which corresponds to resolutions of $\sim 28$ and $\sim 13$ "
on the boundary. there will be a response in meridional circulation and dillerential rotation in (he interior that contains the same rv.,"on the boundary, there will be a response in meridional circulation and differential rotation in the interior that contains the same $n$."
 Since (he problem is linear. solutions wilh multiple n values can be constructed simply by. adding together solutions lor each individual ».," Since the problem is linear, solutions with multiple $n$ values can be constructed simply by adding together solutions for each individual $n$."
 The relative amplitudes of each of these solutions would be determined by the relative amplitudes ol the forcing for different 7., The relative amplitudes of each of these solutions would be determined by the relative amplitudes of the forcing for different $n$.
" If equations (27) and (28) were combined into a single equation for V,. il would be sixth order. vielding a total of six independent solutions."," If equations (27) and (28) were combined into a single equation for $\Psi_n$, it would be sixth order, yielding a total of six independent solutions."
 We would need to apply a total of six boundary conditions: (hese include four on the 2 axis. ancl (wo at the outer radial boundary.," We would need to apply a total of six boundary conditions; these include four on the $z$ axis, and two at the outer radial boundary."
"For anv added differenal rotation component Cj that satisfies (he equation d(s(dUy/ds))/ds=0 the boundary conditions are Uy)=0 and dU,/ds=ϐ al s=0. and Uy specified al s=Fi.","For any added differential rotation component $U_0$ that satisfies the equation $d(s(d U_0/ds))/ds=0$ the boundary conditions are $U_0=0$ and $dU_0/ds=0$ at $s=0$, and $U_0$ specified at $s=R$."
" €, is Che only climensionless parameter that is explicit in the equation svstem (21)-(29). but in [act there are others. implied or implicit in (his svstem. which may be useful in evaluating (he results."," $\epsilon_n$ is the only dimensionless parameter that is explicit in the equation system (27)-(29), but in fact there are others, implied or implicit in this system, which may be useful in evaluating the results."
 We define them here. and discuss their possible sienilicance.," We define them here, and discuss their possible significance."
 A traditional dimensionless number used to characterize the relative influence of Coriolis and viscous forces in a Πα dynamical problem is the so-called Tavlor mnmunber 40?ήν., A traditional dimensionless number used to characterize the relative influence of Coriolis and viscous forces in a fluid dynamical problem is the so-called Taylor number $Ta=4\Omega^2 H^4/\nu^2$ .
" By inspection. it is related to €, by the relationship e,=naTal?."," By inspection, it is related to $\epsilon_n$ by the relationship $\epsilon_n=n\pi {Ta}^{1/2}$."
 In a typical problem involving both rotation and viscosity. Ta needs to be 10* or higher to show substantial influence of rotation.," In a typical problem involving both rotation and viscosity, $Ta$ needs to be $10^3$ or higher to show substantial influence of rotation."
 If we take v~I0Pem?s.|. Ta=4x10* [or the whole depth of the solar convection zone. so we should expect a substantial influence of rotation on the solutions of most interest for (he Sun.," If we take $\nu\sim 10^{12}
{\rm cm}^2\,{\rm s}^{-1}$, $Ta=4 \times 10^6$ for the whole depth of the solar convection zone, so we should expect a substantial influence of rotation on the solutions of most interest for the Sun."
 Another number often used in such problems is the Ekiman number E—1/2Ta*7., Another number often used in such problems is the Ekman number $E=1/2Ta^{1/2}$.
 This munber would be small for the solar convection zone: il measures the thickness of the boundary lavers that would form if the top or bottom of the convection zone were considered to be nonslip., This number would be small for the solar convection zone; it measures the thickness of the boundary layers that would form if the top or bottom of the convection zone were considered to be 'nonslip'.
 But. more realisticlv. we (take these boundaries {ο be stress free. so no Ekman lavers ave allowed to form.," But, more realisticly, we take these boundaries to be stress free, so no Ekman layers are allowed to form."
 Because (he rotational velocity Ü is specified on the outer boundary of the cvlinder. we can also define a Rossby number Ro=U/20// and a Revnolds nunber Re=UlIlfv.," Because the rotational velocity $U$ is specified on the outer boundary of the cylinder, we can also define a Rossby number $Ro=U/2 \Omega H$ and a Reynolds number $Re=UH/\nu$."
 A plausible linear rotational velocity at the outer boundary would be GOms!. for which Ro=0.115.," A plausible linear rotational velocity at the outer boundary would be $60 {\rm m}\,{\rm s}^{-1}$, for which $Ro=0.115$."
 When Ro<<1 the flow tends to be geostrophic: that is. (here is a near balance in latitude (radius in (he cvlinder) between Coriolis aud pressure gradient. forces.," When $Ro<<1$ the flow tends to be geostrophic; that is, there is a near balance in latitude (radius in the cylinder) between Coriolis and pressure gradient forces."
 This balance should therefore be checked in the solutions we find., This balance should therefore be checked in the solutions we find.
 With the scaling we have used. the Reynolds number is the velocity itself.," With the scaling we have used, the Reynolds number is the velocity itself."
 We should expect different behavior of the solutions depending on whether Re>> lor Re<<1., We should expect different behavior of the solutions depending on whether $Re>>1$ or $Re<<1$.
 We will see thal we can get He>>| in our model only if we assume quite low turbulent viscosity v~10ens54," We will see that we can get $Re>>1$ in our model only if we assume quite low turbulent viscosity $\nu \sim 10^{10}
{\rm cm}^2\,{\rm s}^{-1}$."
 For most of (he parameter space of interest Re< 1. in many cases much less.," For most of the parameter space of interest $Re<1$ , in many cases much less."
 In general. the implication ol small He is that the flows are likelv to be smooth and laminar. i.e.. not turbulent.," In general, the implication of small $Re$ is that the flows are likely to be smooth and laminar, i.e., not turbulent."
 If the, If the
realized that (hev have general properties similar (to those of the /4. models 1984):: in particular. for values of v21. sullicientlv concentrated models along the sequence tend (to settle into a “stable” overall structure. except Lor (he development of a more and more compact nucleus. as the value of V increases. and are characterized by a projected density profile verv well fitted by the Jua] aw Characteristic of the surface brightness prolile of bright elliptical galaxies.,"realized that they have general properties similar to those of the $f_{\infty}$ models \citep{ber84}; in particular, for values of $\nu \approx 1$, sufficiently concentrated models along the sequence tend to settle into a “stable"" overall structure, except for the development of a more and more compact nucleus, as the value of $\Psi$ increases, and are characterized by a projected density profile very well fitted by the $R^{1/4}$ law characteristic of the surface brightness profile of bright elliptical galaxies."
 This property is illustrated in Fie., This property is illustrated in Fig.
2. Now. by inspection of Fig.," Now, by inspection of Fig."
 and by analogy with the study. of the isothermal sphere (Lyvnden-BellandWood 1963).. we can identify the location al Vx9 as the location for thecatastrophe.," and by analogy with the study of the isothermal sphere \citep{lyn68}, , we can identify the location at $\Psi \approx 9$ as the location for the."
 This sequence of models (hus has the surprising result (hat (he value of V that defines the onset of the eravothermal catastrophe is precisely that around which the models appear to become realistic representations of bright elliptical ealaxies., This sequence of models thus has the surprising result that the value of $\Psi$ that defines the onset of the gravothermal catastrophe is precisely that around which the models appear to become realistic representations of bright elliptical galaxies.
 We leave to other papers (see BerlinandStiavelli 1993)) the detailed discussion of (he issues that have to be addressed when comparison is made with the observations., We leave to other papers (see \citealt{ber93}) ) the detailed discussion of the issues that have to be addressed when comparison is made with the observations.
 We note that in this regime of high concentration the general properties of (he gravothermal cabastrophe are reasonably well recovered by the use of the that the temperature parameter conjugale to the total energv is à. a quantity directly. related. to the velocity dispersion in (he central regions.," We note that in this regime of high concentration the general properties of the gravothermal catastrophe are reasonably well recovered by the use of the that the temperature parameter conjugate to the total energy is $a$, a quantity directly related to the velocity dispersion in the central regions."
 Basically. (hiis was the made in (he discussion of the possible occurrence of the gravothermal catastrophe for the Ning models or for other sequences of models (e.g.. see Lyuden-BellandWood1968.. Ixatz 1980.. 1993)).," Basically, this was the made in the discussion of the possible occurrence of the gravothermal catastrophe for the King models or for other sequences of models (e.g., see \citealt{lyn68}, \citealt{kat80}, \citealt{mag98}) )."
 Here we have proved that the application of a rigorous derivation. which is available in our case. gives rise lo relatively modest «quantitative changes in the (ζω1/1) diagram for values of V close to and bevond the onset of the catastrophe (see Fig. 3).," Here we have proved that the application of a rigorous derivation, which is available in our case, gives rise to relatively modest quantitative changes in the $(E_{tot},1/T)$ diagram for values of $\Psi$ close to and beyond the onset of the catastrophe (see Fig. )."
 However. in sect.," However, in Sect."
 6 we will draw the attention to an interesting. qualitatively new phenomenon nissed in the previous derivations based on the use of the a-ansatz.," 6 we will draw the attention to an interesting, qualitatively new phenomenon missed in the previous derivations based on the use of the $a$."
" In passing. we note that in this regime ol relatively high concentrations. the /"" models possess one intrinsic property that makes them more appealing (han the widely studied. f, models."," In passing, we note that in this regime of relatively high concentrations, the $f^{(\nu)}$ models possess one intrinsic property that makes them more appealing than the widely studied $f_{\infty}$ models."
 ‘This is related to the way the models compare to the phase space properties of the products of collisionless collapse. as observed in N-bocly simulations (vanAlbada1932).," This is related to the way the models compare to the phase space properties of the products of collisionless collapse, as observed in N-body simulations \citep{van82}."
. In fact. one noted unsatisfactory property of the concentrated f/4 modelswas their excessive degree of isotropy. will respect to the models produced in (he llere we can," In fact, one noted unsatisfactory property of the concentrated $f_{\infty}$ modelswas their excessive degree of isotropy with respect to the models produced in the Here we can"
with a eood opportunity to detect and measure smaller subhalo masses in clusters.,with a good opportunity to detect and measure smaller subhalo masses in clusters.
 As the first step. we select Coma cluster for the target to measure sublialo masses by weak lensing analysis alone.," As the first step, we select Coma cluster for the target to measure subhalo masses by weak lensing analysis alone."
 The redshitt of Coma cluster is 0.0226 and is known as one of the most massive clusters near us., The redshift of Coma cluster is 0.0236 and is known as one of the most massive clusters near us.
 We analyze archival Subaru/Suprime-Cam data (Mivazaki et al., We analyze archival Subaru/Suprime-Cam data (Miyazaki et al.
 2002) to measure subhalo masses found in projected mass distributions as well as cluster virial mass. and caleulate the mass fraction of substructures.," 2002) to measure subhalo masses found in projected mass distributions as well as cluster virial mass, and calculate the mass fraction of substructures."
 We also investigate lensing from backeround larec-scale structure (LSS) ina quantitative way. using SDSS bauds aud photometric cata.," We also investigate lensing from background large-scale structure (LSS) in a quantitative way, using SDSS multi-bands and photometric data."
 The outline of this paper is as follows., The outline of this paper is as follows.
 We buüefiv describe the data analysis iu refsecidata and measure the threc-dinensional mass enuclosed withiu— a spherical region of a given radius usine a tangential shear profile iu rofsecuuass.., We briefly describe the data analysis in \\ref{sec:data} and measure the three-dimensional mass enclosed within a spherical region of a given radius using a tangential shear profile in \\ref{sec:mass}.
 &l represents projected distributions of nass and menboer ealaxies. quantifies false lensing peaks and estimate backeround lensing effects on the weak. chsing mass reconstruction.," \ref{sec:map} represents projected distributions of mass and member galaxies, quantifies false lensing peaks and estimate background lensing effects on the weak lensing mass reconstruction."
 In §5.. we measure the two-dimensional masses for subchuups with aud without LSS chsing correction.," In \ref{sec:submass}, we measure the two-dimensional masses for subclumps with and without LSS lensing correction."
 Iu 86.. we fit a tanecutial shear profile over an euseumble of subclump caucidates and obtain the vpical truncated radius and mass of ublialos.," In \ref{sec:stack}, we fit a tangential shear profile over an ensemble of subclump candidates and obtain the typical truncated radius and mass of subhalos."
 ds devoted to the discussion., \\ref{sec:dis} is devoted to the discussion.
" Throughout the eer we adopt cosmologv parameters 0,4,=0.27 and Q4=0.73.", Throughout the paper we adopt cosmology parameters $\Omega_{m0}=0.27$ and $\Omega_{\Lambda}=0.73$.
 At the redshift of Coma cluster 20.05. ipe., At the redshift of Coma cluster $1\farcm=20.0h^{-1}{\rm kpc}$ .
 We retrieved two Z7. image data (Yoshida et al., We retrieved two $R_{\rm c}$ image data (Yoshida et al.
 2008) from the Subaru archival data (S, 2008) from the Subaru archival data ).
MOKA?)). MEM of imaging data are the central region of rZ305M from cD ealaxy NGCLs?l and the outskirts region Fon30. 607., Pointings of imaging data are the central region of $r\simlt 30\farcm$ from cD galaxy NGC4874 and the outskirts region of $r\sim30-60\farcm$ .
 They cover the southwest part of this cluster., They cover the southwest part of this cluster.
 The data were reduced by the same imaging process of using standard pipeline reduction software for Suprinic-Cam. SDFRED (Yaeictal.2002:Ouchi2001).. as described. iu Okabe Uinetsn (2008).," The data were reduced by the same imaging process of using standard pipeline reduction software for Suprime-Cam, SDFRED \citep{yag02,ouc04}, as described in Okabe Umetsu (2008)."
 Astrometiy and the photometric calibration were couducted using the Sloan Digital Sky Survey (SDSS) data catalog., Astrometry and the photometric calibration were conducted using the Sloan Digital Sky Survey (SDSS) data catalog.
" The exposure times are 12 and 16 minutes for the central and outskirt regions. respectively,"," The exposure times are $42$ and $16$ minutes for the central and outskirt regions, respectively."
 Our weak lensing analvsis was done using the AT package providedby N. KaiserCxaiscr. Squires unmBroachurst 1995°)).," Our weak lensing analysis was done using the IMCAT package provided by N. Kaiser(Kaiser, Squires Broadhurst )."
 We use the same pipeline as et al. (, We use the same pipeline as Okabe et al. (
2009) with some mocifications followed by Erben et al. (,2009) with some modifications followed by Erben et al. (
2001) (also see Okabe Uinietsu 2008).,2001) (also see Okabe Umetsu 2008).
" Iu the pipeline.we first measure the nuage ellipticity. C4. trom the weighted moments of the surface brightuess of cach object cedenpoleand then correct the PSF anisotropy ase2e,—Puαλοκ, where {οι is the sinear polutaality tensor aud the asterisk denotes the stellar objects."," In the pipeline,we first measure the image ellipticity, $e_\alpha$, from the weighted quadrupole moments of the surface brightness of each object and then correct the PSF anisotropy as $e_\alpha'=e_\alpha-P_{\rm
sm}^{\alpha\beta}(P_{\rm sm}*)^{-1}_{\beta\gamma}e^\gamma*$, where $P_{\alpha\beta}$ is the smear polarizablity tensor and the asterisk denotes the stellar objects."
th We ft the stellar anisotropy kernel (μιN CY the second-order bi-polvnomials function in several subiiiages whose sizes are determined based on the typical cohereut scale of the measured PSF auisotropy pattern., We fit the stellar anisotropy kernel $(P_{\rm sm}*)^{-1}_{\alpha\beta}e^\beta*$ with the second-order bi-polynomials function in several subimages whose sizes are determined based on the typical coherent scale of the measured PSF anisotropy pattern.
" We finally obtain the reduced shear g,=r,/(lor)ο. using the pre-secing shear polarizablity tensor 2."," We finally obtain the reduced shear $g_\alpha=\gamma_{\alpha}
/(1-\kappa)=(P_g)_{\alpha\beta}^{-1}e_{\beta}'$ using the pre-seeing shear polarizablity tensor $P_g$."
" We adopt the scalar value άνωmTr|P,δν. following the technique described in Erben (2001)."," We adopt the scalar value $(P_g)_{\alpha\beta}={\rm Tr}[P_g]\delta_{\alpha\beta}/2$, following the technique described in Erben (2001)."
 Woran the pipeline for cach imaging data aud obtained the shear catalogue of source galaxies whose magnitude ranges are 3025 ADuiunag and halflieht-radius are d<_<10 pixel. where sy and σης) are thepy meanc(ry) aud lo error for stellar objects. respectively.," We ran the pipeline for each imaging data and obtained the shear catalogue of source galaxies whose magnitude ranges are $20-25$ ABmag and half-light-radius are $\bar{r}_{h}^*+\sigma (r_h^*) < r_h < 10$ pixel, where $\bar{r}_h^*$ and $\sigma (r_h^*)$ are the mean and $1\sigma$ error for stellar objects, respectively."
 ere the upper Hnüt of magnitude is doeteriunued bv the outskirt data of short exposure tine. although fait ealaxies in the range of 25.26AB mag are usable in the data of central region.," Here the upper limit of magnitude is determined by the outskirt data of short exposure time, although faint galaxies in the range of $25-26$ AB mag are usable in the data of central region."
 Since apparent sizes of uuleused ealaxies. mainly cluster members. are large in general. our source galaxy selection efficicutly excludes nieniber ealaxies which dilutes lensing streneths.," Since apparent sizes of unlensed galaxies, mainly cluster members, are large in general, our source galaxy selection efficiently excludes member galaxies which dilutes lensing strengths."
 The nuuber density of source galaxies is 223arcmin?, The number density of source galaxies is $\simeq23{\rm~arcmin}^{-2}$.
 We ieasure a tangential shear coupoucut. gj;=gyCOR247gosin2y aud the 145 degree rotated coniponeut. go=gqsineys|gocos2y. with respect to the cluster ceuter. where. Qo ds the position angle iu counter clockwise direction from the first coordinate.," We measure a tangential shear component, $g_+=-g_{1}\cos2\varphi-g_{2}\sin2\varphi$ and the $45$ degree rotated component, $g_\times=-g_{1}\sin2\varphi+g_{2}\cos2\varphi$, with respect to the cluster center, where $\varphi$ is the position angle in counter clockwise direction from the first coordinate."
" Then. the profiles of shear components qi=(g,.g.} are obtained from the weighted azimuthal average of the distortion compoucuts of source galaxies as ο)MuiduMtyi with a statistical weight «gal1(0.!y.;p o2) here subscripts “wand 3 denote the uth radial bin aud i-th source object."," Then, the profiles of shear components $g_\beta=(g_+, g_\times)$ are obtained from the weighted azimuthal average of the distortion components of source galaxies as $\langle{g_{\beta}}\rangle(\theta_n)=\sum_{i}u_{g,i}
g_{\beta,i}/\sum_i u_{g,i}$ with a statistical weight $u_{g,i}=1/(\sigma_{g,i}^2+\alpha^2)$ , where subscripts 'n' and 'i' denote the n-th radial bin and i-th source object."
" We adopt the softening constant a=0.1 which is a typical value of the mean YS 7, Over ποιος galaxies.", We adopt the softening constant $\alpha=0.4$ which is a typical value of the mean rms ${\bar \sigma}_g$ over source galaxies.
 There are two cD ealaxies (NGC 187E and NGC. 19550) in the central region of Coma cluster., There are two cD galaxies (NGC 4874 and NGC 4889) in the central region of Coma cluster.
 We adopt the ceuter of Coma cluster as NGC. [871 because a number of huninous galaxies are concentrated around NGC. [871 ii our optical miage. and the peak of N-rav surface brightness is close to NGC 1871 (see also Figure. 10)).," We adopt the center of Coma cluster as NGC 4874 because a number of luminous galaxies are concentrated around NGC 4874 in our optical image, and the peak of X-ray surface brightness is close to NGC 4874 (see also Figure \ref{fig:xmm}) )."
 The shear profile covers the range of Lo607 with 5 bius., The shear profile covers the range of $4\farcm-60\farcm$ with 5 bins.
 It corresponds to the first bin of Kubo et al. (, It corresponds to the first bin of Kubo et al. (
2007).,2007).
 We fit the shear profile with the universal profile proposed by Navarro. Frenk White (1996: hereafter NEW. profile) and a smeular isothermal sphere (SIS) halo model.," We fit the shear profile with the universal profile proposed by Navarro, Frenk White (1996; hereafter NFW profile) and a singular isothermal sphere (SIS) halo model."
 We asstuue that the redshift of source background.ealaxies Is estiniates(2)=d.," We assume that the redshift of source backgroundgalaxies is $\langle
z_s \rangle=1$."
" An uncertainty of source redshift im mass is negligiblebecause the lens distance ratio. Di,/Do at such a low redshift cluster weakly depeuds on source redshifts."," An uncertainty of source redshift in mass estimates is negligible because the lens distance ratio, $D_{ls}/D_s$, at such a low redshift cluster weakly depends on source redshifts."
 The NEW iass model is described by two parameters of the threc-dinieusional mass Mg(ra) and the halo concentration ον= ra/ry. Where rj is a scale radius aud ry is a radius at which the mean deusitv is A times the critical mass density. pi). at the cluster redshift.," The NFW mass model is described by two parameters of the three-dimensional mass $M_{\rm NFW}(<r_\Delta)$ and the halo concentration $c_{\rm \Delta}=r_{\Delta}/r_s$ where $r_s$ is a scale radius and $r_\Delta$ is a radius at which the mean density is $\Delta$ times the critical mass density, $\rho_{\rm cr}(z)$ , at the cluster redshift."
 The density profile of NEW. mass mocel is expressed in the form of The three-dimensional cluster mass for NEW mass model is obtained by with, The density profile of NFW mass model is expressed in the form of The three-dimensional cluster mass for NFW mass model is obtained by with
downward trend in abundance with increasing atomic number seen in some metal poor stars.,downward trend in abundance with increasing atomic number seen in some metal poor stars.
 More exploration of ir-process calculations is obviously needed. but the general trend Is encouraging.," More exploration of tr-process calculations is obviously needed, but the general trend is encouraging."
 In principle. a test of the (r-process model would be provided by a large set of data for metal poor stars that spans the masses of the nuclides produced in the r-process from mass ~80 to the heaviest observable nuclides that the r-process svuthesizes. usually thorium.," In principle, a test of the tr-process model would be provided by a large set of data for metal poor stars that spans the masses of the nuclides produced in the r-process from mass $\sim$ 80 to the heaviest observable nuclides that the r-process synthesizes, usually thorium."
 Unfortunately this is challenging due to the diffieiltv of observing the higher mass rare-earth nuclides. starting al mass 160.," Unfortunately this is challenging due to the difficulty of observing the higher mass rare-earth nuclides, starting at mass $\sim$ 160."
 Thus all r-process events (hat terminate at masses between 160 and lead would appear to terminate al mass 160. producing the effect. observed. by Roedereretal.(2010a).," Thus all r-process events that terminate at masses between 160 and lead would appear to terminate at mass 160, producing the effect observed by \citet{roederer10a}."
. Anv standard initial mass function (IMF) reflects the fact that less-massive stars are more numerous than more-massive stars., Any standard initial mass function (IMF) reflects the fact that less-massive stars are more numerous than more-massive stars.
 Assuming that stars from 8 to 40 solar masses mav produce comparable amounts of r-process material. we can use (he IME to estimate the fraction of stars whose r-process max be truncated by collapse to a black hole.," Assuming that stars from 8 to 40 solar masses may produce comparable amounts of r-process material, we can use the IMF to estimate the fraction of stars whose r-process may be truncated by collapse to a black hole."
 We adopt the Salpeter(1954) IMF. for which dN/dm x 77 for massive stars. where m is the stellar mass in units of the solar mass. ancl \ is (he number of stars of a given mass per unit volume.," We adopt the \citet{salpeter54} IMF, for which dN/dm $\propto$ $^{-2.35}$ for massive stars, where m is the stellar mass in units of the solar mass, and N is the number of stars of a given mass per unit volume."
 The ratio of the number of stars that would be expected to collapse to black holes (25-40 solar masses) to those expected to collapse to neutron stars (8-25 solar masses) is 0.13 in a well-saapled IMF., The ratio of the number of stars that would be expected to collapse to black holes (25-40 solar masses) to those expected to collapse to neutron stars (8-25 solar masses) is 0.13 in a well-sampled IMF.
 While a number of r-process rich stars (here taken to mean stars with [Eu/Fe| > 41.0) have been discovered ancl studied in detail in the last two decades. these stars constitute a relatively minor traction of all metal-poor stars.," While a number of r-process rich stars (here taken to mean stars with [Eu/Fe] $>$ +1.0) have been discovered and studied in detail in the last two decades, these stars constitute a relatively minor fraction of all metal-poor stars."
 More unbiased samples (MeWilliam1995:Darklemetal.2005) find that stars with |Eu/Fe] > +1.0 comprise «1054 of all stars with [Fe/H] < -2.0.," More unbiased samples \citep{mcwilliam95, barklem05} find that stars with [Eu/Fe] $>$ +1.0 comprise $<$ of all stars with [Fe/H] $<$ -2.0."
 Figure 11 of Roedereretal.(2010a) suggests that stars with [Eu/Fe| <Q are candidates for enrichment by a truncated r-process., Figure 11 of \citet{roederer10a} suggests that stars with [Eu/Fe] $<$ 0 are candidates for enrichment by a truncated r-process.
 Difficulües in detecting Eu in metal-poor stars with [Eu/Fe] < 0 make it even more challenging to estimate how numerous (hese stars are., Difficulties in detecting Eu in metal-poor stars with [Eu/Fe] $<$ 0 make it even more challenging to estimate how numerous these stars are.
 Da is more easily detected and may be used to represent Eu and other heavy elements in stars lacking s-process enrichment., Ba is more easily detected and may be used to represent Eu and other heavy elements in stars lacking s-process enrichment.
 From the Ba abundances in (the large survey of Darklemetal.(2005) we estimate a lower limit of ~55% of metal-poor stars as candidates for enrichment by a (runcated r-process., From the Ba abundances in the large survey of \citet{barklem05} we estimate a lower limit of $\sim$ of metal-poor stars as candidates for enrichment by a truncated r-process.
 This is significantly higher than the derived above assuming a Salpeter IAIF. vet Figure 2 demonstrates (hat a (r-process may be one wav to produce the heavy nuclides observed in some metal-poor stus.," This is significantly higher than the derived above assuming a Salpeter IMF, yet Figure \ref{ele_abun} demonstrates that a tr-process may be one way to produce the heavy nuclides observed in some metal-poor stars."
 The discrepancy in (hese fractions could indicate that additional nucleosvnthesis channels. such as those proposed by.," The discrepancy in these fractions could indicate that additional nucleosynthesis channels, such as those proposed by,"
Criterion 1 djs essential iu order to explore the role of iuteractious iu the generation of WT clouds.,Criterion 1 is essential in order to explore the role of interactions in the generation of HI clouds.
 We attempted to choose galaxv groups with different levels of galaxy interactions., We attempted to choose galaxy groups with different levels of galaxy interactions.
 Although in sole cases if is obvious that a galaxy interaction is taking place. it is not always a simple matter to determine whether a particular gegalaxy has undergoue a recent interaction (Couscliceetal.2008:Darectal. 2010a).," Although in some cases it is obvious that a galaxy interaction is taking place, it is not always a simple matter to determine whether a particular galaxy has undergone a recent interaction \citep{cons08,dar10}."
. Determine the relative streneth or inteusitv of iuteractious is even lore difficult., Determining the relative strength or intensity of interactions is even more difficult.
" Ποπονο, we have made a first attempt towards quautifvine galaxy interaction strength within ealaxy eroups by creatine “interaction oeidiees. which we have applied to our galaxy eroups in order to rauk them in order of iiteraction streneth (see Section 2.6))."," However, we have made a first attempt towards quantifying galaxy interaction strength within galaxy groups by creating “interaction indices"", which we have applied to our galaxy groups in order to rank them in order of interaction strength (see Section \ref{interactions}) )."
 Criteria 2 aud 3 are dificult to reconcile. so the two closest groups (ADSL aud NGC 2103) partially overlap with the Milkv Wav in velocity space.," Criteria 2 and 3 are difficult to reconcile, so the two closest groups (M81 and NGC 2403) partially overlap with the Milky Way in velocity space."
 The eroups discussed in this paper do not overlap iu velocity with the Milkv. Wav., The groups discussed in this paper do not overlap in velocity with the Milky Way.
 The galaxy eroups observed for this study are described below., The galaxy groups observed for this study are described below.
 Table 2 lists all galaxy groups within 7.5 Mpce (Fouqueetal.1992:Tully 1987).," Table \ref{tenmpc} lists all galaxy groups within 7.5 Mpc \citep{fou92,tul87}."
. Our observations cover of galaxy eroups within 7.5 Mpc., Our observations cover of galaxy groups within 7.5 Mpc.
 Figure 1 shows a diagram of the distribution of the observed eroups., Figure \ref{fig:groups} shows a diagram of the distribution of the observed groups.
 Hore we list the eroups., Here we list the groups.
 The M81 group is oue of the closest galaxy eroups to the Milky Wav at a distance of 3.5 Alpe., The M81 group is one of the closest galaxy groups to the Milky Way at a distance of 3.5 Mpc.
 It is comprised of 1 major galaxies (ADSI. M82. NGC 3077. NGC 2976) and over LO dwiirt galaxies.," It is comprised of 4 major galaxies (M81, M82, NGC 3077, NGC 2976) and over 40 dwarf galaxies."
 Although the galaxies are optically uudisturbed. III observatious reveal that the galaxies are undergoiue strong interactions.," Although the galaxies are optically undisturbed, HI observations reveal that the galaxies are undergoing strong interactions."
" Additionally, M82 is an extreme starburst ealaxy and mauy of the dwarf galaxies show morphological aud. kinematic nreenlarities."," Additionally, M82 is an extreme starburst galaxy and many of the dwarf galaxies show morphological and kinematic irregularities."
 Table 3 lists galaxy properties., Table \ref{m81tab} lists galaxy properties.
 The NGC 2103 eroup is located at approximately the same distance as the M81 eroup., The NGC 2403 group is located at approximately the same distance as the M81 group.
 The NGC 2103 oeroup coutains the bright spiral galaxy NGC 2103. 3 additional laree galaxies (NCC 2366. UCGC 1305. UC LI823). and at least Lt chart or low surface brightness satellite. galaxies.," The NGC 2403 group contains the bright spiral galaxy NGC 2403, 3 additional large galaxies (NGC 2366, UGC 4305, UGC 4483), and at least 4 dwarf or low surface brightness satellite galaxies."
 The NGC 2103 eroup does uot show clear sigus of interaction., The NGC 2403 group does not show clear signs of interaction.
 However. some of the group galaxies show subtle regularities which may be due to previous interactions between eroup galaxies.," However, some of the group galaxies show subtle irregularities which may be due to previous interactions between group galaxies."
 The larecst galaxy. NGC 2103. shows a thick. lageine II laver aud a few UT filaments with anomalous velocities that are similar to the MSI/MS82 clouds in mass (Fraternalietal.2002).," The largest galaxy, NGC 2403, shows a thick, lagging HI layer and a few HI filaments with anomalous velocities that are similar to the M81/M82 clouds in mass \citep{frat02}."
. These features may be analogues to Milkv Way TVCs. aud their origius are similarly unclear.," These features may be analogues to Milky Way HVCs, and their origins are similarly unclear."
 They have been attributed to a combination of outflow fromi a galactic fountain and accretion from the intergalactic iiedium (Fraternali&Binney2006): both of these phenomena iav be induced by interactions between eroup galaxies (Larson&Tinsley1978:Saucisietal. 2008).," They have been attributed to a combination of outflow from a galactic fountain and accretion from the intergalactic medium \citep{frat06}; both of these phenomena may be induced by interactions between group galaxies \citep{lar78,san08}."
. UCC 1305 las a colctary appearance in I (Bureau&Carignan 2002).. which may be caused by rain pressure frou the intragroup medium.," UGC 4305 has a cometary appearance in HI \citep{bureau02}, which may be caused by ram pressure from the intragroup medium."
 The dwarf galaxy DDO 53 is also kinciatically irregular in III (Beenetal. 2006)., The dwarf galaxy DDO 53 is also kinematically irregular in HI \citep{beg06}.
. The other galaxies in the group appear to be normal., The other galaxies in the group appear to be normal.
 Table { lists galaxy properties., Table \ref{n2403tab} lists galaxy properties.
 The Canes Venatici I (CV I) galaxy group is located approximately [ Mpe away and coutains ll galaxies distributed iu a diffuse cloud., The Canes Venatici I (CVn I) galaxy group is located approximately 4 Mpc away and contains 41 galaxies distributed in a diffuse cloud.
 The brightest ealaxy. M91. dis apparently isolated but is morphologically disturbed and has a ring (Mulder&vanDried 1993).," The brightest galaxy, M94, is apparently isolated but is morphologically disturbed and has a ring \citep{mul93}."
. Five of the galaxies show bursts of star formation (Naisin&IEarac, Five of the galaxies show bursts of star formation \citep{kk08}.
heutsev 2008).. Table 5. lists galaxy. properties., Table \ref{canes1tab} lists galaxy properties.
 The NGC 672 aud NGC 781 eroups form a G linear filament of ealaxies at a distance of approxinatelv 5 Mpec (Zitriu&Brosch2008)., The NGC 672 and NGC 784 groups form a $^{\circ}$ linear filament of galaxies at a distance of approximately 5 Mpc \citep{zit08}.
. The ealaxies iu both eroups show evideuce that a burst of star formation occurred approximately LO Myr ago., The galaxies in both groups show evidence that a burst of star formation occurred approximately 10 Myr ago.
 Zitrin&Brosch(2008) conclude that these coincident SE bursts are most likely not due to ealaxy interactions. since the SFR of the galaxies," \citet{zit08} conclude that these coincident SF bursts are most likely not due to galaxy interactions, since the SFR of the galaxies"
(ng—mx)gig Chat Granslates into a minimun equivalentwidth yin.,$(m_{\broadband}-m_{\narrowband})_{\mathrm{min}}$ that translates into a minimum equivalentwidth $_{\mathrm{min}}$.
 The dispersion in the maegnitude-color diagram is dominated by Cie uncertainties in ihe magnitudes in Che faint region ancl by the different. colors of the objects in the bright region., The dispersion in the magnitude-color diagram is dominated by the uncertainties in the magnitudes in the faint region and by the different colors of the objects in the bright region.
 Furthermore. the mean value of the color. (mg—mx]. depends on mx. because different (vpes of objects can dominate the color at dillerent πατον)ρα magnitude ranges.," Furthermore, the mean value of the color, $\mu[m_{\broadband}-m_{\narrowband}]$ , depends on $m_{\narrowband}$, because different types of objects can dominate the color at different narrow-band magnitude ranges."
 The method of selection has to account for the different sources of dispersion of the color., The method of selection has to account for the different sources of dispersion of the color.
" A solution is to compute the standard deviation of (he color dispersion ancl consider candidates. with a level of signification n,. the objects with color: The standard deviation of the color distribution. as a function of the namrow-band magnitude. can be caleulated [rom the distribution of objects."," A solution is to compute the standard deviation of the color dispersion and consider candidates, with a level of signification $n_{\sigma}$, the objects with color: The standard deviation of the color distribution, as a function of the narrow-band magnitude, can be calculated from the distribution of objects."
 In the following subsection. we infer an analvlic expression (hat can be useful when there are not enough points in the data to caleulate directly the dispersion.," In the following subsection, we infer an analytic expression that can be useful when there are not enough points in the data to calculate directly the dispersion."
 Let us assunie a population of objects with the same SED. given by f(A). so all the objects have the same color.," Let us assume a population of objects with the same SED, given by $f(\lambda)$, so all the objects have the same color."
" In general. the source (hi in analog to digital units (ADU) collected in a CCD detector from an object are proportional to the integrated [lux of the source through the pass band and the exposure time /: Equation 39. can be written in terms off£... Ay and A as follows! where Z,44peis the maximunm value of the transmittance."," In general, the source flux in analog to digital units (ADU) collected in a CCD detector from an object are proportional to the integrated flux of the source through the pass band and the exposure time $t$: Equation \ref{eq:counts1} can be written in terms of, $\lambda_0$ and $\Delta$ as : where $T_{\mathrm{peak}}$is the maximum value of the transmittance."
In an effort to learn more about the effects of cluster dynamics on the BSS population. we compared the cumulative radial distribution of the BSs to the populations of giant branch (V« Vpo) and main sequence stars.,"In an effort to learn more about the effects of cluster dynamics on the BSS population, we compared the cumulative radial distribution of the BSS to the populations of giant branch $V < V_{TO}$ ) and main sequence stars."
 In order to cover the widest range of radii possible. we combined our data with those of Cotéetal.(2002).," In order to cover the widest range of radii possible, we combined our data with those of \citet{cot02}."
. Field stars were eliminated. using proper motion (Siegelοἱal.2001) and radial velocity (Cotéetal.2002) information [ου the eiut stars. and CMD location for the main-sequence stars.," Field stars were eliminated using proper motion \citep{sie01} and radial velocity \citep{cot02} information for the giant stars, and CMD location for the main-sequence stars."
 After these cuts. there were SJ stars in the giant sample and 543 stus in the main sequence sample.," After these cuts, there were 83 stars in the giant sample and 543 stars in the main sequence sample."
 Tvpicallv the straggler population is compared to brighter populations (for example. horizontal branch stars). but because these stars are so rare in Palomar 13. we were forced to resort to fainter populations.," Typically the straggler population is compared to brighter populations (for example, horizontal branch stars), but because these stars are so rare in Palomar 13, we were forced to resort to fainter populations."
 IXolmogorov-5mnirnov (Ix-S) probability tests were used to test the hypothesis that the populations were drawn [from the same parent population., Kolmogorov-Smirnov (K-S) probability tests were used to test the hypothesis that the populations were drawn from the same parent population.
 The cumulative racial distributions are shown in Fig. 5.., The cumulative radial distributions are shown in Fig. \ref{fig9}.
 The results of the IX-S tests are given in Table 4.. including the absolute deviation D and the probability. P? that the (wo samples were drawn from the same cistribution.," The results of the K-S tests are given in Table \ref{tabks}, including the absolute deviation $D$ and the probability $P$ that the two samples were drawn from the same distribution."
 The central concentration of the blue stragelers relative to the cluster light has been noted before by Siegeletal.(2001)., The central concentration of the blue stragglers relative to the cluster light has been noted before by \citet{sie01}.
. Llowever. our results show Chat there are differences between all three samples. with the BSS clistvibution being the most centrally concentrated. and the MS sample being the least concentrated.," However, our results show that there are differences between all three samples, with the BSS distribution being the most centrally concentrated, and the MS sample being the least concentrated."
 The probability that any one of the populations was drawn from the same distribution as another is less than0., The probability that any one of the populations was drawn from the same distribution as another is less than.
"0656... Just four of the selected. BSS are found outside a radius of 42"" (~3r; according to (2002))).", Just four of the selected BSS are found outside a radius of $42\arcsec$ $\sim 3 r_c$ according to \citet{cot02}) ).
 Because the number of blue stragglers is relatively small. we now examine what effect the exclusion of subsets of stragglers has on the results of the Ix-S tests.," Because the number of blue stragglers is relatively small, we now examine what effect the exclusion of subsets of stragglers has on the results of the K-S tests."
 The elimination ol the six BSS candidates redder than the turnoll color (stars which have a considerably hieher probability of being detachecl binaries) has a minor effect on our conclusions: there is still a probability of less than that the BSS and giant samples come from the same distribution., The elimination of the six BSS candidates redder than the turnoff color (stars which have a considerably higher probability of being detached binaries) has a minor effect on our conclusions: there is still a probability of less than that the BSS and giant samples come from the same distribution.
 We have also looked at the distributions of the brightest 7 and faintest 19 of the stragglers and find that their radial distributions are indistinguishable., We have also looked at the distributions of the brightest 7 and faintest 19 of the stragglers and find that their radial distributions are indistinguishable.
" There is a chance (that the bright. BSS sample was drawn from (he same distribution as the giants. alihough this is primarily due to the small size of the sample and the single bright BSs (BSs 7 from SMCT) at 185"" [rom the cluster center."," There is a chance that the bright BSS sample was drawn from the same distribution as the giants, although this is primarily due to the small size of the sample and the single bright BSS (BSS 7 from SMCT) at $185\arcsec$ from the cluster center."
 The faint sample has just a chance of being drawn from the same distribution as the giants., The faint sample has just a chance of being drawn from the same distribution as the giants.
 The cumulative radial distributions should make it clear that there is a large increase in the relative frequency of blue stragelers going toward (he core of the cluster., The cumulative radial distributions should make it clear that there is a large increase in the relative frequency of blue stragglers going toward the core of the cluster.
 Recent studies ol much more massive globular clusters, Recent studies of much more massive globular clusters
use to validate our method.,use to validate our method.
 The method is based on the use of properties of the red clump giants., The method is based on the use of properties of the red clump giants.
 The RC color is used to derive the reddening map along the minor axis extending from -δ-<b«-0.5»., The RC color is used to derive the reddening map along the minor axis extending from $-8^\circ <b<-0.5^\circ $.
 These regions suffer from high extinction and variations on very small scales are observed., These regions suffer from high extinction and variations on very small scales are observed.
" Therefore a consistent bulge reddening map obtained from a homogenous tracer all across the bulge, from the innermost crowded and extinct regions to the outer parts is very valuable."," Therefore a consistent bulge reddening map obtained from a homogenous tracer all across the bulge, from the innermost crowded and extinct regions to the outer parts is very valuable."
" Our results for the extinction also show good agreement with maps published by ?,, and ?.."," Our results for the extinction also show good agreement with maps published by \citet{dutra03}, , and \citet{schultheis99}."
 We have used the de-reddened magnitudes to build the Ks band luminosity functions and to trace the RC along the minor axis., We have used the de-reddened magnitudes to build the Ks band luminosity functions and to trace the RC along the minor axis.
" When using the RC as a distance indicator, we find excellent agreement with previous findings of a double red clump for latitudes larger than b«—5? which trace the X shape of the Galactic bulge (??).."," When using the RC as a distance indicator, we find excellent agreement with previous findings of a double red clump for latitudes larger than $b<-5^\circ$ which trace the X shape of the Galactic bulge \citep[][]{mcwilliam10,nataf10}."
 We also detect the additional bump in the luminosity function interpreted as the RGBb by ?.., We also detect the additional bump in the luminosity function interpreted as the RGBb by \citet[][]{nataf11}.
 This study will be extended to the complete 300 deg? bulge region and will provide a consistent trace of the structure of the bulge including the inner regions., This study will be extended to the complete 300 $^2$ bulge region and will provide a consistent trace of the structure of the bulge including the inner regions.
" Finally, we used the RC distances and reddening map to build the color magnitude diagrams in the absolute plane and then to obtain individual photometric metallicities for RGB stars in the bulge through interpolation on the RGB ridge lines of cluster sample from ?.."," Finally, we used the RC distances and reddening map to build the color magnitude diagrams in the absolute plane and then to obtain individual photometric metallicities for RGB stars in the bulge through interpolation on the RGB ridge lines of cluster sample from \citet[][]{valenti04}."
 The final metallicity distributions were compared to those obtained in the spectroscopic studies of ? and? showing a remarkable agreement., The final metallicity distributions were compared to those obtained in the spectroscopic studies of \citet[][]{zoccali08} and \citet[][]{johnson11} showing a remarkable agreement.
 We demonstrated clearly the possibility to track the observed metallicity gradient along the minor axis., We demonstrated clearly the possibility to track the observed metallicity gradient along the minor axis.
" This provides, within the errors of the method, the opportunity to obtain clues for metallicity gradients along other regions of the bulge."," This provides, within the errors of the method, the opportunity to obtain clues for metallicity gradients along other regions of the bulge."
 Reddening and metallicity maps for the VVV coverage will be releasedelectronically in the survey website., Reddening and metallicity maps for the VVV coverage will be releasedelectronically in the survey website.
(hat re-lmages a given star approximately every [ον davs with varving intervals between observations.,that re-images a given star approximately every few days with varying intervals between observations.
 For each data stream. we generate 1000 observations at irregular intervals over 1800 simulated days. and then phase the observations for a range of periods from 3.0 to 3.1 davs and a range of transit lengths.," For each data stream, we generate 1000 observations at irregular intervals over 1800 simulated days, and then phase the observations for a range of periods from 3.0 to 3.1 days and a range of transit lengths."
 The number of the observations and the duration of (he simulated survey are arbitrarily chosen as plausible characteristics for the twpe of all-sky süurvev we envislon., The number of the observations and the duration of the simulated survey are arbitrarily chosen as plausible characteristics for the type of all-sky survey we envision.
 The duration of the transit depends on the orientation of the svstem with respect to our line of sight. and we analyze the data for eight equally spaced. progressively more inclined orientations.," The duration of the transit depends on the orientation of the system with respect to our line of sight, and we analyze the data for eight equally spaced, progressively more inclined orientations."
 For each orientation. we test for 16 equally spaced phases.," For each orientation, we test for 16 equally spaced phases."
 We test the resulting data sets for (ransil-like dips in the light curve. which we define simply as intervals during which (he local mean light curve dips significantly below the global average.," We test the resulting data sets for transit-like dips in the light curve, which we define simply as intervals during which the local mean light curve dips significantly below the global average."
 This (8x16) erid structure is chosen empirically: we find that the number of false positives increases linearly with grid density below this density and then flattens above it., This $(8\times 16)$ grid structure is chosen empirically: we find that the number of false positives increases linearly with grid density below this density and then flattens above it.
" The result shows that for this kind of svstem. in order to restrict follow-up analysis to the of the full sample most likely to vield a true transit detection. the value for \\2,;, should be set to ~ 36.6."," The result shows that for this kind of system, in order to restrict follow-up analysis to the of the full sample most likely to yield a true transit detection, the value for $\Delta \chi_{\rm min}^{2}$ should be set to $\sim$ 36.6."
 We take the highest value of Ay? from each of the 1000 sets. and of those highest values. we then sort the 1000 sets from highest value of NA? to lowest.," We take the highest value of $\Delta \chi^{2}$ from each of the 1000 sets, and of those highest values, we then sort the 1000 sets from highest value of $\Delta \chi^{2}$ to lowest."
 In Fig., In Fig.
 2 (inset). we plot the highest value of NA? for each of the 1000 data streams.," \ref{figChi} (inset), we plot the highest value of $\Delta \chi^{2}$ for each of the 1000 data streams."
 To check the robustness of this munber. we run additional simulations of 25 data sets. each with different observation schedules.," To check the robustness of this number, we run additional simulations of 25 data sets, each with different observation schedules."
 First. we generate a set of observations that are randomly distributed (hroughout a 1800 day. mission. with the requirement that no two observations be less (han 10 minutes apart.," First, we generate a set of observations that are randomly distributed throughout a 1800 day mission, with the requirement that no two observations be less than 10 minutes apart."
 Then we regenerate the data set with observations that are evenly spaced throughout the project., Then we regenerate the data set with observations that are evenly spaced throughout the project.
 We also conduct (he analysis on data sets with evenlv spaced pairs of observations. with the observations in each pair separated by 14.4 minutes: and then again with the pair-spacing al 43.2 minutes.," We also conduct the analysis on data sets with evenly spaced pairs of observations, with the observations in each pair separated by 14.4 minutes; and then again with the pair-spacing at 43.2 minutes."
 These different configurations test for different types of observing schedules., These different configurations test for different types of observing schedules.
 For instance. a ground-based. all-sky survey. would most likely observe a star at essentially random times throughout a project.," For instance, a ground-based all-sky survey would most likely observe a star at essentially random times throughout a project."
 On the other hand. a space-based mission with a slowly rotating telescope (similar to the IHipparcos satellite) would observe a star in pairs of observations separated by minutes.," On the other hand, a space-based mission with a slowly rotating telescope (similar to the Hipparcos satellite) would observe a star in pairs of observations separated by minutes."
 For various reasons there could be a certain regularity imposed on either (he space-based or groundbased observations., For various reasons there could be a certain regularity imposed on either the space-based or ground-based observations.
" We find that the value for A\2,,, does not depend strongly on the observing schedule.", We find that the value for $\Delta \chi_{\rm min}^{2}$ does not depend strongly on the observing schedule.
 We determine this by taking the highest value of A\? for each of the 25 independent data streams. sorting the highest values of A\? [rom each set in (he manner described above. and then plotting the results for each tvpe of observing schedule (Fig. 2)).," We determine this by taking the highest value of $\Delta \chi^{2}$ for each of the 25 independent data streams, sorting the highest values of $\Delta \chi^{2}$ from each set in the manner described above, and then plotting the results for each type of observing schedule (Fig. \ref{figChi}) )."
 We find that there is, We find that there is
redshift-distance relation can be used to derive au upper unit to the relativistic correctious applving to classical fractal analyses.,redshift-distance relation can be used to derive an upper limit to the relativistic corrections applying to classical fractal analyses.
 Then. we enlarged our study to a mmucrical simulation of a wide class of parabolic homogeneous models.," Then, we enlarged our study to a numerical simulation of a wide class of parabolic homogeneous models."
 To resolve every ambiguity which could arise from a mixing of classical and ecuecral relativistic notions of distances. surfaces; volunes and averaginegs. we calculated the error which could be mace by an observer. nuuersed ina FLRW universe. aud analysing. with Euclidean statistica tools. an intrinsic homogeneous poiutlike galaxy distribution. as measured on lis past elt conc.," To resolve every ambiguity which could arise from a mixing of classical and general relativistic notions of distances, surfaces, volumes and averagings, we calculated the error which could be made by an observer, immersed in a FLRW universe, and analysing, with Euclidean statistical tools, an intrinsic homogeneous pointlike galaxy distribution, as measured on his past light cone."
 We have shown that. iu these mocels aud up to distances far bevoud those xobed by the current analyses. the curvature effect is ucelieible compared to the measurement uncertainties.," We have shown that, in these models and up to distances far beyond those probed by the current analyses, the curvature effect is negligible compared to the measurement uncertainties."
" For [fy= 65 kan | ο, the three tested models exhibit. at the scale of 200 AIpc. a iscrepancy for the nunericallv calculated fractal dimension of on the order of1%.. aud a limit still holds for the Eimstein-de Sitter case at scales on the order of 150-600 Mpc."," For $H_0=$ 65 km $^{-1}$ $^{-1}$, the three tested models exhibit, at the scale of 200 Mpc, a discrepancy for the numerically calculated fractal dimension of on the order of, and a limit still holds for the Einstein-de Sitter case at scales on the order of 450-600 Mpc."
 Tn fact. coutrary to the authors claiu iu R95. the procedure averaging over many poiuts. far from mereasiug the curvature effect. has some smoothing results. and therefore this effect is weaker on the fractal dimension than on e.g. huuimositv distances.," In fact, contrary to the author's claim in R95, the procedure averaging over many points, far from increasing the curvature effect, has some smoothing results, and therefore this effect is weaker on the fractal dimension than on e.g. luminosity distances."
 We have actually proved this property for the class of universes πιο: study and have eiven grounds to suppose that it can apply to auv other cosmological model., We have actually proved this property for the class of universes under study and have given grounds to suppose that it can apply to any other cosmological model.
 Therfore. as regards the current aud forthceoinmi-is results which could be derived from Euclidean statistical analyses of galaxy data. the relativistic corrections could be consistently ignored. up to the abovementioned scales. aud probably far bevond. iu every wniverse for which the dependence of the huunositv distance on the redshift does not too widely depart from the IIubble law at the probed scales.," Therfore, as regards the current and forthcomimg results which could be derived from Euclidean statistical analyses of galaxy data, the relativistic corrections could be consistently ignored, up to the abovementioned scales, and probably far beyond, in every universe for which the dependence of the luminosity distance on the redshift does not too widely depart from the Hubble law at the probed scales."
 We want to inention. for completeness. that the curvature correction is nof the ouly bias that can mipair the results of such analyses.," We want to mention, for completeness, that the curvature correction is not the only bias that can impair the results of such analyses."
 Evolution effects aud. mainly. Ik-correctious are kuown to eeucrate other kinds of errors. but are bevond the scope of the present work.," Evolution effects and, mainly, K-corrections are known to generate other kinds of errors, but are beyond the scope of the present work."
 For a discussion of the impact of IE-correctious on such au issue. we refor the iuterested reader to Scarancella et al. (," For a discussion of the impact of K-corrections on such an issue, we refer the interested reader to Scaramella et al. ("
1998) aud Jovee et al. (,1998) and Joyce et al. (
1999).,1999).
 Part of this work was performed while one of us (B.T.) was on a sabbatical leave at the Observatoire de. Paris-Meudou., Part of this work was performed while one of us (R.T.) was on a sabbatical leave at the Observatoire de Paris-Meudon.
. He wishes to thauk Drandon Carter aud Nathalie Deruelle for their hospitality., He wishes to thank Brandon Carter and Nathalie Deruelle for their hospitality.
 The authors waut to thauk also the referee for accurate remarks which led them to add interesting developments to this work., The authors want to thank also the referee for accurate remarks which led them to add interesting developments to this work.
 We eive. in this appendix. the expressions for d; aud + retained for the conversion of the (GL.r.0.60) data iuto he €f.:.0.0) quadruplets. in the FLRW models choseu ο perform the ποσα) simulations described in Sect.5.," We give, in this appendix, the expressions for $d_l$ and $z$ retained for the conversion of the $(L,r,\theta, \phi)$ data into the $(f,z,\theta, \phi)$ quadruplets, in the FLRW models chosen to perform the numerical simulations described in Sect.5."
 We have limited these simulations to three examples of he spatially flat subclass: the Eiusteiu-de Sitter case. with Qa; and 94=0. currently the most popular nodel with 1;L3 and O4=0.7 and a low matter density case. with O3;=0.01 and O4=0.99.," We have limited these simulations to three examples of the spatially flat subclass: the Einstein-de Sitter case, with $\Omega_M=1$ and $\Omega_\Lambda=0$, currently the most popular model with $\Omega_M=0.3$ and $\Omega_\Lambda=0.7$ and a low matter density case, with $\Omega_M=0.01$ and $\Omega_\Lambda=0.99$."
" As 1f can ο easily seen from a comparison of the d; expansions in powers of ; calculated below. the low matter density case exhibits the lareer second order terii correction for ""realistic fla models with 0<Qa,I."," As it can be easily seen from a comparison of the $d_l$ expansions in powers of $z$ calculated below, the low matter density case exhibits the larger second order term correction for “realistic” flat models with $0<\Omega_M \leq 1$."
 It can thus been considered as a limiting case for the study presented lore., It can thus been considered as a limiting case for the study presented here.
 For the LEiusteiu-«de Sitter case. we use Ribeiro’s relations ina R95. corrected for consistency from a dimensional point of view: The power series expansion of d; thus reads For the parabolic homogeneous model with a non-zero cosmiolosical constaut. the following expressions can be found in text books (see e.g. Carroll. Press. Turner. 1992): It is casy to derive an exact expression for r from Eqs.(37)) aud (38)): For sinall z. we can Tavlor expand the rigbht-haud side of Eq.(39)) aud invert to obtain Substituting Eq.(10)) iuto Eq.(37)). we ect d; as a fiction of i:," For the Einstein-de Sitter case, we use Ribeiro's relations in R95, corrected for consistency from a dimensional point of view: The power series expansion of $d_l$ thus reads For the parabolic homogeneous model with a non-zero cosmological constant, the following expressions can be found in text books (see e.g. Carroll, Press, Turner, 1992): It is easy to derive an exact expression for $r$ from \ref{lumph}) ) and \ref{dlph})): For small $z$, we can Taylor expand the right-hand side of \ref{rph}) ) and invert to obtain Substituting \ref{zedph}) ) into \ref{lumph}) ), we get $d_l$ as a function of $r$ :"
"Using the definition of ¢ from and the second-order lens equation 13)), we can relate the lensing fields with the spin-1 distortion on the source plane In the same way we compute how 6 transforms: where detA is defined in15,, and In this derivation, we neglected all moments of higher than fourth order since they are practically immesurable.","Using the definition of $\zeta$ from and the second-order lens equation ), we can relate the lensing fields with the spin-1 distortion on the source plane In the same way we compute how $\delta$ transforms: where $\det A$ is defined in, and In this derivation, we neglected all moments of higher than fourth order since they are practically immesurable."
" The combination of these two equations leads to and without all the terms containg µ which come from the inclusion of the centroid shift, which is calculated in the following."," The combination of these two equations leads to and without all the terms containg $\mu$ which come from the inclusion of the centroid shift, which is calculated in the following."
 Normally moments of the light distribution are computed with respect to the centre of light., Normally moments of the light distribution are computed with respect to the centre of light.
" This means mathematically: However, the centroid is not mapped to the origin of the source plane as we assumed in andA2."," This means mathematically: However, the centroid is not mapped to the origin of the source plane as we assumed in and."
". We derive here the mapping between the centroid in the source plane and in the lens plane up to first order in lensing fields: Using the form of the centroid shift calculated above we can compute: and where we made use of the fact that to the order we are interested in, £ is unaffected by the centroid shift."," We derive here the mapping between the centroid in the source plane and in the lens plane up to first order in lensing fields: Using the form of the centroid shift calculated above we can compute: and where we made use of the fact that to the order we are interested in, $\xi^{s}$ is unaffected by the centroid shift."
" The first integral in both expressions can be replaced with the expressions computed in andA2,, while the second and the third integral, including the corrections due to the centroid shift, can be replaced by:"," The first integral in both expressions can be replaced with the expressions computed in and, while the second and the third integral, including the corrections due to the centroid shift, can be replaced by:"
system results in an SN Ia explosion and survives a companion star.,system results in an SN Ia explosion and survives a companion star.
 However. Figures | and 2 are for the moment of SN explosion. which could be modified by the explosion.," However, Figures 1 and 2 are for the moment of SN explosion, which could be modified by the explosion."
 The SN ejecta will interact with its companion., The SN ejecta will interact with its companion.
 The companion stars will be stripped of some mass and receive a kick velocity that is perpendicular to the orbital velocity., The companion stars will be stripped of some mass and receive a kick velocity that is perpendicular to the orbital velocity.
 Adopting a similar method to Meng. Chen Han (2007) we estimated the stripped mass for the companion stars of the WD + He star channel and find that the stripped mass is very low. e.g.. a M.. companion star with 0.274R8. only loses a mass of 0.015M. in our simulation.," Adopting a similar method to Meng, Chen Han (2007), we estimated the stripped mass for the companion stars of the WD + He star channel and find that the stripped mass is very low, e.g., a $\,M_\odot$ companion star with $\,R_\odot$ only loses a mass of $\,M_\odot$ in our simulation."
" We also roughly obtain the kick velocity based on the momentum conservation The kick velocity mainly depends on the ratio of separation to the radius of companions at the moment of SN explosion. A/RSh, and the leading head velocity of SN ejecta. which is assumed to be in the range of 11000 to kkm/s. The velocity of kkm/s is from the SN ejecta kinetic energy 1.0x10°! eerg corresponding to the lower limit ofnormal SN la kinetic energy. while the velocity of kkmm/s is from the SN ejecta kinetic energy 1.5x10°! eerg corresponding to the upper limit of the kinetic energy (Gamezo et al."," We also roughly obtain the kick velocity based on the momentum conservation The kick velocity mainly depends on the ratio of separation to the radius of companions at the moment of SN explosion, $A/R_{\rm 2}^{\rm SN}$, and the leading head velocity of SN ejecta, which is assumed to be in the range of 11000 to km/s. The velocity of km/s is from the SN ejecta kinetic energy $1.0\times10^{51}$ erg corresponding to the lower limit of normal SN Ia kinetic energy, while the velocity of km/s is from the SN ejecta kinetic energy $1.5\times10^{51}$ erg corresponding to the upper limit of the kinetic energy (Gamezo et al."
 2003)., 2003).
"4 We can obtain the spatial velocity by the formula V2""=VIONIUNorbVI. where Vig, and Vo. are the kick velocity and the orbital velocity of the companion star at the moment of SN explosion. respectively."," We can obtain the spatial velocity by the formula $V_{\rm 2}^{\rm SN}=\sqrt{V_{\rm
kick}^{2}+V_{\rm orb}^{2}}$, where $V_{\rm kick}$ and $V_{\rm orb}$ are the kick velocity and the orbital velocity of the companion star at the moment of SN explosion, respectively."
 In Figure 3. we show the distribution of the spatial velocity for the surviving companion stars of the WD + He star channel.," In Figure 3, we show the distribution of the spatial velocity for the surviving companion stars of the WD + He star channel."
 We see that the surviving companion stars have, We see that the surviving companion stars have
law expansion7. characterized which is accelerated for25.,"law expansion, characterized which is accelerated for."
 The growth of perturbations in the above model has been studied in Amenclola Tocchini-Valentini (2002): here we just state the results., The growth of perturbations in the above model has been studied in Amendola Tocchini-Valentini (2002); here we just state the results.
 For scales smaller than the horizon the perturbation equation for the matter density contrast can be written where primes- denote derivation.H withH respect (to e and 14-437/3., For scales smaller than the horizon the perturbation equation for the matter density contrast can be written where primes denote derivation with respect to a and /3.
. EmplovingB the (race of the Einstein equations we lind the solution wherey., Employing the trace of the Einstein equations we find the solution where.
 The observational constraints 0.1 and 0.1 confine the parameters in the shadowed region in Fig., The observational constraints 0.1 and 0.1 confine the parameters in the shadowed region in Fig.
 3. where we also plot 4).," 3, where we also plot )."
" For instance. putting =0.4. as suggested by the SNla. and =0.3 we obtain a growth as fast as 2.. which reduces tom Lili, —0.5."," For instance, putting =0.4, as suggested by the SNIa, and =0.3 we obtain a growth as fast as 2, which reduces to 1 if =0.5."
. This shows that the dark matter fluctuations can grow even during (he accelerated phase. due to the extra pull of the dark enerev coupling.," This shows that the dark matter fluctuations can grow even during the accelerated phase, due to the extra pull of the dark energy coupling."
 The h--th plane-wave component of the scalar field perturbation BLOWS as where For subhorizon wavelengths (which is proportional to ) remains always, The k -th plane-wave component of the scalar field perturbation grows as where For subhorizon wavelengths (which is proportional to ) remains always
 relsec:approach..,\\ref{sec:approach}.
" The concept of Ne, is more appropriate for our approach. since it takes into account the actual galaxy distribution and the BCO mass distribution."," The concept of $N_G$ is more appropriate for our approach, since it takes into account the actual galaxy distribution and the BCO mass distribution."
" As detectors become more sensitive. Ve, grows accordingly."," As detectors become more sensitive, $N_G$ grows accordingly."
 In this formulation ay=Ne Pi.," In this formulation $R_{\mathrm{det}}=N_{G}\,R_{\mathrm{MW}}$ ."
 The Galactic inspiral rate Zi can be calculated based on the current observed sample for NS-NS (INalogeraetal.2003) and from population svnthesis caleulations (e.g.. BIB).," The Galactic inspiral rate $R_{\mathrm{MW}}$ can be calculated based on the current observed sample for NS-NS \citep{kal03} and from population synthesis calculations (e.g., BKB)."
 Interferometric detectors like LIGO are most sensitive to gravitational waves of a single polarization incident normal to the plane of the detectors arms., Interferometric detectors like LIGO are most sensitive to gravitational waves of a single polarization incident normal to the plane of the detector's arms.
 As the Earth rotates about ils axis. (he skv locations ancl polarization of sources to which il is most sensitive rotate as well.," As the Earth rotates about its axis, the sky locations and polarization of sources to which it is most sensitive rotate as well."
 Since galaxies are not uniformly distributed about the skv (he expected rate of detected coalescence events is periodic with the sidereal day., Since galaxies are not uniformly distributed about the sky the expected rate of detected coalescence events is periodic with the sidereal day.
 The detailed variation depends on the eeographical distribution of galaxies. the distribution of coalescing binaries with svstem chirp mass. aud (he signal-to-noise threshold for detection.," The detailed variation depends on the geographical distribution of galaxies, the distribution of coalescing binaries with system chirp mass, and the signal-to-noise threshold for detection."
 Figure 5. shows the probability density for detecüons under (he assumptions that the geographical distribution of galaxies is determined by our galaxy. catalog approach relsec:clistvibution)). the chirp mass distribution of coalesine binaries is given by ΓΙΝΕ model A. and the signal-to-noise ratio py threshold for detection in initial LIGO is 3.," Figure \ref{fig:time} shows the probability density for detections under the assumptions that the geographical distribution of galaxies is determined by our galaxy catalog approach \\ref{sec:distribution}) ), the chirp mass distribution of coalesinc binaries is given by BKB model A, and the signal-to-noise ratio $\rho_0$ threshold for detection in initial LIGO is $8$."
 Here time | ds measured in hours and is given by UT plus the sidereal (mie at Greenwich at Oh UT., Here time $t$ is measured in hours and is given by UT plus the sidereal time at Greenwich at 0h UT.
 The Virgo Cluster is above a point in between (he Lanford and Livingston detectors [or approximately the duration Ish«εκ20h. closely coinciding with the peak in re[fig:time..," The Virgo Cluster is above a point in between the Hanford and Livingston detectors for approximately the duration $18 h< t < 20 h$, closely coinciding with the peak in \\ref{fig:time}."
 selüng aside the actual distribution of galaxies. it is interesting to note (he dependence ol the detectors “range” ον distance to the most distant observable source above tlireshold on source sky position.," Setting aside the actual distribution of galaxies, it is interesting to note the dependence of the detectors “range” — or distance to the most distant observable source above threshold — on source sky position."
 When sampled over sidereal time. the range depends on (the sky position only through declination.," When sampled over sidereal time, the range depends on the sky position only through declination."
 Figure 5. shows. for initial LIGO. the detector range as a function of declination. normalized to 1.42-M. NS-NS binaries.," Figure \ref{fig:D_opt} shows, for initial LIGO, the detector range as a function of declination, normalized to $1.4+1.4 ~\mathrm{M}_{\odot}$ NS-NS binaries."
 For an advanced LIGO withthe ΠΟ interferometer extended to 4 Ixm the declinations of maximum range will shift, For an advanced LIGO withthe H2 interferometer extended to 4 Km the declinations of maximum range will shift
"'The likelihood is now approximated as a finite sum of multivariate Gaussians: where with M; the finite number of Gaussian components of class ci, Να the number of attributes, a, the a priori probability to belong to component k, and ju; and X, the mean vector and covariance matrix of Gaussian component k.","The likelihood is now approximated as a finite sum of multivariate Gaussians: where with $M_i$ the finite number of Gaussian components of class $c_i$, $N_a$ the number of attributes, $\alpha_k$ the a priori probability to belong to component $k$, and $\mu_k$ and $\Sigma_k$, the mean vector and covariance matrix of Gaussian component $k$."
" For each node of the multi-stage tree, the set of variability classes is partitioned."," For each node of the multi-stage tree, the set of variability classes is partitioned."
" The best attributes are selected for that node and the classifier is trained, meaning that the Gaussian mixture for each class is determined."," The best attributes are selected for that node and the classifier is trained, meaning that the Gaussian mixture for each class is determined."
" To do so, we used the Expectation-Maximization (EM) method (see e.g. Gamerman&Migon (1993)))."," To do so, we used the Expectation-Maximization (EM) method (see e.g. \citet{GM:1993}) )."
" Given a variability class, the unknowns are the number of Gaussian components of each class, the prior probability to belong to a particular component, and the mean vectors ju and covariance matrices 3X; of each component."," Given a variability class, the unknowns are the number of Gaussian components of each class, the prior probability to belong to a particular component, and the mean vectors $\mu_k$ and covariance matrices $\Sigma_k$ of each component."
" The EM algorithm is an iterative method for calculating maximum likelihood estimates of parameters in probabilistic models, where the model depends on unobserved latent variables."," The EM algorithm is an iterative method for calculating maximum likelihood estimates of parameters in probabilistic models, where the model depends on unobserved latent variables."
" EM alternates between performing an expectation (E) step, which computes the expectation of the log-likelihood evaluated by using the current estimate for the latent variables, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found in the E step."," EM alternates between performing an expectation (E) step, which computes the expectation of the log-likelihood evaluated by using the current estimate for the latent variables, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found in the E step."
 These parameter-estimates are then used to determine the distribution of the latent variables in the next E step., These parameter-estimates are then used to determine the distribution of the latent variables in the next E step.
" Given the number of Gaussian components N., the remaining unknowns in the model can be determined by using this procedure."," Given the number of Gaussian components $N_c$, the remaining unknowns in the model can be determined by using this procedure."
" The actual number of components is determined using the Bayesian information criterion (BIC), which is a criterion for model selection among a set of parametric models with different number of parameters."," The actual number of components is determined using the Bayesian information criterion (BIC), which is a criterion for model selection among a set of parametric models with different number of parameters."
 We obtained three components in the example in Fig., We obtained three components in the example in Fig.
 1 using BIC., \ref{gm} using BIC.
 The Akaike information criterium (AIC) gives the same number of components., The Akaike information criterium (AIC) gives the same number of components.
" This solution turns out to be very stable when changing initial values, in the sense that the EM algorithm always converges to the same solution."," This solution turns out to be very stable when changing initial values, in the sense that the EM algorithm always converges to the same solution."
" Once the classifiers in each node are trained, the targets can be classified."," Once the classifiers in each node are trained, the targets can be classified."
 In each node we assign a probability to each target that it belongs to a particular class relevant, In each node we assign a probability to each target that it belongs to a particular class relevant
spirals. although he did not find it easy to show why there should be these transitional tvpes.,"spirals, although he did not find it easy to show why there should be these transitional types.”"
 Perhaps we may we have to retum to the view of Daade (1963.p.," Perhaps we may we have to return to the view of Baade (1963,p."
 78) who wrote: “So. we should define it as the class of galaxies in which from their general form we should expect (to find spiral structure. but which. contrary to our expectation. do not show it”.," 78) who wrote: “So, we should define it as the class of galaxies in which from their general form we should expect to find spiral structure, but which, contrary to our expectation, do not show it”."
 The main thrust of the present paper has been to show that a significant fraction of all SO galaxies occur in the field where the effects of collisions and ram-pressure stripping are expected to have been minimal., The main thrust of the present paper has been to show that a significant fraction of all S0 galaxies occur in the field where the effects of collisions and ram-pressure stripping are expected to have been minimal.
 This suggest that an internal. rather than an external. cause might have to be found for the absence of spiral structure in some field SO galaxies.," This suggest that an internal, rather than an external, cause might have to be found for the absence of spiral structure in some field S0 galaxies."
 One might speculate Chat a weak (or absent) magnetic field (Chandrasekhar Fermi 1953ab) in proto-S0 galaxies was responsible for the lack of spiral arms in lenticular field ealaxies., One might speculate that a weak (or absent) magnetic field (Chandrasekhar Fermi 1953ab) in proto-S0 galaxies was responsible for the lack of spiral arms in lenticular field galaxies.
 Allernatively. the present results might be interpreted as supporting the view of Larson et al. (," Alternatively, the present results might be interpreted as supporting the view of Larson et al. ("
1980) and of Bekki et al. (,1980) and of Bekki et al. (
2002) that some SO galaxies are objects that have been starved of inflowing external gas.,2002) that some S0 galaxies are objects that have been starved of inflowing external gas.
 In tliis respect they would differ from normal spirals that might still be fed by an external supply of eas from captured debris. minor mergers with eas-rich satellites. or even cold gas from cosmic filaments.," In this respect they would differ from normal spirals that might still be fed by an external supply of gas from captured debris, minor mergers with gas-rich satellites, or even cold gas from cosmic filaments."
 A possible complicating factor is that the morphology of a galaxy might have been affected by both (1) its location in a cluster. and (2) by the presence of a nearby companion (Hohlnberg 1958. Hwang Park 2009).," A possible complicating factor is that the morphology of a galaxy might have been affected by both (1) its location in a cluster, and (2) by the presence of a nearby companion (Holmberg 1958, Hwang Park 2009)."
 Finally. and. perhaps most plausibly. it might be necessary to invoke internal processes (Silk Norman 2009) to account lor the absence of sienilicaml anziounts of gas in some field lenticular galaxies.," Finally, and perhaps most plausibly, it might be necessary to invoke internal processes (Silk Norman 2009) to account for the absence of significant amounts of gas in some field lenticular galaxies."
 As these authors point out. outflows from active galactic nuclei can (rigeer star formation via the compression of dense clouds.," As these authors point out, outflows from active galactic nuclei can trigger star formation via the compression of dense clouds."
 These star bursts would in turn produce supernovae that will enhance the outflow of gas from active nuclei., These star bursts would in turn produce supernovae that will enhance the outflow of gas from active nuclei.
 ] thank Roberto Abraham for numerous useful discussions and Preethi Nair for making available her PhD thesis., I thank Roberto Abraham for numerous useful discussions and Preethi Nair for making available her PhD thesis.
 Thanks are also due to Marie Martig for useful correspondence., Thanks are also due to Marie Martig for useful correspondence.
 T am also indebted to Brenda Parrish for technical support., I am also indebted to Brenda Parrish for technical support.
 Finally it is a pleasure to thank (he releree [or a very. kind ancl helpful report., Finally it is a pleasure to thank the referee for a very kind and helpful report.
The data for the Fornax Survey. were obtained sequentially from (he period of May 20 2003 through to June 6 2003.,The data for the Fornax Survey were obtained sequentially from the period of May 20 2003 through to June 6 2003.
 Sequence numbers were 300324 to. 800333., Sequence numbers were 800324 to 800333.
 Due {ο increased solar aclivily the observations were halted. within (his period. and sequence 800331 was interrupted and restarted once the solar activity had died down.," Due to increased solar activity the observations were halted within this period, and sequence 800331 was interrupted and restarted once the solar activity had died down."
 Exposure times ranged between 45 and 48 ksec., Exposure times ranged between 45 and 48 ksec.
 A schematic of the mosaic strategv is given in Figure 1. overlaid on an opticalSurvev image of Fornax.," A schematic of the mosaic strategy is given in Figure 1, overlaid on an optical image of Fornax."
 The mosaic was designed to provide a) contiguous coverage over (he cluster core ancl b) high resolution (on-axis) data for the brightest galaxies in (he Fornax core., The mosaic was designed to provide a) contiguous coverage over the cluster core and b) high resolution (on-axis) data for the brightest galaxies in the Fornax core.
 Nine fields provided [full coverage and a tenth was positioned to double the exposure in the region between NGC 1399 and NGC 1404. and ensure (hat the leading edge of NGC 1404 (83.1) was not at a chip gap.," Nine fields provided full coverage and a tenth was positioned to double the exposure in the region between NGC 1399 and NGC 1404, and ensure that the leading edge of NGC 1404 3.1) was not at a chip gap."
 All data were taken using the VEAINT mode. and were reprocessed to take advantage of the increased background discrimination this offers.," All data were taken using the VFAINT mode, and were reprocessed to take advantage of the increased background discrimination this offers."
 The Charge Transfer Inefficienev (CTI) correction was also reapplied., The Charge Transfer Inefficiency (CTI) correction was also reapplied.
 Alter filtering ont periods of high background. the range of usable exposure was 40.3-46.6 ksec across all fields.," After filtering out periods of high background, the range of usable exposure was 40.8-46.6 ksec across all fields."
 Gain corrections were also applied to the data., Gain corrections were also applied to the data.
 In addition to the ACIS-I 0.1.2. and 3 chips. the ACIS-8 $2 (chip 6) was switched on. although we do not consider those data here.," In addition to the ACIS-I 0,1,2, and 3 chips, the ACIS-S S2 (chip 6) was switched on, although we do not consider those data here."
 soft (0.3-1.5 keV). medium (1.5-2.5 keV). and hard band (2.5-3 keV) images of the full mosaic are presented in Figures 2.3. aud 4.," Soft (0.3-1.5 keV), medium (1.5-2.5 keV), and hard band (2.5-8 keV) images of the full mosaic are presented in Figures 2,3, and 4."
 Exposure maps were constructed in (these bands for each individual ACIS-I field using a spatial binning [actor of 4 (27) and spectral weights calculated assuming a thermal MEINAL spectrum of 1.2 keV and 0:3 solar metal abundance., Exposure maps were constructed in these bands for each individual ACIS-I field using a spatial binning factor of 4 $2''$ ) and spectral weights calculated assuming a thermal MEKAL spectrum of 1.2 keV and 0.3 solar metal abundance.
" Each field/band was binned by a [actor 4 and then smoothed using the adaptive smoothing algorithm limited to a maximum smoothing scale of I0"".", Each field/band was binned by a factor 4 and then smoothed using the adaptive smoothing algorithm limited to a maximum smoothing scale of $10''$.
 The smoothing scales eeneraled [or each image were then applied to the band appropriate exposure maps. all smoothed images and exposure maps were (hen merged. and an exposure-corrected mosaiced image was produced in each energy. band.," The smoothing scales generated for each image were then applied to the band appropriate exposure maps, all smoothed images and exposure maps were then merged, and an exposure-corrected mosaiced image was produced in each energy band."
