diff --git "a/batch_s000007.csv" "b/batch_s000007.csv" new file mode 100644--- /dev/null +++ "b/batch_s000007.csv" @@ -0,0 +1,10364 @@ +source,target + According to our information. G89-1H with ΠΠ=—1.9 (CLLA) is the most metal-poor quadruple svstem known to date. which makes it an interesting object lor a more detailed study.," According to our information, G89-14 with $\mathrm{[m/H]}=-1.9$ (CLLA) is the most metal-poor quadruple system known to date, which makes it an interesting object for a more detailed study." + Stellar streams (e.g.. Eggen 1996a.b)) are associations of stars possessing simular kinematies and metallicity.," Stellar streams (e.g., \citealt{eggen_1996a,eggen_1996b}) ) are associations of stars possessing similar kinematics and metallicity." + The study of such streams allows restoring (ο a certain degree the picture of the formation of various dynamical structures in our Galaxy., The study of such streams allows restoring to a certain degree the picture of the formation of various dynamical structures in our Galaxy. + Traditionally. the stellar streams are being selected in a certain phase space and then (heir origin is interpreted using the data of spectroscopic analvsis.," Traditionally, the stellar streams are being selected in a certain phase space and then their origin is interpreted using the data of spectroscopic analysis." + Ii a phase space. a fine structure like stellar multiplicity can give additional information on the dynamical evolution of the stream and ils primogenitor.," In a phase space, a fine structure like stellar multiplicity can give additional information on the dynamical evolution of the stream and its primogenitor." + However. until now il was not taken into due consideration.," However, until now it was not taken into due consideration." + The following six stars of our sample:QG10-4..G13-9..G60-48... G24-3.. GI8-54.. G28-43.. ave part of the moving group (Eegen1996a).. 10 other objects:G130-65.. G'15-56..G5-35..G40-14.. GI14-25.. GII-4H..G13-35.. GISS-IL1.. GIS2-32.. G126-52.. belong to the moving group (Eeeen1996b).," The following six stars of our sample:, are part of the moving group \citep{eggen_1996a}, 10 other objects:, , , belong to the moving group \citep{eggen_1996b}." +. In Table G we are listing some characteristics ofthese (wo halostreams., In Table \ref{streams} we are listing some characteristics ofthese two halostreams. + In the penultimate columnof the table. vou," In the penultimate columnof the table, you" +regime on the HR diagram.,regime on the HR diagram. + The peak of the mass loss rate ts reached when the helium mass fraction at the centre decreases to 0.54 (0.031). and the total mass to 9.35 (6.50 Μ.Ο. for 25 (20 M.)) model sequence.," The peak of the mass loss rate is reached when the helium mass fraction at the centre decreases to 0.54 (0.031), and the total mass to 9.35 (6.50 ), for 25 (20 ) model sequence." + As shown for the 20M sequence. such a mass loss history of runaway increase followed by sudden decrease can be repeated as the star moves in and out the unstable regime.," As shown for the 20 sequence, such a mass loss history of runaway increase followed by sudden decrease can be repeated as the star moves in and out the unstable regime." +" The 20 star finally ends its life as a yellow supergiant of Mj,26.1M... with only a small amount of hydrogen of about 0.5."," The 20 star finally ends its life as a yellow supergiant of $M_\mathrm{tot} = 6.1$, with only a small amount of hydrogen of about 0.5." +... The most likely outcome of the death of such a star would be a Type IIb supernova., The most likely outcome of the death of such a star would be a Type IIb supernova. + The 25 star has a hydrogen envelope of 0.22 at core helium exhaustion... and would produce either a Type Ib or a IIb supernova depending on the subsequent history of mass loss.," The 25 star has a hydrogen envelope of 0.22 at core helium exhaustion, and would produce either a Type Ib or a IIb supernova depending on the subsequent history of mass loss." + When the mass loss rate reaches the maximum. the growth rate given by Eq. (1))," When the mass loss rate reaches the maximum, the growth rate given by Eq. \ref{eq1}) )" + becomes as high as 11.3 and 10.6 for 25 and 20 models. respectively.," becomes as high as 11.3 and 10.6 for 25 and 20 models, respectively." + We checked tf non-linear evolutionary.. calculations also give such high growth rates. given that the relation of Eq. (1))," We checked if non-linear evolutionary calculations also give such high growth rates, given that the relation of Eq. \ref{eq1}) )" + 1s only based on the result with 1)<8.0 (Fig. 3)., is only based on the result with $\eta \la 8.0$ (Fig. \ref{fig:eta}) ). + We find that. at the reference points marked by the filled circles in Fig. 4..," We find that, at the reference points marked by the filled circles in Fig. \ref{fig:evol}," + the hydrodynamie calculations give jj= 9.9 and 9.0 for 25 and 20M. models respectively. which are comparable to the values given by Eq. (1)).," the hydrodynamic calculations give $\eta = $ 9.9 and 9.0 for 25 and 20 models respectively, which are comparable to the values given by Eq. \ref{eq1}) )." + If a pulsationally-driven super-wind (PDSW) phase could be induced by strong pulsations. this would have very important implications for supernova progenitors.," If a pulsationally-driven super-wind (PDSW) phase could be induced by strong pulsations, this would have very important implications for supernova progenitors." + As implied by our model sequences presented above. such a PDSW can significantly reduce the eritical ZAMS mass (Ma) above which a huge fraction of the stellar envelope is removed before core collapse. thus producing no Type H-P supernova.," As implied by our model sequences presented above, such a PDSW can significantly reduce the critical ZAMS mass $M_\mathrm{crit}$ ) above which a huge fraction of the stellar envelope is removed before core collapse, thus producing no Type II-P supernova." + Based on our results. we suggest M with a PDSW (see Figs.," Based on our results, we suggest $M_\mathrm{crit} \sim$ with a PDSW (see Figs." + | and [ 4)). while the models with the JNH88 mass loss rate predict SN II-P. progenitors up to ~....," \ref{fig:hr} and \ref{fig:evol}) ), while the models with the JNH88 mass loss rate predict SN II-P progenitors up to $\sim$." + Interestingly. this value of M. 1s comparable to what other alternative prescriptions of RSG winds mass loss predict (Salasnichetal.1999:Vanbeveren2007).," Interestingly, this value of $M_\mathrm{crit}$ is comparable to what other alternative prescriptions of RSG winds mass loss predict \citep{Salasnich99, vanBeveren07}." +. Note that Mi could be even further reduced by rotation. as implied by the result of Hegeretal.(1997) (seealsoMeynet&Maeder 2003).," Note that $M_\mathrm{crit}$ could be even further reduced by rotation, as implied by the result of \citet{Heger97}~ \citep[see also][]{Meynet03}." + This might provide a plausible solution to the so-called RSG problem. t.e. the observed lack of type II-P progenitors with Mii216.53:1.5M. (Smarttetal.2009).," This might provide a plausible solution to the so-called RSG problem, i.e. the observed lack of type II-P progenitors with $M_\mathrm{init} \ga 16.5 \pm 1.5$ \citep{Smartt09}." +. Such observation could also result from the presence of dusty circumstellar material around the stars. as an obscured progenitor would be estimated to have a lower initial mass in pre-SN images.," Such observation could also result from the presence of dusty circumstellar material around the stars, as an obscured progenitor would be estimated to have a lower initial mass in pre-SN images." + However Smartt(2009) also noted that the number of SNe type II-P in their sample is consistent with the expected number of stars in the range 8.5-16.5 assuming a Salpeter IMF, However \citet{Smartt09} also noted that the number of SNe type II-P in their sample is consistent with the expected number of stars in the range 8.5-16.5 assuming a Salpeter IMF. + This could be a possible indication of the fact that stars with higher initial mass do actually lose most of their hydrogen envelope. which cannot be easily understood with the canonical mass loss rate of JNH88.," This could be a possible indication of the fact that stars with higher initial mass do actually lose most of their hydrogen envelope, which cannot be easily understood with the canonical mass loss rate of JNH88." + The PDSW is expected to significantly affect the circumstellar medium around a RSG (van Veelen. in prep.).," The PDSW is expected to significantly affect the circumstellar medium around a RSG (van Veelen, in prep.)." + When the star dies. the shock produced by the collision between the SN ejecta and the circumstellar material transforms kinetic energy into thermal energy.," When the star dies, the shock produced by the collision between the SN ejecta and the circumstellar material transforms kinetic energy into thermal energy." + This energy can be radiated away at different wavelengths. resulting in brightnening the supernova remnant for long times (Chevalier1977).," This energy can be radiated away at different wavelengths, resulting in brightnening the supernova remnant for long times \citep{Chevalier77}." +. If the collision occurs directly after the SN explosion. the emission can even alter the spectrum and light curve of the SN.," If the collision occurs directly after the SN explosion, the emission can even alter the spectrum and light curve of the SN." + This scenario 1s usually invoked to explain the class of Type IIn supernovae (Schlegel1990:Filippenko1997).," This scenario is usually invoked to explain the sub-class of Type IIn supernovae \citep{Schlegel90,Filippenko97}." +. 'To reproduce the light curve of the most luminous Type ΠΠ supernovae (SNe IIn) like SN 2006gy and SN 2006tf. very massive shells are required. which need to be ejected in eruptive events a few years before core collapse (e.g...vanMarleetal.2010).," To reproduce the light curve of the most luminous Type IIn supernovae (SNe IIn) like SN 2006gy and SN 2006tf, very massive shells are required, which need to be ejected in eruptive events a few years before core collapse \citep[e.g., ][]{vanMarle10}." +. Pulsational pair instability (Woosleyetal.2007) and LBV-like eruptions (e.g..Smithetal.2007) have been discussed to explain the presence of shells of around the progenitors of luminous SNe IIn.," Pulsational pair instability \citep{Woosley07} and LBV-like eruptions \citep[e.g., ][]{Smith07} + have been discussed to explain the presence of shells of around the progenitors of luminous SNe IIn." + A PDSW phase is an unlikely explanation for such extreme environments., A PDSW phase is an unlikely explanation for such extreme environments. + However it might be interesting for those type In where the required mass in the stellar vicinity ts of the order of a few solar masses or less., However it might be interesting for those type IIn where the required mass in the stellar vicinity is of the order of a few solar masses or less. + In this context it is interesting to consider the circumstellar medium around the RSG VY CMa., In this context it is interesting to consider the circumstellar medium around the RSG VY CMa. + The stellar surrounding appears shaped by episodic mass ejections which occurred about 500-1000 yr ago (Smithetal.2009).., The stellar surrounding appears shaped by episodic mass ejections which occurred about 500-1000 yr ago \citep{Smith09}. . + The complex morphology of the CSM is suggestive of a possible interaction between convection and pulsation (seeFig.13inSmithetal.2009). which for these stars are predicted to occur on similar timescales (e.g..Hegeretal.1997).," The complex morphology of the CSM is suggestive of a possible interaction between convection and pulsation \citep[see Fig.~13 in][]{Smith09}, which for these stars are predicted to occur on similar timescales \citep[e.g., ][]{Heger97}." +. The mass loss rate of 1—2«107Myer! derived by Smithetal.(2009) is comparable to the one expected during the PDSW phase (see Fig. 4))., The mass loss rate of $1-2\times10^{-3}~\mathrm{M_\odot yr^{-1}}$ derived by \citet{Smith09} is comparable to the one expected during the PDSW phase (see Fig. \ref{fig:evol}) ). + Even if the mass loss prescription for PDSW we used is somewhat arbitrary. we want to stress that the energy available from the growth of pulsation is enough to drive mass loss rates up to ~107M.yr!.," Even if the mass loss prescription for PDSW we used is somewhat arbitrary, we want to stress that the energy available from the growth of pulsation is enough to drive mass loss rates up to $\sim +10^{-2}~\mathrm{M_\odot yr^{-1}}$." + Smithetal.(2009) state that an extreme RSG like VY CMa would produce a Type IIn event like SN 1988Z if it were to explode in its current state., \citet{Smith09} state that an extreme RSG like VY CMa would produce a Type IIn event like SN 1988Z if it were to explode in its current state. + Therefore the occurrence of pulsation-driven super-winds in RSG might explain moderately luminous SN IIn if the enhanced mass loss takes place less than about ~10? years before core collapse., Therefore the occurrence of pulsation-driven super-winds in RSG might explain moderately luminous SN IIn if the enhanced mass loss takes place less than about $\sim10^3$ years before core collapse. + With the mass loss prescription of Eq., With the mass loss prescription of Eq. + 2. with a sufficiently large à (~ 2). this would occur in a narrow range around — for non-rotating stars.," \ref{eq2} with a sufficiently large $\alpha$ $\sim 2$ ), this would occur in a narrow range around $\sim$ for non-rotating stars." + An accurate determination of the expected.. rate of type In due to PDSW requires a more realistic mass loss prescription., An accurate determination of the expected rate of type IIn due to PDSW requires a more realistic mass loss prescription. + To conclude. if a pulsationally-driven super-wind phase could be induced by strong pulsations. we would expect a substantial change in the late evolution of single massive stars.," To conclude, if a pulsationally-driven super-wind phase could be induced by strong pulsations, we would expect a substantial change in the late evolution of single massive stars." + The mass loss rate during the RSG phase would increase dramatically for stars with Mini2Moi compared to the JNH88 rate. and the PDSW phaseshould start earlier in the evolution of more massive stars.," The mass loss rate during the RSG phase would increase dramatically for stars with $M_\mathrm{init} \ga M_\mathrm{crit}$ compared to the JNH88 rate, and the PDSW phaseshould start earlier in the evolution of more massive stars." + The resulting pre-supernova structure of these stars is affected. as well as their CSM.," The resulting pre-supernova structure of these stars is affected, as well as their CSM." + For single stars. this suggests the following sequence in supernova types as function of increasing initial mass: P>I-L ," For single stars, this suggests the following sequence in supernova types as function of increasing initial mass: II-P $\xrightarrow{}$ " +N-rayv source (Isracl&Stella1996:Vaughan2005).,"X-ray source \citep{Israel96,Vaughan05}." +. We fitted the power versus frequency relation for periods im the range 6280 davs to a power-law form aud found a spectral index of —1.01dk0.06., We fitted the power versus frequency relation for periods in the range 6–280 days to a power-law form and found a spectral index of $-1.04 \pm 0.06$. + We generated red noise with a spectral index of —1.10 and with mean aud variance equal to those of the data using the routine of the IDL subroutine library provided by the Institut fiürr Astronomie und Astroplisik of the Universitàtt Tibbinecu (Timmer&Konig1991)., We generated red noise with a spectral index of $-1.10$ and with mean and variance equal to those of the data using the routine of the IDL subroutine library provided by the Institut fürr Astronomie und Astrophysik of the Universitätt Tübbingen \citep{Timmer94}. + The duration of each generated light curve is longer than the actual data im order to minimize the effects of red noise leakage., The duration of each generated light curve is longer than the actual data in order to minimize the effects of red noise leakage. + Each light curve coutains 8192 data points with uniform spacing of 0.66 days and a subset of 330 points from the muddle of this set. with relative times matching the actual observations are extracted for analysis., Each light curve contains 8192 data points with uniform spacing of 0.66 days and a subset of 330 points from the middle of this set with relative times matching the actual observations are extracted for analysis. + These 330 simulated fluxes were processed with the same procedures used to analyze the real cata., These 330 simulated fluxes were processed with the same procedures used to analyze the real data. + We generated 2«10° trial Πο curves aud searched for cases where the power at periods of 10 to 150 days was greater than or equal to the observed value of 77.9., We generated $2 \times 10^{6}$ trial light curves and searched for cases where the power at periods of 10 to 150 days was greater than or equal to the observed value of 77.9. + We found one such case and estimate the probability of chance ocemrence of our obscrved signal to be 5«10., We found one such case and estimate the probability of chance occurrence of our observed signal to be $5 \times 10^{-7}$. +* Fitting the distribution of maxima observed powers. we estimate that the probability of chance occurrence of our observed signal is 6«LO*. iu good agreement.," Fitting the distribution of maximum observed powers, we estimate that the probability of chance occurrence of our observed signal is $6 \times 10^{-7}$, in good agreement." + This procedure is conservative because it includes the signal in the caleulation of the power-law slope aud he variance aud because the period search range. 10150 davs. extends to significantly lower frequencies than he observed period where the red noise produces high amplitude fluctuations.," This procedure is conservative because it includes the signal in the calculation of the power-law slope and the variance and because the period search range, 10--150 days, extends to significantly lower frequencies than the observed period where the red noise produces high amplitude fluctuations." + If we restrict the search range to veriods of 62 davs or less. then a fit to the distribution of the maxiuun observed powers indicates that the xobabilitv of chance occurrence of our observed. signal i310P.," If we restrict the search range to periods of 62 days or less, then a fit to the distribution of the maximum observed powers indicates that the probability of chance occurrence of our observed signal is $3 \times 10^{-13}$." + The coliereuce or quality value of the peak signal. the oeriod of the peak divided by the full width at half uaxinmun power. is Q=22.3.," The coherence or quality value of the peak signal, the period of the peak divided by the full width at half maximum power, is $Q = 22.3$." + This is fully cousisteut with that expected for a periodic process eiven the observation curation., This is fully consistent with that expected for a periodic process given the observation duration. + Fig., Fig. + 3. shows the data folded at the best fit period., \ref{phase} shows the data folded at the best fit period. + Each point is the average flux of the observations falling within the eiven phase bin aud the error bar is the standard error. the standard deviation of the fluxes in each bin divided by the square root of the ΙΟ of fluxes im that bin.," Each point is the average flux of the observations falling within the given phase bin and the error bar is the standard error, the standard deviation of the fluxes in each bin divided by the square root of the number of fluxes in that bin." +" The amplitude of the modulation. taken as the miaxinmni average flux in one bin minus the πα, is (0.99£0.10)ς1οHerecni24ot."," The amplitude of the modulation, taken as the maximum average flux in one bin minus the minimum, is $(0.99 \pm +0.10) \times 10^{-11} \rm \, erg \, cm^{-2} \, s^{-1}$." + To search for rapid variability. we extracted event files with high time resolution data for the 187 observations.," To search for rapid variability, we extracted event files with high time resolution data for the 187 observations." + Eveuts in the 2.1-11.9 keV energy. band were selected in the good time intervals defined above aud split iuto segments of 256 x. Au FFT with a time resolution of ls was calculated for cach scemenut., Events in the 2.4-11.9 keV energy band were selected in the good time intervals defined above and split into segments of 256 s. An FFT with a time resolution of 1 s was calculated for each segment. + The FFTs within cach observation were added iucolercutly., The FFTs within each observation were added incoherently. + The resulting, The resulting +"As described in the introduction, observational evidence for vortical motion on the solar surface typically refers to larger scales than the strong, small-scale vortices studied here, although the general characteristics are similar (e.g., the association with downflows).","As described in the introduction, observational evidence for vortical motion on the solar surface typically refers to larger scales than the strong, small-scale vortices studied here, although the general characteristics are similar (e.g., the association with downflows)." + The reported mean lifetimes of granular-scale vortices of 5-8 minutes (??) are not drastically different from the value of 3.5min estimated above.," The reported mean lifetimes of granular-scale vortices of 5–8 minutes \citep{2008Bonet,2010Bonet} are not drastically different from the value of $3.5\unit{min}$ estimated above." +" However, because their rotation periods are different, our vortices make about 2 revolutions during their lifetimes, while the observed vortices can be followed for only a fraction of one rotation (forinstance,about2596ofaperiodinthecase?).."," However, because their rotation periods are different, our vortices make about 2 revolutions during their lifetimes, while the observed vortices can be followed for only a fraction of one rotation \citep[for instance, about 25\% of +a period in the case of][]{2010Bonet}." + It is conceivable that the observed vortical motions represent the peripheral parts of the much stronger small-scale vortex cores that show up in the simulations but are too small to be observed directly., It is conceivable that the observed vortical motions represent the peripheral parts of the much stronger small-scale vortex cores that show up in the simulations but are too small to be observed directly. + The outer vortex parts would be much more strongly affected by the evolving granulation pattern and thus be detectable only for a fraction of a rotation period., The outer vortex parts would be much more strongly affected by the evolving granulation pattern and thus be detectable only for a fraction of a rotation period. +" To see whether the vortices studied in this paper would be detectable in observational data through feature tracking techniques, we consider horizontal pseudo pathlines (trajectories of fluid elements) in Fig. 13.."," To see whether the vortices studied in this paper would be detectable in observational data through feature tracking techniques, we consider horizontal pseudo pathlines (trajectories of fluid elements) in Fig. \ref{fig:cork}." + The pathlines are determined from 10 snapshots of the horizontal velocity field at the average height of the optical surface with a temporal spacing of )., The pathlines are determined from 10 snapshots of the horizontal velocity field at the average height of the optical surface with a temporal spacing of. +".T heyare'pseudo"" becausetheverticalvelocityisignored.", They are “pseudo” because the vertical velocity is ignored. +" Some pathlines are spiraling in towards a region of high swirling strength, see the feature at )intheleft -handpanelo fFig. 13."," Some pathlines are spiraling in towards a region of high swirling strength, see the feature at in the left-hand panel of Fig. \ref{fig:cork}." +".Inthiscase, thereisaclearassociationwit scalevorticespresentedinthispaper."," In this case, there is a clear association with the small-scale vortices presented in this paper." +"However, wealso findpathlineswhich upregionshowninFig. 13.."," However, we also find pathlines which are curved but for which the association with an actual vortex is not clear, for instance in the blown-up region shown in Fig. \ref{fig:cork}." + We have investigated vortical fluid motions in simulations of near-surface solar convection by calculating the eigenvalues and eigenvectors of the velocity gradient tensor field., We have investigated vortical fluid motions in simulations of near-surface solar convection by calculating the eigenvalues and eigenvectors of the velocity gradient tensor field. + Complex eigenvalues with a large imaginary part indicate regions of strong swirling., Complex eigenvalues with a large imaginary part indicate regions of strong swirling. +" They are found predominantly in and near the intergranular lanes, where cooled fluid is sinking down in a turbulent fashion."," They are found predominantly in and near the intergranular lanes, where cooled fluid is sinking down in a turbulent fashion." +" The swirling regions form an unsteady network of highly tangled filaments, some of which protrude above the optical surface."," The swirling regions form an unsteady network of highly tangled filaments, some of which protrude above the optical surface." +" Near the optical surface, vertically oriented swirls are preferentially located in the interior of intergranular lanes, where the downflow is strong."," Near the optical surface, vertically oriented swirls are preferentially located in the interior of intergranular lanes, where the downflow is strong." +" Horizontal swirls, on the other hand, are predominantly located at the edges of the granules, where vertical motion is mostly absent."," Horizontal swirls, on the other hand, are predominantly located at the edges of the granules, where vertical motion is mostly absent." +" The 3D structure of contiguous features above the optical surface is manifold, but often in the form of bent and arc-shaped filaments."," The 3D structure of contiguous features above the optical surface is manifold, but often in the form of bent and arc-shaped filaments." +" These type of structures have previously been seen in independent numerical simulations with different codes, notably ? and ?.."," These type of structures have previously been seen in independent numerical simulations with different codes, notably \citet{2010Muthsam} and \citet{1998Stein}." + The swirling direction (rotation axis) is typically aligned with the longitudinal direction(s) in a contiguous feature., The swirling direction (rotation axis) is typically aligned with the longitudinal direction(s) in a contiguous feature. +width observed here. show that the effect described above is unimportant for IHT2O masers.,"width observed here, show that the effect described above is unimportant for $_2$ O masers." + The line widths show that in almost all cases gQὃνFis satistied., The line widths show that in almost all cases $g\Omega \gg R$ is satisfied. + Wiebe Watson (1998) have shown that the wropagation of linear polarization can also resul circular polarization., Wiebe Watson (1998) have shown that the propagation of linear polarization can also result in circular polarization. + For linear polarizatious of z105 he resulting circular polarization is of the same order of naguitude as the polarization due to the regular Zeca interpretation. while maeuetic fields could again be a actor of 1000 less.," For linear polarizations of $\approx 10\%$, the resulting circular polarization is of the same order of magnitude as the polarization due to the regular Zeeman interpretation, while magnetic fields could again be a factor of 1000 less." + Below we indicate that also this 1011”Zeenau interpretation is unlikely duc to the lack of linear volarization., Below we indicate that also this non-Zeeman interpretation is unlikely due to the lack of linear polarization. + Iu the case of the LTE οσα models we first fit a conibination of the 3 strongest lywperfine components to the total power spectrin., In the case of the LTE Zeeman models we first fit a combination of the 3 strongest hyperfine components to the total power spectrum. + From this we ect the line width Acy of the maser feature aud the contribution to the line of the πηραπο compoucuts., From this we get the line width $\Delta v_{\rm L}$ of the maser feature and the contribution to the line of the hyperfine components. + For this combination we calculate a svuthetic V-spectruui. such as shown in Fie.," For this combination we calculate a synthetic V-spectrum, such as shown in Fig." + 1 for the separate hvperfue compoucuts., \ref{vs} for the separate hyperfine components. + The svuthetic spectrum is then fitted to the circular polarization spectrum., The synthetic spectrum is then fitted to the circular polarization spectrum. + As our observations in VOL have shown that the observed. V-spectruui can be narrower than the svuthetic Vespectrmm. we also allow for the narrowing of our svuthetic spectra in the ft.," As our observations in V01 have shown that the observed V-spectrum can be narrower than the synthetic V-spectrum, we also allow for the narrowing of our synthetic spectra in the fit." + Furthermore we need to remove the scaled down replicas of the total intensity., Furthermore we need to remove the scaled down replicas of the total intensity. + We fit the following fiction: Here Av is the velocity in [kiu/s} measured from the peak of the total