 It should be noted (hat some residual structures associated wilh the field overlap regions are still apparent in (he soft. band image. ancl {ο a much lesser degree in the medium and hard images.," It should be noted that some residual structures associated with the field overlap regions are still apparent in the soft band image, and to a much lesser degree in the medium and hard images."
 This is in part cue to the imprecise nature of (he exposure map spectral weighting. which necessarily assumes a uniform spectral model. aud in part due to the inherent difficulty of merging two independenüly smoothed aud exposure corrected. versions of the same part of the sky. containing low surface brightness enmission - as necessitated by current software limitations.," This is in part due to the imprecise nature of the exposure map spectral weighting, which necessarily assumes a uniform spectral model, and in part due to the inherent difficulty of merging two independently smoothed and exposure corrected versions of the same part of the sky, containing low surface brightness emission - as necessitated by current software limitations."
 We will address these issues in subsequent work on the CFS image maps., We will address these issues in subsequent work on the CFS image maps.
values of 3 are 0.68. 1.03. 1.H1. 1.83 and 2.29.,"values of $\beta$ are 0.68, 1.03, 1.41, 1.83 and 2.29."
 The values of 3 are slightly higher for the models witl AICC = 1.0 x 109 and slightly lower for moclels with AICC = 2.0 x 108 (Table 1))., The values of $\beta$ are slightly higher for the models with $M^{\rm CC}$ = 1.0 $\times$ $^{6}$ and slightly lower for models with $M^{\rm CC}$ = 2.0 $\times$ $^{6}$ (Table \ref{tbl-beta}) ).
 The fraction of the euclosed mass of a merger object aud the initial CC mass. ud. is plotted as a function of 2 iu Figure 9..," The fraction of the enclosed mass of a merger object and the initial CC mass, $\frac{M_{\rm encl}}{M^{\rm CC}}$, is plotted as a function of $\beta$ in Figure \ref{massandbeta}."
 The merger objects of the models for the three initial CC masses show the same linear correlation with 0., The merger objects of the models for the three initial CC masses show the same linear correlation with $\beta$.
 The models with Ry = 75 pe start already at the peri-galactic distance with a 9 of about one., The models with $R_{\rm pl}^{\rm CC}$ = 75 pc start already at the peri-galactic distance with a $\beta$ of about one.
 Consequently. all 20 clusters merge.," Consequently, all 20 clusters merge."
 For the more extended models a number of star cluster are initially located outside the tidal radius., For the more extended models a number of star cluster are initially located outside the tidal radius.
 As we use a hiehly eccentric orbit. the CCs move rapidly towards larger Galactic distances. e.g. after LOO Myr they are at a distauce of about 35 kpe.," As we use a highly eccentric orbit, the CCs move rapidly towards larger Galactic distances, e.g. after 100 Myr they are at a distance of about 35 kpc."
 Due to the lower gravitational Geld of the Milky Way at larger distances. the tidal radii increase leadiug to lower values of 3.," Due to the lower gravitational field of the Milky Way at larger distances, the tidal radii increase leading to lower values of $\beta$."
 Figure 10. shows the variation of 3 with time for models with Alo = 1.5 x 10°. For models N.11.11., Figure \ref{betaplot} shows the variation of $\beta$ with time for models with $M^{\rm CC}$ = 1.5 $\times$ $^{6}$.
5.1100. NL311.11.5.1125. and M_LL11.5-1150 the period with 8> Lis getting longer. resulting in lower uumbers of merged clusters for larger CCs.," For models 100, 125, and 150 the period with $\beta >$ 1 is getting longer, resulting in lower numbers of merged clusters for larger CCs."
 The turnover in rag. as shown in Figures ΟΡ aud 8.. occurs at those Ri. where ο) is sulliciently large to allow eutire star clusters to escape the merging process.," The turnover in $r_{\rm eff}$, as shown in Figures \ref{figmassreff}b b and \ref{turnover}, occurs at those $R_{\rm pl}^{\rm CC}$, where $\beta$ is sufficiently large to allow entire star clusters to escape the merging process."
 We use the CC parameters of model 11.11.5.1100 as a basis to analyze the iuflueuce of the detailed distribution of star clusters in the CC., We use the CC parameters of model 100 as a basis to analyze the influence of the detailed distribution of star clusters in the CC.
 We calculate the evolution of five adcditioual inodels. of which two (N.22.11.5.1100 and N.33.11.5.1100) have a similar concentration of clusters in their center as 1100. whereas the other three models 1100. 1100 and M_66_11.5_1100) show a less concentrated distribution of star clusters (see Figure lee).," We calculate the evolution of five additional models, of which two 100 and 100) have a similar concentration of clusters in their center as 100, whereas the other three models 100, 100 and 100) show a less concentrated distribution of star clusters (see Figure \ref{figinimodel}c c)."
 All six moclels result (roin exactly the same Plummer moclel but with differeut. raudom number seeds., All six models result from exactly the same Plummer model but with different random number seeds.
 The average aud the staucdard deviatiou of the effective radii aud euclosed masses of the merger objects of all six models are rey = 23.843.2 pe and Alene = 0.9520.17. x 109 M... respectively.," The average and the standard deviation of the effective radii and enclosed masses of the merger objects of all six models are $r_{\rm eff}$ = $\pm$ 3.2 pc and $M_{\rm encl}$ = $\pm$ 0.17 $\times$ $^{6}$ $_{\odot}$, respectively."
 The standard deviations. which correspond to relative deviations of (reg) aud (Magy). provide au order of maguitude estimate of the influence of the distribution of star clusters on the structural parameters of the merger objects.," The standard deviations, which correspond to relative deviations of $r_{\rm eff}$ ) and $M_{\rm encl}$ ), provide an order of magnitude estimate of the influence of the distribution of star clusters on the structural parameters of the merger objects."
 The mergere objects resulting[eJ from compact initial coufigurationsOm l to 3 have ou averagee a significantly higher mass (Mj = 1.10270.06 x 109 ML.) than the less concentrated coufigurations Lto 6 (Alone = 0.812:0.06 o 109 NL. )., The merger objects resulting from compact initial configurations 1 to 3 have on average a significantly higher mass $M_{\rm encl}$ = $\pm$ 0.06 $\times$ $^{6}$ $_{\odot}$ ) than the less concentrated configurations 4 to 6 $M_{\rm encl}$ = $\pm$ 0.06 $\times$ $^{6}$ $_{\odot}$ ).
 In contrast. no clear difference in the effective radii of the merger objects can be seen between coucentrated and extended iuitial distributious.," In contrast, no clear difference in the effective radii of the merger objects can be seen between concentrated and extended initial distributions."
 For comparison. an accditioual model M_77_11.5_2200 has been calculated.," For comparison, an additional model 200 has been calculated."
 It has à CC Plumaner radius o£ 200 pe aud a relatively small cutoff radius of LOO pe., It has a CC Plummer radius of 200 pc and a relatively small cutoff radius of 400 pc.
 A scaled version of model 1100 with HE = 200 pc aud a CC cutoll radius of 800 pe. which is four times the CC Pluuuner radius.," A scaled version of model 100 with $R_{\rm pl}^{\rm CC}$ = 200 pc and a CC cutoff radius of 800 pc, which is four times the CC Plummer radius,"
example Puzia et al.,example Puzia et al.
 2005 and Caldwell et al. 2009.. 2011)).," \cite{puzia} and Caldwell et al. \cite{C09}, \cite{C11}) )."
 Another widely used method to age-date extragalactic star clusters relies on multi-band. photometry: the age can be derived from the spectral energy distributions (SED) measured in broad-band photometric systems. by comparing them with simple stellar population (SSP*)) synthesis models (e.g. Jiang et al. 2003:: ," Another widely used method to age-date extragalactic star clusters relies on multi-band photometry: the age can be derived from the spectral energy distributions (SED) measured in broad-band photometric systems, by comparing them with simple stellar population ) synthesis models (e.g. Jiang et al. \cite{jiang03}; ;"
Fan et al. 2006.2008.2010::," Fan et al. \cite{fan06,fan08,fan10};"
 Ma et al. 2007.2009:;," Ma et al. \cite{ma07,ma09};"
 and Wang et al. 20105)., and Wang et al. \cite{wang10}) ).
 Clearly. photometry-based technique are prone to errors owing to the uncertainty in the interstellar extinction. while spectral indices are virtually free from this effect.," Clearly, photometry-based technique are prone to errors owing to the uncertainty in the interstellar extinction, while spectral indices are virtually free from this effect."
 In a recent analysis adopting the most up-to-date theoretical tools and methodology. Puzia et al. (2005:: ," In a recent analysis adopting the most up-to-date theoretical tools and methodology, Puzia et al. \cite{puzia}; ;"
POS hereafter) derived spectroscopic ages. metallicities and [o/Fe]. ratios for 70 GCs in M31 based on Lick indices.," P05 hereafter) derived spectroscopic ages, metallicities and $[\alpha/Fe]$ ratios for 70 GCs in M31 based on Lick indices."
 Within. this sample. the authors find a population of - 20 GCs with ages between ~5 and 9 Gyr and mean metallicity of [Z/H]- —0.6.," Within this sample, the authors find a population of $\sim$ 20 GCs with ages between $\sim 5$ and 9 Gyr and mean metallicity of $[Z/H] \sim -0.6$ ."
 Independently. Burstein et al. (2004))," Independently, Burstein et al. \cite{burst04}) )"
 and Beasley et al. (2005)), and Beasley et al. \cite{beas05}) )
 also claimed to have found two (B232 and B3l1) and six (8120. B292. B301. B337. NBI6. NB67) intermediate-age GCs inM31... respectively. in common with Puzia’s sample.," also claimed to have found two (B232 and B311) and six (B126, B292, B301, B337, NB16, NB67) intermediate-age GCs in, respectively, in common with Puzia's sample."
 The presence of a population of intermediate-age GCs in M31 was also supported by other spectrophotometric analyses (Fan et al. 20101:, The presence of a population of intermediate-age GCs in M31 was also supported by other spectrophotometric analyses (Fan et al. \cite{fan10};
 Wang et al., Wang et al.
 and reference therein; see Table 2))., \cite{wang10} and reference therein; see Table \ref{tab:age}) ).
 On the other hand. Strader et al. (2009))," On the other hand, Strader et al. \cite{strad09}) )"
 showed that three of the candidate intermediate-age M31 GCs studied by POS. Burstein et al. (2004)).," showed that three of the candidate intermediate-age M31 GCs studied by P05, Burstein et al. \cite{burst04}) ),"
 and Beasley et al. (2005)), and Beasley et al. \cite{beas05}) )
 have M/Ly and V—K colors typical of old GCs., have $M/L_V$ and $V-K$ colors typical of old GCs.
 Twelve of the spectroscopically identified intermediate-age GC candidates were also detected by Rey et al. (2007)), Twelve of the spectroscopically identified intermediate-age GC candidates were also detected by Rey et al. \cite{rey07}) )
 in. far-ultraviolet (FUV) and/or near-ultraviolet (NUV) GALEX images., in far-ultraviolet (FUV) and/or near-ultraviolet (NUV) GALEX images.
 From the comparison of their UV photometry with theoretical models these authors concluded that most of these spectroscopically identified intermediate-age clusters may in fact be classical old GCs with many blue HB stars., From the comparison of their UV photometry with theoretical models these authors concluded that most of these spectroscopically identified intermediate-age clusters may in fact be classical old GCs with many blue HB stars.
 These hot stars would contribute to enhance the UV flux as well as the strength of Balmer lines. thus mimicking younger ages.," These hot stars would contribute to enhance the UV flux as well as the strength of Balmer lines, thus mimicking younger ages."
 A possible example ts provided by the cluster B311. reported to be 5 Gyr old by Burstein. et al. (2004)).," A possible example is provided by the cluster B311, reported to be 5 Gyr old by Burstein et al. \cite{burst04}) ),"
 that reveals an extended HB in the CMD presented by Rich et al. (2005)).," that reveals an extended HB in the CMD presented by Rich et al. \cite{rich05}) ),"
 clearly not consistent with such a young age., clearly not consistent with such a young age.
 Therefore. deep HST imaging of intermediate-age GCs candidates is crucial to check if they are genuinely intermediate-age or. instead. old clusters with blue HB.," Therefore, deep HST imaging of intermediate-age GCs candidates is crucial to check if they are genuinely intermediate-age or, instead, old clusters with blue HB."
 The presence of bright intermediate-age clusters in M31. 1f confirmed. would be especially interesting because these objects are not observed in our own Galaxy. possibly implying a significant difference in the star- (or. at least. cluster) formation history between the two galaxies.," The presence of bright intermediate-age clusters in M31, if confirmed, would be especially interesting because these objects are not observed in our own Galaxy, possibly implying a significant difference in the star- (or, at least, cluster) formation history between the two galaxies."
 In HST cycle 14 deep ACS/WFC imaging was acquired of four M31 GCs. which were identified by POS as candidate intermediate-age cluster.," In HST cycle 14 deep ACS/WFC imaging was acquired of four M31 GCs, which were identified by P05 as candidate intermediate-age cluster."
 In this paper we present the CMDs of the four main targets of this observational program. discussing the compatibility with the parameters obtained by POS from the integrated spectroscopy (see Tables 2 and 3)).," In this paper we present the CMDs of the four main targets of this observational program, discussing the compatibility with the parameters obtained by P05 from the integrated spectroscopy (see Tables \ref{tab:age} and \ref{tab:met}) )."
 We also present the CMDs for two other GCs that were in the target fields in both passbands: B336 and the newly detected cluster B531., We also present the CMDs for two other GCs that were in the target fields in both passbands: B336 and the newly detected cluster B531.
 Finally. we provide firmer classification for three additional objects listed in the RBC that were imaged only in one passband.," Finally, we provide firmer classification for three additional objects listed in the RBC that were imaged only in one passband."
 In Sect., In Sect.
 2. we describe the HST/ACS data. the adopted reduction procedure. the photometric uncertainties and the completeness of the data.," \ref{data} we describe the HST/ACS data, the adopted reduction procedure, the photometric uncertainties and the completeness of the data."
 Sect., Sect.
 3 is devoted to describe the CMDs of the individual clusters. thefield-decontamination procedure. and the method we used to estimate the metallicity. reddening. and distance.," \ref{cmd} is devoted to describe the CMDs of the individual clusters, thefield-decontamination procedure, and the method we used to estimate the metallicity, reddening, and distance."
 InSect., InSect.
 4 we describe the method for searching variable stars and the results for the individual, \ref{RR-Lyrae} we describe the method for searching variable stars and the results for the individual
y.ronglv ou the twisting structure. the illunuinatiug source o»eomietry aud the line of sight to the observer.,"strongly on the twisting structure, the illuminating source geometry and the line of sight to the observer."
 Iu principle rey can be modeled with high sigual-to-noise spectra of ie object by varving the model parameters., In principle they can be modeled with high signal-to-noise spectra of the object by varying the model parameters.
 Iuowledee Mf the twisting structure may allow the determination of sole very important characteristics of AGN. at first order 10 spin momentum of the black hole aud the viscosity xumueter of the accretion disk.," Knowledge of the twisting structure may allow the determination of some very important characteristics of AGN, at first order the spin momentum of the black hole and the viscosity parameter of the accretion disk."
 Then determination bv other methods is still uureliable., Their determination by other methods is still unreliable.
"Throughout this paper. we assume a flat. cosmological model with O,,=0.3. Q4=0.7. and Lf)=71 kms ! !.","Throughout this paper, we assume a flat cosmological model with $\Omega_{m}=0.3$ , $\Omega_\Lambda=0.7$ , and ${H_{0}=71}$ km $^{-1}$ $^{-1}$."
 In this model. at the distance of J14272-3312. 1 mas corresponds lo 5.6 pe.," In this model, at the distance of J1427+3312, 1 mas corresponds to 5.6 pc."
 The QSO J1427--3312 was observed with the Verv Large Array (VLA) of the in A configuration on 2007 July 9., The QSO J1427+3312 was observed with the Very Large Array (VLA) of the in A configuration on 2007 July 9.
 The lrequency of the observations was 8.4 GlIIz and the total bandwidth was 100 MIIz in both right aud left-hand circular polarizations., The frequency of the observations was 8.4 GHz and the total bandwidth was 100 MHz in both right and left-hand circular polarizations.
 The source 3C286 was used as the primary. flux. calibrator. and. J1416+3444 as the phase calibrator.," The source 3C286 was used as the primary flux calibrator, and J1416+3444 as the phase calibrator."
 The total time was 6 hours with 23 antennas participating in the observations., The total time was 6 hours with 23 antennas participating in the observations.
 The VLA cata was reduced using standard: Astronomical Image Processing Svstem (AIPS) routines., The VLA data was reduced using standard Astronomical Image Processing System (AIPS) routines.
 Table 1 summarizes the parameters of the VLA observations., Table 1 summarizes the parameters of the VLA observations.
 The VLBI observations of JI427+3312 were carried out al 1.4 GIIz on 2007 June 11 and 12. using the Verv Long Baseline Array (VLBA) of the NRAO.," The VLBI observations of J1427+3312 were carried out at 1.4 GHz on 2007 June 11 and 12, using the Very Long Baseline Array (VLBA) of the NRAO."
 Eight adjacent 8 MIIz baseband channel pairs were used in the observations. both with right and left-hand circular polarizations. and sampled at two bits.," Eight adjacent 8 MHz baseband channel pairs were used in the observations, both with right and left-hand circular polarizations, and sampled at two bits."
 The data were correlated at the VLBA correlator in Socorro. NM. with 2 s correlator integration time.," The data were correlated at the VLBA correlator in Socorro, NM, with 2 s correlator integration time."
 The total observing time was 12 hr., The total observing time was 12 hr.
 Table 2 summarizes (he parameters of the VLBA observations., Table 2 summarizes the parameters of the VLBA observations.
" The VLBA observations emploved nocdcding-stvle phase referencing. using the calibrator J14224-3223 (54.4cu,=O4 Jv). with a evele time of 4 min. 3 min on the target source and 1 min on the calibrator."," The VLBA observations employed nodding-style phase referencing, using the calibrator J1422+3223 $S_{\rm 1.4~GHz}=0.4$ Jy), with a cycle time of 4 min, 3 min on the target source and 1 min on the calibrator."
 The angular separation between the lareel source and the phase calibrator is 14°., The angular separation between the target source and the phase calibrator is $1.4^{\circ}$.
 A munber of test eveles were also included to monitor the coherence of the phase referencing., A number of test cycles were also included to monitor the coherence of the phase referencing.
" These tests involved switching between (wo calibrators. the phase calibrator J1422+3223 and the phase-check calibrator J14162-2444 (53.4oy,=1.9 Jv). using a similar evele time to Chat used for the target source."," These tests involved switching between two calibrators, the phase calibrator J1422+3223 and the phase-check calibrator J1416+3444 $S_{\rm 1.4~GHz}=1.9$ Jy), using a similar cycle time to that used for the target source."
 The angular separation betweenthe phase calibratorand(he phase-check calibrator is 2.17, The angular separation betweenthe phase calibratorandthe phase-check calibrator is $2.7^{\circ}$ .
be expected in the starless cores as well.,be expected in the starless cores as well.
 Analytic (Ketoetal.2006) and numerical (Keto&Field2005;Broder-icketal.2007) models of oscillating cores easily reproduce the characteristic asymmetric shapes of molecular lines seen in the starless cores.," Analytic \citep{Keto2006} and numerical \citep{KetoField2005,Broderick2007} models of oscillating cores easily reproduce the characteristic asymmetric shapes of molecular lines seen in the starless cores."
" While the spectral-line profiles of the low-order modes (the dipolar and breathing modes are observational indistinguishable from simple contraction, expansion and rotation) a few cores show simultaneous inward and outward motions (Agutietal.2007;Lada2003;Redmanetal.2006) that are consistent only with modes."," While the spectral-line profiles of the low-order modes (the dipolar and breathing modes are observational indistinguishable from simple contraction, expansion and rotation) a few cores show simultaneous inward and outward motions \citep{Aguti2007,Lada2003,Redman2006} that are consistent only with oscillatory modes."
" Oscillations produce density perturbationsoscillatory as well, and the and quadrupole modes naturally reproduce the ellipsoidal dipolemorphologies (Ketoetal.2006) characteristically seen in observations of the cores (Bacmannetal.2000;Ward-Thompsonetal.1999;Kirk 2005)."," Oscillations produce density perturbations as well, and the dipole and quadrupole modes naturally reproduce the ellipsoidal morphologies \citep{Keto2006} characteristically seen in observations of the cores \citep{Bacmann2000,Ward-Thompson1999,KirkWTAndre2005}."
". Observations suggest that these oscillations, rather than a minor perturbation on quasi-static equilibrium, provide a substantial contribution to the dynamical stability and therefore are important in the evolution of the cores toward star formation."," Observations suggest that these oscillations, rather than a minor perturbation on quasi-static equilibrium, provide a substantial contribution to the dynamical stability and therefore are important in the evolution of the cores toward star formation."
" First, a significant fraction of starless cores have observed density that can be matched by a BE sphere if the gas profilestemperature in the onlymodel sphere is made than is known to be the case in the starless cores considerably(Evanshigheretal.2001;Kirk2005;Kandori 2005)."," First, a significant fraction of starless cores have observed density profiles that can only be matched by a BE sphere if the gas temperature in the model sphere is made considerably higher than is known to be the case in the starless cores \citep{Evans2001,KirkWTAndre2005,Kandori2005}."
". Second, the sizes of of the starless cores imply that they should be unstable to manygravitational collapse (Evansetal.2001;Kandori 2005)."," Second, the sizes of many of the starless cores imply that they should be unstable to gravitational collapse \citep{Evans2001,Kandori2005}."
". However, statistical analyses of the relative numbers of stars and cores in a sample of different lifetimes that are several times the relevant star-formingfree-fall regionstime imply(Beichmanetal.1986;Jes-sop&Ward-Thompson2000;etal. 2007)."," However, statistical analyses of the relative numbers of stars and cores in a sample of different star-forming regions imply lifetimes that are several times the relevant free-fall time \citep{Beichman1986,JessopWT2000,Ward-Thompson2007}."
. Reconciling these observations require a Ward-Thompsonsource of energy within the cores in addition to the thermal , Reconciling these observations require a source of energy within the cores in addition to the thermal energy.
Internal oscillations or turbulence are suggested by the energy.observation that the line widths in cores are larger than the expected spectralthermal width (Dickmanmany&Clemens1983;MyersBenson1983;Ladaetal.2008) implying internal subsonic velocities on spatial scales unresolved in the observing beam.," Internal oscillations or turbulence are suggested by the observation that the spectral line widths in many cores are larger than the expected thermal width \citep{DickmanClemens1983,MyersBenson1983,Lada2008} implying internal subsonic velocities on spatial scales unresolved in the observing beam."
" These observations combined with modelling suggest the following evolution for the starless cores: The cores are formed at the bottom of the supersonic turbulent cascade that dominates the larger-scale ISM (Fieldetal.2008),, producing cores with a spectrum of masses and internal turbulent energies."," These observations combined with modelling suggest the following evolution for the starless cores: The cores are formed at the bottom of the supersonic turbulent cascade that dominates the larger-scale ISM \citep{Field2008}, producing cores with a spectrum of masses and internal turbulent energies."
" Those cores massive enough to be gravitationally unstable immediately begin contraction to form star, while those with mass and internal abecome self-supported and appropriateself-gravitating."," Those cores massive enough to be gravitationally unstable immediately begin contraction to form a star, while those with appropriate mass and internal energy become self-supported and self-gravitating."
 These cores are energydecoupled from the cascade in the sense that exist as individual dynamical entities independent of the theylarger-scale flows (Keto&Field 2005)., These cores are decoupled from the cascade in the sense that they exist as individual dynamical entities independent of the larger-scale flows \citep{KetoField2005}.
". The internal turbulence inherited from the flow, and present when a core forms, is part of its initial parentdynamical but is to over time."," The internal turbulence inherited from the parent flow, and present when a core forms, is part of its initial dynamical stability but is expected to dissipate over time."
" of as a stabilityspectrum of individualexpected modes of dissipateoscillation, the Thoughtturbulence non-linear mode-mode (collisions between decaysmodes) by(Brodericketal.2007) and by couplingtransmission through the core into the ISM (Brodericketal. 2008)."," Thought of as a spectrum of individual modes of oscillation, the turbulence decays by non-linear mode-mode coupling (collisions between modes) \citep{Broderick2007}
 and by transmission through the core boundary into the larger-scale ISM \citep{Broderick2008}."
. The boundarygradual loss of this larger-scaleinternal turbulent energy leads (on time scales of several crossing times) to gravitational eventuallyinstability and star formation., The gradual loss of this internal turbulent energy leads eventually (on time scales of several crossing times) to gravitational instability and star formation.
 In this paper we explore the latter half of this evolution., In this paper we explore the latter half of this evolution.
 We develop a model for the internal turbulence of the cores and examine its consequences for the evolution toward star formation and for the interpretation of dust continuum observations., We develop a model for the internal turbulence of the cores and examine its consequences for the evolution toward star formation and for the interpretation of dust continuum observations.
" Using the fact that the turbulence can be fully described as a collection of oscillating modes, we consider three models for the turbulent energy distribution, a Kolmogorov spectrum, a flat spectrum, and a spectrum dominated long wave lengths."," Using the fact that the turbulence can be fully described as a collection of oscillating modes, we consider three models for the turbulent energy distribution, a Kolmogorov spectrum, a flat spectrum, and a spectrum dominated by long wave lengths."
 In Section ?? we compute the effective bypressure arising from this turbulence., In Section \ref{sec:AME} we compute the effective pressure arising from this turbulence.
" We find that the breathing modes are destabilizing, but modes with shorter wave lengths generate a supporting pressure."," We find that the breathing modes are destabilizing, but modes with shorter wave lengths generate a supporting pressure."
" In Section ??,, we generate random realizations of turbulent cores and find that a typical stable, oscillating core would appear to be dynamically unstable, if the observations were fit to a static BE model."," In Section \ref{sec:MSEC}, we generate random realizations of turbulent cores and find that a typical stable, oscillating core would appear to be dynamically unstable, if the observations were fit to a static BE model."
" In Section ??,, we follow the evolution of the turbulent spectrum as it decays."," In Section \ref{sec:EoaMSSC}, we follow the evolution of the turbulent spectrum as it decays."
 We find that the spectrum of the turbulence evolves toward dominance the longer wave lengths., We find that the spectrum of the turbulence evolves toward dominance by the longer wave lengths.
" In conclusion, we find that we can bydescribe the evolution of the cores toward star formation as a purely hydrodynamic phenomenon without the necessity of support by large-scale magnetic fields (though a tangled magnetic field co-exist in equipartition with the turbulence without substantiallymay changing the findings)."," In conclusion, we find that we can describe the evolution of the cores toward star formation as a purely hydrodynamic phenomenon without the necessity of support by large-scale magnetic fields (though a tangled magnetic field may co-exist in equipartition with the turbulence without substantially changing the findings)."
 In this labelsec:section we compute the dynamical consequences of large-scale oscillations for the underlying starless core., In this section we compute the dynamical consequences of large-scale oscillations for the underlying starless core.
" We find it is possible for pulsations both to support the core and to initiate collapse, the distinction lying in the relative importance of the low and higher-order oscillation modes."," We find it is possible for pulsations both to support the core and to initiate collapse, the distinction lying in the relative importance of the low and higher-order oscillation modes."
 It is possible to do this with a macroscopic description similar, It is possible to do this with a macroscopic description similar
Llowever. zr is sulliciently large to safely assume that the radiation field in the disc is in LPE.,"However, $\tau_{eff}$ is sufficiently large to safely assume that the radiation field in the disc is in LTE."
 Then. close to the equatorial plane the radiation intensity approaches a blackbody.," Then, close to the equatorial plane the radiation intensity approaches a blackbody."
 In traversing the cise atmospheric layers radiation goes out of equilibrium. ancl scattering. effects are likely to change the spectrum. as we will discuss in more detail in Section 4..," In traversing the disc atmospheric layers radiation goes out of equilibrium and scattering effects are likely to change the spectrum, as we will discuss in more detail in Section \ref{result}."
 The total flux distribution for each stage of the evolution is shown in Fig. 6.., The total flux distribution for each stage of the evolution is shown in Fig. \ref{flux}.
 Neglecting relativistic effects. the total luminosity of the cise in theour dillerent stages Luss. can be computed integrating the lux over the cise surface (see Table 13).," Neglecting relativistic effects, the total luminosity of the disc in thefour different stages $L_{disc}$ can be computed integrating the flux over the disc surface (see Table \ref{tabmod}) )."
" H should be noted hat L,5;;. becomes larger than the Edcington limit in the outburst. phase.", It should be noted that $L_{disc}$ becomes larger than the Eddington limit in the outburst phase.
 Super-Exddington luminosities may. indeed » produced. during the non-steady evolution and/or in a non-spherical flow., Super-Eddington luminosities may indeed be produced during the non-steady evolution and/or in a non-spherical flow.
 In this particular case. this happens oecause of the significant. transient increase in the disc empoerature.," In this particular case, this happens because of the significant transient increase in the disc temperature."
 The flux together with the disc thickness will »e used in the next section to caleulate the emergent spectra., The flux together with the disc thickness will be used in the next section to calculate the emergent spectra.
 1n this section we outline the numerical method. usec in computing the evolution of the radiation spectrum emitted bv the transonic accretion cise., In this section we outline the numerical method used in computing the evolution of the radiation spectrum emitted by the transonic accretion disc.
 As discussed. previously (see Section. 2)). we consider four stages that correspond to the maximal evacuation stage (model 2) and three replenishment stages (model 1. 3 and 4).," As discussed previously (see Section \ref{hydro}) ), we consider four stages that correspond to the maximal evacuation stage (model 2) and three replenishment stages (model 1, 3 and 4)."
" The radial &rid of each numerical disc model is mace up of ~250 points dividing the integration domain. +,*PoutN 10"". into a succession. of comovingEM annular ""mzones. cach one 114ο moreB massiveHe than the one interior to it."," The radial grid of each numerical disc model is made up of $\sim$ 250 points dividing the integration domain, $r_{in} = 2.5<r<r_{out} = 2.8\times 10^5$ , into a succession of comoving annular zones, each one $11\%$ more massive than the one interior to it."
 Phe mass of the innermost zone was determined in accordance with numerical convenience., The mass of the innermost zone was determined in accordance with numerical convenience.
 In order to compute the spectrum. of these models. we introduce coarser radial zones (or rings) whose width is fixed by the requirement that their contribution to the total luminosity is ~5%.," In order to compute the spectrum of these models, we introduce coarser radial zones (or rings) whose width is fixed by the requirement that their contribution to the total luminosity is $\sim
5\%$."
 We have found more convenient to keep the ring boundaries coincident with the mesh points of the hydrodynamic calculation. avoiding unnecessary interpolations.," We have found more convenient to keep the ring boundaries coincident with the mesh points of the hydrodynamic calculation, avoiding unnecessary interpolations."
" The luminosity £, and average height , of each ring are then computed as where +; and Ar; are the racial mesh and grid spacing of the time-dependent. hydrodynamie code. £5;peo and fh;pes are the radiative lux and disc height (evaluated at the point) and IN is the number of radial points within the ring."," The luminosity $L_r$ and average height $h_r$ of each ring are then computed as where $r_i$ and $\Delta r_i$ are the radial mesh and grid spacing of the time-dependent hydrodynamic code, $F_{i-1/2}$ and $h_{i-1/2}$ are the radiative flux and disc height (evaluated at the mid-point) and $N$ is the number of radial points within the ring."
 Clearly. since the ring luminosity is calculated as the sum of the contributions from the original zones. it «ους slightly from one annulus to another.," Clearly, since the ring luminosity is calculated as the sum of the contributions from the original zones, it differs slightly from one annulus to another."
" In terms of the width Ar=ryr, and the average radius 1,=(ry|rx)7/2 of each ring. the luminosity can be approximately written as We found that the aforementioned. zoning procedure guarantees a sullicient accuracy when summing up all the rings and comparing the total disc luminosity to that computed. from the output of the transfer. calculation."," In terms of the width $\Delta r = r_N - r_1$ and the average radius $r_m = (r_1 +
r_N)/2$ of each ring, the luminosity can be approximately written as We found that the aforementioned zoning procedure guarantees a sufficient accuracy when summing up all the rings and comparing the total disc luminosity to that computed from the output of the transfer calculation."
 llowever. especially in model 2. the temperature. may change significantly within a ring and this contrasts the assumption. which will be introduced later on. that it may be approximated. as isothermal.," However, especially in model 2, the temperature may change significantly within a ring and this contrasts the assumption, which will be introduced later on, that it may be approximated as isothermal."
 Therefore. we further ask that the fractional temperature variation in each ring does not exceed 2.54. independently of thezone. luminosity.," Therefore, we further ask that the fractional temperature variation in each ring does not exceed $2.5\%$ , independently of thezone luminosity."
 Decause the outermost zones of the original eric do. not contribute appreciably to the total luminosity. they are," Because the outermost zones of the original grid do not contribute appreciably to the total luminosity, they are"
The energy requirements of Model 5.3 are substantial. but not excessive.,"The energy requirements of Model 5.3 are substantial, but not excessive."
" The reheating cucrey of 0.1«OMeAt should be compared to the total energv available from superuovae explosious which is approximately 0.7«10MereAZ,3 for a Salpeter IMP. ov 0.9«LOMoreAL? for the Kennicutt IME adopted inG"," The reheating energy of $0.41 \times 10^{49} \ergMsol$ should be compared to the total energy available from supernovae explosions which is approximately $0.7 \times 10^{49}
\,\hbox{erg}\,M_{\odot}^{-1}$ for a Salpeter IMF, or $0.9 \times
10^{49} \,\hbox{erg}\,M_{\odot}^{-1}$ for the Kennicutt IMF adopted in."
ALEFORAL Iu a halo of circular velocity 250 kis. the nass of eas reheated is more than 3 times the mass of σας formed into stars.," In a halo of circular velocity 250 km/s, the mass of gas reheated is more than 3 times the mass of gas formed into stars."
 If the level of reheating is reduced. as illustrated by models 5.1. (eaa 0.03) and 5.2 (eqq= 0.123). then the formation of small galaxies is nof suppressed sufficieutlv to match the observed Iuniuositv function.," If the level of reheating is reduced, as illustrated by models 5.1 $\erh= 0.03$ ) and 5.2 $\erh= 0.13$ ), then the formation of small galaxies is not suppressed sufficiently to match the observed luminosity function."
 Iu Models 6.16.3 (Fig 3)). we investigate the effect of asstuuineg that a fraction of the supernova and stellar wind energev heats the diffuse eas halo. causing it to expand.," In Models 6.1–6.3 (Fig \ref{fig:models_5}) ), we investigate the effect of assuming that a fraction of the supernova and stellar wind energy heats the diffuse gas halo, causing it to expand."
 This form of feedback suppresses the formation of both bright aud faint galaxies. but it does not produce a sharp break iu the luminosity function.," This form of feedback suppresses the formation of both bright and faint galaxies, but it does not produce a sharp break in the luminosity function."
 Models 6.1 aud 6.2 illustrate how as the euergv speut in heating the diffuse halo mereases. the break iu the Iunuinositv function becomes less pronounced.," Models 6.1 and 6.2 illustrate how as the energy spent in heating the diffuse halo increases, the break in the luminosity function becomes less pronounced."
 If the heating is niade even stronecr. the resulting ποσατν function approaches a power-law (Model 6.3).," If the heating is made even stronger, the resulting luminosity function approaches a power-law (Model 6.3)."
 This form of feedback clearly cannot solve the problem of overproduction of bright ealaxies., This form of feedback clearly cannot solve the problem of overproduction of bright galaxies.
 We now consider two possible schemes that are capable of producing a good match to the observed luuinosity function., We now consider two possible schemes that are capable of producing a good match to the observed luminosity function.
 The first involves balancing radiative cooling with thermal conduction., The first involves balancing radiative cooling with thermal conduction.
 The second involves expelling eas from dark matter halos at such high cucreies that it is subsequently unable to cool., The second involves expelling gas from dark matter halos at such high energies that it is subsequently unable to cool.
 Thermal coucduction is expected to aprit a specia scale ou the galaxy population because of the strong temperature depeudence of the Spitzer conductivity rate., Thermal conduction is expected to imprint a special scale on the galaxy population because of the strong temperature dependence of the Spitzer conductivity rate.
 Model 7.3 (solid Hue in Fie. 1)), Model 7.3 (solid line in Fig. \ref{fig:models_6}) )
" shows the result of including conduction with Αμα=25 iu Model 5.3 (Erchear=OL. ena,= 0)."," shows the result of including conduction with $\alpha_{\rm cond}=25$ in Model 5.3 $\erh=0.41$, $\eho=0$ )."
 Such a high value of he conductivity is indeed effective im suppressiug the orlation of the most massive galaxies since it prevents cficient eas cooling in group and cluster-sized halos., Such a high value of the conductivity is indeed effective in suppressing the formation of the most massive galaxies since it prevents efficient gas cooling in group and cluster-sized halos.
 The xiehtest galaxies iu the luminosity function are mstea mult through mereers., The brightest galaxies in the luminosity function are instead built through mergers.
 The result is a rather good match o the observed galaxy huninosity function., The result is a rather good match to the observed galaxy luminosity function.
 However. the conduction efficiency that we have assumed is extremely üeh.," However, the conduction efficiency that we have assumed is extremely high."
 To operate at the required level. we ust assunie voth that the conductivity is uot suppressed below the Spitzer value. aud that the effective temperature eradieut is steeper than £Xk? in the region of the cooling radius.," To operate at the required level, we must assume both that the conductivity is not suppressed below the Spitzer value, and that the effective temperature gradient is steeper than $T\propto
r^{2.5}$ in the region of the cooling radius."
 Note that the Spitzer formula for thermal conductivity in au ionized plasiuna breaks down if the conductivity becomes too high. i.c. if the conduction “saturates” as described by Cowie&Mel&ee(1977).," Note that the Spitzer formula for thermal conductivity in an ionized plasma breaks down if the conductivity becomes too high, i.e. if the conduction “saturates” as described by \citet{cowie77}."
. The models shown in this paper do not take account of this saturation limit., The models shown in this paper do not take account of this saturation limit.
 Towever. using the estimate of the saturated heat flux from Cowie&Nelvee (1977).. we have checked that our results ave not sjeuificautlv affected by saturation (for model 7.3. which has the most extreme conduction of all our models. there is onlv a stnall increase im the number of the very brightest ealaxies).," However, using the estimate of the saturated heat flux from \citet{cowie77}, we have checked that our results are not significantly affected by saturation (for model 7.3, which has the most extreme conduction of all our models, there is only a small increase in the number of the very brightest galaxies)."
 Iu Models 7.1 aud 7.2. we show the effect of assuming," In Models 7.1 and 7.2, we show the effect of assuming"
"at (wey)={170.3720}, is the best match to the snapshot shown in Fig.","at $(x,y)=\{470, 3720\}$, is the best match to the snapshot shown in Fig."
 5 of Steiner et al. (, 5 of Steiner et al. (
2010).,2010).
" According to the model data, the plateau normally develops into a structure reminiscent of the grain described here."," According to the model data, the plateau normally develops into a structure reminiscent of the grain described here."
" Also, both the observed size of the vortex tube, measured from the BGL to the intergranular lane (0.8 Mm) and the distance between the BGL and the grain (0.3 Mm) closely match the model data."," Also, both the observed size of the vortex tube, measured from the BGL to the intergranular lane (0.8 Mm) and the distance between the BGL and the grain (0.3 Mm) closely match the model data."
 Figure 3. shows three images of the above event as seen in and TiO spectral lines., Figure \ref{tio_ha_vt} shows three images of the above event as seen in and TiO spectral lines.
" The left panel is a -- nm image, while the right panel shows a |0.07 nm image taken nearly 1 min later."," The left panel is a -0.1 nm image, while the right panel shows a +0.07 nm image taken nearly 1 min later."
 The middle panel is a TiO image at 17:55:32U UT., The middle panel is a TiO image at 17:55:32U UT.
 The faint white contours are the same in all three images and they are intended to facilitate the comparison between all three panels., The faint white contours are the same in all three images and they are intended to facilitate the comparison between all three panels.
" The contours encircle the darkest TiO features, and they also show that the co-aliment between the TiO and data sets Is not worse than 3 pixels or 0"".11."," The contours encircle the darkest TiO features, and they also show that the co-aliment between the TiO and data sets is not worse than 3 pixels or 0”.11."
 Note that the short ticks separate 10 pixel intervals., Note that the short ticks separate 10 pixel intervals.
" The field of view of these images is «15"" or «11 Mm.", The field of view of these images is $\times$ 15” or $\times$ 11 Mm.
" We note that both the BGL and the grain can be identified in all three images, which means that the vortex-tube signatures are present in the lower chromosphere."," We note that both the BGL and the grain can be identified in all three images, which means that the vortex-tube signatures are present in the lower chromosphere."
" Also, this event was associated with a faint chromospheric darkening in the blue Ha0.1 nm, image (left panel), not present in the red shifted, Ha|0.07 nm, image (right panel), which indicates that the absorption features accompanying vortex-tube events are chromospheric upflows."," Also, this event was associated with a faint chromospheric darkening in the blue $\alpha - 0.1$ nm, image (left panel), not present in the red shifted, $\alpha + 0.07$ nm, image (right panel), which indicates that the absorption features accompanying vortex-tube events are chromospheric upflows."
" The event shown in Figures 1 and 3 can be characterized as an exemplary event, meaning that the BGL has a nearly ideal semi-circular shape."," The event shown in Figures \ref{vt} and \ref{tio_ha_vt} can be characterized as an exemplary event, meaning that the BGL has a nearly ideal semi-circular shape."
" The majority of observed BGLs are less ideal and they may appear as a nearly straight line with (sometimes) jagged edges, especially in cases when two or three bright grains are present."," The majority of observed BGLs are less ideal and they may appear as a nearly straight line with (sometimes) jagged edges, especially in cases when two or three bright grains are present."
" At the peak of the BGL development, one or two jet-like darkenings, co-spatial with the BGL, may appear in the blue-shifted Hn images."," At the peak of the BGL development, one or two jet-like darkenings, co-spatial with the BGL, may appear in the blue-shifted $\alpha$ images."
 These absorption features seem to originate in the intergranular lane adjacent to the bright grain., These absorption features seem to originate in the intergranular lane adjacent to the bright grain.
 Figures 4--5 show three examples of chromopheric activity (i)-(iii) associated with the formation of a BGL., Figures \ref{ev1}- \ref{ev2} show three examples of chromopheric activity (i)-(iii) associated with the formation of a BGL.
 The first event began at 17:45:59 UT and lasted for about 100 s until 17:47:08 UT (Figure 4))., The first event began at 17:45:59 UT and lasted for about 100 s until 17:47:08 UT (Figure \ref{ev1}) ).
" The arrow in the 45:49 panel indicates the location of a BGL, which assumed a crescent-like shape and moved toward the center of a granule revealing a bright grain."," The arrow in the 45:49 panel indicates the location of a BGL, which assumed a crescent-like shape and moved toward the center of a granule revealing a bright grain."
" A single strand dark jet-like feature (i) began to develop at the same time and its intensity peaked at about 17:46:49 UT, while the 47:28 frame shows that chromospheric feature gone."," A single strand dark jet-like feature (i) began to develop at the same time and its intensity peaked at about 17:46:49 UT, while the 47:28 frame shows that chromospheric feature gone."
 The BGL features had faded out by about the same time., The BGL features had faded out by about the same time.
 The two bottom rows of Figure 4 show a second small-scale event immediately following the first one., The two bottom rows of Figure \ref{ev1} show a second small-scale event immediately following the first one.
" Frame 48:17 clearly shows that the newly developed feature is reminiscent of an inverted ""Y"" jet reported by Shibataetal.(2007).", Frame 48:17 clearly shows that the newly developed feature is reminiscent of an inverted “Y” jet reported by \cite{shibata2007}.
". This inverted ""Y"" feature (ii) had one footpoint co-spatial with the fading BGL, while the other one appeared to be rooted in the adjacent intergranular lane."," This inverted “Y” feature (ii) had one footpoint co-spatial with the fading BGL, while the other one appeared to be rooted in the adjacent intergranular lane."
" Figure 5 is an example of an extended BGL, where its shape is oblong rather than semi-circular."," Figure \ref{ev2} is an example of an extended BGL, where its shape is oblong rather than semi-circular."
" Similarly to other events, this BGL lane (arOWS in the 59:02 and 00:24 frames) shifted to the center of the granule giving way to a bright grain (lower arrow in the 00:24 panel), which is elongated in the direction of the BGL along the intergranular lane."," Similarly to other events, this BGL lane (arrows in the 59:02 and 00:24 frames) shifted to the center of the granule giving way to a bright grain (lower arrow in the 00:24 panel), which is elongated in the direction of the BGL along the intergranular lane."
" Starting at 17:03:50 UT, two small chromospheric darkenings (iii) began to intensify on either side of the elongated grain (04:20 frame) and these features asted for about 50 s. The three types of events (i)-(iii) discussed above are the most frequently observed types."," Starting at 17:03:50 UT, two small chromospheric darkenings (iii) began to intensify on either side of the elongated grain (04:20 frame) and these features lasted for about 50 s. The three types of events (i)-(iii) discussed above are the most frequently observed types."
" Other, although less numerous, BGL-jet events may include 2 or 3 absorption features, two simultaneous BGLs in one host granule and well-defined grains elongated in the direction perpendicular"," Other, although less numerous, BGL-jet events may include 2 or 3 absorption features, two simultaneous BGLs in one host granule and well-defined grains elongated in the direction perpendicular"
 , 
(e.tet?)Biueeeli.OO'Tareughi.&Saudage1990) Sugeooest that euvironmental influences tay play a key roleint 1e gas-loss process.,"\citep[e.g.,][]{BTS90} suggest that environmental influences may play a key role in the gas-loss process."
 Possible evolutior lexianisius include triggeredMD bursts of star formation with susequent blow-out of t1e ISM (e.g.Dekel&Silk1956)... or rani pressure strippiug of the ISM as he galaxy plunges {ηςieli the hot itra-cluster gas (e.g..Liun&Faber|L083).," Possible evolution mechanisms include triggered bursts of star formation with subsequent blow-out of the ISM \citep[e.g.,][]{DS86}, or ram pressure stripping of the ISM as the galaxy plunges through the hot intra-cluster gas \citep[e.g.,][]{LF83}."
. Both of these scenarios will result in an OveLleabuudauce o: dwarf elliptical galaxies in high density regious. but the restHine star formatio1 hisstories are equite different.," Both of these scenarios will result in an overabundance of dwarf elliptical galaxies in high density regions, but the resulting star formation histories are quite different."
 In a triggeredMD starbu‘st scenario. most of the star formation activi “wil take place in discrete events which uay be cor‘elatecl with passage througl the cluster.," In a triggered starburst scenario, most of the star formation activity will take place in discrete events which may be correlated with passage through the cluster."
 Ou tlthe [9]ver haul. if he ISM is lost throug1 ral pressure stripplug. most of the sar formation activitylv will take placὁ prior to tle passage through tve cluster. and. may OCCUL Ib a more quiescen laluer. typical o‘cls (vanZee2001).," On the other hand, if the ISM is lost through ram pressure stripping, most of the star formation activity will take place prior to the passage through the cluster, and may occur in a more quiescent manner, typical of dIs \citep{vZ01}."
. Thus. examuation of the stell: populatlous auc relative clenical enrichineits in cwarf eliptical egaaxies may provide insight ii which of hese inechanisimns is he dominant process for tle evolutio1 of ds to Es in high densi regions.," Thus, examination of the stellar populations and relative chemical enrichments in dwarf elliptical galaxies may provide insight into which of these mechanisms is the dominant process for the evolution of dIs to dEs in high density regions."
 Within the Local Stpercluster. the Virgo cluster is he nearest high deusity region aud thus provides an excellent environiielr in which to explore stelar populations ad kinematic properties ol low lulinosity galaxies.," Within the Local Supercluster, the Virgo cluster is the nearest high density region and thus provides an excellent environment in which to explore stellar populations and kinematic properties of low luminosity galaxies."
 At tlle same time. Virgo is dylalicalVY νοιι[n]0 fee.Tully al contallis several subsructural units (Biuggeliueeelieal.1987): ths. with a well selected saliple it jay be possibe to study the evolution of«bwarf ellitical galaxies within the cluster itself.," At the same time, Virgo is dynamically young \citep[e.g.,][]{TS84}
 and contains several substructural units \citep{BTS87}; thus, with a well selected sample it may be possible to study the evolution of dwarf elliptical galaxies within the cluster itself."
 Recent observations of Surface brielituess [letuatiois (Jerjeretal.2001) ave shown that the dE populatio is stretchec in depth similarly to the brieht elipical populatio (Neilsen&Blakeslee2000) out not as extelced as clClaimed previously by (1995).," Recent observations of surface brightness fluctuations \citep{JBB04} have shown that the dE population is stretched in depth similarly to the bright elliptical population \citep{NT00,WB00} but not as extended as claimed previously by \citet{YC95}."
. Furtlelmore. 1ucleated ¢Es appear to be 1iore strongly1 clustered {μα non-nucleated ¢Es in tlie cluster (eGee0BuMDcoelielal.1987).," Furthermore, nucleated dEs appear to be more strongly clustered than non-nucleated dEs in the cluster \citep[e.g.,][]{BTS87}."
. In this paper. W'e examine broad bancl optical colors aud optical syectroscopy Of 16 dwarf elliptical galaxies in the Vireo Cluster to investigate their star [formatioi histories ancl to search for correlations beween kinematic properties auc past star formation activity.," In this paper, we examine broad band optical colors and optical spectroscopy of 16 dwarf elliptical galaxies in the Virgo Cluster to investigate their star formation histories and to search for correlations between kinematic properties and past star formation activity."
 The sixteen galaxies in this sample were selected as part of a kinematic stiον oL dwart ellipical galaxies in Virgo (vanZeeetal.200 1):: approximately half of the sample have a significant rotaticla COonupolieM., The sixteen galaxies in this sample were selected as part of a kinematic study of dwarf elliptical galaxies in Virgo \citep{vSH04}; ; approximately half of the sample have a significant rotational component.
" As discussec Lin vanZeeetal.(200L).. ois likely that the rotating dwarf elliptical galaxies are remunauts of «ls hat have een stripped of t1eir gas: the rotating dwarl elliptical galaxies tend to be located ue:uw the outskiris of the cluster aid their rotation curves aud ανά amplitude velocities afe Conparable to siαλα luminosity dw""ar irregular galaxies."," As discussed in \citet{vSH04}, it is likely that the rotating dwarf elliptical galaxies are remnants of dIs that have been stripped of their gas; the rotating dwarf elliptical galaxies tend to be located near the outskirts of the cluster and their rotation curves and maximum amplitude velocities are comparable to similar luminosity dwarf irregular galaxies."
 At the same time. the origin of the non-rotatiig dwarf elli)icals is unclear.," At the same time, the origin of the non-rotating dwarf ellipticals is unclear."
 A'e these low luminosity galaxies which began with little-to-no augular moment, Are these low luminosity galaxies which began with little-to-no angular momentum?
 Wwere they formed through the collision of even lower mass galaxies aud thus euded ip with no el aigular luolnelrtun?, Were they formed through the collision of even lower mass galaxies and thus ended up with no net angular momentum?
 Did they trausler their angular momenttin as they moved tlrough the «ense cluser?, Did they transfer their angular momentum as they moved through the dense cluster?
 Iu support of the latter process. have shown tha “tidal stirriug — or repeated tidal shocks sullered by cdwarf satellite galaxies — cal remove the cinematic signature f‘on a low ass galaxy without signiflicaut. alteration of its stellar distribution.," In support of the latter process, \citet{Me01a,Me01b} have shown that “tidal stirring” – or repeated tidal shocks suffered by dwarf satellite galaxies – can remove the kinematic signature from a low mass galaxy without significant alteration of its stellar distribution."
 While it is diffieut todistinguish between these scenarios based on the data, While it is difficult todistinguish between these scenarios based on the data
to three-body systems.,to three-body systems.
" In Table 2 we list some statistics of our 10"") vear integration based on 36.55n day output intervals in astrocentric coordinates.", In Table 2 we list some statistics of our $10^6$ year integration based on 36.5 day output intervals in astrocentric coordinates.
 Superscripts min and mere refer to the minimum ancl maximum values achieved. respectively.," Superscripts $min$ and $max$ refer to the minimum and maximum values achieved, respectively."
 Clearly (he actual diauiaamies of this svstem depend on (he presence and properties of planet b. aud. in principle. anv additional unconfirmed planets. but without better data on these objects. Table 2 is the best available characterization of the orbital evolution of these (wo planets.," Clearly the actual dynamics of this system depend on the presence and properties of planet b, and, in principle, any additional unconfirmed planets, but without better data on these objects, Table 2 is the best available characterization of the orbital evolution of these two planets."
 They may also be used (to evaluate (he origins scenarios deseribed in the following two sections., They may also be used to evaluate the origins scenarios described in the following two sections.
 D is à distant M4.5. 0.2 M. companion star to A (Lowrance 2002: AleArthur 2010).," B is a distant M4.5, 0.2 $\msun$ companion star to A (Lowrance 2002; McArthur 2010)."
 Its orbit can not be estimated. vet. hence we do not know if it is eravitationally bound. (Patience > 2 1*7: 107: and 1 case out of the 13.200 reached Ψ=34°.," Its orbit can not be estimated yet, hence we do not know if it is gravitationally bound (Patience >; 26 with $\Psi^{max}
> 10^\circ$ ; and 1 case out of the 13,200 reached $\Psi^{max} =
34^\circ$."
 The 192 non-planar cases were spread throughout. parameter space. wilh no significant clustering.," The 192 non-planar cases were spread throughout parameter space, with no significant clustering."
 To explore effectis on longer üimescales. we integrated 20 cases to 1 Gyr.," To explore effects on longer timescales, we integrated 20 cases to 1 Gyr."
 Four of the previous simulations (hat had led to significant. mutual inclinations (including that which led to ψ*= 347) were tested. in order to examine stability.," Four of the previous simulations that had led to significant mutual inclinations (including that which led to $\Psi^{max} =
34^\circ$ ) were tested, in order to examine stability."
 The other 16 were chosen from among those in which !ye’ saved <1° over 250 orbits of D. in order to determine if mutual inclinations could develop over longer timescales.," The other 16 were chosen from among those in which $\Psi^{max}$ stayed $<1^\circ$ over 250 orbits of B, in order to determine if mutual inclinations could develop over longer timescales."
 We find that most of these simulations. in fact. ejected a planet.," We find that most of these simulations, in fact, ejected a planet."
 Therefore the orbit of, Therefore the orbit of
(PPM. Rosser et al.,"(PPM, Rösser et al.,"
 1993) as relereuce system. aud also with the HST unpublished result. of Iwallivayalil et al. (," 1993) as reference system, and also with the HST unpublished result of Kallivayalil et al. ("
2005). who used QSOs as reference system.,"2005), who used QSOs as reference system."
 On the other hand. there still is a siguilicaut discrepaney with ALP’s result in Decl.," On the other hand, there still is a significant discrepancy with ALP's result in Decl."
 We will further discuss this issue in 36., We will further discuss this issue in 6.
 Iu Table 9 we have not included a recent determination of the LACs PM by Momauy Zageia (2005) using the USNO CCD Astroeraph all-sky Catalog (UCAC2. Zacharias et al.," In Table 9 we have not included a recent determination of the LMC's PM by Momany Zaggia (2005) using the USNO CCD Astrograph all-sky Catalog (UCAC2, Zacharias et al."
 2001). because. as confirmed by the errors declared by the authors themselves (73 ) imas in both coordinates). the internal accuracy of their methodology is uot comparable with ours.," 2004), because, as confirmed by the errors declared by the authors themselves $\sim$ 3 mas in both coordinates), the internal accuracy of their methodology is not comparable with ours."
 Numerous tests carried out by our group. favor the use of fiducial reference points in combination with a LBS defined by relatively few. well studied (bona-fide members. free of contamination rom neighboring stars. good etc.)," Numerous tests carried out by our group, favor the use of fiducial reference points in combination with a LRS defined by relatively few, well studied (bona-fide members, free of contamination from neighboring stars, good signal-to-noise, etc.)"
 LMC stars. to determine a PM of this nature.," LMC stars, to determine a PM of this nature."
 Interestingly. their result. [fi cos. 415] ~ [40.804L32] mas J| is in reasonable agreement with that of ALP.," Interestingly, their result $\mu_{\alpha}$ $\delta$ $\mu_{\delta}$ ] $\sim$ [+0.84,+4.32] mas $^{-1}$ is in reasonable agreement with that of ALP."
 Combining the components given in the last entry of Table 9. we derive a total LMC PM of po = (42.040.1) mas vet. with a position angle of 0 = 143.1) . Ineasurecl eastward [rom the mevriciau joiniug the center of the LMC to the north celestial pole.," Combining the components given in the last entry of Table 9, we derive a total LMC PM of $\mu$ = $+$ $\pm$ 0.1) mas $^{-1}$, with a position angle of $\theta$ = $\pm$ $^\circ$, measured eastward from the meridian joining the center of the LMC to the north celestial pole."
 This result is compatible (particularly the ΟΛΕΣ absolute value) with theoretical models (Gardiner et al., This result is compatible (particularly the PM's absolute value) with theoretical models (Gardiner et al.
 1991). which predict a PM for the LMC in the range 1.5-2.0 mas +. with a position angle of907.," 1994), which predict a PM for the LMC in the range $-$ 2.0 mas $^{-1}$, with a position angle of."
 Usiug the PM of the LMC determined in 3.) and tlie radial velocity of the center of the LMC (adopted from the literature). we can calculate the radial and trausverse components of the velocity for the LMC. as seen from the center of the Galaxy. along with other parameters described below.," Using the PM of the LMC determined in 3, and the radial velocity of the center of the LMC (adopted from the literature), we can calculate the radial and transverse components of the velocity for the LMC, as seen from the center of the Galaxy, along with other parameters described below."
 To do this we basically followed the procedure outlined by Jones et al. (, To do this we basically followed the procedure outlined by Jones et al. (
199D).,1994).
" In the calculations we used as basic LALC parameters those given in Table 8 of ALP. aud assumed a rotational velocity vq = 20 kinsF and a radial velocity V, = 250 kms ! for the Iu order to determiue. [rom our measured PM values. the space velocity components of the LMC. aud its PM with respect to the Galactic Rest Frame (GRE). a series of steps were required."," In the calculations we used as basic LMC parameters those given in Table 8 of ALP, and assumed a rotational velocity $_{\Phi}$ = 50 km $^{-1}$ and a radial velocity $_r$ = 250 km $^{-1}$ for the In order to determine, from our measured PM values, the space velocity components of the LMC, and its PM with respect to the Galactic Rest Frame (GRF), a series of steps were required."
 These include: 1., These include: 1.
 A correction to our ueasured PA values to account for the rotation of the plane of the LMC: 2., A correction to our measured PM values to account for the rotation of the plane of the LMC; 2.
 A transformation of he corrected PM into trausverse velocity components with respect the the center of the LMC. tve Sun. the LSR aud the center of the Galaxy: both in the equatorla uil galactic coordinate systems.," A transformation of the corrected PM into transverse velocity components with respect the the center of the LMC, the Sun, the LSR and the center of the Galaxy; both in the equatorial and galactic coordinate systems."
 These trausverse velocities. in combination with the radial velocity of the center of the LIC (adopted (rom the literature). allowed us to derive the components of the space velocity of the LAC corrected Lor the Stu's peculiar motion relative to the ΤΗ. aud also corrected for the velociv of the LSHR itself. relative to the center of the Galaxy.," These transverse velocities, in combination with the radial velocity of the center of the LMC (adopted from the literature), allowed us to derive the components of the space velocity of the LMC corrected for the Sun's peculiar motion relative to the LSR, and also corrected for the velocity of the LSR itself, relative to the center of the Galaxy."
 The above calculatious were made using an «d—hoc computer program. developed by oue of the authorW. (MHP). which generates results consistent. with those [rom an iudependeut software (Piatek. 2005: private," The above calculations were made using an $ad-hoc$ computer program, developed by one of the authors (MHP), which generates results consistent with those from an independent software (Piatek, 2005; private"
These models have been analvzed in detail bv Ixassiola&Ixovner(1993). and by IXormann. Schneider. ancl Bartelmann (1994).,"These models have been analyzed in detail by \citet{kk93}
 and by Kormann, Schneider, and Bartelmann (1994)."
 Particularly convenient formulas are given by &Ixochanek (1998)., Particularly convenient formulas are given by \citet{kk98}.
. We refer the reader to these papers for analvtic lensing potential expressions and for detailed discussions of the models. lensing behavior., We refer the reader to these papers for analytic lensing potential expressions and for detailed discussions of the models' lensing behavior.
 Wherever numerical solution of (he lens equation (2)) is needed. we use our own implementation of (he grid-based nunmerical lens-equation solution algorihm with 2D Newton-method solution refinement described bv Schneider.Ehlers.&Falco(1992).," Wherever numerical solution of the lens equation \ref{lens_eq}) ) is needed, we use our own implementation of the grid-based numerical lens-equation solution algorithm with 2D Newton-method solution refinement described by \citet{sef92}."
. The simplest reasonable model for an extended astroplvsical mass distribution is the familiar singular isothermal sphere(SIS)., The simplest reasonable model for an extended astrophysical mass distribution is the familiar singular isothermal sphere.
.. It is parametrizecl solely by ils velocity dispersion σι., It is parametrized solely by its velocity dispersion $\sigma_v$.
 The scaled. projected mass distribution (convergence) of the SIS is given bv IIere. X is the physical surface mass density of the lens and X4=(62/4xzC)6Da4/DiDia) is the so-called. critical surface mass densitv.," The scaled, projected mass distribution (convergence) of the SIS is given by Here, $\Sigma$ is the physical surface mass density of the lens and $\Sigma_{\mathrm{cr}} = (c^2 / 4 \pi G)
(D_{\mathrm{S}} / D_{\mathrm{L}} D_{\mathrm{LS}})$ is the so-called critical surface mass density."
" £j is the “Einstein radius"" that sets the sole angular scale of the mocdel for given lens and source redshifts: The lensing potential of the SIS is simply ο(0)=0/8."," $\theta_{\mathrm{E}}$ is the “Einstein radius” that sets the sole angular scale of the model for given lens and source redshifts: The lensing potential of the SIS is simply $\psi(\vec{\theta}) = \theta_{\mathrm{E}}
| \vec{\theta} |$."
 We can obtain o(fGai.Maya) for the SIS analvtically.," We can obtain $\sigma(\mu_{\mathrm{min}}, \Delta t_{\mathrm{max}})$ for the SIS analytically."
 Hf the angular distance > from the source (1.e.. SN) position to the lens center is less than θε. lwo images will be observed along a line on (he sky through the source position and the lens center: one al a distance £j+9 from the lens center (in the direction of (he source) with magnification 1+):/ and one at a distance 6j;—3 (n the direction opposite the source) with magnilication 1—65/5 (NaravanBartelmann1996.lor exaanple)..," If the angular distance $\beta$ from the source (i.e., SN) position to the lens center is less than $\theta_{\mathrm{E}}$, two images will be observed along a line on the sky through the source position and the lens center: one at a distance $\theta_{\mathrm{E}} + \beta$ from the lens center (in the direction of the source) with magnification $1 + \theta_{\mathrm{E}} / \beta$ and one at a distance $\theta_{\mathrm{E}} - \beta$ (in the direction opposite the source) with magnification $1 - \theta_{\mathrm{E}} / \beta$ \citep[for example]{nb96}."
 This second. fainter image corresponds to a saddle point of the arrival me function (1)): ils negative magnification signals a reversal of image parity.," This second, fainter image corresponds to a saddle point of the arrival time function \ref{arrival_time}) ); its negative magnification signals a reversal of image parity."
" It is this magnification that determines the fni, dependence of e(t.Mas) as defined."," It is this magnification that determines the $\mu_{\mathrm{min}}$ dependence of $\sigma(\mu_{\mathrm{min}}, \Delta t_{\mathrm{max}})$ as defined."
 If we substitute the solutions 9j+9% into (1)) (taking into account vectorial considerations) and form the difference. we find that the time clelav between the two images is," If we substitute the solutions $\theta_{\mathrm{E}} \pm \beta$ into \ref{arrival_time}) ) (taking into account vectorial considerations) and form the difference, we find that the time delay between the two images is"
"where X, scales as 1?2 from (7)) and for grains with ©=©,.",where $\Sigma_g$ scales as $R^{-\frac32}$ from \ref{sigr}) ) and for grains with $\phi=\phi_c$.
 For the dise model we have chosen in Sec., For the disc model we have chosen in Sec.
 2.2..," 2.2.,"
" we find lor ὁ=©, Lad that portion of the disk where this quantity is less (han 1 in the Epstein drag regime. the inward transport. prevents the grains from growing above 7 =Q!."," we find for $\phi=\phi_c$ that In that portion of the disk where this quantity is less than $1$ in the Epstein drag regime, the inward transport prevents the grains from growing above $\tau=\Omega^{-1}$."
"For our canonical disc parameters this occurs everywhere that 7=ο! occurs for Epstein drag (ie. 27H,,).", For our canonical disc parameters this occurs everywhere that $\tau=\Omega^{-1}$ occurs for Epstein drag (i.e. $R>R_{tp}$ ).
" Because the time seale (o reach ©, is an increasing funetion of. R while the total mass contained within an annulus of width 4H is a decreasing [nnction of 22. changes in X, as the dust [alls inward do not alter the basic conclusion."," Because the time scale to reach $\phi_c$ is an increasing function of $R$ while the total mass contained within an annulus of width $dR$ is a decreasing function of $R$, changes in $\Sigma_d$ as the dust falls inward do not alter the basic conclusion."
" Increasing X, increases the triple point {πρ of (Eq. (36)))", Increasing $\Sigma_g$ increases the triple point $R_{tp}$ of (Eq. \ref{RTriple}) ))
" and increasing the ratio X,/X, decreases the radius where (47)) drops below unity.", and increasing the ratio $\Sigma_g/\Sigma_d$ decreases the radius where \ref{epgrowth}) ) drops below unity.
" Thus the critical radius above which planetesimal growth is prevented is indeed It, Ehe effect remains important if the basic disc parameters are altered. but the radius of the triple point and ancl the critical radius where (47)) drops below unity and the triple point radius (36)) can change."," Thus the critical radius above which planetesimal growth is prevented is indeed $R_{tp}$ The effect remains important if the basic disc parameters are altered, but the radius of the triple point and and the critical radius where \ref{epgrowth}) ) drops below unity and the triple point radius \ref{RTriple}) ) can change."
 The important upshot of the effect just described is that gravitational instability cannot be easily reached at radii larger (han the triple point. (discussed im section 5.1) of the curve without additional physics like vortices. or a significantly different disc model.," The important upshot of the effect just described is that gravitational instability cannot be easily reached at radii larger than the triple point (discussed in section 5.1) of the $\tau=\Omega^{-1}$ curve without additional physics like vortices, or a significantly different disc model."
 II is interesting. if not unsurprising in hindsight. (hat the drag induced grain agelomeralion benelit [rom vortices (Barge&Sonuneria1995) is maximized for the same 7=Q! condition that gives the maximal infall speed we found fom (44)).," It is interesting, if not unsurprising in hindsight, that the drag induced grain agglomeration benefit from vortices \citep{Barge95} is maximized for the same $\tau = \Omega^{-1}$ condition that gives the maximal infall speed we found from \ref{vr}) )."
 The conclusions drawn from (47)) and the limits on p Irom Fig. (9)), The conclusions drawn from \ref{epgrowth}) ) and the limits on $p$ from Fig. \ref{HWrc}) )
 are essentially independent of a because its effects on c. and Jy in Eq. (2)), are essentially independent of $\alpha$ because its effects on $v_c$ and $H_d$ in Eq. \ref{main}) )
 for (he relevant regimes cancel., for the relevant regimes cancel.
 This allows us to use Fie. (9)), This allows us to use Fig. \ref{HWrc}) )
 to constrain our sticking parameter. indepedent of a (at least for HR« SAU).," to constrain our sticking parameter, indepedent of $\alpha$ (at least for $R<8AU$ )."
 This makes our constrains on a more meaninglul., This makes our constrains on $\alpha$ more meaningful.
 Our model ends at the point when gravitational instabiliies take over., Our model ends at the point when gravitational instabilities take over.
 We have calculated whether gravitational enhancement (to dust-dust collisions plavs any role before that time., We have calculated whether gravitational enhancement to dust-dust collisions plays any role before that time.
 We find the effect to be small (tvpically under 5%) for all but the largest a even lor the largest scale dust., We find the effect to be small (typically under $5\%$ ) for all but the largest $\alpha$ even for the largest scale dust.
"from the core, which responds by contracting in a vain attempt to find equilibrium (Lynden-Bell&Eggleton1980).","from the core, which responds by contracting in a vain attempt to find equilibrium \citep{lynden-bell80}."
". 'The evolutionary timescale is approximately the half-mass relaxation time, where R; is the half-mass radius, N the number of stars, and m the mean stellar mass."," The evolutionary timescale is approximately the half-mass relaxation time, where $R_{h}$ is the half-mass radius, $N$ the number of stars, and $m$ the mean stellar mass."
" We take as the argument in the Coulomb logarithm =0.02, appropriate for our mass function (Giersz&Heggie1996)."," We take as the argument in the Coulomb logarithm $\gamma = 0.02$, appropriate for our mass function \citep{giersz96}."
". Core collapse of a Plummer sphere with equal masses takes place after about 15 trn, although the presence of a mass function accelerates the collapse as mass segregation drives the massive stars to the core."," Core collapse of a Plummer sphere with equal masses takes place after about 15 $t_{rh}$, although the presence of a mass function accelerates the collapse as mass segregation drives the massive stars to the core."
" Once there, the mass-segregation instability (Spitzer1969) drives the core to collapse faster than in the equal-mass case, and core collapse occurs at less than a relaxation time (Gürkanetal.2004)."," Once there, the mass-segregation instability \citep{spitzer69} drives the core to collapse faster than in the equal-mass case, and core collapse occurs at less than a relaxation time \citep{gurkan04}."
". For our 1k systems, the initial relaxation time is trn,o&:32."," For our 1k systems, the initial relaxation time is $t_{rh,0} \approx 32$."
" Core collapse occurs at about tec&27, after which binaries in the core drive the expansion by heating their surroundings as they harden."," Core collapse occurs at about $t_{cc} \approx 27$, after which binaries in the core drive the expansion by heating their surroundings as they harden."
" As two-body relaxation conducts this heat outwards, the cluster expands in response on the relaxation timescale."," As two-body relaxation conducts this heat outwards, the cluster expands in response on the relaxation timescale."
" This expansion is approximately self-similar, and the post core-collapse evolution can be reasonably described by where rr, is someLagrangian radius."," This expansion is approximately self-similar, and the post core-collapse evolution can be reasonably described by where $r_L$ is someLagrangian radius."
" For the half-mass radius itself, one can analytically show that 6=2/3, and while this value fits well interior to the half-mass radius, the outer radii expand with a slightly steeper power over the length of time we simulate."," For the half-mass radius itself, one can analytically show that $\delta=2/3$, and while this value fits well interior to the half-mass radius, the outer radii expand with a slightly steeper power over the length of time we simulate."
" The factor χ depends on the cluster mass function; Gielesetal.(2010) give 0.1(Mmax/m)°"", which we use here to find xzz1.15."," The factor $\chi$ depends on the cluster mass function; \citet{gieles10b} give $\chi \approx 0.1(m_{max}/\bar{m})^{0.7}$ , which we use here to find $\chi \approx 1.15$."
" In figure 1 we plot, in addition to the Lagrangian radii, the time of formation and radius in the cluster of all the binaries that are present at the end of the simulation."," In figure \ref{1024lagr} we plot, in addition to the Lagrangian radii, the time of formation and radius in the cluster of all the binaries that are present at the end of the simulation."
" While we identify the final binaries at the end of the simulation (t=5x103 for the 1k runs), we only plot those binaries that formed before t=2.5x10*, guaranteeing that they are truly long-lived binaries and not a transient population."," While we identify the final binaries at the end of the simulation $t = 5 \times 10^4$ for the 1k runs), we only plot those binaries that formed before $t = 2.5 \times 10^4$, guaranteeing that they are truly long-lived binaries and not a transient population."
 This population of binaries is referred to throughout the paper as ‘permanent’., This population of binaries is referred to throughout the paper as `permanent'.
" There are two clear populations; those that form in the center of the cluster and that are supplying the energy to drive the cluster expansion, and a class of wide binaries that form in the outskirts of the cluster."," There are two clear populations; those that form in the center of the cluster and that are supplying the energy to drive the cluster expansion, and a class of wide binaries that form in the outskirts of the cluster."
 These are the soft binaries that primarily concern us here., These are the soft binaries that primarily concern us here.
" In figure 2 we plot the distribution of semi-major axes for the permanent binaries, and the spectrum of binary energies for three sets of binaries."," In figure \ref{1024semidist} we plot the distribution of semi-major axes for the permanent binaries, and the spectrum of binary energies for three sets of binaries."
 The black energy histogram shows the permanent binaries; the medium gray histogram shows all binaries (i.e. bound nearest neighbours) at t=2.5x10* regardless of their eventual permanence or destruction (the ‘instantaneous’ binary population); and the lightest gray shows the distribution of all bound pairs at t=2.5x10* regardless of their proximity (the ‘statistical’ binary population)., The black energy histogram shows the permanent binaries; the medium gray histogram shows all binaries (i.e. bound nearest neighbours) at $t = 2.5 \times 10^4$ regardless of their eventual permanence or destruction (the `instantaneous' binary population); and the lightest gray shows the distribution of all bound pairs at $t = 2.5 \times 10^4$ regardless of their proximity (the `statistical' binary population).
 The latter two populations will be discussed in the following section., The latter two populations will be discussed in the following section.
" The final distributions are characterized, as Kouwenhovenetal.(2010) pointed out, by a peak of hard binaries at small semi-major axes, and a peak at large separations which is the focus of that work and this one."," The final distributions are characterized, as \citet{kouwenhoven10} pointed out, by a peak of hard binaries at small semi-major axes, and a peak at large separations which is the focus of that work and this one."
" The borderline between a hard and soft binary is a&s~R,N7', and so evolves with time in the same sense as the cluster expansion."," The borderline between a hard and soft binary is $a_{h-s} \sim R_v N^{-1}$, and so evolves with time in the same sense as the cluster expansion."
 When plotted as their energy spectrum they are revealed as a distribution that rises smoothly towards low binding energy., When plotted as their energy spectrum they are revealed as a distribution that rises smoothly towards low binding energy.
 The relation between these three populations can be seen in figure 2.., The relation between these three populations can be seen in figure \ref{1024semidist}.
" The statistical population extends to the lowest energies, bounded only by the size of the cluster."," The statistical population extends to the lowest energies, bounded only by the size of the cluster."
 The instantaneous population is further restricted by the definition that the stars need to be nearest neighbours., The instantaneous population is further restricted by the definition that the stars need to be nearest neighbours.
 At late times the difference between the instantaneous and permanent populations is only clear at the softest energies., At late times the difference between the instantaneous and permanent populations is only clear at the softest energies.
" In a star cluster with a Maxwellian velocity distribution, any two stars have a statistical chance of having instantaneously negative relative energy."," In a star cluster with a Maxwellian velocity distribution, any two stars have a statistical chance of having instantaneously negative relative energy."
" In an infinite, uniform distribution of stars, there is a population of soft binaries at all energies, maintained by detailed balance as stars are perturbed into and out of bound states."," In an infinite, uniform distribution of stars, there is a population of soft binaries at all energies, maintained by detailed balance as stars are perturbed into and out of bound states."
" While an individual binary is a transient object, the statistical distribution is steady; this has been known for a long time (Heggie 1975).."," While an individual binary is a transient object, the statistical distribution is steady; this has been known for a long time \citep{heggie75}. ."
" The simple statistics that describe the very soft energies become complicated when one moves closer to the hard-soft border,"," The simple statistics that describe the very soft energies become complicated when one moves closer to the hard-soft border,"
equal to half the local radius of the cone. whereas the dashed ine is for a ENIM twice as large.,"equal to half the local radius of the cone, whereas the dashed line is for a FWHM twice as large."
 Because of the radial motion of the gas. thicker walls result in wider lines.," Because of the radial motion of the gas, thicker walls result in wider lines."
 This simulation can be compared. with the spectrum of Fig., This simulation can be compared with the spectrum of Fig.
 2 aken from the core (top spectral plot)., \ref{oiiispec} taken from the core (top spectral plot).
 In Fig., In Fig.
 7 à model image of a wedge is shown with the observed. MES. iimage for comparison., \ref{modim} a model image of a wedge is shown with the observed MES image for comparison.