intensity. V is the svuthetic spectra Vieurk.," We fit the following function: Here $\Delta v$ is the velocity in [km/s] measured from the peak of the total intensity, $V^*$ is the synthetic spectrum $V_{\rm +synth}$ ." + We fi for the parameters ay. e» and a3.," We fit for the parameters $a_1$, $a_2$ and $a_3$." + The paracter ay controls the amplitude of he V-spectruni. while e» determines the amount of narrowing of the observed spectra with respect to the model spectra.," The parameter $a_1$ controls the amplitude of the V-spectrum, while $a_2$ determines the amount of narrowing of the observed spectra with respect to the model spectra." +" Finally, the removal of the scaled down total iuteusity profile is determined by a3."," Finally, the removal of the scaled down total intensity profile is determined by $a_3$." +" The auplituce e4 of the best fitted model determines Vi, aud Vias."," The amplitude $a_1$ of the best fitted model determines $V_{\rm min}$ and $V_{\rm +max}$." + Together with the peak intensity of the maser feature lis gives Py., Together with the peak intensity of the maser feature this gives $P_{\rm V}$. + With the previously determined line width ο we calculate By using Eq. L..," With the previously determined line width $\Delta +v_{\rm L}$ we calculate $B_{||}$ using Eq. \ref{eq2}." + For the nou-LTE case. we fit out inodels to both total intensity aud circular polarization simultaneously.," For the non-LTE case, we fit out models to both total intensity and circular polarization simultaneously." + We use Eq., We use Eq. + 3 with VVinsda," \ref{eq4} with $V^* = +V_{\rm model}$." + Because the noi-LTE models are already intrinsically iuore uarrow. we first fik the width of the V-spectruu by setting ου=1.0 and only fitting ο aud a3.," Because the non-LTE models are already intrinsically more narrow, we first fix the width of the V-spectrum by setting $a_2 += 1.0$ and only fitting $a_1$ and $a_3$." +" We have chosen to fit models with Crheaual0.58 and 1.0 kms. as the line widths of the maser features indicate that wach higher iutziusic thermal widths are unlikely,"," We have chosen to fit models with $v_{\rm thermal} = 0.8$ and $1.0$ km/s, as the line widths of the maser features indicate that much higher intrinsic thermal widths are unlikely." + We fiud that iu some cases the circular polarization spectrum is still narrower than the model spectrin., We find that in some cases the circular polarization spectrum is still narrower than the model spectrum. + For these features we allow for narrowing bx releasing e»., For these features we allow for narrowing by releasing $a_2$. + The combined fitting determines the circular polarization percentage Py aud the line width Acer., The combined fitting determines the circular polarization percentage $P_{\rm V}$ and the line width $\Delta v_{\rm L}$. + The coefficient “lpp is specifically determined for the best fitted model., The coefficient $A_{\rm F-F'}$ is specifically determined for the best fitted model. + Using this Eq., Using this Eq. + L again gives By., \ref{eq2} again gives $B_{||}$. + The observations were performed at the Very Loug baseline Array (VLBA) on December 13th 1998., The observations were performed at the Very Long baseline Array (VLBA) on December 13th 1998. +" At the frequency of the 6,5555 rotational transition of ITO. 22.235 (11. the average beam width is 2:0.5< mas."," At the frequency of the $6_{16}-5_{23}$ rotational transition of $_{2}$ O, 22.235 GHz, the average beam width is $\approx 0.5 \times +0.5$ mas." + This allows us to resolve the different TeO maser features in the CSE., This allows us to resolve the different $_{2}$ O maser features in the CSE. + The data were correlated twice. ounce with modest (7.8 kIIz 20.1 lans. +) spectral resolution. which enabled us to generate all Ll polarization combinations (RR. LL. RE aud LR).," The data were correlated twice, once with modest $7.8$ kHz $= 0.1$ km $^{-1}$ ) spectral resolution, which enabled us to generate all 4 polarization combinations (RR, LL, RL and LR)." + The secoud correlator run was performed with high spectral resolution (1.95 kIIz =0.027 kii C) necessary fo detect the circular polarization signature of the TeO Zeeman splitting. aud therefore ouly contained the two polarization combinations RR aud LL.," The second correlator run was performed with high spectral resolution $1.95$ kHz $= 0.027$ km $^{-1}$ ), necessary to detect the circular polarization signature of the $_{2}$ O Zeeman splitting, and therefore only contained the two polarization combinations RR and LL." + We have performed 6 hours of observations per source-calibrator pair., We have performed 6 hours of observations per source-calibrator pair. + The calibrator was observed for 11/2 hours imm a number of scans equally distributed over the 6 hours., The calibrator was observed for $1~1/2$ hours in a number of scans equally distributed over the 6 hours. + We used 2 filters (TFs) of 1 MIIz width. which were overlapped to get a velocity coverage of z22 laus. This covers most of the velocity range of the Πο Ο maser.," We used 2 filters (IFs) of 1 MHz width, which were overlapped to get a velocity coverage of $\approx 22$ km/s. This covers most of the velocity range of the $_2$ O maser." + The data analvsis followed the method. of Keimball. Diamond Cotton (1995).," The data analysis followed the method of Kemball, Diamond Cotton (1995)." +" The reduction path. shown in Fig. δν,"," The reduction path, shown in Fig. \ref{fig1}," + was performed in the AIPS data reduction package., was performed in the AIPS data reduction package. + The first standard calibration steps were performed on the data-set with modest spectral resolution., The first standard calibration steps were performed on the data-set with modest spectral resolution. + We used the svsteui temperature measurements provided with the data to perform the amplituce calibration for both the calibrators aud the sources., We used the system temperature measurements provided with the data to perform the amplitude calibration for both the calibrators and the sources. + Parallactic auele correction. flageineao aud sinele- aud imultibanud delay calibration were all oue τοσα] on the calibrators observed with each source.," Parallactic angle correction, flagging and single- and multi-band delay calibration were all done regularly on the calibrators observed with each source." +" During 1/3 of the observatiou tie, he first IF suffered strong interference. which forced us to Πας several of the frequency clamuels (àL1 MITZ) iu addition to the normal flaeeime."," During 1/3 of the observation time, the first IF suffered strong interference, which forced us to flag several of the frequency channels $\approx 0.1$ MHz) in addition to the normal flagging." + Also. for most of the observations IF 1 of the Los Alamos (LÀ) auteuna was nutsable.," Also, for most of the observations IF 1 of the Los Alamos (LA) antenna was unusable." + The solutions obtained at these calibration steps were copied aud applied to the high spectral resolution data set., The solutions obtained at these calibration steps were copied and applied to the high spectral resolution data set. + The complex bandpasses were then determined for bothdata-sets separately., The complex bandpasses were then determined for bothdata-sets separately. + Additional calibration steps were needed for accurate processing of polarization data., Additional calibration steps were needed for accurate processing of polarization data. + The gain ratio between the R- (vight-}) and L- hand polarizations was determined using the auto- data of the reference antenna on a short scan of the maser source., The gain ratio between the R- (right-) and L- (left-) hand polarizations was determined using the auto-correlation data of the reference antenna on a short scan of the maser source. + This step contains the critical, This step contains the critical +thus. the line of sight is unbiased for intervening-metal line absorbers.,"thus, the line of sight is unbiased for intervening–metal line absorbers." + The stronger absorption proliles are resolved. auc required. a two-component Gaussian fit., The stronger absorption profiles are resolved and required a two–component Gaussian fit. + A2803 15 blended. with Galactic A2852: this resulted in an unphysical doublet ratio for the red component of the Gaussian fit., $\lambda 2803$ is blended with Galactic $\lambda 2852$; this resulted in an unphysical doublet ratio for the red component of the Gaussian fit. + Ouly a C270H spectrum was available for this line of sight., Only a G270H spectrum was available for this line of sight. + Because of the relatively high redshift of this emission liue object. the strougFell trausitious fell in tle [orest.," Because of the relatively high redshift of this emission line object, the strong transitions fell in the forest." + A2600 is Just recdhward of the emission. but it is hopelessly bleucded in a strong absorption complex.," $\lambda 2600$ is just redward of the emission, but it is hopelessly blended in a strong absorption complex." + À2822 is quite strong.," $\lambda +2852$ is quite strong." + The data are preseuted iu Figure 3. and the rest-frame equivalent wicltlis are presented in Table 2., The data are presented in Figure \ref{fig:q1327} and the rest–frame equivalent widths are presented in Table 2. + This object was observed for a program (PID 6781) to investigate the iouizine coutinuum in ACUN: this is an unbiased line of sight., This object was observed for a program (PID 6781) to investigate the ionizing continuum in AGN; this is an unbiased line of sight. + The system is the weakest of the four ancl the ouly one in which the profiles are uuresolved at FOS resolution (subsequently. the widths of the Craussians used for the equivalent width measurements were held coustant at the value of the FOS instrumental spreacl Πιοτοι: this leaves a somewhat significaut residual to the fit iu the liue cores).," The system is the weakest of the four and the only one in which the profiles are unresolved at FOS resolution (subsequently, the widths of the Gaussians used for the equivalent width measurements were held constant at the value of the FOS instrumental spread function; this leaves a somewhat significant residual to the fit in the line cores)." + Both a GI30H and a CU90H spectrum were available for this line of sight., Both a G130H and a G190H spectrum were available for this line of sight. + The rest-frame equivalent width is 3.05x0.26A. indicatiug that this systems is not a DLA.," The rest–frame equivalent width is $3.95\pm0.26$, indicating that this systems is not a DLA." + No nor absorption was detected to a 5o detection limit of 0.27 and 0.36. A. respectively.," No nor absorption was detected to a $5~\sigma$ detection limit of $0.27$ and $0.36$ , respectively." + AI331 was detected., $\lambda 1334$ was detected. + Also detected were A2301. 2371. 2382. ancl 2600.," Also detected were $\lambda 2344$, 2374, 2382, and 2600." + A2852 was not detected to 0.19 (5 σ]., $\lambda 2852$ was not detected to 0.49 $5~\sigma$ ). + The data are presented in Figure | aud the rest-frame equivalent widths are presented in Table 2., The data are presented in Figure \ref{fig:pg1427} and the rest–frame equivalent widths are presented in Table 2. + Iu the spectrum of PISS O151039 (Boisséetal.1998).. absorption at 2=0.072 is associated with a post-star burst dwarf galaxy. (Steidel.Dickinson.&Bowen1993).," In the spectrum of PKS $0454+039$ \citep{boisse}, absorption at $z=0.072$ is associated with a post–star burst dwarf galaxy \citep{ccs0454}." +. Bolssé state that the presence of this galaxy was “one additional motivation for observing this quasar”., Boissé state that the presence of this galaxy was “one additional motivation for observing this quasar”. + Thus. this quasar was dropped Crom this survey.," Thus, this quasar was dropped from this survey." + Bowen.Blades.&Pettini(1996) published this system. which arises in the inclined galaxy M61.," \citet{bbp96} published this system, which arises in the inclined galaxy M61." +" This quasar was observed because it was a sightliue that ""lies fortuitously behind [agalaxy] whose existenceisalready known.""", This quasar was observed because it was a sightline that “lies fortuitously behind [agalaxy] whose existenceisalready known.” + Thus. thisline of sielt was also dropped from this survey.," Thus, thisline of sight was also dropped from this survey." +The clustering of sources broadens the flux PDF and creates a value tail in the distribution (e.g. ??)).,"The clustering of sources broadens the flux PDF and creates a high-value tail in the distribution (e.g. \citealt{MD08, Dijkstra08}) )." + How strong is this effect and how much do the properties of the underlying sources affect these trends?, How strong is this effect and how much do the properties of the underlying sources affect these trends? +" In Fig. 4,,"," In Fig. \ref{fig:cluster}," +" we plot flux PDFs at z=10, assuming Aurp Mpc."," we plot flux PDFs at $z=10$, assuming $\lmfp=10$ Mpc." +" The dotted curve in the figure was generated from the semi-numeric calculation assuming a step-function attenuation at Amtp=10 Mpc, shown to be an adequate approximation in Fig. 2.."," The dotted curve in the figure was generated from the semi-numeric calculation assuming a step-function attenuation at $\lmfp=10$ Mpc, shown to be an adequate approximation in Fig. \ref{fig:mfp_att}." +" The dashed curve is obtained in the same manner, but with randomized source locations."," The dashed curve is obtained in the same manner, but with randomized source locations." + We see that ignoring source clustering can severely underestimate the widths of the flux PDF., We see that ignoring source clustering can severely underestimate the widths of the flux PDF. + Even the shape of the curves is quite different., Even the shape of the curves is quite different. + Fig., Fig. + 4 also compares the PDF to our analytic model., \ref{fig:cluster} also compares the PDF to our analytic model. +" The dot-dashed line uses the analog of equation (2)) but for step-wise attenuation (see ? and ?)), again assuming Poisson distributed sources."," The dot-dashed line uses the analog of equation \ref{eq:jdist_r0}) ) but for step-wise attenuation (see \citealt{Zuo92} and \citealt{Furlanetto09}) ), again assuming Poisson distributed sources." + It closely matches the semi-numeric results for the same assumptions., It closely matches the semi-numeric results for the same assumptions. + The solid line includes linear clustering over the scale Amsp as described in equation (4))., The solid line includes linear clustering over the scale $\lambda_{\rm mfp}$ as described in equation \ref{eq:jdistbn_cluster}) ). +" The clustering length of 10?Mg halos is ~ 2 Mpc at this redshift, so the clustering on scales larger than the m.f.p."," The clustering length of $M \sim \Mmin \sim 10^8 \Msun$ halos is $\sim$ 2 Mpc at this redshift, so the clustering on scales larger than the m.f.p." + should be well into the linear regime and accurately predicted by the analytic model., should be well into the linear regime and accurately predicted by the analytic model. +" Obviously, this simple prescription provides a relatively poor match to the full semi-numeric results: although the large-scale clustering does broaden the distribution by a comparable amount, the shapes still disagree."," Obviously, this simple prescription provides a relatively poor match to the full semi-numeric results: although the large-scale clustering does broaden the distribution by a comparable amount, the shapes still disagree." + Part of this difference is easy to understand and is a consequence of the analytic model's simple prescription for clustering: the model not only fixes the attenuation volume, Part of this difference is easy to understand and is a consequence of the analytic model's simple prescription for clustering: the model not only fixes the attenuation volume + , +(intermediate mass) black holes in the Galactic center region.,(intermediate mass) black holes in the Galactic center region. + Our current observations support limits between those plotted bv Hansen&Milosavljevió(2003) in their Fig., Our current observations support limits between those plotted by \citet{HM03} in their Fig. +" 2 for “astrometric resolutions"" of 0.1 and 1.0 mas.", 2 for “astrometric resolutions” of 0.1 and 1.0 mas. +" The limits on (hese parameters are complex and depend on both parameters. but roughly we can exclude secondary. black holes with niasses greater than ~LO! and senmi-major axes between LO? and 10"" AU [romÀ*."," The limits on these parameters are complex and depend on both parameters, but roughly we can exclude secondary black holes with masses greater than $\sim10^4$ and semi-major axes between $10^3$ and $10^5$ AU from." +. Excluding stellar mass black holes (<100 )) will require more than an order of magnitude better astrometric accuracy and is unlikely in the near future., Excluding stellar mass black holes $<100$ ) will require more than an order of magnitude better astrometric accuracy and is unlikely in the near future. + We have measured the position of the compact non-thermal radio source.A... al the center of the Galaxy relative to extragalactic radio sources.," We have measured the position of the compact non-thermal radio source, at the center of the Galaxy relative to extragalactic radio sources." + The apparent motion of is consistent with that expected. [rom the orbit of the Sun around the Galactic center., The apparent motion of is consistent with that expected from the orbit of the Sun around the Galactic center. + Ànv peculiar motion of perpendicular to the plane of the Galaxy is less than L8 (20)., Any peculiar motion of perpendicular to the plane of the Galaxy is less than 1.8 $2\sigma$ ). + This result is complementary to infrared observations of stellar orbits at the Galactic center. which require 4x10° within a radius of 100 AU ofA*.," This result is complementary to infrared observations of stellar orbits at the Galactic center, which require $4\times10^6$ within a radius of 100 AU of." +. The results of several different analvses indicate a significant fraction. if not all. of the mass in ihe central LOO AU is tied toA*.," The results of several different analyses indicate a significant fraction, if not all, of the mass in the central 100 AU is tied to." +. Were not a SABIL. it must be bound to the inner 4 AU of the dvnamical center of the Galaxy.," Were not a SMBH, it must be bound to the inner 4 AU of the dynamical center of the Galaxy." + This would imply an extraordinarily high mass density. ancl probably require a SMDII., This would imply an extraordinarily high mass density and probably require a SMBH. + The gravitational attractions of the ~10to10* stars within 2 pe of the Galactic center impart a significant motion toÀ*., The gravitational attractions of the $\sim10^6~{\rm to}~10^7$ stars within 2 pc of the Galactic center impart a significant motion to. +. Based on nunerical simulations of the central star cluster and our upper limit to the motion of out of the plane of the Galaxy. a maxinnun-likelihood lower limit [or the mass of is 0.4x10AL.," Based on numerical simulations of the central star cluster and our upper limit to the motion of out of the plane of the Galaxy, a maximum-likelihood lower limit for the mass of is $0.4\times10^6$." +.. These analyses make very conservative assumptions that would tend to underestimate the motion of and. hence. underestimate (he mass limit.," These analyses make very conservative assumptions that would tend to underestimate the motion of and, hence, underestimate the mass limit." + This is the first evidence (hat a compact radiative source al (he center of a galaxy is a super-lassive object., This is the first evidence that a compact radiative source at the center of a galaxy is a super-massive object. + Other measurements determine a large mass. but can onlyindirectly associate il wilh the radiative source through positional agreement.," Other measurements determine a large mass, but can only associate it with the radiative source through positional agreement." + The observed radio frequency size of is less than 1 AU. after accounting for the elects of interstellar scattering.," The observed radio frequency size of is less than 1 AU, after accounting for the effects of interstellar scattering." + The mass density implied by having at least 0.4x109 within a 0.5 AU radius is a staggering 7x107 7!, The mass density implied by having at least $0.4\times10^6$ within a 0.5 AU radius is a staggering $7\times10^{21}$ $^{-3}$! + This is only about 3 lower than the mass density of a 4x109 black hole within its Schwarzschild, This is only about 3 orders-of-magnitude lower than the mass density of a $4\times10^6$ black hole within its Schwarzschild +"profile reseiubling a star rotating at οsni=Uskinss ! (ervey dashed line, which is identical to the widest profile shown in veffiie:Sun)).","profile resembling a star rotating at $v\,\sin{i} = 4$ $^{-1}$ (grey dashed line, which is identical to the widest profile shown in \\ref{fig:Sun}) )." + The profile expected frou: a star rotating atf οκ;= dkknnss to is a very eood match to the profile of Sanders 1152. with only the far wings bevond +6kkuiss ! differing slightly.," The profile expected from a star rotating at $v\,\sin{i} = 4$ $^{-1}$ is a very good match to the profile of Sanders 1452, with only the far wings beyond $\pm 6$ $^{-1}$ differing slightly." + This again may be an effect of the image slicer. but the far wines of the decouvolved broadening fiction are also less well defined due to the existence of uncaptured nue bleuds and limited SNR in the data.," This again may be an effect of the image slicer, but the far wings of the deconvolved broadening function are also less well defined due to the existence of uncaptured line blends and limited SNR in the data." + From the close match between the broadening function of Sanders 1152 and the artificially broadened versions of the Camvimede spectruii. we derive a value for the projected rotation velocity of Sanders 1152 of esiu;={4£0.5kkinss +.," From the close match between the broadening function of Sanders 1452 and the artificially broadened versions of the Ganymede spectrum, we derive a value for the projected rotation velocity of Sanders 1452 of $v\,\sin{i} = 4 \pm 0.5$ $^{-1}$." + The uncertaiuty is an eiipirical estimate deduced. frou a comparison with broadcuing functions with different values of esin;.," The uncertainty is an empirical estimate deduced from a comparison with broadening functions with different values of $v\,\sin{i}$." + Broadening fuuctious witli esiné=3.5 and L5kkniss+ can be distinguished from the data.," Broadening functions with $v\,\sin{i} = 3.5$ and $^{-1}$ can be distinguished from the data." + The results of our detailed spectroscopic analysis enable us to discuss the rauge of chromospheric activity seen in M67 in conjunction with the additional -information on rotation. at least for à representative subset of solu-tvpoe stars in M67.," The results of our detailed spectroscopic analysis enable us to discuss the range of chromospheric activity seen in M67 in conjunction with the additional information on rotation, at least for a representative subset of solar-type stars in M67." + We therefore briefly iscuss du the following some relevant issues in this contest. namely. (1) the potential rauge of brightuess variability in sun-like stars at solar age and. by inference. in the Sun itself. and (2) some facets of angular monentun evolution m solu-tvpo stars. including the possible origin of relatively rapid rotation at the age of the M67 open cluster.," We therefore briefly discuss in the following some relevant issues in this context, namely, (1) the potential range of brightness variability in sun-like stars at solar age and, by inference, in the Sun itself, and (2) some facets of angular momentum evolution in solar-type stars, including the possible origin of relatively rapid rotation at the age of the M67 open cluster." + The potential excursions of the activity. cvcles of the M67 solu-like stars and possibly the Sun itself to exceptionally high values. as inferred from the II distvibution of the M67. solu-tvpo stars given iu Ciunupapaetal(2006.theirFie.Όλι now must be considered in the light of the rotation measures and estimates eiven herein.," The potential excursions of the activity cycles of the M67 solar-like stars and possibly the Sun itself to exceptionally high values, as inferred from the HK distribution of the M67 solar-type stars given in \citet[][their Fig. 3]{Giampapa06}, now must be considered in the light of the rotation measures and estimates given herein." + In particubu. since 81152 with a meu HE iudex of Ll is rotating at more than twice the equatorial solar rotation velocity. aud $8717 with a mean HER = 351mA is a spectroscopic binary. the implication is that excursions iu the eveles of M67 solar-type stars aud the Suu itself appear to be less than about TIS ~ 250mA. re. the next highest ITI iudex found iu the Cdammpapa et al.," In particular, since S1452 with a mean HK index of 414 is rotating at more than twice the equatorial solar rotation velocity, and S747 with a mean HK = 354 is a spectroscopic binary, the implication is that excursions in the cycles of M67 solar-type stars and the Sun itself appear to be less than about HK $\sim$ 250, i.e., the next highest HK index found in the Giampapa et al." + sample. which is roughly higher than the representative riaxiniuun value seen in the modern solar evele of HIS. z 225mA.," sample, which is roughly higher than the representative maximum value seen in the modern solar cycle of HK $\approx$ 225." + Within the reported BW color range of the Sum of about 0.63 to 0.67 (VandeuBere&Dridees198£).. the only star iu the Cdaimpapa et al.," Within the reported $B-V$ color range of the Sun of about 0.63 to 0.67 \citep{VandenBerg84}, the only star in the Giampapa et al." + sample that exceeds the maxima solar III iudex (8 1011) also is a short-period biuuv with a period of 16.2 davs aud mean IIR. = 218mA., sample that exceeds the maximum solar HK index (S 1014) also is a short-period binary with a period of 16.2 days and mean HK = 248. + The determination of definitive τηραΠΠ to the ITI iudex for single sun-like astars at solar age aud metallicitv will require a more extensive survev of rotation in the MIG? sobu-tvpo stars., The determinination of a definitive upper-limit to the HK index for single sun-like stars at solar age and metallicity will require a more extensive survey of rotation in the M67 solar-type stars. + Caven our results and the well-known correlation between variations in chromospheric ciission aud changes in the solar radiance or. correspoucinely. ii stellar brightness. it is of interest to consider the implications of the plausible upper liit to chromospheric emissiou in solar-type aud solu-age stars. as inferred from the M67. sample. for the possible rauge of brightuess variability that nav occur.," Given our results and the well-known correlation between variations in chromospheric emission and changes in the solar irradiance or, correspondingly, in stellar brightness, it is of interest to consider the implications of the plausible upper limit to chromospheric emission in solar-type and solar-age stars, as inferred from the M67 sample, for the possible range of brightness variability that may occur." + Using the dependent calibration approach described i Cdampapa and adopting a color of B.V=0.65 as representativo of analogs of the Sun. we find that the upper Init eiven above of IT& z 250 corresponds to log Rope~LO. where Πέις is the ratio of the total chromospheric IT aud Is emission core flux to the stellar bolometric flux. corrected for the non-chromospheric (plotospheric) contribution.," Using the color-dependent calibration approach described in \citet{Giampapa06} and adopting a color of $B-V = 0.65$ as representative of analogs of the Sun, we find that the upper limit given above of HK $\simeq$ 250 corresponds to log $^{\prime}_{HK} \sim -4.70$, where $^{\prime}_{HK}$ is the ratio of the total chromospheric H and K emission core flux to the stellar bolometric flux, corrected for the non-chromospheric (photospheric) contribution." + Inspection of the results of long-term. high precision photometry of solu-tvpe stars by Lockwoodetal.(19907.theirFig.17) as a muction of the paramcter Πτι suggests that this level of activity would correspond to an annual mean level of rum brightuess variations of roughly 0.002 mae. ie. varlabilitv in the brightness as recorded in the Strouuugren b and y bands. or about twice the ~0.1% variation in total irracliance that has been measured thus aa for the coutemporary Sun curing the solar cycle.," Inspection of the results of long-term, high precision photometry of solar-type stars by \citet[][their Fig. 17]{Lockwood97} + as a function of the parameter $^{\prime}_{HK}$ suggests that this level of activity would correspond to an annual mean level of rms brightness variations of roughly 0.002 mag, i.e. variability in the brightness as recorded in the Strömmgren $b$ and $y$ bands, or about twice the $\sim 0.1\%$ variation in total irradiance that has been measured thus far for the contemporary Sun during the solar cycle." + Therefore. we suggest that 0.2% represents au upper iuit to the likely excursion of the solar Iuuninous output as a result of cuhanced levels of magnetic activity.," Therefore, we suggest that $\sim 0.2\%$ represents an upper limit to the likely excursion of the solar luminous output as a result of enhanced levels of magnetic activity." + We can refine this estimate of the upper lint further x nofiug that the brightucss changes given by Lockwoodetal.