 The agreement ids very good. considering the simplicity of this kinematic model.," The agreement is very good, considering the simplicity of this kinematic model."
 Phe main dillerences arise [rom not taking into account the central point source which produces a bright core at the vertex of the cone and a bright feature in the Ilongslit spectrum., The main differences arise from not taking into account the central point source which produces a bright core at the vertex of the cone and a bright feature in the longslit spectrum.
 Lence. spectra produced from cuts through the model cone considerably closer to the core would not be expected. to agree with the observed spectra.," Hence, spectra produced from cuts through the model cone considerably closer to the core would not be expected to agree with the observed spectra."
 However. at. (roughly 2 widths of the point spread function) we can expect a very. reduced. inlluence of the core emission. which alfects mainl« the height ratio of the spectral cone components.," However, at (roughly 2 widths of the point spread function) we can expect a very reduced influence of the core emission, which affects mainly the height ratio of the spectral cone components."
 1n our model. the height ratio is determined mainly by the emissivity variation along the axis of the cone.," In our model, the height ratio is determined mainly by the emissivity variation along the axis of the cone."
 Varving the parameters like the outllow: velocity. the EAWHIAL of the emissivity along the axis. the opening angle or the angle to the line of sight will produce results consistent with the observations with ranges of approximately. plus or minus Ar=30 |. ANEWIIM. —20 pe. Aa=2deg. and AO=5deg. respectively.," Varying the parameters like the outflow velocity, the FWHM of the emissivity along the axis, the opening angle or the angle to the line of sight will produce results consistent with the observations with ranges of approximately plus or minus $\Delta v$ =30 , $\Delta{\rm
FWHM}_z$ =20 pc, $\Delta\alpha=2\deg$, and $\Delta\theta=5\deg$, respectively."
 Based on this model. we suggest that in NGC 4051 the wwedge represents a radial conical outllow with a hall opening angle near aancl a velocity of approximately aab an angle to the line of sight of roughly," Based on this model, we suggest that in NGC 4051 the wedge represents a radial conical outflow with a half opening angle near and a velocity of approximately at an angle to the line of sight of roughly."
 Note that in the two-component fit to the spectrum in Fig. 2..," Note that in the two-component fit to the spectrum in Fig. \ref{oiiispec},"
 the component which is bluc-shifted most &racually moves towards the svstemic radial velocity and broadens as the core of the galaxy is approached., the component which is blue-shifted most gradually moves towards the systemic radial velocity and broadens as the core of the galaxy is approached.
 This does. of course. not happen in our model and may be due to a significant contribution of the redder line to the Gaussian fit of the bluer one.," This does, of course, not happen in our model and may be due to a significant contribution of the redder line to the Gaussian fit of the bluer one."
 Unfortunately. the data quality does not allow a well constrained three component fit to separate the core component [rom the cone components.," Unfortunately, the data quality does not allow a well constrained three component fit to separate the core component from the cone components."
 An alternative reason for this line shift may be that the cone does not have straight sides and may even change direction closer to the centre of the galaxy., An alternative reason for this line shift may be that the cone does not have straight sides and may even change direction closer to the centre of the galaxy.
 This could also be combined with inhomogeneities in the cone wall., This could also be combined with inhomogeneities in the cone wall.
 An observational indication of this is the position angle of the inner radio source. which is noticeably cülferent. from. the outer one and the structure of the emission line gas in the HS'T-image (compare Fig.," An observational indication of this is the position angle of the inner radio source, which is noticeably different from the outer one and the structure of the emission line gas in the HST-image (compare Fig."
 and 4)).,\ref{vband} and \ref{hst}) ).
 However. these," However, these"
white dwarts (recognizablefromZecmansplitspectrallines.Liebertetal.2003:INawka 2007).. another orien nav also be necessary. possibly as proposed by Toutetal.(2005).,"white dwarfs \citep[recognizable from
Zeeman split spectral lines,][]{liebert03,kawka07}, another origin may also be necessary, possibly as proposed by \citet{tout08}."
 Dynamo-type mechanisius have also been proposed to explain the putative weak magnetic field in the pulsating DD white dwarf CD 358 (Alarkicletal.1991:Thomasetal. 1995).," Dynamo-type mechanisms have also been proposed to explain the putative weak magnetic field in the pulsating DB white dwarf GD 358 \citep{markiel94,thomas95}."
. Tlowever. if is quite uulikelv that such uechanisuis could account for a field as hieh as 1.2 ALG in he carbonaich atinosphere of SDSS J1126|5752. or iu a white dwarf iu general.," However, it is quite unlikely that such mechanisms could account for a field as high as 1.2 MG in the carbon-rich atmosphere of SDSS J1426+5752, or in a white dwarf in general."
 Indeed. to produce a dyiauuo-ype maguetic field. convective motions must be strong enough to twist and move seed magnetic lines.," Indeed, to produce a dynamo-type magnetic field, convective motions must be strong enough to twist and move seed magnetic lines."
 As the fell grows. due to dynamo amplification. couvection is having a harder tine to move the field lines.," As the field grows, due to dynamo amplification, convection is having a harder time to move the field lines."
" Thus. he final large-scale field can never reach an amplitude comparable to the so-called equipartition feld streneth eiven by the coucdition Be,Sr=1/2<per,.>. where he last term correspouds to a suitable average over the convection zone of the convective cucrey density."," Thus, the final large-scale field can never reach an amplitude comparable to the so-called equipartition field strength given by the condition $B_{eq}^2/8\pi = 1/2 ~ <\rho ~ v_{conv}^2>$, where the last term corresponds to a suitable average over the convection zone of the convective energy density."
 Typical values of D44. calculated for IL. Που aud even C-atinosphere white dwarfs by Foutaineetal.(1973) are ~ 10-100 kG. While these results need to be revisited. in particular using a state-ofthe art model for SDSS J11261|5752. it would be extremely surprising to find that the order of magnitude estimates of Foutaineetal.(1973). could change siguificautly.," Typical values of $B_{eq}$, calculated for H-, He- and even C-atmosphere white dwarfs by \citet{fontaine73} are $\sim$ 10-100 kG. While these results need to be revisited, in particular using a state-of-the art model for SDSS J1426+5752, it would be extremely surprising to find that the order of magnitude estimates of \citet{fontaine73} could change significantly."
 We thus believe that the 1.2 MIG magnetic field. found. iu SDSS J1126|5752 is a fossil field. probably originating from an Ap star.," We thus believe that the 1.2 MG magnetic field found in SDSS J1426+5752 is a fossil field, probably originating from an Ap star."
 To date. there is no clear evidence for the presence of an observable maguetie field i anv of the kuown pulsating white dwarts.," To date, there is no clear evidence for the presence of an observable magnetic field in any of the known pulsating white dwarfs."
 None of the 51 bright ZZ Ceti stars from the Berecrou sample show anv sign of Zecman splitting iu the optical spectra. which translates. eiven the typical S/N ratio aud resolution of the observations. to limits on the maenetic field streneth of about 500 kC (P. Bergeron. private conmmunication).," None of the 51 bright ZZ Ceti stars from the Bergeron sample show any sign of Zeeman splitting in the optical spectra, which translates, given the typical S/N ratio and resolution of the observations, to limits on the magnetic field strength of about 500 kG (P. Bergeron, private communication)."
 Also. noue of the known pulsating DB white dwarfs have a maeguctic field strong chough to be detected from Zeeman splitting.," Also, none of the known pulsating DB white dwarfs have a magnetic field strong enough to be detected from Zeeman splitting."
 This is also the case for the 18 known pulsating white dwarts of the CAV Vir type., This is also the case for the 18 known pulsating white dwarfs of the GW Vir type.
 Iu order to detect weaker magnetic fields down to a few kC. spectropoluimetrie measurements are needed.," In order to detect weaker magnetic fields down to a few kG, spectropolarimetric measurements are needed."
" Unfortunately, only a siall προς of pulsating white dwarts have been investigated with this more precise method."," Unfortunately, only a small number of pulsating white dwarfs have been investigated with this more precise method."
 Nevertheless. no significant maeuetic field has ever been found in auyv of the few pulsating white dwarts for which spectropolarinetrie nieasurenieuts are available (Schiuidt&CanerL997:Valvavinetal.2006).. and very sinall upper Πιν of a few kG are obtained iu all cases (with perhaps an wucertain marginal detection Il one case).," Nevertheless, no significant magnetic field has ever been found in any of the few pulsating white dwarfs for which spectropolarimetric measurements are available \citep{schmidt97,valyavin06}, and very small upper limits of a few kG are obtained in all cases (with perhaps an uncertain marginal detection in one case)."
 The fact that the samples of magnetic aud. pulsating white dwarts do not intersect may not be very surprising from a theoretical poiut of view., The fact that the samples of magnetic and pulsating white dwarfs do not intersect may not be very surprising from a theoretical point of view.
 Iudeed. pulsating white dwarts of both the V?77 Ter aud ZZ Ceti types are found iu a regiue of effective temperature where au imuportant superficial couvectiou zone is present.," Indeed, pulsating white dwarfs of both the V777 Her and ZZ Ceti types are found in a regime of effective temperature where an important superficial convection zone is present."
" The latter is due to the partial ionization of either Te or IL aud contributes significantly to the excitation of pulsation modes,"," The latter is due to the partial ionization of either He or H, and contributes significantly to the excitation of pulsation modes."
 For a large scale maguetie field of magnitude much stronger than the equipartition field streneth. it is likely that the couvective motious are larecly queuched. which perhaps extinguishes completely pulsatioual driving.," For a large scale magnetic field of magnitude much stronger than the equipartition field strength, it is likely that the convective motions are largely quenched, which perhaps extinguishes completely pulsational driving."
" One example of a white dwarf where adnaenetic field (2B.=—1000+500κ,Putuey1997) nueht have “killed” the pulsations is the coustant DD star LB ss27 (PC0853]161.Wesemaeletal.2001)."," One example of a white dwarf where a magnetic field \citep[$B_e = -1000 \pm
500$ kG,][]{putney97} might have ”killed” the pulsations is the constant DB star LB 8827 \citep[PG~0853+164,][]{wesemael01}."
. Unfortunately. the effective temperature of this object is uncertain. auditis not kuown with certaity whether it is inside the DD instability strip or not.," Unfortunately, the effective temperature of this object is uncertain, and it is not known with certainty whether it is inside the DB instability strip or not."
 The only case where the detection of a magnetic field has beeu claimed im a pulsating white dwarf is that of GD 358., The only case where the detection of a magnetic field has been claimed in a pulsating white dwarf is that of GD 358.
 Iu that case. the maeuetic field has been indirectly inferred frou asteroscismological analysis (Wingetetal.1991).," In that case, the magnetic field has been indirectly inferred from asteroseismological analysis \citep{winget94}."
 It should be noted that this interpretation of the asteroseisnuological data iu ternis of a magnetic field is far from being accepted by all (sec. e.g.. Fontaine Brassard 2008. iu preparation).," It should be noted that this interpretation of the asteroseismological data in terms of a magnetic field is far from being accepted by all (see, e.g., Fontaine Brassard 2008, in preparation)."
 Iu any case. follow-up circular polarization nicasureimoeuts of GD 358 bv Scliuidt&(απο(1997). have uot succeeded i. detecting the presence of a weal field. but their detection threshold was significantly above the value of 1300 + 300 eauss sugeested by Wingetetal.(1991).," In any case, follow-up circular polarization measurements of GD 358 by \citet{schmidt97} have not succeeded in detecting the presence of a weak field, but their detection threshold was significantly above the value of 1300 $\pm$ 300 gauss suggested by \citet{winget94}."
. Such a sanall Seld is certainly not strong euoush to affect the convection zone significautlv. and is apparently unable to stop the pulsations iu this variable white dwarf.," Such a small field is certainly not strong enough to affect the convection zone significantly, and is apparently unable to stop the pulsations in this variable white dwarf."
 Iu this section. we briefly discuss the possibility that rotation might be a significant ingredient in this puzzle.," In this section, we briefly discuss the possibility that rotation might be a significant ingredient in this puzzle."
 Tudeed. rapid rotation is known to be important iu at least two variable maeuctic white dwarf svstcms where the variability is explained bv changes with rotational phase instead of pulsational instabilities.," Indeed, rapid rotation is known to be important in at least two variable magnetic white dwarf systems where the variability is explained by changes with rotational phase instead of pulsational instabilities."
 The first of these cases; RE JO317-853 (Barstowetal.1995:Burleighetal. 1999).. is a highly magnetic. rotating white chwart with a period of 725 s that is most probably the result of a double degenerate merger.," The first of these cases, RE J0317-853 \citep{barstow95, burleigh99}, is a highly magnetic, rotating white dwarf with a period of 725 s that is most probably the result of a double degenerate merger."
 The second case. Feige T (Liebertetal.1977).. is also a rotating magnetic white dwiuf but. this time. with a period of 2.2 hours.," The second case, Feige 7 \citep{liebert77}, is also a rotating magnetic white dwarf but, this time, with a period of 2.2 hours."
 Its spectrum shows Zeeman splitting for both bydrogeu and helimu that appears to vary with rotational phase (Achilleosetal.1992)., Its spectrum shows Zeeman splitting for both hydrogen and helium that appears to vary with rotational phase \citep{achilleos92}.
. Could it be that SDSS 1126|5752 is a rare maguctic white dwarf spinning very fast Qvhich would make it. with a period of 117 s. the fastest white dwarf amougst isolated white cwwarts)?," Could it be that SDSS J1426+5752 is a rare magnetic white dwarf spinning very fast (which would make it, with a period of 417 s, the fastest white dwarf amongst isolated white dwarfs)?"
 Several factors lead us to believe that. ou the contrary. tlis star is most likely a pulsator and uot a rotator.," Several factors lead us to believe that, on the contrary, this star is most likely a pulsator and not a rotator."
 The exposure tine for cach of our iutegratious at the MAIT (600 s) is well above the period of I17 s found bv Moutgoieryctal.(2008).. meaning that our spectra are averaged over a variability cycle.," The exposure time for each of our integrations at the MMT (600 s) is well above the period of 417 s found by \citet{montgomery08}, meaning that our spectra are averaged over a variability cycle."
 If the luminosity variations are due to fast rotation of the star. it is quite probable that the average magnetic field along our line of sight. depeudiug on the ecometry aud the aliguinent of the field with respect to the rotation axis or the presence of mmaeuctic spots. would vary over oue cvele.," If the luminosity variations are due to fast rotation of the star, it is quite probable that the average magnetic field along our line of sight, depending on the geometry and the alignment of the field with respect to the rotation axis or the presence of magnetic spots, would vary over one cycle."
 The resulting Zeeman splitting of atomic line should thus vary in magnitude as the fold strenetl changes. leading to verv broad or bleuded lines in our average spectra. not three well separated and sharp conrponeuts as observed (see bottom panels in Figure 1).," The resulting Zeeman splitting of atomic line should thus vary in magnitude as the field strength changes, leading to very broad or blended lines in our average spectra, not three well separated and sharp components as observed (see bottom panels in Figure 1)."
 (r~1l2007).., \citep{wei93}. \\citep{nat00}. $\tau\sim1$.
 In these data. silicate enission becomes weaker at later spectral types. which could be explained bv more advanced erain evolution or sedimentation m disks around low-niass objects or a luuinositv depeudeuce of the radius iu the disk at which silicate cussion is produced. (INessler-Silaecietal.2007:Sicilin-Aguilarcti.2001 ).," In these data, silicate emission becomes weaker at later spectral types, which could be explained by more advanced grain evolution or sedimentation in disks around low-mass objects or a luminosity dependence of the radius in the disk at which silicate emission is produced \citep{kes07,sic07}."
. Recent studies also have begun to explore the evolutiou of silicate chussion with time for low-mass svstenis., Recent studies also have begun to explore the evolution of silicate emission with time for low-mass systems.
 Observations with theTelescope have found that disks around low-niass stars and brown cdwarfs exhibit weaker silicate eiissiou in Upper Scorpius 5My.Scholzetal.2007). than in Chamacleou I (7—3MyrApaietal.2005). and Taurus (7~1My.Furlanetal. 2005).. which is cousistent with the erowtl of exaius to larger sizes. the settling of dust to midplane. or both. as time goes ou.," Observations with the have found that disks around low-mass stars and brown dwarfs exhibit weaker silicate emission in Upper Scorpius \citep[$\tau\sim5$~Myr,][]{sch07} than in Chamaeleon I \citep[$\tau\sim3$~Myr,][]{apa05} and Taurus \citep[$\tau\sim1$~Myr,][]{fur05}, which is consistent with the growth of grains to larger sizes, the settling of dust to midplane, or both, as time goes on."
" Πονονον, according to a receut study. this correlation between silicate emission aud age does not apply to the brown dwarf 221ÀSSW J1207331-393251 (henceforth2M.1207-3932.Cüzis2002) in the TW Ilva Association (TWA.7—10Myr.Miuna-jek2005:DarradowvNavascuésetal. 2006)."," However, according to a recent study, this correlation between silicate emission and age does not apply to the brown dwarf 2MASSW J1207334-393254 \cite[henceforth 2M~1207-3932,][]{giz02} in the TW Hya Association \citep[TWA, $\tau\sim10$~Myr,][]{mam05,bar06}."
. Riaz&Ciüzis(2007) constructed a mid-infrared (IR) spectral enerev distribution (SED) for this object uxiug broad-baud photometry from Sterzikotal.(2001). and Riazetal. (2006). which secimed to indicate the presence of silicate emission.," \citet{ria07} constructed a mid-infrared (IR) spectral energy distribution (SED) for this object using broad-band photometry from \citet{ste04} and \citet{ria06}, , which seemed to indicate the presence of silicate emission."
 As a result. they concluded that the disk around ΑΙ 1207-3932 has experieuced little dust," As a result, they concluded that the disk around 2M 1207-3932 has experienced little dust"
"Since the start of science data taking from the current generation of interferometric detectors (LIGO, 6600, Virgo and TAMA 2004αἱ2008} 2005) searches looking for from a large selection ofknown pulsars (millisecond and young pulsars with spin frequencies greater than ~ 20HHz) have been performed (Abbottεἰal|[2005|2007a\, |2010a)).","Since the start of science data taking from the current generation of interferometric detectors (LIGO, 600, Virgo and TAMA \citealt{Abbott:2004, Acernese:2008, Ando:2005}) ) searches looking for from a large selection of pulsars (millisecond and young pulsars with spin frequencies greater than $\sim 20$ Hz) have been performed \citep{Abbott:2005, Abbott:2007a, Abbott:2010a}."
". In the most recent analysis 116 pulsars were searched for using approximately a year and a half of data from each of the three LIGO detectors (Abbottοἱall/2010al),, which were operating at their design sensitivity (Abbott"," In the most recent analysis 116 pulsars were searched for using approximately a year and a half of data from each of the three LIGO detectors \citep{Abbott:2010a}, which were operating at their design sensitivity \citep{Abbott:2009a}."
" no signal was seen from any of these objects, Unfortunatelybut for the majority the sensitivity was still well above, by factors of 10 to over 100 times, their spin-down limits."," Unfortunately no signal was seen from any of these objects, but for the majority the sensitivity was still well above, by factors of 10 to over 100 times, their spin-down limits."
 The spin-down limit is set by assuming that the star’s spin-down luminosity is equal to its gravi- i.e. the rotational energy lost by the pulsar is due to radiation via gravitational waves from the Q22 mass quadrupole., The spin-down limit is set by assuming that the star's spin-down luminosity is equal to its luminosity all the rotational energy lost by the pulsar is due to radiation via gravitational waves from the $Q_{22}$ mass quadrupole.
" This limit does require one to assume a moment of inertia for the star, generally taken as the canonical value of 10?5 kkg (or 1035 ggccm? in cgs units), and that its distance is precisely known."," This limit does require one to assume a moment of inertia for the star, generally taken as the canonical value of $10^{38}$ $^2$ (or $10^{45}$ $^2$ in cgs units), and that its distance is precisely known."
" For one object, the Crab pulsar, this limit has been passed although still no gravitational seen, and for four others the upper limit obtained was within a factor of 10 from spin-down."," For one object, the Crab pulsar, this limit has been passed \citep{Abbott:2008a, Abbott:2010a} although still no were seen, and for four others the upper limit obtained was within a factor of 10 from spin-down."
 For known pulsars the parameter space to be searched over is comparatively small (position and phase evolution are known) and long observation times can be used in a coherent way., For known pulsars the parameter space to be searched over is comparatively small (position and phase evolution are known) and long observation times can be used in a coherent way.
" This makes such searches more sensitive than semi-targeted, or blind searches for similar sources ⊓ although potentially will miss out on some interesting, but currently unknown, objects."," This makes such searches more sensitive than semi-targeted, or blind searches for similar sources \citep{Abbott:2007b,
Abbott:2008b, Abbott:2009b, Abbott:2009c}, although potentially will miss out on some interesting, but currently unknown, objects."
 discusses the potential strength of a population of emitting Galactic neutron stars.," \citet{Knispel:2008}
 discusses the potential strength of a population of emitting Galactic neutron stars."
" Here, we therefore concentrate our study on estimating the prospects for fully targeted searches."," Here, we therefore concentrate our study on estimating the prospects for fully targeted searches."
" The paper is set out as follows: in refsec:snrestimates we will assess the potential signal-to- ratios at which currently known pulsars could be observed with future detectors, review a detection statistic for these pulsars, and demonstrate the parameter estimation capabilities of the standard search technique at a variety of signal-to-noise ratios; in refsec:eos we review some estimates of the maximum quadrupole moments for neutron stars given a selection ofEoS;; in refsec:limits we assess the potential signals, and associated quadrupoles, observable in future detectors based on spin-down limits and limits on our sensitivity, and how these limits can be thought of in terms of internal magnetic field strengths, and for globular cluster pulsars limits on their spin-down."," The paper is set out as follows: in \\ref{sec:snrestimates} we will assess the potential signal-to-noise ratios at which currently known pulsars could be observed with future detectors, review a detection statistic for these pulsars, and demonstrate the parameter estimation capabilities of the standard search technique at a variety of signal-to-noise ratios; in \\ref{sec:eos} we review some estimates of the maximum quadrupole moments for neutron stars given a selection of; in \\ref{sec:limits} we assess the potential signals, and associated quadrupoles, observable in future detectors based on spin-down limits and limits on our sensitivity, and how these limits can be thought of in terms of internal magnetic field strengths, and for globular cluster pulsars limits on their spin-down."
" Parts of this work are similar in scope to the review by (Owen!(2006),, and the discussions in|Abbott (2007b) and (2011)."," Parts of this work are similar in scope to the review by \citet{Owen:2006}, and the discussions in \citet{Abbott:2007b} and \citet{Andersson:2009}."
". The next (23) generation of interferometric detectors, such as Advanced LIGO (aLIGO) (Harryetal2010),, Advanced Virgo (AdvVirgo) the Large-scale Cryongenic Gravitational wave Telescope2009), (LCGT) and GEO-HF (Willke] expect to provide order of magnitude sensitivity improvements2006], over current detectors, and offer the opportunity to beat spin-down limits for nearly 60 pulsars (see refsec:second))."," The next $^{\rm nd}$ ) generation of interferometric detectors, such as Advanced LIGO (aLIGO) \citep{Harry:2010}, Advanced Virgo (AdvVirgo) \citep{Virgo:2009}, the Large-scale Cryongenic Gravitational wave Telescope (LCGT) \citep{Kuroda:2010} and GEO-HF \citep{Willke:2006}, expect to provide order of magnitude sensitivity improvements over current detectors, and offer the opportunity to beat spin-down limits for nearly 60 pulsars (see \\ref{sec:second}) )."
" A 3""? generation detector called the Einstein Telescope (ET) is also under design study, and would offer another order of magnitude increase in sensitivity."," A $^{\rm rd}$ generation detector called the Einstein Telescope (ET) \citep{Punturo:2010} is also under design study, and would offer another order of magnitude increase in sensitivity."
" This would bring hundreds of currently known pulsars into the range where we could beat spin-down limits (see refsec:third)), and also may coincide with the completion of the Square Kilometre Array (SKA) radio telescope, which may give us a vastly larger number of sources to target."," This would bring hundreds of currently known pulsars into the range where we could beat spin-down limits (see \\ref{sec:third}) ), and also may coincide with the completion of the Square Kilometre Array (SKA) radio telescope, which may give us a vastly larger number of sources to target."
 Estimates suggest the SKA may detect over half of the observable pulsars within the Galaxy giving ~20000 potential sources with ~1000 of them being millisecond pulsars and some of which could have large spin-down luminosities.," Estimates suggest the SKA may detect over half of the observable pulsars within the Galaxy giving $\sim 20\,000$ potential sources \citep{Cordes:2004} with $\sim 1000$ of them being millisecond pulsars and some of which could have large spin-down luminosities."
" Design strain curves for aLIGO, AdvVirgo and the ET in two different potential configurations are shown in Fig. [I]."," Design strain curves for aLIGO, AdvVirgo and the ET in two different potential configurations are shown in Fig. \ref{fig:strains}."
" Assuming that the star is emitting at its spin-down limit, and that a fully coherent search can be performed, we have estimated the angle averaged signal-to-noise ratios (S/N) for all known pulsars for which a spin-down limit can be given one year observation times, for joint aLIGO and calculated?|AdvVirgo observations (ALV) and for the ET"," Assuming that the star is emitting at its spin-down limit, and that a fully coherent search can be performed, we have estimated the angle averaged signal-to-noise ratios (S/N) for all known pulsars for which a spin-down limit can be given one year observation times, for joint aLIGO and AdvVirgo observations (ALV) and for the ET"
star. a configuration which is significantly different from the OGLE-LAIC-CEDP-0227 svstem whose stable secondary giant star has (he same mass. and a slightly larger diameter than the Cepheid in (hat svstem.,"star, a configuration which is significantly different from the OGLE-LMC-CEP-0227 system whose stable secondary giant star has the same mass, and a slightly larger diameter than the Cepheid in that system."
 The configuration is also quite uuusual [rom an evolutionary point of view because (he svstem consists of two well separated stars in a relatively short stage of common giant phase evolution in spite of the large mass difference., The configuration is also quite unusual from an evolutionary point of view because the system consists of two well separated stars in a relatively short stage of common giant phase evolution in spite of the large mass difference.
 According to the DaSTI evolutionary. tracks (Pietrinferni et al., According to the BaSTI evolutionary tracks (Pietrinferni et al.
 2004) a star with mass 3.74 A/Ae will enter the instabilitw strip from the giant. branch aller approximately 190. Myr of evolution. whereas asta of mass 2.64 M/Mg will reach a radius of 12.1 R/Re on the subgiant branch alter approximately 369 Myr of evolution.," 2004) a star with mass 3.74 $M/M_{\bigodot}$ will enter the instability strip from the giant branch after approximately 190 Myr of evolution, whereas a star of mass 2.64 $M/M_{\bigodot}$ will reach a radius of 12.1 $R/R_{\bigodot}$ on the subgiant branch after approximately 369 Myr of evolution."
 While detailed evolutionary models of the (vo stars in the binary will be needed. these estimates call into question the assumption Chat the stars are members of a coeval binary svstem.," While detailed evolutionary models of the two stars in the binary will be needed, these estimates call into question the assumption that the stars are members of a coeval binary system."
 In order to calculate the pulsational mass of CIEP-1812 we adopted a period-mass- based on nonlinear. convective Cepheid models constructed Lor the (vpical chemical composition of LAIC Cepheids (Z(netals)-0.008. Y(helium)-0.256) (Bono et al.," In order to calculate the pulsational mass of CEP-1812 we adopted a period-mass-relation based on nonlinear, convective Cepheid models constructed for the typical chemical composition of LMC Cepheids (Z(metals)=0.008, Y(helium)=0.256) (Bono et al."
 2000. Luck et al.," 2000, Luck et al."
 1998)., 1998).
 We note that the caleulation of the pulsation mass depends neither on the asstuned distance nor on the reddening., We note that the calculation of the pulsation mass depends neither on the assumed distance nor on the reddening.
 The resulting. pulsation mass (3.27 d 0.64 M) agrees very well with the dvnaimical mass of the star., The resulting pulsation mass (3.27 $\pm$ 0.64 $M_{\bigodot}$ ) agrees very well with the dynamical mass of the star.
 Pieirzevnski et al. (, Pietrzynski et al. (
2010) came to the same conclusion for CEP-227.,2010) came to the same conclusion for CEP-227.
 Therefore. we have now strong observational evidence that the pulsation mass of a Cepheid variable is indeed correctly measuring ils (rue. current mass.," Therefore, we have now strong observational evidence that the pulsation mass of a Cepheid variable is indeed correctly measuring its true, current mass."
 The dvnamical mass determinations for both stars in OGLE-LMC-CEP-1312 are accurate io about1.5%... adding them to the very short list of evolved massive stars with very accurate mass determinations.," The dynamical mass determinations for both stars in OGLE-LMC-CEP-1812 are accurate to about, adding them to the very short list of evolved massive stars with very accurate mass determinations."
 In a forthcoming studs. we will discuss evolutionary models [or the Cepheid in the svstem which will farther add to the solution of the Cepheicl mass discrepancy problem. and to a deeper understanding of the physics and evolution of classical Cepheid variable stars.," In a forthcoming study, we will discuss evolutionary models for the Cepheid in the system which will further add to the solution of the Cepheid mass discrepancy problem, and to a deeper understanding of the physics and evolution of classical Cepheid variable stars."
 We gratefully acknowledge financial support for (his work Irom the Chilean Center [ου Astrophvsies FONDAP 15010003. and from the BASAL Centro de Astrolisica v Tecnologias Alines (CATA) PFB-06/2007.," We gratefully acknowledge financial support for this work from the Chilean Center for Astrophysics FONDAP 15010003, and from the BASAL Centro de Astrofisica y Tecnologias Afines (CATA) PFB-06/2007."
 Support from the Polish grant N203 387337. ancl the FOCUS and TEAM subsidies of the Fundation for Polish Science (FNP) is also acknowledged.," Support from the Polish grant N203 387337, and the FOCUS and TEAM subsidies of the Fundation for Polish Science (FNP) is also acknowledged."
 [BT acknowledges the support of NSF grant. AST-0507325., IBT acknowledges the support of NSF grant AST-0507325.
 The OGLE project has received [funding from the European Research Council under the European Communitys Seventh Framework Programme (EDP7/2007-2013) / ERC grant agreement no., The OGLE project has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement no.
 246678., 246678.
 It is a pleasure to thank the support stalf at ESO-Paranal ancl at Las Campanas Observatory Dor (heir expert help in obtaining the observations., It is a pleasure to thank the support staff at ESO-Paranal and at Las Campanas Observatory for their expert help in obtaining the observations.
 We also thank the ESO OPC and CNTAC for allotting eenerous amounts of observing time to (his project., We also thank the ESO OPC and CNTAC for allotting generous amounts of observing time to this project.
In microlensing experiments. (he light curves are the primary sources of information. and the singular behavior of the caustics commands attention.,"In microlensing experiments, the light curves are the primary sources of information, and the singular behavior of the caustics commands attention."
 It is rather amusing that the weired shapes of the caustics with spiky cusps faithhuly manifest themselves as towering hieht curves., It is rather amusing that the weired shapes of the caustics with spiky cusps faithfully manifest themselves as towering light curves.
 We may sav a pleasure of studying reality through. precision illusion., We may say a pleasure of studying reality through precision illusion.
 If we imagine a lime in the plane in figure 2.. the magnilication pattern along the line consitutes a light curve. with a caveat. that the motion of the observer (such as on the earth) or the orbital motion of the binary objects can cause variations.," If we imagine a line in the plane in figure \ref{fig-add}, the magnification pattern along the line consitutes a light curve, with a caveat that the motion of the observer (such as on the earth) or the orbital motion of the binary objects can cause variations."
 In astro-ph/02017612. we showed an example of a connected caustic and also briefly discussed diamond caustics which are typical of binary lenses with relatively large separations.," In astro-ph/0207612, we showed an example of a connected caustic and also briefly discussed diamond caustics which are typical of binary lenses with relatively large separations."
 We discussed (hat cusps olf the lens axis of a connected caustic are negative cusps., We discussed that cusps off the lens axis of a connected caustic are negative cusps.
 Llere we show that that is true for all binary lenses., Here we show that that is true for all binary lenses.
 Namely. the (rianguar caustics have cusps olf the lens axis and (he cusps are all negative cusps.," Namely, the trianguar caustics have cusps off the lens axis and the cusps are all negative cusps."
 The positive iso-/ contours line the triangular caustics [from inside., The positive $J$ contours line the triangular caustics from inside.
 As JJ converges to (he maxinunm value 1. the families of iso-/ contours shrink to the points that generate images al the finite limit points where /=1.," As $J$ converges to the maximum value 1, the families of $J$ contours shrink to the points that generate images at the finite limit points where $J =1$."
 Near (he cusps. the lens equation becomes cubic because there are three images with small values of the Jacobian determinant. J. two of which can be unrealized images (or complex solutions to the cubic equation).," Near the cusps, the lens equation becomes cubic because there are three images with small values of the Jacobian determinant $J$, two of which can be unrealized images (or complex solutions to the cubic equation)."
 When a source trajectory approaches a caustic. the lisht curve can be more dominated bv the behavior of the line caustic or more by a cusp.," When a source trajectory approaches a caustic, the light curve can be more dominated by the behavior of the line caustic or more by a cusp."
 The distinction is made by the singlet, The distinction is made by the singlet
are found. to be dynamically. segregated with respect. to both Luminosity ancl morphology in simulations (Yepes 1991: Fuseo-Femiano Alenei L998). which is supported by observations of dynamical segregation in both eroups and clusters (Girardi 2003: Lares 2004).,"are found to be dynamically segregated with respect to both luminosity and morphology in simulations (Yepes 1991; Fusco-Femiano Menci 1998), which is supported by observations of dynamical segregation in both groups and clusters (Girardi 2003; Lares 2004)."
 Llere we examine evidence [for both spatial and dynamical segregation amongst our galaxy group sample., Here we examine evidence for both spatial and dynamical segregation amongst our galaxy group sample.
 ‘To address the question of spatial segregation we subcivide our total sample by morphology. (early- vs. late-tvpes) and luminosity (where AM4Mg—.—16.8 mamag is used as the break between cwarf and giant galaxies). the results of which are shown in Figs.," To address the question of spatial segregation we subdivide our total sample by morphology (early- vs. late-types) and luminosity (where $M_B=-16.8$ mag is used as the break between dwarf and giant galaxies), the results of which are shown in Figs."
 16. and 17.., \ref{dg} and \ref{el}.
 When split by luminosity (Fig. 16)).," When split by luminosity (Fig. \ref{dg}) ),"
 galaxies show no significant evidence lor a radial bias. Le. the two Luminosity sub-samples are similarly distributed with radius.," galaxies show no significant evidence for a radial bias, i.e. the two luminosity sub-samples are similarly distributed with radius."
 The hypothesis that dwarf. ancl giant galaxies have the same radial distribution is only marginally rejected at the TO percent level by a WKolmogorov-Smirnoy (INS) test. confirming the visually apparent lack of a strong radial bias with luminosity.," The hypothesis that dwarf and giant galaxies have the same radial distribution is only marginally rejected at the 70 percent level by a Kolmogorov-Smirnov (KS) test, confirming the visually apparent lack of a strong radial bias with luminosity."
 This is consistent with the known trend in chwarl-to-giant ratios (DCGIU for groups and clusters. where the DOR. is independent of position observed in the group (see e.g. E591).," This is consistent with the known trend in dwarf-to-giant ratios (DGR) for groups and clusters, where the DGR is independent of position observed in the group (see e.g. FS91)."
 Splitting galaxies based on morphology (Eis. 17)), Splitting galaxies based on morphology (Fig. \ref{el}) )
 gives a markedly different result in that galaxies are cüfferentlv cistributed at the 5 @ level as determined. using a WKS test., gives a markedly different result in that galaxies are differently distributed at the 5 $\sigma$ level as determined using a KS test.
 This is consistent with expectations from the morphology-density and morphology-racius relations (Butcher Oemler 1976: Dressler 1980) and our findings from 56.1.., This is consistent with expectations from the morphology-density and morphology-radius relations (Butcher Oemler 1976; Dressler 1980) and our findings from $\S$ \ref{colours}.
 Lt is important to keep in mind that our group sample is assembled. [rom a variety of sources with dilfering spatial coverage. selection ancl completeness (see Fig.," It is important to keep in mind that our group sample is assembled from a variety of sources with differing spatial coverage, selection and completeness (see Fig."
 5. and §3)) all of whieh could. be inducing a radial bias in the results presented. in Figs.," \ref{spatial} and $\S$ \ref{data}) ), all of which could be inducing a radial bias in the results presented in Figs."
 10 and 17.., \ref{dg} and \ref{el}.
 In. particular. the region within 600 kkpc of the eroup center (approximately the area covered by E890. and. therefore. our AAOmega observations) includes significant. numbers of faint (dwarl) galaxies that are likely not included in the samples at larger radii," In particular, the region within $\sim$ kpc of the group center (approximately the area covered by FS90 and, therefore, our AAOmega observations) includes significant numbers of faint (dwarf) galaxies that are likely not included in the samples at larger radii."
 Repeating the KS test on only galaxies within the central kkpe gives similar results to those above: dwarf and giant galaxies appear similarly distributed (at the 60 percent. level) while earlv- and late-twpe galaxies show a dilference in their racial clistributions significant at the 3 o level., Repeating the KS test on only galaxies within the central kpc gives similar results to those above; dwarf and giant galaxies appear similarly distributed (at the $\sim$ 60 percent level) while early- and late-type galaxies show a difference in their radial distributions significant at the 3 $\sigma$ level.
 The clynamical segregation of galaxies in the 55044 eroup has been examined. previously by Cellone Buzzoni (2005) using a sample of 26 carly- and [ate-tvpe galaxies., The dynamical segregation of galaxies in the 5044 group has been examined previously by Cellone Buzzoni (2005) using a sample of 26 early- and late-type galaxies.
 When clivicding their sample based on morphology. they find carly- and Iate-tvpe galaxies exhibit velocity dispersions that differ at the 93 percent level (às measured using an f° test).," When dividing their sample based on morphology, they find early- and late-type galaxies exhibit velocity dispersions that differ at the 93 percent level (as measured using an $F$ test)."
 Cellone DBuzzoni (2005) find no evidence for. luminosity segregation in their earlv-tvpe galaxies. however were unable to examine Iuminosity segregation between their earlv- and Iate-tvpe samples due to low numbers of late-twpe galaxies.," Cellone Buzzoni (2005) find no evidence for luminosity segregation in their early-type galaxies, however were unable to examine luminosity segregation between their early- and late-type samples due to low numbers of late-type galaxies."
 Llere we revisit the question of dynamical segregation in 16 55044 eroup using the morphology ane luminosity gsub-samiples described. above., Here we revisit the question of dynamical segregation in the 5044 group using the morphology and luminosity sub-samples described above.
 We then compare the line-ο velocity. distributions of sub-samples using two iWerent methocls to look for dynamically clistinet behaviour., We then compare the line-of-sight velocity distributions of sub-samples using two different methods to look for dynamically distinct behaviour.
 The first comparison is carried out using a INS test. which 'omputes the likelihood of the two cdilferent samples being rawn from the same parent velocity distribution.," The first comparison is carried out using a KS test, which computes the likelihood of the two different samples being drawn from the same parent velocity distribution."
 The second test we use is an b-test. which gives the likelihood of 1ο two distributions having significantly dillerent variances.," The second test we use is an F-test, which gives the likelihood of the two distributions having significantly different variances."
 ‘Table 5. summarises the results of the KS and E-test for our Iuminosity and morphology. sub-samples., Table \ref{disp_tab} summarises the results of the KS and F-test for our luminosity and morphology sub-samples.
 Our results for morphological segregation. computed using the F-test are consistent with Cellone juzzoni (2005). however increasing the sample of galaxies from 26 to 105 has decreased the significance slightly.," Our results for morphological segregation computed using the F-test are consistent with Cellone Buzzoni (2005), however increasing the sample of galaxies from 26 to 105 has decreased the significance slightly."
 There is marginal evidence of a variation in the, There is marginal evidence of a variation in the
"where €>0 is a tuning parameter and s(-,-) is a defined pairwise distance between objects.","where $\epsilon >0$ is a tuning parameter and $s(\cdot,\cdot)$ is a user-defined pairwise distance between objects."
" Here, s is a distance measure, meaning that it should be small only if Xj and X; are similar (in refss:lcdist we define the distance measure we use for SN light curve data)."," Here, $s$ is a distance measure, meaning that it should be small only if $\X_i$ and $\X_j$ are similar (in \\ref{ss:lcdist} we define the distance measure we use for SN light curve data)."
" In this construction, the probability of stepping from X; to X; in one step of a diffusion process is (Xi,X;j)=w(XiXj)/w(Xi,Xx)."," In this construction, the probability of stepping from $\X_i$ to $\X_j$ in one step of a diffusion process is $p_1(\X_i, \X_j) = w(\X_i,\X_j)/ \sum_k w(\X_i, \X_k)$."
" We store the one step probabilities between $5,all N data points in the Nx matrix P; then, by the theory of Markov chains, for any positive integer t, the element p;(X;,X5) of the matrix power P gives the probability of going from X; to X; in t steps."," We store the one step probabilities between all $N$ data points in the $N \times N$ matrix $\P$ ; then, by the theory of Markov chains, for any positive integer $t$, the element $p_t(\X_i, \X_j)$ of the matrix power $\P^t$ gives the probability of going from $\X_i$ to $\X_j$ in $t$ steps."
" See, e.g., Chapter 6 in ? for an introduction to Markov chains."," See, e.g., Chapter 6 in \citet{grim2001} for an introduction to Markov chains."
" We define the diffusion map at scale t as where Y; and A; are the right eigenvectors and eigenvalues of P, respectively, in a biorthogonal spectral decomposition and m is the number of diffusion map coordinates chosen to represent the data."," We define the diffusion map at scale $t$ as where $\mathbf{\Psi}_j$ and $\lambda_j$ are the right eigenvectors and eigenvalues of $\P$, respectively, in a biorthogonal spectral decomposition and $m$ is the number of diffusion map coordinates chosen to represent the data."
" The Euclidean distance between any two points in the m-dimensional space described by equation (2) approximates the diffusion distance, a distance measure that captures the intrinsic geometry of the data set by simultaneously considering all possible paths between any two data points in the t-step Markov random walk constructed above."," The Euclidean distance between any two points in the $m$ -dimensional space described by equation \ref{eqn:dmap2}) ) approximates the diffusion distance, a distance measure that captures the intrinsic geometry of the data set by simultaneously considering all possible paths between any two data points in the $t$ -step Markov random walk constructed above."
" The choice of the parameters e (in equation I) and m gives the map a great deal of flexibility, and it is feasible to vary these parameters in an effort to obtain the best classifier via cross-validation, as described in refss:classtune.."," The choice of the parameters $\epsilon$ (in equation \ref{eqn:dmap1}) ) and $m$ gives the map a great deal of flexibility, and it is feasible to vary these parameters in an effort to obtain the best classifier via cross-validation, as described in \\ref{ss:classtune}."
" We note that in the random forest classifier used to predict object type (see refss:rf)), the scale of each coordinate of W'(X) does not influence the method because each classification tree is constructed by splitting one coordinate at a time."," We note that in the random forest classifier used to predict object type (see \\ref{ss:rf}) ), the scale of each coordinate of $\mathbf{\Psi}^t(\X)$ does not influence the method because each classification tree is constructed by splitting one coordinate at a time."
" Therefore, the parameter t, whose role in the diffusion map is to rescale each coordinate, has no influence on our (25)analyses."," Therefore, the parameter $t$, whose role in the diffusion map \ref{eqn:dmap2}) ) is to rescale each coordinate, has no influence on our analyses."
 We choose to fix t to have the value 1., We choose to fix $t$ to have the value 1.
" For the remainder of this paper, we will use V'; to stand for the m-dimensional vector of diffusion map coordinates, V!(X;)."," For the remainder of this paper, we will use $\mathbf{\Psi}_i$ to stand for the $m$ -dimensional vector of diffusion map coordinates, $\mathbf{\Psi}^1(\X_i)$."
" In finding the diffusion map representation of each object, the idea is that this parameterization will hopefully obey a simple relationship with respect to object type."," In finding the diffusion map representation of each object, the idea is that this parameterization will hopefully obey a simple relationship with respect to object type."
" Then, simple modeling can be performed to build a class-predictive model from the diffusion map coordinates."," Then, simple modeling can be performed to build a class-predictive model from the diffusion map coordinates."
" That is, once we have the m-dimensional diffusion map representation of each object’s light curve (equation we construct a model to predict the type, yi, of the ZRi*” object as a function of its diffusion map representation, W;."," That is, once we have the $m$ -dimensional diffusion map representation of each object's light curve (equation \ref{eqn:dmap2}) ), we construct a model to predict the type, $y_i$ , of the $i^{th}$ object as a function of its diffusion map representation, $\mathbf{\Psi}_i$."
" In other words, using the set of n SNe with known classification labels, we estimate the underlying function h that relates each m-dimensional diffusion map representation with a classification label."," In other words, using the set of $n$ SNe with known classification labels, we estimate the underlying function $h$ that relates each $m$ -dimensional diffusion map representation with a classification label."
" We will ultimately use this estimate, h, to predict the classification, y;=h(W;) for each unlabeled supernova j—n41,...,N."," We will ultimately use this estimate, $\widehat{h}$, to predict the classification, $\widehat{y}_j = \widehat{h}(\mathbf{\Psi}_j)$ for each unlabeled supernova $j=n+1,...,N$."
 Any classification procedure that can handle more than two classes could be applied to the diffusion map representation of the SNe., Any classification procedure that can handle more than two classes could be applied to the diffusion map representation of the SNe.
" By adapting the predictors to the underlying structure in the data, standard classification procedures should be able to separate the SNe of different types."," By adapting the predictors to the underlying structure in the data, standard classification procedures should be able to separate the SNe of different types."
" We choose to use the method of ? due to its observed success in many multiclass classification settings, including in astrophysics (???))."," We choose to use the method of \citet{brei2001} due to its observed success in many multiclass classification settings, including in astrophysics \citealt{2003sca..book..243B,rich2011,2011arXiv1101.2406D}) )."
" The basic idea of the random forest is to build a large collection of decorrelated classification tree estimates and then toaverage these estimates to obtain the final predictor, h."," The basic idea of the random forest is to build a large collection of decorrelated classification tree estimates and then to average these estimates to obtain the final predictor, $\widehat{h}$ ."
" This approach usually works well because classification tree estimates are notoriously noisy, but tend to be unbiased."," This approach usually works well because classification tree estimates are notoriously noisy, but tend to be unbiased."
" By averaging decorrelated tree estimates, the random forest produces classification estimates that are both unbiased and have small variance with respect to the choice of training set."," By averaging decorrelated tree estimates, the random forest produces classification estimates that are both unbiased and have small variance with respect to the choice of training set."
 See the Appendices A and B for a brief overview of classification trees refss:classificationTrees)) and random forest refss:randomForests) )., See the Appendices A and B for a brief overview of classification trees \\ref{ss:classificationTrees}) ) and random forest \\ref{ss:randomForests}) ).
 The first step of our analysis is to use the entire dataset of supernova light curves to learn an appropriate representation of each supernova using diffusion map., The first step of our analysis is to use the entire dataset of supernova light curves to learn an appropriate representation of each supernova using diffusion map.
 This is the part of our semi-supervised approach., This is the part of our semi-supervised approach.
 We apply the methods described in to the dataset of the SN 82] Photometric Classification Challenge (?))., We apply the methods described in \ref{sec:meth} to the dataset of the SN Photometric Classification Challenge \citealt{kess2010}) ).
 We use data from the “Updated as described in §66 of ?..," We use data from the “Updated, as described in 6 of \citet{kess2010a}."
 These data were simulated to Simulations’?mimic the observing conditions of the DES., These data were simulated to mimic the observing conditions of the DES.
" Note that these data are significantly different than the data used in the Challenge, with several bug fixes andimprovements to make the simulations more realistic."," Note that these data are significantly different than the data used in the Challenge, with several bug fixes andimprovements to make the simulations more realistic."
" For instance, the ratio of photometric to spectroscopic SNe was 13:1 in the Challenge data, but 18:1 in the UpdatedSimulations."," For instance, the ratio of photometric to spectroscopic SNe was 13:1 in the Challenge data, but 18:1 in the UpdatedSimulations."
" Therefore, we refrain from comparing our current results directly to the results in the We denote the updated Challenge data as D. Challenge"," Therefore, we refrain from comparing our current results directly to the results in the We denote the updated Challenge data as $\mathcal{D}$."
}There are, There are
X-ray cluster catalogs with SDSS and used infall patterns to compute cluster mass profiles.,X-ray cluster catalogs with SDSS and used infall patterns to compute cluster mass profiles.
" The c299 concentration has significant scatter — values ranging from 5—17 — but their best-fit average profile, with fitsrestricted to rX:Rago, yields 200=5.2 which, at an average mass of Mooo~10!1!Mo, is in agreement with our predictions."," The $c_{200}$ concentration has significant scatter – values ranging from $5-17$ – but their best-fit average profile, with fitsrestricted to $r\leq R_{200}$, yields $c_{200}=5.2$ which, at an average mass of $M_{200}\simeq 10^{14} \mau$, is in agreement with our predictions."
 More recently Wojtak&Lokas(2010) have published an analysis of 41 relaxed galaxy clusters (0.013«z« 0.095); we compare our predictions with their results in Fig. 10.., More recently \cite{wojtak10} have published an analysis of 41 relaxed galaxy clusters $0.013<z<0.095$ ); we compare our predictions with their results in Fig. \ref{fig:kin}.
 Although their data has considerable scatter it is in quite reasonable agreement with the predictions from simulations., Although their data has considerable scatter it is in quite reasonable agreement with the predictions from simulations.
" Thus, despite possible systematic difficulties with such methods (see, e.g., White,Cohn,&Smit 2010)), the current results are in reasonable accord with theoretical expectations."," Thus, despite possible systematic difficulties with such methods (see, e.g., \citealt{white10}) ), the current results are in reasonable accord with theoretical expectations."
 We presented results for the concentrations of dark matter halos using a set of large-volume simulations., We presented results for the concentrations of dark matter halos using a set of large-volume simulations.
" With a total volume roughly 1-2 orders of magnitude larger compared to previous simulations, we focused on studying the c—M relation for massive clusters."," With a total volume roughly 1-2 orders of magnitude larger compared to previous simulations, we focused on studying the $c-M$ relation for massive clusters."
" As shown in the past, at the high mass end, the c-M relation becomes flatter at z=0 and the flattening becomes more significant at higher z."," As shown in the past, at the high mass end, the $c-M$ relation becomes flatter at $z=0$ and the flattening becomes more significant at higher $z$."
" The mean concentration of the sample when expressed in terms of the peak height parameter, v(M,z)=0. /0(M,z), shows a roughly uniform slope at all redshifts."," The mean concentration of the sample when expressed in terms of the peak height parameter, $\nu(M,z)=\delta_c/\sigma(M,z)$ , shows a roughly uniform slope at all redshifts."
" Indeed, the slope of the c—v relation does not change with redshift."," Indeed, the slope of the $c-\nu$ relation does not change with redshift."
 The amplitude of the c—v relation evolves by about 30% at the high mass end from z20—2., The amplitude of the $c-\nu$ relation evolves by about $30\%$ at the high mass end from $z=0-2$.
" The z-evolution is consistent with the results of Gaoetal.(2008),, although the overall amplitude of the concentration differs because of the different choices of og."," The $z$ -evolution is consistent with the results of \cite{gao07}, although the overall amplitude of the concentration differs because of the different choices of $\sigma_8$ ."
" We do not observe rise in concentration at higher masses as reported by Klypin,aTrujillo-Gomez,&Primack(2010) and Pradaetal.(2011) (the Appendix includes further discussion).", We do not observe a rise in concentration at higher masses as reported by \cite{klypin10} and \cite{prada11} (the Appendix includes further discussion).
disc population. which is an almost identical ratio to our CAD sample.,"disc population, which is an almost identical ratio to our CAB sample."
 The distribution of the corrected C. V. M velocities on he (0.3) and (WV) planes are displayed in Fig.," The distribution of the corrected $U$ , $V$, $W$ velocities on the $(U, V)$ and $(W, V)$ planes are displayed in Fig."
 2., 2.
 At irst elance. the general look of the current (C.V) diagram (lig.," At first glance, the general look of the current $(U, V)$ diagram (Fig."
 2a) appears to have similar characteristics to. the (C.V) diagram of Eker (1992) of the same sample but ewer stars (146) with much lower accuracy.," 2a) appears to have similar characteristics to the $(U, V)$ diagram of Eker (1992) of the same sample but fewer stars (146) with much lower accuracy."
 Quantitatively speaking. the average motion of the current sample with respect to the Sun is ((.1.M)=(135.19.7.8.1) k«n/s having the dispersion. of (37.3. 26.0. 194) kms with respect to the LSR. which are indeed close to the values of Eker (1992): (οΕς=(10.20.7) km/s and the dispersions of (37. 27. 23) km/s. Later. Aslan οἱ al. (," Quantitatively speaking, the average motion of the current sample with respect to the Sun is $(U, V, W)=(-13.5, -19.7, -8.1)$ km/s having the dispersion of (37.3, 26.0, 19.4) km/s with respect to the LSR, which are indeed close to the values of Eker (1992): $(U, V, W)=(-10, -20, -7)$ km/s and the dispersions of (37, 27, 23) km/s. Later, Aslan et al. ("
1999) also studied the kinematics of the 178 CAD using the Llipparcos astrometric data.,1999) also studied the kinematics of the 178 CAB using the Hipparcos astrometric data.
 The shape and the clistribution characteristics of the (C.Y) diagram of Aslan et al. (," The shape and the distribution characteristics of the $(U, V)$ diagram of Aslan et al. ("
1999) also has a similar appearance to the mean motion o[f(C.V.M)-(ILS.20.5.6.4) kms relative to the Sun and (35.8.22.4.18.2) kms dispersions in the space velocities with respect to LSIx.,"1999) also has a similar appearance to the mean motion of $(U, V, W)=(-11.8, -20.5, -6.4)$ km/s relative to the Sun and $(35.8, 22.4, 18.2)$ km/s dispersions in the space velocities with respect to LSR."
 The similar appearance. the similar mean velocity and the similar. distribution of the current sample on the (C.V) does not seem to display any advantage of increased accuracy and increased number over the previous studies.," The similar appearance, the similar mean velocity and the similar distribution of the current sample on the $(U, V)$ does not seem to display any advantage of increased accuracy and increased number over the previous studies."
 Llowever. as soon as our first (0.V) diagram was produced. he 5 shaped. concentration of (£V) velocities near the LSIt (See Fig.," However, as soon as our first $(U, V)$ diagram was produced, the $\gamma$ shaped concentration of $(U, V)$ velocities near the LSR (See Fig."
 2a) was noticed., 2a) was noticed.
 Such a concentration of kinematically voung systems is not noted by neither Eker (1992) nor Aslan et al. (, Such a concentration of kinematically young systems is not noted by neither Eker (1992) nor Aslan et al. (
1999).,1999).
 However. the 7 shaped concentration is very clear in Fig.," However, the $\gamma$ shaped concentration is very clear in Fig."
 2a., 2a.
 The concentration of the voung systems is also noticeable on the (WV) plane (Lig.," The concentration of the young systems is also noticeable on the $(W, V)$ plane (Fig."
 2b) but in a rather spherical shape., 2b) but in a rather spherical shape.
 Containing stars [rom EF to M spectral types on the main sequence. together with the evolved G and Ix giants and even with the super giants. the studied samples of CAB happens to be very heterogeneous.," Containing stars from F to M spectral types on the main sequence, together with the evolved G and K giants and even with the super giants, the studied samples of CAB happens to be very heterogeneous."
 On the other hand. the orbital periods of the binaries in the sample range from fractions of a dav to more than 300 davs.," On the other hand, the orbital periods of the binaries in the sample range from fractions of a day to more than 300 days."
 This may mean that there ave dilferent. evolutionary paths (Plavec— 11968: Thomas 11977) indicating cillerent ages existing together among the sample stars., This may mean that there are different evolutionary paths (Plavec 1968; Thomas 1977) indicating different ages existing together among the sample stars.
 As Eker (1992) investigated and Aslan et al. (, As Eker (1992) investigated and Aslan et al. (
1999) announced. there could be no significant kinematical dillerences between the sub-samples of the CAB except some indication of the main sequence RS CVn svstems tending to have smaller velocity cispersions implving smaller ages.,"1999) announced, there could be no significant kinematical differences between the sub-samples of the CAB except some indication of the main sequence RS CVn systems tending to have smaller velocity dispersions implying smaller ages."
 The difficulty. of separating kinematically voung and old populations in the velocity space alone is obvious., The difficulty of separating kinematically young and old populations in the velocity space alone is obvious.
 The dispersions increase with age but there are always some stars left near the LSR., The dispersions increase with age but there are always some stars left near the LSR.
 Lt is therefore not safe to pick stars randomly near the LSIt and then to form a kinematically voung group with them., It is therefore not safe to pick stars randomly near the LSR and then to form a kinematically young group with them.
 The classical approach would be to form the sub groups according to certain objective criteria at first. then to investigate and to compare the dispersions among the sub groups.," The classical approach would be to form the sub groups according to certain objective criteria at first, then to investigate and to compare the dispersions among the sub groups."
 llowever. the concentration. of velocities around (0.V)=(17.8). (eV)=(4.26). (U.V)=(37.14). and ((.V)=(0.0) km/s perhaps rellect. some kinds of group motions of the stars in the solar vicinitv.," 	 However, the concentration of velocities around $(U, V)=(17, -8)$, $(U, V)=(-4, -26)$, $(U, V)=(-37, -14)$, and $(U, V)=(0, 0 )$ km/s perhaps reflect some kinds of group motions of the stars in the solar vicinity."
 liegen (1958a-b. 1989. 1995) and Montes et al. (," Eggen (1958a-b, 1989, 1995) and Montes et al. ("
2001a) discuss the possible moving groups (Local Association. Ursa Major. Castor. IC. 2391. and. Hvades). which might cause the concentration of space velocities as described above.,"2001a) discuss the possible moving groups (Local Association, Ursa Major, Castor, IC 2391, and Hyades), which might cause the concentration of space velocities as described above."
 Fherefore. as a first step before examining the classical sub groups. it was decided to determine the ALG members of our sample and then investigate if the ~ shaped concentration is caused by them.," Therefore, as a first step before examining the classical sub groups, it was decided to determine the MG members of our sample and then investigate if the $\gamma$ shaped concentration is caused by them."
 Moreover. the membership ofone of the known MC. would. be an objective criterion to discriminate the kinematically voung population of the present. CAD sample.," Moreover, the membership ofone of the known MG would be an objective criterion to discriminate the kinematically young population of the present CAB sample."
epochs. when the cluster has lost respectively the 20%. the 35% and the 75% of its initial mass.,"epochs, when the cluster has lost respectively the $20\%$, the $35\%$ and the $75\%$ of its initial mass."
 As the cluster loses stars in the galactic field. the mass function evolves towarcls flatter configurations. because of the preferential loss of low-mass stars. (hal. accordingly (o {he initial mass segregation. are located mostly in the external regions of the cluster.," As the cluster loses stars in the galactic field, the mass function evolves towards flatter configurations, because of the preferential loss of low-mass stars, that, accordingly to the initial mass segregation, are located mostly in the external regions of the cluster."
 The evolution of the mass function appears to be driven by the fraction of mass loss. rather (han bv other parameters (like the total number of stars in (hie svstem and (he orbital tvpe of the parent cluster) confirming the findings of Dawmgardt&Makino(2003).," The evolution of the mass function appears to be driven by the fraction of mass loss, rather than by other parameters (like the total number of stars in the system and the orbital type of the parent cluster) confirming the findings of \citet{bm03}."
.. This is evident from the fact that. for a given fraction of mass lost. the eurves found lor the dillerent orbits in practice coincide.," This is evident from the fact that, for a given fraction of mass lost, the curves found for the different orbits in practice coincide."
 The main results of our work may be resumed as follows: Part of this work has been done using the IDM. SP4 platform located at CINECA.," The main results of our work may be resumed as follows: Part of this work has been done using the IBM SP4 platform located at CINECA,"
The Main Belt Comets (MBCs) are a recently discovered class of objects. composed until now by only four objects (Table 1)).,"The Main Belt Comets (MBCs) are a recently discovered class of objects, composed until now by only four objects (Table \ref{tab1}) )."
 These objects are puzzling because they are orbiting in the Main Belt on stable orbits. with Tisserand invariant with respect to Jupiter higher than 3. but at the same time they are showing a more or less stable cometary activity.," These objects are puzzling because they are orbiting in the Main Belt on stable orbits, with Tisserand invariant with respect to Jupiter higher than 3, but at the same time they are showing a more or less stable cometary activity."
 Four known objects implies many more presently inactive or faintly active and as a consequence undetectable., Four known objects implies many more presently inactive or faintly active and as a consequence undetectable.
 It 1s probable that as a result of the surveys being conducted (Gilbert Wigert 2009)) more objects will be added to this new class in a near future., It is probable that as a result of the surveys being conducted (Gilbert Wigert \cite{gilbert}) ) more objects will be added to this new class in a near future.
 The first of the MBCs that has been discovered is 133P/Elst-Pizarro., The first of the MBCs that has been discovered is 133P/Elst-Pizarro.
 At the moment of the discovery. in. 1992 (Elst et al. 1996)).," At the moment of the discovery, in 1992 (Elst et al. \cite{elst}) ),"
 it has been designated as 7968 Elst-Pizarro., it has been designated as 7968 Elst-Pizarro.
 When in July 1996 the body was found showing a dust tail. the activity was initially attributed to an impact (Boehnhardt et al. 1998::," When in July 1996 the body was found showing a dust tail, the activity was initially attributed to an impact (Boehnhardt et al. \cite{boehnhardt};"
 Toth 2000). but when later on the object was found periodically active at the successive perihelions (2002 and then 2007) it became clear that a different explanation had to be found (Hsieh et al. 2004)).," Toth \cite{toth}) ), but when later on the object was found periodically active at the successive perihelions (2002 and then 2007) it became clear that a different explanation had to be found (Hsieh et al. \cite{hsieh0}) )."
 P/2005 UI (Read) and 176P/LINEAR followed in a short time (Read et al. 2005::, P/2005 U1 (Read) and 176P/LINEAR followed in a short time (Read et al. \cite{read};
 Green 2006)). both active and orbiting on similar orbits (Table 1)).," Green \cite{green}) ), both active and orbiting on similar orbits (Table \ref{tab1}) )."
 More recently. P/2008 RI (Garradd) has been discovered (Garradd et al. 2008).," More recently, P/2008 R1 (Garradd) has been discovered (Garradd et al. \cite{garradd}) )."
 The Tisserand invariant values rule out the possibility that these bodies are newcomers in this part of the Solar System., The Tisserand invariant values rule out the possibility that these bodies are newcomers in this part of the Solar System.
 The orbits of two of them. 133P/Elst-Pizarro and I76P/LINEAR. can be linked with the 2 Gyr-old Themis dynamical family (Zappala et al. 1990))," The orbits of two of them, 133P/Elst-Pizarro and 176P/LINEAR, can be linked with the 2 Gyr-old Themis dynamical family (Zappalá et al. \cite{zappala}) )"
 and the smaller and younger (10 Myr) Beagle family (Nesvorny et al. 2008))., and the smaller and younger (10 Myr) Beagle family (Nesvorny et al. \cite{nesvorny}) ).
 The orbit of P/2005 U1 (Read) is falling just outside the Themis family. and P/2008 R1 (Garradd) appears to be a dynamically unstable object. probably formed in a different part of the Main Belt (Jewitt et al. 2009)).," The orbit of P/2005 U1 (Read) is falling just outside the Themis family, and P/2008 R1 (Garradd) appears to be a dynamically unstable object, probably formed in a different part of the Main Belt (Jewitt et al. \cite{jewitt1}) )."
 As for the causes of dust ejection. it became soon evident that it is due to sublimation.," As for the causes of dust ejection, it became soon evident that it is due to sublimation."
 Not only this activity is recurrent. as in the case of 133P/Elst-Pizarro. but it is also lasting for weeks and months.," Not only this activity is recurrent, as in the case of 133P/Elst-Pizarro, but it is also lasting for weeks and months."
 Moreover. dust velocities. estimated from the sunward extent of the coma. are greatly in excess of what would be expected from electrostatic levitation or rotational ejection (Hsieh Jewitt 2006)).," Moreover, dust velocities, estimated from the sunward extent of the coma, are greatly in excess of what would be expected from electrostatic levitation or rotational ejection (Hsieh Jewitt \cite{hsieh}) )."
 If these bodies formed in-situ. the question of how can they still contain ice arises.," If these bodies formed in-situ, the question of how can they still contain ice arises."
 In the protoplanetary disk. opacity due to grains inhibited radiative cooling and raised the mid-plane kinetic temperature (Jewitt et al. 2007)).," In the protoplanetary disk, opacity due to grains inhibited radiative cooling and raised the mid-plane kinetic temperature (Jewitt et al. \cite{jewitt}) )."
 Growth and migration of solids in the disk would have caused the opacity to change. so moving the snow line. that for a fraction of a million years may have been within the Main Belt.," Growth and migration of solids in the disk would have caused the opacity to change, so moving the snow line, that for a fraction of a million years may have been within the Main Belt."
 In this way. asteroids orbiting in the Main Belt could have incorporated water ice upon formation.," In this way, asteroids orbiting in the Main Belt could have incorporated water ice upon formation."
 It is well know that many asteroids lack the hydration feature in their spectra., It is well know that many asteroids lack the hydration feature in their spectra.
 This has been interpreted as asign that their ice never reached the liquid phase and so could still be found frozen in the interior (Jones et al. 1990:;, This has been interpreted as a sign that their ice never reached the liquid phase and so could still be found frozen in the interior (Jones et al. \cite{jones};
 Carvano et al. 2003))., Carvano et al. \cite{carvano}) ).
 These bodies would be possible candidates for the new class of The recent detection of water ice on the surface of 24 Themis (Campins et al. 2010::, These bodies would be possible candidates for the new class of The recent detection of water ice on the surface of 24 Themis (Campins et al. \cite{campins};
 Rivkin Emery 2010)) came as no surprise. and give a strong support to the sublimation-driven explanation for the MBCs activity.," Rivkin Emery \cite{rivkin}) ) came as no surprise, and give a strong support to the sublimation-driven explanation for the MBCs activity."
 At the end of 2009. two independent teams observing 24 Themis in the infrared range detected the presence of water ice widespread on the surface of the body.," At the end of 2009, two independent teams observing 24 Themis in the infrared range detected the presence of water ice widespread on the surface of the body."
 It has been interpreted as frost. replenished by some subsurface source.," It has been interpreted as frost, replenished by some subsurface source."
 This detection. and those of Main Belt comets. are contributing to definitively shatter the old. traditional view of the Main Belt as the realm of rocky bodies as opposed to the icy. active bodies that can be found farther.," This detection, and those of Main Belt comets, are contributing to definitively shatter the old, traditional view of the Main Belt as the realm of rocky bodies as opposed to the icy, active bodies that can be found farther."
 The implications deriving from the existence of a third source (besides the Oort Cloud and the Edgeworth-Kuiper Belt) of “cometary” bodies are remarkable.," The implications deriving from the existence of a third source (besides the Oort Cloud and the Edgeworth-Kuiper Belt) of ""cometary"" bodies are remarkable."
 The water contained in the terrestrial oceans 1s thought to come from impacting icy bodies. but the few D/H ratios measured until now in comets," The water contained in the terrestrial oceans is thought to come from impacting icy bodies, but the few D/H ratios measured until now in comets"
calibrate CRB intrinsic luminosity. allowing perliaps a few huudred of the brightest GRBs currently detected by the Burst and Transient Source Experiment (BATSE) on board the Compton Gauna- Observatory (CORO) oact as standard caudles.,"calibrate GRB intrinsic luminosity, allowing perhaps a few hundred of the brightest GRBs currently detected by the Burst and Transient Source Experiment (BATSE) on board the Compton Gamma-Ray Observatory (CGRO) to act as standard candles."
 Specifically. Norris.Marani.&Bounell(2000) lave proposed that the time-lag between BATSE DISCSC energy channels 3 aud L. as measured by a cross-correlatiou Auction. migu calibrate this sauclard candle.," Specifically, \citet{Nor00} have proposed that the time-lag between BATSE DISCSC energy channels 3 and 1, as measured by a cross-correlation function, might calibrate this standard candle."
 More recently. Fenimore(2000) las sroposed that geeral variability across the whole GRB may also act to calibrate these explosions as standard cailles.," More recently, \citet{Fen00} has proposed that general variability across the whole GRB may also act to calibrate these explosions as standard candles."
 TThe data behind these claiurs reimnaius sinall. however. and. proposed physical nechanisims belinc 1011 1Lup“OVELL.," The data behind these claims remains small, however, and proposed physical mechanisms behind them unproven."
" Desai(1051) ort[n]0inal vou--oted that GRBs iive characteristic ""separated times"" iu events. au illusion to structures lthat are oday known as pκος."," \citet{Des81} originally noted that GRBs have characteristic “separated times"" in events, an illusion to structures that are today known as pulses."
 Norrisetal.(1996) recenly fit and analyzed he pulses in 11 BATSE GRBs with a minima [unctional form., \citet{Nor96} recently fit and analyzed the pulses in 41 BATSE GRBs with a minimal functional form.
 Ixatz(199f) has suggestedMOD that he shape of a €‘RB pi]ses orieinates from time delays inherent iu he geomet‘y of its sj»herically expaucdiug emission front., \citet{Kat94} has suggested that the shape of a GRB pulses originates from time delays inherent in the geometry of its spherically expanding emission front.
 Liaigetal.(1997) have provided argutrjeuts that saturated C'omptou Ip-scattering of softer photons may be the dominant. physical meciuismi tha creates he shape ol GRB pulses., \citet{Lia97} have provided arguments that saturated Compton up-scattering of softer photons may be the dominant physical mechanism that creates the shape of GRB pulses.
 Stunuer&Feiimore(1098):Bzunirez-HuizFeni1iore.(1999):Fenimore(2000 Claim that the rise time of GRB Fast Rise Exponentia Decay (FRED)-like striclues is 'elated t[9] the sound speed of the pulse inedium. but the decay {4je is relatec oa time-celay inherent in tlT geometry of au expaucineg. spherical GRB wave front uucergolig ripid svuchrotron cooliug.," \citet{Sum98,Ram99,Fen00} claim that the rise time of GRB Fast Rise Exponential Decay (FRED)-like structures is related to the sound speed of the pulse medium, but the decay time is related to a time-delay inherent in the geometry of an expanding, spherical GRB wave front undergoing rapid synchrotron cooling."
 How the spectrum of GRBs change with time also as a loug histoVON reaton1973:VedrentCline198[:Norrisetal. 1986).," How the spectrum of GRBs change with time also has a long history \citep{Whe73,Ved81,Nor83,Cli84,Nor86}."
. Recent uotable worς incldes Baud(1997). wl¢ κος auto- amd c‘oss-Correlatio1 statistics to track hardess variability in 209 b‘ieht BATSE bursts. and Crideretal.(1999) who racked the peak of phoou [requeucy lines lix of [I pulses it 26) jursts. finding tat this quantiy decays linearly. with j»ulse energy. [Itence.," Recent notable work includes \citet{Ban97} who used auto- and cross-correlation statistics to track hardness variability in 209 bright BATSE bursts, and \citet{Cri99} who tracked the peak of photon frequency times flux of 41 pulses in 26 bursts, finding that this quantity decays linearly with pulse energy fluence."
" lutlis paper a bright GRB dominated by a single s1n00hi. pulse is alavzed in au elfor [9] )elter uuderstaid GRB pulses iu general. aud 1jore specifically to hel» calib""ulte euergy depeiuxeut »ulse attributes that are beiug sec as stanmdarc Callles fcwv GRBs."," In this paper a bright GRB dominated by a single smooth pulse is analyzed in an effort to better understand GRB pulses in general, and more specifically to help calibrate energy dependent pulse attributes that are being used as standard candles for GRBs."
 TIlese al4butes may also 1 clistinguish or eliminate some plvsical processes proIOSEC to create GRB puses., These attributes may also help distinguish or eliminate some physical processes proposed to create GRB pulses.
 In. 82 data fr BATSE viewer 2193 will be int'oduced aud ciscussecl., In 2 data from BATSE trigger 2193 will be introduced and discussed.
 Ii 83 the Pulse Start Conjecttwe wil proposed., In 3 the Pulse Start Conjecture will be proposed.
 In 81. the Pulse Scale Conjecture wil be introd(cec. discussed. aud tested on data fr1i 2193.," In 4, the Pulse Scale Conjecture will be introduced, discussed, and tested on data from 2193."
 In 85 the next [our most |tent GRBs wi] also Use to test the Pulse Start aud Pulse Scale Conjectures., In 5 the next four most fluent GRBs will also used to test the Pulse Start and Pulse Scale Conjectures.
 Iu 86. the paper wi| couclude wit!] estitates of the theoretical unplications followitge [rom the potential truths of these conjectures.," In 6, the paper will conclude with estimates of the theoretical implications following from the potential truths of these conjectures."
 This project started with the search [or a single. isolated. fIuent. loug CRB pulse to study iu detail.," This project started with the search for a single, isolated, fluent, long GRB pulse to study in detail."
 The single pulse that appears to compose GRB 93021le (BATSE trigger 2193) was chosen because of its isolated. nature. high fluence. aud long duration.," The single pulse that appears to compose GRB 930214c (BATSE trigger 2193) was chosen because of its isolated nature, high fluence, and long duration."
 A list of GRBs with durations, A list of GRBs with durations
Since the discovery of jets in SS133 in 1978. there has )oen discussion about their uniqueness.,"Since the discovery of jets in SS433 in 1978, there has been discussion about their uniqueness."
 By now the zoo of various jets las culareed., By now the zoo of various jets has enlarged.
 There have already been detected hudreds relativistic jets of ACNs. low velocity jets of voune stars and a dozen jets of compact stars.," There have already been detected hundreds relativistic jets of AGNs, low velocity jets of young stars and a dozen jets of compact stars."
 Jets of ο133 staxl out anoue the other* for they harbour cool clouds witli ithe relativistic flox, Jets of SS433 stand out among the others for they harbour cool clouds within the relativistic flow.
" ""It is not clear. however. row the clouds could survive 1 itje relativistic jets aud )e observed."," It is not clear, however, how the clouds could survive in the relativistic jets and be observed."
 Tt is also worth ieifieniue. iat the thermal Taction is liselv to he domumaxr iu the jes of SS133.," It is also worth mentioning, that the thermal fraction is likely to be dominant in the jets of SS433."
 On he contrary. the lack of observatioial evieuce of thermal eas in ACN jets stronely restric 81ts volunc-filliug factor (κ10 5) aud implies that it caunot be important iu t1ο enerev budget of these jets (Colotictal. 1998)).," On the contrary, the lack of observational evidence of thermal gas in AGN jets strongly restricts its volume-filling factor $<10^{-8}$ ) and implies that it cannot be important in the energy budget of these jets \cite{Celotti et al. 1998}) )."
 These peculiarities make the jets of SS133 uniqi5, These peculiarities make the jets of SS433 unique.
" Jets of SS133 are highly collimated. 0;<1° Le nklv relativistic. ο=7.8-109 and powerful with kinetic hnunünositv Ly,~--1982 lo"," Jets of SS433 are highly collimated, $\theta_\mathrm{j} \le 1^\circ$ .4, mildly relativistic, $v_\mathrm{j}=7.8\cdot 10^{9}$ $^{-1}$, and powerful, with kinetic luminosity $L_\mathrm{k} \approx 10^{39}$ $^{-1}$."
" Chev appear from funnels of the supercritical accretion disk axd folow its precession rotation with a half opeuiug angle of about 207 and a period of ,16215. (seo Fie. 1).", They appear from funnels of the supercritical accretion disk and follow its precession rotation with a half opening angle of about $20^\circ$ and a period of $P_\mathrm{pr}=162^\mathrm{d}.5$ (see Fig. \ref{wall}) ).
 At the distance of a few 1072 cin the jets baXdlv cool aud radiate iu the N-rav domain., At the distance of a few $10^{12}$ cm the jets rapidly cool and radiate in the X-ray domain.
 The X-rav cluission does not show any structure of the jets., The X-ray emission does not show any structure of the jets.
 Therefore. the X-ray jets are thought to be contiuuous (Sewartetal. 1987)).," Therefore, the X-ray jets are thought to be continuous \cite{Stewart et al. 1987}) )."
 By contrast. the optical jets are observed as fraeioeuted. (Vermeulenetal.199353).," By contrast, the optical jets are observed as fragmented \cite{Vermeulen
 et al. 1993b}) )."
 Their chnipuess αμα. be roughly deduced from energetic COsiderations., Their clumpness may be roughly deduced from energetic considerations.