(1997) were for the mean variation of the smu of he Strónuueren hb aud y bands., We can refine this estimate of the upper limit further by noting that the brightness changes given by \citet{Lockwood97} were for the mean variation of the sum of the Strömmgren $b$ and $y$ bands. + Hence. the variation of he total irraciance must be less than what is observed in these visible spectral bands.," Hence, the variation of the total irradiance must be less than what is observed in these visible spectral bands." + Radicketal.(1998) estimated (for simall variations) a factor for converting )etwoeen ao fractional change in bolometric fux iuto he corresponding magnitude difference iu (5|y)/2.," \citet{Radick98} estimated (for small variations) a factor for converting between a fractional change in bolometric flux into the corresponding magnitude difference in $(b + +y)/2$." + Adopting their conversion factor of 1.39 aud the estimate of brightuess variations of nunae eiven above viclds an estimate of for the uppor limit for variations in the bolometric fux., Adopting their conversion factor of 1.39 and the estimate of brightness variations of mag given above yields an estimate of for the upper limit for variations in the bolometric flux. + This is only slightly larecr thu the mean variation of iu the total solar irradiance observed durius the course of the solar cvele., This is only slightly larger than the mean variation of in the total solar irradiance observed during the course of the solar cycle. + The relatively more rapid rotation of 81152 invites further consideration iu the context of aneular momentum evolution aud the determination of stellar ages based on rotation. known as evrochrouologv (Barnes2007).," The relatively more rapid rotation of S1452 invites further consideration in the context of angular momentum evolution and the determination of stellar ages based on rotation, known as ""gyrochronology"" \citep{Barnes07}." + At its measured (projected) rotation velocity and assumuime a stellar radius close to solar. the vevro-age’ of Sanders 1152 is 1.0+0.2 CC (Barues2007).," At its measured (projected) rotation velocity and assuming a stellar radius close to solar, the “gyro-age” of Sanders 1452 is $1.0 \pm 0.2$ Gyr \citep{Barnes07}." +. This value is an upper Πιτ because we mncasure only the projected velocity ¢sin/.," This value is an upper limit because we measure only the projected velocity $v\,\sin{i}$." + A more direct comparison can be obtained with the esins age correlation given by Pace&Pasquini(2001.their 9)..," A more direct comparison can be obtained with the $v\,\sin{i}$ –age correlation given by \citet[][their Fig. +9]{Pace04}." + The interred age (upper Iit) of 51152 based ou the three possible power law fits adopted by Pace Pasquini is iu the rauge of 1.21.5 Cox., The inferred age (upper limit) of S1452 based on the three possible power law fits adopted by Pace Pasquini is in the range of 1.2–1.5 Gyr. + In either approach. the rotatiou-based age estiuiate for 81152 is in vivid coutrast to the age ranee for M67 of 3.5LS Cyr (Yadav or that of the Sun. namely. GGsyr (e...Do- and the simular solar age inuplied for the slow rotators of our sample.," In either approach, the rotation-based age estimate for S1452 is in vivid contrast to the age range for M67 of 3.5–4.8 Gyr \citep{Yadav08} or that of the Sun, namely, Gyr \citep[e.g.,][]{Bonanno02, Baker05} and the similar solar age implied for the slow rotators of our sample." + Given its ligher rotational velocity. 81152 therefore represents an alternative path for angular momentum," Given its higher rotational velocity, S1452 therefore represents an alternative path for angular momentum" +"where z(8) is Earth's column density as a function of angle and c, is the total v-matter crossection.",where $z(\theta)$ is Earth's column density as a function of angle and $\sigma_T$ is the total $\nu$ -matter crossection. + We have calculated the expected number of events for a km? detector., We have calculated the expected number of events for a $^3$ detector. + We have used CTEQS5 for the neutrino-matter cross-section (Laietal2000).., We have used CTEQ5 for the neutrino-matter cross-section \citep{2000EPJC...12..375L}. + We follow the calculation by Stanev1991) of average muon range., We follow the calculation by \citep{1991PhRvD..44..3543L} of average muon range. + The Earth column density is taken from the Preliminary Earth Reference Model (Dziewonski&Anderson1981)., The Earth column density is taken from the Preliminary Earth Reference Model \citep{1981PEPI...25..297D}. +". Using approximations A and B and the neutrino spectrum derived from the Band function, we have studied a GRB with a photon break energy e"".=300 keV, located at a redshift z=1 and with Lorentz bulk boost I'=300."," Using approximations A and B and the neutrino spectrum derived from the Band function, we have studied a GRB with a photon break energy $\epsilon^b_\gamma += 300$ keV, located at a redshift z=1 and with Lorentz bulk boost $\Gamma=300$." + We also set the spectral indices to a.=—2 and 3.=—1., We also set the spectral indices to $\alpha_\gamma=-2$ and $\beta_\gamma=-1$. + We have normalized the neutrino fluence of all three spectra to the same (arbitrary) value as described in section 3.., We have normalized the neutrino fluence of all three spectra to the same (arbitrary) value as described in section \ref{sec:photopion}. +" For this GRB the effective break energy is €,=110 keV. The neutrino break energy for approximation A is 5.98x10! eV and for approximation B it's 1.63x10!"" eV. For all cases we have fixed the synchrotron energy break at 10!"" eV. Figure 2. shows the three neutrino spectra."," For this GRB the effective break energy is $\bar{\epsilon}_\gamma=110$ keV. The neutrino break energy for approximation A is $\times 10^{14}$ eV and for approximation B it's $\times +10^{15}$ eV. For all cases we have fixed the synchrotron energy break at $^{16}$ eV. Figure \ref{fig:NuFlux} shows the three neutrino spectra." + Again it is clear that approximation A is inadequate because it overestimates the contribution of low energy neutrinos., Again it is clear that approximation A is inadequate because it overestimates the contribution of low energy neutrinos. + Figure 3 the ratio approximation A to B of expected number of events as a function cos(4) for this example GRB., Figure \ref{fig:ratio} the ratio approximation A to B of expected number of events as a function $\cos(\theta)$ for this example GRB. + For all GRB locations in the sky we see that approximation A overestimates the expected number of events., For all GRB locations in the sky we see that approximation A overestimates the expected number of events. + For steeper angles the ratio 1s larger. because for approximation B the characteristic neutrino energy is higher and therefore Earth's attenuation is higher.," For steeper angles the ratio is larger, because for approximation B the characteristic neutrino energy is higher and therefore Earth's attenuation is higher." + We have shown that the usual choice to describe the photon spectra in the calculation of neutrino fluxes from GRBs overestimates the contribution of high energy photons (and therefore contribution of low energy neutrinos is overestimated)., We have shown that the usual choice to describe the photon spectra in the calculation of neutrino fluxes from GRBs overestimates the contribution of high energy photons (and therefore contribution of low energy neutrinos is overestimated). + This results in a higher exepected event rate by a factor of z 2 for all models that make this assumption., This results in a higher exepected event rate by a factor of $\approx$ 2 for all models that make this assumption. + The actual value of the overestimation of the expected number of events depends on the matter column depth that neutrinos must cross through Earth in the direction of the GRB., The actual value of the overestimation of the expected number of events depends on the matter column depth that neutrinos must cross through Earth in the direction of the GRB. + Also we have shown that the typical neutrino energy is zz 1012 eV. The characteristic energy of neutrinos is a factor of ¢ larger than the values obtained by Guettaetal(2004) and a factor of 10 than the average value used by Waxman&Bahcall(1997).., Also we have shown that the typical neutrino energy is $\approx$ $^{15}$ eV. The characteristic energy of neutrinos is a factor of $e$ larger than the values obtained by \citet{2004APh....20..429G} and a factor of 10 than the average value used by \citet{1997PhRvL..78.2292W}. + For back of the envelope calculations we provide a new approximation to the Band function that is adequate for the computation of neutrino spectra., For back of the envelope calculations we provide a new approximation to the Band function that is adequate for the computation of neutrino spectra. + Kashti&Waxman(2005) have discussed the effects of muon and pion energy losses leading, \citet{2005PhRvL..95..181101K} have discussed the effects of muon and pion energy losses leading +The standard. theory of big bang nucleosvnthesis (SBBN: og. Boeseaard Steigman 1985: Steigman 1980: Walker et al.,"The standard theory of big bang nucleosynthesis (SBBN; e.g., Boesgaard Steigman 1985; Steigman 1989; Walker et al." +" 1991) accurately predicts the primordial abundances of the light elements D. ο, tHe and Li. as a function of the cosmic barvon density. nxQiA7. or. equivalently. of the barvon-to-photon ratio. η."," 1991) accurately predicts the primordial abundances of the light elements D, $^3$ He, $^4$He and $^7$ Li, as a function of the cosmic baryon density, $\rho_{\mathrm{b}} \propto + \Omega_{\mathrm{b}} \, h^2$, or, equivalently, of the baryon-to-photon ratio, $\eta$." + Since the barvon density is the sole. parameter. in he SBBN. observations of D. He. Πο and SLi in astrophysical environments. not. vet alecteck by subsequent. stellar evolution oller a direct way to infer the barvon density of the universe ancl to assess whether the SBBN theory correetly describes the first three minutes of the hot early universe.," Since the baryon density is the sole parameter in the SBBN, observations of D, $^3$ He, $^4$ He and $^7$ Li in astrophysical environments not yet affected by subsequent stellar evolution offer a direct way to infer the baryon density of the universe and to assess whether the SBBN theory correctly describes the first three minutes of the hot early universe." + Nowadavs. there is still disagreement on which is the value of 5 as inferred from limits on theprimordial deuterium abundance from high-redshift absorption systems (mostly Danipec Lyman à or Lyman limit absorbers: e... Carswell et al.," Nowadays, there is still disagreement on which is the value of $\eta$ as inferred from limits on theprimordial deuterium abundance from high-redshift absorption systems (mostly Damped Lyman $\alpha$ or Lyman limit absorbers; e.g., Carswell et al." + 1994: Songaila et al., 1994; Songaila et al. + 1994: Tytler. Fan Burles 1996: Rugers Hogan 1996: Songaila. Wanipler Cowie 1997: Webb et al.," 1994; Tytler, Fan Burles 1996; Rugers Hogan 1996; Songaila, Wampler Cowie 1997; Webb et al." +" 1997: 3urles ""Tytler 1998: Levshakov. Ixegel Takahara 1998: O'Moeara et al."," 1997; Burles Tytler 1998; Levshakov, Kegel Takahara 1998; O'Meara et al." + 2001: Pettini Bowen 2001: Levshakoy et al., 2001; Pettini Bowen 2001; Levshakov et al. + 2002): estimates of the primordial ‘He abundance from oxtragalactic regions (e.g.. Olive. Skillman Steigman 1997: Izotov et al.," 2002); estimates of the primordial $^4$ He abundance from extragalactic regions (e.g., Olive, Skillman Steigman 1997; Izotov et al." +" 1999: Peimbert. Peimbert Luriciana 2002: see also Pagel 2000 for a review) and estimates of the. pristine ""Li content in old. metal-poor (FefL] 1.5 dex). warm (dc5700 Ix) clwarl stars in the solar neighbourhood (e.g.. Spite Spite 1982: Spite. Maillard Spite 1984: Spite Spite 1986: Itebolo. Molaro Beckman 1988: Thorburn 1992. 1994: Bonifacio Alolaro 1997: Vauclai Charbonnel 1995. LOOS: Vhéeaado Vauclair Wl: Pinsonneault ct al."," 1999; Peimbert, Peimbert Luridiana 2002; see also Pagel 2000 for a review) and estimates of the pristine $^7$ Li content in old, metal-poor ([Fe/H] $\le -1.5$ dex), warm $T_{\mathrm{eff}} \ge 5700$ K) dwarf stars in the solar neighbourhood (e.g., Spite Spite 1982; Spite, Maillard Spite 1984; Spite Spite 1986; Rebolo, Molaro Beckman 1988; Thorburn 1992, 1994; Bonifacio Molaro 1997; Vauclair Charbonnel 1995, 1998; Théaado Vauclair 2001; Pinsonneault et al." + 1999. 2002).," 1999, 2002)." + Measurements of Ηο in regions in the outer parts of the Galactic disc should provide values very close to the primordial one. owing to the slow evolution of the disc in these regions. but they appear to poorly constrain the 7 range (e.g.. Rood et al.," Measurements of $^3$ He/H in regions in the outer parts of the Galactic disc should provide values very close to the primordial one, owing to the slow evolution of the disc in these regions, but they appear to poorly constrain the $\eta$ range (e.g., Rood et al." + 1998: Dania. Hood Balser 2002).," 1998; Bania, Rood Balser 2002)." + Data on cosmic microwave background (CM) anisotroples oovide an alternative. independent method [or constraining η].," Data on cosmic microwave background (CMB) anisotropies provide an alternative, independent method for constraining $\eta$." + The first. release of results from. the(WALAP: )onnett et al., The first release of results from the; Bennett et al. + 2003: Spergel et al., 2003; Spergel et al. + 2003) makes the CALB the prime cosmic barvometer. owing to the high. precision.," 2003) makes the CMB the prime cosmic baryometer, owing to the high precision." + A combination of data with other finer scale CMD experiments. (ACBAR lxuo et. al., A combination of data with other finer scale CMB experiments (ACBAR – Kuo et al. + 2002 and CDI Pearson οἱ al., 2002 – and CBI – Pearson et al. + 2002) ancl with astronomical measurements of the power spectrum (2dbk Galaxy Reelshilt Survey measurements Pereival et al., 2002) and with astronomical measurements of the power spectrum (2dF Galaxy Redshift Survey measurements – Percival et al. + 2001 0 and Lyman a forest data Croft et al., 2001 – and Lyman $\alpha$ forest data – Croft et al. + 2002: Cinedin. Llamilton 2002) gives Onh?=0.0224 40.0009. or. equivalently. qocsi=6.1n (Spergel et. al. ," 2002; Gnedin Hamilton 2002) gives $\Omega_{\mathrm{b}} \, h^2 = 0.0224 + \pm 0.0009$ , or, equivalently, $\eta_{\mathrm{10, \, CMB}} = + 6.1^{+0.3}_{-0.2}$ (Spergel et al. ," +where mo—n 10755.By adopting the SBBN predictions and using this y value. one obtains," where $\eta_{\mathrm{10}} \equiv 10^{10} \, \eta$ .By adopting the SBBN predictions and using this $\eta$ value, one obtains" +maenification of the density for. 1000. in. this. case, the amount of emission∙∙ and absorption∙ seen in∙Het A10833 will strongly depend on the orbital of the system."," This range of velocities is consistent with $\lambda$ 10833 being formed in the wind of Eta Car A. Eta Car B might significantly influence the $\lambda$ 10833 line profile through photoionization of the outer parts of the wind of Eta Car A and, in this case, the amount of emission and absorption seen in $\lambda$ 10833 will strongly depend on the orbital parameters of the system." +" Nevertheless, at phases sufficiently farparameters from periastron such as at @=11.875, there is no evidence for additional velocity fields in our line-of-sight, such as one would expect in the case that the absorption was formed in the wind of Eta Car B or in high-velocity material from the wind-wind collision zone."," Nevertheless, at phases sufficiently far from periastron such as at $\phi=11.875$, there is no evidence for additional velocity fields in our line-of-sight, such as one would expect in the case that the absorption was formed in the wind of Eta Car B or in high-velocity material from the wind-wind collision zone." +The profiles from ¢=11.991 and ó=11.998 show very different 410833 absorptions compared to theone from à=11.875.,The profiles from $\phi=11.991$ and $\phi=11.998$ show very different $\lambda$ 10833 absorptions compared to theone from $\phi=11.875$. +" The low-velocity: absorption: strengthened, becoming. nearly saturated from -40 to kms™,−↥∙ with the exception of the equatorial ejecta emission-580 at —250kms""."," The low-velocity absorption strengthened, becoming nearly saturated from $-40$ to $-580~\kms$, with the exception of the equatorial ejecta emission at $-250~\kms$." +" A broad, high-velocity absorption ranging from —580 to —-1900kms""! appeared by ϕ=11.991 and strengthened by $=11.998."," A broad, high-velocity absorption ranging from $-580$ to $-1900~\kms$ appeared by $\phi=11.991$ and strengthened by $\phi=11.998$." +" We would not expect this high-velocity absorption from the velocity field of the wind of Eta Car A, as seen in the spectrum from ¢=11.875."," We would not expect this high-velocity absorption from the velocity field of the wind of Eta Car A, as seen in the spectrum from $\phi=11.875$." +" Therefore, the 210833 absorption line profile strongly indicates that, in addition to the wind of Eta Car A, at least one more velocity structure is crossing our line-of-sight to Eta Car."," Therefore, the $\lambda$ 10833 absorption line profile strongly indicates that, in addition to the wind of Eta Car A, at least one more velocity structure is crossing our line-of-sight to Eta Car." +" That high-velocity absorption is transient; as the considerablspectrum observed at ¢=12.014 hows, it kms!has faded y and isΡpresent only urup to li-900900kms."," That high-velocity absorption is transient; as the spectrum observed at $\phi=12.014$ shows, it has faded considerably and ispresent only up to $-900~\kms$." +" By ὁ°=12.041, theHer 410833 profile ist quite similar to that recorded at ὁ=11.875, but the —40 to —580kms! absorption is saturated, indicating a higher column density of Het."," By $\phi=12.041$, the $\lambda$ 10833 profile is quite similar to that recorded at $\phi=11.875$, but the $-40$ to $-580~\kms$ absorption is saturated, indicating a higher column density of ." +" The 410833 and 420587 line profiles, recorded at ¢=11.998, demonstrate that the high-velocity absorption component is much stronger in 410833 than in the 420587 line (Fig. 2))."," The $\lambda$ 10833 and $\lambda$ 20587 line profiles, recorded at $\phi=11.998$, demonstrate that the high-velocity absorption component is much stronger in $\lambda$ 10833 than in the $\lambda$ 20587 line (Fig. \ref{fig2}) )." +" While noticeable from —600 to —1000kms-!, the absorption is 1much weaker inthe range of —1100 to —1600kms-'. ! The 410833 line -2p element[][3]P)) absorption— originates⋅⋅ from the metastable triplet state, while the Her 420587 line — 1]P))originates from the metastable state."," While noticeable from $-600$ to $-1000~\kms$, the absorption is much weaker inthe range of $-1100$ to $-1600~\kms$ The $\lambda$ 10833 line – ) absorption originates from the metastable triplet state, while the $\lambda$ 20587 line – )originates from the metastable state." + The population of the, The population of the +"smoother. xexp[7(v/1,)""C7] (Fritz1989:Zirakashvili&Aharonian 2007)).","smoother, $\propto \exp[-(\nu/\nu_{*})^{\beta/(\beta+2)}]$ \citealt{frit89,zirak07}) )." +" The position of the svuchrotvon peak flux. νο. is then also dependent on 2. and one can show that for 3=1 (or a,=0 in the previous notation) an important [actor ~10 arises. so that ij=9.51. whereas for 2=3 the svuchrotron peak corresponds approximately to the electron cut-off as py=1.2/5. (e.g.. Fig. 3))."," The position of the synchrotron peak flux, $\nu_p$, is then also dependent on $\beta$, and one can show that for $\beta=1$ (or $\alpha_p=0$ in the previous notation) an important factor $\sim 10$ arises, so that $\nu_{p}=9.5\nu_{c}$, whereas for $\beta=3$ the synchrotron peak corresponds approximately to the electron cut-off as $\nu_{p}=1.2\nu_{c}$ (e.g., Fig. \ref{SSCmax}) )." + Expansion of the source could change the conclusions drawn above., Expansion of the source could change the conclusions drawn above. + In particular. if one assiiies a verv low magnetic field such that svnchrotron losses are negligible. then adiabatie losses may become important and alter the electron distribution.," In particular, if one assumes a very low magnetic field such that synchrotron losses are negligible, then adiabatic losses may become important and alter the electron distribution." + In this section. we examine the behavior of the svstem for a power-law electron distribution wilh a hieh value of the cut-off discussed above.," In this section, we examine the behavior of the system for a power-law electron distribution with a high value of the low-energy cut-off discussed above." + For simplicitv. we consider a spherical source that expands with a constant. velocity à. The relativistic electron population will be affected by svinchirotron losses. and by aciabatic losses (e.g.. Longair 1932). As the emission region expands. the magnetic field decreases.," For simplicity, we consider a spherical source that expands with a constant velocity $u$, The relativistic electron population will be affected by synchrotron losses, and by adiabatic losses (e.g., Longair 1982), As the emission region expands, the magnetic field decreases." +" We consider a scaling (L/D0"" with 1 P. Le. aciabatic losses dominate over radiative losses.," A simple comparison of the above relations shows that when $P_{\rm ad}>P_{\rm syn}$ , i.e., adiabatic losses dominate over radiative losses." + For example. if one considers expansion al speed 4~e and an initial source dimension2y~LO! em. then [or energies below," For example, if one considers expansion at speed $u \sim c$ and an initial source dimension$R_0\sim 10^{14}$ cm, then for energies below" +Paper I showed that the region of maximun polarization is offset by oA+35° along the ecliptic plane Irom the laree-erain inflow direction.,Paper I showed that the region of maximum polarization is offset by $ \delta \lambda \sim +35\deeg$ along the ecliptic plane from the large-grain inflow direction. + The present note provides support lor this hypothesis (hat the polarization originates wilh interstellar dust at the heliosphere. using additional polarization data (§??)). evidence for olivine grains wilh stable alignment as the grains approach the heliosphere (§8??.. 77)). and a diseussion of the still-uncertain grain alignment mechanisms in the context of the heliosphere interaction with the ISM 7?7)).," The present note provides support for this hypothesis that the polarization originates with interstellar dust at the heliosphere, using additional polarization data \ref{sec:data}) ), evidence for olivine grains with stable alignment as the grains approach the heliosphere \ref{sec:licdust}, \ref{sec:disrupt}) ), and a discussion of the still-uncertain grain alignment mechanisms in the context of the heliosphere interaction with the ISM \ref{sec:alignment}) )." + Charged ISDGs spin rapidly and will always be aligned so that (he observed polarization.P.. of starlight is parallel to the magnetic field direction.hy. regardless of the alignment mechanism)mainBodyCitationEnd524]Lazarian:2003.," Charged ISDGs spin rapidly and will always be aligned so that the observed polarization, of starlight is parallel to the magnetic field direction, regardless of the alignment mechanism." + Evidently aligned grains do not behave like dumb compass needles. but rather trace the coupling between (he erain angular momentum andByy.," Evidently aligned grains do not behave like dumb compass needles, but rather trace the coupling between the grain angular momentum and." +. Thus. the T32 data indicate that iis approximately parallel to the ealactic plane aud oriented towards (~90° ((see Fig.," Thus, the T82 data indicate that is approximately parallel to the galactic plane and oriented towards $\sim$ (see Fig." + 6 of T82). or as found here (~105°.," 6 of T82), or as found here $\sim$." +. A similar orientation for iis indicated by the 2.6 kIIz Langmuir emission events observed by VovagerIXGO3)., A similar orientation for is indicated by the 2.6 kHz Langmuir emission events observed by Voyager. +. Driangulation by Vovager 1 and 2 show that tlie dozen emission events detected in the 1990's arise in the outer heliosphere at ~100 AU from the Sun. and that these dozen enission events are approximately aligned with the galactic planemechanisms).," Triangulation by Voyager 1 and 2 show that the dozen emission events detected in the 1990's arise in the outer heliosphere at $\sim$ 100 AU from the Sun, and that these dozen emission events are approximately aligned with the galactic plane." +. The tenuous nature of the interstellar eloud surrounding the Sun reduces the collisional disruption of grain alignment, The tenuous nature of the interstellar cloud surrounding the Sun reduces the collisional disruption of grain alignment +The paramcters of the thick disk aud the power-law halo have wide 47 distributions.,The parameters of the thick disk and the power-law halo have wide $\chi^2$ distributions. + The scale height of the thick disk (2.55 kpc) is about twice of that of the thin disk aud agrees with the 7;;=1 kpc (ih.=29/2) even by Burstein1979. for SO ealaxies., The scale height of the thick disk (2.55 kpc) is about twice of that of the thin disk and agrees with the $h_z=1$ kpc $h_z=z_0/2$ ) given by \cite{Burstein79} for S0 galaxies. + The thick disk scale leneth is 11.03 kpc. larger than that of the thin disk.," The thick disk scale length is 11.03 kpc, larger than that of the thin disk." + The Imminosity of the thick disk is of the thin disk., The luminosity of the thick disk is of the thin disk. + The core radius of the power-law halo is 11.1 spe. iudicatiug a flat halo.," The core radius of the power-law halo is 14.4 kpc, indicating a flat halo." + This agrees with the third component of three disk models of NJ and that of Shaw (μονο (1989). iu which the scale leneths of their third disks are about 13.9 kpe (at a distance of 11.5 Alpe).," This agrees with the third component of three disk models of NJ and that of Shaw Gilmore (1989), in which the scale lengths of their third disks are about 13.9 kpc (at a distance of 14.5 Mpc)." + The values of + concentrate in the rauge of 3.2 to L0. which indicates that there does not exist ar7 halo in this galaxy.," The values of $\gamma$ concentrate in the range of 3.2 to 4.0, which indicates that there does not exist a $r^{-2}$ halo in this galaxy." + The best power index is 3.88. between the 3.5 of Milkv Way (Zinn1985)) aud the of M31 (Pritchet&vandenBergh199 1)).," The best power index is 3.88, between the 3.5 of Milky Way \cite{Zinn85}) ) and the 4.0 of M31 \cite{PB94}) )." +" The (5,4; of the thin aud the thick disks slow several local minimus. owing to data sample."," The $r_{max}$ of the thin and the thick disks show several local minimums, owing to data sampling." + The cutoffs of the thin aud thick disks are about 32 kpc aud 37 kpe. respectively.," The cutoffs of the thin and thick disks are about 32 kpc and 37 kpc, respectively." + Analyses of correlation between anv two paraiucters show that some of the parameters are correlated. which means some of the parameters can not be determined indepeudenutlv.," Analyses of correlation between any two parameters show that some of the parameters are correlated, which means some of the parameters can not be determined independently." + For example. we fluc correlation between tyy and zg» aud amoug pos. ry aud 5.," For example, we find correlation between $z_{01}$ and $z_{02}$ and among $\mu_{03}$, $r_0$ and $\gamma$." + The similar «7 distiibutious of pgs. ry and 5 in Figure 8 also show such a correlation.," The similar $\chi^2$ distributions of $ \mu_{03}$, $ r_0$ and $ \gamma$ in Figure 8 also show such a correlation." + The error for cach paramcter is obtained in the following way., The error for each parameter is obtained in the following way. + Raucom values are selected for the observed data such that they obey a normal distribution. with sigias determined by the known errors iu each s;iuupled bin.," Random values are selected for the observed data such that they obey a normal distribution, with sigmas determined by the known errors in each sampled bin." + We then obtain the bestfitted parameters for that set of data., We then obtain the best–fitted parameters for that set of data. + This procedure is repeated three hundred times. giving us 300 separate determinations of the best-fitted value for cach parameter.," This procedure is repeated three hundred times, giving us 300 separate determinations of the best-fitted value for each parameter." + The statistical standard deviation of each parameter from this procedure is adopted as the fal error for this paraiicter., The statistical standard deviation of each parameter from this procedure is adopted as the final error for this parameter. + The best fit parameters and errors are listed in Table 6., The best fit parameters and errors are listed in Table 6. + Table 6 also lists the total magnitude iu A-band to a surface brightuess of 28 mae 7. ug66n)=8.99 (or broad-band R = 9.10 frou the Zhou et al.," Table 6 also lists the total magnitude in $\rm\AA$ -band to a surface brightness of 28 mag $^{-2}$, $\rm m_{6660} = 8.99$ (or broad-band R = 9.10 from the Zhou et al." + transformation). which is measured by replacing masked areas around the galaxy by the corrsponding parts of the muuasked galaxy.," transformation), which is measured by replacing masked areas around the galaxy by the corrsponding parts of the unmasked galaxy." + Figure 5 presents the best fitting values for the three components compared to our data in both the « and directions., Figure 5 presents the best fitting values for the three components compared to our data in both the $z$ and $R$ directions. + The fits are quite good in the range of R=10' to —δ for the z-profiles aud in the range of 2=30° to 1207 for R-profiles.," The fits are quite good in the range of $R = 1'$ to $R = 8'$ for the $z$ -profiles and in the range of $z= 30""$ to $120""$ for $R$ -profiles." + As expected. the model deviates significantly from the data in the region of the bulge (not-Btted) aud where the warp of the disk becomes sizeable.," As expected, the model deviates significantly from the data in the region of the bulge (not-fitted) and where the warp of the disk becomes sizeable." +CAIDs of MA (NGC 6121) and. MIOT (NGC 6171) which have both BIID and RIID.,CMDs of M4 (NGC 6121) and M107 (NGC 6171) which have both BHB and RHB. + Even ihe RIB of 47 Tue (NGC 104). whieh has only RIIDB. is clearly tilled.," Even the RHB of 47 Tuc (NGC 104), which has only RHB, is clearly tilted." +" So in the A, vs. (J—N,) CMDs it is difficult to determine the HB level of anv GGC and to correlate RGB Inuup positions and IIB levels in (he near-infrared CMDs. in contrast to the case for optical CMDSs."," So in the $K_{s}$ vs. $(J-K_{s})$ CMDs it is difficult to determine the HB level of any GGC and to correlate RGB bump positions and HB levels in the near-infrared CMDs, in contrast to the case for optical CMDs." + second. the brightness interval between the MSTO (Alain Sequence Turnoff) and RGB lip is larger (9 mag) than in optical CMDs (76.5 mag). as can be easily seen in M4.," Second, the brightness interval between the MSTO (Main Sequence Turnoff) and RGB tip is larger $\sim$ 9 mag) than in optical CMDs $\sim$ 6.5 mag), as can be easily seen in M4." +" So the magnitude resolution in the A, vs. (/—νι) CAIDs is larger than in optical CMDs.", So the magnitude resolution in the $K_{s}$ vs. $(J-K_{s})$ CMDs is larger than in optical CMDs. +" However. color resolution in the A, vs. (J—Av.) CMDs is smaller (han in optical CALDs because in ihe latter the RGB and AGB (Asymptotic Giant Branch) are separated [rom one another at least in the lower part of the AGB."," However, color resolution in the $K_{s}$ vs. $(J-K_{s})$ CMDs is smaller than in optical CMDs because in the latter the RGB and AGB (Asymptotic Giant Branch) are separated from one another at least in the lower part of the AGB." +" In contrast. in the A, vs. (J—IN.) CMDs the RGB and AGB overlap. as clearly shown in the CMD of 47 Tue whose AGB is relatively rich."," In contrast, in the $K_{s}$ vs. $(J-K_{s})$ CMDs the RGB and AGB overlap, as clearly shown in the CMD of 47 Tuc whose AGB is relatively rich." +" In the optical CMDs of NGC 362. 47 Tuc. and M71 (NGC 6333). the separation of their RGBs and BIIDs is clearly seen but they partially overlap in the A, vs. (J—A.) CMDs."," In the optical CMDs of NGC 362, 47 Tuc, and M71 (NGC 6838), the separation of their RGBs and RHBs is clearly seen but they partially overlap in the $K_{s}$ vs. $(J-K_{s})$ CMDs." +" This also results from the fact Chat the color resolution in the A, vs. (J—dv.) CMDsS is lower than that in optical CAIDs.", This also results from the fact that the color resolution in the $K_{s}$ vs. $(J-K_{s})$ CMDs is lower than that in optical CMDs. + Thircl. in the case of M22 (NGC 6656). its RGB is broader than those of other GGCs as found in the optical CMD (Peterson Cuclworth 1994).," Third, in the case of M22 (NGC 6656), its RGB is broader than those of other GGCs as found in the optical CMD (Peterson Cudworth 1994)." + Moreover. in the lower part of the RGB. contamination from bulge component stars is severe.," Moreover, in the lower part of the RGB, contamination from bulge component stars is severe." + To the right of the RGB of M22 there exists another RGB component., To the right of the RGB of M22 there exists another RGB component. + This RGB component would be due to bulge RGB stars. which extend prominently reclwarcl in the optical CMD Gn our unpublished data) because of the strong blanketing effects of heavy metals as found in metal-rich. GGCs such as NGC 6553 (Ortolani. Darbuy. Dica 1990).," This RGB component would be due to bulge RGB stars, which extend prominently redward in the optical CMD (in our unpublished data) because of the strong blanketing effects of heavy metals as found in metal-rich GGCs such as NGC 6553 (Ortolani, Barbuy, Bica 1990)." + Last. because NGC 362 and 47 Tuc CALDs are located in the direction of the SAIC. a contribution from the SAIC appears in (he lower right region of their CMDs.," Last, because NGC 362 and 47 Tuc CMDs are located in the direction of the SMC, a contribution from the SMC appears in the lower right region of their CMDs." + In order to accurately measure (he luminosity of the RGB bump and construct luminosity funelions of the GGCs. we applied several standard procedures to delineate only the RGB sequences lor all GGCs except for M22 ancl MT1.," In order to accurately measure the luminosity of the RGB bump and construct luminosity functions of the GGCs, we applied several standard procedures to delineate only the RGB sequences for all GGCs except for M22 and M71." + First we rejected. visually clear HB stars and AGB stars in the process of distinguishing outlving field stars [rom RGB stars., First we rejected visually clear HB stars and AGB stars in the process of distinguishing outlying field stars from RGB stars. + Second. bv binning the RGB sequences in 0.5 mag intervals we measured (he average ancl sigma of each bin and rejected stars 2σ away from the mean value of each bin.," Second, by binning the RGB sequences in 0.5 mag intervals we measured the average and sigma of each bin and rejected stars $\sigma$ away from the mean value of each bin." + We Chen remeasured, We then remeasured +IIul«t 1989: Dablem et al. 1995j).,Hulst \cite{HuHu}; Dahlem et al. \cite{DaLi}) ). + However. the galaxy its been listed in the sample of TRAS bright ealaxies (Soifer ct al. 1987)).," However, the galaxy has been listed in the sample of IRAS bright galaxies (Soifer et al. \cite{So87}) )," + so there seenis clear evideuce for chhanced SE but it is presently not clear if 32011 josts a starburst nucleus., so there seems clear evidence for enhanced SF but it is presently not clear if 3044 hosts a starburst nucleus. + In a spectroscopic study where he DIC. was investigated at two differcut slit positions oerpendicular to the galaxy disk. the positious of the detected DIC in the diagnostic diagrams fall in between he areas occupied by normal regions aud starburst (Tülliuaun Dettmar 2000)).," In a spectroscopic study where the DIG was investigated at two different slit positions perpendicular to the galaxy disk, the positions of the detected DIG in the diagnostic diagrams fall in between the areas occupied by normal regions and starburst (Tülllmann Dettmar \cite{TuDe}) )." + Therefore no clear auswer of this debate can be eiven vet., Therefore no clear answer of this debate can be given yet. + Even the term ‘starburst? is sometimes not clearly defined. as various researchers use different definitions.," Even the term `starburst' is sometimes not clearly defined, as various researchers use different definitions." + We will come back to this point in 55, We will come back to this point in 5. +", The galaxy type is listed as SBc (Tully 1988)).", The galaxy type is listed as SBc (Tully \cite{Tu88}) ). + Even classifications as a nonbarred galaxy (Sc) are listed (Nilson 1973))., Even classifications as a non–barred galaxy (Sc) are listed (Nilson \cite{Ni73}) ). + There ave iudicatious that iun 33011a bar is present. aud kinematics by Lee biu (1997) has indeed discerued a bar.," There are indications that in 3044 a bar is present, and kinematics by Lee Irwin \cite{LeIr}) ) has indeed discerned a bar." + It might be worth to notice that in the cighties a supernova (SNI1983E)) has been detected in this galaxy. (Darbon et al. 1989))., It might be worth to notice that in the eighties a supernova ) has been detected in this galaxy (Barbon et al. \cite{BaCa}) ). + Iu Fig., In Fig. + 2 we present the Πα image., \ref{F2} we present the $\alpha$ image. + The morphology of: the DIC shows various: ]features., The morphology of the DIG shows various features. + An eDIG. laver can be detected at extraplanar distances up to z=0.8Ikpec.," An eDIG layer can be detected at extraplanar distances up to $z=0.8-1\,\rm{kpc}$." + Several single plumes can also be diseerued., Several single plumes can also be discerned. +" South of the ealactic plane an extended structure is visible, which hasa looplike appearance."," South of the galactic plane an extended structure is visible, which has a loop–like appearance." + This loop exteuds out to ~ L&kkpe with a radius of about Lkkpe. aud resembles the galactic πλ," This loop extends out to $\sim$ kpc with a radius of about kpc, and resembles the galactic supershells." + The disk appears slightly warped. which is also apparent in the Roland image.," The disk appears slightly warped, which is also apparent in the R–band image." + The Πα flix of the ealaxy has been to be estimated2.50&LOeresbem2 and fromthe computed Πα huninosity the (global) star formation rate (SFR) las been derived. which is SFR=O.71\Mow -.," The $\alpha$ flux of the galaxy has been estimated to be $\rm{2.50 \times +10^{-12}\,erg\,s^{-1}\,cm^{-2}}$ and fromthe computed $\alpha$ luminosity the (global) star formation rate (SFR) has been derived, which is $\rm{SFR = +0.71\,M_{\sun}\,yr^{-1}}$ ." +" This southern edgeou spiral is slightly larger than the EFOSC? field of view which is BisSHES,", This southern edge–on spiral is slightly larger than the EFOSC2 field of view which is $5\farcm8 \times 5\farcm8$. + 22531 is secu perfectly edge.on., 2531 is seen perfectly edge–on. +" Ta our Πα image alinost no extraplanar tse cutission has beeu detected,", In our $\alpha$ image almost no extraplanar diffuse emission has been detected. + One fbuneut. (the ChimneyTike feature) is clearly seen. emergiug from the disk radius at A kkpe south of the plane into the halo 6866 Fig.," One filament (the chimney–like feature) is clearly seen, emerging from the disk radius at $R$ kpc south of the plane into the halo (see Fig." + 3 ).," \ref{F3} + )." + This feature is marked in Fig., This feature is marked in Fig. +" 3) with a circle,", \ref{F3} with a circle. + It reaches a height of :—2Xkkpe above the galactic plane., It reaches a height of $z$ kpc above the galactic plane. + The Πα nage looks pretty much like a strine of pearls., The $\alpha$ image looks pretty much like a string of pearls. + Several disk regionscan be ideutified. but only the largest ave surrounded by DIG. which is probably not," Several disk regionscan be identified, but only the largest are surrounded by DIG, which is probably not" +10 “bootstrap” [luxes of 2005|403 at these frequencies to rose given in the University of Michigan Radio Astronomy Observatory (UMIUXO) flux database shows that. where closely contemporancous Observations are. available. the agreement with UMICAO Iluxes at these frequencies is within La.,"the “bootstrap” fluxes of 2005+403 at these frequencies to those given in the University of Michigan Radio Astronomy Observatory (UMRAO) flux database shows that, where closely contemporaneous observations are available, the agreement with UMRAO fluxes at these frequencies is within $1\%$." + Given the excellent agreement at these two frequencies. it is reasonable to assume that the Dux scales at the other observed frequencies are good.," Given the excellent agreement at these two frequencies, it is reasonable to assume that the flux scales at the other observed frequencies are good." + Aside from the initial amplitude calibration of the ALERLIN observations. the calibration ancl subsequent imaging of the data were carried out using the NILAO software package.," Aside from the initial amplitude calibration of the MERLIN observations, the calibration and subsequent imaging of the data were carried out using the NRAO software package." + The complex antennae gains were initially clerived for 2005|403 and then interpolated (phase-referenced) to the observations of WIULI146., The complex antennae gains were initially derived for 2005+403 and then interpolated (phase-referenced) to the observations of 146. + Lo addition. several iterations of phase-only self-calibration were used to refine the antennae gains during the ALERLIN observations of W1t1146 to improve the dynamic range of the final synthesized images.," In addition, several iterations of phase-only self-calibration were used to refine the antennae gains during the MERLIN observations of 146 to improve the dynamic range of the final synthesized images." + At 1.5 and 4.9 Cillz the VLA data reveal an unresolved source. whereas at 8.4 (11 the radio emission is marginallv resolved.," At 1.5 and 4.9 GHz the VLA data reveal an unresolved source, whereas at 8.4 GHz the radio emission is marginally resolved." + Llowever. WIULIId6 is well resolved. into a double radio source at 22 CGlLIz.," However, 146 is well resolved into a double radio source at 22 GHz." + The final synthesized 22-Cillz image is shown in Fig. 2.., The final synthesized 22-GHz image is shown in Fig. \ref{fig:22GHz}. + We identify the northern and southern components as No» and So»., We identify the northern and southern components as $_{22}$ and $_{22}$. + The visibility cata suggest both these components are resolved. (Figure 3))., The visibility data suggest both these components are resolved (Figure \ref{fig:22ghz_visibs}) ). + Gaussian model fits to the visibilities give the diameter of the radio, Gaussian model fits to the visibilities give the diameter of the radio +Note that &* is also a function of r and Equation (31)) only applies when a«1.,Note that $k_z^*$ is also a function of $r$ and Equation \ref{eq:kzcrit}) ) only applies when $\alpha < 1$. + The absolute stability of the continuum is guaranteed for k- larger than the maximum value of A> in the equilibrium., The absolute stability of the continuum is guaranteed for $k_z$ larger than the maximum value of $k_z^*$ in the equilibrium. + Figure 2. shows the thermal continuum computed from Equation (28)) for our equilibrium, Figure \ref{fig:continuum} shows the thermal continuum computed from Equation \ref{eq:cont}) ) for our equilibrium +The three high-density regious in the cluster mass distribution. as traced by the hot XN-rav gas (seo Fie. 53).,"The three high-density regions in the cluster mass distribution, as traced by the hot X-ray gas (see Fig. \ref{x_3sig}) )," + ave populated by passive galaxies exclusively., are populated by passive galaxies exclusively. + All the star-forming galaxies noticcably avoid these regions., All the star-forming galaxies noticeably avoid these regions. + A few ealaxies with narrow cuuission lines are observed close to the southern edge of the southern clump (see Fig. 8))., A few galaxies with narrow emission lines are observed close to the southern edge of the southern clump (see Fig. \ref{el_membs}) ). +" These galaxies are about ((~ 230 kpe) from the centroid of the southeru N-rav substructure, which corresponds to a region where the local ICA density is about one-third of the central density of the southern chump. as derived from the Nay surface brightuess profile."," These galaxies are about $\sim$ 230 kpc) from the centroid of the southern X-ray substructure, which corresponds to a region where the local ICM density is about one-third of the central density of the southern clump, as derived from the X-ray surface brightness profile." + Iu ters of spectral classification. passive galaxies are split iuto two main groups: k type galaxies (see Dressler et al.," In terms of spectral classification, passive galaxies are split into two main groups: k type galaxies (see Dressler et al." + 1999: Pogeiauti ct al., 1999; Poggianti et al. +" 1999) aud post-starburst ealaxies (Dressler Coma 1983). also called ""E|A” ealaxies."," 1999) and post-starburst galaxies (Dressler Gunn 1983), also called “E+A” galaxies." + Based on the streneth of the IL;((A £102). line.," Based on the strength of the $_{\delta}$ $\lambda$ 4102) line," +"quiet region considered where emission is nearly absent has the value of about 4100 erg s! cm"" ?sr-!.",quiet region considered where emission is nearly absent has the value of about 4100 erg $^{-1}$ $^{-2}$ $^{-1}$. +" The SERTS-97 observation at pointing 1 showed variations of intensities in “quiet region"" from 4500 to 12000 erg s-lem-?sr-! over the -long slit."," The SERTS-97 observation at pointing 1 showed variations of intensities in “quiet region"" from 4500 to 12000 erg $^{-1}$ $^{-2}$ $^{-1}$ over the $^{''}$ -long slit." + DelZanna&Andretta showed that the irradiance measured during (2011)this solar minimum (2006-2008) is about a factor of 1.3 smaller than that measured in 1998 at the beginning of the last solar cycle., \citet{del11} showed that the irradiance measured during this solar minimum (2006–2008) is about a factor of 1.3 smaller than that measured in 1998 at the beginning of the last solar cycle. + The dispersion of intensities shown in Table 5 suggests that one should be cautious about using the quiet-Sun line as a standard light source., The dispersion of intensities shown in Table \ref{tabhe} suggests that one should be cautious about using the quiet-Sun line as a standard light source. +" In addition, we may verify the EUNIS-07 radiometric calibration by comparing the measured quiet-Sun 304 iintensity with the radiance converted from irradiance measurements (the full-disk flux measured at Earth from this line or a narrow waveband centered at 304 during the solarminimum."," In addition, we may verify the EUNIS-07 radiometric calibration by comparing the measured quiet-Sun 304 intensity with the radiance converted from irradiance measurements (the full-disk flux measured at Earth from this line or a narrow waveband centered at 304 ) during the solarminimum." +" Since the lines have À))negligible limb-brightening and off-limb contribution (DelZanna&Andretta 2011), the conversion for the quiet Sun can be simplymade by the relation (Warrenetal.1998) where is the irradiance, Ro is the solar radius, R is the Fj,Earth-Sun distance, and Ig, is the intensity at disk-center."," Since the lines have negligible limb-brightening and off-limb contribution \citep{del11}, the conversion for the quiet Sun can be simplymade by the relation \citep{war98} + where $F_{qs}$ is the irradiance, $R_{\sun}$ is the solar radius, $R$ is the Earth-Sun distance, and $I_{qs}$ is the intensity at disk-center." +" When the irradiance uses the unit of photons s! cm-? and the intensity is in erg sσι ια, the conversion coefficient between Fy, and I4, at 304 iis 1.04x10° sr photons erg-!."," When the irradiance uses the unit of photons $^{-1}$ $^{-2}$ and the intensity is in erg $^{-1}$ $^{-2}$ $^{-1}$, the conversion coefficient between $F_{qs}$ and $I_{qs}$ at 304 is $\times$ $^{6}$ sr photons $^{-1}$ ." +" From the quiet-Sun intensity of 4960 erg s-!cm-?sr! by EUNIS-07, it derives irradiance to be 52x10? photons s! cm?, which"," From the quiet-Sun intensity of 4960 erg $^{-1}$ $^{-2}$ $^{-1}$ by EUNIS-07, it derives irradiance to be $52\times10^8$ photons $^{-1}$ $^{-2}$ , which" +work.,work. + Their results are consistent with the ones presented here., Their results are consistent with the ones presented here. + Analvziug the secondary eclipse data. we report here the detection of a secondary eclipse aud draw conclusions about the thermal emüssion of LI36bb. aud. refine its orbital parameters. allowing a better πιοταιπας of L136 dynamics by exploring the coutingency of a supplementary plauct.," Analyzing the secondary eclipse data, we report here the detection of a secondary eclipse and draw conclusions about the thermal emission of b and refine its orbital parameters, allowing a better understanding of 436 dynamics by exploring the contingency of a supplementary planet." + Iu addition. we report here ou additional ground based observations to determine the stellar rotational period.," In addition, we report here on additional ground based observations to determine the stellar rotational period." + We followed the photometric intensity and the Ca IT IT|KR activity iudex of 1036., We followed the photometric intensity and the Ca II H+K activity index of 436. + Although the photometric data are sparse aud cover only 50 davs. we find some evidence that the stellar rotational period is of the order of 50 days. which is also cousisteut with loug-terui Call micasurcmicuts.," Although the photometric data are sparse and cover only 50 days, we find some evidence that the stellar rotational period is of the order of 50 days, which is also consistent with long-term CaII measurements." + Section 2 describes the observations and the reduction procedure., Section 2 describes the observations and the reduction procedure. + Our analysis of the obtained secondary eclipse time series is described in Section 3., Our analysis of the obtained secondary eclipse time series is described in Section 3. + Iu Section [. we analyze the infrared cussion from the planet and draw sole couclisions about its atmosphere composition.," In Section 4, we analyze the infrared emission from the planet and draw some conclusions about its atmosphere composition." + We detail an orbital analysis. enconipassimg the possibility of a perturbing planet. stellar activity aud bb orbital paramcters refinements in Section 5.," We detail an orbital analysis, encompassing the possibility of a perturbing planet, stellar activity and b orbital parameters refinements in Section 5." + Our couchisions are presented in Section 6., Our conclusions are presented in Section 6. + L136 has been observed on June 30th UT for 6 hours. ο cover the secondary eclipse. resulting m 19920 frames.," 436 has been observed on June 30th UT for 6 hours, to cover the secondary eclipse, resulting in 49920 frames." + Observations were made so as to enconipass the expected secondary eclipse window. whose tinue caleulatious were uade by taking iuto account transit timing and orbital eccentricity.," Observations were made so as to encompass the expected secondary eclipse window, whose timing calculations were made by taking into account transit timing and orbital eccentricity." + Due to the uncertainties on ecceutricitv iud argunenut of poeriastron. a larger time-window was chosen o eusure the detection of the secondary eclipse.," Due to the uncertainties on eccentricity and argument of periastron, a larger time-window was chosen to ensure the detection of the secondary eclipse." + Data acquisition was made using TRAC in its 58-442 band with he same mode and strategy enmiploved for the primary ransit (CCUOTb)., Data acquisition was made using IRAC in its $\mu$ m band with the same mode and strategy employed for the primary transit (G07b). + We combine cach set of 61 images using a Dg clipping to get rid off transicut eveuts m the pixel exid. vielding τοῦ stacked nuages for the secondary eclipse. with a temporal sampling of ~ 28s.," We combine each set of 64 images using a $\sigma$ clipping to get rid off transient events in the pixel grid, yielding 780 stacked images for the secondary eclipse, with a temporal sampling of $\sim$ 28s." + Helioceutric Julian Dax CIID) couversion was made according to the mean Spitzer orbital position at the time of cach exposure aud L136 apparent position., Heliocentric Julian Day (HJD) conversion was made according to the mean $Spitzer$ orbital position at the time of each exposure and 436 apparent position. + Spitrer position cplemerides were obtained through JPL-Iorizous web interface (9) aud converted frou TT (Terrestrial Dynamic Time) to UTC., $Spitzer$ position ephemerides were obtained through JPL-Horizons web interface \citep{Giorgini:1996ai} and converted from TT (Terrestrial Dynamic Time) to UTC. + We faced the same instrumental rise issue noticed iu our work on primary transit., We faced the same instrumental rise issue noticed in our work on primary transit. + To mitigate its effect. we zero weight the eclipse and the first LOO points of the time-serics.," To mitigate its effect, we zero weight the eclipse and the first 100 points of the time-series." + We then divide the liehteurve bv the best fitting asvinptotic function with three free parameters aud evaluate the average flux outside the eclipse to normalize the ine series. exactly as for the primary transit.," We then divide the lightcurve by the best fitting asymptotic function with three free parameters and evaluate the average flux outside the eclipse to normalize the time series, exactly as for the primary transit." +" The of the resulting time series evaluated outside the eclipse is the same as for the primary (COT): 0.7 παπα, which is 1.2 times 1136s photon noise."," The of the resulting time series evaluated outside the eclipse is the same as for the primary (G07b): 0.7 mmag, which is 1.2 times 436's photon noise." + To assess the variability of the star. we observed L136 with the Euler Swiss telescope located at La Silla Observatory (Chile) aud the Fraucoois-Navicr Bagnoud Observatorv's (OFXB) 0.6120. telescope located at Saint-Luc (Switzerland).," To assess the variability of the star, we observed 436 with the Euler Swiss telescope located at La Silla Observatory (Chile) and the Françoois-Xavier Bagnoud Observatory's (OFXB) 0.6m telescope located at Saint-Luc (Switzerland)." + Observations occurred in Ll nights from Mav Ith to May. 21th., Observations occurred in 14 nights from May 4th to May 21th. + A sequence of LO exposures was done every night., A sequence of 10 exposures was done every night. + The same strategy used for our 6servation ofthe May 2ud transit (0Τα) was applied (V-baud filter. SOs exposure time. defocus to ~ 97).," The same strategy used for our observation of the May 2nd transit (G07a) was applied (V-band filter, 80s exposure time, defocus to $\sim$ 9”)." + The data reduction was also simular., The data reduction was also similar. + We also use for our analysis of the 1136. variability the Mav δις out-of-trausit data and the photometric lightcurves obtained with the OFNB 0.6120 telescope curing our search for the transits of bb (CO7a)., We also use for our analysis of the 436 variability the May 2nd out-of-transit data and the photometric lightcurves obtained with the OFXB 0.6m telescope during our search for the transits of b (G07a). + We scale OEXD points with Euler ones because of the filters slightly differeut baudpasses., We scale OFXB points with Euler ones because of the filters slightly different bandpasses. + At the eud. our data amounts to 21 poiuts spamming Ls dave.," At the end, our data amounts to 24 points spanning 48 days." + The Leltcurve is represented in Fie., The lightcurve is represented in Fig. + 6. aud. discussed iu Sect.," 6, and discussed in Sect." + 5.3., 5.3. + Since the discovery of hb) (7). we obtained additional spectra of the star with the ESO spectrograph (?3..," Since the discovery of b \citep{Butler:2004dq}, , we obtained additional spectra of the star with the ESO spectrograph \citep{Mayor:2003pb}." + is mounted on ESO 3.611 telescope aud is dedicated to Ligh precision racial-velocity measurements thanks to its resolution of 110000 and a wavelength range coverage between 3800 aud6800À., is mounted on ESO 3.6m telescope and is dedicated to high precision radial-velocity measurements thanks to its resolution of 110'000 and a wavelength range coverage between 3800 and. +. To assess the stellar activity and rotation we used 23 high SNR spectra from which we measured the Ca IW Iv index., To assess the stellar activity and rotation we used 23 high SNR spectra from which we measured the Ca II H+K index. + Results are discussed in Sect., Results are discussed in Sect. + 5.3 We fit a non-Iub-darkenued eclipse profile to the secondary eclipse data using the ? algorithm., 5.3 We fit a non-limb-darkened eclipse profile to the secondary eclipse data using the \citet{Mandel:2002wd} algorithm. + The eccentricity of the orbit is considered as described in G07). taking the values for the eccentricity e aud the aremment of periastrou uw from ALO7.," The eccentricity of the orbit is considered as described in G07b, taking the values for the eccentricity $e$ and the argument of periastron $\omega$ from M07." + The forumla counecting w to the true anomaly f at the orbital location of the secondary eclipse is: We fix the stellar aud orbital parameters to the values mentioned m Cra., The formula connecting $\omega$ to the true anomaly $f$ at the orbital location of the secondary eclipse is: We fix the stellar and orbital parameters to the values mentioned in G07a. + The free parameters are the ceutra epoch of the secondary eclipse T; aud the fiux decremeut AF..., The free parameters are the central epoch of the secondary eclipse $T_s$ and the flux decrement $\Delta F_s$. + The fit procedure aud the error lars estimation is sinular to the oue described in GOT)., The fit procedure and the error bars estimation is similar to the one described in G07b. + The obtaiue« value for Ty aud AF. ποπιο their respective error bars are eiven in Table 1.," The obtained value for $T_s$ and $\Delta F_s$, including their respective error bars are given in Table 1." + Figure 1 shows the best-fit theoretical curvesuperimposed ou the lighteuve (zoonie«, Figure 1 shows the best-fit theoretical curvesuperimposed on the lightcurve (zoomed +The FIR luminosity is often used as a measure of the current star formation rate (SFR). since 1t is assumed that FIR emission is mainly due to dust heating by massive young stars.,"The FIR luminosity is often used as a measure of the current star formation rate (SFR), since it is assumed that FIR emission is mainly due to dust heating by massive young stars." +" The total IR luminosity of iis 1.3x10"" eeress7!. according to the precepts of Draine&Li(2007). and with fluxes from Daleetal.(2005)."," The total IR luminosity of is $\times10^{44}$ $^{-1}$, according to the precepts of \citet{draine07} and with fluxes from \citet{dale05}." +.. This corresponds to à SFR of -6 MM. yyr! (Kennicutt1998)., This corresponds to a SFR of $\sim6$ $_\odot$ $^{-1}$ \citep{kennicutt98}. +. In the bulge of3627.. there is little observed SF 1994;Reganetal. 