" The eas ust be dense enough to radiate the bulk of the emission: and amass loading of the jet by dense eas ist xoxinuatelv satisfv: where VES9PS Las the vohme of the jet. & is its cheth. nm; ds electron deity. eg, is the IL, emission rate."," The gas must be dense enough to radiate the bulk of the emission: and mass loading of the jet by dense gas must approximately satisfy: where $V \approx \theta_\mathrm{j}^2 R^3/4$ is the volume of the jet, $R$ is its length, $n_\mathrm{e}$ is electron density, $\epsilon_\mathrm{H_\alpha}$ is the $\mathrm{H_\alpha}$ emission rate."
" Thus. one finds that οςαν10H. 3 aud a volumie-filline factor of f=10 ypropriate paraiueters: πιuinositv in IL, line Ly=107 +. total jet kinetic luuinositv Lj=10? L ej,=10ol CCL? L R—Rcxs10H cm leugth of e-fokliug IL, line xiehtuess."," Thus, one finds that $n_\mathrm{e}\approx 5\cdot 10^{11}$ $^{-3}$ and a volume-filling factor of $f\approx
10^{-5}$ for appropriate parameters: luminosity in $\mathrm{H_\alpha}$ line $L_\mathrm{H_\alpha}=10^{36}$ $^{-1}$, total jet kinetic luminosity $L_\mathrm{k}=10^{39}$ $^{-1}$ , $\epsilon_\mathrm{H_\alpha}=
10^{-24}$ $^3$ $^{-1}$, $R=R_\mathrm{e} \approx 8.4\cdot 10^{14}$ cm — length of -folding $\mathrm{H_\alpha}$ line brightness."
" If ποστς that the jets become hup iu the eap between the X-ray ]art aud the opical jet beeiuniug at about fh2,3.101 cni {Borisov&Fabrika 1987).", It seems that the jets become lumpy in the gap between the X-ray part and the optical jet beginning at about $R_\mathrm{in}=2.3\cdot 10^{14}$ cm \cite{Borisov Fabrika 1987}) ).
 The gas could coudeuse there due to a thernal imstabilitv as Diukuiuu ct al. (Briukniuiuetal. 1988)), The gas could condense there due to a thermal instability as Brinkmann et al. \cite{Brinkmann et al. 1988}) )
 have shown iu a siniulation of the thermal evolution of the X-ray jets., have shown in a simulation of the thermal evolution of the X-ray jets.
 The instability takes place ouly in the interior jet. until a distance of LOY? c1.," The instability takes place only in the interior jet, until a distance of $10^{13}$ cm."
 The parameters o the clouds found iu their work are close to those obtained by Panterov Fabrika (Pauterov&Fabrika 19973) from the Daliner clecrements o the jets: hiydroeen density àc1055 5m ald size of the clouds /x105 cim., The parameters of the clouds found in their work are close to those obtained by Panferov Fabrika \cite{Panferov Fabrika 1997}) ) from the Balmer decrements of the jets: hydrogen density $n \ge 10^{13}$ $^{-3}$ and size of the clouds $l\le 10^8$ cm.
 It should be noted that tl‘SC paralueers as well as the filling factor fz1-10 foud there are more appropriate for the distance of luuxnuun optical brightuess of the jets Ray~--1.101! cni., It should be noted that these parameters as well as the filling factor $f \approx 4\cdot 10^{-6}$ found there are more appropriate for the distance of maximum optical brightness of the jets $R_\mathrm{m} \approx 4\cdot 10^{14}$ cm.
 These parameters will be represeutative onesm what follows., These parameters will be representative onesin what follows.
 The clouds are grouped iu clusters with sizes of about anl?10272 cm (Pauferov.&Fabrika⋅↽− 1997))., The clouds are grouped in clusters with sizes of about $10^{12}$ cm \cite{Panferov Fabrika 1997}) ).
 Still- bieeer, Still bigger
 Still- bieeer., Still bigger
convey the idea of eclipses that are complete or very nearly. so.,convey the idea of eclipses that are complete or very nearly so.
 Iu aclclition. we observed several eclipse (imines using a SBIC ST-8 CCD camera attached to the 35-cm reflector at the campus station of the Chunebuk National Uuiversity Observatory (CbNUQO) in IWworea.," In addition, we observed several eclipse timings using a SBIG ST-8 CCD camera attached to the 35-cm reflector at the campus station of the Chungbuk National University Observatory (CbNUO) in Korea."
 The observations were mace without a filter and reduced with the conventional IRAF package., The observations were made without a filter and reduced with the conventional IRAF package.
 The details of the ChNUO observatious have been given by im et al. (, The details of the CbNUO observations have been given by Kim et al. (
2006).,2006).
 We cletermined ifteeu times of nuinunum lieit from all our CCD observations tsiug tlie method of INwee van Woerden (1956. hereafter IXvW).," We determined fifteen times of minimum light from all our CCD observations using the method of Kwee van Woerden (1956, hereafter KvW)."
 These timings are listed in Table 3 together with all other CCD timies: the SOAO data are weiehtecd means from the observatiois in the BVRI baidpasses., These timings are listed in Table 3 together with all other CCD timings; the SOAO data are weighted means from the observations in the $BVRI$ bandpasses.
 ΤΙe second columu οἱves the standard deviation of each timing., The second column gives the standard deviation of each timing.
 For he period study “CL Aur. 198 arcival timings (16 plate. 10:| visual. 5 photographic aud 73 CCD) lave been lected Grom he lierature and f‘Ol OUr Lueasirements.," For the period study of CL Aur, 198 archival timings (16 plate, 101 visual, 8 photographic and 73 CCD) have been collected from the literature and from our measurements."
 Most of the earlier linines were actually racted [rom the clata base pubished by Ixrejner e al. (, Most of the earlier timings were actually extracted from the data base published by Kreiner et al. (
2001).,2001).
 Because altost all but the CCD ings were piblisled without error informatiii. the following standard devialious were assigued ) timing residuals based ou obse'vational metrod: + -0.022 «d for sky-patrol slate or photographic luintima. and -zE0.007 d for visual minima.," Because almost all but the CCD timings were published without error information, the following standard deviations were assigned to timing residuals based on observational method: $\pm$ 0.022 d for sky-patrol plate or photographic minima, and $\pm$ 0.007 d for visual minima."
 Realive weights were then calculated. as the inverse squares of these values cousistent with the errors aux weiehts for the CCD tinines., Relative weights were then calculated as the inverse squares of these values consistent with the errors and weights for the CCD timings.
 In order to examine whether the period change of CL Aur cau be produced by a quadratic LTT ephemeris as suggestedMOD by WOT. we fitted all times of ininimuun light to that ephemeris form: where 4 svinbolizes he LTT effect due to a third body (Irwiu 1952. 1959) and includes five yarameters (cpsiti. e.w.naucd T).," In order to examine whether the period change of CL Aur can be produced by a quadratic LTT ephemeris as suggested by W07, we fitted all times of minimum light to that ephemeris form: where $\tau_{3}$ symbolizes the LTT effect due to a third body (Irwin 1952, 1959) and includes five parameters $a_{12}\sin i_3$, $e$ , $\omega$, $n$ and $T$ )."
 Here. i aud T denote the Ixeplerian mean motion X the mass center of the eclipsing pair aud the epoch of its periastron passage. respectively.," Here, $n$ and $T$ denote the Keplerian mean motion of the mass center of the eclipsing pair and the epoch of its periastron passage, respectively."
 In this analysis. he Leveubere-Ma“quart echuique (P‘ess et αἱ.," In this analysis, the Levenberg-Marquart technique (Press et al."
 1992) was apdliecL to solve for the eigh unknown yarameters of the ephemeris., 1992) was applied to solve for the eight unknown parameters of the ephemeris.
 By usi& the thircd-body paraneters of WOT as initial values. we obtained improve fin tle sellse of e‘rors sinaller han fornerly) parameters [or them ancl the 'esults are listed i Table | together with other related quautiies.," By using the third-body parameters of W07 as initial values, we obtained improved (in the sense of errors smaller than formerly) parameters for them and the results are listed in Table 4 together with other related quantities."
 In this table. P4 aud A inclicate he cycle length anc seiii-amplitucde of the LTT orbi. respectively. aud f(AM) i the mass fuuction oL the system.," In this table, $P_3$ and $K$ indicate the cycle length and semi-amplitude of the LTT orbit, respectively, and $f(M_{3})$ is the mass function of the system."
 Witun errors. our LUT JaLammeters are not signicantly different [rou those of WOT.," Within errors, our LTT parameters are not significantly different from those of W07."
" The sample inasses (Al,siu £4) of the assumed third )odsy iu the table were c:ileulated by using the absolute dimeusiois of the eclipsing pair preseuted 1 a later section.", The sample masses $M_3 \sin i_3$ ) of the assumed third body in the table were calculated by using the absolute dimensions of the eclipsing pair presented in a later section.
 The O-C' diagram of CL Aur coustructed wit the linear terms in Table Lis drawn in the top pauel of Figure 2., The $O$ $C$ diagram of CL Aur constructed with the linear terms in Table 4 is drawn in the top panel of Figure 2.
 The timiugs are marked by different sviubols according to observatioial method aud type of eclipse., The timings are marked by different symbols according to observational method and type of eclipse.
 The continuous curve audthe dashed. parabolic one represeut he," The continuous curve andthe dashed, parabolic one represent the"
involved in the FD method over the mean and median methods.,involved in the FD method over the mean and median methods.
 For comparing image quality of the templates. we find that the resolution of the resulting images is very similar as (he 50th percentile of the fitted EWIIM of the FD method is less than smaller than the 50th percentile of the fitted FWIIM of the mean method.," For comparing image quality of the templates, we find that the resolution of the resulting images is very similar as the 50th percentile of the fitted FWHM of the FD method is less than smaller than the 50th percentile of the fitted FWHM of the mean method."
 We find that the value added by the FD method over the mean or median procedures does not overcome its added: cost ancl complexity., We find that the value added by the FD method over the mean or median procedures does not overcome its added cost and complexity.
 This leads us (to the conclusion that there is room lor improvement over all three methods., This leads us to the conclusion that there is room for improvement over all three methods.
 We are currently exploring various possible improvements ancl theoretical justifications for some of the approaches outlined in (his paper., We are currently exploring various possible improvements and theoretical justifications for some of the approaches outlined in this paper.
(?).. the radiative intensity from the pulsar (see also Sill) at the distance of the WD is approximately 3.108 teu 7. about of the outward radiative flux: we therefore neglect it in our modchue.,"\citep{2008ApJ...679..675V}, the radiative intensity from the pulsar (see also 4) at the distance of the WD is approximately $\times10^8$ $^{-1}$ $^{-2}$, about of the outward radiative flux; we therefore neglect it in our modeling."
 We describe in detail the model fitting process., We describe in detail the model fitting process.
 The spectimm of the WD companion was modeled sine white chwarf atimosphere (WDA) models that count for recently introduced japrovements im the escriptiou of the atimosphere of these stars. especially Ly-a absorption iu the UV (?).. opacity of helium onunated medium (27). aud refraction (?)..," The spectrum of the WD companion was modeled using white dwarf atmosphere (WDA) models that account for recently introduced improvements in the description of the atmosphere of these stars, especially $\alpha$ absorption in the UV \citep{2006ApJ...651L.137K}, , opacity of helium dominated medium \citep{2006ApJ...641..488K,2007PhRvB..76g5112K}
 and refraction \citep{2004ApJ...607..970K}."
 The mocels sed in the analysis were successful im describing the sutire spectral energy distributions of may cool WDs. oewcluding the UV. spectra of purc-IE atimosphere WD BPAL 1729 (7). and the near UV spectra of WDs with Tap4000AN (2).," The models used in the analysis were successful in describing the entire spectral energy distributions of many cool WDs, including the UV spectrum of pure-H atmosphere WD BPM 4729 \citep{2006ApJ...651L.137K} and the near UV spectra of WDs with $T_{\rm eff}\sim4000 \, K$ \citep{2010ApJ...715L..21K}."
 The fit in effective temperature and eravitv for ο and ID atmospheres was performed for the known photometry. BYRI of ?.. and Alagcllan JITIN audSpitzer TR ameasurcinents reported here. assuniug that the distance to the system is 156.3ppe (7) and the reddening is E(D.—V)=0.03.," The fit in effective temperature and gravity for He and H atmospheres was performed for the known photometry, BVRI of \citet{1993A&A...276..382D}, and Magellan JHK and IR measurements reported here, assuming that the distance to the system is $156.3$ pc \citep{2008ApJ...685L..67D} and the reddening is $E(B-V)=0.03$."
 The spectral energv distribution of the WD is best reproduced by a pure hydrogen atinosphere model., The spectral energy distribution of the WD is best reproduced by a pure hydrogen atmosphere model.
 The hydrogen is clearly visible. when comparing with pure-Ie model spectrum. bv strong absorption in the UV. due to strong Ly-a red wing opacity (2?) and fux suppression in the IR due to collisioninduced absorption (CTA) by molecular hydrogen (7)..," The hydrogen is clearly visible, when comparing with pure-He model spectrum, by strong absorption in the UV, due to strong $\alpha$ red wing opacity \citep{2006ApJ...651L.137K} and flux suppression in the IR due to collision-induced absorption (CIA) by molecular hydrogen \citep{1999ApJ...511L.107S}."
 The best-fit model closely. matches the VLT/FORSL spectrum (see Figure 7))., The best-fit model closely matches the VLT/FORS1 spectrum (see Figure \ref{WD_PL}) ).
" The best-fit effective temperature, T=3950+150 KK. is dn agreement with previous estimates (?77) andl the BB fit from above. see Figure 7.."," The best-fit effective temperature, $T= 3950\pm150$ K, is in agreement with previous estimates \citep{1993Natur.364..603B,2006A&A...450..295B,1993A&A...276..382D} and the BB fit from above, see Figure \ref{WD}."
 The obtained gravity (logg=6.98£0.15 |ces|) fits the models of a helium core white dwarf (C?7).. assundue the mass of the companion to be 0.25M... (2)...," The obtained gravity $\log g=6.98\pm0.15$ [cgs]) fits the models of a helium core white dwarf \citep{2001AN....322..405S,2009A&A...502..207A}, assuming the mass of the companion to be $M_{\sun}$ \citep{2008ApJ...679..675V}."
 The uncertainties are estimated from the uncertainty£L in the photometric fluxes (Table 2)). and the small πασάΙον in the distance aud WD lass.," The uncertainties are estimated from the uncertainty in the photometric fluxes (Table \ref{phot}) ), and the small uncertainties in the distance and WD mass."
 We include the fit parameters in Table [: we also list the radius. AR. which is fitted nuplicitly via log (because the mass is well known): the quoted error reflectsg uncertamties in the temperature aud distance.," We include the fit parameters in Table \ref{bb_pl}; we also list the radius, $R$, which is fitted implicitly via $\log g$ (because the mass is well known); the quoted error reflects uncertainties in the temperature and distance."
 Without spectral lines. the spectrum provides uo cdistauce-iudependeut constraiuts ou the gravity).," Without spectral lines, the spectrum provides no distance-independent constraints on the gravity)."
 While some of cool WD pulsar companions have optical photometry. this is usually not enough for definitive assiguiuent of their atmospheric chemiuca composition and parameters (see discussion iu ?)).," While some of cool WD pulsar companions have optical photometry, this is usually not enough for definitive assignment of their atmospheric chemical composition and parameters (see discussion in \citealt{2006A&A...450..295B}) )."
 At so low temperatures the admixture of heliun shouk produce substantially differcut CTIA effect due to IL. Te collisious aud therefore would be different from pure hydrogen atinosphere spectrum in the IR. as indicate in Figure 5 of 7..," At so low temperatures the admixture of helium should produce substantially different CIA effect due to $_2$ --He collisions and therefore would be different from pure hydrogen atmosphere spectrum in the IR, as indicated in Figure 5 of \citet{2008AJ....136...76H}."
 Iu this study we present the ful spectral cherey distribution of the companion. aud by obtaining ooeood match with the pure-I atmosphere mode we can be confident that the object is indeed a ILatmosphere WD.," In this study we present the full spectral energy distribution of the companion, and by obtaining good match with the pure-H atmosphere model we can be confident that the object is indeed a H-atmosphere WD."
 This allows for proper derivation of the atinosphere parameters (Zig. g) aud the age of the WD.," This allows for proper derivation of the atmosphere parameters $T_{\rm eff}$, $g$ ) and the age of the WD."
 Moeasurenieuts of near and -mid IR fluxes are essential for a defiuitive assiguiment of the atinosphere conrposition of other cool WD pulsar conipauious., Measurements of near- and -mid IR fluxes are essential for a definitive assignment of the atmosphere composition of other cool WD pulsar companions.
 The WD companion atinosplere of PSR J0751|1507 was classified as hebluunuedeh by ?.. which is at odds with the evolutionary models for such stars.," The WD companion atmosphere of PSR J0751+1807 was classified as helium-rich by \citet{2006A&A...450..295B}, which is at odds with the evolutionary models for such stars."
 Iu that ourtieulu work such a conclusion was reached hy »erformine: analysis with the WD atinosphere models of 7T.., In that particular work such a conclusion was reached by performing analysis with the WD atmosphere models of \citet{1995ApJ...443..764B}.
 However. these models teud to bias the prediction of the atinosplierie content of a cool white dwrfs frou iedrosenaich to hbelimmerich. as they do uot fully account for the red wine of the La-a absorption aud he free-free opacity of deuse heliuma (see discussion iu ?..," However, these models tend to bias the prediction of the atmospheric content of a cool white dwarfs from hydrogen-rich to helium-rich, as they do not fully account for the red wing of the $\alpha$ absorption and the free-free opacity of dense helium (see discussion in \citet{2006ApJ...651L.137K}."
 Our conclusion for the atmospheric composition of WD companion of JOL37 L715. obtained by a good fit to he cutire WD spectral energy distribution by the pure-II atmosphere model. is in line with other works. which ostulate a pure hydrogen outermost laver (??)..," Our conclusion for the atmospheric composition of WD companion of $-$ 4715, obtained by a good fit to the entire WD spectral energy distribution by the pure-H atmosphere model, is in line with other works, which postulate a pure hydrogen outermost layer \citep{1998MNRAS.294..569H,2001AN....322..405S}."
 Usiug this (now fixed) model for the WD spectrum. we can again fit à PL to the pulsar part of the spectimm.," Using this (now fixed) model for the WD spectrum, we can again fit a PL to the pulsar part of the spectrum."
 We choose to fit the rauge À«3575AA. where the pulsar dominates.," We choose to fit the range $\lambda<3575$, where the pulsar dominates."
 The fit is to be compared with the black-body fits in Table lH: we fund a=2.16017). νι= LOI(19)x10 tem 7A +.," The fit is to be compared with the black-body fits in Table \ref{bb_pl}; we find $\alpha=-2.46(17)$, $N_{\rm PL}=4.61(19)\times10^{-18}$ $^{-1}$ $^{-2}$ $^{-1}$."
 From Figure 7.. it would appear that the fit is good. except for the portion of the spectrum in the NUV. where the WD atmosphere and the PL are of similar streneths.," From Figure \ref{WD_PL}, it would appear that the fit is good, except for the portion of the spectrum in the NUV, where the WD atmosphere and the PL are of similar strengths."
 Also. the value of the power-law index is somewhat puzzling. since it is no longer thermalhke. nor is it typical for a pulsar nou-thermal spectrum.," Also, the value of the power-law index is somewhat puzzling, since it is no longer thermal-like, nor is it typical for a pulsar non-thermal spectrum."
 Iudeed. the residuals in the FUV. appear to slow a systematic slope.," Indeed, the residuals in the FUV appear to show a systematic slope."
" This suggests that the UV spectra may actually consist of two compoucuts. for iustauce a thermal BRavleigh-Jeaus tail (PL with a= Lauda nonthermal PL more typical of old AISPs (PL with 170:2 Ίο, photon index 1«DE<2) - see Section L."," This suggests that the UV spectrum may actually consist of two components, for instance a thermal Rayleigh-Jeans tail (PL with $\alpha=-4$ ) and a non-thermal PL more typical of old MSPs (PL with $-1\geq\alpha\geq-2$, i.e., photon index $1\leq\Gamma\leq2$ ) - see Section 4."
 Using IIST/STIS. I01 were able to measure the FUV spectrin in { bius with low S/N. which rendered the meastrement of the spectral slope rather uncertiiu.," Using HST/STIS, K04 were able to measure the FUV spectrum in 4 bins with low S/N, which rendered the measurement of the spectral slope rather uncertain."
 Our mich better quality FUW spectrum from ACS matches those STIS fluxes rather well (Figure 6)) aud also the FUV broad-band photometry., Our much better quality FUV spectrum from ACS matches those STIS fluxes rather well (Figure \ref{spec}) ) and also the FUV broad-band photometry.
 This gives us confidence in the accuracy of the cross-calibration betweenthe ΠΠπο, This gives us confidence in the accuracy of the cross-calibration betweenthe instruments.
 Under the assumption that the FUV. PL-like eiissiou is indeed a Rayleigh-Jeaus bw (FyxA tor Byx v7). we can constrain the temperature and radius of the cuutting body for the known distance. d=156.3 ppc.," Under the assumption that the FUV PL-like emission is indeed a Rayleigh-Jeans law $F_\lambda\propto\lambda^{-4}$ or $F_\nu\propto\nu^2$ ), we can constrain the temperature and radius of the emitting body for the known distance, $d=156.3$ pc."
 We calculate TR-—1.«10 ku’., We calculate $TR^2 = 1.9\times10^7$ $^2$.
 In the case here. however. a black-body law starts' to deviate from a Ravleigh-Jeaus law in the FUV for temperatures T<5«10 IIS. Note that R=RY and T=Ty. io. the temperature aud radius as nieasured by a distant observer.," In the case here, however, a black-body law starts to deviate from a Rayleigh-Jeans law in the FUV for temperatures $T<5\times10^5$ K. Note that $R\equiv R_\infty$ and $T\equiv T_\infty$, i.e., the temperature and radius as measured by a distant observer."
 We show possible thermal fits to the FUWV spectrum in Figure 8.., We show possible thermal fits to the FUV spectrum in Figure \ref{BBs}. .
 We include the lowest-cucrey poiuts from the ταν spectra iu Section ?? these constrain the lüieh-teniperature linut of the possible thermal emission to T«3.5«109 KI. The lower limit ou the temperature is set by requiring that the enüttiug area be reasonable for a NS., We include the lowest-energy points from the X-ray spectra in Section \ref{rawX} – these constrain the high-temperature limit of the possible thermal emission to $T\leq3.5\times10^6$ K. The lower limit on the temperature is set by requiring that the emitting area be reasonable for a NS.
 Whereas temperatures as low as 7«10! KK can still roughly fit the data. the required radius. 2 Liskin. is larecr than the largest plausible value of kkin (2).. ," Whereas temperatures as low as $7\times10^4$ K can still roughly fit the data, the required radius, $24$ km, is larger than the largest plausible value of km \citep{2010NewAR..54..101L}. ."
For R= kk. the corresponding surface temperature is T=1.25«10 KK. aud the likely NS size of R=13 kk vieldsa surface temperature of 1.5«10 KK. All of these estimates are affected by the choice of reddeningin the FUV and extinction in N-ravs (for," For $R=15$ km, the corresponding surface temperature is $T=1.25\times10^5$ K, and the likely NS size of $R=13$ km yieldsa surface temperature of $1.5\times10^5$ K. All of these estimates are affected by the choice of reddeningin the FUV and extinction in X-rays (for"
An initial source spectrum should also be taken into account.,An initial source spectrum should also be taken into account.
" In the soft X-ray band. (his is given by the Band spectrum (Dandetal.1993) where 2 is a parameter in units of erescm7keVland 9~0 and LE,""mc200keV are suggested by Preece οἱ al. ("," In the soft X-ray band, this is given by the Band spectrum \citep{b93}
 where $B$ is a parameter in units of ${\rm ergs}\,{\rm
cm}^{-2}\,{\rm keV}^{-1}$ , and $\delta\simeq 0$ and $E_p\simeq 200$ keV are suggested by Preece et al. ("
2000).,2000).
 Thus. we can caleulate the measured e.g.. in the 0.3—10 keV band by ART.," Thus, we can calculate the measured flux, e.g., in the $0.3-10$ keV band by XRT."
 Consequently. Tere the unabsorbed initial emission is still taken to be a pulse of light. approximately as in equation (10).," Consequently, Here the unabsorbed initial emission is still taken to be a pulse of light, approximately as in equation (10)."
 In the case of a beam of light. the difference in the echo lieht curve is the short rising time at the beginning time (e.g.. see Fig.," In the case of a beam of light, the difference in the echo light curve is the short rising time at the beginning time (e.g., see Fig."
 2)., 2).
 Equation (13) can be evaluated numerically with different parameters considered., Equation (13) can be evaluated numerically with different parameters considered.
" We lind (hat the temporal behavior of Fy, significantly depends on three observable quantities of dust grains.", We find that the temporal behavior of $F_h$ significantly depends on three observable quantities of dust grains.
 The first quantity is the position of dust. Dy..., The first quantity is the position of dust $D_{ds}$.
" This is because /, depends prominently on the position of the dust. which is inferred. Gon equation (1)."," This is because $t_d$ depends prominently on the position of the dust, which is inferred from equation (1)."
 The second quantity is (he maximal size of a dust grain. e... which is the laree-size eutolf for the size distribution.," The second quantity is the maximal size of a dust grain, $a_+$, which is the large-size cutoff for the size distribution."
 The third quantity is the index s in the dependence of dust-scattering optical depth on X-ray. energy., The third quantity is the index $s$ in the dependence of dust-scattering optical depth on X-ray energy.
 One prominent characteristic of (his temporal behavior is a distinguishable broken power law. with a break time dependent on the parameters cliseussecl above.," One prominent characteristic of this temporal behavior is a distinguishable broken power law, with a break time dependent on the parameters discussed above."
 As shown in Figure 3. a shallow decay before the break and a slope —2.0 after the break are clearly present in the light curves.," As shown in Figure 3, a shallow decay before the break and a slope $\simeq -2.0$ after the break are clearly present in the light curves."
 The shallow decay before the break is expected Irom our previous discussion and roughly consistent with our estimates of small-angle scattering. shown by equation (3). while (he steep decay alter the break can be attributed to the quickly decreasing cross section of larger angle scattering al later limes.," The shallow decay before the break is expected from our previous discussion and roughly consistent with our estimates of small-angle scattering, shown by equation (3), while the steep decay after the break can be attributed to the quickly decreasing cross section of larger angle scattering at later times."
 This feature of the flux (x/ 7) is also implied in ihe previous discussion. e.g.. as shown in Figure 2. which is roughly consistent with the decreasing maxinia.," This feature of the flux $\propto
t^{-2}$ ) is also implied in the previous discussion, e.g., as shown in Figure 2, which is roughly consistent with the decreasing maxima."
 Figure 4 plots the spectral evolution during dust scattering., Figure 4 plots the spectral evolution during dust scattering.
 In. general. (he spectra soften as (he flux decreases.," In general, the spectra soften as the flux decreases."
 The softening of the spectra can be attributed physically to the diffraction effect. (treated as scattering here) which is described in the differential cross seclion versus scattering angle (eq. [, The softening of the spectra can be attributed physically to the diffraction effect (treated as scattering here) which is described in the differential cross section versus scattering angle (eq. [
8]).,8]).
 Softer X-rays tend to be scattered at a larger angle a. with high-order maxima in thedifferential cross section. and are thus received at a larger," Softer X-rays tend to be scattered at a larger angle $\alpha$, with high-order maxima in thedifferential cross section, and are thus received at a larger"
"facility, since the experiments require a close detector and only the ions close to the ends of the straight sections contribute.","facility, since the experiments require a close detector and only the ions close to the ends of the straight sections contribute."
" Alternatively, the low energy neutrino fluxes might be obtained by putting one/two detectors at off-axis of the storage ring planned for the CP violation search [19].."," Alternatively, the low energy neutrino fluxes might be obtained by putting one/two detectors at off-axis of the storage ring planned for the CP violation search \cite{Lazauskas:2007va}."
 A comparison of the physics potential of low energy beta-beams and conventional sources is made in [14]., A comparison of the physics potential of low energy beta-beams and conventional sources is made in \cite{McLaughlin:2004va}.
.In [20] it is shown that interesting information on the spin-dipole as well as higher multipoles might be obtained by the vaying the y of the ions., In \cite{Lazauskas:2007bs} it is shown that interesting information on the spin-dipole as well as higher multipoles might be obtained by the vaying the $\gamma$ of the ions.
 Instead of varying the ions one might take different parts of the fluxes at a detector [22].., Instead of varying the ions one might take different parts of the fluxes at a detector \cite{Amanik:2007zy}.
 Gathering more experimental constraints on the corresponding transition amplitudes is important since the same nuclear matrix elements are involved in the neutrinoless double-beta decay due to exchange of a massive Majorana neutrino [49].., Gathering more experimental constraints on the corresponding transition amplitudes is important since the same nuclear matrix elements are involved in the neutrinoless double-beta decay due to exchange of a massive Majorana neutrino \cite{Volpe:2005iy}.
 These measurements can furnish a new constraints to the half-lives calculations that are still plagued by important discrepancies., These measurements can furnish a new constraints to the half-lives calculations that are still plagued by important discrepancies.
" Finally, a combination of the neutrino beams at different boost can be used to reconstruct the signal from a supernova explosion in an observatory [17].."," Finally, a combination of the neutrino beams at different boost can be used to reconstruct the signal from a supernova explosion in an observatory \cite{Jachowicz:2006xx}."
 The proposed method has the advantage that it is free from the cross section uncertainties., The proposed method has the advantage that it is free from the cross section uncertainties.
" Various scenarios for the study of CP violation have been proposed where the energy of the ions is much higher, the  ranging from 150 [28] to several hundreds to thousands [31-35,38].."," Various scenarios for the study of $\cal{CP}$ violation have been proposed where the energy of the ions is much higher, the $\gamma$ ranging from 150 \cite{bur05} to several hundreds to thousands \cite{bur04,don05,hub06,Agarwalla:2006vf,Agarwalla:2006gz,Coloma:2007nn}."
 The value of 150 GeV per nucleon comes from the maximum acceleration that can be attained in the SPS., The value of 150 GeV per nucleon comes from the maximum acceleration that can be attained in the SPS.
 The baseline scenario in this case is the same as the original one., The baseline scenario in this case is the same as the original one.
"On the contrary, the medium","On the contrary, the medium"
roughly exponentially with height. A increases inversely.,"roughly exponentially with height, $A$ increases inversely."
 In a flux tube the increase in radius goes as p~VA. while in a sheet the magnetic field only expands in the direction perpendicular to the sheet. so that r~A.," In a flux tube the increase in radius goes as $r \sim \sqrt{A}$, while in a sheet the magnetic field only expands in the direction perpendicular to the sheet, so that $r \sim A$."
 Consequently. r increases far more rapidly in sheets than tubes.," Consequently, $r$ increases far more rapidly in sheets than tubes."
 we only synthesize radial cuts for rays pointing in the perpendicular direction., we only synthesize radial cuts for rays pointing in the perpendicular direction.
 The expansion rate for a magnetic feature consisting of several flux tubes. which merge above a height follows the same scaling.," The expansion rate for a magnetic feature consisting of several flux tubes, which merge above a height follows the same scaling."
 Below the merging height the flux tubes expand individually., Below the merging height the flux tubes expand individually.
 Above this. they expand as a single feature following A(z)~ Ao/B(z). where Ao is the summed section of the individual tubes at z=0.," Above this, they expand as a single feature following $A(z) \sim A_{0}/B(z)$ , where $A_{0}$ is the summed cross-section of the individual tubes at $z=0$."
 To study flux expansion under more realistic conditions we use radiative magnetohydrodynamic (MHD) simulations., To study flux expansion under more realistic conditions we use radiative magnetohydrodynamic (MHD) simulations.
 the MuRAM code (MPS/University of Chicago Radiative MHD. Vógleretal. 2005).," the MuRAM code (MPS/University of Chicago Radiative MHD, \citealt{Voegler+others2005}) )."
 The code takes into account effects of ful compressibility. open boundary conditions as well as non-gray radiative transfer and partial tonization.," The code takes into account effects of full compressibility, open boundary conditions as well as non-gray radiative transfer and partial ionization."
 In the current study the simulation domain is mx24Mmx 1.68Mm (576x576 120 erid points) of which approximately 700 km is abovethe lo@(Tso0nm)=O level., In the current study the simulation domain is $\times$ $\times$ 1.68Mm $\times$ $\times$ 120 grid points) of which approximately 700 km is abovethe $log(\tau_{500nm})=0$ level.
"The turbulent nature of the interstellar medium (ISM) is believed to play a crucial role on the determination of its density and velocity structure (see Elmegreen Scalo 2004; Scalo Elmegreen 2004; and Mac Low Klessen 2004,for recent reviews).","The turbulent nature of the interstellar medium (ISM) is believed to play a crucial role on the determination of its density and velocity structure (see Elmegreen Scalo 2004; Scalo Elmegreen 2004; and Mac Low Klessen 2004,for recent reviews)."
 A useful characterization of the properties of a random density or velocity distribution is given by the spatial power spectrum., A useful characterization of the properties of a random density or velocity distribution is given by the spatial power spectrum.
 This function can be measured for different components of the interstellar gas by using different observational techniques., This function can be measured for different components of the interstellar gas by using different observational techniques.
" In the warm ionized medium (WIM) interstellar scintillation (ISS) measurements have lead to a Kolmogorov slope density power spectrum, which is valid for scales expanding over ~5 orders of magnitude from 109? to 1015 cm (e.g. Armstrong, Rickett Spangler 1995)."," In the warm ionized medium (WIM) interstellar scintillation (ISS) measurements have lead to a Kolmogorov slope density power spectrum, which is valid for scales expanding over $\approx 5$ orders of magnitude from $10^{8.3}$ to $10^{15}$ cm (e.g. Armstrong, Rickett Spangler 1995)."
" The same authors found that when ISS data are combined with measurements of differential Faraday rotation angle and electron density gradients, constraints can be put on the spectrum at much larger scales, suggesting an extension of the precedent result to scales of =10?9 cm."," The same authors found that when ISS data are combined with measurements of differential Faraday rotation angle and electron density gradients, constraints can be put on the spectrum at much larger scales, suggesting an extension of the precedent result to scales of $\approx 10^{20}$ cm."
" For the atomic gas, the 21cm hydrogen line provides a variety of useful tools to measure statistical properties of turbulence."," For the atomic gas, the 21cm hydrogen line provides a variety of useful tools to measure statistical properties of turbulence."
" In particular, some estimates of the spatial power spectrum for"," In particular, some estimates of the spatial power spectrum for"
"This implies that the stability of the outflow cavity is strongly effected by the direct stellar irradiation of the massive star, independent of the symmetry.","This implies that the stability of the outflow cavity is strongly effected by the direct stellar irradiation of the massive star, independent of the symmetry."
" In ?,, the authors presented six self-gravity radiation hydrodynamics simulations of the collapse of a pre-stellar core."," In \citet{Yorke:2002p1}, the authors presented six self-gravity radiation hydrodynamics simulations of the collapse of a pre-stellar core."
" The initial core mass in the simulations was chosen to be 30, 60, and with an outer core radius of 0.05, 0.1, and 0.2 pc."," The initial core mass in the simulations was chosen to be 30, 60, and with an outer core radius of 0.05, 0.1, and 0.2 pc."
 The density profile drops proportional to r7., The density profile drops proportional to $r^{-2}$.
" Since in these simulations an additional inflow of mass at the outer boundary into the computational domain is allowed, the total mass reservoir of the forming star is not limited to these initial core masses."," Since in these simulations an additional inflow of mass at the outer boundary into the computational domain is allowed, the total mass reservoir of the forming star is not limited to these initial core masses."
 The initial isothermal temperature of the core is 20 K. The pre-stellar core is initially in solid- rotation without any turbulent motion., The initial isothermal temperature of the core is 20 K. The pre-stellar core is initially in solid-body rotation without any turbulent motion.
 The equations are solved on a static nested grid of three levels in cylindrical coordinates assuming axial symmetry and midplane symmetry., The equations are solved on a static nested grid of three levels in cylindrical coordinates assuming axial symmetry and midplane symmetry.
 The forming massive star is represented by a sink cell at the origin of the domain., The forming massive star is represented by a sink cell at the origin of the domain.
 The radiation transport method used is the gray as well as the frequency-dependent FLD approximation., The radiation transport method used is the gray as well as the frequency-dependent FLD approximation.
 The outflow properties in the simulations with gray FLD and initial core masses of 30 and are neither visualized nor discussed in ?.., The outflow properties in the simulations with gray FLD and initial core masses of 30 and are neither visualized nor discussed in \citet{Yorke:2002p1}.
" In the simulation with gray FLD and an initial core mass of,, the massive star stops its mass growth at Μ.=20.7Mo and maintains a luminosity of L,=5.2x104Lg."," In the simulation with gray FLD and an initial core mass of, the massive star stops its mass growth at $M_* = 20.7\Msol$ and maintains a luminosity of $L_* = 5.2 \times 10^4 \Lsol$."
 No polar cavity forms before the end of the simulation at 110 kyr., No polar cavity forms before the end of the simulation at 110 kyr.
" In the three simulations with frequency-dependent FLD, polar cavities are formed."," In the three simulations with frequency-dependent FLD, polar cavities are formed."
" In the case, the cavity interacts with the infalling envelope and collapses within a few thousand years."," In the case, the cavity interacts with the infalling envelope and collapses within a few thousand years."
" In the two higher mass cases, the infall even at larger radii is reversed shortly after the launch of the outflow cavity; therefore the cavity does not interact with a gravitationally driven infall anymore and simply expands in time."," In the two higher mass cases, the infall even at larger radii is reversed shortly after the launch of the outflow cavity; therefore the cavity does not interact with a gravitationally driven infall anymore and simply expands in time."
 The simulation run was stopped after an evolutionary age of 45 kyr., The simulation run was stopped after an evolutionary age of 45 kyr.
" Nevertheless, in the case, the radiation pressure evacuates the stellar environment in all directions, including the disk midplane."," Nevertheless, in the case, the radiation pressure evacuates the stellar environment in all directions, including the disk midplane."
" After its first expansion phase, this radiation-pressure-dominated cocoon-like structure decreases again, especially in the direction of the highest optical depth (the midplane), similar to the behavior of the expansion of the cavity shell in the FLD simulation by ? as well as in our FLD simulations."," After its first expansion phase, this radiation-pressure-dominated cocoon-like structure decreases again, especially in the direction of the highest optical depth (the midplane), similar to the behavior of the expansion of the cavity shell in the FLD simulation by \citet{Krumholz:2009p10975} as well as in our FLD simulations."
 The expansion velocity of the cavities of v>lOkms! corresponds more to the velocities observed in our FLD simulation (v=6—30km s!) than those using the ray-tracing method (v~100km s!)., The expansion velocity of the cavities of $v \gtrsim 10 \mbox{ km s}^{-1}$ corresponds more to the velocities observed in our FLD simulation $v = 6-30 \mbox{ km s}^{-1}$ ) than those using the ray-tracing method $v \sim 100 \mbox{ km s}^{-1}$ ).
 The frequency dependence of the FLD solver (as in our RT method) might also be important., The frequency dependence of the FLD solver (as in our RT method) might also be important.
" Using the FLD approximation in the gray limit leads to a downgrading of the radiation field throughout the cavity region, i.e. the dust grains in the cavity shell absorb the stellar flux with the Rosseland mean opacity at the local radiation temperature of the cavity shell, which does not resemble the broad stellar irradiation spectrum."," Using the FLD approximation in the gray limit leads to a downgrading of the radiation field throughout the cavity region, i.e. the dust grains in the cavity shell absorb the stellar flux with the Rosseland mean opacity at the local radiation temperature of the cavity shell, which does not resemble the broad stellar irradiation spectrum."
" By dividing the stellar flux into several frequency bins and treating the flux of each bin in the FLD approximation, one also can ensure that the high-frequency part of the stellar spectrum is absorbed with the appropriate absorption coefficient."," By dividing the stellar flux into several frequency bins and treating the flux of each bin in the FLD approximation, one also can ensure that the high-frequency part of the stellar spectrum is absorbed with the appropriate absorption coefficient."
" absorption behavior in the cavity shell, the RT approach provides a most realistic representation of the photon paths emitted at the stellar photosphere."," absorption behavior in the cavity shell, the RT approach provides a most realistic representation of the photon paths emitted at the stellar photosphere."
" Owing to the integral over the solid angle in the FLD approximation, the resulting flux does not include the correct propagation direction."," Owing to the integral over the solid angle in the FLD approximation, the resulting flux does not include the correct propagation direction."
" Moreover, including the long-wavelength part of the stellar spectrum explicitly can accelerate the layers on top of the swept-up cavity shell, which is optically thick for the short wavelengths only."," Moreover, including the long-wavelength part of the stellar spectrum explicitly can accelerate the layers on top of the swept-up cavity shell, which is optically thick for the short wavelengths only."
" Furthermore, ? demonstrated in numerical simulations using a RT approach for the radiation feedback, the acceleration of a gas clump by radiation pressure against a gravitational potential is inversely proportional to the optical depth of the clump, as expected by analytic estimates similar to the computation of the Eddington limit."," Furthermore, \citet{Schartmann:2011p17754} demonstrated in numerical simulations using a RT approach for the radiation feedback, the acceleration of a gas clump by radiation pressure against a gravitational potential is inversely proportional to the optical depth of the clump, as expected by analytic estimates similar to the computation of the Eddington limit."
 ? derived a criterion for the stability of radiation-pressure-dominated cavities for the adiabatic approximation., \citet{Jacquet:2011p18452} derived a criterion for the stability of radiation-pressure-dominated cavities for the adiabatic approximation.
 They provided growth times of the radiative Rayleigh-Taylor instability in cavity shells around massive stars., They provided growth times of the radiative Rayleigh-Taylor instability in cavity shells around massive stars.
 This analytic analysis fully supports the outcome of our investigations., This analytic analysis fully supports the outcome of our investigations.
" From our estimate of the accelerations in Sect. 7,,"," From our estimate of the accelerations in Sect. \ref{sect:Analytic},"
" we compute the expansion timescale of the cavity shell to be In the case of FLD simulations, the radiation pressure onto the cavity shell is in marginal equilibrium with gravity (E« 1) for long epochs in time."," we compute the expansion timescale of the cavity shell to be In the case of FLD simulations, the radiation pressure onto the cavity shell is in marginal equilibrium with gravity $E \approx 1$ ) for long epochs in time."
" The corresponding shell expansion timescale goes to infinity during these epochs, allowing the radiative Rayleigh-Taylor instability to set in."," The corresponding shell expansion timescale goes to infinity during these epochs, allowing the radiative Rayleigh-Taylor instability to set in."
" In the case of RT simulations, radiation pressure exceeds gravity by 1-2 orders of magnitude, leading to a much shorter cavity shell expansion timescale."," In the case of RT simulations, radiation pressure exceeds gravity by 1-2 orders of magnitude, leading to a much shorter cavity shell expansion timescale."
" For a stellar mass of and a cavity radius of Reavity=1400 AU, one obtains an expansion timescale of teavity©0.68 kyr."," For a stellar mass of and a cavity radius of $R_\mathrm{cavity} = 1400$ AU, one obtains an expansion timescale of $t_\mathrm{cavity} \approx 0.68$ kyr."
" ? stated that the growth times of the radiative Rayleigh-Taylor instability in cavity shells around massive stars should always be shorter then 1 kyr, but actually the numbers one reads from their plots are instead 6.3—40 kyr depending on the actual stellar mass and the wavelength of the instability."," \citet{Jacquet:2011p18452} stated that the growth times of the radiative Rayleigh-Taylor instability in cavity shells around massive stars should always be shorter then 1 kyr, but actually the numbers one reads from their plots are instead $6.3 - 40$ kyr depending on the actual stellar mass and the wavelength of the instability."
" Hence, the expansion timescale of the shell is at least one order of magnitude shorter than the timescale for the growth of the radiative Rayleigh-Taylor instability."," Hence, the expansion timescale of the shell is at least one order of magnitude shorter than the timescale for the growth of the radiative Rayleigh-Taylor instability."
" Even, for the largest"," Even, for the largest"
Some stars are young (~10 MMyr) yet already have bright debris disces of large radius (~100 AAU).,Some stars are young $\sim 10$ Myr) yet already have bright debris discs of large radius $\sim 100$ AU).
 Such discs cannot have self-stirred unless the dise is sufficiently dense. and in such systems planet-stirring may be a viable alternative.," Such discs cannot have self-stirred unless the disc is sufficiently dense, and in such systems planet-stirring may be a viable alternative."
 To quantify this. we calculated the minimum ον required for a dise to self stir in less than the system age. for dises around 23 FGK stars and 35 A stars with published 24/25 and 70/60 micron excesses (22222. ," To quantify this, we calculated the minimum $x_{\mathrm{m}}$ required for a disc to self stir in less than the system age, for discs around 23 FGK stars and 35 A stars with published 24/25 and 70/60 micron excesses \citep{2006ApJ...644..525M,2006ApJ...652.1674B,2006ApJ...653..675S,2007ApJ...658.1289T, 2008ApJ...677..630H}."
Disc radii were estimated by fitting black-body curves to the IR excess., Disc radii were estimated by fitting black-body curves to the IR excess.
 For FGK stars we increased these radii by a factor of three because a comparison with the radii known directly from those discs which have been imaged showed that the black body fits systematically underestimate the radii by roughly this amount: this is likely due to the small blow-out size for dust in these discs., For FGK stars we increased these radii by a factor of three because a comparison with the radii known directly from those discs which have been imaged showed that the black body fits systematically underestimate the radii by roughly this amount; this is likely due to the small blow-out size for dust in these discs.
 If radii were available from imaging. we used these in preference to the black-body fits.," If radii were available from imaging, we used these in preference to the black-body fits."
 We identified that a dise would have trouble self-stirring Π μεcLO.," We identified that a disc would have trouble self-stirring if $x_{\mathrm{m,min}} \ge 10$."
 Very massive discs would also have been gravitationally unstable when gas was still present., Very massive discs would also have been gravitationally unstable when gas was still present.
 We can calculate the minimum density for gravitational instability using the Toomre criterion for instability. where n is the mean motion of the disc. ος is the sound speed in the disc gas. and “i. is the surface density of gas.," We can calculate the minimum density for gravitational instability using the Toomre criterion $Q=\frac{c_{\mathrm{s}}n}{\pi \mathcal{G}\Sigma_{\mathrm{g}}}\lesssim 1$ for instability, where $n$ is the mean motion of the disc, $c_{\mathrm{s}}$ is the sound speed in the disc gas, and $\Sigma_{\mathrm{g}}$ is the surface density of gas."
" The sound speed ος7(αλrie, (0. where f is the dise scale height."," The sound speed $c_{\mathrm{s}}\approx (h/a)v_{\mathrm{kep}}$ \citep{1981ARA&A..19..137P}, , where $h$ is the disc scale height."
" Assuming P/e=0.1 and a dust:gas ratio of 1:100. so that X,=LOON with X given by Equation (29). this gives for instability."," Assuming $h/a=0.1$ and a dust:gas ratio of 1:100, so that $\Sigma_{\mathrm{g}}=100\Sigma$ with $\Sigma$ given by Equation \ref{eq:sigma}) ), this gives for instability."
" For a dise at AAU. this corresponds to a maximum ory, of ~LO."," For a disc at AU, this corresponds to a maximum $x_{\mathrm{m}}$ of $\sim 10$."
" Higher aru, would still be possible through metallicity enhancement without affecting the gas mass and therefore gravitational stability,", Higher $x_{\mathrm{m}}$ would still be possible through metallicity enhancement without affecting the gas mass and therefore gravitational stability.
 We identify two discs with a minimum surface density for self-stirring iainc10: HD 181327 μμ= 17) and HD 202917 Crinauin= 10).," We identify two discs with a minimum surface density for self-stirring $x_{\mathrm{m,min}} \ge 10$: HD 181327 $x_{\mathrm{m,min}} = 17$ ) and HD 202917 $x_{\mathrm{m,min}} = 10$ )."
 Both these dises have been imaged. with radii α= S6AAU (2). and àz SOAAU (?) respectively.," Both these discs have been imaged, with radii $a=86$ AU \citep{2006ApJ...650..414S} and $a\approx 80$ AU \citep{2007lyot.confE..32K} respectively."
 It may be that such dises do indeed have wryin10: Le. they may be at the top end of the dise mass distribution. in which case they may be self-stirred. assuming that they have managed to avoid the gravitational instability mentioned in the previous paragraph.," It may be that such discs do indeed have $x_{\mathrm{m,min}} \ge 10$; i.e., they may be at the top end of the disc mass distribution, in which case they may be self-stirred, assuming that they have managed to avoid the gravitational instability mentioned in the previous paragraph."
 In the case of HD 181327. however. there is independent evidence in support of planet stirring: the dise has an azimuthal asymmetry which could be due to planetary secular perturbations (2).. so this system in particular warrants further investigation.," In the case of HD 181327, however, there is independent evidence in support of planet stirring: the disc has an azimuthal asymmetry \citep{2008ApJ...689..539C} which could be due to planetary secular perturbations \citep{1999ApJ...527..918W}, so this system in particular warrants further investigation."
 In such a dise. we can place constraints on the parameters of the planet responsible for stirring by requiring foros.<<fase.," In such a disc, we can place constraints on the parameters of the planet responsible for stirring by requiring $t_{\mathrm{cross}} < t_{\mathrm{age}}$."
 Figure 8. shows that such planets are likely to be be far from the star., Figure \ref{fig:hd181327} shows that such planets are likely to be be far from the star.
 This. together with the host stars” youth. makes them good targets for direct imaging.," This, together with the host stars' youth, makes them good targets for direct imaging."
 We now attempt to ascertain whether there is any observational evidence for planet stirring., We now attempt to ascertain whether there is any observational evidence for planet stirring.
 We begin by looking at a statistical sample of exoplanets., We begin by looking at a statistical sample of exoplanets.
 If planets are a common cause of disc stirring then we might expect there to be a correlation between the planetary parameters ᾧ and e? and the presence of infrared excess. higher values of these parameters correlating with IR excess.," If planets are a common cause of disc stirring then we might expect there to be a correlation between the planetary parameters $\Phi$ and $a^*$ and the presence of infrared excess, higher values of these parameters correlating with IR excess."
 Of the two. « is the more fundamental because it describes the planet's absolute ability to stir a dise within the context of the planet- model. independently of any other sources of stirring.," Of the two, $a^*$ is the more fundamental because it describes the planet's absolute ability to stir a disc within the context of the planet-stirring model, independently of any other sources of stirring."
 A star hosting a planet may also host a planetesimal disc., A star hosting a planet may also host a planetesimal disc.
 If it does. and if planet-stirring were the sole stirring mechanism. then we would expect only those planets with high enough « to exhibit IR excess.," If it does, and if planet-stirring were the sole stirring mechanism, then we would expect only those planets with high enough $a^*$ to exhibit IR excess."
 The parameter < quantifies the relative importance of the planet- and self-stirring models. so the interpretation of any correlation between high «P and a disc. should one exist. is not so clear.," The parameter $\Phi$ quantifies the relative importance of the planet- and self-stirring models, so the interpretation of any correlation between high $\Phi$ and a disc, should one exist, is not so clear."
 We take 57 planet-hosting stars with published shotometry (2222)...," We take 57 planet-hosting stars with published photometry \citep{2006ApJ...652.1674B,2007ApJ...658.1312M,2008ApJ...674.1086T,2009ApJ...690.1522B}."
 Our sample is identical to that of Bryden e al. G, Our sample is identical to that of Bryden et al. (
in prep.,"in prep.),"
 but with the two M dwarfs GJ 436 and GJ 376. anc he G dwarf HD 33636 whose companion has been determinee ο be of stellar mass (2).. removed.," but with the two M dwarfs GJ 436 and GJ 876, and the G dwarf HD 33636 whose companion has been determined to be of stellar mass \citep{2007AJ....134..749B}, removed."
 Of these 57 stars. LO show significant excess emission at 24 sem and/or 70 jim. and are classec as dise hosts.," Of these 57 stars, 10 show significant excess emission at 24 $\mu$ m and/or 70 $\mu$ m, and are classed as disc hosts."
 Exoplanet data are from ?. for most planets. excep or¢ Eridani (2) and HD 69830 (2)..," Exoplanet data are from \cite{2006ApJ...646..505B} for most planets, except for $\epsilon$ Eridani \citep{2006AJ....132.2206B} and HD 69830 \citep{2006Natur.441..305L}."
 In Figure (9)) we plot parameters «P and « for the 57 systems., In Figure \ref{fig:bryden}) ) we plot parameters $\Phi$ and $a^*$ for the 57 systems.
 For multi-planet systems. we plot «b and e for the plane which stirs the dise quickest. treating the system as if the planets? perturbations acted independently: see refs:multi for a more detailed discussion.," For multi-planet systems, we plot $\Phi$ and $a^*$ for the planet which stirs the disc quickest, treating the system as if the planets' perturbations acted independently; see \\ref{s:multi} for a more detailed discussion."
 We also plot the line for constant ej=OL. ini=10IAL. G typical planet’). and varying e. Which fits the points rather well. showing that most of the range of «P and « can be accounted for by spread in aj.," We also plot the line for constant $e_{\mathrm{pl}}=0.1$, $m_{\mathrm{pl}}=10^{-3}\mathrm{\,M}_\odot$ (a `typical planet'), and varying $a_{\mathrm{pl}}$ , which fits the points rather well, showing that most of the range of $\Phi$ and $a^*$ can be accounted for by spread in $a_{\mathrm{pl}}$."
 The planet's semi-major axis is the most important parameter in determining whether a dise can be self- or planet-stirred., The planet's semi-major axis is the most important parameter in determining whether a disc can be self- or planet-stirred.
" The region on the right shows the region of parameter space inwhich a planet can stir an e=IO AAU..r,,=I disc. according to Equations (30)) and (261)."," The region on the right shows the region of parameter space inwhich a planet can stir an $a=10$ AU, $x_{\mathrm{m}}=1$ disc, according to Equations \ref{eq:phipl}) ) and \ref{eq:a*weak}) )."
 Figure (9)) does not suggest a difference in the distributions of « and « between planets orbiting disc hosting and nondise hosting stars., Figure \ref{fig:bryden}) ) does not suggest a difference in the distributions of $\Phi$ and $a^*$ between planets orbiting disc hosting and nondisc hosting stars.
 This is confirmed by Kolmogorov-Smirnov tests., This is confirmed by Kolmogorov–Smirnov tests.
 The p-values® from one-dimensional KS tests comparing the dise hosting and non dise hosting samples are 0.986 when, The $p$ from one-dimensional KS tests comparing the disc hosting and non disc hosting samples are 0.986 when
Space missions like ((Baglin 22006) and ((Borucki 22010a) are designed to find transiting Earth-size planets.,Space missions like (Baglin 2006) and (Borucki 2010a) are designed to find transiting Earth-size planets.
 Transit observations provide the size of the transiting planets (more exactly. the planet-to-star radius ratios).," Transit observations provide the size of the transiting planets (more exactly, the planet-to-star radius ratios)."
 Spectroscopic measurements of the host star's radial-velocity variations are then required to determine the masses of the transiting objects., Spectroscopic measurements of the host star's radial-velocity variations are then required to determine the masses of the transiting objects.
 In addition. velocimetry can rule out grazing transits of binary stars and stellar blends. which could mimic a planetary transit signal.," In addition, velocimetry can rule out grazing transits of binary stars and stellar blends, which could mimic a planetary transit signal."
 Consequently. there is a definite symbiosis between both techniques. since on the one hand. velocimetry is needed to establish the true nature of the transit candidates. while on the other. transiting systems have an orbital inclination on the sky ;~90°. allowing the degeneracy to be lifted on the minimum mass 75sin/ provided by velocimetry.," Consequently, there is a definite symbiosis between both techniques, since on the one hand, velocimetry is needed to establish the true nature of the transit candidates, while on the other, transiting systems have an orbital inclination on the sky $i\sim90\degr$, allowing the degeneracy to be lifted on the minimum mass $m_2 \sin i$ provided by velocimetry."
 Two puzzling and challenging transiting systems were recently identified among the candidates revealed by the mmission., Two puzzling and challenging transiting systems were recently identified among the candidates revealed by the mission.
 Rowe ((2010) present light curves featuring the transits and occultations of Kepler Objects of Interest KOI 74 and KOI 81., Rowe (2010) present light curves featuring the transits and occultations of Kepler Objects of Interest KOI 74 and KOI 81.
 Here. we focus on KOI 74. for which the occultation is deeper than the It means that this transiting object has a higher surface brightness than its host star. an AIV star with Tay=9400 K. The story became even more intriguing when Rowe ((2010) calculated the radius ο of this hot object from the transit observations as 0.4 Jovian radius (Ry)).," Here, we focus on KOI 74, for which the occultation is deeper than the It means that this transiting object has a higher surface brightness than its host star, an A1V star with $T_\mathrm{eff} = 9\,400$ K. The story became even more intriguing when Rowe (2010) calculated the radius $r_2$ of this hot object from the transit observations 	as 0.4 Jovian radius )."
" The depth of the occultation is (72/riF(GF3/F1). where Fo and F, are the brightnesses of the companion and the primary star. respectively. and (2/riX is the depth of the transit with rs and rj the radii of the companion and its primary. star. respectively."," The depth of the occultation is $(r_2/r_1)^2(F_2/F_1)$, where $F_2$ and $F_1$ are the brightnesses of the companion and the primary star, respectively, and $(r_2/r_1)^2$ is the depth of the transit with $r_2$ and $r_1$ the radii of the companion and its primary star, respectively."
 It is therefore possible to calculate the surface temperature of the companion. found to be around 13000 K (van Kerkwijk 22010).," It is therefore possible to calculate the surface temperature of the companion, found to be around $13\,000$ K (van Kerkwijk 2010)."
 This peculiar transiting object is hot and compact: however. a mass estimation is required to unravel its nature further.," This peculiar transiting object is hot and compact; however, a mass estimation is required to unravel its nature further."
 Without any available radial velocities. Rowe ((2010) tentatively derive a mass for the companion assuming that the ~ 45-ppm amplitude in the half-period photometric variations exhibited by this system was due to changes in the observable stellar surface area caused by tidal distortions of the host star.," Without any available radial velocities, Rowe (2010) tentatively derive a mass for the companion assuming that the $\sim45$ -ppm amplitude in the half-period photometric variations exhibited by this system was due to changes in the observable stellar surface area caused by tidal distortions of the host star."
 The amplitude of these ‘ellipsoidal’ variations is indeed proportional to the mass ratio between the two components of the system (Pfahl. Arras Paxton 2008).," The amplitude of these `ellipsoidal' variations is indeed proportional to the mass ratio between the two components of the system (Pfahl, Arras Paxton 2008)."
 They find a mass between 0.02 and 0.11 ((or 20.9 and 115 Mj) for KOI 74b. re. in the brown-dwarf or low-mass star domain. but with an unexplained. much hotter temperature than expected from such a body.," They find a mass between 0.02 and 0.11 (or 20.9 and 115 ) for KOI 74b, i.e., in the brown-dwarf or low-mass star domain, but with an unexplained, much hotter temperature than expected from such a body."
" After re-analysing the ddata. van Kerkwik ((2010) show that the ellipsoidal variations were themselves asymmetrically modulated. an effect they interpreted as the signature of ""Doppler boosting’ (also known as the ‘beaming"," After re-analysing the data, van Kerkwijk (2010) show that the ellipsoidal variations were themselves asymmetrically modulated, an effect they interpreted as the signature of `Doppler boosting' (also known as the `beaming"
spectral index a.,spectral index $\alpha$.
 There must. be other. cncrey-dependent narrowing mechanisms underlying., There must be other energy-dependent narrowing mechanisms underlying.
" Similar to this conclusion. Dermer (2004) pointed out that other processes inclucling adiabatie and racliative cooling. a non-uniform jet. or the external shock process. rather than the curvature ellect. should be needed to explain the relationship between the measured peak photon energy ZZ, and the measured £7, lux at £, in the decaving phase of a GRB pulse."," Similar to this conclusion, Dermer (2004) pointed out that other processes including adiabatic and radiative cooling, a non-uniform jet, or the external shock process, rather than the curvature effect, should be needed to explain the relationship between the measured peak photon energy $E_p$ and the measured $\nu F_{\nu}$ flux at $E_p$ in the decaying phase of a GRB pulse."
 They found the curvature relationship does not agree with the observation (Borgonovo Itvde 2001)., They found the curvature relationship does not agree with the observation (Borgonovo Ryde 2001).
 For simplicity we have assumed a spherically svnimetric radiation surface in this paper. though there is. some observational evidence indicating that the CRB outllow may be collimated.," For simplicity we have assumed a spherically symmetric radiation surface in this paper, though there is some observational evidence indicating that the GRB outflow may be collimated."
 Derived [rom the afterglow observations. the jet coming from the GRB2 central source eencrally has a half opening angle 8;>Lot (brail et al.," Derived from the afterglow observations, the jet coming from the GRB central source generally has a half opening angle $\theta_j > \Gamma^{-1}$ (Frail et al."
 2001)., 2001).
 Assuming a jet ecometry with the jet opening angle of 1 or 4 and the same parameter values (EL. 2 and £;) used in the spherical geometry. we calculated the observed. pulse shapes and the ags: they show no difference from those of the spherical geometry.," Assuming a jet geometry with the jet opening angle of $1^{\circ}$ or $4^{\circ}$ and the same parameter values $\Gamma$, $R$ and $t_d$ ) used in the spherical geometry, we calculated the observed pulse shapes and the lags; they show no difference from those of the spherical geometry."
 Phe reason for this is as follows., The reason for this is as follows.
 Leven in the case of the isotropic radiation surface. the contribution of the lux from the outer side region where the observing angle 0 is larger than LE is relatively very small. because the ocal flux contribution [rom the radiation surface (1.e.. the irst-part integrand of Equation 5 in Section 2) will decrease drastically with 8 as x(1|L767) when 8 is small.," Even in the case of the isotropic radiation surface, the contribution of the flux from the outer side region where the observing angle $\theta$ is larger than $\Gamma^{-1}$ is relatively very small, because the local flux contribution from the radiation surface (i.e., the first-part integrand of Equation 5 in Section 2) will decrease drastically with $\theta$ as $\propto(1+\Gamma^2\theta^2)^{-5}$ when $\theta$ is small."
 We thank the referee. for their. careful. reading of the manuscript and for many valuable suggestions., We thank the referee for their careful reading of the manuscript and for many valuable suggestions.
 This work was supported in part by the Special Funds for Major State Basie Science. Research Projects of the Ministry of Science anc Technology. and by the National Natural Science Foundation of China through grant. 10473010.," This work was supported in part by the Special Funds for Major State Basic Science Research Projects of the Ministry of Science and Technology, and by the National Natural Science Foundation of China through grant 10473010."
the Max Planck Society. and the Higher Education Funding Council for England.,"the Max Planck Society, and the Higher Education Funding Council for England."
 The SDSS Web site is hitp://www.scss.ore/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions., The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions.
 The Participating Institutions are the American Aluseum of Natural History. Astrophysical Institute Potsdam. University of Basel. University ol Cambridge. Case Western Reserve University. University of Chicago. Drexel University. Fermilab. the Institute for Advanced Study. the Japan Participation Group. Johns Hopkins University. the Joint Institute for Nuclear Astrophysics. the Kavli Institute for Particle Astrophvsies and Cosmology. the Korean Scientist Group. the Chinese Academy of Sciences (LAMOST). Los Alamos National Laboratory. the\lax-Planck- Institute for Astronomy (MPIA). the Max-Planek-Institute for Astrophvsies (AIPA). New Mexico State University. Ohio State University. University of Pittsburgh. University of Portsmouth. Princeton University. the United States Naval Observatory. and the University of Washington.," The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, theMax-Planck- Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington."
is set to ensure that there will twpically be 1 chance detection over an ACLS chip.,is set to ensure that there will typically be $\sim1$ chance detection over an ACIS chip.
 No source is detected a he position of KZ 2109., No source is detected at the position of RZ 2109.
 Given the vignetting ancl dither outern's elfects. the elfective exposure time at the source's »osition. as estimated. [from the exposure map. is abou 20000 seconds.," Given the vignetting and dither pattern's effects, the effective exposure time at the source's position, as estimated from the exposure map, is about 20000 seconds."
 We then use aperture photometry with radius 12.2 pixels. appropriate for containing all the flux roni the source at this angleoll-axisl.. and we detec 19 counts between 0.5 and S keV. The expected rate of ickeround. photons over a region this size at this position is LOS.," We then use aperture photometry with radius 12.2 pixels, appropriate for containing all the flux from the source at this angle, and we detect 19 counts between 0.5 and 8 keV. The expected rate of background photons over a region this size at this position is 10.8."
 Phe net number of counts in the region is then TL3. giving a roughly chance of a Iluctation in he background: producing this Illux at this position., The net number of counts in the region is then $8.2\pm3.3$ – giving a roughly chance of a fluctation in the background producing this flux at this position.
" Using WS3PIAIAIS with either a P—1.7 power law or a Ad=1 keV Mackbods (spectra roughly consistent with the lowhard and high/soft states for stellar mass black holes). we find a flux of about 4LO+"" ergs/sec/cnr. which corresponds o a source luminosity of 107. ergs/sec."," Using W3PIMMS with either a $\Gamma=1.7$ power law or a $kT=1$ keV blackbody (spectra roughly consistent with the low/hard and high/soft states for stellar mass black holes), we find a flux of about $4\times10^{-15}$ $^2$, which corresponds to a source luminosity of $10^{38}$ ergs/sec."
 The 36 upper limit rom the source is about 2«1077 ergs/sec., The $\sigma$ upper limit from the source is about $2\times10^{38}$ ergs/sec.
 We have triggered. the Swift. X-ray Telescope to observe NAIM 1229039.7|075333. live times on 2007 December 25 and 2 January 2008. roughly simultaneously. with our Ixeck spectroscopy. (Zepl et al.," We have triggered the Swift X-ray Telescope to observe XMMU 122939.7+075333 five times – on 2007 December 25 and 2 January 2008, roughly simultaneously with our Keck spectroscopy (Zepf et al."
 2007:2008). and three times in late March. of 2010 in response to the non-detection in the observations presented above.," 2007;2008), and three times in late March of 2010 in response to the non-detection in the observations presented above."
 The observation ID numbers are 0031078001 through 0031078005., The observation ID numbers are 0031078001 through 0031078005.
 We also note that an additional short NMM observation was mace at about the same time as the Ixeck. spectrum. but. that strong Ilaring background. prevented those data from being useful.," We also note that an additional short XMM observation was made at about the same time as the Keck spectrum, but that strong flaring background prevented those data from being useful."
 We analvse the Swift data using the standard. cleaned events files. after final. versions hack been entered. into the archive.," We analyse the Swift data using the standard cleaned events files, after final versions had been entered into the archive."
 A quick. visual inspection of the data revealed that the source would be. at best. mareinally detected. by Swift in our observations.," A quick visual inspection of the data revealed that the source would be, at best, marginally detected by Swift in our observations."
 For that reason. we use a 207 aperture to extract a number of detected: photons.," For that reason, we use a 20” aperture to extract a number of detected photons."
 This radius corresponds to the encircled energy. region. for Swift XNIUE (need ref for Swift SRL 7). but it allows for a much lower background count rate than using the standard encircled. energy. region of 477.," This radius corresponds to the encircled energy region for Swift XRT (need ref for Swift XRT PSF), but it allows for a much lower background count rate than using the standard encircled energy region of 47”."
 We extract events in channels 50-500 (approximately 0.5-5 keV)., We extract events in channels 50-500 (approximately 0.5-5 keV).
 We use a 2007 aperture oll-axis region to estimate the background. count rate., We use a 200” aperture off-axis region to estimate the background count rate.
" We combine the two observations in 2007/2008 with one another to make ""Swift epoch 1 and the three observations rom 2010 to make Swift epoch 27.", We combine the two observations in 2007/2008 with one another to make “Swift epoch 1” and the three observations from 2010 to make “Swift epoch 2”.
 For Swift epoch 1. we detect. 4 source counts. anc 95 background. counts in a total of 3843 seconds.," For Swift epoch 1, we detect 4 source counts, and 95 background counts in a total of 3843 seconds."
 Given that the background region las a radius ten times as large as the source region. we estimate that the source region should contain 1.95c0.09 ckeround. counts.," Given that the background region has a radius ten times as large as the source region, we estimate that the source region should contain $0.95\pm0.09$ background counts."
 There is thus a chance that the 4 detected counts could. be produced by Poisson Iuctuations of the background., There is thus a chance that the 4 detected counts could be produced by Poisson fluctuations of the background.
" LE we assume a spectrum. of an 0.2 keV blackbody for the source convolved with the foregound Galactic absorption and use WS3PIALAIS to convert counts o energv. then the inferred source X-ray luminosity is about 107"" ores/sec for this marginal detection."," If we assume a spectrum of an 0.2 keV blackbody for the source convolved with the foregound Galactic absorption and use W3PIMMS to convert counts to energy, then the inferred source X-ray luminosity is about $10^{39}$ ergs/sec for this marginal detection."
 A Poisson process with mean of 9.3 counts will produce 4 or fewer detecte counts of the time., A Poisson process with mean of 9.3 counts will produce 4 or fewer detected counts of the time.
" We can then take as an upper limi [or the source count rate S.3 counts over the time interval. eiving an upper limit to the source luminosity of abou 3.10"" eres/see. with some additional uncertainty based on the spectral model used to convert counts to energy."," We can then take as an upper limit for the source count rate 8.3 counts over the time interval, giving an upper limit to the source luminosity of about $3\times10^{39}$ ergs/sec, with some additional uncertainty based on the spectral model used to convert counts to energy."
 This observation thus provides weakly suggestive evidence tha XMAMU 122939.7|O753:3 hacl alreaciy started to fade in the X-rays by late 2007., This observation thus provides weakly suggestive evidence that XMMU 122939.7+075333 had already started to fade in the X-rays by late 2007.
 Ehe cata from Swift epoch 2 show source photon and 134 background photons in 500:3 seconds of summed exposure time — the background count rate per pixel is nominally higher than the source region rate., The data from Swift epoch 2 show 1 source photon and 134 background photons in 5003 seconds of summed exposure time – the background count rate per pixel is nominally higher than the source region rate.
 The confidence level upper limit on the number of source plus background. counts is about 5.8) vielding an upper limit to the net source count rate of about 4.5 counts in 5000 seconds about half the upper limit in 2007 with Swift., The confidence level upper limit on the number of source plus background counts is about 5.8 – yielding an upper limit to the net source count rate of about 4.5 counts in 5000 seconds – about half the upper limit in 2007 with Swift.
 In this case. it is clear that the source must have either faded or changed spectrum significantly since the deep. Chandra ancl NMM observations taken from 2002 through 2004.," In this case, it is clear that the source must have either faded or changed spectrum significantly since the deep Chandra and XMM observations taken from 2002 through 2004."
 Three possibilities have been laid out for the nature of XMMU 122939.7|075333., Three possibilities have been laid out for the nature of XMMU 122939.7+075333.
 One of these possibilities is that the source is a red giant-black hole binary. with the change in brightness in the 2004 NMM observation caused by a grazing eclipse of the inner accretion disk by a pully. precessing outer disk (Shih et al.," One of these possibilities is that the source is a red giant-black hole binary, with the change in brightness in the 2004 XMM observation caused by a grazing eclipse of the inner accretion disk by a puffy, precessing outer disk (Shih et al."
 2008): this possibility is no longer viable because the large ratio of O LU] to Balmer emission strongly favors an evolved. donor star., 2008); this possibility is no longer viable because the large ratio of [O III] to Balmer emission strongly favors an evolved donor star.
 Alternatively. the accreting object may a stellar mass black hole accreting from a WD in à short. period binary system. or it may be the result of a tidal detonation of a WD by an intermediate mass DLE (Irwin et al.," Alternatively, the accreting object may a stellar mass black hole accreting from a WD in a short period binary system, or it may be the result of a tidal detonation of a WD by an intermediate mass BH (Irwin et al."
 2010)., 2010).
 We can then consider the implications of the X-ray variability on these cilferent classes of mocels., We can then consider the implications of the X-ray variability on these different classes of models.
 The strong variability seen from: ΧΑΛΙΛ 122930.7|075333 is easy to explain in a model where the accretion is taking place in a hierarchical triple star svstem. with the inner binary being WD-DII X-ray binary.," The strong variability seen from XMMU 122939.7+075333 is easy to explain in a model where the accretion is taking place in a hierarchical triple star system, with the inner binary being WD-BH X-ray binary."
 Such a scenario is the preferred means for forming a WD-DII X-ray binary according to the theoretical work of Ivanova et al. (, Such a scenario is the preferred means for forming a WD-BH X-ray binary according to the theoretical work of Ivanova et al. (
2010).,2010).
 An aspect of the triple star system that was not explored by. lvanova ct al. (, An aspect of the triple star system that was not explored by Ivanova et al. (
2010) may have profound consequences Lor the observahility of the svstem.,2010) may have profound consequences for the observability of the system.
 Phe Ixozai eveles that are invoked for grinding down the svsteni to Roche lobe overllow should continue after the svstem has come into Roche lobe overtlow., The Kozai cycles that are invoked for grinding down the system to Roche lobe overflow should continue after the system has come into Roche lobe overflow.
 The eccentricity of the inner binary will then continue to oscillate., The eccentricity of the inner binary will then continue to oscillate.
 Ht bas been shown previously that even. small eccentricities can produce Large changes in mass accretion rates (llut Daczvnski 1984) the mass transfer. rate should. increase as the density of material at the Roche lobe radius., It has been shown previously that even small eccentricities can produce large changes in mass accretion rates (Hut Paczynski 1984) – the mass transfer rate should increase as the density of material at the Roche lobe radius.
 To first order. that should. give a dependence as erplel/f). where e is the eccentricity of the binary. P is the scale height of the star. and is the radius of the star.," To first order, that should give a dependence as $exp(eR/h)$, where $e$ is the eccentricity of the binary, $h$ is the scale height of the star, and $R$ is the radius of the star."
 Phe value of P£I? is typically 103 for a main sequence star. and should be a bit. smaller /presentations/allenféincslDBs nunless. they are very hot.," The value of $h/R$ is typically $10^{-4}$ for a main sequence star, and should be a bit smaller for WDs unless they are very hot."
 A triple system could, A triple system could
detected beyond this energy.,detected beyond this energy.
 The clip like structure (in pulse hase range 0.35-0.45) is found to be very prominent up to wd keV. The width and depth of this structure decrease eradually with energy up to 10. keV. beyond: which it »ecomes. indistinguishable in the pulse profile. making the ird X-ray pulse profiles smooth and single peaked.," The dip like structure (in pulse phase range 0.35-0.45) is found to be very prominent up to $\sim$ 4 keV. The width and depth of this structure decrease gradually with energy up to $\sim$ 10 keV, beyond which it becomes indistinguishable in the pulse profile, making the hard X-ray pulse profiles smooth and single peaked."
 Pulse hase resolved spectroscopy would help in understanding the nature of the energy dependence of the dip like structure in he pulse profile of1008-57., Pulse phase resolved spectroscopy would help in understanding the nature of the energy dependence of the dip like structure in the pulse profile of.
.. The broad-band spectrum of aceretion powered. X-ray pulsars are generally described. by a power-law. broken power-law or power-law with high energy cutoll continuum models.," The broad-band spectrum of accretion powered X-ray pulsars are generally described by a power-law, broken power-law or power-law with high energy cutoff continuum models."
 1n some cases. the pulsar spectrum has also been deseribed by the NPEX continuum model (Alihara 1995: Makishima et al.," In some cases, the pulsar spectrum has also been described by the NPEX continuum model (Mihara 1995; Makishima et al."
 1999: Terada et al., 1999; Terada et al.
 2006: Naik et al., 2006; Naik et al.
 2008 and references therein)., 2008 and references therein).
 ln. case of a few X- pulsars. it has been reported that the absorption has two cdillerent. components (Indo. et al.," In case of a few X-ray pulsars, it has been reported that the absorption has two different components (Endo et al."
 2000: Alukherjee Paul 2004)., 2000; Mukherjee Paul 2004).
 In this model. one absorption component absorbs the entire spectrum where as the other component absorbs the spectrum partially.," In this model, one absorption component absorbs the entire spectrum where as the other component absorbs the spectrum partially."
 “Phis model is. known as partial absorption model., This model is known as partial absorption model.
 The choice of appropriate continuum model. therefore. is very much important to unclerstanel the properties of the pulsars.," The choice of appropriate continuum model, therefore, is very much important to understand the properties of the pulsars."
 We tried to find a suitable continuum model to fit the broac-bancl spectrum ofJ1008-57., We tried to find a suitable continuum model to fit the broad-band spectrum of.