2002).. and the SFR given by wwithin a nuclear region of diameter ~ iis 0.078M..yr! (Reganetal.2002)... ~3 times lower than found in the bar itself. and ~4 times lower than the spiral arms (Reganetal.2002).," In the bulge of, there is little observed SF \citep[][]{smith94,regan02}, and the SFR given by within a nuclear region of diameter $\sim$ is $^{-1}$ \citep[][]{regan02}, $\sim$ 3 times lower than found in the bar itself, and $\sim$ 4 times lower than the spiral arms \citep[][]{regan02}." +. Part of this deficit in the nuclear -derived SFR may arise from dust extinction. given that the mean Ay in the inner ((diameter) is ~2mmag (Calzettietal.2007).," Part of this deficit in the nuclear -derived SFR may arise from dust extinction, given that the mean $_V$ in the inner (diameter) is $\sim$ mag \citep{calzetti07}." +. In any case. in3627.. most of the SF is extranuclear. along the bar. particularly where it terminates and the spiral arms emerge (see Figs.," In any case, in, most of the SF is extranuclear, along the bar, particularly where it terminates and the spiral arms emerge (see Figs." + 17 and 18))., \ref{fig:mips70-bima} and \ref{fig:mips160-bima}) ). + The eemission is confined mainly to the nucleus and the bar. particularly the ansae (see Fig. 17)).," The emission is confined mainly to the nucleus and the bar, particularly the ansae (see Fig. \ref{fig:mips70-bima}) )." + The eemission (albeit with lower resolution). is more broadly distributed. especially the bar.," The emission (albeit with lower resolution), is more broadly distributed, especially the bar." + This IR. morphology suggests that the dust along the bar is warmer than around the bar. probably heated by the massive stars in the recent formation episodes.," This IR morphology suggests that the dust along the bar is warmer than around the bar, probably heated by the massive stars in the recent star-formation episodes." + In galaxies with weak SF activity. (e.g.NGC4736.Smithetal. 1994).. dust heating by non-OB stars may also contribute significantly (e.g..deJongetal.1984;Bothun 1989)..," In galaxies with weak SF activity \citep[e.g. NGC 4736,][]{smith94}, dust heating by non-OB stars may also contribute significantly \citep[e.g.,][]{dejong84,bothun89}." + This more quiescent heating source may be especially important in the central regions of early/type spiral galaxies with massive bulges and little nuclear or eircumnuclear SF. such as3627.," This more quiescent heating source may be especially important in the central regions of early/type spiral galaxies with massive bulges and little nuclear or circumnuclear SF, such as." +. The ratio of FIR to luminosity for the bulge of us of «8100. significantly larger than for the star-forming regions in this galaxy. between -1000 and -2000.," The ratio of FIR to luminosity for the bulge of is of $\sim$ 8100, significantly larger than for the star-forming regions in this galaxy, between $\sim$ 1000 and $\sim$ 2000." + The L(FIR)/L(Ha)) ratio is also higher than can be accounted for by obscured SF with a normal initial. mass function. using extinction measurements derived from CO(1-0) and FIR data (Smithetal.1994).," The ) ratio is also higher than can be accounted for by obscured SF with a normal initial mass function, using extinction measurements derived from $^{12}$ CO(1–0) and FIR data \citep[][]{smith94}." +. Thus. the older stars probably contribute significantly to the dust heating in the bulge of citep[]| |smith94..," Thus, the older stars probably contribute significantly to the dust heating in the bulge of \\citep[][]{smith94}." + A low nuclear SER 1s consistent with the CO/HCN ratio (10) discussed in Sect. 3.., A low nuclear SFR is consistent with the CO/HCN ratio (10) discussed in Sect. \ref{sec:30m}. +" Higher ratios suggest that excitation by SF is dominant over AGN excitation in the cireumnuclear region. but we found a ""normal"" CO/HCN ratio for3627.. not surprisingly given its low SER."," Higher ratios suggest that excitation by SF is dominant over AGN excitation in the circumnuclear region, but we found a “normal” CO/HCN ratio for, not surprisingly given its low SFR." + The gravitational torques derived from the stellar potential in the inner region of aallow to account for the gas kinematies derived from CO and examine the efficiency of gravitational torques exerted on the gas., The gravitational torques derived from the stellar potential in the inner region of allow to account for the gas kinematics derived from CO and examine the efficiency of gravitational torques exerted on the gas. + As described in previous NUGA papers (e.g..García-Burilloetal. 2005).. to compute the gravitational torques we assume that NIR images give the best approximation for the total stellar mass distribution. being less affected than optical images by dust extinction or stellar population bias.," As described in previous NUGA papers \citep[e.g.,][]{santi05}, to compute the gravitational torques we assume that NIR images give the best approximation for the total stellar mass distribution, being less affected than optical images by dust extinction or stellar population bias." + We computed the torques using both HST--NICMOS F160W and Spitzer--IRAC limages., We computed the torques using both -NICMOS F160W and -IRAC images. + They yield complementary. results. the torques computed from the HST--NICMOS FI60W image compared," They yield complementary results, the torques computed from the -NICMOS F160W image compared" +possible since Chere were no other sources in the field.,possible since there were no other sources in the field. + We estimate the telescope pointing accuracy to be less than 5 aresec., We estimate the telescope pointing accuracy to be less than 5 arcsec. + Fig., Fig. + shows a map of the IH» emission towards ΗνΛο 16547—4247., \ref{plotone} shows a map of the $_2$ emission towards IRAS $-$ 4247. + There is a complex chain of emission with three major concentrations (labeled A to C)., There is a complex chain of emission with three major concentrations (labeled A to C). + Several of the brightest emission knots within each concentration have been labeled and their coordinates and fIuxes are given in Table 1.., Several of the brightest emission knots within each concentration have been labeled and their coordinates and fluxes are given in Table \ref{tableone}. + The projected distance between the two outermost knots (At and C2) is 110 aresee (1.5 pe at the distance of 2.9 kpc. DronBnan private communication).," The projected distance between the two outermost knots (A4 and C2) is 110 arcsec (1.5 pc at the distance of 2.9 kpc, Bronfman private communication)." + Both of (hese knots are approximately svimmetrically offset [rom the raclio jet detected by (2003).., Both of these knots are approximately symmetrically offset from the radio jet detected by \citet{Garay03}. . + No emission arising from the Dr5 line was detected., No emission arising from the $\gamma$ line was detected. + The II» emission has the morphological characteristics of HII objects arising from the interaction of a collimated flow with the ambient medium., The $_2$ emission has the morphological characteristics of HH objects arising from the interaction of a collimated flow with the ambient medium. + Concentration A has several knots in the shape of bow-shocks. all pointing away from the direction of the radio jet.," Concentration A has several knots in the shape of bow-shocks, all pointing away from the direction of the radio jet." + Their arrangement is consistent with an elongated outflow cavity., Their arrangement is consistent with an elongated outflow cavity. + Another series of emission knots may exist. further north but is difficult to distinguish against the artifacts from the bright star., Another series of emission knots may exist further north but is difficult to distinguish against the artifacts from the bright star. + The morphology of concentration D is more complex and consists of two main enission structures., The morphology of concentration B is more complex and consists of two main emission structures. + Both structures appear to delineate flows originating from a direction that is skewecl from the location of the radio jet: one in à northeast.southwest direction (Bl. D2. and BG) and one in a north.south direction (D3. Bt and D5).," Both structures appear to delineate flows originating from a direction that is skewed from the location of the radio jet: one in a northeast–southwest direction (B1, B2, and B6) and one in a north–south direction (B3, B4 and B5)." + This may be evidence of additional oulllows [rom less-massive stars or an indication of precession of the flow originating from the detected radio jet., This may be evidence of additional outflows from less-massive stars or an indication of precession of the flow originating from the detected radio jet. + There are fewer bright emission knots in concentration C and the morphology is less well-defined., There are fewer bright emission knots in concentration C and the morphology is less well-defined. + There are a couple of Taint filaments in the shape of pointing away [rom the direction of the radio jet., There are a couple of faint filaments in the shape of bow-shocks pointing away from the direction of the radio jet. + These are most likely part of the counter-flow to concentration A. Fie., These are most likely part of the counter-flow to concentration A. Fig. + 3 illustrates the comparison between the IH» emission (without any continuum subtraction) and (a) the 1.2-mm dust continuum emission and (b) the 8.6-Gllz continuum enission (taken from Qarayetal.(2003)., \ref{plottwo} illustrates the comparison between the $_2$ emission (without any continuum subtraction) and (a) the 1.2-mm dust continuum emission and (b) the 8.6-GHz continuum emission taken from \citet{Garay03}. +.. The actual thermal radio jet corresponds to the brightest 8.6-GlIIz emission component., The actual thermal radio jet corresponds to the brightest 8.6-GHz emission component. + There is a fainter source offset to (he southeast and whose spectral index is not known., There is a fainter source offset to the southeast and whose spectral index is not known. + It is not certain what role (if anv) this source plavs., It is not certain what role (if any) this source plays. + The chain of Hà emission is oriented in the same direction as (he triple radio source and is contained within the molecular core traced by the 1.2-imm continuum emission., The chain of $_2$ emission is oriented in the same direction as the triple radio source and is contained within the molecular core traced by the 1.2-mm continuum emission. + One of theII emission knots (Bl) is associated will the southern non-thermal radio component., One of the$_2$ emission knots (B1) is associated with the southern non-thermal radio component. +any given epoch.,any given epoch. + As an illustrative case. we have shown iu figure 3. the spectral energy distributions corrected for Ay=0.09 of SMC type dust.," As an illustrative case, we have shown in figure \ref{sedfig} the spectral energy distributions corrected for $A_V = 0.09$ of SMC type dust." + This correction gives the minimum \7/cof (1.15 for I degrees of [reedoim)) for the residuals of the plotted spectral energy. distributious relative to the spectral slopes reported iu table 3.., This correction gives the minimum $\chi^2 / \dof$ $1.45$ for 4 degrees of freedom) for the residuals of the plotted spectral energy distributions relative to the spectral slopes reported in table \ref{slopetable}. + LAIC extinction does mareinally worse than SAIC extinction. whileH any zunouut ofH MilkyH Way- extinctionH inH the host clegrades V7.," LMC extinction does marginally worse than SMC extinction, while any amount of Milky Way extinction in the host degrades $\chi^2$." +> We- have used the analyticH extinction law fitting forms of Pei (1992) in deriving these estimates., We have used the analytic extinction law fitting forms of Pei (1992) in deriving these estimates. + Jeuseu et al (2000) have applied a similar analysis iucorporatiug optical spectra as well as broadband colors., Jensen et al (2000) have applied a similar analysis incorporating optical spectra as well as broadband colors. + They also fiud a siguificautly better fit for SMC extinetion than for eitherMW or LMC extinction. auc derive Ay=O1LL40.01 magnitudes for the SMC model.," They also find a significantly better fit for SMC extinction than for eitherMW or LMC extinction, and derive $A_V = 0.14 \pm 0.01$ magnitudes for the SMC model." +" Usine our multiple epoch SEDs. we find a 2,. ⋅ ⋅ ⋅ ⋅ ⊳∖∩∐↕≺↵∖∖↽∐⋜∐∖∖↽∩↕⋅↜∖≺↵∖−↙∕∕≼⇂⋅∩⋅↥∶⊔∫↖∖↥∩↕⋅↕∐↩∐⋅≺↵⊸∖⋃∐∢∙⊔∩↥≺↵⊳∖∐↕⋜↕↕≺↵↕∐⋜↕∐↥∩↕⋅∩⋃⋅⊳∖⋅∣≻⋯↕⇂≺↵↕∖∖↽∩↕⋅≺↲⊳∖⋃∐⊳∖ ⋜⋃⋅≺↵↥↽∐⋅∩∣≻⋜≹∣≻↥⊽∖⇁∢∙∩∐⊳∖↥⊳∖↕≺↵∐↕∖∖↽∐∐↥∐↕∐↩≺↵⋅⋅∩↓∷∖⋅↩⊳∖↥↽≻≺↵∢∙↥⋜↕∐⊽∖⊽∐∎↕≺↵↕⋅≺↲⋜↕↓⋅≺↵⋯∏≺⇂≺↵∐↕∐∎∐↵≺⇂⊳∖⊽∖⇁⊳∖↕≺↵⋯⋜↕∏∢∙≺↲⊔⋅∩↥⋅⊳∖∩↥∎ ≧⋋↴∪⋅∪↖∖⋝⋯⋜↕∑≟∐∐⋯⇂↩↕∐↕∐≺↵↥↽≻∐"," Using our multiple epoch SEDs, we find a somewhat worse $\chi^2 / \dof = 1.98$ for their extinction estimate than for ours, but the two results are probably consistent within the errors, especially if there are unidentified systematic errors of $\ga 0.08$ magnitude in the photometry (see section \ref{colsec}) )." +∩↕∩⋯≺↵⋃⋅⊽∖⇁↸⋮⊳∖≺↵≺↵↠∖≺↲∢∙∏∩⊔⋅↴⊔⋅ ⊺∐≺↵⋜↕↥↽≻↥↽≻⋜⋃⋅≺↵∐↕∖∖↽≺↵⋜↕↕⊆∐≺↲↜∖↠∖∩↥∎↕∐≺↲⊇↽⋡⊤⋅↴⇀−∖ ∐∎≺↵⋜↕⊓⊔⋅≺↵↥∐↕∐↩↩⊸∖∏∐∢∙∏∩∐∢∙⋯⋅∖⊽≺↵∩⊓∐≺↵∐∩⊳∖↕∑∸⋜↕↥⋜∟∖⊽∖⊽↥⊳∖↕⋅≺↵∐∐∐↥⊳∖∢∙≺↲∐↕∩↥∎≺⇂⋃⊳∖↕⋜↕⊓≺↵⋯⇂⋜↕∏∩∐↥⋜↕∖∖⋱∖↥∎∩↓⋅⋜↕∢∙∏∖⇁≺↵↥⊽∖⇁ ⊳∖↕⋜↕↓⋅↥∎≺∐⋅∐∏∐∑≟∑≟⋜↕⋜∟∖↥↩⊳∖↸⋮≺↵⋅∑≟⋅⋅↕∐↩↥∖↓⋜↕∑≟≺↵∐⋜↕∐↥∢∙∊↽⊲↥∩⋯⇂↠∖∐⊃≺↲↥⊽∐⋯⊇⋜↕∐≺⊔⋅≺↵↥∎≺↵↕⋅≺↲∐∢∙≺↵⊳∖↕∐≺↵↓⋅≺↵↥∐↴⋜↕∐≺⇂⊳∖↕⋜↕↓⋅∣∥⊔⋅⊳∖↕ ealaxies [Gordon. Calzetti. Witt 1997]).," The apparent weakness of the $2175$ feature in the extinction curve of the host galaxy is reminiscent of dust attenuation laws for actively star forming galaxies (e.g., the Magellanic Clouds [Pei 1992 and references therein] and starburst galaxies [Gordon, Calzetti, Witt 1997])." + This may be further cireumstantial evidence linking GBRBs to actively star forming ealaxies., This may be further circumstantial evidence linking GRBs to actively star forming galaxies. + Alternatively. such au extinction law mieht be observed if GRBs preferentially destroy the sinall carbonaceous particles thought to be carriers of the 2175 feature. but this explanation would only work if much of the dust optical depth arises near the uiaximnunr radius where the burst cau destroy graius WWasman Draine 2000: Fruchter. νο. Rhoads 2000).," Alternatively, such an extinction law might be observed if GRBs preferentially destroy the small carbonaceous particles thought to be carriers of the $2175$ feature, but this explanation would only work if much of the dust optical depth arises near the maximum radius where the burst can destroy grains Waxman Draine 2000; Fruchter, Krolik, Rhoads 2000)." + Iu order to determine pliysical parameters of the afterglow. we need to measure the peak fIux density aud the locatious of breaks in the afterglow spectrum (Wijers Calama 1999).," In order to determine physical parameters of the afterglow, we need to measure the peak flux density and the locations of breaks in the afterglow spectrum (Wijers Galama 1999)." + We now do this (iusolar as possible) by combinine our optical-IR spectral slope measurements with the sttbuatllimeter aud radio data., We now do this (insofar as possible) by combining our optical-IR spectral slope measurements with the submillimeter and radio data. +" We are lookingfor four uumbers: The frequency riposo, aud fux deusity fjiax at the peak in f/,: the cooling frequency (. aud the self-absorptiou [requeney 7abs:"," We are lookingfor four numbers: The frequency $\nu_{hbox{max}}$ and flux density $f_{\nu,\hbox{max}}$ at the peak in $f_\nu$; the cooling frequency $\nu_c$ , and the self-absorption frequency $\nu_{\hbox{abs}}$." + The spectral slope is expected to be —p/2 for v>νο. —(p—1)/2 for max€rb \nu_c$, $-(p-1)/2$ for $\nu_{\hbox{max}} < \nu < \nu_c$, $+1/3$ for $\nu_{\hbox{abs}} < \nu < +\nu_{\hbox{max}}$, and $+2$ for $\nu < \nu_{\hbox{abs}}$ (Sari, Piran, Narayan 1998)." + Here p is the power law iudex of electrons recently accelerated at the external shock of the expanding GRB remnant., Here $p$ is the power law index of electrons recently accelerated at the external shock of the expanding GRB remnant. + Extrapolating the optical-IR spectral slopes to lower frequencies. we see that a strong spectral break is required wear or above the 250GHz measurement by Bertoldi (2000) on March. L385.," Extrapolating the optical-IR spectral slopes to lower frequencies, we see that a strong spectral break is required near or above the $250 +\GHz$ measurement by Bertoldi (2000) on March 4.385." +" The radio data from March 5.67 (Berger et al 2000) are compatible with fj,xvt between 22 aud 250GHz. so we determine rax aud [μας by extrapolating this beliavior until it intersects the extrapolation [rom optical-IR. data (see figure £))."," The radio data from March 5.67 (Berger et al 2000) are compatible with $f_\nu +\propto \nu^{1/3}$ between $22$ and $250 \GHz$, so we determine $\nu_{\hbox{max}}$ and $f_{\nu,\hbox{max}}$ by extrapolating this behavior until it intersects the extrapolation from optical-IR data (see figure \ref{sedwide}) )." + Using fluxes corrected for both Galactic dust and Ay=0.009 magnitude of SMC type extinction at 2=) 2.03. we obtain log(Áax/ and log(iinax/qmdJy) 0.100.050. where the error bars account onlyfor photometric errors ou the data.," Using fluxes corrected for both Galactic dust and $A_V = 0.09$ magnitude of SMC type extinction at $z=2.03$ , we obtain $\log(\nu_{\hbox{max}}/\Hz) = 11.81 \pm 0.10$ and $\log(f_{\nu,\hbox{max}} / \mJy ) = 0.46 \pm 0.05$ , where the error bars account onlyfor photometric errors on the data." + If we do not apply any correction lor host galaxy extiuction. we instead obtain," If we do not apply any correction for host galaxy extinction, we instead obtain" +objects from PLJ have the same average color is.,objects from PLJ have the same average color is. + The Nohuogorov-Siniznoy two-sample test applied to the same samples indicates probability that the distributions of 7 ICKBOs and the 31 objects from PLJ have the same average color ls«, The Kolmogorov-Smirnov two-sample test applied to the same samples indicates probability that the distributions of 7 ICKBOs and the 34 objects from PLJ have the same average color is. + The decrease in sample size of the « ssuuples presunablv accounts for the slight increase m probability for the Μαμά] samples., The decrease in sample size of the $<$ samples presumably accounts for the slight increase in probability for the smaller samples. + When we began this particular project. we thought that the low aud immer bolt objects were a natural sunward extension of the cold classical population found between 12 1 of the free-fall time-scale. where (he latter is written for the spherical uniform density distribution.," We consider the contraction time-scale of a cylindrical molecular cloud as a multiple $\eta \geq 1$ of the free-fall time-scale, where the latter is written for the spherical uniform density distribution." + The cooling time-scale /=3AT/2im and the Iree-Iall time-scale (2)) areshown in Fig. 2.., The cooling time-scale $t_c \equiv 3kT/2m\Lambda$ and the free-fall time-scale \ref{freetime}) ) areshown in Fig. \ref{timescale}. + In. [ast contraction (4)~ 1). This important in small densities (e.g. less than 10H.? for T—LOOK). while in slow contraction (7>> 1) in which the cooling time-scale is much smaller than (he contraction Gime-scale. (he importance of TI as a trigger mechanism is niuch evident.," In fast contraction $\eta \sim 1$ ), TI is important in small densities (e.g., less than $10^{14} m^{-3}$ for $T=100\mathrm{K}$ ), while in slow contraction $\eta >>1$ ) in which the cooling time-scale is much smaller than the contraction time-scale, the importance of TI as a trigger mechanism is much evident." + There are several different heating mechanisms in models of interstellar matters., There are several different heating mechanisms in models of interstellar matters. + Since the ultraviolet photons are mostly screened out in dense molecular clouds. heating by collisional de-excitation of Πο molecules after radiative excitation. of Lyman bands. photoemission from grains. radiative dissociation of ο. and by chemical reactions is not important.," Since the ultraviolet photons are mostly screened out in dense molecular clouds, heating by collisional de-excitation of $H_2$ molecules after radiative excitation of Lyman bands, photoemission from grains, radiative dissociation of $H_2$, and by chemical reactions is not important." + In addition. because of the small neutral hydrogen abundance. heating due to ejection of newly lormed // molecules from grain surfaces is negligible.," In addition, because of the small neutral hydrogen abundance, heating due to ejection of newly formed $H_2$ molecules from grain surfaces is negligible." + The heating due to cosmic ravs with sufficient. energies (~ 100MeV) to penetrate dense clouds is commonly about Tep=25x10“JketsἘν with assumption of an ionization rate per //» molecule of 2x10Ms Land amean energy gains per ionization of 19eV (e.g.. Glassgold and Langer 1973).," The heating due to cosmic rays with sufficient energies $\sim 100 +\mathrm{MeV}$ ) to penetrate dense clouds is commonly about $\Gamma_{CR} = 2.5 \times 10^{-8} \mathrm{J.kg^{-1}.s^{-1}}$, with assumption of an ionization rate per $H_2$ molecule of $2\times +10^{-17} \mathrm{s^{-1}}$ and a mean energy gains per ionization of $19 \mathrm{eV}$ (e.g., Glassgold and Langer 1973)." + Following Black (1987) the turbulence dissipation heating rate can be estimated as where ty) is the turbulent. velocity and / is the eddy seale., Following Black (1987) the turbulence dissipation heating rate can be estimated as where $v_{turb}$ is the turbulent velocity and $l$ is the eddy scale. + With Όρων~1kins! and {ο1pe. we obtain Fogc1.6x10“keFs !. comparable to half of the heating rate of cosmic ravs.," With $v_{turb} \sim 1~ \mathrm{km.s}^{-1}$ and $l\sim +1~\mathrm{pc}$, we obtain $\Gamma_{TR} \sim 1.6 \times 10^{-8} +\mathrm{J.kg}^{-1}.\mathrm{s}^{-1}$ , comparable to half of the heating rate of cosmic rays." + In this way. we collect the values of these two heating rates to obtain ~Ll1x10kgts !.," In this way, we collect the values of these two heating rates to obtain $\sim 4.1\times 10^{-8} +\mathrm{J.kg}^{-1}.\mathrm{s}^{-1}$ ." + Another important heating mechanism of sell-gravitating contracting cloud is the heating produced by gravitational compression work., Another important heating mechanism of self-gravitating contracting cloud is the heating produced by gravitational compression work. + Anestimation lor this, Anestimation for this +blending is the line at 74.860 wwhich contains Mg VIII and Fe XIII.,blending is the line at 74.860 which contains Mg VIII and Fe XIII. + We have measured line ratios of density-sensitive He-like triplets from the LETGS and RGS spectra. taking into account the photo-exciting UV flux (Porquet et al.," We have measured line ratios of density-sensitive He-like triplets from the LETGS and RGS spectra, taking into account the photo-exciting UV flux (Porquet et al." + 2001)., 2001). + Our results are consistent in both instruments (ων.~1029 7) and similar to those of Ness et al. (, Our results are consistent in both instruments $n_\mathrm{e} \approx 10^{10}$ $^{-3}$ ) and similar to those of Ness et al. ( +2001) and our values given in Table 4.,2001) and our values given in Table 4. + These results are also comparable to values obtained by Schrijver et al. (, These results are also comparable to values obtained by Schrijver et al. ( +1995) and Schmitt et al. (,1995) and Schmitt et al. ( +1996) and to values for the Sun (Drake et al.,1996) and to values for the Sun (Drake et al. + The RGS and LETGS spectra of the corona of Procyon below 40 aare dominated by the H- and He-like transitions of C. N. and O and by Fe XVII lines.," The RGS and LETGS spectra of the corona of Procyon below 40 are dominated by the H- and He-like transitions of C, N, and O and by Fe XVII lines." + Above 40 tthe LETGS spectrum shows many L-shell lines of e.g.. Ne. Mg. and Si. together with lines of Fe VIII-XIII of which the Fe IX line at 171.075 is very prominent.," Above 40 the LETGS spectrum shows many L-shell lines of e.g., Ne, Mg, and Si, together with lines of Fe VIII-XIII of which the Fe IX line at 171.075 is very prominent." + All methods applied in Sect., All methods applied in Sect. + 3.2 to the spectra of the RGS+MOS and the LETGS show temperatures of the corona of Procyon between 1-3 MK., 3.2 to the spectra of the RGS+MOS and the LETGS show temperatures of the corona of Procyon between 1–3 MK. + No indication for à considerably higher temperature component (T> 4+ MK) is found., No indication for a considerably higher temperature component $T \ga$ 4 MK) is found. + The total EM obtained using RGS and LETGS is about L.1(.5)«10° °., The total $EM$ obtained using RGS and LETGS is about $4.1(.5) \times 10^{50}$ $^{-3}$. + The EAL distributioαυ] shows a smooth continuous structure without separated peak structures., The $EM$ distribution shows a smooth continuous structure without separated peak structures. + Our results improve on those of Schmitt et al. (, Our results improve on those of Schmitt et al. ( +1996) who obtain an A distribution with à maximum temperature around 1.6 MK and a cutoff beyond 6.3 MK.,1996) who obtain an $EM$ distribution with a maximum temperature around 1.6 MK and a cutoff beyond 6.3 MK. + No significant variability of the coronal conditions took place between the observations by RGS and LETGS., No significant variability of the coronal conditions took place between the observations by RGS and LETGS. + The abundances of C and Ν. relative to O are somewhat higher ( factor 1.5) than the values obtained in the solar photosphere (Anders Grevesse 1989).," The abundances of C and N, relative to O are somewhat higher $\sim$ factor 1.5) than the values obtained in the solar photosphere (Anders Grevesse 1989)." + The Fe abundance is about I-1.5 « solar., The Fe abundance is about 1–1.5 $\times$ solar. + No significance for a FIP effect. as observed in the solar corona (Feldman et al.," No significance for a FIP effect, as observed in the solar corona (Feldman et al." + 1992). is found.," 1992), is found." + The same was concluded by Drake et al (1995). based on EUVE observations.," The same was concluded by Drake et al (1995), based on EUVE observations." + This result is an exception of the trends found by Audard et al. (, This result is an exception of the trends found by Audard et al. ( +20019) for RS CVn systems and by Giiddel et al. (,2001c) for RS CVn systems and by Güddel et al. ( +20019) for solar analogs.,2001c) for solar analogs. + These authors have found indications for the evolution from an inverse FIP effect for highly active stars - via the absence of a FIP effect in intermediately active stars - towards a normal FIP effect for less active stars., These authors have found indications for the evolution from an inverse FIP effect for highly active stars - via the absence of a FIP effect in intermediately active stars - towards a normal FIP effect for less active stars. + Clearly. the weakly active star Procyon does not fit into this picture.," Clearly, the weakly active star Procyon does not fit into this picture." +whilst a neighbouring ray passing through a more rarefied region is not split.,whilst a neighbouring ray passing through a more rarefied region is not split. + Once the ionization front is located along a ray. the propagation of that ray is terminated. in order to reduce the computational overhead: this is. particularly. important during the early stages of evolution. when the Strómgren sphere only involves a small fraction of the total number of SPH particles.," Once the ionization front is located along a ray, the propagation of that ray is terminated, in order to reduce the computational overhead; this is particularly important during the early stages of evolution, when the mgren sphere only involves a small fraction of the total number of SPH particles." + Although heavy elements play an important role in determining the temperature of interstellar gas. we do not consider their chemistry here.," Although heavy elements play an important role in determining the temperature of interstellar gas, we do not consider their chemistry here." + Instead. we assume that the composition of the gas is X=0.7 hydrogen and Y=0.3 helium. by mass: and that the helium is everywhere neutral.," Instead, we assume that the composition of the gas is $X=0.7$ hydrogen and $Y=0.3$ helium, by mass; and that the helium is everywhere neutral." +" In the neutral gas we assume that the temperature is 7,=LOK and the hydrogen is all molecular: hence the mean molecular welght is jjj,=2.35 and the isothermal sound speed is cy= 0.2kms~!."," In the neutral gas we assume that the temperature is $T_{\rm n}=10\,{\rm K}$ and the hydrogen is all molecular; hence the mean molecular weight is $\mu_{\rm n}=2.35$ and the isothermal sound speed is $c_{\rm n}=0.2\,{\rm km}\,{\rm s}^{-1}$ ." + In the ionized gas we assume that the temperature is T;=10K and the hydrogen is all ionized: hence py=0.678 and c;=11kms7!.," In the ionized gas we assume that the temperature is $T_{\rm i}=10^4\,{\rm K}$ and the hydrogen is all ionized; hence $\mu_{\rm i}=0.678$ and $c_{\rm i}=11\,{\rm km}\,{\rm s}^{-1}$." + In the transition region between the molecular and ionized regions. we impose a linear temperature gradient between these two limiting values.," In the transition region between the molecular and ionized regions, we impose a linear temperature gradient between these two limiting values." + We explore three cases. (, We explore three cases. ( +1) In the first case. the star lies at the centre of a spherical cloud. and the is spherically symmetric throughout its expansion. (,"i) In the first case, the star lies at the centre of a spherical cloud, and the is spherically symmetric throughout its expansion. (" +11) In the second case. the star is placed off-centre inside a spherical cloud: here the breaks out of the cloud on one side. and the remainder of the cloud ts accelerated by the rocket effect. (,"ii) In the second case, the star is placed off-centre inside a spherical cloud; here the breaks out of the cloud on one side, and the remainder of the cloud is accelerated by the rocket effect. (" +111) In the third case. the star is located outside the cloud from the outset. and à shock is driven into the cloud ahead of the ionization front (i.e. radiation driven compression).,"iii) In the third case, the star is located outside the cloud from the outset, and a shock is driven into the cloud ahead of the ionization front (i.e. radiation driven compression)." + These cases are presented only as illustrative examples of what the code can simulate., These cases are presented only as illustrative examples of what the code can simulate. + Detailed investigations of these phenomena will be presented in subsequent papers., Detailed investigations of these phenomena will be presented in subsequent papers. + The paper is organized as follows., The paper is organized as follows. + In Section 2. we discuss briefly the expansion of anregion. once the initial Strómgren sphere has formed.," In Section \ref{sec.physics} we discuss briefly the expansion of an, once the initial mgren sphere has formed." + In Section 3 we describe in detail how we treat the propagation of ionizing radiation., In Section \ref{sec.numerical} we describe in detail how we treat the propagation of ionizing radiation. + In Section 4 we test the algorithm on the three cases described above. and in Section 5 we discuss the results and conclude.," In Section \ref{sec.applications} we test the algorithm on the three cases described above, and in Section \ref{sec.discussion} we discuss the results and conclude." + Consider an arbitrary density field. p(r). and suppose that there is an Ionizing star at the centre of co-ordinates.," Consider an arbitrary density field, $\rho({\bf r})$, and suppose that there is an ionizing star at the centre of co-ordinates." +" Assuming ionization equilibrium. and neglecting the diffuse radiation field. the position of the ionization front CIF). in the direction of the unit vector €. is given by R,.=R,6. where R, is obtained from Here. ni=my/X2.4x10—7& is the mass associated with one hydrogen nucleus when account is taken of the contribution from helium. zi, is the proton mass. N,,.. is the rate at which the exciting star emits Lyman continuum photons. and a, is the recombination coetficient into excited states only."," Assuming ionization equilibrium, and neglecting the diffuse radiation field, the position of the ionization front (IF), in the direction of the unit vector $\bf{\hat e}\,$, is given by ${\bf R}_{_{\rm IF}}=R_{_{\rm IF}}{\bf{\hat e}}\,$, where $R_{_{\rm IF}}$ is obtained from Here, $m=m_{\rm p}/X=2.4\times 10^{-24}\,{\rm g}$ is the mass associated with one hydrogen nucleus when account is taken of the contribution from helium, $m_{\rm p}$ is the proton mass, $\dot{\cal N}_{_{\rm LyC}}$, is the rate at which the exciting star emits Lyman continuum photons, and $\alpha_{_{\rm B}}$ is the recombination coefficient into excited states only." + Eqn. (1)), Eqn. \ref{integral}) ) + assumes that the material inside the is fully ionized., assumes that the material inside the is fully ionized. + Thus Eqn. (1)), Thus Eqn. \ref{integral}) ) + determines the radius Αι. at which all the ionizing photons emitted in the direction @ have been used up balancing recombinations into excited states., determines the radius $R_{_{\rm IF}}$ at which all the ionizing photons emitted in the direction $\bf{\hat e}$ have been used up balancing recombinations into excited states. + We ignore recombinations straight into the ground state by invoking theon-the-spot approximation (Osterbrock 1974)., We ignore recombinations straight into the ground state by invoking the approximation (Osterbrock 1974). + Strómgren (1939) was the first to show that the transition from a state of almost completely tonized material to a state of almost completely neutral material occurs 1n a very short distance compared with the dimensions of theregion., mgren (1939) was the first to show that the transition from a state of almost completely ionized material to a state of almost completely neutral material occurs in a very short distance compared with the dimensions of the. +. For example. for a spherically-symmetric expanding into a cloud of uniform density py. the radius of the ionization front is given by the Strómgren radius and the distance over which the degree of ionization changes from 90% to 106c is given by Here &=7x107env. is the mean photoionization cross section presented by a hydrogen atom to Lyman continuum photons from an OB star.," For example, for a spherically-symmetric expanding into a cloud of uniform density $\rho_{\rm n}$, the radius of the ionization front is given by the mgren radius and the distance over which the degree of ionization changes from $90\,\%$ to $10\,\%$ is given by Here $\bar\sigma=7\times10^{-18}\,{\rm cm}^2$ is the mean photoionization cross section presented by a hydrogen atom to Lyman continuum photons from an OB star." +" Because the squared sound speed in the 1onized gas inside the is et=22knyY$7. whereas the squared sound speed in the neutral material outside the is cE0.0352km? s, there is a large pressure difference betwee! the two regimes (more than three orders of magnitude). and this results in rapid expansion of the region."," Because the squared sound speed in the ionized gas inside the is $c_{\rm i}^2\simeq122\,{\rm km}^2\,{\rm s}^{-2}$, whereas the squared sound speed in the neutral material outside the is $c_{\rm n}^2\simeq 0.0352\,{\rm km}^2\,{\rm s}^{-2}$ , there is a large pressure difference between the two regimes (more than three orders of magnitude), and this results in rapid expansion of the ." + The outward propagation of the ionization front is subsonic relative to the ionized gas (where the sound speed is c;~11 kms). but supersonic relative to the neutral gas (where the sound speed is cy02 kms7!).," The outward propagation of the ionization front is subsonic relative to the ionized gas (where the sound speed is $c_{\rm i}\sim 11\,{\rm km\,s^{-1}}$ ), but supersonic relative to the neutral gas (where the sound speed is $c_{\rm n}\sim 0.2\,{\rm km}\,{\rm s}^{-1}$ )." + Consequently a strong shock front appears ahead the ionization front (for a detailed discussion see Kahr 1954)., Consequently a strong shock front appears ahead the ionization front (for a detailed discussion see Kahn 1954). + Spitzer (1978) has obtained an approximate analytic solution for this phase of the evolution., Spitzer (1978) has obtained an approximate analytic solution for this phase of the evolution. + In this solution. the radius of the ionization front is given by the density of the tonized gas by the mass of ionizedgas by and the speed at which the ionization front propagates by," In this solution, the radius of the ionization front is given by the density of the ionized gas by the mass of ionizedgas by and the speed at which the ionization front propagates by" +"cannot be ruled out as the cause of the velocity separation. (he energetics are uncomlLortably light,","cannot be ruled out as the cause of the velocity separation, the energetics are uncomfortably tight." +" Moreover. the spatio-velocity structure of the (wo components. as shown in figure 4.. shows the greatest departiures [rom the centroid velocity at around 182""00*.— the futhest projected distance Irom the central star."," Moreover, the spatio-velocity structure of the two components, as shown in figure \ref{lv}, shows the greatest departures from the centroid velocity at around $^h$ $^m$ $^s$ – the furthest projected distance from the central star." + This does not fit the classical pattern of a shell-like expansion around a central source. and suggests that at least some component of the cloud velocily separation is unrelated (o (heir interaction with the central star We here suggest that much of the observed motion of the clouds does not arise as a direct result of the stellar cluster but is instead svstenic ie. present [rom before the clusters birth.," This does not fit the classical pattern of a shell-like expansion around a central source, and suggests that at least some component of the cloud velocity separation is unrelated to their interaction with the central star We here suggest that much of the observed motion of the clouds does not arise as a direct result of the stellar cluster but is instead systemic — i.e. present from before the cluster's birth." + Yet the 2 kins + cloud and cloud C are clearly associated with M20 and in close spatial proximity (o one another., Yet the 2 km $^{-1}$ cloud and cloud C are clearly associated with M20 and in close spatial proximity to one another. + We suggest (hal a scenario in which a cloud-cloud. collision triggered the formation of the central stars is highlv consistent with these observational characteristics., We suggest that a scenario in which a cloud-cloud collision triggered the formation of the central stars is highly consistent with these observational characteristics. + In this scenario the 2 kms ! cloud and cloud C collided each other ο]. Myr ago at a relative velocity of ~7.5 km 1 or more., In this scenario the 2 km $^{-1}$ cloud and cloud C collided each other $\sim$ 1 Myr ago at a relative velocity of $\sim$ 7.5 km $^{-1}$ or more. + The rapid collision between the (wo clouds strongly compressed the molecular gas and triggered the formation of the central star and surrounding first generation stars., The rapid collision between the two clouds strongly compressed the molecular gas and triggered the formation of the central star and surrounding first generation stars. + In this model. the 2 km ! cloud. and cloud € must be moving in the opposite directions: the former is moving toward us and the latter is moving away [rom us.," In this model, the 2 km $^{-1}$ cloud and cloud C must be moving in the opposite directions; the former is moving toward us and the latter is moving away from us." + As shown in Section 3.1. the 2 kins ! cloud is apparently located at the front side of M20. whereas cloud C is not in the near side. suggesting that it is located either on the far side or within M20.," As shown in Section 3.1, the 2 km $^{-1}$ cloud is apparently located at the front side of M20, whereas cloud C is not in the near side, suggesting that it is located either on the far side or within M20." + This relative configuration is in [act consistent with the cloud-cloucl collision scenario. because we must be witnessing a moment alter (he collision occurred. Myr ago.," This relative configuration is in fact consistent with the cloud-cloud collision scenario, because we must be witnessing a moment after the collision occurred Myr ago." + We would expect a reversed cloud location prior to the collision., We would expect a reversed cloud location prior to the collision. + This scenario is similar to (hat cdiscussecl by Furukawaetal.(2009) and later expanded on by Ohamaetal.(2010)., This scenario is similar to that discussed by \citet{fur2009} and later expanded on by \citet{oha2010}. +. These authors Found two GAICs closely associated with the ROW 49 WIT region and its exciting cluster. the super star cluster Westerlund 2.," These authors found two GMCs closely associated with the RCW 49 HII region and its exciting cluster, the super star cluster Westerlund 2." + The two, The two +Globular Clusters (6€) are thought to be the oldest bound stellar svstems in our Galaxy.,Globular Clusters (GC) are thought to be the oldest bound stellar systems in our Galaxy. + Their study provides therefore valuable information. about the early Galactic. evolution., Their study provides therefore valuable information about the early Galactic evolution. + In this respect. a major problem is that we do not. know whether what we presently observe is still representative of the initial conditions and. thus. a fossil imprint. of the formation process. or whether the initial conditions have been wiped out by a GC long evolution within the tidal fields of the Alilky Way.," In this respect, a major problem is that we do not know whether what we presently observe is still representative of the initial conditions and, thus, a fossil imprint of the formation process, or whether the initial conditions have been wiped out by a Gyr long evolution within the tidal fields of the Milky Way." + Modelling the dynamical evolution of the Galactic Globular Cluster Svstem (GCS) is thus of ereat interest as it helps us to go back in time to the earliest stages of the cluster svstem and to disentangle the formation and evolutionary. fingerprints (see. e.g.. Cinedin Ostriker 1997. Baumgardt 1998. Vesperini 1998. Fall Zhang 2001).," Modelling the dynamical evolution of the Galactic Globular Cluster System (GCS) is thus of great interest as it helps us to go back in time to the earliest stages of the cluster system and to disentangle the formation and evolutionary fingerprints (see, e.g., Gnedin Ostriker 1997, Baumgardt 1998, Vesperini 1998, Fall Zhang 2001)." + The GCs most vulnerable to evaporation and disruption are the low-mass clusters located at small galactocentric distance., The GCs most vulnerable to evaporation and disruption are the low-mass clusters located at small galactocentric distance. + As a result. the evolution with time of a GCS is markedly determined by the initial distribution of the GCs in space around the Galactic centre as well as by their initial Mass spectrunmi.," As a result, the evolution with time of a GCS is markedly determined by the initial distribution of the GCs in space around the Galactic centre as well as by their initial mass spectrum." + As for the presently. observed: spatial distribution. of the Galactic halo GC's. it is centrally concentrated with the density varving as D77 (D is the Galactocentric distance) over most of the halo (Zinn 1985).," As for the presently observed spatial distribution of the Galactic halo GCs, it is centrally concentrated with the density varying as $D^{-3.5}$ $D$ is the Galactocentric distance) over most of the halo (Zinn 1985)." + In the inner kkpe. the distribution Uattens to something closer to an 4) τιependence.," In the inner kpc, the distribution flattens to something closer to an $D^{-2}$ dependence." + As a result. the overall distribution is convenicntly described by a power-law with a core (see Section 2).," As a result, the overall distribution is conveniently described by a power-law with a core (see Section 2)." + Phe observed. central [lattening probably arises from a combination of several ellects: our failure to discover some GCs in the heavily absorbed. central regions of the Galaxy. distance errors. and the real Uattening of the distribution.," The observed central flattening probably arises from a combination of several effects: our failure to discover some GCs in the heavily absorbed central regions of the Galaxy, distance errors, and the real flattening of the distribution." + It is still unclear whether such a Hlattening is of primordial origin and rellects the initial spatial distribution of the system. or whether it has been completely determined by evolutionary. processes.," It is still unclear whether such a flattening is of primordial origin and reflects the initial spatial distribution of the system, or whether it has been completely determined by evolutionary processes." + “The latter are especially effective at small galactocentric distances where the GC relaxation time is short. causing the cisruοι of some GC's and the partial evaporation of some others.," The latter are especially effective at small galactocentric distances where the GC relaxation time is short, causing the disruption of some GCs and the partial evaporation of some others." + More generally. as far as," More generally, as far as" +" where Ais the area of a cell face (see figure 1)) aud the £s are fluxes defined as To obtain the deusitics at the iterfaces (97,4) straight averages are computed of centered densities adjacent to the interface.",as where $A$ is the area of a cell face (see figure \ref{fig:cell}) ) and the $F$ s are fluxes defined as To obtain the densities at the interfaces $\rho_{i\pm 1/2}^n$ ) straight averages are computed of centered densities adjacent to the interface. + The two centered subscripts have intentionally con. onütted In the expressions for the fluxes aud areas to reduce equation leneth (e.g. { was left off mt 71/2 was ΚΟ))., The two centered subscripts have intentionally been omitted in the expressions for the fluxes and areas to reduce equation length (e.g. $i$ was left off but $i+1/2$ was kept). + Note that the densities iji the fluxes aro af tine 5 and not »|1/2. so «mr solution algorithui is sraiehttorwardly explicit. as ds true for many 1D calculations.," Note that the densities in the fluxes are at time $n$ and not $n+1/2$, so our solution algorithm is straightforwardly explicit, as is true for many 1D calculations." + It is uot possible to properly time ceuter all terms without introducing a more conrplex inyplicit or imulti-«ep explicit algorithin., It is not possible to properly time center all terms without introducing a more complex implicit or multi-step explicit algorithm. + Wih this expression for the fluxes. we can cirectly solve equation (10)) for the ceusity at the new time step.," With this expression for the fluxes, we can directly solve equation \ref{eq:mass-cons-fv}) ) for the density at the new time step." + The final piece needed o coniplete the description is the calculation of the erid velocity., The final piece needed to complete the description is the calculation of the grid velocity. + For a spherical shell to have costant mass. the net flow of 1iass into and out of hat spherical shell ust be zero.," For a spherical shell to have constant mass, the net flow of mass into and out of that spherical shell must be zero." + Suwine up all he fluxes iuto and out of the individua| horizoutal cells iu a spherical shell. substituting ¢quation (11 )) iu for the outer radial flux (at ὁ| 2) and setine the result equal to zero we arrive at the equation. Solving for the outer erid velocity. (wetUrilye|l2 produces an equation for calculating the new erid velocity. The inner radial flux. FYy. is depenudeu ou the erid velocity at the inner interface.," Summing up all the fluxes into and out of the individual horizontal cells in a spherical shell, substituting equation \ref{eq:outer-flux}) ) in for the outer radial flux (at $i+1/2$ ) and setting the result equal to zero we arrive at the equation, Solving for the outer grid velocity, $v_{0r,i+1/2}^{n+1/2}$, produces an equation for calculating the new grid velocity, The inner radial flux, $F_{i-1/2}^{n+1/2}$, is dependent on the grid velocity at the inner interface." + A the first radial zone boundary next to the ei core we impose both a zero radial velocity anc erid velocity., At the first radial zone boundary next to the rigid core we impose both a zero radial velocity and grid velocity. + Thus. equation (15)) can be solve recursively frou. the model iterior boundary to the surface to determine the erid velocity at al interfaces.," Thus, equation \ref{eq:rad-grid-vel}) ) can be solved recursively from the model interior boundary to the surface to determine the grid velocity at all interfaces." + The initial model for our adiabatic simulations is generated by requiring that it be iu livdrostatic equilibrimu., The initial model for our adiabatic simulations is generated by requiring that it be in hydrostatic equilibrium. + When this constraint is applied to the conservation equations the ouly terms that remain are the pressure and eravitv terms in the radial momentum couscrvation equation., When this constraint is applied to the conservation equations the only terms that remain are the pressure and gravity terms in the radial momentum conservation equation. + Iu particular. there are no terms left im the internal energy conservation equation. and thus no equation to solve for the energv structure.," In particular, there are no terms left in the internal energy conservation equation, and thus no equation to solve for the energy structure." +" To provide this information. an enerev profile παν. generaed from aotier stelar modeling code ROTORC (DeuprecL990) Hand eicrgies were interpolaed in loe(AL.) ο cel cenutcYs,"," To provide this information, an energy profile was generated from another stellar modeling code ROTORC \citep{Deupree-1990} and energies were interpolated in $\log(M_r)$ to cell centers." + Once we impose he energv disributiol. we can sinultaneouslv solve the racial wdrostatic ecuilibriuui fuite differeice equation a1 the equation of state for the pressure aud ceusivo structure of the model given he spacing of he indepevent variahle AZ.," Once we impose the energy distribution, we can simultaneously solve the radial hydrostatic equilibrium finite difference equation and the equation of state for the pressure and density structure of the model given the spacing of the independent variable $M_r$." + The Lacjus is deernüned from the vohune required to produce the calculated density from the iass of the shell., The radius is determined from the volume required to produce the calculated density from the mass of the shell. + No convecive model is incbluded iu the starting model because RR Lyrae do not have extensive convective regions to affect the structure., No convective model is included in the starting model because RR Lyrae do not have extensive convective regions to affect the structure. + To induce pulsation a racial velocity profile from the linear. noun-adiabatic. radial," To induce pulsation a radial velocity profile from the linear, non-adiabatic, radial" +"ray and cosmic ray measurements, is that it is practically insensitive to the complications caused by the nonlinear evolution of the cosmic density field.","ray and cosmic ray measurements, is that it is practically insensitive to the complications caused by the nonlinear evolution of the cosmic density field." +" As our analysis shows, for any realistic structure formation scenario the CMB bounds on annihilating DM arise solely around the redshifts of z~1000, while the contribution from lower redshift cosmic structures is completely negligible."," As our analysis shows, for any realistic structure formation scenario the CMB bounds on annihilating DM arise solely around the redshifts of $z\sim 1000$, while the contribution from lower redshift cosmic structures is completely negligible." + CMB constraints on annihilating DM have been obtained in several earlier studies: e.g. ??7?????..," CMB constraints on annihilating DM have been obtained in several earlier studies: e.g. \citet{2005PhRvD..72b3508P,2006MNRAS.369.1719M,2006PhRvD..74j3519Z,2009PhRvD..80b3505G,2009PhRvD..80d3526S,2009JCAP...10..009C,2009A&A...505..999H,2010PThPh.123..853K}." +" Even though most of these analyses have assumed a simple ‘on the spot’ approximation for the energy more recent studies (??) followed the energydeposition}, transport problem including various energy-loss mechanisms in a more realistic way."," Even though most of these analyses have assumed a simple `on the spot' approximation for the energy, more recent studies \citep{2009PhRvD..80d3526S,2009A&A...505..999H} followed the energy transport problem including various energy-loss mechanisms in a more realistic way." +" Compared to the analysis of ?,, which partially relies on the previously derived ‘on the spot’ results of ?,, in this paper we perform a more elaborate treatment for the energy deposition joined to the analysis of the CMB data via Markov chain Monte Carlo calculations that incorporate the most recent WMAP likelihood code."," Compared to the analysis of \citet{2009PhRvD..80d3526S}, which partially relies on the previously derived `on the spot' results of \citet{2009PhRvD..80b3505G}, in this paper we perform a more elaborate treatment for the energy deposition joined to the analysis of the CMB data via Markov chain Monte Carlo calculations that incorporate the most recent WMAP likelihood code." +" Also, we make an attempt to unify the results from various annihilation channels and provide a simple and rather generic fitting formula for calculating CMB constraints on annihilation cross section (cv) for a broad range of annihilating DM models."," Also, we make an attempt to unify the results from various annihilation channels and provide a simple and rather generic fitting formula for calculating CMB constraints on annihilation cross section $\cs$ for a broad range of annihilating DM models." + Our paper is organized as follows., Our paper is organized as follows. + In Section 2 we give a brief description of the energy input from DM annihilation and provide a simple treatment for its propagation., In Section 2 we give a brief description of the energy input from DM annihilation and provide a simple treatment for its propagation. + The effect on CMB temperature and polarization fluctuations is investigated in Section 3., The effect on CMB temperature and polarization fluctuations is investigated in Section 3. + Section 4 presents our main results about current and future CMB constraints., Section 4 presents our main results about current and future CMB constraints. + Our summary is given in Section 5., Our summary is given in Section 5. +" As in ??,, we treat our input signals from DM annihilation in an as model independent a way as possible."," As in \citet{2009NuPhB.813....1C,2011JCAP...03..051C}, we treat our input signals from DM annihilation in an as model independent a way as possible." +" In? the two-particle annihilation channels to all Standard Model (SM) particles were considered: leptons, quarks, photons, gluons, weak-interaction gauge bosons, Higgs boson, and neutrinos."," In \citet{2011JCAP...03..051C} the two-particle annihilation channels to all Standard Model (SM) particles were considered: leptons, quarks, photons, gluons, weak-interaction gauge bosons, Higgs boson, and neutrinos." +" In addition, annihilations to four leptons via an intermediate new boson V were considered."," In addition, annihilations to four leptons via an intermediate new boson $V$ were considered." + Such a treatment can be considered as model independent since realistic models can always be decomposed into these basic channels where the particular branching ratios between the channels are given by the underlying theoretical particle physics model., Such a treatment can be considered as model independent since realistic models can always be decomposed into these basic channels where the particular branching ratios between the channels are given by the underlying theoretical particle physics model. +" Since in our work we focus on DM particle masses below 100 GeV, out of allof the above channels the following remain: DM DM — SM SM, where SM={e, ,7,9,¢,0,7,9}3; plus 4-lepton channels via V."," Since in our work we focus on DM particle masses below $100$ GeV, out of allof the above channels the following remain: DM DM $\rightarrow$ SM $\overline{{\rm SM}}$, where $=\{e,\mu,\tau,q,c,b,\gamma,g$ ; plus 4-lepton channels via $V$." +" Here q denotes the light quarks u, d, and s."," Here $q$ denotes the light quarks $u$, $d$, and $s$ ." +" Because the masses of interest in this work are mostly below the masses of the electroweak gauge bosons, W- and Z, those channels are left out."," Because the masses of interest in this work are mostly below the masses of the electroweak gauge bosons, $W^{\pm}$ and $Z$, those channels are left out." + For the same reason we also do not need to distinguish between left- and right-handed particles., For the same reason we also do not need to distinguish between left- and right-handed particles. +" Also, the neutrino channels in this case provide only trivial output; i.e. 10096 of the energy is carried away by neutrinos, which escape freely at the redshifts of interest, so are not treated any further."," Also, the neutrino channels in this case provide only trivial output; i.e. $100\%$ of the energy is carried away by neutrinos, which escape freely at the redshifts of interest, so are not treated any further." +" Even though the channels y and g are included in our model-independent approach, these are strongly suppressed for realistic models since DM should not carry color or interact electromagnetically."," Even though the channels $\gamma$ and $g$ are included in our model-independent approach, these are strongly suppressed for realistic models since DM should not carry color or interact electromagnetically." +" For all channels, the spectra of the emerging stable particles, e, p, y, v, after treatment of several decays, parton showers, and hadronization were calculated using PYTHIA Monte (?).."," For all channels, the spectra of the emerging stable particles, $e$, $p$, $\gamma$, $\nu$, after treatment of several decays, parton showers, and hadronization were calculated using PYTHIA Monte \citep{2008CoPhC.178..852S}." + All input spectra are downloadable from[PPPCADMID., All input spectra are downloadable from. +"html.. For more details, and in particular for a discussion on the level of possible uncertainties, we refer the reader to ?.."," For more details, and in particular for a discussion on the level of possible uncertainties, we refer the reader to \citet{2011JCAP...03..051C}." +" Among the stable output particles, neutrinos propagate freely at the redshifts of interest, while e* immediately interact with the ubiquitous CMB photons and upscatter those to the gamma-ray energy range via the inverse Compton (IC) mechanism."," Among the stable output particles, neutrinos propagate freely at the redshifts of interest, while $e^{\pm}$ immediately interact with the ubiquitous CMB photons and upscatter those to the gamma-ray