. In. the process. we attempted to fit the pulsar spectra with different continuum. models with aclelitional spectral components such as blackbocly radiation. iron emission line ete.," In the process, we attempted to fit the pulsar spectra with different continuum models with additional spectral components such as blackbody radiation, iron emission line etc."
 Ehe models giving. statistically acceptable parameters are described here in this section., The models giving statistically acceptable parameters are described here in this section.
 The source spectrum was extracted. from the events selected. in the οποιον ranges of 0.3-10.0 keV for the back illuminated COD (XIS-1). 0.5-10. keV. for the front illuminated CCDs (Νο ancl 3) and 10-70 keV for the HIEND/PIN. detectors.," The source spectrum was extracted from the events selected in the energy ranges of 0.3-10.0 keV for the back illuminated CCD (XIS-1), 0.5-10 keV for the front illuminated CCDs (XISs-0 and 3) and 10-70 keV for the HXD/PIN detectors."
 After appropriate background, After appropriate background
Iu Fig.,In Fig.
" 5. we plot the redslift so where the optical deph for photons reaches unity (i.e... T0.s)= 1) for several ""observers redshifts”: 2=ο,LO.100.500.1000."," \ref{fig3} we plot the redshift $z^{'}$ where the optical depth for photons reaches unity (i.e., $\tau_{\nu}(z,z^{'})=1$ ) for several “observer's redshifts”: $z=0,10,100,500,1000$."
 Tere the energy plotted is the photon cuerey at redshift 2., Here the energy plotted is the photon energy at redshift $z$.
 The lowest curve is the analog of the curve plotted iu Fig., The lowest curve is the analog of the curve plotted in Fig.
 2 of Zdziarski&Svensson(1989).., 2 of \citet{1989ApJ...344..551Z}.
 Having a method to calculate the intensity of the photon field sourced by the auuihilatiug DAL at cach redshift we can go on aud express the enerev deposition rate in the cosmic mediuni as To esiuate the fraction of the deposited energy eudius up iu ionizing and heating the imediun we use the approximation motivated by the orginal work of Shull and used in several subsequenut papers (Chen&I&uuionkowski.2001:PacinanabhanNatarajan&Sclavarz. 2008): ~(1su) gocs ito lonization aud ~(1|2.0.)/3 oeinto heating.," Having a method to calculate the intensity of the photon field sourced by the annihilating DM at each redshift we can go on and express the energy deposition rate in the cosmic medium as To estimate the fraction of the deposited energy ending up in ionizing and heating the medium we use the approximation motivated by the original work of \citet{1985ApJ...298..268S} and used in several subsequent papers \citep{2004PhRvD..70d3502C,2005PhRvD..72b3508P,2006MNRAS.369.1719M,2006PhRvD..74j3519Z,2008PhRvD..78j3524N}: $\sim (1-x_e)/3$ goes into ionization and $\sim (1 + 2x_e)/3$ into heating."
 Tere a). is the ionization fractio1., Here $x_e$ is the ionization fraction.
 To calculate the evolution of the ionization fraction and matter temperature we modif the recombination code REC'FAST following the description in Padmanabhan&Fiukbei101) (2005)., To calculate the evolution of the ionization fraction and matter temperature we modify the recombination code RECFAST \citep{1999ApJ...523L...1S} following the description in \citet{2005PhRvD..72b3508P}.
". For their modification we ueed the total energv deposition rate per hydrogen particle which is given as To eo bhevoud their ""ou the spot” approximation the f-piuruneter in thei Eq. (", For their modification we need the total energy deposition rate per hydrogen particle which is given as To go beyond their “on the spot” approximation the $f$ -parameter in their Eq. (
5) should be replaced by the following function of τ (see also Slatveretal.(2009))} which gives us the ratio of the total energy. deposition and local “smooth” cucrey injection rates.,5) should be replaced by the following function of $z$ (see also \citet{2009arXiv0906.1197S}) ) which gives us the ratio of the total energy deposition and local “smooth” energy injection rates.
 The function Εν) is plotted on the lower panel of Fig., The function $f(z)$ is plotted on the lower panel of Fig.
" 2 for two cliffercut concentration models. two leptouic annihilation chauncls (DAF|DALΣο416DAL| DAL5p|p) assidue the aumililating DAI particle with mass ipa,=1Tc\ The upturn of the curves at redshift 2—LOO ninuies the shuuilar treu seen in the upper panel aud is caused by the onset of the structure formation."," \ref{fig2} for two different concentration models, two leptonic annihilation channels $DM+DM\rightarrow e^{-}+e^{+}$, $DM+DM\rightarrow \mu^{-}+\mu^{+}$ ), assuming the annihilating DM particle with mass $m_{DM}=1$ TeV. The upturn of the curves at redshift $z\sim100$ mimics the similar trend seen in the upper panel and is caused by the onset of the structure formation."
 The short dashed lines show the ratio e/(lay) where for calculating € onc takes B=1in Eq. (60)., The short dashed lines show the ratio $\bar{\epsilon}/(4\pi \bar{\jmath})$ where for calculating $\bar{\epsilon}$ one takes $B=1$ in Eq. \ref{eq06}) ).
 These last two curves cau be directly colmpared with the results preseuted in Fie., These last two curves can be directly compared with the results presented in Fig.
 { of Slatveretal.(2009).., 4 of \citet{2009arXiv0906.1197S}.
 For clarity we have not shown the results for the annihilation channel DAL|»7|r as those are very similar to the grpl case., For clarity we have not shown the results for the annihilation channel $DM+DM\rightarrow \tau^{-}+\tau^{+}$ as those are very similar to the $\mu^{-}+\mu^{+}$ case.
 At large redshifts. where the Universe ects optically thick to photous. aud where the structure boost Bl.)=1. oue expects f(:) to asvinptotically approach unity.," At large redshifts, where the Universe gets optically thick to photons, and where the structure boost $B(z)=1$, one expects $f(z)$ to asymptotically approach unity."
 This is indeed what we see in the case ofοή¢| annihilation channel., This is indeed what we see in the case of $e^{-}+e^{+}$ annihilation channel.
 However. the asvinptotic f(:) values for the jilye! aud τ7| CHSOSN are snialler since a large fracion of euergv Is carried away by neutriuos (see Table 1)).," However, the asymptotic $f(z)$ values for the $\mu^{-}+\mu^{+}$ and $\tau^{-}+\tau^{+}$ cases are smaller since a large fraction of energy is carried away by neutrinos (see Table \ref{tab1}) )."
 Iu Fie., In Fig.
 1 we show some example x-ray spectra at redshift +=O calculated with the above formalisin for he annihilating DAL particle with mass pa;= TeV. Tere the Wo most extreme concentration models of Fig., \ref{fig4} we show some example $\gamma$ -ray spectra at redshift $z=0$ calculated with the above formalism for the annihilating DM particle with mass $m_{DM}=1$ TeV. Here the two most extreme concentration models of Fig.
 2 have been used aud the results are given for all threc eptonic annihilation channels considered in this paper., \ref{fig2} have been used and the results are given for all three leptonic annihilation channels considered in this paper.
 The thermally averaged anuililation cross-section has ο set to 25 tiues its. standard value of. ~3.410.22907., The thermally averaged annihilation cross-section has been set to $25$ times its standard value of $\sim 3\times10^{-26}{\rm cm}^2$.
 The low ejerev bump of the characteristic double-buniped spectrin is due to the inverse Compton process whereas he high energy o» is the prompt photon contribution., The low energy bump of the characteristic double-bumped spectrum is due to the inverse Compton process whereas the high energy bump is the prompt photon contribution.
 The points with crrorbars correspoxl to the ECRET ucasureineuts of the extragalactic euuna backeround as even in Sreekumarctal. (1998).., The points with errorbars correspond to the EGRET measurements of the extragalactic gamma background as given in \citet{1998ApJ...494..523S}. .
 The solic horizoutal ine. whichis used in he following as an Wwyper bound or the level of diffuse -yav backeround. represcuts the EGRET neasurements reduced by a factor of three to approximately account or the following: (1) dependent on he modeling details. it is predicted that from 25 up to 100'4 ofthe diffuse extragalactic ο-ταν backerouud is due o unresolved ACNs (Stecker&Salamon.1996:Chiane2000).. Gi) the inxoved model for the Galactic contribution further suppresses the 1ieasureiments (Strong D.. (3) there is a1 aciditional component due to," The solid horizontal line, whichis used in the following as an upper bound for the level of diffuse $\gamma$ -ray background, represents the EGRET measurements reduced by a factor of three to approximately account for the following: (i) dependent on the modeling details, it is predicted that from $25\%$ up to $100\%$ of the diffuse extragalactic $\gamma$ -ray background is due to unresolved AGNs \citep{1996ApJ...464..600S,1998ApJ...496..752C,1999APh....11..213M,2000MNRAS.312..177M},, (ii) the improved model for the Galactic contribution further suppresses the measurements \citep{2004ApJ...613..956S}, , (iii) there is an additional component due to"
Proton-protoun collisions at s = 900 GeV have already appeared at the LIC aud the results will © compared with SppS data on proton-autiproton collisions at the same center of mass cucrey mnoeasured x UAS collaboration.,Proton-proton collisions at $\sqrt{s}$ = 900 GeV have already appeared at the LHC and the results will be compared with $p\bar{p}$ S data on proton-antiproton collisions at the same center of mass energy measured by UA5 collaboration.
 In this paper we point out some mances coucerning UAS measurements aud results and show that the uucertainties of measurements are nuiderestimated by CAS., In this paper we point out some nuances concerning UA5 measurements and results and show that the uncertainties of measurements are underestimated by UA5.
 This can lead to discrepancics jctween pp and pp at Ys = 900 GeV and be wronely interpreted in future theoretical analyses., This can lead to discrepancies between $pp$ and $p\bar{p}$ at $\sqrt{s}$ = 900 GeV and be wrongly interpreted in future theoretical analyses.
 First we investigate the result of measurcients of cross-sections aud then the result of measurements of charged particles pseudorapiditv distribution., First we investigate the result of measurements of cross-sections and then the result of measurements of charged particles pseudorapidity distribution.
 Iu this section we investigate the results of UAS lnüieasnrenunt on cross-sections of single-diffractive. uon-siuele diffractive aud inclastic pp The UAH detector and eveut analysis procedures are described iu [1].," In this section we investigate the results of UA5 measuremnt on cross-sections of single-diffractive, non-single diffractive and inelastic $p\bar{p}$ The UA5 detector and event analysis procedures are described in \cite{UA5detector}."
 Two large streamer chambers were placed above and below the SppS beam pipe., Two large streamer chambers were placed above and below the $p\bar{p}$ S beam pipe.
 The chambers were triggered by requiring oue or nore hits iu scintillation counter hodoscopes at cach eud of the chambers covering o-2«μή<5.6., The chambers were triggered by requiring one or more hits in scintillation counter hodoscopes at each end of the chambers covering $2 < |\eta| < 5.6$.
" Two triggersoo were taken in parallel: à 72-arnr trigecr requiring hits at both cuds to select mainly non sinele-dittractive events. and a leu trigger demanding a lit iu oulv oue arii to select hiehlv asvuumetric eveuts such as sinele diffractive Iu case of sinele-diffaction dissociation UAS trigeered particles produced from auti-protou dissociation and the measured lum triggering cross-section multiplied by factor 2 in order to correct for proton dissociation (assmnius proton and proton dissociations to be the The triggering cross sections σι aud 86» for luu and 2-arm trigecrs are related to the sinele-diffractive and uou-siuele diffractive cross-sections by the trigger efficiencies €)SD.,NSD5 as follows: Solving Eq. (1))"," Two triggers were taken in parallel: a ""2-arm"" trigger requiring hits at both ends to select mainly non single-diffractive events, and a ""1-arm"" trigger demanding a hit in only one arm to select highly asymmetric events such as single diffractive In case of single-diffraction dissociation UA5 triggered particles produced from anti-proton dissociation and the measured 1-arm triggering cross-section multiplied by factor 2 in order to correct for proton dissociation (assuming proton and anti-proton dissociations to be the The triggering cross sections $\sigma_1$ and $\sigma_2$ for 1-arm and 2-arm triggers are related to the single-diffractive and non-single diffractive cross-sections by the trigger efficiencies $\epsilon^{SD, NSD}_{1,2}$ as follows: Solving Eq. \ref{Eq:TRXS}) )"
" for v«sp/ovsp one finds: Where r—04/0» aud the result of the measurement is [2]:: Determining lun aud 2-arm trigeeriug cfiicicucies for single-diffractive and nou-single diffractive events based on MC simulations, VAS reported the following value for R=esp/eoxsp |2|: The first error is statistical aud the second. The trigecring efficieucies epp Pda Eq. (1))"," for $\sigma_{SD}/\sigma_{NSD}$ one finds: Where $r\equiv \sigma_{1}/\sigma_{2}$ and the result of the measurement is \cite{UA5diff}: Determining 1-arm and 2-arm triggering efficiencies for single-diffractive and non-single diffractive events based on MC simulations, UA5 reported the following value for $R \equiv \sigma_{SD}/\sigma_{NSD}$ \cite{UA5diff}: The first error is statistical and the second The triggering efficiencies $\epsilon^{SD, NSD}_{1,2}$ in Eq. \ref{Eq:TRXS}) )"
 were estimated by UAS based on Monte Carlo simulations., were estimated by UA5 based on Monte Carlo simulations.
 UA5 detector did not have maguet aud was not able to ieasure the transverse momentum of particles., UA5 detector did not have magnet and was not able to measure the transverse momentum of particles.
 The AIC generator used for simulations was tuned to, The MC generator used for simulations was tuned to
 (SSEICZSEIL/AL.) as a function of Aja... using large-scale cosmological hyelrodynaniic simulations with various outflow models.,"$\equiv$ $/M_*$ ) as a function of $M_{\rm halo}$, using large-scale cosmological hydrodynamic simulations with various outflow models."
details). The upper left pancl shows the case without oulllows., The upper left panel shows the case without outflows.
 Lf all gas entering into the halo ended. up in the ISAL. Le. Miu=Magu: then the relation would be as shown by the solid line. having a positive slope.," If all gas entering into the halo ended up in the ISM, i.e. $\dot{M}_{\rm in}=\dot{M}_{\rm grav}$, then the relation would be as shown by the solid line, having a positive slope."
 Leven without any fecdback. gravitational heating results in a negative slope (clasheel line).," Even without any feedback, gravitational heating results in a negative slope (dashed line)."
 Phe results from our simulations are in good agreement with Equation 62011).. since the simulations themselves are quite similar: the main dillerence is that ours include metal-Iine cooling. but this is not. very important until hot. gaseous halos form αἱ AdnanLOMAL. since cold accretion is generally limited by the infall time rather than the cooling time.," The results from our simulations are in good agreement with Equation \ref{eqn:zetagrav} , since the simulations themselves are quite similar; the main difference is that ours include metal-line cooling, but this is not very important until hot gaseous halos form at $M_{\rm halo}\ga 10^{12}M_\odot$ since cold accretion is generally limited by the infall time rather than the cooling time."
 The simulations in the two right panels assume i=2., The simulations in the two right panels assume $\eta=2$.
" Lf Miu is unchanged. then one expects both the SER and AL, to be lowered by a factor of three (eq. 3))."," If $\dot{M}_{\rm in}$ is unchanged, then one expects both the SFR and $M_*$ to be lowered by a factor of three (eq. \ref{eqn:sfr}) ),"
 resulting in no change in sSER. from the no-wind case (the no-wind evan curve is reproduced in all panels for comparison)), resulting in no change in sSFR from the no-wind case (the no-wind cyan curve is reproduced in all panels for comparison).
 But clearly. there is à change. which relects the impac ofoutllows on Mi.," But clearly there is a change, which reflects the impact of outflows on $\dot{M}_{\rm in}$."
 At large masses. wind reeveling CA4o) returns material to the galaxy rapidly once t16 wind speed (680 km/s in the upper right. 340 km/s in the lower right) cLrops below the escape velocity2010).," At large masses, wind recycling $\dot{M}_{\rm
recyc}$ ) returns material to the galaxy rapidly once the wind speed (680 km/s in the upper right, 340 km/s in the lower right) drops below the escape velocity."
 llence at large masses nis clleetively 0JOS).. ancl sSETU jumps owing to Aic.," Hence at large masses $\eta$ is effectively 0, and sSFR jumps owing to $\dot{M}_{\rm recyc}$."
 For the case of the slower 340 km/s wines (lower right). the jump occurs at à factor of eight lower in mass às expected from the factor of two dillerence in wind speeds.," For the case of the slower 340 km/s winds (lower right), the jump occurs at a factor of eight lower in mass as expected from the factor of two difference in wind speeds."
 Winds also affect sSER at. low masses. where it is suppressed relative to no winds.," Winds also affect sSFR at low masses, where it is suppressed relative to no winds."
 This reflects Gena. which is as expected stronger in the case of the higher wind speed.," This reflects $\zeta_{\rm winds}$, which is as expected stronger in the case of the higher wind speed."
 La the lower left we show simulations using momoentunm-driven wind scalings of (approximately) 5xMnog, In the lower left we show simulations using momentum-driven wind scalings of (approximately) $\eta\propto M_{\rm halo}^{-1/3}$.
 This Hlattens SSER(AMa). in addition to exhibiting cdillerent. behaviors for wind recycling and suppression.," This flattens $(M_{\rm halo})$, in addition to exhibiting different behaviors for wind recycling and suppression."
 These examples illustrate how star formation rates at a given mass in simulations are impacted. by the various jective and. preventive feedback. processes described above., These examples illustrate how star formation rates at a given mass in simulations are impacted by the various ejective and preventive feedback processes described above.
 For instance. the fact. that. observations find no sudden increase in sSER at any characteristic mass suggests that galaxies do not eject material at à characteristic wind velocity.(," For instance, the fact that observations find no sudden increase in sSFR at any characteristic mass suggests that galaxies do not eject material at a characteristic wind velocity.,"
2010)..(2010).. and also present empirical. models based. on acecretion-driven star formation. focusing on the form and evolution of the SSETL.," and also present empirical models based on accretion-driven star formation, focusing on the form and evolution of the sSFR."
 Interestingly. demonstrates that à model in which ¢=1 for 10H<81077Al. and zero elsewhere nicely reprocuces some key observed. properties of high-redshift’ star-forming galaxies. including the observed lack of sSEIt amplitude evolution from z7.»2.," Interestingly, demonstrates that a model in which $\zeta=1$ for $10^{11}<M_{\rm
halo}<10^{12.2} M_\odot$ and zero elsewhere nicely reproduces some key observed properties of high-redshift star-forming galaxies, including the observed lack of sSFR amplitude evolution from $z\sim
7\rightarrow 2$."
 Simulations. in contrast. predict that πο. evolution. tracks the accretion rate. and thus continues to rise to hieh redshifts2008): analytic models that do not. include such a low-mass cutoll show xnmilar behavior2010).," Simulations, in contrast, predict that sSFR evolution tracks the accretion rate, and thus continues to rise to high redshifts; analytic models that do not include such a low-mass cutoff show similar behavior."
.. 1£ this. low-mass cutoll for accretion were true. it would suggest that there are additional feedback. processes alfecting small svstems bevond what is shown in Figure L.. namely. metagalactic photo-ionisation.," If this low-mass cutoff for accretion were true, it would suggest that there are additional feedback processes affecting small systems beyond what is shown in Figure \ref{fig:zeta}, namely, metagalactic photo-ionisation."
 An alternative explanation that does no employ a sharp mass cutoll but still reproduces the observec «ο behavior is to invoke an observationally-motivatec metallicitv-dependent star formation law. as explored. by," An alternative explanation that does not employ a sharp mass cutoff but still reproduces the observed sSFR behavior is to invoke an observationally-motivated metallicity-dependent star formation law, as explored by."
 Pushing such observations of sSELR out to higher redshifts anc lower masses shoule provide interesting constraints on the physical mechanisms regulating carly. low-mass galaxy. growth.," Pushing such observations of sSFR out to higher redshifts and lower masses should provide interesting constraints on the physical mechanisms regulating early, low-mass galaxy growth."
 A galaxys gas fraction is defined here as, A galaxy's gas fraction is defined here as
The comparison between the PCs obtained from using Hpase= ACDM and Hbase=cte is shown in figure (2)).,The comparison between the PCs obtained from using $H_{base}=\Lambda$ CDM and $H_{base}=cte$ is shown in figure \ref{fig:PCS}) ).
" From this plot, we can see that the difference exist, but the overall shape of the PCs are not very sensitive to the choice of Ηιαςς."," From this plot, we can see that the difference exist, but the overall shape of the PCs are not very sensitive to the choice of $H_{base}$."
" To clear illustrate the standard-procedure results of PCA reconstruction in the specific case studied here, we show in Fig."," To clear illustrate the standard-procedure results of PCA reconstruction in the specific case studied here, we show in Fig."
 3 reconstructions using one to six PCs with corresponding values of £y., \ref{fig:toy_rec_full} reconstructions using one to six PCs with corresponding values of $t_M$.
" From this plot, it is clear that our"," From this plot, it is clear that our"
As alveady nmeutioned. V892 Tau aud V892 Tau NE are unresolved by the PPSF. nevertheless the evidence that the origin of the observed flare is the Herbig Ac star is compelling.,"As already mentioned, V892 Tau and V892 Tau NE are unresolved by the PSF, nevertheless the evidence that the origin of the observed flare is the Herbig Ae star is compelling."
 First. as sununnarnsed in Table 1.. the ppositiou. before aud during the flare. of the source associated with system the V892 Tau is between 2.1 and 3.1 aresec from the radio position of the main star σου Tau. while is between 6 and 6.5 arcsec off the," First, as summarised in Table \ref{tab:coord}, the position, before and during the flare, of the source associated with system the V892 Tau is between 2.4 and 3.1 arcsec from the radio position of the main star V892 Tau, while is between 6 and 6.8 arcsec off the"
observed distribution of stars obtained from IR surveys.,observed distribution of stars obtained from IR surveys.
 In our model. the Galactic bulge accounts for ~45 percent of the compact remnants born in the MW.," In our model, the Galactic bulge accounts for $\sim\,45$ percent of the compact remnants born in the MW."
 Our results show that the initial conditions play a fundamental role in the final fate of an ICoR. At variance with disk-born objects. almost all of those born in the bulge are likely retained by the Galaxy. and thus they give the major contribution to the microlensing rate toward the bulge itself.," Our results show that the initial conditions play a fundamental role in the final fate of an ICoR. At variance with disk-born objects, almost all of those born in the bulge are likely retained by the Galaxy, and thus they give the major contribution to the microlensing rate toward the bulge itself."
 We found that the microlensing optical depth of ICoRs is lower than that obtained without dynamical evolution (1.8. no kick at birth)., We found that the microlensing optical depth of ICoRs is lower than that obtained without dynamical evolution (i.e. no kick at birth).
 On the other hand. the net effect of the high velocities on microlensing is an increase of the event rate and a decrease in the typical time scale of the events.," On the other hand, the net effect of the high velocities on microlensing is an increase of the event rate and a decrease in the typical time scale of the events."
 Indeed. we found that the contribution to the event rate is higher than without kinematics effects.," Indeed, we found that the contribution to the event rate is higher than without kinematics effects."
 The average time scale of events associated to ICoRs ts also lower than that expected, The average time scale of events associated to ICoRs is also lower than that expected
16 SMC Oe/Doe stars would then have a specific angular uonmientuni only a few times ercater than the one that is supposedlv appropriate for producingo a stable disk over 16 black hole after the stellar collapse.,the SMC Oe/Be stars would then have a specific angular momentum only a few times greater than the one that is supposedly appropriate for producing a stable disk over the black hole after the stellar collapse.
 Since part ofthis aneular momentum will be lost durius the evolutionary ‘ollowing the MS phase. the SMC Oc/Be stars do not seen o have angular moment. that is to prevent the formation of cireuustellar disks iuifor the expected jets (?)..," Since part of this angular momentum will be lost during the evolutionary following the MS phase, the SMC Oe/Be stars do not seem to have angular momenta that is to prevent the formation of circumstellar disks and/or the expected jets \citep{macfad1999}."
 Because it iav affect the properties of Oc/Be stars. after we take the average of the O/O rates over the masses in the ZAMS and in the MS. the equatorial velocity of these objects decreases from the ZAMS to the MS by a factor 0.76. while O/O. varies from 00.95 to 00.99.," Because it may affect the properties of Oe/Be stars, after we take the average of the $\Omega/\Omega_{\rm c}$ rates over the masses in the ZAMS and in the MS, the equatorial velocity of these objects decreases from the ZAMS to the MS by a factor $0.76$, while $\Omega/\Omega_{\rm c}$ varies from 0.95 to 0.99."
" This change iu Q/Q. implies that the ratio V/V. varies from 0.87 to 0.97 and the ratio 4j of the surface equatorial ceutrifugal to gravitational acceleration passes from 0.76 to Thanks to the combined effects mainly of rotation aid ietallicitv. a series of models suggest that massive fast-rotating stars can fulfill the requirements imposed by the collapsar eugime aud be so progenitors of LGRDs οον, "," This change in $\Omega/\Omega_{\rm c}$ implies that the ratio $V/V_{c}$ varies from 0.87 to 0.97 and the ratio $\eta$ of the surface equatorial centrifugal to gravitational acceleration passes from $0.76$ to Thanks to the combined effects mainly of rotation and metallicity, a series of models suggest that massive fast-rotating stars can fulfill the requirements imposed by the collapsar engine and be so progenitors of LGRBs \citep{hirschi2005, yoon2006}."
To colply with the SN-LGRB relation. the involved stellar masses need to be higher than 10 AL...," To comply with the SN-LGRB relation, the involved stellar masses need to be higher than 10 $_{\odot}$."
 Thus. while ? conclude. on the basis of nou magneticmodels. that for he SMC metallicity stars with masses between 32 aud 92 AL. are able to produce LGRDsz. the latest 1nodols by ?.. which iuclude naenetic fields decrease the lower luit of uasses to those of carly B-type stars.," Thus, while \citet{hirschi2005} conclude, on the basis of non magneticmodels, that for the SMC metallicity stars with masses between 32 and 92 $_{\odot}$ are able to produce LGRBs, the latest models by \citet{yoon2006}, which include magnetic fields decrease the lower limit of masses to those of early B-type stars."
 According to these uodoels. fast rotation favors a strong mixiug of chemicals. which means that the stars can evolve as quasi-chemically rolmogencous and finally cud wp as massive helium stars.," According to these models, fast rotation favors a strong mixing of chemicals, which means that the stars can evolve as quasi-chemically homogeneous and finally end up as massive helium stars."
 Since the lower the iuetalliitv. the faster the stellar rotation can be. these phenomenon can m principle be avored in media with low metallicity. which accordingly inpede strong stellar winds.," Since the lower the metallicity, the faster the stellar rotation can be, these phenomenon can in principle be favored in media with low metallicity, which accordingly impede strong stellar winds."
 In turn. this makes the stars conserve high amounts of angular momentum.," In turn, this makes the stars conserve high amounts of angular momentum."
" The models wv? xediet a lower lint to the ratio of equatorial lear velocities V/V. (Ve is the critical or breakup velocity) as a function of mass for the LORB progenitors that do not ποσο] to change strongly according to the metallicity. but the limiting V/V, ratio icreases if the stellar uiass is lower."," The models by \citet{yoon2006}
 predict a lower limit to the ratio of equatorial linear velocities $V/V_{\rm c}$ $V_{\rm c}$ is the critical or breakup velocity) as a function of mass for the LGRB progenitors that do not seem to change strongly according to the metallicity, but the limiting $V/V_{\rm c}$ ratio increases if the stellar mass is lower."
" Moreover. the zoue above the threshold V/V, ratio of potential LGRD progenitors widens towards lower aud ligher masses as the metallicity 7oandreferencestherein indicate that the LCRD had a progenitor with an initial mass of 20 AD.. nes a BOB! star. where the metallicity is Z=LOOL. similar to the SAIC."," Moreover, the zone above the threshold $V/V_{\rm c}$ ratio of potential LGRB progenitors widens towards lower and higher masses as the metallicity \citet[][ and references therein]{campana2008} indicate that the LGRB had a progenitor with an initial mass of 20 $_{\odot}$, i.e., a B0-B1 star, where the metallicity is $Z\!=\!0.004$ , similar to the SMC."
" The chemical composition of the jiebulae surrounding the star. if if is assumed hat it reflects the chemical abundance of the progenitor. indicates that the progenitor was a near critical rotator. as iu the ""De phenomenon”."," The chemical composition of the nebulae surrounding the star, if it is assumed that it reflects the chemical abundance of the progenitor, indicates that the progenitor was a near critical rotator, as in the “Be phenomenon”."
" Such a fast rotation is required O0 produce an efficient mixing process in the star. which avors the stellar chemically homoecucous evolution aud nakes 1 possible for the euvironing nebulae reflect. the stellar To compare the models with the inferred ZAMS ratiosQ/O.., we transformed the CUV.)zais ratios of the Oc/Be star subsmuples in the SAIC into irafios by considering the lo dispersion of masses aud equatorial velocities intervening in each average."," Such a fast rotation is required to produce an efficient mixing process in the star, which favors the stellar chemically homogeneous evolution and makes it possible for the environing nebulae reflect the stellar To compare the models with the inferred ZAMS ratios, we transformed the $(V/V_{\rm c})_{\rm ZAMS }$ ratios of the Oe/Be star subsamples in the SMC into ratios by considering the $1\sigma$ dispersion of masses and equatorial velocities intervening in each average."
 The V/V; and rratios for massive stars are related as (2) which is also valid for the SAIC metallicity.," The $V/V_{\rm c}$ and ratios for massive stars are related as \citep{chauville01}
 which is also valid for the SMC metallicity."
 These results aro given in Table 2.., These results are given in Table \ref{table2}.
 The indicated mass category. ic. ÀAczoM. should be understood as Af(A)+ 6M. The boldfaced value of the inm corresponds to the average mass AL of the corresponding subsample.," The indicated mass category, i.e. $\pm\sigma$ M, should be understood as $M({\rm A})\pm\sigma$ M. The boldfaced value of the in corresponds to the average mass $\langle{\rm M}\rangle$ of the corresponding subsample."
" The natural upper limit ofthe surface stellar rotation ix obviously eiven bv V/V,=1.0.", The natural upper limit of the surface stellar rotation is obviously given by $V/V_{\rm c}\!=\!1.0$.
 In Table 2. all values VV;>1.0 mre the axithiuetic consequences of the imuposed svuuuetric lo dispersions ancl they should be understood as V/V.>1.0., In Table \ref{table2} all values $V/V_{\rm c}\!>\!1.0$ are the arithmetic consequences of the imposed symmetric $1\sigma$ dispersions and they should be understood as $V/V_{\rm c}\!\to\!1.0$.
" In Table 3.. the values of Table 2. are corrected for the effect of magnetic fields from the ? models as explained iu Sect, 2.2."," In Table \ref{table3}, the values of Table \ref{table2} are corrected for the effect of magnetic fields from the \citet{yoon2006} models as explained in Sect. \ref{ZAMSrotvel}. ."
", The inferred ZAMS zoues of O/O, ratios per mass category of SAIC Oc/Be stars given in Table 3 are compared in Fig.", The inferred ZAMS zones of $\Omega/\Omega_{\rm c}$ ratios per mass category of SMC Oe/Be stars given in Table \ref{table3} are compared in Fig.
 3 with the theoretically predicted region contaiine the LGORB progenitors for Z=0.002 by ?.., \ref{fig3} with the theoretically predicted region containing the LGRB progenitors for $Z\!=\!0.002$ by \citet{yoon2006}. .
as lt had on the previous cycle atcd as it did on the nest cycle.,as it had on the previous cycle and as it did on the next cycle.
 Cearly. the occulting edge does uot advauce uuiformly or. equivaleutly. it las some structure — bumps aud wigeles. perliaps corrugatiou — to it.," Clearly, the occulting edge does not advance uniformly or, equivalently, it has some structure – bumps and wiggles, perhaps corrugation – to it."
 To investigate this phenotjenon. we have used the pliotorretry duriug miid-ineress aud to piupoint the location o“the edge.," To investigate this phenomenon, we have used the photometry during mid-ingress and mid-egress to pinpoint the location of the edge."
" At these times the xiehtuess of the system is higily sensitive to the location of the ecee with respect to the center o""star A. In Fig.", At these times the brightness of the system is highly sensitive to the location of the edge with respect to the center of star A. In Fig.
 10 we show the clierence between the computed value of AN. based on the Model 3 aud the “observed” value based ou he kule edge model (corrected [or he ὃςatterecd light Component) versus time.," \ref{fig9} we show the difference between the computed value of $\Delta$ X, based on the \citet{w06} Model 3 and the “observed"" value based on the knife edge model (corrected for the scattered light component) versus time."
 We close Mocel 3 ECALse it is most consistent with al of je Observational aud astroplivsical constraints ou tlie sysem., We chose Model 3 because it is most consistent with all of the observational and astrophysical constraints on the system.
 A positive deviation from zero on us plot iudicates that the observed. occilting edge was lower tian expected for that eycle based ii the moclel. Le. that tlie system was o»xerved to be brighter than the moclel predicted at tliat line.," A positive deviation from zero on this plot indicates that the observed occulting edge was lower than expected for that cycle based on the model, i.e. that the system was observed to be brighter than the model predicted at that time."
 It is clear fom this figure tlat the Wietal.(2006) Moclel :) needs some revision to match the ast five years o ‘photometry., It is clear from this figure that the \citet{w06} Model 3 needs some revision to match the last five years of photometry.
 It ias beeu preclictilg a more rapid aclvauce of the occultiug edge than actually observed., It has been predicting a more rapid advance of the occulting edge than actually observed.
 Most likely. a sinall adjIstnel| to the orbits or o tlie inodel of the advancement ol the edge will correct this. athough a fuller revision is uecessary to properly account for the scattered ligit component.," Most likely, a small adjustment to the orbits or to the model of the advancement of the edge will correct this, although a fuller revision is necessary to properly account for the scattered light component."
 Here we focus only on the scatter about the treud. which measures the degree of smoothluiess of the occiting edge on a timescale of the orbital period to a lew years.," Here we focus only on the scatter about the trend, which measures the degree of smoothness of the occulting edge on a timescale of the orbital period to a few years."
 These sinall scale [icluatious are not depeudenut ou the details of the moclel used to compare with the observations., These small scale fluctuations are not dependent on the details of the model used to compare with the observations.
 The example of 22008-9 appears as tlie last set of data poinuts on this ligure around JD=2151800., The example of 2008-9 appears as the last set of data points on this figure around JD=2454800.
 [t is evident that the third peak oftus set is about 0.1 stellar radii lower than the second or fou‘th peaks. quautifving the phenomenon uoted above.," It is evident that the third peak of this set is about 0.4 stellar radii lower than the second or fourth peaks, quantifying the phenomenon noted above."
 This degree of variation within a single observing season. tormally c«)uprising four o‘bital eycles. is clearly characteristic of the star. as the eight vears of intensive )i0tometry. dispaved reveal.," This degree of variation within a single observing season, normally comprising four orbital cycles, is clearly characteristic of the star, as the eight years of intensive photometry displayed reveal."
 The standard deviation of the data aroud the inean trend is aboL 0.25 stellar radii., The standard deviation of the data around the mean trend is about 0.25 stellar radii.
 Some of this is due to photometric errors. of couwe. but the stellar b‘jelituess drops so rapidiy in the regime to which we have litmitecl the expOration (—0.3« AN< 0.6) liat the expected scatter from photometric variations characteristic of he star out of eclipse. is 0.12 stellar radii or less.," Some of this is due to photometric errors, of course, but the stellar brightness drops so rapidly in the regime to which we have limited the exploration $-0.3<\Delta$ $<0.6$ ) that the expected scatter from photometric variations characteristic of the star out of eclipse, is 0.15 stellar radii or less."
 This suggests that the true cycle-to-cyee variations of the oceulling edge are characterized by a staudard deviation of aout. 0.2 stellar racii. or a mere 1/10 Of a stellar cliameter!," This suggests that the true cycle-to-cycle variations of the occulting edge are characterized by a standard deviation of about 0.2 stellar radii, or a mere 1/10 of a stellar diameter!"
 One may ask whether this stall. nut Measurable. variajon in the locatio1 of the occultiug edge from evele to cycle is fully responsible for the scatter :ibout the mean laife-edge model or whether other physical phenomena are 'equired.," One may ask whether this small, but measurable, variation in the location of the occulting edge from cycle to cycle is fully responsible for the scatter about the mean knife-edge model or whether other physical phenomena are required."
 To address tlat question. we slow. in Fig.," To address that question, we show, in Fig."
 11. all oL the CCD data obtained curing ai eg‘ess OF Ingress., \ref{fig13} all of the CCD data obtained during an egress or ingress.
 For the post-2005 data. the plotted value of AX was obtained by correcting the precicted value [rom Winetal.(2006) for each ingress/egress pair by a small amount based ou the atalysis of Fig. 10..," For the post-2005 data, the plotted value of $\Delta$ X was obtained by correcting the predicted value from \citet{w06} for each ingress/egress pair by a small amount based on the analysis of Fig. \ref{fig9}."
 For the pre-2005 data a single correction value of -0.1 was applied to all of the data., For the pre-2005 data a single correction value of -0.1 was applied to all of the data.
 Ou each panel. two models are shown. oue being a," On each panel, two models are shown, one being a"
lensing data is slight. the increased. lensing strength. being balanced by the decreased: number of observed. background galaxies due to the smaller field of view.,"lensing data is slight, the increased lensing strength being balanced by the decreased number of observed background galaxies due to the smaller field of view."
 The improvement in σας mass estimation is more marked. due to a combination of reduced primordial CALB at the higher f-values. and the more comprehensive we-plane coverage alforded by ΑΛΛΗ.," The improvement in gas mass estimation is more marked, due to a combination of reduced primordial CMB at the higher $l$ -values, and the more comprehensive $uv$ -plane coverage afforded by AMI."
 ‘Table 20 gives the evidence ratios for the experiments outline above., Table \ref{tab:AMIevid} gives the evidence ratios for the experiments outline above.
 In the case where no contaminant. primordial CALB is present the most probable model matches that used in simulating the data., In the case where no contaminant primordial CMB is present the most probable model matches that used in simulating the data.
 Phe factor by which the true mocel is more likely is larger when the illSIE model is used: this model is both simpler. and. it. provides a better fit.," The factor by which the true model is more likely is larger when the iHSE model is used: this model is both simpler, and it provides a better fit."
 The same is true when the primordial luctuations are present. with suitably (but not greatly) reduced evidence ratios. with the variation in the evidence ratios being due to cillering noise realisations.," The same is true when the primordial fluctuations are present, with suitably (but not greatly) reduced evidence ratios, with the variation in the evidence ratios being due to differing noise realisations."
 We again see the sensitivity to the noise realisation. with confident model selection possible in only 4 out of the 6 analyses.," We again see the sensitivity to the noise realisation, with confident model selection possible in only 4 out of the 6 analyses."
 For the Beta model cluster. the samc balance between model complexity ancl goodness of fit: is," For the Beta model cluster, the same balance between model complexity and goodness of fit is"
To describe the general properties of the electrosphere of the quark stars with respect to the effect of the multiple scattering on electromagnetic radiation we introduce a parameter. called suppression factor. and delined as The LPM elleet is important for reeions lor which s;(:.7)>1: for regions in the electrosphere with ος.72)<1. the LPAI effect can be salelv ignored.,"To describe the general properties of the electrosphere of the quark stars with respect to the effect of the multiple scattering on electromagnetic radiation we introduce a parameter, called suppression factor, and defined as The LPM effect is important for regions for which $s_{l}(z,T)\geq
1$; for regions in the electrosphere with $s_{l}(z,T)<1$, the LPM effect can be safely ignored."
 The variation of the suppression factor s; as a function of z for (wo sets of values of the surface electric potential of the quark star and for different values of the temperature is represented in Fig., The variation of the suppression factor $s_l$ as a function of $z$ for two sets of values of the surface electric potential of the quark star and for different values of the temperature is represented in Fig.
 2., 2.
 As one can see [rom Fie., As one can see from Fig.
 2. the effect of the multiple scattering is extremely importan in (he dense laver situated near the quark star surface.," 2, the effect of the multiple scattering is extremely important in the dense layer situated near the quark star surface."
 For the electrons situated [ar away for the surface. the suppression due to multiple scattering can be ignored.," For the electrons situated far away for the surface, the suppression due to multiple scattering can be ignored."
" In the absence of an external field electromagnetic radiation emission of electrons is strongly suppressed mean square multiple scattering angle over the distance whentheLy. 0?FS= (e./e)(L)/Nu)- where e,=m,y/4z/o and Xj=παρ]1(184)]— isthe radiation length. is greater than or equal to 62. 62).FS>6? (IXlein1999:Hansenetal.etal. 1995)."," In the absence of an external field electromagnetic radiation emission of electrons is strongly suppressed when the mean square multiple scattering angle over the distance $%
L_{\parallel $\theta _{ms}^{2}=$ $\left( \epsilon
_{s}/\epsilon \right) ^{2}\left( L_{\parallel }/X_{0}\right) $, where $\epsilon _{s}=m_{e}\sqrt{4\pi /\alpha }$ and $X_{0}=\left[
4n\alpha r_{e}^{2}\ln \left( 184\right) \right]
 ^{-1}$ isthe radiation length, is greater than or equal to $\theta _{\gamma }^{2}$, $\theta _{ms}^{2}\geq \theta
_{\gamma }^{2}$ \citep{Kl99,Ha03,An95}."
. Hence the radiation emission dillerential cross section for the production of a photon is suppressed when where For the electrosphere of the quark stars. in the ealeulation of the LPAI critical Irequencey cppar the elfect of the external electric field has also to be included.," Hence the radiation emission differential cross section for the production of a photon is suppressed when where For the electrosphere of the quark stars, in the calculation of the LPM critical frequency $\omega _{LPM}$ the effect of the external electric field has also to be included."
 By assuming that the temperature of the star T<<pp=pre. with py the Fermi momentum. the Fermi distribution [actors force all the electrons to have (e)2µV.," By assuming that the temperature of the star $T<<p_{F}=\mu _e$, with $p_{F}$ the Fermi momentum, the Fermi distribution factors force all the electrons to have $\left\langle \epsilon \right\rangle \approx \mu
_e\approx V$."
" Therefore the critical (2-dependent) LPM frequency for the bremsstrahlung photon emission in (he electron laver at the surface of the quark star is given by where the parameter ¢=eEefim?5E/E, lakes into account the modifications of the LPM critical frequency. due {ο (he presence of the external electric field 1936)..", Therefore the critical $z$ -dependent) LPM frequency for the bremsstrahlung photon emission in the electron layer at the surface of the quark star is given by where the parameter $\zeta =eE\epsilon /m_e^3=\gamma E/E_{cr}$ takes into account the modifications of the LPM critical frequency due to the presence of the external electric field \citep{BaTi86}. .
 The LPAI frequency lor fee electrons (in the absence of an externa, The LPM frequency for free electrons (in the absence of an external
Unexpected accelerating expansion of the universe was first discovered by observing type Ia supernovae (SNe Ia) (??)..,"Unexpected accelerating expansion of the universe was first discovered by observing type Ia supernovae (SNe Ia) \citep{Riess:1998cb,Perlmutter:1998np}."
 This acceleration ts attributed to dark energy. whose presence was corroborated later by other independent sources including the WMAP and other observations of the CMB (?).. X-ray clusters (2).. ete.," This acceleration is attributed to dark energy, whose presence was corroborated later by other independent sources including the WMAP and other observations of the CMB \citep{Spergel:2003cb}, X-ray clusters \citep{Allen:2002sr}, etc."
 With more observational data available (e.g.99999999992222222222).) we are getting more stringent constraints on the nature of dark energy: nevertheless. the underlying physics of dark energy remains mysterious.," With more observational data available \citep[e.g.][]{Hawkins:2002sg, Abazajian:2003jy,
 Spergel:2006hy, Riess:2006fw, WoodVasey:2007jb, Davis:2007na,
 Schaefer:2006pa, Percival:2007yw, Komatsu:2008hk, Dunkley:2008ie}, we are getting more stringent constraints on the nature of dark energy; nevertheless, the underlying physics of dark energy remains mysterious."
 In addition to the cosmological constant. many other dark energy models have been suggested. including models of scalar fields (see ?. for à recent review) and modification of general relativity (seeforexample 22222???..," In addition to the cosmological constant, many other dark energy models have been suggested, including models of scalar fields (see \citet{Copeland:2006wr} for a recent review) and modification of general relativity \citep[see for example][]{Deffayet:2000uy, Binetruy:1999hy,
 Maartens:2006qf, Capozziello:2003gx, Dvali:2000rv, Carroll:2003wy,
 Nojiri:2003ft, Nojiri:2006ri}."
 Measuring the expansion history directly may be the best way to constrain the properties of dark energy., Measuring the expansion history directly may be the best way to constrain the properties of dark energy.
 To measure the expansion history. we need standard candles at different redshifts.," To measure the expansion history, we need standard candles at different redshifts."
 SNe la. which are now viewed as nearly ideal standard candles. have played an important role in constraining cosmological parameters.," SNe Ia, which are now viewed as nearly ideal standard candles, have played an important role in constraining cosmological parameters."
 We now have 192 samples of SN Ia (???) that can be used to determine the expansion history.," We now have $192$ samples of SN Ia \citep{Riess:2006fw,WoodVasey:2007jb,Davis:2007na} that can be used to determine the expansion history."
 And the proposed SNAP (seeforexample?) will d= about 2000 samples per year.," And the proposed SNAP \citep[see for
example][]{Aldering:2004ak}
 will add about $2000$ samples per year."
 Increasing SN Ia samples will provide more and more precise description of the cosmic expansion., Increasing SN Ia samples will provide more and more precise description of the cosmic expansion.
 However. the redshift of the present 192 SNe la ranges only up to about 1.7 and the mean redshift is about 0.5.," However, the redshift of the present $192$ SNe Ia ranges only up to about $1.7$ and the mean redshift is about $0.5$."
 They cannot provide any information on the cosmic expansion beyond redshift 1.7., They cannot provide any information on the cosmic expansion beyond redshift $1.7$.
 Here gamma-ray bursts (GRBs) come in and fill the void., Here gamma-ray bursts (GRBs) come in and fill the void.
With their higher luminosities. GRBs are visible across much greater distances than supernovae.,"With their higher luminosities, GRBs are visible across much greater distances than supernovae."
 The presently available 69 compiled GRBs (?) extend the redshift to z>6 and the mean redshift is about 2.1., The presently available $69$ compiled GRBs \citep{Schaefer:2006pa} extend the redshift to $z>6$ and the mean redshift is about $2.1$.
 After being calibrated with Juminosity relations. GRBs may be used as standard candles to provide information on cosmic expansion at high redshift and. at the same time. to tighten the constraints on cosmic expansion at low redshift.," After being calibrated with luminosity relations, GRBs may be used as standard candles to provide information on cosmic expansion at high redshift and, at the same time, to tighten the constraints on cosmic expansion at low redshift."
 See. for example. ?.. ?.. 2. 2. MD 2. 2.. 2..2.. 2.. 2.. and ?. for works on GRB cosmology.," See, for example, \citet{Dai:2004tq}, \citet{Ghirlanda:2004fs}, \citet{DiGirolamo:2005ze}, \citet{Firmani:2005gs}, \citet{Friedman:2004mg}, \citet{Lamb:2005cw}, \citet{Liang:2005xb}, \citet{Xu:2005uv}, \citet{Wang:2005ic}, \citet{Li:2006ev}, \citet{Su:2006jp}, \citet{Schaefer:2006pa}, \citet{Wright:2007vr}, and \citet{Wang:2007rz}
 for works on GRB cosmology."
 Among parameters that describe the properties of dark energy. the equation of state (EOS) is the most important.," Among parameters that describe the properties of dark energy, the equation of state (EOS) is the most important."
 Whether and how it evolves with time is crucial in distinguishing different cosmological models., Whether and how it evolves with time is crucial in distinguishing different cosmological models.
 Due to not understanding of the behaviors of dark energy. simple parametric forms such as w(z)=wo+72 (2) and wis)=wo+Waz/Cb+2) (2?) have been proposed for studying the possible evolution of dark energy.," Due to not understanding of the behaviors of dark energy, simple parametric forms such as $w(z)=w_0+w'z$ \citep{Cooray:1999da} and $w(z)=w_0+w_az/(1+z)$ \citep{Chevallier:2000qy, Linder:2002et}
 have been proposed for studying the possible evolution of dark energy."
 However. a simple parameterization itself greatly restricts the allowed wandering of wu(z). and 1s equivalent to a strong prior on the nature of dark energy (?)..," However, a simple parameterization itself greatly restricts the allowed wandering of $w(z)$, and is equivalent to a strong prior on the nature of dark energy \citep{Riess:2006fw}."
 To avoid any strong prior before comparing data. one can utilize an alternative approach in which uncorrelated estimates are made of discrete w(z) of different redshifts.," To avoid any strong prior before comparing data, one can utilize an alternative approach in which uncorrelated estimates are made of discrete $w(z)$ of different redshifts."
 This approach was proposed by ? and ? and has been adopted in previous analyses using SNe Ia (?2)..," This approach was proposed by \citet{Huterer:2002hy} and \citet{Huterer:2004ch} and has been adopted in previous analyses using SNe Ia \citep{Riess:2006fw,Sullivan:2007pd}."
 In this work. we apply this approach to GRB luminosity data (?).. in addition to SN Ta data (222).. and compare our results with those in the previous work that does not include GRB luminosity data (?)..," In this work, we apply this approach to GRB luminosity data \citep{Schaefer:2006pa}, in addition to SN Ia data \citep{Riess:2006fw,WoodVasey:2007jb,Davis:2007na}, and compare our results with those in the previous work that does not include GRB luminosity data \citep{Sullivan:2007pd}."
 We first briefly review the techniques for uncorrelated estimates of dark energy evolution in section 2.., We first briefly review the techniques for uncorrelated estimates of dark energy evolution in section \ref{sec:methodology}.
 The observational data and how they are included n the data analysis are deseribed in section 3.., The observational data and how they are included in the data analysis are described in section \ref{sec:observational_data}.
 We present our results in section 4.. followed by a summary in section 5..," We present our results in section \ref{sec:results}, followed by a summary in section \ref{sec:summary}."
 Standard candles impose constraints on cosmological parameters essentially through a comparison of the luminosity distance from observation with that from theoretical models., Standard candles impose constraints on cosmological parameters essentially through a comparison of the luminosity distance from observation with that from theoretical models.
 Observationally. the luminosity distance is given by where L and F are the luminosity of the standard candles and the observed flux. respectively.," Observationally, the luminosity distance is given by where $L$ and $F$ are the luminosity of the standard candles and the observed flux, respectively."
 Theoretically. the," Theoretically, the"
or based on photometry.,or based on photometry.
 For these stars we adopt the values from our spectroscopic analysis., For these stars we adopt the values from our spectroscopic analysis.
 The only high-resolution study in the literature is by Nordstrometal.(1997) for the star 007798339 1173109)., The only high-resolution study in the literature is by \citet{nordstrom} for the star 07798339 173109).
" These authors analysed echelle spectra in the narrow wavelength range 5165.77—5211.25 tto obtain 7;g 77000KK, logg==33.5 and vsini--11l5.4kkmss ! (no errors available)."," These authors analysed echelle spectra in the narrow wavelength range $5165.77 - 5211.25$ to obtain $T_{\rm eff}$ K, $\log g$ 3.5 and $v\sin i$ $^{-1}$ (no errors available)."
" The difference of 300KK in Τε is not significant within the errors, and the logg and vsini values are in good agreement with our results."," The difference of K in $T_{\rm eff}$ is not significant within the errors, and the $\log g$ and $v \sin i$ values are in good agreement with our results."
" It is useful to compare the values of Teg derived spectroscopically with those obtained via photometric methods (IRFM, (V - K) calibration, KIC)."," It is useful to compare the values of $T_{\rm eff}$ derived spectroscopically with those obtained via photometric methods (IRFM, (V - K) calibration, KIC)."
" Inspection of Fig. 2,,"," Inspection of Fig. \ref{confrTeff},"
" which illustrates such a comparison, shows a general good agreement among all these values."," which illustrates such a comparison, shows a general good agreement among all these values."
" Quantitatively, a weighted mean of such differences gives: TIRFM. 5002-200; TZP**— T(Y-79——1304-200; TSP?—THC ——502-300, non significant to the 1c level."," Quantitatively, a weighted mean of such differences gives: $T_{\rm eff}^{\rm Spec}-T_{\rm eff}^{\rm IRFM}$ $-$ $\pm$ 200; $T_{\rm eff}^{\rm Spec}-T_{\rm eff}^{\rm (V-K)}$ $-$ $\pm$ 200; $T_{\rm eff}^{\rm Spec}-T_{\rm eff}^{\rm KIC}$ $-$ $\pm$ 300, non significant to the $\sigma$ level."
 Similarly a very good agreement is found between TZ and Teg estimated through uvbyf photometry (see Table 2))., Similarly a very good agreement is found between $T_{\rm eff}^{\rm Spec}$ and $T_{\rm eff}$ estimated through $uvby\beta$ photometry (see Table \ref{tab2}) ).
 However there are two exceptions to this trend: This star shows a large difference between the spectroscopic Teg and that estimated from photometry + KK)., However there are two exceptions to this trend: This star shows a large difference between the spectroscopic $_{\rm eff}$ and that estimated from photometry $\pm$ K).
" This difference is at a level of 2222.9 c, and deserves some comments."," This difference is at a level of $\approx$ $\sigma$, and deserves some comments."
" Indeed, there is no a clear explanation for such a large difference."," Indeed, there is no a clear explanation for such a large difference."
" The Loiano and INAF—OOACT spectra give exactly the same values for T.g and log g, suggesting that there could be a problem with the photometry.", The Loiano and OACT spectra give exactly the same values for $T_{\rm eff}$ and $\log g$ suggesting that there could be a problem with the photometry.
" The uvby values reported for this star by Hauck&Mermillod(1998) are the average of the measurements by Olsen(1983) and Jordietal. (1996),, while the 6 value, on which the Tig depends, was measured only by the latter authors."," The $uvby$ values reported for this star by \citet{hauck} are the average of the measurements by \citet{olsen} and \citet{jordi}, while the $\beta$ value, on which the $T_{\rm eff}$ depends, was measured only by the latter authors."
" The two quoted uvby values are slightly discrepant, but the difference is not large enough to change significantly the derived value of logg."," The two quoted $uvby$ values are slightly discrepant, but the difference is not large enough to change significantly the derived value of $\log g$."
 We also considered the possibility that a close companion is affecting the photometric measurements., We also considered the possibility that a close companion is affecting the photometric measurements.
" We visually inspected bothII and2MASS images of 005724440 1187234), where the star appears to be isolated in the near infrared."," We visually inspected both and images of 05724440 187234), where the star appears to be isolated in the near infrared."
 In the optical it is surrounded by a few very close faint stars whose contribution can hardly be considered significant., In the optical it is surrounded by a few very close faint stars whose contribution can hardly be considered significant.
" By using the calibration by Masanaetal.(2006),, the discrepancy is reduced to only KK, reinforcing our suspicion that there is something wrong with the uvbyB photometry of this star."," By using the calibration by \citet{masana06}, the discrepancy is reduced to only K, reinforcing our suspicion that there is something wrong with the $uvby\beta$ photometry of this star."
" The Τοκ--9000-Ε200 K derived spectroscopically for this star is in good agreement with the value derived from IRFM, and consistent within the errors with the Τομ derived from (V—K) color."," The $T_{\rm eff}$ $\pm$ 200 K derived spectroscopically for this star is in good agreement with the value derived from IRFM, and consistent within the errors with the $T_{\rm eff}$ derived from $(V-K)$ color."
 However there is a large discrepancy with respect to the KIC estimate., However there is a large discrepancy with respect to the KIC estimate.
" This occurrence could perhaps be explained in terms of a visual binary, with a companion star dimmer by 3 mag at a distance of 0.9 arcsec."," This occurrence could perhaps be explained in terms of a visual binary, with a companion star dimmer by 3 mag at a distance of 0.9 arcsec."
" Even if nothing is known about the companion,due to the small separation, it is likely that the photometric values are affected by the secondary star flux."," Even if nothing is known about the companion,due to the small separation, it is likely that the photometric values are affected by the secondary star flux."
The kev point to establish Theorem 1.1 is the gradient entropy estimate (1.5)).,The key point to establish Theorem \ref{EM:th1} is the gradient entropy estimate \ref{EM:entropy}) ).
 We first consider the parabolic regularization of the svstem (1.1)) ancl we show that the smooth solution admits the £* bound (1.4)) and the fundamental gradient. entropy inequality (1.5))., We first consider the parabolic regularization of the system \ref{EM:burger}) ) and we show that the smooth solution admits the $L^{\infty}$ bound \ref{EM:max_pri}) ) and the fundamental gradient entropy inequality \ref{EM:entropy}) ).
 Then. these estimates will allow us to pass to the limit when the regularization vanishes. which will provide the existence of a solution.," Then, these estimates will allow us to pass to the limit when the regularization vanishes, which will provide the existence of a solution."
 Let us mention that a similar gradient entropy inequality was introduced in Cannone et al., Let us mention that a similar gradient entropy inequality was introduced in Cannone et al.
" [?] to prove the existence of a solution of a (vo-dimensional svstem of (wo coupled. transport equations,", \cite{EC} to prove the existence of a solution of a two-dimensional system of two coupled transport equations.
 Up to our knowledge. the result stated in Theorem 1.1 seems new.," Up to our knowledge, the result stated in Theorem \ref{EM:th1} seems new."
 In relation with our result. we can cite the paper of Poupaud |?].. where a result of existence and uniqueness ol Lipschitz solutions is proven for a particular quasi-linear hyperbolic Ivperbolie svstems (1.1)) in the case d=2 are called strictly hyperbolic if and only if we have: In this case. a result of Lax ΤΕ implies the existence of Lipschitz monotone solutions of (1.1))-(1.2)).," In relation with our result, we can cite the paper of Poupaud \cite{Poupaud}, where a result of existence and uniqueness of Lipschitz solutions is proven for a particular quasi-linear hyperbolic Hyperbolic systems \ref{EM:burger}) ) in the case $d=2$ are called strictly hyperbolic if and only if we have: In this case, a result of Lax \cite{Lax} implies the existence of Lipschitz monotone solutions of \ref{EM:burger}) \ref{EM:initialdata}) )."
 This result was also extended by Serre |?.VolLI] in the case of (dxd) rich hyperbolic svstems (see also Subsection ?? for more related references)., This result was also extended by Serre \cite[Vol II]{Serre12} in the case of $(d\times d)$ rich hyperbolic systems (see also Subsection \ref{EM:ref} for more related references).
 Their results, Their results
"100 kpc seems a reasonable compromise between an upper limit of a few hundreds of kpc for Ag based on the turn- time of largest eddies (?) and the typical galactic scales ~10— 30kpc, see ? for a detailed discussion.","$100\,$ kpc seems a reasonable compromise between an upper limit of a few hundreds of kpc for $\lambda_B$ based on the turn-around time of largest eddies \citep{Waxman:1998yy} and the typical galactic scales $\sim\,10-30\,$ kpc, see \cite{KL08a} for a detailed discussion."
" The generation of secondary photons and electrons and positrons through pion production is treated in a discrete manner, as in ? for nuclei projectiles with A>1 and with SOPHIA (?) for proton and neutron cosmic rays."," The generation of secondary photons and electrons and positrons through pion production is treated in a discrete manner, as in \cite{Allard06}
 for nuclei projectiles with $A> 1$ and with SOPHIA \citep{Mucke99} for proton and neutron cosmic rays."
 Electron and positron pair creation through photo-hadronic processes is implemented as in ?.., Electron and positron pair creation through photo-hadronic processes is implemented as in \cite{ASM06}.
" For each time step (chosen to be much larger than the typical mean free path of pair photo-production processes), we assume that an ensemble of electron and positron pairs are generated with energies distributed according to a power law, and maximum energy depending on the primary particle."," For each time step (chosen to be much larger than the typical mean free path of pair photo-production processes), we assume that an ensemble of electron and positron pairs are generated with energies distributed according to a power law, and maximum energy depending on the primary particle."
" The use of an improved pair spectrum as computed in ? would lower the gamma ray flux resulting from direct pair production by factor of a few in the range E,x10 GeV, and leave unchangeda the prediction at a higher energy (Armengaud, private communication)."," The use of an improved pair spectrum as computed in \cite{KA08} would lower the gamma ray flux resulting from direct pair production by a factor of a few in the range $E_{\gamma}\lesssim 10\,$ GeV, and leave unchanged the prediction at a higher energy (Armengaud, private communication)."
" Furthermore, we will show in the following that direct pair production processes provide a sub-dominant contribution to the overall gamma ray flux in the range E,z0.1 GeV, hence the overall difference is expected to be even smaller."," Furthermore, we will show in the following that direct pair production processes provide a sub-dominant contribution to the overall gamma ray flux in the range $E_{\gamma} \,\gtrsim\,0.1\,$ GeV, hence the overall difference is expected to be even smaller."
 We investigate in this paper the possible detection of photons in the GeV-TeV energy range., We investigate in this paper the possible detection of photons in the GeV-TeV energy range.
" Equation (2)) suggests that, unless the source is embedded in a particularly strong field, the major contribution in this range will come from electrons of energy E,=1015 eV. The flux will thus essentially result from cosmic rays of energy higher than E~101 eV. For this reason, we chose to inject cosmic rays at the source between Emin=10!7 eV et Emax=10795 eV. We assume our source to be stationary with (isotropic) cosmic ray luminosity integrated over E=1015 eV of Lgio=1042-46 erg sl, anda spectral index of a=2.3."," Equation \ref{eq:Esyn}) ) suggests that, unless the source is embedded in a particularly strong field, the major contribution in this range will come from electrons of energy $E_e\gtrsim 10^{18}$ eV. The flux will thus essentially result from cosmic rays of energy higher than $E\sim 10^{19}~$ eV. For this reason, we chose to inject cosmic rays at the source between $E_{\rm
 min}=10^{17}$ eV et $E_{\rm max}=10^{20.5}$ eV. We assume our source to be stationary with (isotropic) cosmic ray luminosity integrated over $E=10^{19}$ eV of $L_{E,19} = 10^{42-46}~$ erg $^{-1}$, and a spectral index of $\alpha = 2.3$."
 We take into account photo-hadronic interactions with CMB and infrared photons., We take into account photo-hadronic interactions with CMB and infrared photons.
 The diffuse infrared background is modelled according to the studies of ?.., The diffuse infrared background is modelled according to the studies of \cite{SMS06}.
" We do not take into account redshift evolution, as its effect is negligible as compared to the uncertainties on our other parameters."," We do not take into account redshift evolution, as its effect is negligible as compared to the uncertainties on our other parameters."
 We also neglect baryonic interactions in view of the negligible density in the source environment., We also neglect baryonic interactions in view of the negligible density in the source environment.
" Once the secondary particles produced during the propagation have been computed, we calculate the synchrotron photon fluxes, taking into account the competition with inverse Compton scattering by Monte Carlo over steps of size 100 kpc."," Once the secondary particles produced during the propagation have been computed, we calculate the synchrotron photon fluxes, taking into account the competition with inverse Compton scattering by Monte Carlo over steps of size 100 kpc."
" The mean effective electron loss length is calculated following ?,, using the radio background data of ?.."," The mean effective electron loss length is calculated following \cite{GA05}, using the radio background data of \cite{CBA70}."
" We assume that each electron emits a synchrotron photon spectrum dV,/dE,ocE,""? with a sharp cut-off above E;~(2/3)Eysyn, where Eysy is given by Eq. (2))."," We assume that each electron emits a synchrotron photon spectrum ${\rm d}N_\gamma/{\rm d}E_\gamma \propto E_\gamma^{-2/3}$ with a sharp cut-off above $E_{\rm c}\sim (2/3)\,E_{\rm \gamma,syn}$, where $E_{\rm \gamma,syn}$ is given by Eq. \ref{eq:Esyn}) )."
" Regarding the photons produced through the neutral pion channel, we draw the interaction positions with CMB and radio photons using the mean free paths computed by ?.."," Regarding the photons produced through the neutral pion channel, we draw the interaction positions with CMB and radio photons using the mean free paths computed by \cite{Lee98}."
 We assume that one of the electron-positron pair inherits of the total energy of the parent photon., We assume that one of the electron-positron pair inherits of the total energy of the parent photon.
 We first study the influence of inhomogeneous magnetic fields on the gamma ray flux produced by ultrahigh energy cosmic rays near their source., We first study the influence of inhomogeneous magnetic fields on the gamma ray flux produced by ultrahigh energy cosmic rays near their source.
" In particular, we examine the case of a source placed in a rather dense region of a filament of large scale structure, see Fig. 1.."," In particular, we examine the case of a source placed in a rather dense region of a filament of large scale structure, see Fig. \ref{fig:slices}."
" On the transverse scale of the structure J,, of order of a few Mpc, one expects the secondary electrons and positrons to be distributed isotropically around the source."," On the transverse scale of the structure $l_\perp$, of order of a few Mpc, one expects the secondary electrons and positrons to be distributed isotropically around the source."
 A population of ultrahigh energy cosmic rays seeds the intergalactic medium with secondary pairs in a roughly, A population of ultrahigh energy cosmic rays seeds the intergalactic medium with secondary pairs in a roughly
the N-ravs and those that produce radio svuchrotrou enissiou observable from the Earth with sufticicut resolution to measure accurate spectral indices. there is a large unecrtainty iu the expected spectral shape of the electron distribution at low enereies. and couscquently iu the predicted spectral shape aud the intensity of tle Nav CLUISSIO-,"the X-rays and those that produce radio synchrotron emission observable from the Earth with sufficient resolution to measure accurate spectral indices, there is a large uncertainty in the expected spectral shape of the electron distribution at low energies, and consequently, in the predicted spectral shape and the intensity of the X-ray emission."
 Although most of the sources in Table 3 display spatial coincidence between the radio. X-rav. and optical morphologies. there are a few sources where this is not the case.," Although most of the sources in Table \ref{tab:sources} display spatial coincidence between the radio, X-ray, and optical morphologies, there are a few sources where this is not the case."
 Cen A. 3€ G6D. aud PINS 1127 are the three examples of this ychavior iu our collection.," Cen A, 3C 66B, and PKS 1127 are the three examples of this behavior in our collection."
" We do not believe that lis effect results from luted augular resolution since it occurs in both the nearest (Cem À) aud ""urthest (PISSII27) source.", We do not believe that this effect results from limited angular resolution since it occurs in both the nearest (Cen A) and furthest (PKS1127) source.
 Iu the case of Cen A. some offsets between the peak brightuess of radio and N-ray are of order 27 (31pc) while other catures are colucideut.," In the case of Cen A, some offsets between the peak brightness of radio and X-ray are of order $^{\prime\prime}$ (34pc) while other features are coincident."
" For PISII2T. au offset of L8"" observed for knot D. corresponds to 9 pe."," For PKS1127, an offset of $^{\prime\prime}$ observed for knot B corresponds to 9 kpc."
 For these jets. it is dificult to measure radio aud X-rav intensities for well defined voles.," For these jets, it is difficult to measure radio and x-ray intensities for well defined volumes."
 It is also the case that the PISSI127 jet is very weak in the radio (the source is a VLA calibrator) aud the published radio data for Cen A do not lave the conibination of high resolution aud s/n which are necessary for reliable iuter-baud comparisons., It is also the case that the PKS1127 jet is very weak in the radio (the source is a VLA calibrator) and the published radio data for Cen A do not have the combination of high resolution and s/n which are necessary for reliable inter-band comparisons.
 For 3C 66B and PKSII27. the peak Nay. brightucss occurs upstream of the peak radio brightuess.," For 3C 66B and PKS1127, the peak X-ray brightness occurs upstream of the peak radio brightness."
 To obtain significant X-ray emissiou with little or uno radio cussion would require extreme beamine paralcters or a distinct low cuereyv electrou population (sec. 773) , To obtain significant X-ray emission with little or no radio emission would require extreme beaming parameters or a distinct low energy electron population (sec. \ref{sec:distinct}) )
for the beamine model or a flat high euergv component of the electron spectrum for svuchrotrou models., for the beaming model or a flat high energy component of the electron spectrum for synchrotron models.
 Since data have not vot been published. we have uot classified 3€ 15. 3€ 31. PIRS0521. aud NGC1261 in Table 3..," Since data have not yet been published, we have not classified 3C 15, 3C 31, PKS0521, and NGC4261 in Table \ref{tab:sources}."
 The beamine model introduced by Tavecchio et al. (, The beaming model introduced by Tavecchio et al. (
2000) and Celotti et al. (,2000) and Celotti et al. (
2001) is appealing because it offers a method of increasing the IC Cluission relative to the svuchrotron emission aud because it was already clear from EINSTEIN aud ROSAT results on M87. 3€ 120. and 3€ 390.3 that all known X-ray cutting jet features were one sided.,"2001) is appealing because it offers a method of increasing the IC emission relative to the synchrotron emission and because it was already clear from EINSTEIN and ROSAT results on M87, 3C 120, and 3C 390.3 that all known X-ray emitting jet features were one sided."
" Most of the new examples from Claudia detections maintain the one sided nature of N-ray Cluission. a natural consequence of the beaming model,"," Most of the new examples from Chandra detections maintain the one sided nature of X-ray emission, a natural consequence of the beaming model."
 The following formmlation is based on the assunption of equipartition iu the svuchrotron source in order to evaluate the magnetic field streneth and accounts for the anisotropic nature of the IC emission in the jet frame., The following formulation is based on the assumption of equipartition in the synchrotron source in order to evaluate the magnetic field strength and accounts for the anisotropic nature of the IC emission in the jet frame.
 The details are eiven in the Appendix., The details are given in the Appendix.
 We define the constraints ou the bulls relativistic flow velocity of the jet fiuid. E: the viewing augle of the Lue of sight of the observer with respect to the jet velocity vector. 6: aud the relativistic Doppler factor. 9.," We define the constraints on the bulk relativistic flow velocity of the jet fluid, $\Gamma$; the viewing angle of the line of sight of the observer with respect to the jet velocity vector, $\theta_{\rm j}$; and the relativistic Doppler factor, $\delta$."
 Once these coustraiuts lave been evaluated. we examine a umber of source parameters: Over the vears since its introduction (Burbidec. 1956). the concept « ‘niin energv (or ‘equipartition) has eenerated cousiderable debate and some confusion.," Once these constraints have been evaluated, we examine a number of source parameters: Over the years since its introduction (Burbidge, 1956), the concept of 'minimum energy' (or 'equipartition') has generated considerable debate and some confusion."
 Our view is that although it was originally borue of twin desperatious (the stagecring amount of uou-thermal energy required for large svuchrotron radio sources aud the realization. that it was almost impossible to disentangle the two primary parameters of svuchrotron enmuüssion). a reasonable case can be advanced that ιο oextragalactie svuchrotron sources are not more than a factor of a few from. having their average maeuctic field energy density equal to the average enerev deusitv in relativistic particles: u(p) z u(B).," Our view is that although it was originally borne of twin desperations (the staggering amount of non-thermal energy required for large synchrotron radio sources and the realization that it was almost impossible to disentangle the two primary parameters of synchrotron emission), a reasonable case can be advanced that most extragalactic synchrotron sources are not more than a factor of a few from having their average magnetic field energy density equal to the average energy density in relativistic particles: u(p) $\approx$ u(B)."
 Obviously we are unconcerued with the condition u(p) << w(B): it is the converse that has generated, Obviously we are unconcerned with the condition u(p) $<<$ u(B); it is the converse that has generated
where D is (he thickness of the considered region and &~A.(4)¢/3 is the diffusion coellicient of the electrons with mean free path Ac(5) and Lorentz factor5.,"where $D$ is the thickness of the considered region and $\kappa \sim \lambda_{\rm e}(\gamma) \, c / 3$ is the diffusion coefficient of the electrons with mean free path $\lambda_{\rm e}(\gamma)$ and Lorentz factor$\gamma$."
" Assuming that (ο) is comparable to the electron gvroradius. one obtains where the radiative loss time scale /7,, is given in Appendix D. The time scale between subsequent shocks can be estimated as where dis the mean separation of the shocks in the comoving frame of the radiating plasma between the shocks (moving will bulk Lorentz factor DS 1)."," Assuming that $\lambda_{\rm e}(\gamma)$ is comparable to the electron gyroradius, one obtains where the radiative loss time scale $t'_{\rm rad}$ is given in Appendix D. The time scale between subsequent shocks can be estimated as where $d'$ is the mean separation of the shocks in the comoving frame of the radiating plasma between the shocks (moving with bulk Lorentz factor $\Gamma \gg 1$ )."
 Second-order Fermi acceleration can be eharacterized bv the time scale where the velocity of the scattering centers involved in the turbulent acceleration V4. can be identified with the Alfven speed. V4. and the particle gvroradius can be taken for À«(5) (Stawarz&Ostrowski 2002)..," Second-order Fermi acceleration can be characterized by the time scale where the velocity of the scattering centers involved in the turbulent acceleration $V_{\rm sc}$ can be identified with the Alfven speed, $V_{\rm A}$, and the particle gyroradius can be taken for $\lambda_{\rm e}(\gamma)$ \citep{sta02}. ."
 Hence. one obtains the ratio Wy/e.REFERENCES," Hence, one obtains the ratio where$\beta_{\rm A} \equiv V_{\rm A} / c$ ."
"other at 1.0 « 7? < 2.0 (""outer halo”) in cach merger model.",other at 1.0 $<$ $R$ $\le$ 2.0 (“outer halo”) in each merger model.
" The simulated SIDE of the ""inner halo” and that of the 7""outer halo” are compared with the observed. MDE derived for the S kpe field and with that derived for the combined 2] and 31 kpe fields.", The simulated MDF of the “inner halo” and that of the “outer halo” are compared with the observed MDF derived for the 8 kpc field and with that derived for the combined 21 and 31 kpc fields.
 Although we investigated ~20 models. we here present only the results ofresulls.," Although we investigated $\sim 20$ models, we here present only the results of."
 “Phat is. we attempt to outline the range of model parameter space which leacs to realistic results.," That is, we attempt to outline the range of model parameter space which leads to realistic results."
 For example. our simulations have shown that. if thefraction of the merger progenitor spirals is ereater than 0.2. the resultant MDE has [ar too many metal-poor stars to agree with the observed AIDE.," For example, our simulations have shown that, if the of the merger progenitor spirals is greater than 0.2, the resultant MDF has far too many metal-poor stars to agree with the observed MDF."
 Equallv. if the initial discs mean metallicity in a merger is much larger than m/l} = 0.0. the peak value of the resultant AIDE is too metal-rich to be consistent with observations.," Equally, if the initial disc's mean metallicity in a merger is much larger than [m/H] = 0.0, the peak value of the resultant MDF is too metal-rich to be consistent with observations."
" We will not show the results of these obviously inconsistent. models here but. rather. we present the results of the more realistic models in which the mean disc metallicity mIJ, ) is equal to -0.15 and. 0.0. and in which the halo mass fraction is no more than 0.2."," We will not show the results of these obviously inconsistent models here but, rather, we present the results of the more realistic models in which the mean disc metallicity ${\rm [m/H]}_{\rm d}$ ) is equal to -0.15 and 0.0, and in which the halo mass fraction is no more than 0.2."
" Solow. we describe the results of LO mocels and in Table lsummarize their input parameters: model number (column 1). bulge mass fraction A, (column 2). metallicity eracicnt vpe (3). mean metallicity of disc in mM], (4). orbital tvpe of galaxy merging (5). halo mass fraction fi, (6). and initial ido mean metallicity mI], (7)."," Below, we describe the results of 10 models and in Table 1 summarize their input parameters: model number (column 1), bulge mass fraction $M_{\rm b}$ (column 2), metallicity gradient type (3), mean metallicity of disc in ${\rm [m/H]}_{\rm d}$ (4), orbital type of galaxy merging (5), halo mass fraction $f_{\rm h}$ (6), and initial halo mean metallicity ${\rm [m/H]}_{\rm h}$ (7)."
 For convenience we refer o the model MI as themodel., For convenience we refer to the model M1 as the.
 It shows typical xhavior of stellar halo formation in major merging and its AIDE. is reasonably consistent with the observations of the GC 5128 stellar halo., It shows typical behavior of stellar halo formation in major merging and its MDF is reasonably consistent with the observations of the NGC 5128 stellar halo.
 Accorcinely we describe mainly the results of this model in the following sections., Accordingly we describe mainly the results of this model in the following sections.
 “Phe MDEs of this model for each. component (disc. bulge. halo. and GCs) are summarized in Table 1.," The MDFs of this model for each component (disc, bulge, halo, and GCs) are summarized in Table 1."
" Phe metallicity gradient types 7OC"" and “CAS” in the third column represent the two choices for disc metallicity eracient: described: above.", The metallicity gradient types “OC” and “GAS” in the third column represent the two choices for disc metallicity gradient described above.