energy range via the inverse Compton (IC) mechanism." + The total output energy in hadrons (p and d) is typically quite negligible., The total output energy in hadrons $p$ and $d$ ) is typically quite negligible. +" Only in gluon and quark channels does it reach up to ~ 1596, and that only for thehighestDM particle masses considered in this paper."," Only in gluon and quark channels does it reach up to $\sim 15\%$ , and that only for thehighestDM particle masses considered in this paper." + We therefore did not model this component in detail., We therefore did not model this component in detail. +" However, in Sect."," However, in Sect." + B] we give some, \ref{sec:protons} we give some +"kinematics and stellar populations (?) obtained using exactly the same data analysis technique, i.e. the full spectral fitting FLAMES-LR04 spectra having similar although slightly wider wavelength range but twice lower spectral resolution.","kinematics and stellar populations \citep{CCB08} obtained using exactly the same data analysis technique, i.e. the full spectral fitting FLAMES-LR04 spectra having similar although slightly wider wavelength range but twice lower spectral resolution." + The velocity dispersion measurements agree remarkably well for all three objects., The velocity dispersion measurements agree remarkably well for all three objects. +" The metallicity measurements agree within a few hundredths dex for UCD 3 and UCD 4, however being discrepant by ~0.4 dex for UCD 2."," The metallicity measurements agree within a few hundredths dex for UCD 3 and UCD 4, however being discrepant by $\sim +0.4$ dex for UCD 2." +" For this object, the age estimations also differ: intermediate in ? and old in our present study."," For this object, the age estimations also differ: intermediate in \citet{CCB08} and old in our present study." +" We notice, however, that the discrepancy of the UCD 2 age and metallicity measurements in ? and our present study follow the age-metallicity degeneracy."," We notice, however, that the discrepancy of the UCD 2 age and metallicity measurements in \citet{CCB08} and our present study follow the age–metallicity degeneracy." + Given quite poor data quality and large size of stellar population confidence levels in ? we conclude that the discrepancy between the measurements can be explained by statistical effects., Given quite poor data quality and large size of stellar population confidence levels in \citet{CCB08} we conclude that the discrepancy between the measurements can be explained by statistical effects. + Age determinations for UCD 3 and UCD 4 agree between the two studies within 2c of their statistical uncertainties., Age determinations for UCD 3 and UCD 4 agree between the two studies within $\sigma$ of their statistical uncertainties. +" It is worth mentioning, that the metallicity estimates for all three UCDs presented in ? are systematically lower by 0.20...0.25 dex compared to our present measurements."," It is worth mentioning, that the metallicity estimates for all three UCDs presented in \citet{MHIJ06} are systematically lower by $\dots$ 0.25 dex compared to our present measurements." + In Fig 7 (black data points) we present the comparison of published velocity dispersion measurements for 19 UCDs (?) with those obtained in our study with the full-spectral fitting technique.," In Fig \ref{figsigsig} (black data points) we present the comparison of published velocity dispersion measurements for 19 UCDs \citep{Mieske+08} + with those obtained in our study with the full-spectral fitting technique." +" Although the general trend agrees, the measurements for individual objects are often notably discrepant."," Although the general trend agrees, the measurements for individual objects are often notably discrepant." + The reasons for the discrepancy are: (1) template mismatch during cross-correlation due to the metallicity difference between UCDs and w Cen giant stars served as templates; (2) slightly different wavelength ranges used for the data analysis (inclusion of the Mgb triplet region in our study); (3) our correction for the contamination of UCD spectra by the NGC 1399 halo which ? did not apply., The reasons for the discrepancy are: (1) template mismatch during cross-correlation due to the metallicity difference between UCDs and $\omega$ Cen giant stars served as templates; (2) slightly different wavelength ranges used for the data analysis (inclusion of the $b$ triplet region in our study); (3) our correction for the contamination of UCD spectra by the NGC 1399 halo which \citet{Mieske+08} did not apply. +" The metallicity difference between the spectra and templates used to analyse them may lead to biased velocity dispersion measurements (see Section 1.3.1 in ?)) at least if the analysis is done in the pixel space, thus affecting both full spectral fitting andFXCOR cross-correlation measurements."," The metallicity difference between the spectra and templates used to analyse them may lead to biased velocity dispersion measurements (see Section 1.3.1 in \citealp{Chilingarian06}) ) at least if the analysis is done in the pixel space, thus affecting both full spectral fitting and cross-correlation measurements." +" The low metallicity of a template star resulting in shallower absorption lines may be compensated by decreasing the velocity dispersion, i.e. smearing absorption lines to a lower degree than it should be in order to match the line depth in the target spectrum being analysed."," The low metallicity of a template star resulting in shallower absorption lines may be compensated by decreasing the velocity dispersion, i.e. smearing absorption lines to a lower degree than it should be in order to match the line depth in the target spectrum being analysed." +" Then we would expect to see the correlation between UCD metallicities and differences of velocity dispersion measurements in ? and our present study, which we do not detect at a statistically significant level."," Then we would expect to see the correlation between UCD metallicities and differences of velocity dispersion measurements in \citet{Mieske+08} and our present study, which we do not detect at a statistically significant level." + This can be explained because the described degeneracy between metallicity and velocity dispersion mostly affects the data for targets with velocity dispersions similar to or lower than the instrumental spectral resolution., This can be explained because the described degeneracy between metallicity and velocity dispersion mostly affects the data for targets with velocity dispersions similar to or lower than the instrumental spectral resolution. +" In our case, most c targets have low metallicities well corresponding to those of the w Cen template stars."," In our case, most $\sigma$ targets have low metallicities well corresponding to those of the $\omega$ Cen template stars." +" On the other hand, massive metal-rich UCDs with relatively high velocity dispersions are bright,hence their spectra have good signal-to-noise ratios reducing the degeneracy effects."," On the other hand, massive metal-rich UCDs with relatively high velocity dispersions are bright,hence their spectra have good signal-to-noise ratios reducing the degeneracy effects." + ? had to exclude the Mgb triplet region from their analysis as it seemed to bias the velocity dispersion measurements obtained using the cross-correlation technique., \citet{Mieske+08} had to exclude the $b$ triplet region from their analysis as it seemed to bias the velocity dispersion measurements obtained using the cross-correlation technique. +" However, Mgb is the most prominent spectral feature in the wavelength range of our spectra, thus containing a large fraction of spectral information."," However, $b$ is the most prominent spectral feature in the wavelength range of our spectra, thus containing a large fraction of spectral information." + We performed the spectral fitting in the wavelength range Acestframe>5200 aand compared the measurements of velocity dispersion with those obtained from the fitting in the entire available wavelength range aimed at checking whether the full spectral fitting technique also suffers from similar biases.," We performed the spectral fitting in the wavelength range $\lambda_{\mathrm{restframe}} > +5200$ and compared the measurements of velocity dispersion with those obtained from the fitting in the entire available wavelength range aimed at checking whether the full spectral fitting technique also suffers from similar biases." +" The values turned to be consistent within their uncertainties, however, being almost half as precise in case of the truncated wavelength range."," The values turned to be consistent within their uncertainties, however, being almost half as precise in case of the truncated wavelength range." +" Therefore, we conclude that the biases of velocity dispersion measurements obtained by cross-correlation including the Mgb triplet in the wavelength range probably originate from the template mismatch when using stellar spectra as references, which is minimized in our case by selecting the best-matching SSP from the grid of stellar population models."," Therefore, we conclude that the biases of velocity dispersion measurements obtained by cross-correlation including the $b$ triplet in the wavelength range probably originate from the template mismatch when using stellar spectra as references, which is minimized in our case by selecting the best-matching SSP from the grid of stellar population models." +" As far as these biases affect only measurements of low velocity dispersions in objects like globular clusters made on relatively high resolution spectra and do not seem to show up in studies of relatively massive galaxies, we suppose that this mismatch between the spectra of individual stars and unresolved stellar populations originates from subtle absorption-line features and becomes important only at high spectral resolution."," As far as these biases affect only measurements of low velocity dispersions in objects like globular clusters made on relatively high resolution spectra and do not seem to show up in studies of relatively massive galaxies, we suppose that this mismatch between the spectra of individual stars and unresolved stellar populations originates from subtle absorption-line features and becomes important only at high spectral resolution." +" Finally, we repeated the velocity dispersion measurements of ? using the task inIRAF, but now applied to the UCD spectra corrected for the contamination of NGC 1399."," Finally, we repeated the velocity dispersion measurements of \citet{Mieske+08} using the task in, but now applied to the UCD spectra corrected for the contamination of NGC 1399." +" Using the same stellar templates of w Cen as in ?,, the discrepancy to the results obtained with the technique has dramatically decreased which is clearly seen in Fig 7 (red data points)."," Using the same stellar templates of $\omega$ Cen as in \citet{Mieske+08}, the discrepancy to the results obtained with the technique has dramatically decreased which is clearly seen in Fig \ref{figsigsig} (red data points)." +" We obtain à good agreement between the two datasets, with only a small residual systematic offset in the sense that dispersions are slightly larger thanNBURST dispersions for low dispersion values."," We obtain a good agreement between the two datasets, with only a small residual systematic offset in the sense that dispersions are slightly larger than dispersions for low dispersion values." +" Thus, we conclude that the contamination of the spectra by the host galaxy halo is the main reason for biases of the estimated kinematical"," Thus, we conclude that the contamination of the spectra by the host galaxy halo is the main reason for biases of the estimated kinematical" +observations were made in the compact array configuration of the SMA. where the projected shortest and longest baselines were ~ [4 m and ~ 69 m CIO and 53 kA) respectively.,"observations were made in the compact array configuration of the SMA, where the projected shortest and longest baselines were $\sim$ 14 m and $\sim$ 69 m (10 and 53 $\lambda$ ) respectively." + We used Uranus for both bandpass calibration and flux calibration., We used Uranus for both bandpass calibration and flux calibration. + Amplitude and phase calibrations were done with the quasar 1751+096 and the quasar 1743-038 was observed to verify the quality of phase referencing from 17514096., Amplitude and phase calibrations were done with the quasar 1751+096 and the quasar 1743-038 was observed to verify the quality of phase referencing from 1751+096. + The visibility data were calibrated using the MIR package and the maps were generated and CLEANed using the NRAO AIPS package., The visibility data were calibrated using the MIR package and the maps were generated and CLEANed using the NRAO AIPS package. + Even after calibration the continuum visibility data of the reference quasar 1743-038 showed evidence for phase decorrelation at longer baselines., Even after calibration the continuum visibility data of the reference quasar 1743-038 showed evidence for phase decorrelation at longer baselines. + The degree of decorrelation was similar for 1743-038 and MWC 297., The degree of decorrelation was similar for 1743-038 and MWC 297. + We self calibrated the visibility data for both 1743-038 and MWC 297 at a time interval of 4 min. which significantly reduced the phase decorrelation.," We self calibrated the visibility data for both 1743-038 and MWC 297 at a time interval of 4 min, which significantly reduced the phase decorrelation." + The vector averaged visibility amplitude plotted against the av distance for MWC 297 and the quasar 1743-038 after self calibration is shown in Fig. 1.., The vector averaged visibility amplitude plotted against the $uv$ distance for MWC 297 and the quasar 1743-038 after self calibration is shown in Fig. \ref{vis}. + We imaged the self calibrated continuum visibilities of MWC 297., We imaged the self calibrated continuum visibilities of MWC 297. + The resultant size ofthe synthesized beam was 3.71] « 2.97 with uniform weighting (PA — 45. )., The resultant size ofthe synthesized beam was $^{\prime \prime}$ 11 $ \times$ $^{\prime \prime}$ 97 with uniform weighting (PA $\sim$ 45 $^{\degr}$ ). + The contour map of the observed continuum emission at 1.3 mm is shown in Fig. 2.., The contour map of the observed continuum emission at 1.3 mm is shown in Fig. \ref{map}. . + We expect the maximum uncertainty in source positions to be <0.ff3 based on the positions of quasars mapped in our SMA observations., We expect the maximum uncertainty in source positions to be $\leqslant$ $0.^{\arcsec}3$ based on the positions of quasars mapped in our SMA observations. + Uncertainties in the absolute flux is estimated to be20%., Uncertainties in the absolute flux is estimated to be. +. Compact continuum emission with a total measured flux density of 300 mJy is detected towards MWC 297 at 1.3 mm., Compact continuum emission with a total measured flux density of 300 mJy is detected towards MWC 297 at 1.3 mm. + The angular separation between the 1.3 mm continuum peak and the stellar position is less than 0. 3., The angular separation between the 1.3 mm continuum peak and the stellar position is less than $^{\arcsec}$ 3. + Therefore. we assume that the compact continuum source is centered upon the star.," Therefore, we assume that the compact continuum source is centered upon the star." +" A two-dimensional Gaussian fit to the continuum map of MWC 297 yields an observed size of 3.” 14 « 3.702 and a deconvolved size of 0.76470, « OLINOF at PA = + ."," A two-dimensional Gaussian fit to the continuum map of MWC 297 yields an observed size of $^{\prime + \prime}$ 14 $ \times$ $^{\prime \prime}$ 02 and a deconvolved size of $^{\prime \prime}$ $^{+0.^{\prime \prime}10}_{-0.^{\prime + \prime}64}$ $\times$ $^{\prime \prime}$ $^{+0.^{\prime + \prime}60}_{-0.^{\prime \prime}11}$ at PA = $^{\degr}$ $\pm$ $^{\degr}$." + Allowing for the possibility of the phase decorrelation in our observations affecting the observed size. we take the longer dimension of the deconvolved size as an upper limit to the source size.," Allowing for the possibility of the phase decorrelation in our observations affecting the observed size, we take the longer dimension of the deconvolved size as an upper limit to the source size." + At the distance of MWC 297. it gives a source radius of 80 AU.," At the distance of MWC 297, it gives a source radius of 80 AU." + MWC 297 is known to have an ionized wind associated with it (Malbetetal.2007:Drew1997).," MWC 297 is known to have an ionized wind associated with it \citep{malbet07,drew97}." +". The flux densities at 3.6 em and 6 cm. measured towards MWC 297 with the VLA (Skinneretal.1993).. give a spectral index of 0.6 (E, x 1°). appropriate for free-free emission from an optically thick. tronized wind."," The flux densities at 3.6 cm and 6 cm, measured towards MWC 297 with the VLA \citep{skin93}, give a spectral index of 0.6 $_{\nu}$ $\propto$ $\nu^{0.6}$ ), appropriate for free-free emission from an optically thick, ionized wind." + Assuming that this emission continues to the mm wavelengths with the same spectral index. we subtracted the possible contribution due to the free-free emission from the total observed flux at 1.3 mm and obtained a flux density of 200 mJy as due to dust emission.," Assuming that this emission continues to the mm wavelengths with the same spectral index, we subtracted the possible contribution due to the free-free emission from the total observed flux at 1.3 mm and obtained a flux density of 200 mJy as due to dust emission." +" If the dust emission is optically thin at mm wavelengths. assuming a gas-to-dust mass ratio of 100 and a dust opacity per unit mass of dust plus gas &,, = [5272] eng? (Cesaronietal.2007:Kramer1998)... we obtain a total mass of 0.07 M... for the circumstellar material (gas+dust) associated with MWC 297."," If the dust emission is optically thin at mm wavelengths, assuming a gas-to-dust mass ratio of 100 and a dust opacity per unit mass of dust plus gas $\kappa_{\nu}$ = $\left[ \frac{\nu (GHz)}{230.6} \right +]^{\beta}$ $cm^2g^{-1}$ \citep{cesaroni07,kramer98}, we obtain a total mass of 0.07 $_{\odot}$ for the circumstellar material (gas+dust) associated with MWC 297." + A dust temperature of 100 K is assumed in this calculation., A dust temperature of 100 K is assumed in this calculation. + From the mass and the upper limit to the source radius. we computed the optical extinctions along the line of sight through the continuum source to the central star to probe the geometry of the circumstellar material.," From the mass and the upper limit to the source radius, we computed the optical extinctions along the line of sight through the continuum source to the central star to probe the geometry of the circumstellar material." + If. the circumstellar material is. distributed in à spherical envelope of uniform density. the optical. V-band extinction would be 107 mag.," If the circumstellar material is distributed in a spherical envelope of uniform density, the optical V-band extinction would be $\ge$ $^4$ mag." + However. the observed extinction Ay is only 8 mag (Drewetal.1997).," However, the observed extinction $A_V$ is only 8 mag \citep{drew97}." +. This strongly suggests that the circumstellar dust is likely distributed in a comparatively flattened and inclined. morphology around MWC 297. perhaps in the form of a disk.," This strongly suggests that the circumstellar dust is likely distributed in a comparatively flattened and inclined morphology around MWC 297, perhaps in the form of a disk." + In Fig., In Fig. + 3 we present the spectral energy distribution (SED) of MWC 297 at submm. mm andem wavelengths.," \ref{sed} we present the spectral energy distribution (SED) of MWC 297 at submm, mm andcm wavelengths." + We fit the observed points with a combination of free-free emission arising in an ionized wind and optically thin dust emission from a circumstellar disk of mass 0.07 ..., We fit the observed points with a combination of free-free emission arising in an ionized wind and optically thin dust emission from a circumstellar disk of mass 0.07 $_{\odot}$. + The best fit is obtained when the dust opacity power-law exponent ./ has a value between 0.1 and 0.3., The best fit is obtained when the dust opacity power-law exponent $\beta$ has a value between 0.1 and 0.3. + This ts much lower than that observed for interstellar grains (./ 2 2) and the representative value used for circumstellar disks (./ = 1)., This is much lower than that observed for interstellar grains $\beta$ = 2) and the representative value used for circumstellar disks $\beta$ = 1). + The low value of } 1s often interpreted as arising due to the average size of the emitting dust grains being relatively larger., The low value of $\beta$ is often interpreted as arising due to the average size of the emitting dust grains being relatively larger. + Larger grain size in the circumstellar environment around MWC 297 has also been reported independently from studies on the wavelength dependence of extinction. towards the star at the optical wavelengths (Gorti&Bhatt 1993).., Larger grain size in the circumstellar environment around MWC 297 has also been reported independently from studies on the wavelength dependence of extinction towards the star at the optical wavelengths \citep{gortibhatt93}. . +" This argues for possible graingrowth in the optically thin circumstellar material around MWC 297,", This argues for possible graingrowth in the optically thin circumstellar material around MWC 297. + In order to construct the SED and to the value of ./ we have used large beam (~ ) determinesingle dish measurements. at submm wavelengths with JCMT," In order to construct the SED and to determine the value of $\beta$ , we have used large beam $\sim$ $^{\arcsec}$ ) single dish measurements at submm wavelengths with JCMT" + , +source being a binary companion or to have formed from the same cloud core as MWC 297 (Li ct al.,source being a binary companion or to have formed from the same cloud core as MWC 297 (Li et al. + 1991)., 1994). + Accurate photometry of the newly fouud object is challenging as it is found close to the bright host star., Accurate photometry of the newly found object is challenging as it is found close to the bright host star. + Usiug the 2MAÀSS Παπά imaenitude of NWC 297. Wwe caibrated our zeropoiut by usine open-loop nuages of AIWC 297.," Using the 2MASS $H$ -band magnitude of MWC 297, we calibrated our zeropoint by using open-loop images of MWC 297." + PSF photometry ou the companion was perforued by fitting Gaussians., PSF photometry on the companion was performed by fitting Gaussians. + In addition. we performed apertire photometry.," In addition, we performed aperture photometry." + The resulting £7-haxd magnitudes agree arly well with each other. aud we fiud an Z7-baud imaenitude dierence of ATF = 8.5 + 0.25 mae.," The resulting $H$ -band magnitudes agree fairly well with each other, and we find an $H$ -band magnitude difference of $\Delta H$ = 8.5 $\pm$ 0.25 mag." + Using the 2QATASS inaguitude of AWC 297. we fine II = 12.9 4 0.25 mae for he source.," Using the 2MASS magnitude of MWC 297, we find $H$ = 12.9 $\pm$ 0.25 mag for the source." + To investigae whether our discovered ob.ject at a PA of ccould be resx»usible for the N-rav flaring of MNC 297. we turn to the relevant archival X-ray satelite data.," To investigate whether our discovered object at a PA of could be responsible for the X-ray flaring of MWC 297, we turn to the relevant archival X-ray satellite data." + The N-rav inage of the region near MWC 297 is shown in the Ieft panel of Fig. 2..," The X-ray image of the region near MWC 297 is shown in the left panel of Fig. \ref{f_xray}," + where we note four objects., where we note four objects. + The positions of these objects are listed iu Table 1.., The positions of these objects are listed in Table \ref{t_chan}. . + The two X-ray sources with a separation of & aat PA of ~ aare an exact iatcli to our ZJ-baud inagiug of AIWC 297 (source 1) and our newly discovered source (source 2)., The two X-ray sources with a separation of $\simeq$ at PA of $\simeq$ are an exact match to our $H$ -band imaging of MWC 297 (source 1) and our newly discovered source (source 2). + Note that if Source 1 and 2 form a binary system. the large period implied by the 850 AU separation cans that proper motion will not be significant. and source 2 will be at the same position in theA and images.," Note that if Source 1 and 2 form a binary system, the large period – implied by the 850 AU separation – means that proper motion will not be significant, and source 2 will be at the same position in the and images." + We cannot exclude the possibility that the remaimine A-rav cussion from Source 1. which is cousistent with ADWC 2977's position. is vet due to one or more other conipauions tha reniadu uuresolved in the nuage.," We cannot exclude the possibility that the remaining X-ray emission from Source 1, which is consistent with MWC 297's position, is yet due to one or more other companions that remain unresolved in the image." +" Also visible in t10 1HAGE aro SOUPCCS 3 and 4. at roughly from, AIWC 297."," Also visible in the image are sources 3 and 4, at roughly from MWC 297." + Source counts were extracted using a radius of 3 pixes for sources l and 2. auc a radius of 5 jxels for sources 3 aud d.," Source counts were extracted using a radius of 3 pixels for sources 1 and 2, and a radius of 5 pixels for sources 3 and 4." + The total 0.3.10. keV. source counts are listed in Table 1.., The total 0.3–10 keV source counts are listed in Table \ref{t_chan}. + Note tha the sum of source counts from sources 3 and Lis about του times ereater han that for sources 1 aud 2., Note that the sum of source counts from sources 3 and 4 is about three times greater than that for sources 1 and 2. + These cata raise he question of whether the low spatial resolution of nav have led to a uisiclentification of he reported N-arax daring of MAVC 297., These data raise the question of whether the low spatial resolution of may have led to a misidentification of the reported X-ray flaring of MWC 297. + We therefore tu to the flaring data., We therefore turn to the flaring data. + Fig., Fig. + 2) Gight) shows the combines SIS image of the flaring data on AIWC 297 ou the same scale as he nage., \ref{f_xray}~ (right) shows the combined SIS image of the flaring data on MWC 297 – on the same scale as the image. + We have indicated the positions of sources 1. 