 Orbital twpe labels “PPT. “PRY and “RRO represent à nearly prograce-prograde orbital configuration. à prograce-retrograde one. and a nearly retrogracde-retrogracde one.," Orbital type labels “PP”, “PR” and “RR” represent a nearly prograde-prograde orbital configuration, a prograde-retrograde one, and a nearly retrograde-retrograde one."
 The structural properties of merger remnants are briellv summarized in Appendix A. Figs., The structural properties of merger remnants are briefly summarized in Appendix A. Figs.
 2 and 3 summarize the final mass distributions of the stellar components that are initially within discs. haloes. ancl bulges of the merger progenitor spirals for the fiducial major merger model ALL.," 2 and 3 summarize the final mass distributions of the stellar components that are initially within discs, haloes, and bulges of the merger progenitor spirals for the fiducial major merger model M1."
 Since the bulges initially have more compact configurations than the discs. only a small fraction of bulge stars are tidally stripped to form the inner stellar halo with 0.5 < / — 1.0 of the merger remnant. where 7? is the radius from the center ofthe developed elliptical galaxy in units of 24.," Since the bulges initially have more compact configurations than the discs, only a small fraction of bulge stars are tidally stripped to form the inner stellar halo with 0.5 $<$ $R$ $\le$ 1.0 of the merger remnant, where $R$ is the radius from the center of the developed elliptical galaxy in units of $R_d$."
 The stars in the discs. on the other hand. are very efficienti stripped owing to the strong tidal field of major merging (or bv angular momentum redistribution during merging) so that they end up in both the inner and outer halo (1.0 < 2 x 2.0) ofthe elliptical galaxy.," The stars in the discs, on the other hand, are very efficiently stripped owing to the strong tidal field of major merging (or by angular momentum redistribution during merging) so that they end up in both the inner and outer halo (1.0 $<$ $R$ $\le$ 2.0) of the elliptical galaxy."
" Although the initial stellar haloes of the spirals are also stripped. (or ""pulfec up’) elliciently to form the inner and the outer stellar haloes.discs: about of the elliptical halo comes from the initial disc stars at 1: « R (For comparison. the outer parts of the"," Although the initial stellar haloes of the spirals are also stripped (or `puffed up') efficiently to form the inner and the outer stellar haloes,; about of the elliptical halo comes from the initial disc stars at 1 $<$ $R$ (For comparison, the outer parts of the"
As birthplaces for the majority of stars (e.g. Lada Lada ¢(2003))) stellar clusters ean be considered the building blocks of galaxies.,As birthplaces for the majority of stars (e.g. Lada Lada \cite{2003ARA&A..41...57L}) ) stellar clusters can be considered the building blocks of galaxies.
 The vast majority of them only reaches ages of a few Myrs after which their member stars dissolve into the general field star population., The vast majority of them only reaches ages of a few Myrs after which their member stars dissolve into the general field star population.
 The disruption timescales are dependent e.g. on the local tidal gravitational field. (interaction. with nearby giant molecular clouds). the star formation efficiency in the cluster. the mass of the cluster and the efficiency. of the feedback. from the young stars in the cluster (jets. winds. supernova explosions).," The disruption timescales are dependent e.g. on the local tidal gravitational field (interaction with nearby giant molecular clouds), the star formation efficiency in the cluster, the mass of the cluster and the efficiency of the feedback from the young stars in the cluster (jets, winds, supernova explosions)."
 There is evidence that the disruption timescales are increasing with distance from the Galactic Center (e.g. Lamers Gieles (2006). Goodwin Bastian (2006).. Piskunov et al. (2007))).," There is evidence that the disruption timescales are increasing with distance from the Galactic Center (e.g. Lamers Gieles \cite{2006A&A...455L..17L}, Goodwin Bastian \cite{2006MNRAS.373..752G}, Piskunov et al. \cite{2007A&A...468..151P}) )."
 A number of clusters. however. survive this initial infant mortality phase and become open clusters. whieh then can reach ages of up to several Gyrs.," A number of clusters, however, survive this initial infant mortality phase and become open clusters, which then can reach ages of up to several Gyrs."
 These old stellar systems. including both. open and globular clusters. provide us with laboratory like conditions.," These old stellar systems, including both, open and globular clusters, provide us with laboratory like conditions."
 All stars within such a cluster can be considered as being situated at the same distance. having the same age and metallicity.," All stars within such a cluster can be considered as being situated at the same distance, having the same age and metallicity."
 Due to their age. they are usually not associated with giant molecular clouds. thus there is a constant reddening towards all cluster members.," Due to their age, they are usually not associated with giant molecular clouds, thus there is a constant reddening towards all cluster members."
 Hence. one can fit theoretical isochrones to the cluster diagram to determine the age. distance and reddening simultaneously. provided the metallicity is known.," Hence, one can fit theoretical isochrones to the cluster diagram to determine the age, distance and reddening simultaneously, provided the metallicity is known."
 As current catalogues of old open clusters are rather incomplete (e.g. Bonatto Bica (2007b))). our aim is to establish a large. well detined sample of such old stellar systems and to determine its properties in a homogeneous way.," As current catalogues of old open clusters are rather incomplete (e.g. Bonatto Bica \cite{2007A&A...473..445B}) ), our aim is to establish a large, well defined sample of such old stellar systems and to determine its properties in a homogeneous way."
 This will then be used to investigate the distribution of these old clusters in the Galaxy which will improve our understanding not just of the old stellar systems. but also on issues such as the interstellar extinction law. disruption timescales of clusters. and ultimately the chemical evolution and enrichment history of the Galactic Disk.," This will then be used to investigate the distribution of these old clusters in the Galaxy which will improve our understanding not just of the old stellar systems, but also on issues such as the interstellar extinction law, disruption timescales of clusters, and ultimately the chemical evolution and enrichment history of the Galactic Disk."
 To obtain a large sample «Xf old clusters and analyse its properties homogeneouslv. we utiise the 2 Micron All Sky Survey (2MASS. Skrutskie et al. (20060) )," To obtain a large sample of old clusters and analyse its properties homogeneously, we utilise the 2 Micron All Sky Survey (2MASS, Skrutskie et al. \cite{2006AJ....131.1163S}) )"
 point source catalogue and the star cluster candidate list provided by Froebrich et al. (2007a).., point source catalogue and the star cluster candidate list provided by Froebrich et al. \cite{2007MNRAS.374..399F}.
 We identify the old systems amongst fτοις catalogue by investigation of decontaminated colour-magnitude and colour-colour diagrams and determine their parameters by fiting theoretical isochrones from Girardi et al., We identify the old systems amongst their catalogue by investigation of decontaminated colour-magnitude and colour-colour diagrams and determine their parameters by fitting theoretical isochrones from Girardi et al.
 (2002) to the 2MASS photometry., \cite{2002A&A...391..195G} to the 2MASS photometry.
 Our paper is structured as follows., Our paper is structured as follows.
 In refdataanalysis we describe the selection of our cluster sample and the determination of its properties., In \\ref{dataanalysis} we describe the selection of our cluster sample and the determination of its properties.
 This includes the automatic decontamination of foreground stars in the cluster fields. the selection and identification of the old stellar systems and the determination of their ages. distances and reddening via isochrone tits.," This includes the automatic decontamination of foreground stars in the cluster fields, the selection and identification of the old stellar systems and the determination of their ages, distances and reddening via isochrone fits."
 In, In
"Since M is a much stronger function of a than of AM; it is dillicult for us to place tight constraints on the allowed range of M,",Since $\dot M$ is a much stronger function of $\alpha$ than of $M_{min}$ it is difficult for us to place tight constraints on the allowed range of $M_{min}$.
 lig., Fig.
" 13 shows that we can. however. place a constraint on the allowed up»r limit of Αν. since very high values of A4,,;, result mass loss rates >10.""M.vr.5L."," \ref{fig:param_space} shows that we can, however, place a constraint on the allowed upper limit of $M_{min}$ , since very high values of $M_{min}$ result mass loss rates $> 10^{-5}\mathrm{M_{\odot}yr^{-1}}$."
 Lor a1.25. we fit a 3rd. degree polynomial (the dashed line in Fig. 13))," For $\alpha > 1.25$, we fit a 3rd degree polynomial (the dashed line in Fig. \ref{fig:param_space}) )"
" to the Al=10""Above+ contour.", to the $\dot M = 10^{-5}\mathrm{M_{\odot} yr^{-1}}$ contour.
" This fit analytically expresses the upper limit of AZ,,;, as a function ofa.", This fit analytically expresses the upper limit of $M_{min}$ as a function of $\alpha$ .
 We provide the coellicients of this fit in the caption of lig. 13.., We provide the coefficients of this fit in the caption of Fig. \ref{fig:param_space}. .
 Vhe small cilference between the solid anc dashed lines at. ry (.06pc in Fig., The small difference between the solid and dashed lines at $r_{gal} = 0.06$ pc in Fig.
 δρ suggests that. even for stellar encounters involving small impact. parameters. our integration does not miss many collisions by ignoring eravitational focusing.," \ref{fig:diff_coll_rate}b b suggests that, even for stellar encounters involving small impact parameters, our integration does not miss many collisions by ignoring gravitational focusing."
 ‘To estimate the contribution to the total mass loss rate in Fie., To estimate the contribution to the total mass loss rate in Fig.
 13. [rom gravitational focusing. we take ο{ρω the typical amount. of mass [ost per collision. to be simply a function of b.," \ref{fig:param_space} from gravitational focusing, we take $\delta M_{typ}$, the typical amount of mass lost per collision, to be simply a function of $b$ ."
 This avoids the multi-dimensional integrations involved in equations (20 and 21)). since for these equations δρ is a function of b. Myr. Mya and ο," This avoids the multi-dimensional integrations involved in equations \ref{eq:mass_loss_indir} and \ref{eq:mass_loss_dir}) ), since for these equations $\Delta_{pd}$ is a function of $b$, $M_{pr}$ , $M_{pd}$, and $v_{rel}(r_{gal})$."
" For simplicity. we choose 0M,Cb) to decrease linearly from PAL. (we assume that both stars are completely destroved) at b=Oto Oat 6=by."," For simplicity, we choose $\delta M_{typ} (b)$ to decrease linearly from $_{\odot}$ (we assume that both stars are completely destroyed) at $b=0$ to 0 at$b=b_0$."
 We find by bv noting from Fig., We find $b_0$ by noting from Fig.
 1 thatfor all values of the polytropic index. the amount of mass loss for an indirect collision goes to zeroat around 5;=0.98.," \ref{fig:mass_loss} thatfor all values of the polytropic index, the amount of mass loss for an indirect collision goes to zeroat around $\gamma =0.98$."
" By recalling the definition of * (equation (6))). we solve for by at +=0.98 bv setting AM,= 1. and taking ear2e(rg44=0.06pc)."," By recalling the definition of $\gamma$ (equation \ref{eq:def_of_gamma}) )), we solve for $b_0$ at $\gamma =0.98$ by setting $\tilde M_{pr} =1$ , and taking $v_{rel} \sim 2\sigma(r_{gal}=0.06 \mathrm{pc})$."
" ὃν calculating dvfdb(«rgat) (lor Salpeter values) evaluated. at. O.06pe across a range of b. anc multiplying by 9A4,,,0(5). we are able to estimate dA/db."," By calculating $d\Gamma/db~( < r_{gal})$ (for Salpeter values) evaluated at 0.06pc across a range of $b$, and multiplying by $\delta M_{typ} (b)$, we are able to estimate $d \dot M /db$."
 We do this for dl/db(<μα) with and without &ravitational focusing. and integrate across b.," We do this for $d \Gamma/db~( < r_{gal})$ with and without gravitational focusing, and integrate across $b$."
 Subtracting the two numbers results in our estimate of the contribution to the total mass loss rate due to gravitational focusing: 2.3«LO M..., Subtracting the two numbers results in our estimate of the contribution to the total mass loss rate due to gravitational focusing: $2.3 \times 10^{-7}$ $_{\odot}$.
 This is about twice the mass loss rate [rom Fig., This is about twice the mass loss rate from Fig.
 13 evaluated at Salpeter values., \ref{fig:param_space} evaluated at Salpeter values.
 We perform the same calculation across the Ms; - 0 parameter space. and find that. gravitational focusing contributes a factor of at most 2.5 to the total mass loss rate.," We perform the same calculation across the $M_{min}$ - $\alpha$ parameter space, and find that gravitational focusing contributes a factor of at most $\sim 2.5$ to the total mass loss rate."
 An underestimate of a factor of 2.5 slightly alfects the region of parameter space that we are able to rule out. as shown by the line contours in Fig. 13..," An underestimate of a factor of 2.5 slightly affects the region of parameter space that we are able to rule out, as shown by the line contours in Fig. \ref{fig:param_space}."
" The contours are on a linear scale. starting at +10 ""M. "". and ending. at 2.5«10 M. vr in intervals of 1.5 Πλ..."," The contours are on a linear scale, starting at $4 \times 10^{-6}$ $_{\odot}$ $^{-1}$, and ending at $2.5 \times 10^{-5}$ $_{\odot}$ $^{-1}$, in intervals of $1.5 \times 10^{-6}$ $_{\odot}$ $^{-1}$."
 The 410 AL. 1 Conour (2.5 times less than the 10 contour) shows that the region of the parameter space that is rulecl out is Mis 14M. andaxpd., The $4 \times 10^{-6}$ $_{\odot}$ $^{-1}$ contour (2.5 times less than the $10^{-5}$ contour) shows that the region of the parameter space that is ruled out is $M_{min} \gtrsim 1.4$ $_{\odot}$ and $\alpha \lesssim 1.4$.
 As noted in 282.3. the amount of mass oss that we calculate for a single direct. collision sometimes over or under-precicts the amount of mass lost (as compared to the work of Freitag&Benz (2005))) by a factor o Sa Lew to at most a factor of about LO (see Figs.," As noted in \ref{sec:mass_loss_direct}, the amount of mass loss that we calculate for a single direct collision sometimes over or under-predicts the amount of mass lost (as compared to the work of \citet{freitag:2005}) ) by a factor of a few to at most a factor of about 10 (see Figs."
 5 and 6))., \ref{fig:comp_1} and \ref{fig:comp_2}) ).
" We find that our calculation of mass loss for direct. colisions shows nopreference over whether the amount of mass lost is over.or under-predicted when considering diferent combinations of Mj. Ab. 6,4 and b."," We find that our calculation of mass loss for direct collisions shows nopreference over whether the amount of mass lost is over,or under-predicted when considering different combinations of$\tilde M_1$ , $\tilde M_2$ , $\tilde v_{rel}$ and $\tilde b$ ."
 We therefore. suspec thatwhen integrating over all of these parameters to obtain the total amount of mass lost. our error will roughly cancel.," We therefore suspect thatwhen integrating over all of these parameters to obtain the total amount of mass lost, our error will roughly cancel."
 The line contours in Fig., The line contours in Fig.
 13. serve asagood gauge of how our constraints on the allowed region of the parameter change, \ref{fig:param_space} serve asagood gauge of how our constraints on the allowed region of the parameter change
The package DDIx. is designed to extract the fundamental parameters of llt stars from high-quality CBVGe: observations.,The package BBK is designed to extract the fundamental parameters of RR stars from high-quality $UBV(RI)_C$ observations.
 A brief description and some technical details are given here., A brief description and some technical details are given here.
 Lt is important to have the colours ancl colour indices as close as possible to the international colour svstem which was applied by Ixurucz(1907) in order to convert the physical fluxes of the ATLAS models to the stellar magnitude and colour svstem., It is important to have the colours and colour indices as close as possible to the international colour system which was applied by \citet{kuru1} in order to convert the physical fluxes of the ATLAS models to the stellar magnitude and colour system.
 An error (or errors) in the colour indices can lead to false results., An error (or errors) in the colour indices can lead to false results.
 To obtain reliable results. some ;N five colour observations are needed.," To obtain reliable results, some $N \ga 300$ five colour observations are needed."
 These must be distributed27300 uniformly. over a representative light curve because the physical quantities P. fy must be dilTerentiated.," These must be distributed uniformly over a representative light curve because the physical quantities $\vartheta$, $h_0$ must be differentiated."
 Proper use of the program package requires. basic knowledge of absolute stellar photometry. the theory. of stellar atmospheres and hydrodynamies.," Proper use of the program package requires basic knowledge of absolute stellar photometry, the theory of stellar atmospheres and hydrodynamics."
 As Ixurucz(1997) said: “Neither the programs nor cata are black boxes., As \citet{kuru1} said: 'Neither the programs nor data are black boxes.
 You should not be using them if vou do not have some understanding of the physics and. of the programming in the source codes, You should not be using them if you do not have some understanding of the physics and of the programming in the source code.'
 This warning is appropriate for 1119., This warning is appropriate for BBK.
 1911 consists of FORTRAN programs. z-shell scripts. input files. data files. and a manual (Bareza|2011).," BBK consists of FORTRAN programs, z-shell scripts, input files, data files, and a manual \citep{barc7}."
". UNIX or LINUX environment. installation of a FORTRAN compiler. z-shell. eraphical packages (c.g. SUPERALONGO., or GNUPLOT) are necessary."," UNIX or LINUX environment, installation of a FORTRAN compiler, z-shell, graphical packages (e.g. SUPERMONGO, or GNUPLOT) are necessary."
 Five steps are involved. a detailed. description of which can be found in the manual.," Five steps are involved, a detailed description of which can be found in the manual."
 Inspection. evaluation. plots of the partial results are necessary before continuing to the next step.," Inspection, evaluation, plots of the partial results are necessary before continuing to the next step."
 The atmospheric metallicity anc the interstellar reddening of the star are determined. from selected: phases when the atmosphere is free of shocks (i.e. from. colour indices in the descending branch)., The atmospheric metallicity and the interstellar reddening of the star are determined from selected phases when the atmosphere is free of shocks (i.e. from colour indices in the descending branch).
 The conversions are executed to select the static APLAS models with the best fit to the observed and theoretical colour indices to obtain logq. and T; as a function of phase., The conversions are executed to select the static ATLAS models with the best fit to the observed and theoretical colour indices to obtain $\log g_{\rm e}$ and $T_{\rm e}$ as a function of phase.
 The variation of His determined by comparing the physical lluxes of the star with those of the selected theoretical models., The variation of $\vartheta$ is determined by comparing the physical fluxes of the star with those of the selected theoretical models.
 The physical luxes V. He. V| bolometric correction are used. those of he star are calculated from the absolute calibration of Vega (Tie.White&Lockwood1977)..)," The physical fluxes $V$, $R_C$, $V+$ bolometric correction are used, those of the star are calculated from the absolute calibration of Vega \citep{tug1}. .)"
 Polynomial fits are calculated to obtain loggo. Lo. hy. angular velocity ancl acceleration. P.) as à function of ohase.," Polynomial fits are calculated to obtain $\log g_{\rm e}$, $T_{\rm e}$, $h_0$ , angular velocity and acceleration ${\dot\vartheta},{\ddot\vartheta}$ as a function of phase."
 The upper limit d;<duas=GAyds must. be fixed w inspecting P as a function of phase., The upper limit $d_j \le d_{\rm max}=g_{\rm e}{\ddot\vartheta}^{-1}_{\rm max}$ must be fixed by inspecting ${\ddot\vartheta}$ as a function of phase.
 The fits are introduced in the Euler equation of werodyvnamics to determine the angular acceleration. ane o find the acceleration-Eree. phases of the atmosphere., The fits are introduced in the Euler equation of hydrodynamics to determine the angular acceleration and to find the acceleration-free phases of the atmosphere.
 The ransient acceleration-free intervals in the ascending branch (i.c. in the shocked. phases) must be manually deleted. rom. he averaging to find Md B. B.," The transient acceleration-free intervals in the ascending branch (i.e. in the shocked phases) must be manually deleted from the averaging to find ${\cal M}_{\rm a}d^{-2}$. $\vartheta$,"
 B. bu. OhofOl. go and Mad.7 are introduced in Eqs.V) (4..5))," ${\dot \vartheta}$ , ${\ddot\vartheta}$, $h_0$, $\partial h_0/\partial t$ , $g_{\rm e}$ and ${\cal M}_{\rm a}d^{-2}$ are introduced in Eqs. \ref{4.100}, \ref{4.101}) )"
 and Ίσα. (4)) , and Eq. \ref{4.100}) )
is solved for d with the whole (or xwtial) set containing IN. (or «IN) phase points.,is solved for $d$ with the whole (or partial) set containing $N$ (or $<N$ ) phase points.
 The upper imit eΕνανnpperLimits must be specified to exelude the phase »oints [rom the final solution for di.e. from IN| to achieve aidMBNegecya.EPPSupperlimitiSSS qn: all phase points:givingeld.," The upper limit $a^{\rm (dyn, \; upper\; limit)}$ must be specified to exclude the phase points from the final solution for $d$[i.e. from $N^{\rm (II)}$ ] to achieve $\vert a^{\rm (dyn)}\vert < a^{(\rm dyn,\; upper\; limit)}$ in all phase pointsgiving$d$ ."
 One or two runs might be necessary with decreasing ;V., One or two runs might be necessary with decreasing $N$ .
 , 
reveals that the general agreement. between both sets of estimations is far [rom being good. the larger discrepancies reaching dillerences up to Q.2AL..,"reveals that the general agreement between both sets of estimations is far from being good, the larger discrepancies reaching differences up to $\sim 0.2 M_{\odot}$."
 However. the bulk of the points in Fig.," However, the bulk of the points in Fig."
 9 accumulate around the dotted. line. demonstrating that no appreciable olfset exists between the spectroscopic ancl asteroscismic estimations of the stellar mass.," \ref{massmass} accumulate around the dotted line, demonstrating that no appreciable offset exists between the spectroscopic and asteroseismic estimations of the stellar mass."
 The clistribution of stellar masses according to asteroseismologv and spectroscopy ds. depicted. in the histograms of the upper and lower panel of Fie. 10..," The distribution of stellar masses according to asteroseismology and spectroscopy is depicted in the histograms of the upper and lower panel of Fig. \ref{histo-mass},"
 respectively., respectively.
" The mean value of the asteroseismological mass is CAMsi.0.636+0.019... slightly larger 0.954) than the spectroscopic one. CALspe0.630+0Λ/ 029Τι, "," The mean value of the asteroseismological mass is $\langle M_*\rangle_{\rm seis}= 0.636\pm
0.019 M_{\odot}$, slightly larger $\sim 0.95 \%$ ) than the spectroscopic one, $\langle M_*\rangle_{\rm spec}= 0.630\pm 0.028
M_{\odot}$ ."
Given the very different methods emploved. to infer both values. the excellent. agreement between these AVOLALE pessos is encouraging.," Given the very different methods employed to infer both values, the excellent agreement between these average masses is encouraging."
 Castanheira Ixepler (2008. 2009) have performed the lirst. asteroseismological study. of an ensemble of ZZ Ceti stars.," Castanheira Kepler (2008, 2009) have performed the first asteroseismological study of an ensemble of ZZ Ceti stars."
 They have studied a total of 83 ZZ Ceti stars including the bright variables and also a subset of the SDSS variables., They have studied a total of 83 ZZ Ceti stars including the bright variables and also a subset of the SDSS variables.
 The average mass of the ZZ Ceti stars as derived by these authors is CAuu=0.668AM.. about 5% higher than our value. (AL.ας=0.6368...," The average mass of the ZZ Ceti stars as derived by these authors is $\langle M_*\rangle_{\rm seis}=
0.668 M_{\odot}$, about $5 \%$ higher than our value, $\langle
M_*\rangle_{\rm seis}= 0.636 M_{\odot}$."
" We note that Castanheira Kepler (2008. 2009) have included several Very massive ZZ Coti stavs (AL,z 1M.) that have not. been. considered in our study."," We note that Castanheira Kepler (2008, 2009) have included several very massive ZZ Ceti stars $M_* \gtrsim 1 M_{\odot}$ ) that have not been considered in our study."
 Given the fact that the numerical tools used in modeling the structure. evolution and pulsations of ZZ Ceti stars used by the two groups are independent. and. eiven that the samples of stars analysed. are not the same. we consider that the Ανα value derived in this work and," Given the fact that the numerical tools used in modeling the structure, evolution and pulsations of ZZ Ceti stars used by the two groups are independent, and given that the samples of stars analysed are not the same, we consider that the $\langle M_*\rangle_{\rm seis}$ value derived in this work and"
"ib was shown that the odd multipole preferences Uclily connected with (he anomalies of the two-point correlation function. in particular. the lack of correlations at 60""σοκ180"" (Schwarzοἱal.2004:Copiet2010).. and newly discovered anomaly of the correlations at 1""<@<30° (Nim&Naselsky2011)..","it was shown that the odd multipole preferences tidily connected with the anomalies of the two-point correlation function, in particular, the lack of correlations at $60^{\rm o}\le \Theta\le 180^{\rm o}$ \citep{schwarz1,copi1}, and newly discovered anomaly of the correlations at $1^{\rm o}\le \Theta\le 30^{\rm o}$ \citep{jk3}."
 In combination with the widely discussed. anomalies of (he CMD map aud (he power spectrum (Eriksenetal.2004) (see for review (Bennettetal. 2011))). investigation of the origin of these anomalies could put a new light on the physics of the early. Universe. the methods of the Doregrounds reductions and calibration of the CMD data sets. improving our knowledge of the most fundamental cosmological parameters and (he theory of inflation.," In combination with the widely discussed anomalies of the CMB map and the power spectrum \citep{eriksen1} (see for review \citep{wmap_anomly}) ), investigation of the origin of these anomalies could put a new light on the physics of the early Universe, the methods of the foregrounds reductions and calibration of the CMB data sets, improving our knowledge of the most fundamental cosmological parameters and the theory of inflation."
 The local motion of an observer through the CAIB frame produces (he so-called Kinematic Dipole (XD) anisotropy. of the CMD. which is the most powerful component of the signal and fitted out from the CMD cata before cosmological analysis.," The local motion of an observer through the CMB frame produces the so-called Kinematic Dipole (KD) anisotropy of the CMB, which is the most powerful component of the signal and fitted out from the CMB data before cosmological analysis."
 In (his paper. we are going to show that some of the discovered features of the Wilkinson Microwave Anisotropy Probe (WMADP) CAIB TT anisotropy. including the odd-parity preference of the power spectrum. could have common origin associated with the AD of the CMD.," In this paper, we are going to show that some of the discovered features of the Wilkinson Microwave Anisotropy Probe (WMAP) CMB TT anisotropy, including the odd-parity preference of the power spectrum, could have common origin associated with the KD of the CMB."
 Previously. the possible contamination of the CMD by KD has been assessed by multipole vector statistic (alignment of the quadrupole and octupole components) (Gordonetal.2005:Peiris&Smith.," Previously, the possible contamination of the CMB by KD has been assessed by multipole vector statistic (alignment of the quadrupole and octupole components) \citep{gordon,peiris}."
2010).. Additional. we will show that the low multipole anomalies are associated with other anomalies such as the lack of angular correlation. the even/odd-paritv asvinmnetry. and the planarity of the multipole /=5.," Additionally, we will show that the low multipole anomalies are associated with other anomalies such as the lack of angular correlation, the even/odd-parity asymmetry and the planarity of the multipole $l=5$."
 First. we will focus on |1 properties of the CAMB TT correlation function C(O)=AT(n)AT(n’) at angle O=arecos(n-n')Ai and show that C(Ox) is connected (o the paritv parameter g(/).," First, we will focus on the properties of the CMB TT correlation function $C(\Theta)=\Delta T(\hat{\mathbf n})\Delta T(\hat{\mathbf n'})$ at angle $\Theta=\arccos(\hat{\mathbf n}\cdot\hat{\mathbf n'} )=\pi$ and show that $C(\Theta=\pi)$ is connected to the parity parameter $g(l)$."
 We will estimate the power spectrum without the m=0 mode so that the rotational i1variance of (he angular power spectrum may not be automatically satisfied., We will estimate the power spectrum without the $m=0$ mode so that the rotational invariance of the angular power spectrum may not be automatically satisfied.
" As well know1. these me=0 modes pick up a cerlain direction (ie. the z-axis direction in the spherica coordinate svstem where (d, are defined (Gordonetal. 2005)))."," As well known, these $m=0$ modes pick up a certain direction (i.e. the $z$ -axis direction in the spherical coordinate system where $a_{lm}$ are defined \citep{gordon}) )."
 Using these estimators. we will investigate Cie possible prelerred direction in the CMD field.," Using these estimators, we will investigate the possible preferred direction in the CMB field."
 If our Universe is. indeed. statistically homogeneous and isotropic wilh Gaussian seed perturbations. we should have no or little paritv preference. eiven for our estimators associated with the angular power spectrum.," If our Universe is, indeed, statistically homogeneous and isotropic with Gaussian seed perturbations, we should have no or little parity preference, given for our estimators associated with the angular power spectrum."
 Using the WALAP 7-vr Internal Linear Combination (ILC) map. we compute the parity. parameters for coordinates ol various orientations.," Using the WMAP 7-yr Internal Linear Combination (ILC7) map, we compute the parity parameters for coordinates of various orientations."
 We find some level of alignment between the IND direction and the orientation. in which (he parity asvanmnietry is greatest.," We find some level of alignment between the KD direction and the orientation, in which the parity asymmetry is greatest."
 Therefore. the CAIB parity asymmetry mav be related to the svstematics associated with KD. which may be also responsible [ου the alignment problem of euadrupole and octupole elal. 2006)..," Therefore, the CMB parity asymmetry may be related to the systematics associated with KD, which may be also responsible for the alignment problem of quadrupole and octupole \citep{gordon,dt2}."
 The outline of the paper is (he following., The outline of the paper is the following.
 In Section 2 we introduce the basic characteristics of the CMB parity asvinnetry., In Section 2 we introduce the basic characteristics of the CMB parity asymmetry.
 In. Section 3.D we investigate (he orientations of maximum," In Section 3, we investigate the orientations of maximum"
Dust-cooling models predict a much lower critical metallicity (Zerit3107570).,Dust-cooling models predict a much lower critical metallicity $(\rm Z_{\rm crit} \approx 10^{-5} \rm Z_{\odot})$.
" The conditions for fragmentation in the low-metallicity dust cooling model are predicted to occur in high density gas, where the distances between the fragments can be very small (Omukai,2000;Omukaietal., 2010).."," The conditions for fragmentation in the low-metallicity dust cooling model are predicted to occur in high density gas, where the distances between the fragments can be very small \citep{2000ApJ...534..809O, 2005ApJ...626..627O, 2002ApJ...571...30S, 2006MNRAS.369.1437S, 2010MNRAS.402..429S}."
" In this regime, interactions between fragments will be common, and analytic models of fragmentation are unable to predict the mass distribution of the fragments."," In this regime, interactions between fragments will be common, and analytic models of fragmentation are unable to predict the mass distribution of the fragments."
" A full 3D treatment, following the fragments, is Initial attempts were made by Tsuribe&Omukai(2006,2008) and Clarketal.(2008).."," A full 3D treatment, following the fragments, is Initial attempts were made by \cite{2006ApJ...642L..61T,2008ApJ...676L..45T} and \cite{2008ApJ...672..757C}."
" However, these treatments used a tabulated equation of state, based on results from previous one-zone chemical models (Omukaietal., 2005),, to determine the thermal energy."," However, these treatments used a tabulated equation of state, based on results from previous one-zone chemical models \citep{2005ApJ...626..627O}, to determine the thermal energy."
 This approximation assumes that the temperature adjusts to a new equilibrium gastemperature whenever theinstantaneously density changes and hence ignores thermal inertia effects., This approximation assumes that the gas temperature adjusts instantaneously to a new equilibrium temperature whenever the density changes and hence ignores thermal inertia effects.
" This may yield too much In this work, we improve upon these previous treatments by solving the full thermal energy equation, and calculating the dust temperature through the energy equilibrium equation."," This may yield too much In this work, we improve upon these previous treatments by solving the full thermal energy equation, and calculating the dust temperature through the energy equilibrium equation."
" We assume currently that the only significant external heat source is the CMB, and include its effects in the calculation of the dust We model the collapse of a low-metallicity gas cloud using a modified version of the Gadget 2 (Springel,2005) smoothed hydrodynamics (SPH) code."," We assume currently that the only significant external heat source is the CMB, and include its effects in the calculation of the dust We model the collapse of a low-metallicity gas cloud using a modified version of the Gadget 2 \citep{2005MNRAS.364.1105S} smoothed particle hydrodynamics (SPH) code."
" To enable us to continue our particlesimulation beyond the formation of the first very high density protostellar core, we use a sink particle approach (Bateetal.,1995),, based on the implementation of Jappsenetal.(2005).."," To enable us to continue our simulation beyond the formation of the first very high density protostellar core, we use a sink particle approach \citep{1995MNRAS.277..362B}, based on the implementation of \cite{2005A&A...435..611J}."
" Sink particles are created once the SPH particles are bound, collapsing, and within an accretion radius, gcc, which is taken to be 1.0 AU."," Sink particles are created once the SPH particles are bound, collapsing, and within an accretion radius, $h_{acc}$, which is taken to be 1.0 AU."
 The threshold number density for sink particle creation is 5.0x10cm., The threshold number density for sink particle creation is $5.0 \times 10^{13} \rm cm^{-3}$.
" At the threshold density, the Jeans length at the minimum temperature reached by the gas is approximately one AU, while at higher densities the gas becomes optically thick and to heat "," At the threshold density, the Jeans length at the minimum temperature reached by the gas is approximately one AU, while at higher densities the gas becomes optically thick and begins to heat up."
Further on scales smaller than beginsthe sink particleup. scale is therefore fragmentationunlikely to occur., Further fragmentation on scales smaller than the sink particle scale is therefore unlikely to occur.
 For further discussion see Clarketal.(2011).., For further discussion see \cite{2011ApJ...727..110C}.
" To treat the and thermal balance of the gas, we use the same chemistryapproach as in Clarketal.(2011), with two additions: the inclusion of the effects of dust cooling, as described below, and formation of H2 on the surface of dust grains (seeHollenbach&McKee,1979).."," To treat the chemistry and thermal balance of the gas, we use the same approach as in \citet{2011ApJ...727..110C}, with two additions: the inclusion of the effects of dust cooling, as described below, and formation of H2 on the surface of dust grains \cite[see][]{1979ApJS...41..555H}."
" The Clarketal.(2011) chemical network and cooling function were designed for treating primordial gas and do not include the chemistry of metals such as carbon or oxygen, or the effects of cooling from these atoms, or molecules containing them such as CO or H?O. We justify this approximation by noting that previous studies of very low-metallicity gas (e.g.Omukaietal.,2005,2010) find that metals have little influence on the thermal state of the gas."," The \citet{2011ApJ...727..110C} chemical network and cooling function were designed for treating primordial gas and do not include the chemistry of metals such as carbon or oxygen, or the effects of cooling from these atoms, or molecules containing them such as CO or $_{2}$ O. We justify this approximation by noting that previous studies of very low-metallicity gas \citep[e.g.][]{2005ApJ...626..627O, 2010ApJ...722.1793O} find that gas-phase metals have little influence on the thermal state of the gas."
 gas-phaseOmukaietal.(2010) showed that H2O and OH are efficient coolants at 10°«n<10'°cm™? for their one-zone model., \cite{2010ApJ...722.1793O} showed that H2O and OH are efficient coolants at $10^8 < n < 10^{10} \rm cm^{-3}$ for their one-zone model.
" In their hydrodynamical calculations, however, the collapse is faster, and the effect of H20 and OH is not perceptible."," In their hydrodynamical calculations, however, the collapse is faster, and the effect of H2O and OH is not perceptible."
 Therefore we do not expect oxygen-bearing molecules to have a big effect on the thermal evolution of the gas., Therefore we do not expect oxygen-bearing molecules to have a big effect on the thermal evolution of the gas.
" For the metallicities and dust-to-gas ratios considered in this study, the dominant sources of cooling are the standard primordial coolants (Hz bound-bound emission and collision-induced emission) and energy transfer from the gas to the dust."," For the metallicities and dust-to-gas ratios considered in this study, the dominant sources of cooling are the standard primordial coolants $_{2}$ bound-bound emission and collision-induced emission) and energy transfer from the gas to the dust."
" Collisions between gas particles and dust grains can transfer energy from the gas to the dust (if the gas temperature T is greater than the dust temperature or from the dust to the gas (if T,,> T)."," Collisions between gas particles and dust grains can transfer energy from the gas to the dust (if the gas temperature $T$ is greater than the dust temperature $T_{\rm gr}$ ), or from the dust to the gas (if $T_{\rm gr} > T$ )."
" The rate at which T,,),energy is transferred from gas to dust is given by (Hollenbach&McKee,1979) "," The rate at which energy is transferred from gas to dust is given by \citep{1979ApJS...41..555H}
 "
"bj power spectrum obtained as a solution to equation (18) for cach spectral channel aud AL=100 ο) power spectruun averaged in time. using £=50 sample spectra from d) power spectrum average Lin time. usineο £=50 sample spectra from b). Ίνοι, with REI mitigation.","b) power spectrum obtained as a solution to equation (18) for each spectral channel and $M=100$ c) power spectrum averaged in time, using $L=50$ sample spectra from d) power spectrum averaged in time, using $L=50$ sample spectra from b), i.e., with RFI mitigation."
[ο] Results of computcr simulations of exponential weighting with the algoritlan shown in Fie., Results of computer simulations of exponential weighting with the algorithm shown in Fig.
 spectra of interference over!ap with spectral lines., spectra of interference overlap with spectral lines.
 Other paraincters are similar to Fig., Other parameters are similar to Fig.
" a) time-frequency presentation of the power spectrum consisting of svsteni noise. enission aud absorption lines and REI: b) power specruni obtained as a solution to equation (18) for each spectral chanuel aud AL=100 C) power spectrin average in finie. using £=50 sample spectra from d) power spectrin average’ in time. using £=50 sample spectra from b). 1,6. with REI mitigation."," a) time-frequency presentation of the power spectrum consisting of system noise, emission and absorption lines and RFI; b) power spectrum obtained as a solution to equation (18) for each spectral channel and $M=100$ c) power spectrum averaged in time, using $L=50$ sample spectra from d) power spectrum averaged in time, using $L=50$ sample spectra from b), i.e., with RFI mitigation."
 Both spectral lines are clearly visible., Both spectral lines are clearly visible.
 Results of compter simulations of exponential weighting with the algorithua shown in Fie., Results of computer simulations of exponential weighting with the algorithm shown in Fig.
" 1 when ""ditv and ""elean signals are applied to the correlator: L-50 time sections of the spectrum divided on 256 spectral channels. cach spectrum is the mean of AF=100 instantaneous spectra: the spectra at the first input of the correlator arc| shown. the spectra at the second input are similar to a) aud a) time-frequency prescutation of power spectrum consisting of system noise. and RFI bj power spectrum after RFI initigation - expoucutial weighting of cach iustautaneous spectrum using variances obtained as a soluticπι to equation (18) for cach spectral channel and AL=100 ο) cross-correlation in the presence of REI aud no RFT mitigation. the ceutral 200 channels are d) cross-correlation in the ]xeseuce of RFT and with REI nütisation: take notice of the ciffereucc of the vertical scales iu ο) aud d)."," 4 when “dirty” and “clean” signals are applied to the correlator; L=50 time sections of the spectrum divided on 256 spectral channels, each spectrum is the mean of $M=100$ instantaneous spectra; the spectra at the first input of the correlator are shown, the spectra at the second input are similar to a) and a) time-frequency presentation of power spectrum consisting of system noise, and RFI (frequency-modulated b) power spectrum after RFI mitigation - exponential weighting of each instantaneous spectrum using variances obtained as a solution to equation (18) for each spectral channel and $M=100$ c) cross-correlation in the presence of RFI and no RFI mitigation, the central 200 channels are d) cross-correlation in the presence of RFI and with RFI mitigation; take notice of the difference of the vertical scales in c) and d)."
8. Examples of RET 1uitigation at the Effelsbere radio telescope during observations iu continui at central frequency 1615 MITz. bandwidth ΟΛΠ.," Examples of RFI mitigation at the Effelsberg radio telescope during observations in continuum at central frequency 1645 MHz, bandwidth 20MHz."
 A selection of cight scans of the source EEIS|762 is represcuted., A selection of eight scans of the source 1448+762 is represented.
 Pairwise records were mace simmltaucouslv for the chanuel with REI mitigation aud the chauncl without RFT nütisation., Pairwise records were made simultaneously for the channel with RFI mitigation and the channel without RFI mitigation.
9. Radio image oftre source LiLs|762 built usiug scaus similar to those in Fie., Radio image of the source 1448+762 built using scans similar to those in Fig.
 2: left panel - without REI nütisation. right panel - with RFI mitigation.," 2: left panel - without RFI mitigation, right panel - with RFI mitigation."
10. Puls D0329|51.07 observed at WSRT at 1625MIIz., Pulsar B0329+54.07 observed at WSRT at 1625MHz.
 Data were recorded during 10 sec. LO Msanples/sec.," Data were recorded during 10 sec, 40 Msamples/sec."
 Upper row. let panel: TPD ouputs for two polarizations. raw data with RFI. right pancl: TPD output. REI removed.," Upper row, left panel: TPD ouputs for two polarizations, raw data with RFI, right panel: TPD output, RFI removed."
 MNiddle row. left paucl: time fraement of the ruuuius power spectrum with RET: the same time fragment. RFI removed.," Middle row, left panel: time fragment of the running power spectrum with RFI; the same time fragment, RFI removed."
 Lower row. Left pauecl: pulsar profile made with raw data over 10 sec. middle panel: pulsar profile. REI removed. right panel: pulsar profile observed at 1120 MITz. no RET.," Lower row, Left panel: pulsar profile made with raw data over 10 sec, middle panel: pulsar profile, RFI removed, right panel: pulsar profile observed at 1420 MHz, no RFI."
11. Radio images of he source DÀ210 observed at WSRT. ceutral frequeucy. 357 MIIZ. bandwidth 20 MIIz.," Radio images of the source DA240 observed at WSRT, central frequency 357 MHz, bandwidth 20 MHz."
 Upper row. left pane :dnage without RFT mitigation: right paucl: nage with REI mitigation.," Upper row, left panel: image without RFI mitigation; right panel: image with RFI mitigation."
 Lower row: central parts of the images with and without RFT., Lower row: central parts of the images with and without RFI.
Αννας with masses 70.3 MM. (ος.72)...,M-dwarfs with masses $> 0.3$ $_\odot$ \citep[e.g.][]{Lada06}.
 However. these assumptions at least allow us to discuss the pertinent points.," However, these assumptions at least allow us to discuss the pertinent points."
 We can divide binaries into four broad categories based on their separations., We can divide binaries into four broad categories based on their separations.
 Dinaries with separations «50 AU are Cabwayvs Bard no density of cluster significantly changes the separation clistribution in this range., Binaries with separations $< 50$ AU are `always hard' – no density of cluster significantly changes the separation distribution in this range.
 Binaries with separations of 50° 1000 AU are ‘sometimes hard vigh-cdensity clusters can destroy. some of this population. out. low densitv clusters and. isolated: regions cannot.," Binaries with separations of $50$ – $1000$ AU are `sometimes hard' – high-density clusters can destroy some of this population, but low density clusters and isolated regions cannot."
" Binaries with separations in the range 10/— 107 AU are ""soft-intermecddates? hish density. clusters clestrov such unaries. and low-clensity clusters clestrov some."," Binaries with separations in the range $10^3$ – $10^4$ AU are `soft-intermediates' – high density clusters destroy such binaries, and low-density clusters destroy some."
" Dinaries with separations 10 AU are ""always soft any cluster will destroy. such binaries (i£ they could even form in the irst place).", Binaries with separations $>10^4$ AU are `always soft' – any cluster will destroy such binaries (if they could even form in the first place).
" e Roughly 50 per cent of binaries are ""always hard.", $\bullet$ Roughly 50 per cent of binaries are `always hard'.
 Such systems cannot be destroved by all but the most. extreme cluster densities and so the field population must represent the sum of binaries formed in IDC. LDC anc [SE star formation.," Such systems cannot be destroyed by all but the most extreme cluster densities and so the field population must represent the sum of binaries formed in HDC, LDC and ISF star formation."
 Thus. the binary fraction and. separation distribution below 50 AU must be a fundamental outcome of the star formation process.," Thus, the binary fraction and separation distribution below $50$ AU must be a fundamental outcome of the star formation process."
 Phat is. a combination of IIDC'.. LDC and IS must produce around 30 per cent of and 15 20 per cent of Mechwarls with a companion «50 AU and the combined separation distribution in this range must match the field.," That is, a combination of HDC, LDC and ISF must produce around 30 per cent of and 15 – 20 per cent of M-dwarfs with a companion $< 50$ AU and the combined separation distribution in this range must match the field."
" e Around. 10 15 per cent of binaries in the Ποιά are ""sometimes hard.", $\bullet$ Around 10 – 15 per cent of binaries in the field are `sometimes hard'.
 Therefore star formation would. be expected to slightly over-produce such systems as many. in LDCs will be destroved. but those in LDCs and ISP would be unallected.," Therefore star formation would be expected to slightly over-produce such systems as many in HDCs will be destroyed, but those in LDCs and ISF would be unaffected."
 The over-production in this range need not be extreme as they survive in around GO per cent of star forming regions (LDC's and Li). but up to 50 per cent of those that form may be destroved in LIDCs.," The over-production in this range need not be extreme as they survive in around 60 per cent of star forming regions (LDCs and ISF), but up to 50 per cent of those that form may be destroyed in HDCs."
 Thus. all modes of star. formation. combined must produce about LO per cent of Geedwarls and 5 per cent of Al-cdwarls with a companion between 50 and. 1000 AU.," Thus, all modes of star formation combined must produce about 10 per cent of G-dwarfs and 5 per cent of M-dwarfs with a companion between $50$ and $1000$ AU."
" e A similar fraction of 10. 15 per cent of binaries are ""soft-intermediate'.", $\bullet$ A similar fraction of 10 – 15 per cent of binaries are `soft-intermediate'.
 Those produced in LDC's will be almost all destroyed. many will in LDCs. but. those in IS will remain.," Those produced in HDCs will be almost all destroyed, many will in LDCs, but those in ISF will remain."
 Following the above arguments. 40 per cent of star formation (LIDC's) cannot produce soft-intermediates. in +0 per cent of star formation half of those that form may be destroved (in LDC's). and in 20 per cent (LSE) all survive.," Following the above arguments, 40 per cent of star formation (HDCs) cannot produce soft-intermediates, in 40 per cent of star formation half of those that form may be destroyed (in LDCs), and in 20 per cent (ISF) all survive."
 Thus. all modes. of star formation combined: must produce LO per cent of Gechwarls and 5 per cent of Al-elwarls with a companion between 107 and. 101 AU.," Thus, all modes of star formation combined must produce 10 per cent of G-dwarfs and 5 per cent of M-dwarfs with a companion between $10^3$ and $10^4$ AU."
 Although the fraction formed could be significantly larger., Although the fraction formed could be significantly larger.
 e That leaves around. 20 per cent of binaries that are ‘always soft and cannot survive (or even be formed) in any cluster., $\bullet$ That leaves around 20 per cent of binaries that are `always soft' and cannot survive (or even be formed) in any cluster.
 At first. inspection. it appears that such binaries must all form inE.," At first inspection, it appears that such binaries must all form in."
 If these binaries are produced by the EISE mode. 20 per cent of star formation must. produce 20 per cent of the total number of binaries.," If these binaries are produced by the ISF mode, 20 per cent of star formation must produce 20 per cent of the total number of binaries."
 This implies that almost. all isolated star formation must produce a binary with a separation >lot AU., This implies that almost all isolated star formation must produce a binary with a separation $>10^4$ AU.
 Llowever. it is dillicult to see how even isolated. star ormation can produce binaries with separations >10 AU.," However, it is difficult to see how even isolated star formation can produce binaries with separations $>10^4$ AU."
 Isolated star forming cores only have radii of ~0.1 pe out to he point at which they merge with the background (e.g.?.anclreferencestherein) and so even a companion forming at he very limit of the core from the primary would only have a2. 10! AU separation (and surely disc fragmentation could not work at such distances)., Isolated star forming cores only have radii of $\sim 0.1$ pc out to the point at which they merge with the background \citep[e.g.][and references therein]{Ward-Thompson07} and so even a companion forming at the very limit of the core from the primary would only have a $2 \times 10^4$ AU separation (and surely disc fragmentation could not work at such distances).
 Thus the origin of binaries a ew sLO? AU is a mystery., Thus the origin of binaries $>$ a few $\times 10^3$ AU is a mystery.
 Clearly. the initial binary separation distribution cannot be identical to the field.," Clearly, the initial binary separation distribution cannot be identical to the field."
 Hlowever. the form and universality. (or otherwise) of the initial binary separation distribution. remains unclear.," However, the form and universality (or otherwise) of the initial binary separation distribution remains unclear."
 Note that there are two possible ‘initial’ binary separation distributions. (BSDs)., Note that there are two possible `initial' binary separation distributions (BSDs).
" Firstly. the ""primordial BSD produced. as the immediate outcome of star formation. Le. the clistribution that emerges from Class 0/1 sources."," Firstly, the `primordial' BSD produced as the immediate outcome of star formation, i.e. the distribution that emerges from Class 0/I sources."
 Secondly. the ‘initial’ DSD that evolves rapidly from. the. primordial. BSD cue to circularisation and interactions with disces.," Secondly, the `initial' BSD that evolves rapidly from the primordial BSD due to circularisation and interactions with discs."
 I is the evolution from primordial to initial BSDs that cigenevolution (?) altenipts to capture., It is the evolution from primordial to initial BSDs that eigenevolution \citep{Kroupa95b} attempts to capture.
 77 described a potential initial BSD in which the closer binaries (<50 AU) have a field-like clistribution. ancl wider binaries over-producecl by a factor of ~2 out to 105 AU.," \citet{Kroupa95a,Kroupa95b} described a potential initial BSD in which the closer binaries $< 50$ AU) have a field-like distribution, and wider binaries over-produced by a factor of $\sim 2$ out to $10^4$ AU."
 Llowever. as we have seen. the formation of binaries as wide as 103 AU is problematic at best in LDCs and all will be destroved in LDCs.," However, as we have seen, the formation of binaries as wide as $10^4$ AU is problematic at best in HDCs and all will be destroyed in HDCs."
 We will return to the problem of the form of the initial BSD and whether it is universal in a future paper., We will return to the problem of the form of the initial BSD and whether it is universal in a future paper.
 We use UIN bods simulations to dynamically evolve. star clusters rich. inbinary systems to examine the ellect of dynamical interactions on the initial binary population., We use $N$ –body simulations to dynamically evolve star clusters rich inbinary systems to examine the effect of dynamical interactions on the initial binary population.
 Our main conclusions are:, Our main conclusions are:
values was nunimizecd.,values was minimized.
 We found the best agreement when f is 0.95. at least [or the current sample of metal-poor giants.," We found the best agreement when $f$ is 0.95, at least for the current sample of metal-poor giants."
" For the seven stars wilh Visco<8.5|. the mean olfset is 0.00.4ἐν, with o=0.9I."," For the seven stars with $V_{\rm broad,CfA} < 8.5$, the mean offset is $0.0 \pm 0.4$, with $\sigma = 0.9$."
 For the eight stars with Viae28.5 HF. the mean offset is 0.0+0.5 witha —L4!|.. and for all fifteen stars. (he mean offset is 0.00.3αν στ1," For the eight stars with $V_{\rm broad,CfA} \geq\ 8.5$ , the mean offset is $0.0 \pm 0.5$, with $\sigma = 1.4$, and for all fifteen stars, the mean offset is $0.0 \pm 0.3$, $\sigma = 1.1$."
 The top panel of Figure 9. compares the results from Behr (2003) and our CFIIT program with Chose of this paper and. C2003., The top panel of Figure \ref{fig9} compares the results from Behr (2003) and our CFHT program with those of this paper and C2003.
 For the CFIIT sample. we have eliminated the five variable stars since the temperatures and. eravities derived from photometry mav be less reliable.," For the CFHT sample, we have eliminated the five variable stars since the temperatures and gravities derived from photometry may be less reliable."
 For (μου stars. HD. 25532. IID 184266. and HD 195636. line broadening was determined by both Behr (2003) and from our CFIIT data. and we have drawn lines connecting the two sets of results.," For three stars, HD 25532, HD 184266, and HD 195636, line broadening was determined by both Behr (2003) and from our CFHT data, and we have drawn lines connecting the two sets of results."
 Agreement is excellent. even well below our instrumental resolution of 8.5|.," Agreement is excellent, even well below our instrumental resolution of 8.5."
".. Another recent study. is that of de Mecdeiros et ((2006). who measured V4, sin / (ie. Visa) values at a typical resolving power of 50.000 (6.0 !)). S/N zz.80. and wavelength coverage spanning AA3500-9200."," Another recent study is that of de Medeiros et (2006), who measured $V_{\rm rot}$ sin $i$ (i.e., $V_{\rm broad}$ ) values at a typical resolving power of 50,000 (6.0 ), S/N $\approx\ 80$, and wavelength coverage spanning $\lambda\lambda$ 3500-9200."
 Their work had 22 stars in common with C2003. and with the results [rom the present paper. Chere are 35 stus in common.," Their work had 22 stars in common with C2003, and with the results from the present paper, there are 35 stars in common."
" The range in ""rotational velocities” is more limited. despite the larger sample size."," The range in “rotational velocities"" is more limited, despite the larger sample size."
" For only three of the stars in common have we obtained a Vi,44 value larger than our resolving power. and the largest of those is only 11.7I|."," For only three of the stars in common have we obtained a $V_{\rm broad}$ value larger than our resolving power, and the largest of those is only 11.7."
.. The simplest comparison is then just that [rom matches., The simplest comparison is then just that from star-to-star matches.
 The average difference. in the sense of our values minus those obtained by de Medeiros et ((2006) is 20.4 Fl. with oo—2.7|.," The average difference, in the sense of our values minus those obtained by de Medeiros et (2006) is $-0.4$ , with $\sigma = 2.7$."
" If we compare only the 21 stars for which we estimate μμ <6L|. the mean difference is —1.8Ἐν, with c —25kms'.."," If we compare only the 21 stars for which we estimate $V_{\rm broad}$ $\leq\ 6$, the mean difference is $-1.8$, with $\sigma$ = 2.5."
 The bottom panel of Figure 9. shows the comparison graphically.," The bottom panel of Figure \ref{fig9}
 shows the comparison graphically."
 As the «quantitative comparisons found. (the scatter appears to be larger in the bottom panel (han in the top panel. although most of these comparisons are for stars whose line broadening values are comparable to or smaller than either our instrumental resolution or that of de Meceiros et ((2006).," As the quantitative comparisons found, the scatter appears to be larger in the bottom panel than in the top panel, although most of these comparisons are for stars whose line broadening values are comparable to or smaller than either our instrumental resolution or that of de Medeiros et (2006)."
 We note that de Mecdeiros et ((2006) compared their results with those of Behr (200:WN)., We note that de Medeiros et (2006) compared their results with those of Behr (2003).
 Taking straight differences. we find a mean difference. in the sense of de Meceiros οἱ ((2006) minus Behr (2003). of 40.441.0Fl. wilho—2.8+. for the eight stars common (ο both programs.," Taking straight differences, we find a mean difference, in the sense of de Medeiros et (2006) minus Behr (2003), of $+0.4 \pm 1.0$, with $\sigma = 2.8$, for the eight stars common to both programs."
 The scatter somewhat larger than the value of 1.4 (that de Medeiros et (quoted for comparisons of all the stars common to C2003. Behr (2003). and Peterson (1933).," The scatter somewhat larger than the value of 1.4 that de Medeiros et quoted for comparisons of all the stars common to C2003, Behr (2003), and Peterson (1983)."
 We conclude that our results are in good agreement with all of (he above other studies. alihough perhaps somewhat better with Behr (2003) than with de Medeiros et ((2006).," We conclude that our results are in good agreement with all of the above other studies, although perhaps somewhat better with Behr (2003) than with de Medeiros et (2006)."
 Considering (hat ourspectra have much lower resolution. much lower S/N. and much smaller wavelength coverage. thepower of synthetic spectrum templates is apparent.," Considering that ourspectra have much lower resolution, much lower S/N, and much smaller wavelength coverage, thepower of synthetic spectrum templates is apparent."
Calculations similar to ours have appeared several times over the past four decades.,Calculations similar to ours have appeared several times over the past four decades.
" The most recent are ?,, ?,, and ?.."," The most recent are \citet{shull85}, , \citet{xu91}, , and \citet{valdes08}."
" ?used the degradation equation (?), a fully analytic technique, to compute the energy deposition fractions."," \citet{xu91} used the degradation equation \citep{spencer54}, a fully analytic technique, to compute the energy deposition fractions."
" They took the approximate (but fullyanalytic) ionization and excitation cross-sections from?,, and explicitly included all excitations with 10, although only for a pure hydrogengas."," They took the approximate (but fullyanalytic) ionization and excitation cross-sections from\citet{johnson72}, and explicitly included all excitations with $n \le 10$ , although only for a pure hydrogengas."
" We have generated a similar set of scenarios to ? for comparison purposes, in which we include only hydrogen target atoms, use their Coulomb logarithm, and extrapolate the excitation cross-sections to only n<10 levels."," We have generated a similar set of scenarios to \citet{xu91} for comparison purposes, in which we include only hydrogen target atoms, use their Coulomb logarithm, and extrapolate the excitation cross-sections to only $n \le 10$ levels."
" Over the range x; 10~*-0.9, we find generally good agreement between the two sets of results at E.=2keV (where ? report detailed deposition fractions)."," Over the range $x_i=10^{-4}$ $0.9$, we find generally good agreement between the two sets of results at $E=2 \keV$ (where \citealt{xu91} report detailed deposition fractions)."
" The deviations in the energy deposition fractions are always smaller than a few percent (in absolute terms), with our feat typically slightly larger and our other fractions slightly smaller; the differences are largest at large ionized fractions."," The deviations in the energy deposition fractions are always smaller than a few percent (in absolute terms), with our $f_{\rm heat}$ typically slightly larger and our other fractions slightly smaller; the differences are largest at large ionized fractions."
 We note that ? also found slightly larger heating fractions than ?.., We note that \citet{dalgarno99} also found slightly larger heating fractions than \citet{xu91}.
" At x;«0.01, all of our results agree to within 1% (again in absolute terms)."," At $x_i < 0.01$, all of our results agree to within $1\%$ (again in absolute terms)."
" Given that we use completely different methods and cross-sections, we regard this agreement as excellent."," Given that we use completely different methods and cross-sections, we regard this agreement as excellent."
" There is also good qualitative agreement in the shapes of our energy deposition curves, and especially in the features from excitation and ionization that appear at small αι."," There is also good qualitative agreement in the shapes of our energy deposition curves, and especially in the features from excitation and ionization that appear at small $x_i$."
" In contrast, ? used a Monte Carlo method very similar to ours, although we have added several interactions (namely excitation to higher levels) and updated the cross-sections for most of the others (including the Coulomb logarithm in the heating component)."," In contrast, \citet{shull85} used a Monte Carlo method very similar to ours, although we have added several interactions (namely excitation to higher levels) and updated the cross-sections for most of the others (including the Coulomb logarithm in the heating component)."
" Despite these differences, our results agree to similar (few percent) accuracy in the high-energy limit (or specifically at 3 keV, where ? provide detailed results)."," Despite these differences, our results agree to similar (few percent) accuracy in the high-energy limit (or specifically at 3 keV, where \citealt{shull85} provide detailed results)."
" Figure 4 provides a detailed comparison as a function of x;; the solid and dashed curves show our results and those from ?,, As one might expect given their lack of data for excitations to high n states, ? somewhat underestimate the importance of collisional excitation, which can cause a discrepancy of up to ~6% with respect to our results at small neutral fractions."," Figure \ref{fig:high-energy} provides a detailed comparison as a function of $x_i$; the solid and dashed curves show our results and those from \citet{shull85}, As one might expect given their lack of data for excitations to high $n$ states, \citet{shull85} somewhat underestimate the importance of collisional excitation, which can cause a discrepancy of up to $\sim 6\%$ with respect to our results at small neutral fractions."
" They overestimate fion by a similar amount compared to our calculations, but feat agrees rather well (although our results clearly have more curvature than theirs)."," They overestimate $f_{\rm ion}$ by a similar amount compared to our calculations, but $f_{\rm heat}$ agrees rather well (although our results clearly have more curvature than theirs)."
" Overall, we regard this agreement as quite good."," Overall, we regard this agreement as quite good."
" ? also used a Monte Carlo model to examine the energydeposition fractions for high-energy electrons, with E>3keV."," \citet{valdes08} also used a Monte Carlo model to examine the energydeposition fractions for high-energy electrons, with $E>3 \keV$."
" They included most of the same processes we have, albeit with different cross-sections in most cases."," They included most of the same processes we have, albeit with different cross-sections in most cases."
" The most significant difference is their treatment of collisional excitation; they took values from ?,, who computed their cross-sections with the scaled plane-wave Born approximation."," The most significant difference is their treatment of collisional excitation; they took values from \citet{stone02}, who computed their cross-sections with the scaled plane-wave Born approximation."
 ? show explicit comparisons with the CCC database; the CCC values differ by < 20%., \citet{stone02} show explicit comparisons with the CCC database; the CCC values differ by $\la 20\%$ .
" However, most significantly ? only compute excitation cross-sections to the np angular momentum sublevels."," However, most significantly \citet{stone02} only compute excitation cross-sections to the $np$ angular momentum sublevels."
" Although these transitions are typically dominant, the others are certainly non-negligible."," Although these transitions are typically dominant, the others are certainly non-negligible."
 ? present detailed results for the high-energy limit and offer alternate fitting functions to those from ?;; Figure 4 also includes a comparison to their results (dotted curves)., \citet{valdes08} present detailed results for the high-energy limit and offer alternate fitting functions to those from \citet{shull85}; Figure \ref{fig:high-energy} also includes a comparison to their results (dotted curves).
 The agreement with ours is not nearly as good as for ?.., The agreement with ours is not nearly as good as for \citet{shull85}.
 They find a much lower rate of heating at moderate and large ionized fractions (by up to ~20% at x;~ 0.01) and correspondingly larger rates of excitation and (especially) ionization., They find a much lower rate of heating at moderate and large ionized fractions (by up to $\sim 20\%$ at $x_i \sim 0.01$ ) and correspondingly larger rates of excitation and (especially) ionization.
 The agreement isparticularly poor at x;€1 (although the practicalimportance of this regime is fairly small)., The agreement isparticularly poor at $x_i \la 1$ (although the practicalimportance of this regime is fairly small).
" The source of this discrepancy is unclear; our excitation cross-sections match closely in the high-energy limit (?),, and our ionization cross-sections are in good agreement over the entire energy range (e.g., comparing the CCC database to ?))."," The source of this discrepancy is unclear; our excitation cross-sections match closely in the high-energy limit \citep{stone02},, and our ionization cross-sections are in good agreement over the entire energy range (e.g., comparing the CCC database to \citealt{kim94}) )."
 Another difference between our results and ? is in the fraction of excitation energy deposited as photons., Another difference between our results and \citet{valdes08} is in the fraction of excitation energy deposited as photons.
" As shown in Figure 3,, we find fiya/fexcite20.8 throughout the entire energy range."," As shown in Figure \ref{fig:excite-lya}, , we find $f_{\rm Ly\alpha}/f_{\rm excite} \approx 0.8$ throughout the entire energy range."
" In contrast, ? find fiya/fexcite 0.7."," In contrast, \citet{valdes08} find $f_{\rm Ly\alpha}/f_{\rm excite} \approx 0.7$ ."
" This discrepancy probably results from their inclusion only of excitations to the np sublevels; the mixing fractions for the (rarer) excitations to the other sublevels can be larger, especially at n=3 (where atoms in the 3p state cannot decay throughLya,, but those in the 3s or 3d states must)."," This discrepancy probably results from their inclusion only of excitations to the $np$ sublevels; the mixing fractions for the (rarer) excitations to the other sublevels can be larger, especially at $n=3$ (where atoms in the $p$ state cannot decay through, but those in the $3s$ or $3d$ states must)."
" Over lower energies, the agreement with previous results is less clear."," Over lower energies, the agreement with previous results is less clear."
" ? examined only the high-energy limit, but ? studied the entire range."," \citet{valdes08} examined only the high-energy limit, but \citet{shull85} studied the entire range."
" They presented few numerical results at lower energies, but ? provided the following fits to their results (see also ?)): ii —0.69(Ges ήτα _ 938)? + 0.39 E>28eV fuac 3.9811 (22%) attau 04)? + [1 - (1.0-x927)1-32] E> 11evV,,"," They presented few numerical results at lower energies, but \citet{ricotti02} provided the following fits to their results (see also\citealt{volonteri09}) ): ^R -0.69( (1 - )^2 + 0.39 E>28 ^R 3.9811 ( (1- )^2 + [1 - ] E > 11 ,"
30x15 ss! (see Sect. 2.4.1)).,$30\pm 15$ $^{-1}$ (see Sect. \ref{gravred}) ).
 For the interstellar absorption column densities. our model fits do not put strong constraints.," For the interstellar absorption column densities, our model fits do not put strong constraints."
 Until recently. the most accurate parameters of Sirius B were given by ?..," Until recently, the most accurate parameters of Sirius B were given by \citet{holberg1998}."
 These authors used the Lyman alpha line obtained by IUE together with the EUVE spectrum to constrain the effective temperature and surface gravity., These authors used the Lyman alpha line obtained by IUE together with the EUVE spectrum to constrain the effective temperature and surface gravity.
 With only the IUE observations the effective temperature is known within +285 K. but by including the EUVE spectrum this uncertainty reduces to £100 K. In a recent paper. ? have decreased the formal error bars on the effective temperature even further down to £37 K by using high-accuracy STIS spectra.," With only the IUE observations the effective temperature is known within $\pm 285$ K, but by including the EUVE spectrum this uncertainty reduces to $\pm 100$ K. In a recent paper, \citet{barstow2005} have decreased the formal error bars on the effective temperature even further down to $\pm 37$ K by using high-accuracy STIS spectra."
 However. the quoted uncertaity I8 only the statistical uncertainty. and ? argue that the systematic uncertainty on these numbers is hard to assess. mainly because there is little else to compare with.," However, the quoted uncertainty is only the statistical uncertainty, and \citet{barstow2005} argue that the systematic uncertainty on these numbers is hard to assess, mainly because there is little else to compare with."
 A major reason of concern is the much larger effective temperature 1193 K) found by ? as compared to the value of 7790 K obtained by ?.., A major reason of concern is the much larger effective temperature 193 K) found by \citet{barstow2005} as compared to the value of 790 K obtained by \citet{holberg1998}.
 While the surface gravity given in both papers ts almost equal and consistent within the error bars. this temperature differece Is >Jc and causes the EUV flux at 300 tto increase by a factor of 2.4 according to our own model caleulations.," While the surface gravity given in both papers is almost equal and consistent within the error bars, this temperature difference is $>4\sigma$ and causes the EUV flux at 300 to increase by a factor of 2.4 according to our own model calculations."
 Although the absolute accuracy of the EUVE calibration has its limitations (see Sect. 2.4.3)).," Although the absolute accuracy of the EUVE calibration has its limitations (see Sect. \ref{sect:euve_sir}) ),"
 we believe that a factor of 2.4 cannot be easily accommodated for., we believe that a factor of 2.4 cannot be easily accommodated for.
 Moreover. ? also show that their best normalisation of the G430L spectrum obtained with STIS has systematic uncertainties larger than desirable.," Moreover, \citet{barstow2005} also show that their best normalisation of the G430L spectrum obtained with STIS has systematic uncertainties larger than desirable."
 Given this problem with the EUV flux. we prefer here the older ? parameters with the corresponding error ranges.," Given this problem with the EUV flux, we prefer here the older \citet{holberg1998} parameters with the corresponding error ranges."
 For model |. the temperature is clearly higher (by 570 K) than the value foundby ?.. while for model 2 it is consistent with the Holberg et al.," For model 1, the temperature is clearly higher (by 570 K) than the value foundby \citet{holberg1998}, while for model 2 it is consistent with the Holberg et al."
 value within 2« (only 180 K higher)., value within $2\sigma$ (only 180 K higher).
 For both models. loge is consistent with ?..," For both models, $\log g$ is consistent with \citet{holberg1998}."
 According to ?.. Sirius B contains a small amount of helium so pure hydrogen models are ruled out.," According to \citet{holberg1998}, Sirius B contains a small amount of helium so pure hydrogen models are ruled out."
 For homogeneous H/He models. they found με=(4+1)x1075.," For homogeneous H/He models, they found $n_{\mathrm{He}}/n_{\mathrm{H}}=(4\pm 1)\times 10^{-6}$."
 Our upper limit to the amount of helium of «1.0x10? is well below that value., Our upper limit to the amount of helium of $<1.0\times 10^{-6}$ is well below that value.
 However. the claim of detection of helium is based on the non-significant detection of possible Lyo and Lye lines in the EUVE spectrum. as well as on the global fit to the EUVE spectrum.," However, the claim of detection of helium is based on the non-significant detection of possible $\delta$ and $\epsilon$ lines in the EUVE spectrum, as well as on the global fit to the EUVE spectrum."
 If we evaluate our models for the parameters of ?.. we find that there should be a deep and sharp edge in the model near 230A.. with a depth of 13%.," If we evaluate our models for the parameters of \citet{holberg1998}, we find that there should be a deep and sharp edge in the model near 230, with a depth of 13."
. The edge is very broad. and reaches half of its maximum depth at 100Α.," The edge is very broad, and reaches half of its maximum depth at 100."
. Clearly. such a deep edge is not observed in the EUVE spectrum. and the systematic deviations from their fit model as shown in their Fig.," Clearly, such a deep edge is not observed in the EUVE spectrum, and the systematic deviations from their best-fit model as shown in their Fig."
 + are of the same order of magnitude., 4 are of the same order of magnitude.
 In fact. for wavelengths below the edge the EUVE data show even a small systematic excess. pointing to a lower helium abundance than adopted.," In fact, for wavelengths below the edge the EUVE data show even a small systematic excess, pointing to a lower helium abundance than adopted."
 We conclude that there is no convincing evidence for a substantial amount of helium in Sirius B. As for HZ 43À. our models for Sirius B do not give additional useful constraints for the interstellar absorption columns.," We conclude that there is no convincing evidence for a substantial amount of helium in Sirius B. As for HZ 43A, our models for Sirius B do not give additional useful constraints for the interstellar absorption columns."
 Based on our fits alone. it is not well possible to distinguish between model 1 (short Lyman pseudo-continuum cut-off) or model 2 (long cut-off). as both models reproduce well the observed spectral ratio between Sirius B and HZ 43A (Fig. 1)).," Based on our fits alone, it is not well possible to distinguish between model 1 (short Lyman pseudo-continuum cut-off) or model 2 (long cut-off), as both models reproduce well the observed spectral ratio between Sirius B and HZ 43A (Fig. \ref{fig:ratcomp}) ),"
 albeit with different derived parameters for both stars., albeit with different derived parameters for both stars.
 When we look to those parameters (see previous subsection). it appears that the derived temperature for Sirius B and the surface gravity of HZ 43A are in reasonable agreement with recent literature values only for model 2 (a long cut-off).," When we look to those parameters (see previous subsection), it appears that the derived temperature for Sirius B and the surface gravity of HZ 43A are in reasonable agreement with recent literature values only for model 2 (a long cut-off)."
 Model 2 therefore achieves a better consistency between analyses of the UV/optical and soft X-ray ranges., Model 2 therefore achieves a better consistency between analyses of the UV/optical and soft X-ray ranges.
 Moreover. model 2 seems to match the gravitational redshift of HZ 43A better.," Moreover, model 2 seems to match the gravitational redshift of HZ 43A better."
" The most direct test of the Lyman pseudo-continuum 1s provided by the far-UV spectrum of Sirius B. The FUV spectrum was recorded with the far ultraviolet spectroscopic explorer (FUSE) on 2002 June 14. using medium resolution (MDRS) and the SiC channel covering the range ,L1916-1100AA.."," The most direct test of the Lyman pseudo-continuum is provided by the far-UV spectrum of Sirius B. The FUV spectrum was recorded with the far ultraviolet spectroscopic explorer (FUSE) on 2002 June 14, using medium resolution (MDRS) and the SiC channel covering the range $\lambda\lambda$."
 Model 2 with the long cut-off clearly provides the best match. though discrepancies up to between the model and the FUSE spectrum remain.," Model 2 with the long cut-off clearly provides the best match, though discrepancies up to between the model and the FUSE spectrum remain."
 In particular. the observed spectrum reveals slightly broader high Lyman lines (Ly y and higher lines) than those predicted by model 2.," In particular, the observed spectrum reveals slightly broader high Lyman lines (Ly $\gamma$ and higher lines) than those predicted by model 2."
 The overall continuum flux level is however well matched contrary to model I., The overall continuum flux level is however well matched contrary to model 1.
 A detailed analysis of the FUSE spectrum will be presented in a separate paper., A detailed analysis of the FUSE spectrum will be presented in a separate paper.
 In summary. there seems to be more support for a long (model 2).," In summary, there seems to be more support for a long cut-off (model 2)."
 We have obtained fluxed. order-subtracted spectra of both stars from the public EUVEarchive.," We have obtained fluxed, order-subtracted spectra of both stars from the public EUVE."
. We sampled these fluxed spectra on a grid with 5 sspacing using a spline fit. and estimated the uncertainty on the flux point by looking to the r.m.s.," We sampled these fluxed spectra on a grid with 5 spacing using a spline fit, and estimated the uncertainty on the flux point by looking to the r.m.s."
 variations with respect to this fitin wwide bins centred at the grid points (the fluxed spectra from the public archive do not contain error estimates)., variations with respect to this fit in 5 wide bins centred at the grid points (the fluxed spectra from the public archive do not contain error estimates).
 In addition to these statisticaluncertainties. we added systematic uncertainties of about 2. 3.5 and 5 mm ss! AA! for«150A. 150A i«300A παπά 4|>300Α.. respectively.," In addition to these statisticaluncertainties, we added systematic uncertainties of about 2, 3.5 and 5 $^{-2}$ $^{-1}$ $^{-1}$ for $\lambda<150$, $150$ $<\lambda<300$ and $\lambda > 300$, respectively."
 These are based upon à comparison of the spectra with smoothed spectra on even larger scales of ~50 A., These are based upon a comparison of the spectra with smoothed spectra on even larger scales of $\sim 50$ .
. The ratio of these fluxed spectra of both stars is shown in Fig. 4.., The ratio of these fluxed spectra of both stars is shown in Fig. \ref{fig:ratio_euve}. .
 It 1s evident from this figure that the models that we found using the observed Chandra LETGS ratios agree very, It is evident from this figure that the models that we found using the observed Chandra LETGS ratios agree very
first. called asvinptotically velocity term dominated (AVTD) |l.2].. refers to a cosinology that approaches the Kasucr (vacutun. Bianchi I) solution [3] as TO»x. (,"first, called asymptotically velocity term dominated (AVTD) \cite{ber-els,ber-IM}, refers to a cosmology that approaches the Kasner (vacuum, Bianchi I) solution \cite{ber-kasner} as $\tau \to
\infty$. ("
Spatially homogencous universes can be described as a sequence of homogcucous spaces labeled ly 7.,Spatially homogeneous universes can be described as a sequence of homogeneous spaces labeled by $\tau$.
 Here we shall choose 7 so that τεςκ coincides with the singuarity.), Here we shall choose $\tau$ so that $\tau = \infty$ coincides with the singularity.)
 An example of such a solution is the vacumu Biawhi HE πιο 1 which begins with a fixed set of Kasner-like anisotropic expansion rates. aud. possibly. makes one change of the rates iu a prescribed wav (Mixinaster-like bounce) aud then coutinues to 7x as a fixed Wasucr solution.," An example of such a solution is the vacuum Bianchi II model \cite{ber-taub} which begins with a fixed set of Kasner-like anisotropic expansion rates, and, possibly, makes one change of the rates in a prescribed way (Mixmaster-like bounce) and then continues to $\tau = \infty$ as a fixed Kasner solution."
 In coutrast are the homogencous cosmologies which display Mixiuaster dynamics suchas vacuuiun Biauchi VIIE and TX [5.6.7| and Biauchi VIy aud Biawhi I with a magneic field [8.9.10].," In contrast are the homogeneous cosmologies which display Mixmaster dynamics suchas vacuum Bianchi VIII and IX \cite{ber-BKL,ber-misner,ber-halpern} and Bianchi $_0$ and Bianchi I with a magnetic field \cite{ber-LKW,ber-bkb1,ber-leblanc}."
 Jantzen [11] jas discussed oticr οναuples., Jantzen \cite{ber-jantzen} has discussed other examples.
 Mixiiaster dyαλλος describes au approach to the siieularitv which is a sequence of Ikasuer epochs with a prescription. originally due to Delinskii. Ilidatuikov. aud Lifshitz (DINE) [5|.. for relating oue Kasner epoch to the LON.," Mixmaster dynamics describes an approach to the singularity which is a sequence of Kasner epochs with a prescription, originally due to Belinskii, Khalatnikov, and Lifshitz (BKL) \cite{ber-BKL}, for relating one Kasner epoch to the next."
 Some of the Mixiiaster bounces (era changes) display seusitivitv to initial conditious one usually. associates with chaos aud 1 fact NINluaster dvnanudcs is chaotic |12].., Some of the Mixmaster bounces (era changes) display sensitivity to initial conditions one usually associates with chaos and in fact Mixmaster dynamics is chaotic \cite{ber-cornish}.
" The vacuun Diauchi Τ (INasucr) soution is distinguished fro he other Bianchi types in that the spatizd scalar curvature °R. (proporional fc he mninisuperspace (MSS) potential |6.|E"" vanishes ideutically."," The vacuum Bianchi I (Kasner) solution is distinguished from the other Bianchi types in that the spatial scalar curvature $^3\!R$, (proporional to) the minisuperspace (MSS) potential \cite{ber-misner,ber-ryan}, vanishes identically."
 But 18 arix in other Biauchi types due to spatial de])udence othe metric in à coordina isis., But $^3\!R$ arises in other Bianchi types due to spatial dependence of the metric in a coordinate basis.
 Thus an AVTD sineulavity is also characterized as a reeinie in which tern containing or arising from spatial derivaives no longer influence the dynamics., Thus an AVTD singularity is also characterized as a regime in which terms containing or arising from spatial derivatives no longer influence the dynamics.
 This means that the Mixuiaster models do not wave an AVTD sineulariY since the influence of the spatia derivatives (through the MSS potential) never disappearsthere is no last botlice., This means that the Mixmaster models do not have an AVTD singularity since the influence of the spatial derivatives (through the MSS potential) never disappears—there is no last bounce.
 Iu the late ]960°s. DIL claimed to show that singuarities in generic solutioIs to Eiusteiu's equations are locaIv of the Mixiuaster ype [5|..," In the late 1960's, BKL claimed to show that singularities in generic solutions to Einstein's equations are locally of the Mixmaster type \cite{ber-BKL}."
 This mcaus tliit cach point of a spatially iulioinogenueous universe coulc collapse to the singularity as the Mixiiascr sequence of Ikasuner models. (, This means that each point of a spatially inhomogeneous universe could collapse to the singularity as the Mixmaster sequence of Kasner models. (
It has ]con argued that this coud generate a fractal spatial strucure [15.16. 17]..),"It has been argued that this could generate a fractal spatial structure \cite{ber-montani,ber-belinskii,ber-KK}. .)"
 Iu contrast. cach poiut of a cosmology wit ran AVTD siue]uitv evolves asviipotically as a fixed Ixasuer mocel.," In contrast, each point of a cosmology with an AVTD singularity evolves asymptotically as a fixed Kasner model."
 Althoueh the DKL resut is controversial |11].. it provides a hypothesis for testing.," Although the BKL result is controversial \cite{ber-bt}, it provides a hypothesis for testing."
 O1r ultianate objective is to test the DIL conjecture nuuerically., Our ultimate objective is to test the BKL conjecture numerically.
 The work reported here was performed bv using svuiplectir ODE aud PDE solvers 15.19]..," The work reported here was performed by using symplectic ODE and PDE solvers \cite{ber-fleck,ber-vm83}."
 While other numerical iiethods may be used to solve Eiustein’s equations for the models discussed here. svauplectie ποτος have proved extremely advantageous for \Gixiaster models aud have also worked quite well iu the Cowdy plane svummetric aud polarized ((1) svinmietrice cosinologies 23)..," While other numerical methods may be used to solve Einstein's equations for the models discussed here, symplectic methods have proved extremely advantageous for Mixmaster models and have also worked quite well in the Gowdy plane symmetric and polarized $U(1)$ symmetric cosmologies \cite{ber-bkb96,ber-bkbvm,ber-bggm,ber-bkbvm2}. ."
 Consider a system with one degree of freedom described by q(f) aud its canonically conjugate momentum p(f) with a Tamiltonian, Consider a system with one degree of freedom described by $q(t)$ and its canonically conjugate momentum $p(t)$ with a Hamiltonian
analysis only has no impact on the derived properties when the pparameter ref )ischosencaref ully.,analysis only has no impact on the derived properties when the parameter \\ref{subsec:test_parallel}) ) is chosen carefully.
"However, refsubsec:test,arallel) pparameterareasonablescalingisachieved(§ resjb))"," However, given a suitable choice of the parameter a reasonable scaling is achieved )."
.T hisisespeciallyimportant forthememoryscalin particlesimulations.," This is especially important for the memory scaling, as this is the key allowing for the analysis of billion-particle simulations."
"Inf acthehaveshownin8 subsec: scalabilitythat, givenagoodchoiceof parameters, givenasussebllecvonagwfthetBinc"," In fact he have shown in \\ref{subsec:scalability} that, given a good choice of parameters, scales very well with increasing particle resolution."
r ehaveshownth simulation in this paper and also have easingparticleresolution.Wsuccessfully, We have shown this explicitly for a $1024^3$ simulation in this paper and also have successfully
We used the HARPSpol polarimeter (?).. combined with the HARPS spectrograph (?).. installed at the 3.6m ESO telescope at La Silla Observatory (Chile). yielding spectra with resolving power 2t/A.2 of about 105000. and covering the 380-690 nm wavelength region.,"We used the HARPSpol polarimeter , combined with the HARPS spectrograph , installed at the 3.6m ESO telescope at La Silla Observatory (Chile), yielding spectra with resolving power $\lambda / \Delta \lambda$ of about $105\,000$, and covering the 380–690 nm wavelength region."
 All spectra were recorded as sequences of 4 individual sub-exposures taken in different configurations of the polarimeter. in order to yield a full circular polarisation analysis. as described by?.," All spectra were recorded as sequences of 4 individual sub-exposures taken in different configurations of the polarimeter, in order to yield a full circular polarisation analysis, as described by."
". The data were reduced using the package ""REDUCE"" deseribed by?.", The data were reduced using the package “REDUCE” described by.
". After reduction. we obtained the intensity Stokes 7 and the circular polarisation Stokes V spectra of the stars. both normalised to the continuum,"," After reduction, we obtained the intensity Stokes $I$ and the circular polarisation Stokes $V$ spectra of the stars, both normalised to the continuum."
 A null spectrum (N) was also computed in order to diagnose spurious polarisation signatures. and to help to verify that the signatures in the Stokes V spectrum are of stellar origin.," A null spectrum $N$ ) was also computed in order to diagnose spurious polarisation signatures, and to help to verify that the signatures in the Stokes $V$ spectrum are of stellar origin."
 The log of the observations Is presented in Table |., The log of the observations is presented in Table 1.
 To increase the effective signal to noise ratio (S/N) of our data. we applied the Least Squares Deconvolution procedure using tailored line masks of appropriate temperature and gravity for each star.," To increase the effective signal to noise ratio (S/N) of our data, we applied the Least Squares Deconvolution procedure using tailored line masks of appropriate temperature and gravity for each star."
 The masks were first computed using Kuruez ATLAS 9 models of solar abundance(?).. with intrinsic line depths larger than 0.1.," The masks were first computed using Kurucz ATLAS 9 models of solar abundance, with intrinsic line depths larger than 0.1."
 We then excluded from these masks Balmer lines. and lines whose Landé factor is unknown.," We then excluded from these masks Balmer lines, and lines whose Landé factor is unknown."
 Finally we have modified the line depths take into account the relative depth of the lines of the observed spectra., Finally we have modified the line depths take into account the relative depth of the lines of the observed spectra.
" The resulting masks contain 394. 592, and 394 lines for HD 1030807. HD 122451 and HD 105382. respectively."," The resulting masks contain 394, 592, and 394 lines for HD 1030807, HD 122451 and HD 105382, respectively."
 The S/N of the LSD Stokes V profiles is about 10 times larger than the S/N in the original spectra (Table 1))., The S/N of the LSD Stokes $V$ profiles is about 10 times larger than the S/N in the original spectra (Table \ref{tab:log}) ).
 In order to perform a reliable magnetic field diagnosis. we have computed the detection probability inside the LSD V profiles2).," In order to perform a reliable magnetic field diagnosis, we have computed the detection probability inside the LSD $V$ profiles."
". We consider that an observation displays a “definite detection"" (DD) if the probability is larger than 0.99999, a ""marginal detection” (MD) if it falls between 0.999 and 0.99999, and a “null detection” (ND) otherwise (see Table 1)."," We consider that an observation displays a “definite detection"" (DD) if the probability is larger than 0.99999, a “marginal detection"" (MD) if it falls between 0.999 and 0.99999, and a “null detection"" (ND) otherwise (see Table 1)."
 All observations of HD 130807 and HD 105382 display DD while two DD and one ND have been obtained for HD 122451., All observations of HD 130807 and HD 105382 display DD while two DD and one ND have been obtained for HD 122451.
 The LSD I. V. and N profiles are plotted in Fig. 1..," The LSD $I$, $V$, and $N$ profiles are plotted in Fig. \ref{fig:lsd}. ."
 In almost all of our observations Zeeman signatures. as broad as the 7 profiles. are clearly detected in the V profiles. while the N profiles are consistent with the noise.," In almost all of our observations Zeeman signatures, as broad as the $I$ profiles, are clearly detected in the $V$ profiles, while the $N$ profiles are consistent with the noise."
 These results allow us to confidently affirm that magnetic fields are present at the surface of these stars., These results allow us to confidently affirm that magnetic fields are present at the surface of these stars.
 We measured for each observation the. line-of-sight component of the magnetic field averaged over the visible stellar surface (the so-called longitudinal magnetic field or B;). by integrating the 7 and V profiles over the ranges [—50.60]. |-80.100]. and [-70.105] km.sfor HD 130807. HD 122451. and HD 105382. respectively?).," We measured for each observation the line-of-sight component of the magnetic field averaged over the visible stellar surface (the so-called longitudinal magnetic field or $B_{\ell}$ ), by integrating the $I$ and $V$ profiles over the ranges $[-50,60]$, $[-80,100]$, and $[-70,105]$ for HD 130807, HD 122451, and HD 105382, respectively."
. The values are reported in Table 1., The values are reported in Table 1.
 Accordinng to the angular separation. the light of both components entered the HARPSpol fiberX during our observations of this target.," ng to the angular separation, the light of both components entered the HARPSpol fibers during our observations of this target."
 we fird that most of the spectrun of HD 130807 Is consistent with a synthetic spectrum of d single star of Tay=18000 K. logeg=4.25 (ces). broadened by vsini=25 calculated using TLUSTY non-LTE atmosphere models and the SYNSPEC code(??).," we find that most of the spectrum of HD 130807 is consistent with a synthetic spectrum of a single star of $T_{\rm eff}=18000$ K, $\log g=4.25$ (cgs), broadened by $v\sin i=25$, calculated using TLUSTY non-LTE atmosphere models and the SYNSPEC code."
. However. we observe that all He lines are substantially weaker than the synthetic ones calculated with solar abundance (Fig. 2).," However, we observe that all He lines are substantially weaker than the synthetic ones calculated with solar abundance (Fig. \ref{fig:sphd130807}) ),"
 while the Si lines are considerably stronger., while the Si lines are considerably stronger.
 The Si. N and Fe lines show variability in depth and shape on a timescale of | d. These characteristics suggest that HD 130807 is an He-weak star with abundance spots on its surface(?).," The Si, N and Fe lines show variability in depth and shape on a timescale of 1 d. These characteristics suggest that HD 130807 is an He-weak star with abundance spots on its surface."
. Magnetic signatures are detected in almost all the lines of the spectrum. similar to the LSD one (Fig.," Magnetic signatures are detected in almost all the lines of the spectrum, similar to the LSD one (Fig."
 1. /eft)., \ref{fig:lsd} ).
 Many additional lines are observed in the spectrum that could be due to Fem. Feπι. or Ti enhancements.," Many additional lines are observed in the spectrum that could be due to Fe, Fe, or Ti enhancements."
 All these lines show Zeeman signatures similar to the others. with the same variations from one night to the other.," All these lines show Zeeman signatures similar to the others, with the same variations from one night to the other."
 They can therefore be attributed to the same star. rather than a companion. and they are probably the result of the chemical peculiarities at the surface of the star.," They can therefore be attributed to the same star, rather than a companion, and they are probably the result of the chemical peculiarities at the surface of the star."
 A significant shift in radial velocity (~6 km/s) is detected in thestrongest spectral lines including Balmer lines. between May 22 and May 26-27.," A significant shift in radial velocity $\sim 6$ km/s) is detected in thestrongest spectral lines including Balmer lines, between May 22 and May 26-27."
 The maximum reported angular, The maximum reported angular
where DD. DR. and RR are the paircounts as a function of separation. 0. and Np and Ng are the number of objects in the data and random catalogs for the field.,"where DD, DR, and RR are the paircounts as a function of separation, $\theta$, and $N_D$ and $N_R$ are the number of objects in the data and random catalogs for the field."
 For angular correlation measurements the random catalog consists of objects randomly distributed on the sky in the same shape as the data catalog., For angular correlation measurements the random catalog consists of objects randomly distributed on the sky in the same shape as the data catalog.
 Again. the random catalog is ~10 times larger than the data catalog.," Again, the random catalog is $\sim10$ times larger than the data catalog."
 For each sample. we calculated the 0 separation of every pair and binned them in log(0) over the range —3«log(0)<0.4 with Alog(0)=0.1. where @ ts measured in degrees.," For each sample, we calculated the $\theta$ separation of every pair and binned them in $\log(\theta)$ over the range $-3 <\log(\theta)< 0.4$ with $\Delta\log(\theta)=0.1$, where $\theta$ is measured in degrees."
" The angular correlation function can be related to the spatial correlation function: w,5(0)=App!rr. where App~ni», (?)."," The angular correlation function can be related to the spatial correlation function: $w_{pp}(\theta)=A_{pp}\theta^{1-\gamma_{pp}}$, where $A_{pp} \sim r^{\gamma_{pp}}_{0,pp}$ \citep{1980lssu.book.....P}."
" However. since the observed mean galaxy density in a field is not necessarily representative of the global mean density. our measurements of w,,(0) need to be corrected by an additive factor known as the integral constraint."," However, since the observed mean galaxy density in a field is not necessarily representative of the global mean density, our measurements of $w_{pp}(\theta)$ need to be corrected by an additive factor known as the integral constraint."
" To estimate this. we fit or,,(0) using a power law minus a constant. e.g. ο)=Αρηςη —Cpp. Where Cp, is the integral constraint."," To estimate this, we fit $w_{pp}(\theta)$ using a power law minus a constant, e.g. $w_{pp}(\theta)=A_{pp}\theta^{1-\gamma_{pp}}-C_{pp}$ , where $C_{pp}$ is the integral constraint."
" For measuring the parameters we fit over the range 0.001<00.1"".", For measuring the parameters we fit over the range $0.001^{\circ} <\theta< 0.1^{\circ}$.
 We found that fitting over this smaller range reduced the error in the amplitude measurements. although the error in the integral constraint (which is essentially a nuisance parameter) increases.," We found that fitting over this smaller range reduced the error in the amplitude measurements, although the error in the integral constraint (which is essentially a nuisance parameter) increases."
 For autocorrelation measurements this has little impact., For autocorrelation measurements this has little impact.
" We use the measured 5,,. along with the parameters of the spectroscopic sample (ος) and ro (z)) and an initial guess of ορ to determine an initial guess of me employing the linear biasing assumption that ry=(ομον."," We use the measured $\gamma_{pp}$, along with the parameters of the spectroscopic sample $\gamma_{ss}(z)$ and $r_{0,ss}(z)$ ) and an initial guess of $r_{0,pp}$ to determine an initial guess of $r^{\gamma_{sp}}_{0,sp}$, employing the linear biasing assumption that $r^{\gamma_{sp}}_{0,sp}=(r^{\gamma_{ss}}_{0,ss}r^{\gamma_{pp}}_{0,pp})^{1/2}$."
 We expect the correlation length of the photometric sample. to be a function of redshift. as both the underlying dark l'i.pp.matter correlation function and the large-scale structure bias of the sample will evolve with z. both in the real universe and in our mock catalogs.," We expect the correlation length of the photometric sample, $r_{0,pp}$, to be a function of redshift, as both the underlying dark matter correlation function and the large-scale structure bias of the sample will evolve with $z$, both in the real universe and in our mock catalogs."
" To account for this. we assume the redshift dependence of the scale length. 75. will be similar for both the photometric and spectroscopic samples (we considered several alternatives. but this vielded the best results): for our calculations we set 7j,pp(z)e«ro(z). with an initial guess of 7j,νρίς)=ro)."," To account for this, we assume the redshift dependence of the scale length, $r_0$ , will be similar for both the photometric and spectroscopic samples (we considered several alternatives, but this yielded the best results); for our calculations we set $r_{0,pp}(z) \propto r_{0,ss}(z)$, with an initial guess of $r_{0,pp}(z)=r_{0,ss}(z)$."
 We then refine our initial guess for by measuring the angular cross-ccorrelation function in Foxeach redshift bin.," We then refine our initial guess for $r^{\gamma_{sp}}_{0,sp}$ by measuring the angular correlation function in each redshift bin."
" To find wy,(@.5). we measure the cross-ccorrelation between objects in spectroscopic z-bins with all objects in the photometric sample."," To find $w_{sp}(\theta,z)$ , we measure the correlation between objects in spectroscopic z-bins with all objects in the photometric sample."
" We bin the spectroscopic sample over the range 0.19<z«1.39 with a bin size of Az=0.04 and measure w,,(0) for each bin using the estimator where D,D,. D,Ry. R.D,. and R,R, are the cross pair counts between samples as a function of 0 separation. and N is the number of objects in each sample."," We bin the spectroscopic sample over the range $0.19<z<1.39$ with a bin size of $\Delta z=0.04$ and measure $w_{sp}(\theta)$ for each bin using the estimator where $D_sD_p$, $D_sR_p$, $R_sD_p$, and $R_sR_p$ are the cross pair counts between samples as a function of $\theta$ separation, and $N$ is the number of objects in each sample."
 The cross pair counts are calculated by measuring the observed number of objects from one sample around each object in another sample., The cross pair counts are calculated by measuring the observed number of objects from one sample around each object in another sample.
" For example. D,D, is the number of objects in the photometric sample around each spectroscopic object as a function of separation."," For example, $D_sD_p$ is the number of objects in the photometric sample around each spectroscopic object as a function of separation."
 For this measurement. each sample (the objects in the spec-z bin and the photometric sample) has their own random catalog that is ~10 times bigger than their corresponding data catalog.," For this measurement, each sample (the objects in the spec-z bin and the photometric sample) has their own random catalog that is $\sim10$ times bigger than their corresponding data catalog."
 These are once again constructed by randomly distributing objects on the sky in the same shape as the data catalog., These are once again constructed by randomly distributing objects on the sky in the same shape as the data catalog.
" For each z-bin we measured w,,(0) in logarithmic bins of 0.1 in log(0) over the range —3«log(#)<0.4. with 0 measured in degrees."," For each z-bin we measured $w_{sp}(\theta)$ in logarithmic bins of 0.1 in $\log(\theta)$ over the range $-3 <\log(\theta)< 0.4$, with $\theta$ measured in degrees."
" As with the autocorrelation function. we fit w,,00)ΑνστCui the integral constraint is nonnegligible in these measurements."," As with the autocorrelation function, we fit $w_{sp}(\theta)=A_{sp}\theta^{1-\gamma_{sp}}-C_{sp}$; the integral constraint is nonnegligible in these measurements."
" Again we fit over the range 0.001""<00.1"" to reduce the error in. the amplitude measurements.", Again we fit over the range $0.001^{\circ} <\theta< 0.1^{\circ}$ to reduce the error in the amplitude measurements.
" In some z-bins. particularly wherethe amplitude. A,,. is small. we found a significant degeneracy between A,, and >,, when fitting."," In some z-bins, particularly wherethe amplitude, $A_{sp}$, is small, we found a significant degeneracy between $A_{sp}$ and $\gamma_{sp}$ when fitting."
" One can understand this as there being a pivot scale at which clustering is best constrained: one can simultaneously vary Απρ and >, and still match w, at that scale.", One can understand this as there being a pivot scale at which clustering is best constrained; one can simultaneously vary $A_{sp}$ and $\gamma_{sp}$ and still match $w_{sp}$ at that scale.
 To remove this degeneracy. we fixed ssp In each bin. and only fit for the amplitude and integral constraint.," To remove this degeneracy, we fixed $\gamma_{sp}$ in each bin, and only fit for the amplitude and integral constraint."
" Since the clustering of the samples with each other is expected to be intermediate to the intrinsic clustering of each sample. we estimated 7,, with the arithmetic mean of τρ and των."," Since the clustering of the samples with each other is expected to be intermediate to the intrinsic clustering of each sample, we estimated $\gamma_{sp}$ with the arithmetic mean of $\gamma_{pp}$ and $\gamma_{ss}$."
" Using Ay, and 2,5. as well as the initial guess for 2E we determine an initial guess of the redshift distribution op(z)."," Using $A_{sp}$ and $\gamma_{sp}$, as well as the initial guess for $r^{\gamma_{sp}}_{0,sp}$, we determine an initial guess of the redshift distribution $\phi_p(z)$."
" Rewriting equation 3. gives We then use the resulting ©,,(<). along with Aj, and . to redetermine ορ using Equation 10.. which we use to redetermine and thus o,(z)."," Rewriting equation \ref{eq:wsp} gives We then use the resulting $\phi_p(z)$, along with $A_{pp}$ and $\gamma_{pp}$, to redetermine $r_{0,pp}$ using Equation \ref{eq:wpp}, which we use to redetermine $r^{\gamma_{sp}}_{0,sp}$ and thus $\phi_p(z)$."
 This process is repeated until convergence is “ορreached., This process is repeated until convergence is reached.
 For the remainder of the paper. we will frequently refer to making a “measurement” of the correlation functions and ωρίς).," For the remainder of the paper, we will frequently refer to making a “measurement” of the correlation functions and $\phi_p(z)$."
" Each measurement is done by selecting four fields at random out of the 24 mock catalogs. summing their pair counts. and calculating all necessary quantities: no information on ""universal mean values of any measured quantity is used. but rather only that available from the chosen four fields."," Each measurement is done by selecting four fields at random out of the 24 mock catalogs, summing their pair counts, and calculating all necessary quantities; no information on 'universal' mean values of any measured quantity is used, but rather only that available from the chosen four fields."
" We select four fields in order to emulate redshift surveys like DEEP? and VVDS. in which data is typically obtained from of order four separate fields: hence a ""measurement. in our parlance is roughly equivalent to utilizing the information coming from a single survey."," We select four fields in order to emulate redshift surveys like DEEP2 and VVDS, in which data is typically obtained from of order four separate fields; hence a 'measurement' in our parlance is roughly equivalent to utilizing the information coming from a single survey."
 To obtain the following results. we made 101 measurements: we used the median values to evaluate statistical biases in a given quantity and the standard deviation to evaluate random uncertainties.," To obtain the following results, we made $10^4$ measurements; we used the median values to evaluate statistical biases in a given quantity and the standard deviation to evaluate random uncertainties."
 In each plot following the points are the median values and the error bars are the standard deviations. which gives the error on a single measurement.," In each plot following the points are the median values and the error bars are the standard deviations, which gives the error on a single measurement."
 Because (giventhe large number of measurements) these medians should closely matchthe mean of the 24fields. the standard error in a plotted point should be smaller than the plotted error bars by a factor of νο.," Because (giventhe large number of measurements) these medians should closely matchthe mean of the 24fields, the standard error in a plotted point should be smaller than the plotted error bars by a factor of $\sqrt{6}$ ."
 It should be noted that we are ignoring the weak cross correlation that should result from gravitational lensing by, It should be noted that we are ignoring the weak cross correlation that should result from gravitational lensing by
"Since the 6 and 20 cur survevs have two ciffereut beams Laresec aud 12412 arcsec respectively). the spectral iudices à (Sxvv‘ "") for all the coiucidences were calculaed using the total 20 cm fluxes reported iu de Ruiter et al. (","Since the 6 and 20 cm surveys have two different beams $\times$ 4 arcsec and $\times$ 12 arcsec respectively), the spectral indices $\alpha$ $\propto \nu^{-\alpha}$ ) for all the coincidences were calculated using the total 20 cm fluxes reported in de Ruiter et al. ("
1997) and the iitegrated 6 ci fluxes obtained. after convolving the 6 cm nap with the same beam width as the 20 cin inage.,1997) and the integrated 6 cm fluxes obtained after convolving the 6 cm map with the same beam width as the 20 cm image.
 For 12 of the 63 radio sources the differences vetween the 6 cin fiuxes obtained from the maps with the wo different beam sizes are sinaller than20%... wlile oulv l sources srow a difference between the two fluxes greater han a facor 1.5 {αp to a factor 2.1).," For 42 of the 63 radio sources the differences between the 6 cm fluxes obtained from the maps with the two different beam sizes are smaller than, while only 4 sources show a difference between the two fluxes greater than a factor 1.7 (up to a factor 2.1)."
 Πωπονο these 1 sources have all a radio flux deusitv lower than 0.1 ταν aud have not been cousidered in the statistical analysis of he radio spectral index (see Sect., However these 4 sources have all a radio flux density lower than 0.1 mJy and have not been considered in the statistical analysis of the radio spectral index (see Sect.
 5.1)., 5.1).
 The error in each calculated value of spectral iudex was computed by takine he quadrature sui of the relative errors in the two flux densities 94 aud Sy : with vy = 1190 MITz aud 2» = £860 MIIz., The error in each calculated value of spectral index was computed by taking the quadrature sum of the relative errors in the two flux densities $S_1$ and $S_2$ : with $\nu_1$ = 1490 MHz and $\nu_2$ = 4860 MHz.
 For the 6 ci sources without a 20 emi counterpart. we calcula eda lo 20 cmi upper uit usine co(q4g) = 01? - l.98r ο... where ris the distance (Gu arcinin) from the 20 €n nuaee center (de Ruiter et al..," For the 6 cm sources without a 20 cm counterpart, we calculated a $\sigma$ 20 cm upper limit using $\sigma(\mu Jy)$ = $^2$ - 1.78r +34.4, where r is the distance (in arcmin) from the 20 cm image center (de Ruiter et al.,"
 1997)., 1997).
 The results of the 6 cni cross-correlation are sunmarized in Table 3. where. for cach 6 cni source we report the optical identification (Cols.," The results of the $-$ 6 cm cross-correlation are summarized in Table 3, where, for each 6 cm source we report the optical identification (Cols."
 29. see below). the name of the 20 cii counterpart (from Table 1 ofde Ruiter et al..," 2–9, see below), the name of the 20 cm counterpart (from Table 1 of de Ruiter et al.,"
 1997). he 20 cin flux deusitv (or Lo upper limit). the radio spectral index (or upper Bit) aud the distauce between the two radio positions.," 1997), the 20 cm flux density (or $\sigma$ upper limit), the radio spectral index (or upper limit) and the distance between the two radio positions."
 The two 20 cn sources with more than oue component (r1 aud 99) have been associated with multi couponeut G cm sources., The two 20 cm sources with more than one component (71 and 99) have been associated with multi component 6 cm sources.
 Iu particular the tiple source 71 has been associaed with the three component 6601 J1051I8|5732I8., In particular the triple source 71 has been associated with the three component 6cm J105148+573248.
 For this source we found a eood agreement between the »osition of the coniponents detected at he two radio frequencies., For this source we found a good agreement between the position of the components detected at the two radio frequencies.
 More complex is the situation for the other source (99)., More complex is the situation for the other source (99).
 This double source at 20 cin has been resolved iuto a four component source οσοι J105237|573101) in the 6 ei map., This double source at 20 cm has been resolved into a four component source 6cm J105237+573104) in the 6 cm map.
" Moreover. a new. relatively bright radio source (LOCK_66c¢1u_JJ105233|573057. Όντως211. Jw) has been detected at a distance of 25"" from the eeoinetric center of the multiple source."," Moreover, a new, relatively bright radio source J105233+573057, $_{\rm total}$ =0.241 mJy) has been detected at a distance of $^{\prime\prime}$ from the geometric center of the multiple source."
" This new radio source has avery uuusual inverted radio spectral iudex (a,<Ü. Ls) and au optical counterpart that shows a clear extension iu the direction of the multiple radio source.", This new radio source has a very unusual inverted radio spectral index $\alpha_{\rm r} < - 0.48$ ) and an optical counterpart that shows a clear extension in the direction of the multiple radio source.
 A 6 ci contour plot superiniposed on the V band CCD image is shown in Fie. 9.., A 6 cm contour plot superimposed on the V band CCD image is shown in Fig. \ref{F9}.
 For the two multiple sources we report in Table 3 oulythe spectral index derived from the total integrated fux., For the two multiple sources we report in Table 3 onlythe spectral index derived from the total integrated flux.
"Linearizecl set of equations governing the evolution of perturbations within this flow can be written in the following way Οι=9,+AyΕ.Ο, Due to the stratification some coelficients on the right hand sides of Eqs. (",Linearized set of equations governing the evolution of perturbations within this flow can be written in the following way ${\cal D}_t \equiv \partial_t + (A_y y + A_z z)\partial_x$ ]: Due to the stratification some coefficients on the right hand sides of Eqs. (
17-23) depend on z.,17-23) depend on $z$.
 But when studying the ναός of small-scale perturbations (with (.< τμ) one can consider the mean components as constant., But when studying the dynamics of small-scale perturbations (with $\ell_z \ll z_0$ ) one can consider the mean components as constant.
 In this case the set of first-order. partial differential equations (17-24) can be reduced to the set of ordinary differential equations (ODEs) with time-dependent. coefficients if we look for solutions in the lollowing form: with," In this case the set of first-order, partial differential equations (17-24) can be reduced to the set of ordinary differential equations (ODEs) with time-dependent coefficients if we look for solutions in the following form: with"
At this point it is useful to compare our results with those of previous authors.,At this point it is useful to compare our results with those of previous authors.
 For example. IE97 show SEDs in (heir Figure 10 for spherical envelopes of silicate ancl amorphous carbon dust grains. of varying sizes ancl optical depths.," For example, IE97 show SEDs in their Figure 10 for spherical envelopes of silicate and amorphous carbon dust grains, of varying sizes and optical depths."
 In their plots on the right. where the results for silicate erains are displaved. the upper two plots can be compared roughly with our Figures 2. and 6..," In their plots on the right, where the results for silicate grains are displayed, the upper two plots can be compared roughly with our Figures \ref{sedas} and \ref{sedbs}."
 In Figure 10 of IE97. large differences between the models with «—0.05 and 0.1jan are evident.," In Figure 10 of IE97, large differences between the models with $a = 0.05$ and $0.1 \mu \rm m$ are evident."
 By looking at these plots. the reader is led to believe that the IR SED for grains with sizes 0.05 and 0.μα is intrinsically different.," By looking at these plots, the reader is led to believe that the IR SED for grains with sizes $0.05$ and $0.1 \mu \rm m$ is intrinsically different."
 Llowever. our results show that Chis is not the case.," However, our results show that this is not the case."
 The IR SED of single grain size models whose sizes comply with the conditions of AI have very similar shapes ancl levels., The IR SED of single grain size models whose sizes comply with the conditions of AI have very similar shapes and levels.
 The differences between Figure 10 of IE97 and our Figures 2. and 6 owe to the choice of the model optical depth., The differences between Figure 10 of IE97 and our Figures \ref{sedas} and \ref{sedbs} owe to the choice of the model optical depth.
 In IE97. all models have Che same extinction. V-band optical depth.," In IE97, all models have the same extinction $V$ -band optical depth."
" Our models. on the contrary. have all the same 74, bul very. different 7. as seen in Figues 3. and 7.."," Our models, on the contrary, have all the same $\tau_{\rm rep}$ but very different $\tau_{V}$, as seen in Figures \ref{tauas} and \ref{taubs}."
" Thus in case D. we also find that 7, is the best parameter to reveal the essential similarities of models with different grain sizes (which must be lower than the limit sel bv condition 2 of AI)."," Thus in case B, we also find that $\tau_{\rm rep}$ is the best parameter to reveal the essential similarities of models with different grain sizes (which must be lower than the limit set by condition 2 of AI)."
 In this case. the envelope is so optically thick that of the input radiation is reprocessed by the dust grains.," In this case, the envelope is so optically thick that of the input radiation is reprocessed by the dust grains."
" As a consequence. the quantity 74,4, becomes ill-delined. so another parameter must be found to reveal the similarities resulting from AI."," As a consequence, the quantity $\tau_{\rm rep}$ becomes ill-defined, so another parameter must be found to reveal the similarities resulting from AI."
 By definition. all models. in (his case. are optically Chick to the reprocessed radiation.," By definition, all models, in this case, are optically thick to the reprocessed radiation."
 This means that most of the radiation will emerge at wavelengths larger (han the Wien peak of the cavity wall (1.6... A>34an for 7;— 1000Ix).," This means that most of the radiation will emerge at wavelengths larger than the Wien peak of the cavity wall (i.e., $\lambda > 3 \,\mu \rm m$ for $T_{\rm i}=1000 \rm K$ )."
" For a given wavelength the envelope can be divided into two dilferent regions with different properties concerning (the radiation field: an inner region with radius between rj and rp =). and an outer region. between r=, and re. where ος is the envelope outer radius. ancl r;24 is given bv Le. r410s the point where (he radial optical depth of the envelope is unity (this «quantity depends on the wavelength)."," For a given wavelength the envelope can be divided into two different regions with different properties concerning the radiation field: an inner region with radius between $r_{\rm i}$ and $r_{\tau=1}$ , and an outer region, between $r_{\tau=1}$ and $r_{\rm e}$, where $r_{\rm e}$ is the envelope outer radius, and $r_{\tau=1}$ is given by i.e., $r_{\tau=1}$ is the point where the radial optical depth of the envelope is unity (this quantity depends on the wavelength)."
 By definition. radiation emitted inside (he inner region is unlikely to leave (he envelope because (he optical depth is larger (han 1: hence. a reasonable approximation for the emerging IR flux is given bythe volume integral of the radiation," By definition, radiation emitted inside the inner region is unlikely to leave the envelope because the optical depth is larger than 1; hence, a reasonable approximation for the emerging IR flux is given bythe volume integral of the radiation"
anele (for constaut outflow velocity): aud (b) at auv eiven mstauce. an observer sees smnmltaueously plotous cluitted from a range of radii aud aneles. all fulfilline the requirement set by equation 1..,"angle (for constant outflow velocity); and (b) at any given instance, an observer sees simultaneously photons emitted from a range of radii and angles, all fulfilling the requirement set by equation \ref{eq:time}."
 The (dependence of the photospheric radius miplies that the probability of a photon to be scattered iuto angle ? depends on the radius at which the scattering event takes place (or vice versa)., The $\theta$ -dependence of the photospheric radius implies that the probability of a photon to be scattered into angle $\theta$ depends on the radius at which the scattering event takes place (or vice versa).
 However. here we assume that the probabilities are independent. ie. Por?)=P(r)«& P(O).," However, here we assume that the probabilities are independent, i.e., $P(r,\theta) = P(r) \times P(\theta)$ ."
 This asstuuption is made in order to simplify the calculation. aud is tested against the numerical results (SEC refsec:mmuerics below).," This assumption is made in order to simplify the calculation, and is tested against the numerical results (see \\ref{sec:numerics} below)."
" While clearly this approximation has oulv a Tauited validity. the results obtained are in good agreement with the precise calculation done munerically,"," While clearly this approximation has only a limited validity, the results obtained are in good agreement with the precise calculation done numerically."
 We further discuss this approximation. as well as its Liitations in refsecisununuarv below.," We further discuss this approximation, as well as its limitations in \\ref{sec:summary} below."
 Equation 2 Προς that the optical depth to scattering depends on the radius as r(r)Xri., Equation \ref{eq:tau1} implies that the optical depth to scattering depends on the radius as $\tau(r) \propto r^{-1}$.
" This optical depth is theintegral over the probability of a photon propagating from radius r to |o to be scattered. 1.6. τί)-{>(aredidi. frou which it is readily found that Glrf/dey,.xor7."," This optical depth is theintegral over the probability of a photon propagating from radius $r$ to $+\infty$ to be scattered, i.e., $\tau(r) =
\int_r^{\infty} (d\tau/dr) dr$, from which it is readily found that $(d\tau/dr)|_r \propto r^{-2}$."
 As a photon propagates in the racial direction from radius r to r|dr. the optical depth iu the plaszina changes by é7=(drfdr)|.3r.," As a photon propagates in the radial direction from radius $r$ to $r + \delta r$, the optical depth in the plasma changes by $\delta \tau = (d\tau/dr)|_r \delta r$."
 Therefore. the probability of a photon to be scattered as it propagates from radius kr tor|ὃν is eiven by ," Therefore, the probability of a photon to be scattered as it propagates from radius $r$ to $r + \delta r$ is given by ( r .. r + r) = 1 -."
For the last scattering eveut to take place at ror|ar. it is required that the photon does not undergo inv additional scattering before it reaches the observer.," For the last scattering event to take place at $r.. r+ \delta r$, it is required that the photon does not undergo any additional scattering before it reaches the observer."
 The probability that no additional scatteriug occurs frou radius r to the observer is given by exp(, The probability that no additional scattering occurs from radius $r$ to the observer is given by $\exp(-\tau[r])$.
 The probability density function P(r) for the last r|r].scattering event to occur at radius r. is therefore written as ," The probability density function $P(r)$ for the last scattering event to occur at radius $r$, is therefore written as P(r) =."
The function P(r) im equation 3 js nornalized. fyPordr=1.," The function $P(r)$ in equation \ref{eq:P_r} is normalized, $\int_0^{\infty} P(r) dr = 1$."
" Comparison to equation 2. gives the proportionality coustaut. ry—ry,(0=0)Ry28I7."," Comparison to equation \ref{eq:tau1}
 gives the proportionality constant, $r_0 \equiv r_{ph}(\theta=0) =
R_d/2\pi\Gamma^2$."
" The probability of a photon to be scattered into anele 0 is calculated assuming isotropic scattering in the comoving frame. Le. dofd=Const The comoving spatial aucle is dO""=sind/d0dol; aud therefore the probability of a photou to be scattered to angle 0 (im the comoviue frame) is dP/d0'xsin."," The probability of a photon to be scattered into angle $\theta$ is calculated assuming isotropic scattering in the comoving frame, i.e., $d\sigma/d\Omega' = Const$ The comoving spatial angle is $d\Omega' = \sin \theta' d\theta' d \phi'$, and therefore the probability of a photon to be scattered to angle $\theta'$ (in the comoving frame) is $dP/d\theta' \propto \sin
\theta'$."
 The proportionality constant is obtained bv integratiug over the range (f5 z. aud is equal to 1/2.," The proportionality constant is obtained by integrating over the range $0 \leq \theta' \leq \pi$ , and is equal to $1/2$."
 Thus. the isotropic scattering approxination leads to P(0')=(sin()/2.," Thus, the isotropic scattering approximation leads to $P(\theta') = (\sin
\theta')/2$."
 Assuniug that on the average. pliotous propagate iu the radial direction. bx making Loreutz trausforiuatiou to the observer frame oneobtains the probability of scattering into angle 0 with respect to the flow direction.," Assuming that on the average, photons propagate in the radial direction, by making Lorentz transformation to the observer frame oneobtains the probability of scattering into angle $\theta$ with respect to the flow direction."
 This angle is equal to the observed auele to the Ime of sieht. aud is elven by P(d)) _ y) __," This angle is equal to the observed angle to the line of sight, and is given by ) = ) =."
πώ Defining «=1cos). equation 3. becomes ," Defining $u \equiv 1-\beta \cos \theta $, equation \ref{eq:P_theta}
 becomes P(u) =."
Note that 1psa«Ol|oo. and the function. Pu) iu equation 3 is nonualized. .;Pu)du—1.," Note that $1-\beta \leq u \leq 1+\beta$, and the function $P(u)$ in equation \ref{eq:P_u} is normalized, $\int_{1-\beta}^{1+\beta} P(u)
du = 1$."
 As long as the radiative processes that produce the hermal photons deep inside the flow are active. the observed thermal radiation is dominated by plotous Ομτος on the line of sieht towards the observer.," As long as the radiative processes that produce the thermal photons deep inside the flow are active, the observed thermal radiation is dominated by photons emitted on the line of sight towards the observer."
 Once hese radiative processes are terminated. the radiation )ecomies dominated by pliotous euütted off axis aud from arecr radi. which determine the late time behavior of he spectu and flux.," Once these radiative processes are terminated, the radiation becomes dominated by photons emitted off axis and from larger radii, which determine the late time behavior of the spectrum and flux."
 Therefore. the limiting case of a à- Muction injection. both iu time aud radius (f£=0. r=0) is expected to closely describe the late time behiasiour of the thermal spectzumu.," Therefore, the limiting case of a $\delta$ -function injection, both in time and radius $t=0$, $r=0$ ) is expected to closely describe the late time behaviour of the thermal spectrum."
 We calculate here the observed spectrum and flux of the thermal cussion at late tines. under these assumptions.," We calculate here the observed spectrum and flux of the thermal emission at late times, under these assumptions."
 Denote by T'(r) the photon comoving temperature. its observed temperature is T=T'tjD. where D=Til?!cosbol(Tu)+ is the Doppler factor.," Denote by $T'(r)$ the photon comoving temperature, its observed temperature is $T^{ob} = T'(r) \D$, where $\D = [\Gamma(1-\beta \cos
\theta)]^{-1} = (\Gamma u)^{-1}$ is the Doppler factor."
 The observed photon0)] temperature therefore depeuds ou the viewing angle as well as ou the radius of decoupling., The observed photon temperature therefore depends on the viewing angle as well as on the radius of decoupling.
" Below the photospheric radius. photons lose their energy adiabatically, lence Tr)Xr2/7."," Below the photospheric radius, photons lose their energy adiabatically, hence $T'(r) \propto r^{-2/3}$."
 Tt was shown by Peer(2008). that a simular decay law for the photon eniperature exists even if the energv deusity iu the photon field is wich smaller than the energy deusity iu he electrons (ΙΟ cau in principle be nonaclativistic iu he comoving frame. hence have a different temperature decay law). resulting frou the spatial 3-c expansion of the plasina.," It was shown by \citet{Peer08}, that a similar decay law for the photon temperature exists even if the energy density in the photon field is much smaller than the energy density in the electrons (which can in principle be non-relativistic in the comoving frame, hence have a different temperature decay law), resulting from the spatial 3-d expansion of the plasma."
 The adiabatic losses take place oulv as oug as the photous propagate at radi smaller than ~fewry., The adiabatic losses take place only as long as the photons propagate at radii smaller than $\sim few \times r_0$.
 While photous that propagate at high angles decouple the plaza at much larger radi than ry (see eq. 2)).," While photons that propagate at high angles decouple the plasma at much larger radii than $r_0$ (see eq. \ref{eq:r_ph}) ),"
 above fewsry. the number of scattering ds snall. and hence the photous maintain their energy.," above $few
\times r_0$, the number of scattering is small, and hence the photons maintain their energy."
 As here we are interested in the late time evolution of the spectra aud flux. where late time nuply t09 fa. we can safely asstune that the comoving temperature of photous that dominate the flux at late times is (on the average) constant. T'(r)2 Const.," As here we are interested in the late time evolution of the spectrum and flux, where late time imply $t \gg t_N$ , we can safely assume that the comoving temperature of photons that dominate the flux at late times is (on the average) constant, $T'(r) =
Const$ ."
 Asstune that Ny photous are emitted instantaneously (a é-fiunction injection im time) at the center of the expanding plasua., Assume that $N_0$ photons are emitted instantaneously (a $\delta$ -function injection in time) at the center of the expanding plasma.
 Each photon is advected with the flow. until the last scattering event takes place at radius," Each photon is advected with the flow, until the last scattering event takes place at radius"
We have proposed a new moclel of r-process nucleosvnthesis in O-Ne-Meg-core collapse 5Ne.,We have proposed a new model of $r$ -process nucleosynthesis in O-Ne-Mg-core collapse SNe.
 Unlike previous models based on assumed extremely neutron-rich ejecta (e.g.. 1993:Wanajoetal. 2003)). our model relies on the [ast expansion of the shocked matter in the weakly neutron-rich surface lavers of an Q-Ne-Mg core to achieve a disequilibrium between [ree nucleons. a-particles. and heavier nuclei.," Unlike previous models based on assumed extremely neutron-rich ejecta (e.g., \citealp{1998ApJ...493L.101W,2003ApJ...593..968W}) ), our model relies on the fast expansion of the shocked matter in the weakly neutron-rich surface layers of an O-Ne-Mg core to achieve a disequilibrium between free nucleons, $\alpha$ -particles, and heavier nuclei."
 As shown bv Meyer(2002).. the significant presence of [free nucleons in disequilibrium facilitates the production of seed nuclei with A~140 during the expansion.," As shown by \citet{2002PhRvL..89w1101M}, the significant presence of free nucleons in disequilibrium facilitates the production of seed nuclei with $A\sim 140$ during the expansion."
 For matter with an initial 3.=0.495. the neutron excess is sullicient for an r-process with fission cveline to occur. producing dominanily the nuclei with -l>130 through the actinides.," For matter with an initial $Y_e=0.495$, the neutron excess is sufficient for an $r$ -process with fission cycling to occur, producing dominantly the nuclei with $A>130$ through the actinides."
 The kev to the fast expansion of the shocked matter is the steep density. gradient in the surface lavers of an O-Ne-Mg core. which enables the inner and outer surfaces of a mass element (o expand with significantly different. velocities. (hus making its densitv drop much faster.," The key to the fast expansion of the shocked matter is the steep density gradient in the surface layers of an O-Ne-Mg core, which enables the inner and outer surfaces of a mass element to expand with significantly different velocities, thus making its density drop much faster."
 Q-Ne-Me-core collapse SNe were also proposed as the source for the heavy. r-process elements (r-elements) with A>130 (Da and higher atomic numbers) based on considerations of Galactie chemical evolution (e.g.. Mathewsetal.1992:Ishimaru&Wanajo 1999)).," O-Ne-Mg-core collapse SNe were also proposed as the source for the heavy $r$ -process elements $r$ -elements) with $A>130$ (Ba and higher atomic numbers) based on considerations of Galactic chemical evolution (e.g., \citealp{1992ApJ...391..719M,1999ApJ...511L..33I}) )."
 A strong argument for this proposal was presented using observations of metal-poor stars 2002. 2003)..," A strong argument for this proposal was presented using observations of metal-poor stars \citep{2002ApJ...567..515Q,2003ApJ...588.1099Q}."
 In. addition. the kev issues regarcing the sources [or the r- based on observations and basic understanding of stellar models were summarized in Qian&Wasserburg(2007)..," In addition, the key issues regarding the sources for the $r$ -elements based on observations and basic understanding of stellar models were summarized in \citet{2007PhR...442..237Q}."
 Data on the metal-poor stars C'S 31082001 (Lilletal.2002).. TID 115444. and IID 122563 (Westinetal.2000) show that their abundances of the heavy r-elements differ by a factor up to ~107.," Data on the metal-poor stars CS 31082–001 \citep{2002A&A...387..560H}, , HD 115444, and HD 122563 \citep{2000ApJ...530..783W} show that their abundances of the heavy $r$ -elements differ by a factor up to $\sim 10^2$."
 In contrast. these stars have essentially the same abundances of the elements between O and Ge (e.g.. |Fe/II] =log(Fe/Il)log(Fe/II).~ —3).," In contrast, these stars have essentially the same abundances of the elements between O and Ge (e.g., [Fe/H] $\equiv\log({\rm Fe/H})-\log({\rm Fe/H})_\odot\sim -3$ )."
 Furthermore. when CS 22892052 ([Fe/II] =—3.1. Snedenetal. 2003)) is compared. with HD 221170 (|Fe/Il] = —2.2. Ivansetal. 2006)) and CS 31082001 ([Fe/II] =—2.9) with DD +17°3248 (|Fe/1l] =—2.1. Cowanοἱal.2002)). data show that the stars in either pair have nearly the same abundances of heavy r-elements but (he abundances of the elements between O and Ge differ bv a [actor of ~8 and 6 for the former and latter pair. respectively.," Furthermore, when CS 22892–052 ([Fe/H] $=-3.1$, \citealp{2003ApJ...591..936S}) ) is compared with HD 221170 ([Fe/H] $=-2.2$ \citealp{2006ApJ...645..613I}) ) and CS 31082–001 ([Fe/H] $=-2.9$ ) with BD $+17^\circ 3248$ ([Fe/H] $=-2.1$, \citealp{2002ApJ...572..861C})), data show that the stars in either pair have nearly the same abundances of heavy $r$ -elements but the abundances of the elements between O and Ge differ by a factor of $\sim 8$ and 6 for the former and latter pair, respectively."
 These results appear to require that the production of the heavy ;-elemenis be decoupled from that of the elements between O and Ge (Qian&Wasserburg2002.2003.2007)..," These results appear to require that the production of the heavy $r$ -elements be decoupled from that of the elements between O and Ge \citep{2002ApJ...567..515Q,2003ApJ...588.1099Q,2007PhR...442..237Q}."
 As Fe-core collapse SNe from progenitors of 11AL. are (he major source for the latter eroup of elements at low metallicities. (his strongly suggests that such SNe are not (he source lor the heavy r-elements.," As Fe-core collapse SNe from progenitors of $>11\,M_\odot$ are the major source for the latter group of elements at low metallicities, this strongly suggests that such SNe are not the source for the heavy $r$ -elements."
 The elements between O and Ge are produced between the core ancl the 11 envelope by explosive burning; during a core-collapse SN or by hydrostatic burning during ils pre-SN evolution., The elements between O and Ge are produced between the core and the H envelope by explosive burning during a core-collapse SN or by hydrostatic burning during its pre-SN evolution.
 Models of O-Ne-Meg-core collapse SNe show that the total amount of inalerial ejected [rom between the core aud the IIenvelope is only ~0.01 0:0411. (Alavle& 2006).. much smaller than the ~1M. for Fe-core collapse SNe.," Models of O-Ne-Mg-core collapse SNe show that the total amount of material ejected from between the core and the Henvelope is only $\sim 0.01$ $0.04\,M_\odot$ \citep{1988ApJ...334..909M,2006A&A...450..345K}, , much smaller than the $\sim 1\,M_\odot$ for Fe-core collapse SNe."
 Thus. O-Ne-Meg-core collapse SNe contribute very little to the elements between O and Ge.," Thus, O-Ne-Mg-core collapse SNe contribute very little to the elements between O and Ge."
VVIIE x-ray hunainuosities (130 TeV) and their X-ray huninosities (210 keV) with the spin-down huuinosities. E. and the characteristic ages. το of their pulsars.,"VHE $\gamma$ -ray luminosities (1–30 TeV) and their X-ray luminosities (2–10 keV) with the spin-down luminosities, $\dot{E}$, and the characteristic ages, $\tau_c$, of their pulsars."
 Next we cousider the behaviour of the ratio between the eanuna and X-ray luminosity as a function of the pulsar spin-down power aud age., Next we consider the behaviour of the ratio between the gamma and X-ray luminosity as a function of the pulsar spin-down power and age.
 These relations are discussed in the frame of an evolving electron energy. population., These relations are discussed in the frame of an evolving electron energy population.
 Iu Table 1 we report a sample of the identified oobserved by the eexperineut., In Table \ref{tab:tevpwne} we report a sample of the identified observed by the experiment.
" We further mceluded six candidatePWNe.. selecting unideuti&ed ddiffuse sources located near vouug aud energetic pulsars. with 7,<100 kyr aud E>10% erg |."," We further included six candidate, selecting unidentified diffuse sources located near young and energetic pulsars, with $\tau_c \lesssim 100$ kyr and $\dot{E} > 10^{35}$ erg $^{-1}$ ."
 These pariuneters are defined as £IzIPP? aud n.=oP2P. where P is the pulsar spin period. P its derivative. aud J=1007 em ceni the moment of inertia.," These parameters are defined as $\dot
E \equiv 4\pi^2 I \dot P/P^3$ and $\tau_c \equiv\ P/2\dot P$, where $P$ is the pulsar spin period, $\dot{P}$ its derivative, and $I \equiv
10^{45}$ gm $^{2}$ the moment of inertia."
 We calculated £ aud 7. usine the P aud P values reported in the Australia Telescope National Facility CATNE) pulsar (Manchesteretal, We calculated $\dot{E}$ and $\tau_c$ using the $P$ and $\dot{P}$ values reported in the Australia Telescope National Facility (ATNF) pulsar \citep{ATNF}.
.9005)... The οταν fluxes. F.. are derived from literature and computed iu the 130 TeV energy baud. with statistical errors estimated with standard Montecarlo propagation technique.," The $\gamma$ -ray fluxes, $F_\gamma$, are derived from literature and computed in the 1--30 TeV energy band, with statistical errors estimated with standard Montecarlo propagation technique."
 The ower energv value corresponds to the highest observed detection threshold., The lower energy value corresponds to the highest observed detection threshold.
 The upper value of 30 Te reduces he bias of possible unneasured bhügh-energv V.cut-offs., The upper value of 30 TeV reduces the bias of possible unmeasured high-energy cut-offs.
 The unabsorbed N-ray fluxes. Fy. have been derived roni literature based ou X-ray iuagine observatories. and converted iu the 210 keV. energy. baud.," The unabsorbed X-ray fluxes, $F_X$, have been derived from literature based on X-ray imaging observatories, and converted in the 2–10 keV energy band."
 The lower enerey is chosen in order to minimize the contamination w possible thermal componcuts due to the pulsar or Supernova reninant., The lower energy is chosen in order to minimize the contamination by possible thermal components due to the pulsar or supernova remnant.
 When it was possible to single out he PWN from the pulsar component. only the PWN fiux is reported.," When it was possible to single out the PWN from the pulsar component, only the PWN flux is reported."
" We investigated the relations between the different πιοτ]ος and the pulsar parameters. using the data collected in Table Ἐν,"," We investigated the relations between the different luminosities and the pulsar parameters, using the data collected in Table \ref{tab:tevpwne}."
" The +-rav huuiunosities. L.. do not appear correlated with the pulsar spin-down Iuninuosities {νι nor they do with the characteristic ages το, as shown iu Fie."," The $\gamma$ -ray luminosities, $L_\gamma$, do not appear correlated with the pulsar spin-down luminosities $\dot{E}$, nor they do with the characteristic ages $\tau_c$ , as shown in Fig."
 L (top pauclx)., \ref{fig:fig1} (top panels).
 This is at variance with the observed PWNe X-ray luminosities. for which a scaling relationis apparent with both £ aud 7. (Fig. l..," This is at variance with the observed PWNe X-ray luminosities, for which a scaling relationis apparent with both $\dot{E}$ and $\tau_c$ (Fig. \ref{fig:fig1},"
 muddle panels)., middle panels).
 The weighted least square fit on the whole dataset vields All the uncertainties are at lo level. and E=Eso.107 ore |.," The weighted least square fit on the whole dataset yields All the uncertainties are at $\sigma$ level, and $\dot{E} = \dot{E}_{37} \times 10^{37}$ erg $^{-1}$."
 The LyE scaling is known or the pulsars as well as for the, The $L_X-\dot{E}$ scaling is known for the pulsars as well as for the.
 This scaling was firstly noted by Seward&WaneNe...(1988): further. Decker&Triuuper(1997) investigate a sample of 27 pulsus with ROSAT.. viclding the simple scaling Luaον&lOE.," This scaling was firstly noted by \citet{Seward88}; further, \citet{Becker97} investigate a sample of 27 pulsars with , yielding the simple scaling $L_{X (0.1-2.4 \, \mathrm{keV})} \simeq 10^{-3} \dot{E}$."
 A re-analysis was performed o» Posseutietal.(2002).. who studied a sample of 39 pulsars observed by several X-ray observatories. accounting for the statistical aud systematic errors.," A re-analysis was performed by \citet{Possenti02}, who studied a sample of 39 pulsars observed by several X-ray observatories, accounting for the statistical and systematic errors."
" They ound logoLxy-—(LL360.01)|(1.3120,03)logyE. a relation harder than Eq. (13)."," They found $\log_{10} L_X = (-14.36 \pm 0.01) + (1.34 \pm 0.03) \log_{10} \dot{E}$, a relation harder than Eq. \ref{eq:lxedot}) )."
 However. they could rot separate the PWN from the pulsar coutribution.," However, they could not separate the PWN from the pulsar contribution."
 A better comparison can be done with the results frou INarealtsev&Pavlov(2008).. who receutlv used hieh-resolution data in order to decouple the PWN and the pulsar fluxes.," A better comparison can be done with the results from \citet{Kargaltsev08a}, who recently used high-resolution data in order to decouple the PWN and the pulsar fluxes."
" Iudeed. takine E. τοι aud Lpvy in the 0.58 keV energy from their Tables 1 aud 2. we obtained as fitted values logyLyiu5skew)=(31.02£0.05)|(1.16+0.0L)logy,Esz for their whole sunple. aud logyyLycosκκ=0262003)|(Lsrx0.01)logs)Esz restricting the fit only to the sources also present in our sauuple."," Indeed, taking $\dot{E}$ , $\tau_c$, and $L_{PWN}$ in the 0.5–8 keV energy from their Tables 1 and 2, we obtained as fitted values $\log_{10} L_{X (0.5-8 \, \mathrm{keV})} = (34.02 \pm 0.05) + (1.46 \pm 0.04) \log_{10} \dot{E}_{37}$ for their whole sample, and $\log_{10} L_{X (0.5-8 \, \mathrm{keV})} = (34.26 \pm 0.03) + (1.87 \pm 0.01) \log_{10} \dot{E}_{37}$ restricting the fit only to the sources also present in our sample."
 The latter is compatible in tlic terms of slope with Eq. (019).," The latter is compatible in the terms of slope with Eq. \ref{eq:lxedot}) ),"
 aud the slight difference iu normalization can be dueto the differeut enerey. baud., and the slight difference in normalization can be dueto the different energy band.
 N-rav sources of our whole dataset also show a dependence of Ly on τι with a best-fit relation where 7. is In units of vears.," X-ray sources of our whole dataset also show a dependence of $L_X$ on $\tau_c$ , with a best-fit relation where $\tau_c$ is in units of years."
 The Ly7.scalingwasalready noted by Becker&Triuuper(1997) and Posseuti (2002)..., The $L_X-\tau_c$scalingwasalready noted by \citet{Becker97} and \citet{Possenti02}. .
 Also in this case we compared our fit to the, Also in this case we compared our fit to the
and its growth rate 7 are given in Fig.,and its growth rate $\eta$ are given in Fig.
" 2 (upper and lower circles, respectively, the meaning of the other symbols will be explained below)."," \ref{fig:allgkin} (upper and lower circles, respectively, the meaning of the other symbols will be explained below)."
" The plot reveals that in the region of very high-radial order g-modes (radial order k= 40), there are small variations in the kinetic energy, of no more than one order of magnitude, between different modes."," The plot reveals that in the region of very high-radial order -modes (radial order $k \gtrsim 40$ ), there are small variations in the kinetic energy, of no more than one order of magnitude, between different modes."
 We also see that modes with local minimum values of the kinetic energy have local maximum growth rates and vice versa., We also see that modes with local minimum values of the kinetic energy have local maximum growth rates and vice versa.
 The non-uniform distribution of the kinetic energy resembles the mode trapping phenomenon caused by the potential barrier due to the composition transition regions., The non-uniform distribution of the kinetic energy resembles the mode trapping phenomenon caused by the potential barrier due to the composition transition regions.
" The chemical transition regions act as resonant cavities for the modes, changing the amplitudes of the eigenfunctions in different regions of the star and hence modifying their kinetic energy, which is given by: where c is the eigenfrequency, £. and £j, the radial and horizontal displacement eigenfunctions, and p the local density."," The chemical transition regions act as resonant cavities for the modes, changing the amplitudes of the eigenfunctions in different regions of the star and hence modifying their kinetic energy, which is given by: where $\sigma$ is the eigenfrequency, $\xi_r$ and $\xi_h$ the radial and horizontal displacement eigenfunctions, and $\rho$ the local density."
" It follows that g-modes will have higher kinetic energies than p-modes, as they propagate in denser regions of the star."," It follows that -modes will have higher kinetic energies than -modes, as they propagate in denser regions of the star."
 This is clearly seen by comparing Fig., This is clearly seen by comparing Fig.
" 2 and the corresponding plot for p-modes, Fig. 10.."," \ref{fig:allgkin} and the corresponding plot for p-modes, Fig. \ref{fig:allpkin}."
" Following the asymptotic theory of nonradial oscillations (see e.g. Tassoul1980; Smeyersetal.1995;; Smeyers&Moya2007)), modes of the same degree 6 and consecutive radial order k would have a uniform period separation, AP, given by: where N is the BV frequency."," Following the asymptotic theory of nonradial oscillations (see e.g. \citealp{tassoul80}; \citealp{smeyers95}; ; \citealp{smeyers07}) ), modes of the same degree $\ell$ and consecutive radial order $k$ would have a uniform period separation, $\Delta P$, given by: where $N$ is the BV frequency."
" Thus, mode trapping effects are revealed for certain modes as deviations with respect to the mean period spacing."," Thus, mode trapping effects are revealed for certain modes as deviations with respect to the mean period spacing."
 This can be seen from the data points plotted in red in Fig. 3.., This can be seen from the data points plotted in red in Fig. \ref{fig:allgdeltap}.
" The radial and horizontal displacement eigenfunctions (yi=€/r and yo=(o?r/g)*€n/r, respectively as defined by Dziembowski 1971)) of representative modes with minimum (988), normal (g85) and maximum (983) total kinetic energy are shown in Fig. 4.."," The radial and horizontal displacement eigenfunctions $_1=\xi_r/r$ and $_2=(\sigma^2 r/g) * \xi_h/r$, respectively as defined by \citealt{dziembowski71}) ) of representative modes with minimum 88), normal 85) and maximum 83) total kinetic energy are shown in Fig. \ref{fig:gradial88}."
 The vertical line at logq~-—2.23 marks the location of the maximum composition gradient in the He/H transition region., The vertical line at $\log q \simeq-2.23$ marks the location of the maximum composition gradient in the He/H transition region.
" It is evident that the g88 mode has lower amplitude below the He/H interface, so it is trapped in the envelope."," It is evident that the 88 mode has lower amplitude below the He/H interface, so it is trapped in the envelope."
" As the region below the He/H transition is very dense, it has a high weight in the total kinetic energy, and hence trapped modes have minimum values of the kinetic energy."," As the region below the He/H transition is very dense, it has a high weight in the total kinetic energy, and hence trapped modes have minimum values of the kinetic energy."
" We recall that, for high-radial order g-modes in this model, significant energy interchange is produced in the region below the He/H transition, which is mostly damping (fig."," We recall that, for high-radial order -modes in this model, significant energy interchange is produced in the region below the He/H transition, which is mostly damping (fig."
" 8, Paper I), resulting in trapped modes being less damped and having maximum growth rate values."," 8, Paper I), resulting in trapped modes being less damped and having maximum growth rate values."
" On the other hand, the 983 mode has highest amplitude in the damping region, and it is referred to as a confined mode, which is less likely to be excited, as is reflected in its minimum value of the growth rate."," On the other hand, the 83 mode has highest amplitude in the damping region, and it is referred to as a confined mode, which is less likely to be excited, as is reflected in its minimum value of the growth rate."
" Previous adiabatic studies for sdBs (Charpinetetal.2000) postulated qualitatively, based on the growth rate dependence of the kinetic energy, ηαW/Exi, (where W is the work integral defined as the total energy balance over one period of oscillation), that when a mode had lower amplitude in the damping regions, the mode would be less damped and would be more likely to be excited."," Previous adiabatic studies for sdBs \citep{charpinet00} postulated qualitatively, based on the growth rate dependence of the kinetic energy, $\eta\, \alpha \, W/E_{kin}$ (where $W$ is the work integral defined as the total energy balance over one period of oscillation), that when a mode had lower amplitude in the damping regions, the mode would be less damped and would be more likely to be excited."
" Indeed, we confirm this hypothesis for high-radial order sdO gravity modes in our non-adiabatic study."," Indeed, we confirm this hypothesis for high-radial order sdO gravity modes in our non-adiabatic study."
" We also draw the attention to the fact that the radial eigenfunction for the trapped mode has a node above the He/H transition, while the confined mode has a node below it, and tthe normal mode has a node just about on the interface."," We also draw the attention to the fact that the radial eigenfunction for the trapped mode has a node above the He/H transition, while the confined mode has a node below it, and the normal mode has a node just about on the interface."
" For the horizontal eigenfunction, although there are nodes at similar distances above and below the He/H transition, for the trapped (confined) mode, the closest node to the transition is below (above) it, in good agreement whichwhat is found for sdBs and white dwarfs."," For the horizontal eigenfunction, although there are nodes at similar distances above and below the He/H transition, for the trapped (confined) mode, the closest node to the transition is below (above) it, in good agreement whichwhat is found for sdBs and white dwarfs."
" However, the larger distances of the nodes to the trapping"," However, the larger distances of the nodes to the trapping"
Laudol standards.,Landolt standards.
 The caliation agrees with that of Hesseretal.(1987) to within for B aud V. The stars oreseuted and. aualyzed in this paper are ouly those wlich contribute 50% of the lelt within one PSF racius of their centers., The calibration agrees with that of \cite{hess87} to within for B and V. The stars presented and analyzed in this paper are only those which contribute $> 50\%$ of the light within one PSF radius of their centers.
 TIis criterion results in the loss of many crowded stars. especially at or below the main sequence turuoll.," This criterion results in the loss of many crowded stars, especially at or below the main sequence turnoff."
 However the princidle sequences derived are quite ceau. and the compleeness above the turnoDis high. though not100%.," However the principle sequences derived are quite clean, and the completeness above the turnoff is high, though not."
.. Figure 5 presents the resiltiung CMD., Figure 5 presents the resulting CMD.
 lu order to studs the blle stragelers. we must 1ave a Consistent way o‘selecting ther1 from the color-1uagnuitude diagram.," In order to study the blue stragglers, we must have a consistent way of selecting them from the color-magnitude diagram."
 It is necessary to make tle selection in two colors. slnice ποιό sars which are prese itin the blue strageler region in one color uay show up as photonjetric anomalies in other colors.," It is necessary to make the selection in two colors, since some stars which are present in the blue straggler region in one color may show up as photometric anomalies in other colors."
 Tjese stars could be foreground or backgrouic objects. photometjc errors. Or Oher kiuds ol strange stars which are not blue sraeelers.," These stars could be foreground or background objects, photometric errors, or other kinds of strange stars which are not blue stragglers."
MOD The ilial selection was coie iu the U. U-B diagram (see Fimre 5).," The initial selection was done in the U, U-B diagram (see Figure 5)."
 Àn additional selecion mace in V B-V diagraiu (see Figure 6). aud hen stars far [rom the principle secuence in tje. color-color ci:igraln were ‘ejected (see Figure 7).," An additional selection made in V, B-V diagram (see Figure 6), and then stars far from the principle sequence in the color-color diagram were rejected (see Figure 7)."
 Although some of he stars excluded may still be blue stragelers. we have adopted these criteria so that we cau lave a clean comj»arison of he data to our theoretical distributious.," Although some of the stars excluded may still be blue stragglers, we have adopted these criteria so that we can have a clean comparison of the data to our theoretical distributions."
 The star a Vlr. B-V~0.2 and U-B-0.05 is kiWIL O be a variable star (Exods 1999. private comuullcatiol) auc is likely an $X PhoeiΙΟ] star.," The star at $\sim$ 14.7, $\sim$ 0.2 and $\sim$ -0.05 is known to be a variable star (Edmonds 1999, private communication) and is likely an SX Phoenicis star."
 Howeve dt does 1100 satisfy our selection criteria. aux uerefore las been rejected. [roin ouo sample.," However, it does not satisfy our selection criteria, and therefore has been rejected from our sample."
 Using these criteria. we find 61 bue stragelers (coripared to he 20 found by deMarcul.Paresce&Feraro (1993))).," Using these criteria, we find 61 blue stragglers (compared to the 20 found by \cite{dem93}) )."
 It shoud be noted that some o Ije blue stragelers within 0.75 magnitudes above tte cluster turnolf could resut from the superposition of nail sequence stars. either by chance or from being a physical biwary.," It should be noted that some of the blue stragglers within 0.75 magnitudes above the cluster turnoff could result from the superposition of main sequence stars, either by chance or from being a physical binary."
 The blue strageler requency ‘elative to horizontal branch sars (as defined by Ferraroοἱal. (1999))) is 0.37., The blue straggler frequency relative to horizontal branch stars (as defined by \cite{fer99}) ) is 0.37.
 We macled our heoretical distributiois of BSs to the observations ον forming our distributions from tlOse paris of the evolutiouary paths whicl satisfied the above oervational selection criteria., We matched our theoretical distributions of BSs to the observations by forming our distributions from those parts of the evolutionary paths which satisfied the above observational selection criteria.
 We chose to use his data set alone. rather than combining it with the earlier HST data ou bue stragelers from the core of the cluster.," We chose to use this data set alone, rather than combining it with the earlier HST data on blue stragglers from the core of the cluster."
 In «πο tolave a convincing comj»arisou of theory to data. we ueeda« 'Olislstent way ol selecting the bue strag[n]elers. which can be doie best with a large horyogeneous data set.," In order to have a convincing comparison of theory to data, we need a consistent way of selecting the blue stragglers, which can be done best with a large homogeneous data set."
 In order to understand the prope‘ties of 17 Tuc as awhole. eventually data from all sources aud all regious of the cluster will have to be considered.," In order to understand the properties of 47 Tuc as a whole, eventually data from all sources and all regions of the cluster will have to be considered."
 TIe implicatious of our choice will be discussed in the following section., The implications of our choice will be discussed in the following section.
 The theoretical blue strageler distribution with a coustaut blue strageler formation rate is shown in Figure 8. along with the 61 selected blue stragelers.," The theoretical blue straggler distribution with a constant blue straggler formation rate is shown in Figure 8, along with the 61 selected blue stragglers."
 This distribution does not match the observations in three iniportant ways., This distribution does not match the observations in three important ways.
 Firstly. the models predict a large peak of low Iuminosity blue straeglersMD which is uot observe.," Firstly, the models predict a large peak of low luminosity blue stragglers which is not observed."
 This is likely a selection ellect. since [alnter stars are less likely to pass the contamiuation test noted above.," This is likely a selection effect, since fainter stars are less likely to pass the contamination test noted above."
 Secondly. there are too many observed blue stragelers at the red eund of the distribution.," Secondly, there are too many observed blue stragglers at the red end of the distribution."
" These so-called. ""yellow stragglers"" have been noted", These so-called “yellow stragglers” have been noted
still ongoing and it is expected to cover roughly 14: square degrees in BAL.,still ongoing and it is expected to cover roughly 14 square degrees in $BVI$.
 The available data provide color information for a significant fraction of the ELS cluster candidates., The available data provide color information for a significant fraction of the EIS cluster candidates.
 Nearly all candidates already have 57 ancl over half of them have BV{ clata., Nearly all candidates already have $BI$ and over half of them have $BVI$ data.
 Also available are data obtained. by different groups from. optical/infrared observations of EELS cluster candidates with z0.5., Also available are data obtained by different groups from optical/infrared observations of EIS cluster candidates with $z>0.5$.
 These data were obtained at the NPL Gnfrared observations for 15 clusters) and the Danish 1.5m telescope on La Silla. and the Nordic Optical Telescope. (V and 2 observations for 50 clusters)," These data were obtained at the NTT (infrared observations for 15 clusters) and the Danish 1.5m telescope on La Silla, and the Nordic Optical Telescope $V$ and $R$ observations for 50 clusters)."
 These observations are still ongoing. which will enable doubling the sample within the next vear.," These observations are still ongoing, which will enable doubling the sample within the next year."
 Even though there is no substitute for direct spectroscopic confirmation of candidate cluster of galaxies. these observations are extremely time consuming.," Even though there is no substitute for direct spectroscopic confirmation of candidate cluster of galaxies, these observations are extremely time consuming."
 In fact. for this tvpe of work it is not only important to have a high-confidence that the selected candidates are real associations but also to be able to select. individual &ealaxies likely to be cluster members.," In fact, for this type of work it is not only important to have a high-confidence that the selected candidates are real associations but also to be able to select individual galaxies likely to be cluster members."
 One wav of pre-selecting candidates is to use the available multi-color data to search for galaxies with red. colors corresponding to the cluster. early-tvpe galaxy population., One way of pre-selecting candidates is to use the available multi-color data to search for galaxies with red colors corresponding to the cluster early-type galaxy population.
 Such red-sequences have been detected over a broad. redshift range using optical and optical/infrared. colors for low and high redshift clusters. respectively0].," Such red-sequences have been detected over a broad redshift range using optical and optical/infrared colors for low and high redshift clusters, respectively."
.. As shown below. from the data we have. optical colors are useful for zzz.7. while opticalinfrared data are required to extend the redshif range bevond this limit.," As shown below, from the data we have, optical colors are useful for $z\lsim0.7$, while optical/infrared data are required to extend the redshift range beyond this limit."
 In order to find supporting evidence that the ELS candidates are physica associations. those with available data in the V. and 7 filters have been analyzed to search for the presence of a red-sequence.," In order to find supporting evidence that the EIS candidates are physical associations, those with available data in the $V$ and $I$ filters have been analyzed to search for the presence of a red-sequence."
 This has been done either by. direc inspection of the (Vf)£ color-magnitude diagrams where. at least for clusters with zz0.4. a red-sequence appears as a distinctive13]... or bv evaluating the statistical significance of spatial concentrations of galaxies in dillerent. color," This has been done either by direct inspection of the $(V-I)-I$ color-magnitude diagrams where, at least for clusters with $z\lsim0.4$, a red-sequence appears as a distinctive, or by evaluating the statistical significance of spatial concentrations of galaxies in different color"
it is not vet. possible to sav whether the subpulse crifting continues in the weak nioce.,it is not yet possible to say whether the subpulse drifting continues in the weak mode.
 The main results of this work are as follows: l., The main results of this work are as follows: 1.
 The nulls' in the pulses from PSR 34 are not true “nulls” and the pulsar presents strong and. weak emission modes at 1374 MlIGHT., The `nulls' in the pulses from PSR $-$ 34 are not true `nulls' and the pulsar presents strong and weak emission modes at 1374 MHz.
 In its strong emission mocle. the radiation extends through the whole pulse period. and region Lis stronger than region LLL at this frequency.," In its strong emission mode, the radiation extends through the whole pulse period, and region I is stronger than region III at this frequency."
 In the weak emission mode. the profile is similar to that observed in the strong mode at low radio frequency. at whieh region Lis the weaker.," In the weak emission mode, the profile is similar to that observed in the strong mode at low radio frequency, at which region I is the weaker."
 2., 2.
 Using a phase-tracking method. the drifting subpulses of the pulsar can be traced through the whole pulse. period.," Using a phase-tracking method, the drifting subpulses of the pulsar can be traced through the whole pulse period."
 Thirteen drift bands have been directly observed. covering the whole longitude. range. ancl the drifting occurs in both directions.," Thirteen drift bands have been directly observed, covering the whole longitude range, and the drifting occurs in both directions."
 3., 3.
 The subpulses in region I and their spacing (75) are wider than those in region LIL, The subpulses in region I and their spacing $P_2$ ) are wider than those in region III.
 These dillerences can be accounted for if the magnetic pole is inclined to the rotation axis by about 0.57., These differences can be accounted for if the magnetic pole is inclined to the rotation axis by about $0.5^\circ$.
 4., 4.
 Regions Land ILE are consistent with radiation from inner and outer cones: in regions LL and IV of longitude. the line-of-sight trajectory cuts through a weak emission region between the two cones.," Regions I and III are consistent with radiation from inner and outer cones; in regions II and IV of longitude, the line-of-sight trajectory cuts through a weak emission region between the two cones."
 5 «Το observed. direction. of drift is à true reversal within the polar cap and is not a product of aliasing with the rotation period., 5 .The observed direction of drift is a true reversal within the polar cap and is not a product of aliasing with the rotation period.
amplitudes 0.5 mmag in the J-band and 70.2 mmae in he Ix-band.,amplitudes $>0.5$ mag in the J-band and $>0.2$ mag in the K-band.
 In Fig. 1..," In Fig. \ref{f1},"
 their datapoints are clearly. offset rom the median rms in both bands., their datapoints are clearly offset from the median rms in both bands.
 The lighteurves exhibit variability on a range of timescales. including continuous variations over days and rapid changes over hours.," The lightcurves exhibit variability on a range of timescales, including continuous variations over days and rapid changes over hours."
 MI three rave been identified in SIZ04 as objects with large amplitude variability in the I-band., All three have been identified in SE04 as objects with large amplitude variability in the I-band.
 Objects no., Objects no.
 22 and xwticular have been observed to be highly. variable in two observing runs in January 2001 and. December 2001., 2 and 33 in particular have been observed to be highly variable in two observing runs in January 2001 and December 2001.
 With our new data from November 2005 we extend. the time xwseline., With our new data from November 2005 we extend the time baseline.
 The large-amplitude variability clearly is of erm nature. sustained over almost vvears.," The large-amplitude variability clearly is of long-term nature, sustained over almost years."
 The complementary ραπ lightcurve for #333. obtained in Februar 2006. shows the same tvpe of variations witha total amplitude of mamag and arms of mmag (sce Fig. 3)).," The complementary I-band lightcurve for 33, obtained in Februar 2006, shows the same type of variations with a total amplitude of mag and a rms of mag (see Fig. \ref{f14}) ),"
 clearly higher than in the references stars in the same field., clearly higher than in the references stars in the same field.
 A fourth object in our field of view shows a lighteurve comparable with the three highly variable objects discussed above. marked as well with a square in Fig. 2..," A fourth object in our field of view shows a lightcurve comparable with the three highly variable objects discussed above, marked as well with a square in Fig. \ref{f2}."
 This source is seen as close companion (separation 2.77) to the xieghter object JO53858.32-02 which is identified: as voung cluster member by 2 based 1609.on optical colours.," This source is seen as close companion (separation 2.7"") to the brighter object J053858.32-021609, which is identified as young cluster member by \citet{2004AJ....128.2316S} based on optical colours."
 The right source J0538-0216 is saturated in most of our images., The bright source J0538-0216 is saturated in most of our images.
 lt was flagged as variable in the CIDA variability survey (?).. which covers timescales [rom days to 5 vears.," It was flagged as variable in the CIDA variability survey \citep{2005AJ....129..907B}, which covers timescales from days to 5 years."
 The I-uid value provided by 2? (rom 1996-98 is numag fainter han the one measured by SEO4 in 2001. another indication or variability.," The I-band value provided by \citet{2004AJ....128.2316S} from 1996-98 is mag fainter than the one measured by SE04 in 2001, another indication for variability."
 Since our photometry for the companion is certainly allected by light from the primary. it is likely that variability from the primary causes the large variations seen in the companion lighteurve.," Since our photometry for the companion is certainly affected by light from the primary, it is likely that variability from the primary causes the large variations seen in the companion lightcurve."
 Lacking an information on cluster membership for the companion. we do not. discuss this object any further.," Lacking an information on cluster membership for the companion, we do not discuss this object any further."
 Jased on the variability characteristics. near-infrared colours. ancl (for 22 and 3£333) strong emission lines in optical spectra. S04 conclude that ongoing accretion is the most likely reason for the strong photometric variations.," Based on the variability characteristics, near-infrared colours, and (for 2 and 33) strong emission lines in optical spectra, SE04 conclude that ongoing accretion is the most likely reason for the strong photometric variations."
 In Sect., In Sect.
 5 we will further explore this scenario based on our near-infrared lightcurves., \ref{ori} we will further explore this scenario based on our near-infrared lightcurves.
 The remaining five variable objects show an rms significantly. increased. in comparison with the median rms. in both bands.," The remaining five variable objects show an rms significantly increased in comparison with the median rms, in both bands."
 In these cases. the total photometric variations are Z;0.2 mmag: the rms Z;0.05 mmag.," In these cases, the total photometric variations are $\la 0.2$ mag; the rms $\la 0.05$ mag."
 Such low-level variability is seen in a number of objects in SEO. including #288 and 3 (but not #117 and #229). and is attributed to the presence of cool spots. co-rotating with the objects.," Such low-level variability is seen in a number of objects in SE04, including 8 and 23 (but not 17 and 29), and is attributed to the presence of cool spots, co-rotating with the objects."
 The rms for all five objects are similar in J- and Ix- (within 001 mmag). as expected for cool spots (?)..," The rms for all five objects are similar in J- and K-band (within $\pm 0.01$ mag), as expected for cool spots \citep{2005A&A...438..675S}."
 In combination with literature results. there is now a sample of 4 c OOri objects with masses close to. or xdow the substellar limit. showing high-level variability and spectroscopic signature of accretion: two in this study 2 and 333). one more in SEOL (the source 3£443). and the object SOriJJ053825.4-024241. discussed by 2..," In combination with literature results, there is now a sample of 4 $\sigma$ Ori objects with masses close to or below the substellar limit, showing high-level variability and spectroscopic signature of accretion: two in this study 2 and 33), one more in SE04 (the source 43), and the object J053825.4-024241 discussed by \citet{2006A&A...445..143C}."
" ALL our have a similar type of lighteurve. consistent with the vpical variability signature of accreting voung stars (e.g.77). making them the very low mass representatives of classical E ""Fauri stars."," All four have a similar type of lightcurve, consistent with the typical variability signature of accreting young stars \citep[e.g.][]{1994AJ....108.1906H,1995A&A...299...89B}, making them the very low mass representatives of classical T Tauri stars."
 If photometric variability is due to spots on the surface of the star. the [lux is expected to be modulated. periodically bv the rotation of the object. (see Sect. 5)).," If photometric variability is due to spots on the surface of the star, the flux is expected to be modulated periodically by the rotation of the object (see Sect. \ref{ori}) )."
 Pherefore. a period search procedure was carricd out for the eight objects identified as being variable in Sect. 4.1..," Therefore, a period search procedure was carried out for the eight objects identified as being variable in Sect. \ref{gen}."
 One main intention here is to verify the periods published. in SEO. in particular for the highly variable anc acereting targets.," One main intention here is to verify the periods published in SE04, in particular for the highly variable and accreting targets."
 bor these objects. superimposed irregular variations. e.g. due o à variable accretion rate. may hamper the detection of a whotometric period. particularly if the irregularities occur on imescales shorter than the rotation period.," For these objects, superimposed irregular variations, e.g. due to a variable accretion rate, may hamper the detection of a photometric period, particularly if the irregularities occur on timescales shorter than the rotation period."
 In these cases. repeated. monitoring is required to disentangle the various contributions to the flux changes and to establish the most ikely rotation period.," In these cases, repeated monitoring is required to disentangle the various contributions to the flux changes and to establish the most likely rotation period."
 The period search is based on the J-bancl data: As shown in Sect. 5..," The period search is based on the J-band data: As shown in Sect. \ref{ori},"
 spots will cause more variability in J- han in Ix-band., spots will cause more variability in J- than in K-band.
 Our procedure combines three independent ests. which are introduced in the following: For more details on these algorithms see SEO4. ?.. and the references therein.," Our procedure combines three independent tests, which are introduced in the following; for more details on these algorithms see SE04, \citet{2005A&A...429.1007S}, and the references therein."
 The lighteurves are prepared. for the period search with a simple e-clipping algorithm to exclude outlicrs., The lightcurves are prepared for the period search with a simple $\sigma$ -clipping algorithm to exclude outliers.
 a) We start the period. search with a Scarele periodogram (7).. claimed. to. retain. the exponential distribution of| peak heights for unevenly sampled datapoints (i.c. the probability to find a peak is 262)=exp(z) with 2 the peak height).," a) We start the period search with a Scargle periodogram \citep{1982ApJ...263..835S}, claimed to retain the exponential distribution of peak heights for unevenly sampled datapoints (i.e. the probability to find a peak is $P(z) = \exp{(z)}$ with $z$ the peak height)."
 7? eive a empirically found: equation to estimate the False Alarm Probability (FAP) from the peak height in the Scarele periodogram. which has been used previously to set thresholds for period searches (e.g.?)," \citet{1986ApJ...302..757H} give a empirically found equation to estimate the False Alarm Probability (FAP) from the peak height in the Scargle periodogram, which has been used previously to set thresholds for period searches \citep[e.g.][]{2005A&A...430.1005L}."
 b) For a robust estimate of the FAP for a given period. we fit the lighteurve with a sine function using a least-square procedure. with with amplitude and. zeropoint as [ree parameters.," b) For a robust estimate of the FAP for a given period, we fit the lightcurve with a sine function using a least-square procedure, with with amplitude and zeropoint as free parameters."
 The variance of the original lighteurve anc the variance after subtraction of the sinewave are compared statistically using the F-test., The variance of the original lightcurve and the variance after subtraction of the sinewave are compared statistically using the F-test.
 If the period is not significant. its subtraction will not alter the noise in the lighteurve in a significant way (2)..," If the period is not significant, its subtraction will not alter the noise in the lightcurve in a significant way \citep{2004A&A...419..249S}."
 The resulting phaseplots. shown in Fig.," The resulting phaseplots, shown in Fig."
 4 for the best. periods. also allow us to check the periods visually.," \ref{f3} for the best periods, also allow us to check the periods visually."
 c) The CLEAN algorithm by 7. deconvolves the original periodogram and the window function and thus cleans’ the spectrum. [rom sidelobes. ancl aliases., c) The CLEAN algorithm by \citet{1987AJ.....93..968R} deconvolves the original periodogram and the window function and thus 'cleans' the spectrum from sidelobes and aliases.
 Phe. procedure. can therefore be used to distinguish between spurious features, The procedure can therefore be used to distinguish between spurious features
oe disturbed.,be disturbed.
 The big differences between the values of he velocities of the particles [rom the diferent sides. of he tangential cliscontinuity will lead to the erowth of the instabilities and the two winds will be macroscopically mixec )etween the shocks., The big differences between the values of the velocities of the particles from the different sides of the tangential discontinuity will lead to the growth of the instabilities and the two winds will be macroscopically mixed between the shocks.
 The results of numerical. caleulations of lgumenshchey (1997) verified. such a picture., The results of numerical calculations of Igumenshchev (1997) verified such a picture.
 Then the leavy non relativistic wind slows down the volumes fille w the relativistic electrons ancl positrons and they acquire essentially non relativistic byelrodyvnamic draft velocity 0; along the shock while the energy of electrons ancl positrons does not changes significantlv., Then the heavy non relativistic wind slows down the volumes filled by the relativistic electrons and positrons and they acquire essentially non relativistic hydrodynamic drift velocity $v_{d}$ along the shock while the energy of electrons and positrons does not changes significantly.
" With the decrease of the hyedrodsnamic: velocity of the relativistic plasma the time which it spends near the optical star increases in efe, times.", With the decrease of the hydrodynamic velocity of the relativistic plasma the time which it spends near the optical star increases in $c/v_d$ times.
" The eof small drift. velocity as applied to the svstem ""noL51617303 was MNdiscussed by D'Ereves (1981) The parameter Arr~ thus can be large enough to overcome the discrepancy. udbetween the simple theory and observations."," The idea of small drift velocity as applied to the system $LSI$ $61^{\circ }303$ was discussed by Treves (1981) The effective transformation parameter $K_{eff}\sim
\frac c{v_d}K$ thus can be large enough to overcome the discrepancy between the simple theory and observations."
 Under the assumption of the power law οποιον distribution of the positrons after he shock relativisticandelectronstheiranclisotropicM—7=cle velocity distribution we can estimate the intensitv of the X-ray radiation from the svstem., Under the assumption of the power law energy distribution of the relativistic electrons and positrons after the shock }$ and their isotropic velocity distribution we can estimate the intensity of the X-ray radiation from the system.
 Such a distribution can be either he result of the particle acceleration on the shock or in the case of the intrinsic power law distribution of the electrons and positrons in the pulsar wind and thin collisionless shock. xwsing which the relativistic particles do not change their energy. distribution.," Such a distribution can be either the result of the particle acceleration on the shock or in the case of the intrinsic power law distribution of the electrons and positrons in the pulsar wind and thin collisionless shock, passing which the relativistic particles do not change their energy distribution."
 Lets consider an clement of volume dV. filled with the relativistic plasma locating in the shock on a distance. /? rom the Be star., Lets consider an element of volume $dV$ filled with the relativistic plasma locating in the shock on a distance $R$ from the Be star.
" In the case of the relativistic electrons and positrons isotropic distribution the number of particles »oduces the photons with energy 5 moving in the direction of⋅ the observer in. à unit. solid.. angle is 2004N——SUuο=sectionV5AN,dcosGods=4ANστα. cos@)dedma (see 2.2)."," In the case of the relativistic electrons and positrons isotropic distribution the number of particles produces the photons with energy $\varepsilon $ moving in the direction of the observer in a unit solid angle is $\frac{dN_{e^{\pm }}}{%
d\gamma }\frac{d\Omega }{4\pi }d\gamma =0.5\frac{dN_{e^{\pm }}}{d\gamma }%
d\cos \theta _2d\gamma =\frac 12\frac{dN_{e^{\pm }}}{d\gamma }\frac \omega
{\varepsilon ^2}\left( 1-\cos \theta \right) d\varepsilon d\gam ma (see section 2.2)."
 Then according to (S.. 9.. 10)) the number— of photons coming to the observer in the unit of time per unit square per MeV is where @ is a photon scattering angle.," Then according to \ref{def}, \ref{sigm}, \ref{enscat}) ) the number of photons coming to the observer in the unit of time per unit square per MeV is where $\theta $ is a photon scattering angle."
 For the simplicity we take the photon density along the shock constant and equal to the one at a distance Po=LO Mem. The factor ;iV can be estimated. [rom the energy. conservation law bv equating the energy. enters the shock per second {νο παπά the energy leaving the shock por second AVnmeent2fats2). where © is the solid angle under which the shock wave is seen from the pulsar.," For the simplicity we take the photon density along the shock constant and equal to the one at a distance $%
R=10^{13}c m. The factor $AV$ can be estimated from the energy conservation law by equating the energy enters the shock per second $L_p\Omega /4\pi $ and the energy leaving the shock per second $AVmc^2v_d\gamma _{min}^{2-s}/a(s-2)$, where $\Omega $ is the solid angle under which the shock wave is seen from the pulsar."
 Thus we have AVLuOa(s9]Anceqsunniin," Thus we have $AV\sim L_p\Omega a(s-2)/4\pi mc^2v_d\gamma
_{min}^{2-s}$."
" Then integrating (25)) over the volume of the shock we have for theIN Lor 5i10.52.4.D2kpc.e,; =107em/s we have while the observable value of the radiation at a 100 keV is 2.810μηκο/MeV."," Then integrating \ref{dn}) ) over the volume of the shock we have for the $N$ For $\gamma _{min}=10,s=2.4,D=2$ $,v_d=10^8$ cm/s we have while the observable value of the radiation at a 100 keV is $2.8\times
10^{-3}ph/s/cm^2/MeV$."
 Thus if the small drift velosity is taken into account it is possible to explain the observed spectral shape and intensity of the N-rav. radiation., Thus if the small drift velosity is taken into account it is possible to explain the observed spectral shape and intensity of the X-ray radiation.
 Lt is also worth to mention that for the particles with bie Lorentz actors 25.60476 the assumption of constant Lorentz factor will be not. valid due to the inverse Compton losses and the σα in the photon speciram will appear., It is also worth to mention that for the particles with big Lorentz factor $\gamma >\gamma _{*}v_d/c$ the assumption of constant Lorentz factor will be not valid due to the inverse Compton losses and the break in the photon spectrum will appear.
 Ehe break in the ohoton spectrum at i=ws205/c. will appear., The break in the photon spectrum at $\varepsilon =\omega \gamma _{*}^2v_d^2/c^2$ will appear.
The index of he photon spectrum after the break will be bigger then the original one at 1/2., The index of the photon spectrum after the break will be bigger then the original one at 1/2.
 It can be also seen from (25)) that the ocus elfect will take place - the intensity of the radiation is proportional to the (1cos@)'t2Panel thus the major xwt of the radiation will be emitted toward the direction of he optical star., It can be also seen from \ref{dn}) ) that the focus effect will take place - the intensity of the radiation is proportional to the $(1-\cos \theta )^{(1+s)/2}$ and thus the major part of the radiation will be emitted toward the direction of the optical star.
 We are grateful to V.M.Ixaspi and M.Favani for valuable comments and to V.S.Deskin and Ya., We are grateful to V.M.Kaspi and M.Tavani for valuable comments and to V.S.Beskin and Ya.
N.Istomin for helpful discussions.,N.Istomin for helpful discussions.
 This work is supported in part bv the IUEDIR erant 97-02-16975 and the Cariplo Foundation for Scientific Research., This work is supported in part by the RFBR grant 97-02-16975 and the Cariplo Foundation for Scientific Research.
core than to a cusp.,core than to a cusp.
 This is in the limit of zero disk mass., This is in the limit of zero disk mass.
 As one begins to make allowance for the stars. then the amount of rotation attributable to the dark matter is reduced. further reducing the allowed cusp slope.," As one begins to make allowance for the stars, then the amount of rotation attributable to the dark matter is reduced, further reducing the allowed cusp slope."
 There has been considerable coutroversy over this issue. with much discussion of how beam simeariug in 21 cin data wight hide a cusp (e.g.. van deu Bosch Swaters 2000).," There has been considerable controversy over this issue, with much discussion of how beam smearing in 21 cm data might hide a cusp (e.g., van den Bosch Swaters 2000)."
 The new high resolution Πα data address this issue directly (de Blok et 22001: see also Blais-Oullette et 22001: Salucci 2001: Borricllo Salucci 2001: Cotté et 22000)., The new high resolution $\al$ data address this issue directly (de Blok et 2001; see also Blais-Oullette et 2001; Salucci 2001; Borriello Salucci 2001; Côtté et 2000).
 33 shows the cusp slopes derived from IIo data as à function of pliysical resolution., 3 shows the cusp slopes derived from $\al$ data as a function of physical resolution.
 Resolution has the opposite effect from what is iuplied by van deu Bosch Swaters (2000)., Resolution has the opposite effect from what is implied by van den Bosch Swaters (2000).
 It is only the dai which are poorly resolved which are consistent with a cusp., It is only the data which are poorly resolved which are consistent with a cusp.
 Such data are also consistent with a coustaut density core with a modest (—1 kpc) core radius., Such data are also consistent with a constant density core with a modest $\sim 1$ kpc) core radius.
4. Ou the other hand. those objects which are well resolved strouglv prefer à=0 over a<|.," On the other hand, those objects which are well resolved strongly prefer $\alpha = 0$ over $\al \le -1$."
 the data are cousistent with a=0. while of the best resolved data tolerate a significant cusp.," the data are consistent with $\al = 0$, while of the best resolved data tolerate a significant cusp."
 The inner slope à shown in 33 has beeu derived in the Πιτ of zero disk. mass., The inner slope $\al$ shown in 3 has been derived in the limit of zero disk mass.
 Once allowance is made for the stars. the situation for cusps becomes even worse.," Once allowance is made for the stars, the situation for cusps becomes even worse."
 While there may be very good theoretical reasons to expect cuspy halos. there is no guarautee that reality will be cooperative.," While there may be very good theoretical reasons to expect cuspy halos, there is no guarantee that reality will be cooperative."
 The cusp-core problemi is geuuinc., The cusp-core problem is genuine.
 Rotation curves provide strong constraüiuts on the radial potential iu disk ealaxies., Rotation curves provide strong constraints on the radial potential in disk galaxies.
 This iu turn coustrains the mass aud distribution of the liminous aud dark componenuts of these galaxies., This in turn constrains the mass and distribution of the luminous and dark components of these galaxies.
 Disk masses consistent with those expected for stellar populations are cousistent with the dynamical data. provided halos have constant deusity cores rather than cusps.," Disk masses consistent with those expected for stellar populations are consistent with the dynamical data, provided halos have constant density cores rather than cusps."
 Cuspy halos require abnormally low stellar mnass-to-lieht ratios. aud are strouely at odds with uch of the data even in the extreme limit TY.>0.," Cuspy halos require abnormally low stellar mass-to-light ratios, and are strongly at odds with much of the data even in the extreme limit $\Upsilon_* \rightarrow 0$."
 Tam nost erateful to mv collaborators. Vera Rubin aud Erwin de Blok. for their long. concerted. and ultimately fruitful efforts.," I am most grateful to my collaborators, Vera Rubin and Erwin de Blok, for their long, concerted, and ultimately fruitful efforts."
 E thank Albert Bosnia and Joey Sellwood for their attempts to inject some sanity iuto the debate over disk masses and cuspy halos., I thank Albert Bosma and Jerry Sellwood for their attempts to inject some sanity into the debate over disk masses and cuspy halos.
 All of us who attended this most cutertaining workshop owe a great debt of gratitude to its organizers. especially Priva Natarajan.," All of us who attended this most entertaining workshop owe a great debt of gratitude to its organizers, especially Priya Natarajan."
 The work of SSM is supported in part by NSF evant AST99001663., The work of SSM is supported in part by NSF grant AST9901663.
discrepaney is due to a combination of cloud. deformation. hivelrodvnamical instabilities anc condensation of cooling eas.,"discrepancy is due to a combination of cloud deformation, hydrodynamical instabilities and condensation of cooling gas."
 This can be inferred. from Fig. 4..," This can be inferred from Fig. \ref{fig:cloud_centroid},"
 which shows the centroid velocity for the dissipative (stars) ancl acliabatic (plus signs) standard. simulations with ey=200kms (top). ey=l00kms (centre) and ry=T5kms (bottom).," which shows the centroid velocity for the dissipative (stars) and adiabatic (plus signs) standard simulations with $v_0= 200 \kms$ (top), $v_0 = 100 \kms$ (centre) and $v_0= 75 \kms$ (bottom)."
 It is clear that the analytic formula (solid line in cach diagram) is a goocl description of the general behaviour of cold gas motion over 60Myr only when the cooling is not. allowed. and the initial relative speed. is sullicientlv low (see bottom panel in the figure)., It is clear that the analytic formula (solid line in each diagram) is a good description of the general behaviour of cold gas motion over $\sim 60 \Myr$ only when the cooling is not allowed and the initial relative speed is sufficiently low (see bottom panel in the figure).
 When these conditions are not satisfied. the analytic formula fails. after. some tme. maink because Ixelvin-Helmholtz. instability strips some cold. eas and the ram pressure progressively. squashes the cloud. increasing its cross-section.," When these conditions are not satisfied, the analytic formula fails after some time, mainly because Kelvin-Helmholtz instability strips some cold gas and the ram pressure progressively squashes the cloud increasing its cross-section."
 The net effect is an enhancement of drag elfectiveness (see equation 2))., The net effect is an enhancement of drag effectiveness (see equation \ref{eq:tdrag}) ).
 Let us now compare the evolution of the centroid velocity in the presence and in the absence of cooling., Let us now compare the evolution of the centroid velocity in the presence and in the absence of cooling.
 First. Π must be noticed that in normalised units (ey for velocities and 4/05 for times. shown in the right and. upper axes in the diagrams in Fig. 4))," First, it must be noticed that in normalised units $v_0$ for velocities and $R_{\rm cl}/v_0$ for times, shown in the right and upper axes in the diagrams in Fig. \ref{fig:cloud_centroid}) )"
 the evolution of the centroic velocity is basically the same in all the acllabatic simulations (in the overlapping normalised time intervals)., the evolution of the centroid velocity is basically the same in all the adiabatic simulations (in the overlapping normalised time intervals).
 In particular. the deviation from the analytic estimate becomes apparen at roughly the same normalised time and it can be ascribec mainlv to the Dlattening of the main body of the cloud.," In particular, the deviation from the analytic estimate becomes apparent at roughly the same normalised time and it can be ascribed mainly to the flattening of the main body of the cloud."
 On the other hand. in the presence. of cooling the deviation of the cloud. speed. from the analytic estimate occurs a roughly the samephysicad time (20Myr) for all explores initial speeds.," On the other hand, in the presence of cooling the deviation of the cloud speed from the analytic estimate occurs at roughly the same time $\sim 20 \Myr$ ) for all explored initial speeds."
 In. these dissipative cases the amount. of eas that transfers from the hot to the cold phase has an appreciable impact on the eentroicl velocity. so we are no longer merely looking at the slowing of the original cloud. ancl the deceleration is dominated by condensation ofcooling material that was originally at rest.," In these dissipative cases the amount of gas that transfers from the hot to the cold phase has an appreciable impact on the centroid velocity, so we are no longer merely looking at the slowing of the original cloud, and the deceleration is dominated by condensation of cooling material that was originally at rest."
 We now turn to the momentum transferred to the hot gas., We now turn to the momentum transferred to the hot gas.
" In the simulations. the total momentum. of the hot gas is computed. by summing. over the whole computational domain. the momentum of the cells containing gas at Tom10""R."," In the simulations, the total momentum of the hot gas is computed by summing, over the whole computational domain, the momentum of the cells containing gas at $T > 10^6\K$."
 Figure 5. shows the amount of momentunm. along the clouds direction of motion .r. acquired. by the hot gas as a function of time for the dissipative (stars) ancl adiabatic (plus signs) standard simulations with ey=200.100.75kms. +.," Figure \ref{fig:totalmom200} shows the amount of momentum, along the cloud's direction of motion $x$, acquired by the hot gas as a function of time for the dissipative (stars) and adiabatic (plus signs) standard simulations with $v_0=200,\,100,\,75 \kms$ ."
 From these diagranis it is apparent that the hot eas gains less momentum in the presence than in the absence of radiative cooling., From these diagrams it is apparent that the hot gas gains less momentum in the presence than in the absence of radiative cooling.
 Phe ratio between the final coronal momentum in the dissipative and in the acliahatic simulations is OS when ey=200kms (top panel). ~0.5 when ry=l100kms+ (miclelle panel). and. &0.1 when ο=75kms1 (bottom panel).," The ratio between the final coronal momentum in the dissipative and in the adiabatic simulations is $\sim0.8$ when $v_0 = 200\kms$ (top panel), $\sim0.5$ when $v_0 = 100\kms$ (middle panel), and $\lsim 0.1$ when $v_0 =
75\kms$ (bottom panel)."
 In. particular. when Dy=Tokmso the momentum transferred. from the cold eas to the corona. after an initial phase of erowth lasting or 20Mvr. settles to a nearly constant value: [roni hat moment onwards. the momentum. transferred. to the Corona is Consistent with zero.," In particular, when $v_0 = 75\kms$ the momentum transferred from the cold gas to the corona, after an initial phase of growth lasting for $\sim 20\Myr$, settles to a nearly constant value: from that moment onwards, the momentum transferred to the corona is consistent with zero."
 Thus. the sipulations indicate he existence of a vi below which the ransfer of momentum from the cold. clouds to the corona is suppressed.," Thus, the simulations indicate the existence of a $v_{\rm th}$ below which the transfer of momentum from the cold clouds to the corona is suppressed."
 Given that the cloud keeps losing monentum (is. 4)), Given that the cloud keeps losing momentum (Fig. \ref{fig:cloud_centroid}) )
 and the total momentum is conserved. it. follows hat the momentum lost by the cloud is retained by the coronal gas. which is progressively cooling onto the cloucl’s wake.," and the total momentum is conserved, it follows that the momentum lost by the cloud is retained by the coronal gas, which is progressively cooling onto the cloud's wake."
 The measure of the momentum transferred. from the cold to the hot gas can be allected by the How of coronal gas (ancl associated momentum) through the open boundaries of the computational domain., The measure of the momentum transferred from the cold to the hot gas can be affected by the flow of coronal gas (and associated momentum) through the open boundaries of the computational domain.
 This clflect becomes non- only in the last 10Myr of the simulations. so we take ~50Myr as final time. as far as the measure of the," This effect becomes non-negligible only in the last $\sim 10\Myr$ of the simulations, so we take $\sim 50\Myr$ as final time, as far as the measure of the"
Lick2 data among the others in the analyses.,Lick2 data among the others in the analyses.
" We also note that the same inconsistency remains for the AFOE data when using the three-companion model Af,: in the analyses."," We also note that the same inconsistency remains for the AFOE data when using the three-companion model $\mathcal{M}_{I,3}$ in the analyses."
 Therefore. as also noted by Curieletal.(2011).. we conclude that the AFOE data has additional biases and should not be used together with the rest of the data because the results would be prone to biases as well.," Therefore, as also noted by \citet{curiel2011}, we conclude that the AFOE data has additional biases and should not be used together with the rest of the data because the results would be prone to biases as well."
 To further demonstrate the inconsistency of the AFOE data and the other data sets. we show the RV residuals of the AFOE data when the three-companion model has been used to analyse the combined data of AFOE. Lickl. ELODIE. HET. and HJS (Fig. 3)).," To further demonstrate the inconsistency of the AFOE data and the other data sets, we show the RV residuals of the AFOE data when the three-companion model has been used to analyse the combined data of AFOE, Lick1, ELODIE, HET, and HJS (Fig. \ref{AFOE_bias}) )."
 These residuals appear to show a low- periodicity that roughly corresponds to the period of companion d. despite the fact that the signal of this companion (and those of b and ο) has been subtracted.," These residuals appear to show a low-amplitude periodicity that roughly corresponds to the period of companion d, despite the fact that the signal of this companion (and those of b and c) has been subtracted."
 We continue the analyses of v And RV's by neglecting the AFOE data and by using the older Lickl data set (Fischeretal.. 2003). because of the inconsistencies of the AFOE and Lick? data with the rest of the data sets.," We continue the analyses of $\upsilon$ And RV's by neglecting the AFOE data and by using the older Lick1 data set \citep{fischer2003}, because of the inconsistencies of the AFOE and Lick2 data with the rest of the data sets."
 The combined data set consists of Lickl. HET. ELODIE. and HJS data that contain 248. 79. 7]. and 41 measurements. respectively.," The combined data set consists of Lick1, HET, ELODIE, and HJS data that contain 248, 79, 71, and 41 measurements, respectively."
 This combined data set with 439 measurements was analysed using two models. namely. At;s and At;4. because there are clearly three strong Keplerian signals in the data as demonstrated already by Butleretal.(1999).. and because the noise levels of the different data sets likely differ from one another based on the previous analyses.," This combined data set with 439 measurements was analysed using two models, namely, $\mathcal{M}_{I,3}$ and $\mathcal{M}_{I,4}$, because there are clearly three strong Keplerian signals in the data as demonstrated already by \citet{butler1999}, and because the noise levels of the different data sets likely differ from one another based on the previous analyses."
 Since we removed the AFOE data from the analyses. we need to assess whether the resulting restricted data set can be shown inadequate or not.," Since we removed the AFOE data from the analyses, we need to assess whether the resulting restricted data set can be shown inadequate or not."
 For this purpose. we re-calculate the values in Table 6 and show them in Table 7..," For this purpose, we re-calculate the values in Table \ref{dataset_inconsistency} and show them in Table \ref{dataset_inconsistency2}."
 According to these results. none of the four data sets can be said to conflict with the others.," According to these results, none of the four data sets can be said to conflict with the others."
 Also. using the Bayesian model inadequacy for multiple data sets by calculating BGnj.iin). where mj.i=]..... 4. correspond to Lick1. ELODIE. HJS. and HET data sets. respectively. we receive a value of 1.35x10?. which means that these sets are inconsistent with a probability of less than 10? given the four-companion model.," Also, using the Bayesian model inadequacy for multiple data sets by calculating $B(m_{1}, ..., m_{4})$, where $m_{i}, i=1, ..., 4$ , correspond to Lick1, ELODIE, HJS, and HET data sets, respectively, we receive a value of $\times 10^{9}$, which means that these sets are inconsistent with a probability of less than $10^{-9}$ given the four-companion model."
 Therefore. these four sets can be combined reliably and we calculate our final solution of v And RV's using these four sets.," Therefore, these four sets can be combined reliably and we calculate our final solution of $\upsilon$ And RV's using these four sets."
 The posterior probability of the model Λιν ts less than 10? of the probability of model At;;.," The posterior probability of the model $\mathcal{M}_{I,3}$ is less than $10^{-8}$ of the probability of model $\mathcal{M}_{I,4}$."
 This implies that there are indeed four periodic signals in the combined data set., This implies that there are indeed four periodic signals in the combined data set.
 The revised orbital parameters with respect to the four-companions model are shown in Table 8.., The revised orbital parameters with respect to the four-companions model are shown in Table \ref{upsAnd_parameters}.
 The RV variations corresponding to the longest periodicity in the data are shown in Fig., The RV variations corresponding to the longest periodicity in the data are shown in Fig.
 4 together with the fitted Keplerian signal., \ref{upsAnd_signal} together with the fitted Keplerian signal.
 The signals of the three inner companions have been subtracted from the residuals in Fig. 4.., The signals of the three inner companions have been subtracted from the residuals in Fig. \ref{upsAnd_signal}. .
 When comparing the orbital parameters of our solution in Table 8 with the solution of Curieletal.(2011).. if can be seen that the period of the »And e is significantly lower inour solution.," When comparing the orbital parameters of our solution in Table \ref{upsAnd_parameters} with the solution of \citet{curiel2011}, it can be seen that the period of the $\upsilon$And e is significantly lower inour solution."
 We received à MAP estimate for the orbital period of 2860 days (20999=[2600. 3220]). whereas," We received a MAP estimate for the orbital period of 2860 days $\mathcal{D}_{0.99} = [2600, 3220]$ ), whereas"
handlling and those of bolometric detectors in terms of sensitivity.,ling and those of bolometric detectors in terms of sensitivity.
infinity and. downstream are much larger than for ordinary shocks. so that the downstream turns out to be denser but colder than in the linear case.,"infinity and downstream are much larger than for ordinary shocks, so that the downstream turns out to be denser but colder than in the linear case."
 The missing energy. ends up in the form of accelerated. particles., The missing energy ends up in the form of accelerated particles.
 The effect of suppression of the heating in cosmic ray modified shocks also appears in the spectra of the particles (thermal plus non-thermal) in the shock vicinity., The effect of suppression of the heating in cosmic ray modified shocks also appears in the spectra of the particles (thermal plus non-thermal) in the shock vicinity.
 In Fig., In Fig.
" 12 we show these spectra (including the maxwellian thermal imp) for uy25LOems5 £=3,5 and pusfme=10."," \ref{fig:spec} we show these spectra (including the maxwellian thermal bump) for $u_0=5\times 10^8~\rm cm~s^{-1}$, $\xi=3.5$ and $p_{max}/mc = 10^5$."
 The vertical dashed line shows the position of the hermal peak as expected in the absence of accelerated xwticles., The vertical dashed line shows the position of the thermal peak as expected in the absence of accelerated particles.
 In fact this position should depend on the Mach number. but the dependence is very. weak for large Mach numbers.," In fact this position should depend on the Mach number, but the dependence is very weak for large Mach numbers."
 The positions of the thermal peaks clearly show he elect of cooler downstream gases for modified shocks., The positions of the thermal peaks clearly show the effect of cooler downstream gases for modified shocks.
" At the same time. the clleet is accompanied by increasingly more modified spectra of accelerated particles. with most of he energy pushed toward the highest momenta,"," At the same time, the effect is accompanied by increasingly more modified spectra of accelerated particles, with most of the energy pushed toward the highest momenta."
 The cllicieney of the first order Fermi acceleration. at shock fronts depends in a crucial way upon details of the mechanism that determines the injection of a small fraction of the particles from the thermal pool to thebor., The efficiency of the first order Fermi acceleration at shock fronts depends in a crucial way upon details of the mechanism that determines the injection of a small fraction of the particles from the thermal pool to the.
 In reality the processes of formation of a collisionless shock wave. of plasma heating and particle acceleration are expected to be all parts of the same problem. though on different spatial scales.," In reality the processes of formation of a collisionless shock wave, of plasma heating and particle acceleration are expected to be all parts of the same problem, though on different spatial scales."
 We hide our lack of knowledge of the microphysics of the shock structure in a simple recipe or injection. in which the particles that take part in the acceleration process are those that have momentum larger wea factor £ than the momentum of the thermal particles in the downstream Iuid.," We hide our lack of knowledge of the microphysics of the shock structure in a simple recipe for injection, in which the particles that take part in the acceleration process are those that have momentum larger by a factor $\xi$ than the momentum of the thermal particles in the downstream fluid."
 This is motivated by the fact that or collisionless shocks the thickness of the shock surface is determined. by the gvromotion of the bulk of the thermal xwlicles., This is motivated by the fact that for collisionless shocks the thickness of the shock surface is determined by the gyromotion of the bulk of the thermal particles.
 We estimated that £24., We estimated that $\xi\sim 2-4$.
 This recipe implies hat the fraction of particles that get accelerated. is rather small (0.0110. 7)., This recipe implies that the fraction of particles that get accelerated is rather small $0.01-10^{-5}$ ).
 We implemented. this recipe in a calculation. of the non-linear reaction of cosmic ravs on the shock structure proposed by. Blasi (2002. 2004).," We implemented this recipe in a calculation of the non-linear reaction of cosmic rays on the shock structure proposed by Blasi (2002, 2004)."
 Similarly to other models. also this approach shows the appearance of multiple solutions. for a wide choice of the parameters ofthe problem.," Similarly to other models, also this approach shows the appearance of multiple solutions, for a wide choice of the parameters of the problem."
 When the simple mocel of particle injection is used. this phenomenon is drastically reduced: the multiple solutions disappear for most of the parameter space. and when they appear they look as narrow strips in the parameter space. at the boundary between unmodified ancl mocdified. shocks.," When the simple model of particle injection is used, this phenomenon is drastically reduced: the multiple solutions disappear for most of the parameter space, and when they appear they look as narrow strips in the parameter space, at the boundary between unmodified and modified shocks."
 We argued that this result suggests that the narrow regions may signal the transition between two stable solutions. ithough this needs further confirmation through detailed analyses of the stability of the solutions.," We argued that this result suggests that the narrow regions may signal the transition between two stable solutions, although this needs further confirmation through detailed analyses of the stability of the solutions."
 This interpretation scons to be supported in part by the calculations of Mond Drury (1998). that showed that when three solutions are present. the intermediate one is indeed: unstable for small corrugations of the shock front.," This interpretation seems to be supported in part by the calculations of Mond Drury (1998), that showed that when three solutions are present, the intermediate one is indeed unstable for small corrugations of the shock front."
 Vhis calculations was however performed in the context ofa two-Duid model. while an investigation of the stability for kinetic models is still lacking.," This calculations was however performed in the context of a two-fluid model, while an investigation of the stability for kinetic models is still lacking."
"nature of the power source (although commonly taken to be an AGN in these cases), nor","nature of the power source (although commonly taken to be an AGN in these cases), nor"
One of the most ambitious experiments of next-generation radio-telescopes. such as the newly inauguratecl Low Frequeney Array (LOLVAR) ancl the future Square Ixilometre Array (SILA) ds to explore the nature of the dynamic radio sky at timescales ranging [from nanoseconds to vears.,"One of the most ambitious experiments of next-generation radio-telescopes, such as the newly inaugurated Low Frequency Array (LOFAR) and the future Square Kilometre Array (SKA) is to explore the nature of the dynamic radio sky at timescales ranging from nanoseconds to years."
 Surveys for very fast radio transients necessarily eencrate huge amounts of data. making storage ancl oll-line processing an unattractive solution.," Surveys for very fast radio transients necessarily generate huge amounts of data, making storage and off-line processing an unattractive solution."
 On the other hand. real-time processing ollers the possibilitv to react as fast as possible and conduct. follow-up observations across the electromagnetic spectrum and even. for some events. with eravitational wave detectors.," On the other hand, real-time processing offers the possibility to react as fast as possible and conduct follow-up observations across the electromagnetic spectrum and even, for some events, with gravitational wave detectors."
 Here we will consider the case where time-series data (tied-array. or bezm-ormed. data for array telescopes mentioned. above) are processed to extract astrophysical radio bursts of short duration.," Here we will consider the case where time-series data (tied-array, or beam-formed data for array telescopes mentioned above) are processed to extract astrophysical radio bursts of short duration."
 The multitude of potential astrophysical events that. may. produce. such ransients. ranging from individual pulses from neutron stars o Lorimer bursts (2)... are discussed in ?..," The multitude of potential astrophysical events that may produce such transients, ranging from individual pulses from neutron stars to Lorimer bursts \citep{lorimer2007}, are discussed in \cite{cm04}."
 In this paper we will mostly be concerned. with de-dispersion., In this paper we will mostly be concerned with de-dispersion.
 This refers to a family of techniques emploved o reverse the frequeney-dependent refractive effect. of the interstellar medium. (LSAT) on the radio signals passing hrough it., This refers to a family of techniques employed to reverse the frequency-dependent refractive effect of the interstellar medium (ISM) on the radio signals passing through it.
 We also use interstellar scattering to constrain he parameter space of a given search - see (7.chapter4). for more details on these effects., We also use interstellar scattering to constrain the parameter space of a given search - see \citep[chapter 4]{LorimerKramer2005} for more details on these effects.
 From pulsar studies. it is well determined that. propagation through the ISAT obews the cold. plasma cispersion lav. where the time-delay between two frequencies fy and f» is given by the quadratic relation where DM is the dispersion measure in peem. and. fi and fo are in MlIz.," From pulsar studies, it is well determined that propagation through the ISM obeys the cold plasma dispersion law, where the time-delay between two frequencies $f_1$ and $f_2$ is given by the quadratic relation where DM is the dispersion measure in $\text{pc cm}^{-3}$ and $f_1$ and $f_2$ are in MHz."
 Astrophysical objects have a particular DAL value associated with them. which depends on the total amount of free electrons along the line of sight. ancl. therefore. on the distance to the object from Earth.," Astrophysical objects have a particular DM value associated with them, which depends on the total amount of free electrons along the line of sight and, therefore, on the distance to the object from Earth."
 Removing the οσοι of dispersion from. astrophysica data is typically done in two wavs. depending on the type of data ancl the requirements of the experiment.," Removing the effect of dispersion from astrophysical data is typically done in two ways, depending on the type of data and the requirements of the experiment."
 For tota power filterbank data. where the spectral bandwidth: of the observation is twpically split into a number of narrow frequeney channels. de-clispersion consists of a relative shif in time of all frequency channels according to equation 1..," For total power filterbank data, where the spectral bandwidth of the observation is typically split into a number of narrow frequency channels, de-dispersion consists of a relative shift in time of all frequency channels according to equation \ref{dispRelationshipEquation}."
 This is known as incoherent cle-dispersion as it is performec on incoherent data., This is known as incoherent de-dispersion as it is performed on incoherent data.
 For baseband data. cle-dispersion can be cone by convolution of the observed voltage data with the inverse of the transfer function of the ISM.," For baseband data, de-dispersion can be done by convolution of the observed voltage data with the inverse of the transfer function of the ISM."
 This is known as coherent. de-dispersion: it is more accurate in terms of recovering the intrinsic shape of the astrophysical signal rut much more demanding in computational power., This is known as coherent de-dispersion; it is more accurate in terms of recovering the intrinsic shape of the astrophysical signal but much more demanding in computational power.
 In this uper. we deal with incoherent de-dispersion. applied. to otal power data.," In this paper, we deal with incoherent de-dispersion, applied to total power data."
 De-cispersion is an expensive operation. scaling as for brate-force algorithms. with more optimized O(N?)echniques diminishing this to OQ(Νίοδν," De-dispersion is an expensive operation, scaling as $\mathcal{O}\left(N^2\right)$ for brute-force algorithms, with more optimized techniques diminishing this to $\mathcal{O}\left(Nlog(N)\right)$."
 For. any Xind. fast transient search. de-dispersion. needs. to. be »erformed over a range of DM values. practically multiplving," For any blind, fast transient search, de-dispersion needs to be performed over a range of DM values, practically multiplying"
the running median with a box-car size of 100 points.,the running median with a box-car size of 100 points.
 The thin solid line shows the colours in these filters for the model atmospheres of Bessell et al. (, The thin solid line shows the colours in these filters for the model atmospheres of Bessell et al. (
1998).,1998).
" As discussed in PaperII, the « 0.1mmag discrepancy between models and observations around V—1~0.5 is most likely due to the coarse spectral sampling of the Ho line in the models."," As discussed in I, the $< 0.1$ mag discrepancy between models and observations around $V-I\simeq 0.5$ is most likely due to the coarse spectral sampling of the $\alpha$ line in the models."
" Where the density of observed points decreases considerably, at V-I>1.2, we reduced the box-car size to 10 points and the result is shown by the thick dot-dashed line (which is extrapolated for V—1I> 2)."," Where the density of observed points decreases considerably, at $V-I > 1.2$, we reduced the box-car size to 10 points and the result is shown by the thick dot-dashed line (which is extrapolated for $V-I>2$ )."
 A total of 891 objects have a V—Ha index that of the reference template exceedingat the same V—/ colour by more than four times the uncertainty on their V—Ha values., A total of 891 objects have a $V-H\alpha$ index exceeding that of the reference template at the same $V-I$ colour by more than four times the uncertainty on their $V-H\alpha$ values.
" A total of 791 objects are left after this conservative selection and they are indicated with large dots in reffig3 (shown in red in the on-line version) and, in light of their V—Ha excess at the 4c level, they are excellent PMS candidates."," A total of 791 objects are left after this conservative selection and they are indicated with large dots in \\ref{fig3} (shown in red in the on-line version) and, in light of their $V-H\alpha$ excess at the $4\,\sigma$ level, they are excellent PMS candidates."
" As we shall see later, most of them are indeed bona-fide PMS stars."," As we shall see later, most of them are indeed bona-fide PMS stars."
" Following the detailed procedure outlined in II, we can derive the Ha emission line luminosity L(Ho) for these stars from the AHa colour corresponding to the excess emission, namely: where the superscript obs refers to the observations andref to the reference template."," Following the detailed procedure outlined in I, we can derive the $\alpha$ emission line luminosity $L(H\alpha)$ for these stars from the $\Delta H\alpha$ colour corresponding to the excess emission, namely: where the superscript refers to the observations and to the reference template."
" L(Ho) is then obtained from AHa, from the photometric zero point and absolute sensitivity of the instrumental set-up and from the distance to the sources.Introduction),"," $L(H\alpha)$ is then obtained from $\Delta
H\alpha$, from the photometric zero point and absolute sensitivity of the instrumental set-up and from the distance to the sources.,"
 whereas the photometric— properties of the instrument are as listed inthe ACS Instrument Handbook (Maybhate et al., whereas the photometric properties of the instrument are as listed inthe ACS Instrument Handbook (Maybhate et al.
 2010)., 2010).
 The derived median Ha luminosity of the 791 objects with Ha excess at the 4o level is 2.7x10?! eerg/s or ~10? LLo.," The derived median $H\alpha$ luminosity of the 791 objects with $\alpha$ excess at the $4\,\sigma$ level is $2.7 \times 10^{31}$ erg/s or $\sim 10^{-2}$$_\odot$ ."
 This value is similar to that, This value is similar to that
"in NGC 839 show a more composite source of ionizing radiation, the line ratios become more Ilregion-like close to the nuclear starbursting region.","in NGC 839 show a more composite source of ionizing radiation, the line ratios become more region-like close to the nuclear starbursting region."
 This behavior is consistent with the line ratio structure seen in M82 and the conclusion of Shopbell&Bland-Hawthorn(1998) that close to the nucleus photoionization by the ongoing starburst begins to dominate., This behavior is consistent with the line ratio structure seen in M82 and the conclusion of \citet{Shopbell98} that close to the nucleus photoionization by the ongoing starburst begins to dominate.
" Finally, observations of NGC 839 by González-Martínetal.(2006) show funnels of soft X-ray emission along the minor axis similar to those seen at much higher spatial resolution in images of M82 (Stricklandetal. 2004)."," Finally, observations of NGC 839 by \citet{GonzalezMartin06} show funnels of soft X-ray emission along the minor axis similar to those seen at much higher spatial resolution in images of M82 \citep{Strickland03}."
. This soft X-ray gas is associated with shocks in the galactic wind and in the case of NGC 839 could be contributing very slightly to the diffuse X-ray emission seen surrounding the entire group by Belsoleetal.(2003)., This soft X-ray gas is associated with shocks in the galactic wind and in the case of NGC 839 could be contributing very slightly to the diffuse X-ray emission seen surrounding the entire group by \citet{Belsole03}.
. Our observations of NGC 839 suggest a link between lower-mass starburst and E+A , Our observations of NGC 839 suggest a link between lower-mass starburst systems and E+A galaxies.
"Although NGC 839 is a fairly low-masssystems system, it galaxies.nonetheless has a large-scale organized rotation, and an elliptical-like (r1/4) luminosity profile (MendesdeOliveiraetal.1998)."," Although NGC 839 is a fairly low-mass system, it nonetheless has a large-scale organized rotation, and an elliptical-like $r^{1/4}$ ) luminosity profile \citep{Mendes98}."
. The stellar population of the outer regions away from the superwind funnels is dominated by a classical E+A spectrum., The stellar population of the outer regions away from the superwind funnels is dominated by a classical E+A spectrum.
 These properties are precisely what has been found by Pracyetal.(2009) in a Gemini Multi-Object Spectrograph IFU study of a sample of 10 nearby (z=0.04— 0.20) E+A galaxies selected from the Two Degree Field Galaxy Redshift Survey., These properties are precisely what has been found by \cite{Pracy09} in a Gemini Multi-Object Spectrograph IFU study of a sample of 10 nearby $z = 0.04-0.20$ ) E+A galaxies selected from the Two Degree Field Galaxy Redshift Survey.
" In their sample, they suggest that the large fraction of fast rotators argues against the hypothesis that equal mass mergers are the dominant progenitor to the E+A population."," In their sample, they suggest that the large fraction of fast rotators argues against the hypothesis that equal mass mergers are the dominant progenitor to the E+A population."
 NGC 839 and its similarity with M82 suggest a simple scenario for the formation of E+A galaxies., NGC 839 and its similarity with M82 suggest a simple scenario for the formation of E+A galaxies.
" In this, we start with a gas-rich low-mass galaxy in a cluster or loose group."," In this, we start with a gas-rich low-mass galaxy in a cluster or loose group."
 This a strong interaction during a close passage with another producesgalaxy., This produces a strong interaction during a close passage with another galaxy.
" In the case of M82 this would have been M81, while in the case of NGC 839 this wasmost probably NGC 838, which has slightly higher IR luminosity (logL/Lc=11.05 versus logaL/Lc=11.01; Armusetal. 2009)), and which also shows a strong nuclear starburst, and evidence of tidal interaction and galactic winds in iimages."," In the case of M82 this would have been M81, while in the case of NGC 839 this wasmost probably NGC 838, which has a slightly higher IR luminosity $\log L/L_{\odot} = 11.05$ versus $\log L/L_{\odot} = 11.01$; \citealt{Armus09}) ), and which also shows a strong nuclear starburst, and evidence of tidal interaction and galactic winds in images."
" This interaction drives the disk gas toward the nucleus, triggering a strong nuclear starburst."," This interaction drives the disk gas toward the nucleus, triggering a strong nuclear starburst."
" When this occurs, the starburst acts as a source of viscosity in the accretion disk (Collin&Zahn1999),, since shocks generated mass loss and shells reduce rotationalby increasingangular momentum in the SN-poweredrotationally trailing ISM, and put more angular momentum into the leading ISM, encouraging the development of a galactic wind."," When this occurs, the starburst acts as a source of viscosity in the accretion disk \citep{Collin99}, since shocks generated by increasing mass loss and SN-powered shells reduce rotational angular momentum in the rotationally trailing ISM, and put more angular momentum into the leading ISM, encouraging the development of a galactic wind."
" The process therefore has the potential to run away, as gas is fed into an ever smaller and denser central region, increasing the specific star formation rate, and driving an ever stronger galactic wind along the lines of Equation (4)."," The process therefore has the potential to run away, as gas is fed into an ever smaller and denser central region, increasing the specific star formation rate, and driving an ever stronger galactic wind along the lines of Equation (4)."
 The rotational velocities give further evidence that gas is currently being fed into the central region., The rotational velocities give further evidence that gas is currently being fed into the central region.
" As shown above in3.2, the gaseous disk shows a rotational maximum at the boundary of the central starburst region and in the vicinity of the dust lanes seen in the image."," As shown above in, the gaseous disk shows a rotational maximum at the boundary of the central starburst region and in the vicinity of the dust lanes seen in the image."
" This could be explicable if the outer ionized disk is not in rotational support, and is still infalling into the central star-forming region."," This could be explicable if the outer ionized disk is not in rotational support, and is still infalling into the central star-forming region."
 A very similar rotation curve was observed in the case of M82 by Shopbell&Bland-Hawthorn(1998)., A very similar rotation curve was observed in the case of M82 by \citet{Shopbell98}.
". In this paper, we have provided very strong evidence for a shock-excited superwind in NGC 839."," In this paper, we have provided very strong evidence for a shock-excited superwind in NGC 839."
" Our new shock models cannot only reproduce the line ratios in NGC 839, but also the inferred velocities agree with what is derived from emission line and absorption line kinematics."," Our new shock models cannot only reproduce the line ratios in NGC 839, but also the inferred velocities agree with what is derived from emission line and absorption line kinematics."
" These observations are also consistent with the expected wind-blown shock velocities observed by others (Shopbell&Bland-Hawthorn1998;Veilleux&Rupke2002;SharpBland-Hawthorn 2010),, and confirm the model of shock-excited superwinds suggested by recent studies (Sharp&Bland-Hawthorn2010;Monreal-Iberoetal. 2010)."," These observations are also consistent with the expected wind-blown shock velocities observed by others \citep{Shopbell98,Veilleux02,Sharp10}, and confirm the model of shock-excited superwinds suggested by recent studies \citep{Sharp10,Monreal10}."
". These results are also in line with the picture advocated by Sharp&Bland-Hawthorn(2010) who argue that shocks outshine direct stellar photoionization by the time a galactic scale wind is blown out, but that ongoing star formation contributes to the luminosity and ionization field of the galaxy close to the disk."," These results are also in line with the picture advocated by \citet{Sharp10} who argue that shocks outshine direct stellar photoionization by the time a galactic scale wind is blown out, but that ongoing star formation contributes to the luminosity and ionization field of the galaxy close to the disk."
 Our shock models clearly demonstrate that galactic-wide emission from shocks can shift the global line ratios intermediate-velocityinto the regime of LINERs and “composite” objects., Our shock models clearly demonstrate that galactic-wide emission from intermediate-velocity shocks can shift the global line ratios into the regime of LINERs and “composite” objects.
" Although in the case of NGC 839, the “composite” or LINER emission is generated by shocks in a superwind, we can envisage a number of other scenarios which could produce extended LINER-like intermediate velocity shock emission."," Although in the case of NGC 839, the “composite” or LINER emission is generated by shocks in a superwind, we can envisage a number of other scenarios which could produce extended LINER-like intermediate velocity shock emission."
" These include direct galactic collisions, mergers in which one of the merging galaxies is falling into the stellar wind-blown region of another, and minor mergers involving a gas-rich system falling into the hot gaseous halo of an elliptical galaxy."," These include direct galactic collisions, mergers in which one of the merging galaxies is falling into the stellar wind-blown region of another, and minor mergers involving a gas-rich system falling into the hot gaseous halo of an elliptical galaxy."
 None of these directly involve an AGN., None of these directly involve an AGN.
 These results and reinforce the need for integral field data to interpret highlightcomposite and LINER spectra., These results highlight and reinforce the need for integral field data to interpret composite and LINER spectra.
" Finally, we have proposed that NGC 839 provides a link between lower-mass starburst systems and the enigmatic E+A galaxies."," Finally, we have proposed that NGC 839 provides a link between lower-mass starburst systems and the enigmatic E+A galaxies."
 Outside of the central starburst NGC 839 exhibits a pure E+A spectrum and even within the starbursting nucleus the underlying A-star absorption is still evident., Outside of the central starburst NGC 839 exhibits a pure E+A spectrum and even within the starbursting nucleus the underlying A-star absorption is still evident.
 We have proposed a possible formation scenario consistent with the history of NGC 839 given its environment and similarity to M82 which agrees with the recent observational work of Pracyetal. (2009).., We have proposed a possible formation scenario consistent with the history of NGC 839 given its environment and similarity to M82 which agrees with the recent observational work of \citet{Pracy09}. .
 Further integral field observations of similar to NGC 839 and M82 should provide further insight systemsinto our proposed idea., Further integral field observations of systems similar to NGC 839 and M82 should provide further insight into our proposed idea.
The results show that these svstematic errors are a few percent or less in all parameters.,The results show that these systematic errors are a few percent or less in all parameters.
 The derived parameters depend weakly on the choice of fitting radius (the radius over which owas computed) and these were estimated from simulations of this galaxy. with realistic backgrounds., The derived parameters depend weakly on the choice of fitting radius (the radius over which $\chi^2$ was computed) and these were estimated from simulations of this galaxy with realistic backgrounds.
 For reasonable values of fitting radius. the errors were smaller than3%... bul reached extreme values of [or fitting radii much smaller than the hall-lisht radius.," For reasonable values of fitting radius, the errors were smaller than, but reached extreme values of for fitting radii much smaller than the half-light radius."
 We adopt errors corresponding to those from the individual image fits divided by V5 and then add in quadrature to allow for possible svstematie errors., We adopt errors corresponding to those from the individual image fits divided by $\sqrt 5$ and then add in quadrature to allow for possible systematic errors.
 Details of the parameters of the lensing galaxy are summarized in Table 1., Details of the parameters of the lensing galaxy are summarized in Table 1.
" At this redshift. the lensing galaxy has a hall-light radius of R,=l47X1 kpe and Mag(B)=-22.77£0.1 for IL,=50 km ! to q,=0.5."," At this redshift, the lensing galaxy has a half-light radius of $R_e=14.7\pm 1$ kpc and $M_{AB}(B)=-22.77\pm0.1$ for $_o=50$ km $^{-1}$ $^{-1}$, $_o=0.5$."
 The V—7 color of the ealaxy is (vpical of galaxies with z 1 in the CFRS sample., The $V-I$ color of the galaxy is typical of galaxies with z $\sim$ 1 in the CFRS sample.
 The computed res(-fame color is (UU—VW)yp=1.53., The computed rest-frame color is $(U-V)_{AB}=1.53$.
 The measured properties of the arc image are given in Table 2., The measured properties of the arc image are given in Table 2.
 The arc has a length of 2711 and is centered on the galaxy to within 40705 (the precision of the measurement).," The arc has a length of 1 and is centered on the galaxy to within $\pm
0\farcs05$ (the precision of the measurement)."
 The observed surface brightness is 21.2 magnitudes per square arcsecond in the brightest pixel which corresponds to 16.73 in rest-frame AB(2030) magnitudes., The observed surface brightness is 21.2 magnitudes per square arcsecond in the brightest pixel which corresponds to 16.73 in rest-frame AB(2030) magnitudes.
 This surlace brightness is modulated by pixellation aud by the convolution with the IST point-spread. function., This surface brightness is modulated by pixellation and by the convolution with the HST point-spread function.
 For a compact exponential disk (he implied central surface brightuess would be about 2 magnitudes brighter than the observed surface brightness and for a compact E! bulge the implied central surface brightness would be higher bv ~7 magnitudes., For a compact exponential disk the implied central surface brightness would be about 2 magnitudes brighter than the observed surface brightness and for a compact $R^{1/4}$ bulge the implied central surface brightness would be higher by $\sim 7$ magnitudes.
 The exact values depend on the details of the Iuminosity. profiles., The exact values depend on the details of the luminosity profiles.
 The arc is resolved. across its narrowest dimension. Le.. it has non-zero intrinsic width compared with the point-spreacd function of a star on the same frame.," The arc is resolved across its narrowest dimension, i.e., it has non-zero intrinsic width compared with the point-spread function of a star on the same frame."
 One dimensional eaussian fits across (he are al various points along its length give a median observed width (FWIIM) of 07223 and a dispersion of 070025., One dimensional gaussian fits across the arc at various points along its length give a median observed width (FWHM) of 23 and a dispersion of 025.
 For comparison. a fit to a star gives 0115. implving an equivalent gaussian width of ~0717 for the are itself.," For comparison, a fit to a star gives 18, implying an equivalent gaussian width of $\sim
0\farcs17$ for the arc itself."
 Figure 2 shows the brightness profile along the length of the are (and integrated. across the prolile)., Figure 2 shows the brightness profile along the length of the arc (and integrated across the profile).
 The arc centroid position was traced and the flux. extracted. from the image as if il were a spectrum., The arc centroid position was traced and the flux extracted from the image as if it were a two-dimensional spectrum.
 The error bars are based on the number of electrons in the image ancl the observed sky noise., The error bars are based on the number of electrons in the image and the observed sky noise.
 This figure confirms (he visual impression (hat there is real variation in surface brightness along the length of the are aud the peak of the profile occurs al the center. consistent with a normal galaxy. laminosity profile.," This figure confirms the visual impression that there is real variation in surface brightness along the length of the arc and the peak of the profile occurs at the center, consistent with a normal galaxy luminosity profile."
Detached brown dwarf companions to white dwarfs are rare (2)..,Detached brown dwarf companions to white dwarfs are rare \citep*{fbz05}.
 Proper motion surveys and searches for infra-red (IR) excesses have so far found only three confirmed. examples: 1165 | L4. 2». 11400 | L6/7. 2: 25. and 00137-349 (2). the subject of this paper.," Proper motion surveys and searches for infra-red (IR) excesses have so far found only three confirmed examples: 165 $+$ L4, \citealt{becklin88}) ), 1400 $+$ $6/7$ , \citealt{gd1400}; \citealt{dobbie05}) ), and 0137-349 \citep{maxted06}, the subject of this paper."
 1165 is a widely separated system AAU): the separation of the components in 11400 is currently unknown., 165 is a widely separated system AU); the separation of the components in 1400 is currently unknown.
 In contrast. 00137-349 is a close binary (orbital period 2?zz116 minutes).," In contrast, 0137-349 is a close binary (orbital period $P\approx116$ minutes)."
" Optical spectra of the H-rich DA white dwarf 00137-349 show a narrow H,, emission line due to irradiation of the surface of the unseen companion.", Optical spectra of the H-rich DA white dwarf 0137-349 show a narrow $_\alpha$ emission line due to irradiation of the surface of the unseen companion.
 Radial velocities measured from this line and the white dwarf’s intrinsic Ha absorption line allowed ? to determine the mass ratio of the system., Radial velocities measured from this line and the white dwarf's intrinsic $\alpha$ absorption line allowed \citet{maxted06} to determine the mass ratio of the system.
 Using the white dwarf mass (0.393:0.035M. Y. derived from an analysis of its optical spectrum. ? then determined the mass of the companion to be 0.053+ 0.006M..," Using the white dwarf mass $0.39\pm0.035\Msun$ ), derived from an analysis of its optical spectrum, \citet{maxted06} then determined the mass of the companion to be $0.053\pm0.006\Msun$ ."
 This is well below the limit of 0.075M.. commonly used to distinguish stars from brown dwarfs., This is well below the limit of $0.075\Msun$ commonly used to distinguish stars from brown dwarfs.
 The substellar nature of 00137-349B was reinforced by an analysis of its 2MASS near-IR 77A fluxes (Figure 2. 25).," The substellar nature of 0137-349B was reinforced by an analysis of its 2MASS near-IR $JHK$ fluxes (Figure 2, \citealt{maxted06}) )."
 The J and // band photometry can be fit by a model consistent with the white dwarf alone., The $J$ and $H$ band photometry can be fit by a model consistent with the white dwarf alone.
 There is a slight excess of flux at Avs. which can be matched by a model consisting of the white dwarf plus a brown dwarf spectral type mid- or later.," There is a slight excess of flux at $K_{\rm S}$, which can be matched by a model consisting of the white dwarf plus a brown dwarf spectral type mid-L or later."
 This is consistent with the radial velocity determined mass measurement for 00137-349B. Therefore. 00137-349 is the first close. detached binary to be discovered containing a contirmed substellar companion.," This is consistent with the radial velocity determined mass measurement for 0137-349B. Therefore, 0137-349 is the first close, detached binary to be discovered containing a confirmed substellar companion."
 The brown dwarf must have survived a previous phase of common envelope (CE) evolution during which it was engulfed by the red giant progenitor of the white dwarf (2).., The brown dwarf must have survived a previous phase of common envelope (CE) evolution during which it was engulfed by the red giant progenitor of the white dwarf \citep{politano}.
 The drag on the brown dwarf caused it to spiral in towards the red giant core from an originally much wider orbit., The drag on the brown dwarf caused it to spiral in towards the red giant core from an originally much wider orbit.
 Some fraction of the orbital energy was released and deposited in the envelope. which was ejected rom the system. leaving a close binary.," Some fraction of the orbital energy was released and deposited in the envelope, which was ejected from the system, leaving a close binary."
 Simple physical arguments suggest that low mass companions less than some limit 745 will be evaporated during the CE phase., Simple physical arguments suggest that low mass companions less than some limit $m_{\rm crit}$ will be evaporated during the CE phase.
 00137-349B places an upper limit on mui., 0137-349B places an upper limit on $m_{\rm crit}$.
 Alternatively. 00137-349B. may have originally been a jxanet which accreted a substantial fraction of its mass during the CE phase (2)..," Alternatively, 0137-349B may have originally been a planet which accreted a substantial fraction of its mass during the CE phase \citep{ls83}."
 In this scenario. 00137-349B would be expected o have an effective temperature τω> 2000K. and a spectral type (early L) commensurate with the cooling age of the white dwarf (~ Gyr).," In this scenario, 0137-349B would be expected to have an effective temperature $T_{\rm eff}>2000$ K, and a spectral type (early L) commensurate with the cooling age of the white dwarf $\sim0.25$ Gyr)."
 ? concluded that this model wasprobably not applicable o 00137-349 since the 2MASS fluxes are inconsistent with, \citet{maxted06} concluded that this model wasprobably not applicable to 0137-349 since the 2MASS fluxes are inconsistent with
form of laucs or disks.,form of lanes or disks.
 Oulv in a minority of the B2 galaxies do we see nore complicated structures. like distorted filaments.," Only in a minority of the B2 galaxies do we see more complicated structures, like distorted filaments."
 A good example of Complex dust structures is B2 1350|31 (sce Capetti et al. 2000))., A good example of complex dust structures is B2 1350+31 (see Capetti et al. \cite{capetti00}) ).
 We tried to make quantitative estimates of the amount of dust present. bv conusideriug a positive detection of dust oulv if iu niue pixels that form a single area in theratio naps the pixel value was less than 0.55. (see also de Ίνος ot al. 20003).," We tried to make quantitative estimates of the amount of dust present, by considering a positive detection of dust only if in nine pixels that form a single area in the maps the pixel value was less than 0.85, (see also de Koff et al. \cite{dekoff00}) )."
 We calculated he masses of the clumipy dust catures dn the usual way. following Sadler Cerhare (1985)) and de Ixoff et al. (20003).," We calculated the masses of the clumpy dust features in the usual way, following Sadler Gerhard \cite{sadler85}) ) and de Koff et al. \cite{dekoff00}) ),"
 by determining the covering factor of tle dust: his was doue by stmuuine al yxels in the naps which had a value «0.85. such hat the dust mass is: Vine=NsAy«Tt. where © is he area covered by the dust. A the mean absorption of he area under cousideration and P the mass absorption cocficient. taken as 6&↽0“image kpc?EAl.1 (see de Koffe-. al. 2000)).," by determining the covering factor of the dust; this was done by summing all pixels in the maps which had a value $<$ 0.85, such that the dust mass is: $M_{\rm dust} = \Sigma\times A_{\lambda}\times \Gamma^{-1}$, where $\Sigma$ is the area covered by the dust, $A_{\lambda}$ the mean absorption of the area under consideration and $\Gamma$ the mass absorption coefficient, taken as $6\times 10^{-6}$ mag $^2M_{\sun}^{-1}$ (see de Koff et al. \cite{dekoff00}) )."
 The nass is used on the absorption in the V. luages (see Sect. 3))., The mass is based on the absorption in the $V$ images (see Sect. \ref{sec:presenceofdust}) ).
 The mean visual absorption is iu the range 0.20.5 mae for all objects., The mean visual absorption is in the range 0.2–0.5 mag for all objects.
 The observed properties of the dust σαπαος (morphology. miei absorption and total area) are given in Table 1..," The observed properties of the dust features (morphology, mean absorption and total area) are given in Table \ref{tab:dustdata}."
 Since 3€ sources already had been analyzed by de off et. al. (20003).," Since 3C sources already had been analyzed by de Koff et al. \cite{dekoff00}) ),"
 we did not repea the calculation ofA4. X aud this is accounted for by an asterisk in the respective coluuuis of Table L..," we did not repeat the calculation of $A_\lambda$ , $\Sigma$ and this is accounted for by an asterisk in the respective columns of Table \ref{tab:dustdata}."
 A nou-detection of dust means that less than niue pixels were found with value <0.85 in a sinele area., A non-detection of dust means that less than nine pixels were found with value $<0.85$ in a single area.
 Correspouding upper hits are based on this., Corresponding upper limits are based on this.
 In Table 2. we list the upper nuits to the dust masses for those sources in which no dust was detected., In Table \ref{tab:nodust} we list the upper limits to the dust masses for those sources in which no dust was detected.
 We should remark that the detection of dust lanes or disks around galactic nuclei suffers from a number of selection effects; which are not so casily quantifiable.," We should remark that the detection of dust lanes or disks around galactic nuclei suffers from a number of selection effects, which are not so easily quantifiable."
 First. if the circun-uuclear dust takes. as we believe. the form of disks. then its detection will clearly depend ou oricutation of the disk with respect to the line of sight.," First, if the circum-nuclear dust takes, as we believe, the form of disks, then its detection will clearly depend on orientation of the disk with respect to the line of sight."
 Dust disks will be more casily seen if they are close to edge-on (in which case they will be called “lanes”}: up till now the ouly counter example in the B2 sample is B2 01011232 (3C 31). iu which we are able to see fairly complete ellipses of dust around he nucleus.," Dust disks will be more easily seen if they are close to edge-on (in which case they will be called ""lanes""); up till now the only counter example in the B2 sample is B2 0104+32 (3C 31), in which we are able to see fairly complete ellipses of dust around the nucleus."
 Another obvious selectiou effect is due to redshift: since we require a ninmuiunu of nine jxels with sienificaut absorption du a contiguous area. he detectable dust mass depends on redshift (see Sect. 1.3)).," Another obvious selection effect is due to redshift: since we require a minimum of nine pixels with significant absorption in a contiguous area, the detectable dust mass depends on redshift (see Sect. \ref{subs:dustmass}) )."
 This effect is shown in Fie. 3..," This effect is shown in Fig. \ref{fig:z_mo},"
 where we plot the dus masses as derived for B2 sources. including the upper inte. as a function of redshift.," where we plot the dust masses as derived for B2 sources, including the upper limits, as a function of redshift."
 Is should also be noted hat the distribution of detected masses and upper Inmuits appears to be discontiuuous., Is should also be noted that the distribution of detected masses and upper limits appears to be discontinuous.
 Using the criterion for detection we fine that dust is yequeutly preseut: 30/57 (53 A) of the galaxies show dust catures. either in the form of baucls or disk-like structures. or more iregulu patches.," Using the criterion for detection we find that dust is frequently present: 30/57 (53 ) of the galaxies show dust features, either in the form of bands or disk-like structures, or more irregular patches."
 A sunuuaryv of some general xoperties derived for these thirty sources is given in Table 3.., A summary of some general properties derived for these thirty sources is given in Table \ref{tab:gendata}.
 Most columns of the table are obvious: it should oulv © inentioned that we eive two determinations of dust uasses: the first. iu Col.," Most columns of the table are obvious; it should only be mentioned that we give two determinations of dust masses; the first, in Col."
 6. is the mass calculated frou he absorption map as explained in this paper. while Col.," 6, is the mass calculated from the absorption map as explained in this paper, while Col."
 T gives the dust mass (or au upper uut) derived frou he IRAS IR fuxes (if available)., 7 gives the dust mass (or an upper limit) derived from the IRAS IR fluxes (if available).
 A “J” in Col.," A ""J"" in Col."
 8 means hat the source has a radio jet., 8 means that the source has a radio jet.
 The percentage of dust detections in the B2 sample max. be slishtlv higherthan, The percentage of dust detections in the B2 sample may be slightly higherthan
wo sources of error were added in quadrature. aud the otal errors are reported iu Table 6 as as aud 63 or S(3839) and S32(CII). respectively.,"two sources of error were added in quadrature, and the total errors are reported in Table \ref{t2} as $\sigma_{S}$ and $\sigma_{S2}$ for $S(3839)$ and $S_{2}(CH)$, respectively."
 For the March observing un the S/N in the S2(CI7) band was quite veh aud the fusing errors dominate while for the July observing run. where oulv a single dither set was taken or the final fourth field. the Poissou noise contribution avs a significant coutributiou to the total eror.," For the March observing run the S/N in the $S_{2}(CH)$ band was quite high and the fluxing errors dominate while for the July observing run, where only a single dither set was taken for the final fourth field, the Poisson noise contribution plays a significant contribution to the total error."
 For $(3839). the Poisson error tends to dominate the total error in alb cases.," For $S(3839)$, the Poisson error tends to dominate the total error in all cases."
 Errors in radial velocity are typically l?. or of a pixel as uneutioned in Section 3. and do not have a significant effect on measured baud streugths.," Errors in radial velocity are typically 17, or of a pixel, as mentioned in Section 3, and do not have a significant effect on measured band strengths."
 Shifting our wavelengths to the blue or red by 1l? changes the measured οΠΠ by 0.001 mae. which is sanall relative to the flusine- aud noise-relatecl errors iu σοςΠΠ.," Shifting our wavelengths to the blue or red by 17 changes the measured $S_{2}(CH)$ by 0.001 mag, which is small relative to the fluxing- and noise-related errors in $S_{2}(CH)$."
 Five of the stars in the LRIS data set are also in the VIRUS-P spectroscopic sample. aud the CN aud CI baud streneths measured frou the LRIS spectra are quite simular to band strengths measured from the VIRUS-P data.," Five of the stars in the LRIS data set are also in the VIRUS-P spectroscopic sample, and the CN and CH band strengths measured from the LRIS spectra are quite similar to band strengths measured from the VIRUS-P data."
 Figure P. shows AS(3839) and ASS(CITI) for the stars im conummon between the two data sets; in the seuse VIRUS-P. and differences betweenthe two data sets are quite small.," Figure \ref{fig4} shows $\Delta S(3839)$ and $\Delta S_{2}(CH)$ for the stars in common between the two data sets, in the sense $-$ VIRUS-P, and differences betweenthe two data sets are quite small."
 The baud streneths eiven in Table 6 come exclusively from the VIRUS-P data., The band strengths given in Table \ref{t2} come exclusively from the VIRUS-P data.
" Since the 3882À CN band streneth ciu be used as a proxy for nitrogen abundance. aud the 1320À CTI ud strength for carbon abundauce. a comparison of CN and CID band strength iu a elobular cluster ought o reveal auticorrelated. abundance behavior,"," Since the $3883 \hbox{\AA}$ CN band strength can be used as a proxy for nitrogen abundance, and the $4320 \hbox{\AA}$ CH band strength for carbon abundance, a comparison of CN and CH band strength in a globular cluster ought to reveal anticorrelated abundance behavior."
 As can be seen in Figure 5.. the CN baud strength in our sample rises sheltly with ring bIuninuositv. but does not slow a aree rauge at fixed Ac;," As can be seen in Figure \ref{fig5}, the CN band strength in our sample rises slightly with rising luminosity, but does not show a large range at fixed $M_{V}$."
 The clear outlier. with a large open star drawn around it. is star 1839. the star with he uuusuallv stroug CN aud CII features in Figure 2.," The clear outlier, with a large open star drawn around it, is star 1839, the star with the unusually strong CN and CH features in Figure 2."
 It is excluded. from the rest of our baud streugth aud abundance analysis., It is excluded from the rest of our band strength and abundance analysis.
 The $(3839) baud streugths are correlated. to first order. with huninosity.," The $S(3839)$ band strengths are correlated, to first order, with luminosity."
 To better distinguish stars that aro CN-weak from) stars that are CN-strong. we fit a linear relationship between $(3839) and AJ aud evaluated cach star based on its vertical distance frou: this linear relationship (4.9(3839)).," To better distinguish stars that are CN-weak from stars that are CN-strong, we fit a linear relationship between $S(3839)$ and $M_{V}$ and evaluated each star based on its vertical distance from this linear relationship $\delta S(3839)$ )."
 We divide the sample iuto relatively CN-weak (uegative 6.$(3839). open squares) and CN-strone (positive 055(3839). solid squares) stars.," We divide the sample into relatively CN-weak (negative $\delta S(3839)$, open squares) and CN-strong (positive $\delta S(3839)$, solid squares) stars."
 Unlike iu studies of bhigherauetallicity elobular clusters (see Norris et al., Unlike in studies of higher-metallicity globular clusters (see Norris et al.
 for a typical exanuple). there is not a clear gap between the relatively CN-aveak aud CN-strong eroups.," for a typical example), there is not a clear gap between the relatively CN-weak and CN-strong groups."
 Iu Figure 6 we compare àS(3839) and So(CL) baud streugths. with the same svinbols (open/solid squares) represeutiug CN class. ar here is not a stroug anticorrelation between CN class and CIT baud streneth.," In Figure \ref{fig6} we compare $\delta S(3839)$ and $S_{2}(CH)$ band strengths, with the same symbols (open/solid squares) representing CN class, and there is not a strong anticorrelation between CN class and CH band strength."
 The two large crosses are ceutere at the mean values for 05(3839) aud συΠΠ for the wo groups. with their size set to equal the stand deviations.," The two large crosses are centered at the mean values for $\delta S(3839)$ and $S_{2}(CH)$ for the two groups, with their size set to equal the standard deviations."