3. and d.," We have indicated the positions of sources 1, 3, and 4." + The cices in this nuage ive radi of191. indicatiug fre combined aud position uncertainty.," The circles in this image have radii of, indicating the combined and position uncertainty." + It is inunnediatelv apparent youn Fig., It is immediately apparent from Fig. + 2 (ight) that the sotrees are confused in the image., \ref{f_xray}~ (right) that the sources are confused in the image. + Moreover. tje muaproved astrometry xovided by the corrections of Gothelf e al. (," Moreover, the improved astrometry provided by the corrections of Gotthelf et al. (" +2000) shows hat t16 peak of the observed emission iu the PSF Is inconsistent with the position of sources la xd 2.,2000) shows that the peak of the observed emission in the PSF is inconsistent with the position of sources 1 and 2. + TIustead. he peak is consistent with the positiois of source 3Pa Or l.," Instead, the peak is consistent with the positions of source 3 or 4." + This strongly sugeestsCoco that the origin of the firing vchaviour is due to source 3 or Ll., This strongly suggests that the origin of the flaring behaviour is due to source 3 or 4. + Their yositions dine up with 241ASS point sources. with /7 = 11.3 and 9.1 for sources 3 and Ld respectively.," Their positions line up with 2MASS point sources, with $H$ = 11.3 and 9.4 for sources 3 and 4 respectively." + Caven the fac that Source thas a hager (PFIv) IR excess than SotPCC 3. the flaring is most Likely due to source [.," Given the fact that Source 4 has a larger $(H-K)$ IR excess than Source 3, the X-ray flaring is most likely due to source 4." + Tu any case. at the distance of AIWC 297. these ZI-baud magnitudes are consistent with a T Tauri nature.," In any case, at the distance of MWC 297, these $H$ -band magnitudes are consistent with a T Tauri nature." + We have presented high resolution AO-NIR and Nora Huaging on MWC 297., We have presented high resolution AO-NIR and X-ray imaging on MWC 297. + Caven the carly spectral type of the object (B1.5). the reported X-rav flaring of this carly Herbie Be star has been diffieult to unudoerstaud.," Given the early spectral type of the object (B1.5), the reported X-ray flaring of this early Herbig Be star has been difficult to understand." + UsingCILANDRA. we lave resolved the N-rayv cussion from. objects suvoundiug MW 297 and found that t1C brightest X-ray source is nof associated with MW(C 297 itself.," Using, we have resolved the X-ray emission from objects surrounding MWC 297 and found that the brightest X-ray source is not associated with MWC 297 itself." + Furthermore. we have shown that the peak oft observed flaring is inconsistent with the position ADWC 297.," Furthermore, we have shown that the peak of the observed flaring is inconsistent with the position of MWC 297." + Tustead. it is most likely due to a late-ty source iu the ITerbie Be stars field.," Instead, it is most likely due to a late-type source in the Herbig Be star's field." + The study by Stelzer et al. (, The study by Stelzer et al. ( +2003) oulate-tvpe stars. as well as our coronoeraphic study of tle vou18,"2003) onlate-type B stars, as well as our coronographic study of the young" +2003) oulate-tvpe stars. as well as our coronoeraphic study of tle vou18o,"2003) onlate-type B stars, as well as our coronographic study of the young" + observed NCC 1313 and is X-ray emitting sources on 2002 October 13 (or 20592 sec with the ACIS detector (Carmireetal.2003)., observed NGC 1313 and its X-ray emitting sources on 2002 October 13 for 20592 sec with the ACIS detector \citep{Gar03}. +. The aimpoiut of the detector fell ou the 53 CCD., The aimpoint of the detector fell on the back-illuminated S3 CCD. + We extracted a lel| curve of tie background. masking out all bright sources detectable by eve. to search [or aly sigatures of [kwing events known to affect. back-illumiuatecd CCDs (ChaucraProposers’(μίας2002).," We extracted a light curve of the background, masking out all bright sources detectable by eye, to search for any signatures of flaring events known to affect back-illuminated CCDs \citep{Chan02}." +. No strong lares were cetectecd but a few high points were eliminated. reducing the good exposure ime to 19902 sec.," No strong flares were detected but a few high points were eliminated, reducing the good exposure time to 19902 sec." +" We extracted the events at the loc:itiou of SN]LOTSIN. about 57.88 off-axis. in an aperture of radius 12"" which encloses 2985€ of the j»olnt sprea function (ChandraProposers!Guide2002)."," We extracted the events at the location of SN1978K, about $'$ .88 off-axis, in an aperture of radius $''$ which encloses $>$ of the point spread function \citep{Chan02}." +. The background. was obtained from an anuulus sur'ouudiug the source., The background was obtained from an annulus surrounding the source. + The net count rate was 20.1 10270.00:) counts 1, The net count rate was $\sim$ $\pm$ 0.003 counts $^{-1}$. + A response matrix was constructed specilic to tie olf-axis angle of 9NI978lIx. The matrix was corrected for the time-dependent absorption using t1e fitted functional form which depeuds upou a single parameter. the time from lauuch: for this observation. the time from launch was 1179 days (Plucinskyetal.2003).," A response matrix was constructed specific to the off-axis angle of SN1978K. The matrix was corrected for the time-dependent absorption using the fitted functional form which depends upon a single parameter, the time from launch; for this observation, the time from launch was 1179 days \citep{Plu03}." +. Given the sharp point spread fuuction of the mirrors. we must be concerned with possible event pileup even though the large o[-axis angle 1jtigates the effects of pileup cousiderably.," Given the sharp point spread function of the mirrors, we must be concerned with possible event pileup even though the large off-axis angle mitigates the effects of pileup considerably." + The spectral analysis was undertaken using a pileup mode| (Davis200!L)., The spectral analysis was undertaken using a pileup model \citep{Davis01}. +. The resulting fit iudicated low or zero pileup., The resulting fit indicated low or zero pileup. + Cuven the broader point sj»read Ltuictio rol the mirrors. there is no pileup of the EPIC-pu or MOS spectra from that instruiment.," Given the broader point spread function of the mirrors, there is no pileup of the EPIC-pn or MOS spectra from that instrument." + The resilts of the fits to tle auc spect‘a. to be described )elow. are ve'y similar. as one expects for observations separated by ~2 years of a slowly-evolving «):bject.," The results of the fits to the and spectra, to be described below, are very similar, as one expects for observations separated by $\sim$ 2 years of a slowly-evolving object." + The siuilarity sup»orts the conclusion of OW OL zero pileup., The similarity supports the conclusion of low or zero pileup. + We urther it the spectra witl both XSPEC (Arnaud1996) aud the Sherpa fitting eugiue (Freemal.Doe.Sielmlelnowska2001 and obtaiued identical results., We further fit the spectra with both XSPEC \citep{Arn96} and the Sherpa fitting engine \citep{FDS01} and obtained identical results. +" We first usec the bes-fit moclels derived from tle ROSAT PSPC and SIS/CIS obse""vallons of SNLOTSIL w1ich consistecl of absorbect. sinele-component continuum models (R93. al. 199[.. S99)."," We first used the best-fit models derived from the PSPC and SIS/GIS observations of SN1978K which consisted of absorbed, single-component continuum models (R93, \citealt{Petre94}, S99)." + We lixec the model parameters a the previously-determinecd values. but it was üunmecdiately. evi(ent tha the models no loiger provided a good fit. instead. vieldiug a \7/v = D+) ," We fixed the model parameters at the previously-determined values, but it was immediately evident that the models no longer provided a good fit, instead yielding a ${\chi}^2/{\nu}$ $\geq$ 3." +We then allowed the moclel parameters ο vary: tle resultiug moclel fits remained poor., We then allowed the model parameters to vary; the resulting model fits remained poor. + Figure shows the [it using a siugle absorbed BRavi1ond-Sultli mocel., Figure \ref{oldfit} shows the fit using a single absorbed Raymond-Smith model. + Clearly a sinele-component model is Inaclequate as it cau not simultaueous vlt theeulssion iu the 0.7-1.2 keV region as well as the apparent bard component at energies aJONre 2-3 keV. That theROSAT PSPC inodels do not provide a good fit is not especially surprIIT.g glvel the softer respouse of that detector., Clearly a single-component model is inadequate as it can not simultaneously fit the emission in the 0.7-1.2 keV region as well as the apparent hard component at energies above $\sim$ 2-3 keV. That the PSPC models do not provide a good fit is not especially surprising given the softer response of that detector. + That the spectra do not provide a good Li may be explained as either au iucrease in [lux above2, That the spectra do not provide a good fit may be explained as either an increase in flux above2 +CCC coustraints. aud to understaud our ability to reconstruct the mass distribution from the galaxy data.,"CCC constraints, and to understand our ability to reconstruct the mass distribution from the galaxy data." + Iteparameterizine the observable galaxies by their (dimeusionless) aneular diameter clisalice d rather than redsift 2 makes it clear how he WL CCC method cau provide mocel-iudeperdeut geonetric colπίταus on ο., Reparameterizing the observable galaxies by their (dimensionless) angular diameter distance $d$ rather than redshift $z$ makes it clear how the WL CCC method can provide model-independent geometric constraints on $\Omega_k$. + Τιis methodoogy also reveals that CCC daa ls degenerate 1udderalterations to lub aud lud by quadratic [tuctious of d. if ο is free.," This methodology also reveals that CCC data is degenerate underalterations to $\ln b$ and $\ln d$ by quadratic functions of $d$, if $\Omega_k$ is free." +" A)art from three exact degeneracies. hec""'Oss-COITeallo1 strength. )eing a joint function of the leus and source dista1Ces. is very efficient. at ooduciug cle'oupled estivates of O,. the distauces d; aud the bias factors Dd}. and cau even deterine shea' calibration facors f; lor each source plane wit1 modest degracdalous ol factor 352 in cosuological accWacy."," Apart from three exact degeneracies, the cross-correlation strength, being a joint function of the lens and source distances, is very efficient at producing decoupled estimates of $\Omega_k$, the distances $d_i$ and the bias factors $B_i$, and can even determine shear calibration factors $f_i$ for each source plane with modest degradations of factor $\lesssim 2$ in cosmological accuracy." + With sufficieutly accurate p0tometLic 'eshifts. the same survey data used for weak leislug may be used to determiue the ralisve‘se BAO scale.," With sufficiently accurate photometric redshifts, the same survey data used for weak lensing may be used to determine the transverse BAO scale." +" This gives additional modelLincependent constraints coii d that are of lower orecislo 1ithan he CCC data. but are completely free of degene""cvy."," This gives additional model-independent constraints on $d$ that are of lower precision than the CCC data, but are completely free of degeneracy." +" Such a comjued CCC-BAO strvey shokd s""jeld uicertaluties of e0.0L ος Q4."," Such a combined CCC-BAO survey should yield uncertainties of $\approx0.04 f_{\rm + sky}^{-1/2}$ on $\Omega_k$." + We 'elterate that such ¢Oustralits are competely idepeudeut of any assumptions about tle matte-energy content of je. Uuiverse. any biases Il photonetric redshifis. Or in [act any aleratious to the Friecdinauu equation sor the deecjon ecuations for light.," We reiterate that such constraints are completely independent of any assumptions about the matter-energy content of the Universe, any biases in photometric redshifts, or in fact any alterations to the Friedmann equations or the deflection equations for light." + Tvey merely require that the inetri€ be applicable to wu Universe., They merely require that the Robertson-Walker metric be applicable to our Universe. + Given ie lack of viable dark-energy heories. it seenus prudent to seek cosnological infonusion tha Ολα]is valid even if the acceleration is attributable to an alteraion of General Relativity ‘ather t lalla ϱ'eviously innoticed stress-eneoy contribution.," Given the lack of viable dark-energy theories, it seems prudent to seek cosmological information that remains valid even if the acceleration is attributable to an alteration of General Relativity rather than a previously unnoticed stress-energy contribution." + In the spirit of couservatislh. Wre shoulc| note that the RW metric may uot be suliciently accurate.," In the spirit of conservatism, we should note that the RW metric may not be sufficiently accurate." + TIe clummpiness of the IHter-elle‘oy disributiou uay invalklate our adoptior of the fillecd-beam augular diameter distance. and a ujore sophisticated treatment may be required2001).," The clumpiness of the matter-energy distribution may invalidate our adoption of the filled-beam angular diameter distance, and a more sophisticated treatment may be required." + It is not clear to wlal extell sina]|-scale cltumipiuess can influence the a»parelnt shear of galaxy-scale images as surveyed across the entire σεντς is quite a different regije from studies of srongvy leused quasars or superuovae for which tle Dyer-Boeder clistauces have been most carefully st«lied., It is not clear to what extent small-scale clumpiness can influence the apparent shear of galaxy-scale images as surveyed across the entire sky—this is quite a different regime from studies of strongly lensed quasars or supernovae for which the Dyer-Roeder distances have been most carefully studied. + The cu'vature measurenmieit is limited by tje ability to break the WL CCC degeneracy.i. by the accuracy and redshift spau ofthe BAO or Sv» Weastl‘ements of auetular-diameter distauces.," The curvature measurement is limited by the ability to break the WL CCC degeneracy, by the accuracy and redshift span of the BAO or SN measurements of angular-diameter distances." + Our baseline coistraint asstunes oto-z BAO infonation or 0<2<3 over the full sky., Our baseline constraint assumes $z$ BAO information for $00$." + Fig., Fig. + 3 shows that the mass function can be increased by a factorof 10 at 2=13 for haloes with mass AZ~1071A7. when compared to the standard scenario.," \ref{fig:1a} shows that the mass function can be increased by a factor of 10 at $z=13$ for haloes with mass $M\sim +10^{11}M_{\odot}$ when compared to the standard scenario." +" We should however remark that high-mass haloes (AJ>10A7. ) at early cosmological epochs are rare events. as shown also by the small number density at >=19 in the reference case. n(2»10AL.)25.10 ""IMpe*."," We should however remark that high-mass haloes $M>10^{9}M_{\odot}$ ) at early cosmological epochs are rare events, as shown also by the small number density at $z=13$ in the reference case, $n(>10^{9}M_{\odot})\lesssim +5 \times 10^{-3}$ $^{3}$." + Then this effect is expected to have a little impact on integrated quantities as the total ionized fraction ot the IGM optical depth., Then this effect is expected to have a little impact on integrated quantities as the total ionized fraction ot the IGM optical depth. + Unlike the local model. the scale dependence of non-Gaussianity increases the abundance of the low-mass haloes by a factor of ~10 at 2=13 when compared to the standard case.," Unlike the local model, the scale dependence of non-Gaussianity increases the abundance of the low-mass haloes by a factor of $\sim 10$ at $z=13$ when compared to the standard case." + The opposite applies for (νι<0., The opposite applies for $f_{\rm NL}<0$. + As already noticed by Matarreseetal.(2000). [see also Verdeetal.(2001):Grossi(2007 )]]. this effect is more evident at early cosmological epochs. exactly when the process of IGM ionization starts.," As already noticed by \cite{matarrese2000} [see also \cite{verde2001,grossi2007}] ], this effect is more evident at early cosmological epochs, exactly when the process of IGM ionization starts." + For this reason a non-Gaussian distribution of the primordial density field can affect the way in which reionization occurs. leaving its imprints on it. as we will investigate in the next sections.," For this reason a non-Gaussian distribution of the primordial density field can affect the way in which reionization occurs, leaving its imprints on it, as we will investigate in the next sections." + In this section. we briefly review the main assumptions underlying the analytic model adopted to describe the process of cosmic reionization.," In this section, we briefly review the main assumptions underlying the analytic model adopted to describe the process of cosmic reionization." + This model is based on the approach proposed by Avelino&Liddle(2006) [see also Haiman&Holder(2003):Chenetal.(2003) for further details]: our implementation. however. differs in some aspects which will be discussed later.," This model is based on the approach proposed by \cite{avelino2006} [see also \cite{haiman2003,chen2003} for further details]; our implementation, however, differs in some aspects which will be discussed later." + In this model. the statistical properties of the ionized regions are related to the hierarchical growth of the ionizing sources through simple assumptions on how the galaxies ionize the IGM and on how the IGM recombines.," In this model, the statistical properties of the ionized regions are related to the hierarchical growth of the ionizing sources through simple assumptions on how the galaxies ionize the IGM and on how the IGM recombines." + A one-to-one correspondence between the distribution of galaxies and ΠΠ regions is established. such that a single galaxy of mass Ad... can ionize a region of mass Muu=CM.," A one-to-one correspondence between the distribution of galaxies and HII regions is established, such that a single galaxy of mass $M_{\rm gal}$ can ionize a region of mass $M_{\rm HI\!I}=\zeta +M_{\rm gal}$." + Here ¢ represents the ionization efficiency of the galaxy. and it is strictly dependent on the nature of the ionizing sources.," Here $\zeta$ represents the ionization efficiency of the galaxy, and it is strictly dependent on the nature of the ionizing sources." + We will take it as a constant. fixed in such a way that reionization ends at 2= 6.5.," We will take it as a constant, fixed in such a way that reionization ends at $z=6.5$ ." + Since at high + the cooling of the gas becomes efficient in aloes having a virial temperature Zz:101 K. unlike in Avelino&Liddle (2006).. in our analysis we consider only type Ia (10! K Tox9510! Kyand type Ib CE>9107 Ky haloes. neglecting he contribution of the type II sources. which would correspond to aaloes with 400 K T107 K. We recall that the distinction between the halo types is related to the way in which they impact he IGM: type Ia sources can grow only in neutral regions. while ype Ib haloes can appear also in ionized regions.," Since at high $z$ the cooling of the gas becomes efficient in haloes having a virial temperature $T\ge 10^4$ K, unlike in \cite{avelino2006}, in our analysis we consider only type Ia $10^4$ K $\le T \le 9 \times10^4$ K) and type Ib $T > 9\times 10^4$ K) haloes, neglecting the contribution of the type II sources, which would correspond to haloes with $400$ K $\le T \le 10^4$ K. We recall that the distinction between the halo types is related to the way in which they impact the IGM: type Ia sources can grow only in neutral regions, while type Ib haloes can appear also in ionized regions." + Consequently hey affect differently the ionization phases of IGM., Consequently they affect differently the ionization phases of IGM. +" The total collapsed fraction πως) at different redshifts can be computed using eq.(6)): where po is the present-day matter density and μμ(>) is the minimum mass corresponding to the virial temperature 7. which can be computed by inverting the relation proposed by namely: In the previous equation. A. represents the virial overdensity at redshift 2 and £25, is the matter density parameter at redshift 2."," The total collapsed fraction $F_{\rm coll}(z)$ at different redshifts can be computed using \ref{eq:1c}) ): where $\bar{\rho}_{0}$ is the present-day matter density and $M_{\rm + min}(z)$ is the minimum mass corresponding to the virial temperature $T$, which can be computed by inverting the relation proposed by \cite{barkana2001}, namely: In the previous equation, $\Delta_{\rm c}$ represents the virial overdensity at redshift $z$ and $\Omega_{\rm m}^{z}$ is the matter density parameter at redshift $z$." +" Consequently. the collapsed fractions in Ta and Ib haloes are given by where Adin, and Adin. are the minimum masses for Ib and Tu sources. obtained using in eq.(10)) Z=9«107 and 107 K. respectively."," Consequently, the collapsed fractions in Ia and Ib haloes are given by where $M_{{\rm min},Ib}$ and $M_{{\rm min},Ia}$ are the minimum masses for Ib and Ia sources, obtained using in \ref{eq:3a}) ) $T= 9\times +10^4$ and $10^4$ K, respectively." + The action of the ionizing sources is smoothed down by the recombination of the IGM. here considered as a homogeneous gs.," The action of the ionizing sources is smoothed down by the recombination of the IGM, here considered as a homogeneous gas." + The recombination rate is linearly dependent on the IGM clumping factor Cyy=/^2$, for which, following \cite{haiman2006}, we assume a redshift evolution modeled as: being $\beta$ a free parameter." +" As shown by Avelino&Liddle (2006)... the predicted reionization history of the universe has Significant uncertainties introduced by the poor knowledge of the z-dependence of the clumping factor, which cannot be robustly constrained even considering the 3-year WMAP results for the reionization optical depth."," As shown by \cite{avelino2006}, the predicted reionization history of the universe has significant uncertainties introduced by the poor knowledge of the $z$ -dependence of the clumping factor, which cannot be robustly constrained even considering the 3-year WMAP results for the reionization optical depth." + Since they found good consistency between predicted and observed optical depths irrespectively of the amount of primordial non-Gaussianity in the models they consider. we decide to set ή=0.," Since they found good consistency between predicted and observed optical depths irrespectively of the amount of primordial non-Gaussianity in the models they consider, we decide to set $\beta=0$." + In this case. the z-dependence of C'Hu is neglected and 6Ἡν= 10.," In this case, the $z$ -dependence of $C_{\rm HI\!I}$ is neglected and $C_{\rm HI\!I}=10$ ." + The impact of the assumption of a constant clumping factor will be discussed later., The impact of the assumption of a constant clumping factor will be discussed later. +" The probability that a photon emitted at a given cosmological epoch σι(1) is still ionizing at 2104 vr.," For disks of this size and reasonable values for the companion mass and disk thickness, it can be seen that if $\alpha$ is as low $10^{-3}$ $10^{-4}$ as found by \citet{bel94} to reproduce the flaring time of FU Ori stars, the accretion times would be $\ga +10^4$ yr." + This kind of time scale is completely ruled out bv the short jet-Iags observed., This kind of time scale is completely ruled out by the short jet-lags observed. + For a typical jet-lag of ~300 vr. a disk of radius 1 AU requires a=0.05.," For a typical jet-lag of $\sim 300$ yr, a disk of radius 1 AU requires $\alpha \ga 0.05$." + Thus. if this model proves relevant. the jet-lag has the potential to probe properties of the disks (hat are currently unobservable in any other wavy.," Thus, if this model proves relevant, the jet-lag has the potential to probe properties of the disks that are currently unobservable in any other way." + The points outlined above are consistent with the binary accretion disk model., The points outlined above are consistent with the binary accretion disk model. + In addition. if M 2-9 proves to be a svinbiolic svstem wilh a detached companion (see 822). 1 adds support to this interpretation.," In addition, if M 2-9 proves to be a symbiotic system with a detached companion (see 2), it adds support to this interpretation." + There is. however. one aspect of the observations that is not naturally explained by Chis scenario. and (hat is the ejection of a torus.," There is, however, one aspect of the observations that is not naturally explained by this scenario, and that is the ejection of a torus." + Enhanced, Enhanced +7. first argued. that small bodies in the cistant solar system. could be detected. through stellar occultations.,\citet{Bailey:1976p1677} first argued that small bodies in the distant solar system could be detected through stellar occultations. + ? developed the treatment of cecultation by irregular bodies including clillraction., \citet{1987AJ.....93.1549R} developed the treatment of occultation by irregular bodies including diffraction. + More recently with the cliscovery of the population of Ixuiper Belt objects (2?).. several research eroups have begun searching for more distant. and. smaller bodies through oceultations (777)," More recently with the discovery of the population of Kuiper Belt objects \citep{Kuiper:1951p1773,Jewitt:1999p1844}, several research groups have begun searching for more distant and smaller bodies through occultations \citep{Roques:2000p1661,2008AJ....135.1039B,Roques:2009p1666}." + Because Wuiper Belt objects (INBOs) typically subtend small angles. thediffraction of radiation around the objects may be important even at visible wavelengths and naturally more important at. longer wavelengths (2)..," Because Kuiper Belt objects (KBOs) typically subtend small angles, the diffraction of radiation around the objects may be important even at visible wavelengths and naturally more important at longer wavelengths \citep{Roques:6p1676}." + Phe discovery of more distant and more massive WBOs such as Eris (2) bees the question of whether eravitational lensing of background stars by [large ος and objects in the Oort cloud (2) is important., The discovery of more distant and more massive KBOs such as Eris \citep{2005ApJ...635L..97B} begs the question of whether gravitational lensing of background stars by large KBOs and objects in the Oort cloud \citep{Oort:1950p1427} is important. + ? argued that for distant massive WBOs and Oort cloud objects lensing may be important: furthermore. ? argued that GALA could measure the astrometric displacement from microlensing by an planet more massive than a lew Jupiters within 105 AU regardless of its location on the sky.," \citet{2002astro.ph..9545C} argued that for distant massive KBOs and Oort cloud objects lensing may be important; furthermore, \citet{2005ApJ...635..711G} argued that GAIA could measure the astrometric displacement from microlensing by an planet more massive than a few Jupiters within $10^4$ AU regardless of its location on the sky." + The technique in this paper probes much lower mass objects. but also exploits lensing to provide constraints on the properties of the asteroid.," The technique in this paper probes much lower mass objects, but also exploits lensing to provide constraints on the properties of the asteroid." + Generally. the dillractive. cllects of microlensing are neglected. because the variation in the time celays across he lens is usually much larger than the coherence time of he observation. L/Av where Av is the bandwidth: of the observation.," Generally the diffractive effects of microlensing are neglected because the variation in the time delays across the lens is usually much larger than the coherence time of the observation, $1/\Delta \nu$ where $\Delta \nu$ is the bandwidth of the observation." + However. near a caustic crossing. dillraction may » important as argued by ? to account for rapid. variations in the light from (2237|0305 (Lhe Einstein Cross).," However, near a caustic crossing, diffraction may be important as argued by \citet{1995ApJ...455..443J} to account for rapid variations in the light from Q2237+0305 (The Einstein Cross)." + Typically he differential time delay highly magnified images for a point ens is about 22Mc. the crossing time over the Schwarzschile radius of the lens: consequently. for the cdillractive effects of lensing to be observable the Schwarzschild radius of the ens should be comparable or larger than the wavelength of the radiation.," Typically the differential time delay highly magnified images for a point lens is about $2 GM/c^3$, the crossing time over the Schwarzschild radius of the lens; consequently, for the diffractive effects of lensing to be observable the Schwarzschild radius of the lens should be comparable or larger than the wavelength of the radiation." + The largest. of the Kuiper Belt) objects. Eris. has a Sehwarzschild radius Bs=δέΛΙfemzm 254m. Therefore. quite naturally for observations of large IXDOs dillractive microlensing may be important for observations in the near ancl mid-infrared whenever the gravitational elfects are important.," The largest of the Kuiper Belt objects, Eris, has a Schwarzschild radius $R_S=2GM/c^2 +\approx 25 \mu$ m. Therefore, quite naturally for observations of large KBOs diffractive microlensing may be important for observations in the near and mid-infrared whenever the gravitational effects are important." + This paper focuses on just this regime., This paper focuses on just this regime. + The first section. refsec:dillr-micr.. outlines mücrolensing in the cillractive regime and generalizes the earlier. results to include occultation.," The first section, \\ref{sec:diffr-micr}, outlines microlensing in the diffractive regime and generalizes the earlier results to include occultation." + This vields a expression for the transmission that is nearly identical to the unlensed result., This yields a expression for the transmission that is nearly identical to the unlensed result. + The next section. refseciresults.. outlines the types of objects. lor which dillractive lensing may be important. examines several interesting cases and connects the diffraction patterns to the ecometric limit," The next section, \\ref{sec:results}, outlines the types of objects for which diffractive lensing may be important, examines several interesting cases and connects the diffraction patterns to the geometric limit" +Grauc-cesigu spiral galaxies geierally host. two long syuiuuetric spiral arms which cau be followed over a large azimuthal auge ancl doimiuate he optical disk. e.g.. NGC 1300 (Sauage 1961). NGC 895. NGC 1566 (Elmeg'eeu Elmegreei 1995). M51. M00 (Elmegreen. Seiclen. Eluegreen 1989) and NGC 5218 (e.g.. Patsis. Grosbol. Hiotelis 1997).,"Grand-design spiral galaxies generally host two long symmetric spiral arms which can be followed over a large azimuthal angle and dominate the optical disk, e.g., NGC 1300 (Sandage 1961), NGC 895, NGC 1566 (Elmegreen Elmegreen 1995), M51, M100 (Elmegreen, Seiden, Elmegreen 1989) and NGC 5248 (e.g., Patsis, Grosbol, Hiotelis 1997)." + Within the [rameworsof the spiral density wave (SDW) theoy (e.g. Li1 stu 1961) spiral arms in disk galaxies result [rom a traveling wave pattern that reHalls quasi-slat][9]lary ina [rare of reference rotating aroμιά the galaxy ceuter at a certain patter1 speed.," Within the framework of the spiral density wave (SDW) theory (e.g., Lin Shu 1964) spiral arms in disk galaxies result from a traveling wave pattern that remains quasi-stationary in a frame of reference rotating around the galaxy center at a certain pattern speed." + 5diral aeity waves can be excited by a comparlou or by a bar., Spiral density waves can be excited by a companion or by a bar. + The spiral waves cau ge wlug iun»lifiec as they are sheared from leading to traiine (e.g.. Goldreich Lyuden-Bell 1965) provided he disk is cold enough.," The spiral waves can get swing amplified as they are sheared from leading to trailing (e.g., Goldreich Lynden-Bell 1965) provided the disk is cold enough." + In this Leer. we focus on the drivin£ mecalls1 for a SDW in the nearby (D—15 Mpc) well studied grandesien spiral NGC 5218 aid discuss tie. inuplicatious of au exteuded stellar bar iu his galaxy.," In this Letter, we focus on the driving mechanism for a SDW in the nearby $D$ =15 Mpc) well studied grand-design spiral NGC 5248 and discuss the implications of an extended stellar bar in this galaxy." + Optical i)aglug (e.g.. Fie.," Optical imaging (e.g., Fig." + 1) of NGC 5218 reveals two bright. relatively ονιοίτς spiral arius [rom abou του2.2 kpe) to 80” (6.0 kpc).," 1) of NGC 5248 reveals two bright, relatively symmetric spiral arms from about $30\arcsec$ (2.2 kpc) to $80\arcsec$ (6.0 kpc)." + NGC 5218 does not show evidence of any 'eceut. or ongoltig inteaction with its th‘ee faint irregular neighbors (UGC dora.=e UGC 861L aud UGC 8629: Zaritsky e al.," NGC 5248 does not show evidence of any recent or ongoing interaction with its three faint irregular neighbors (UGC 8575, UGC 8614, and UGC 8629; Zaritsky et al." + 1997) which have similar redshifts and are located more than 30 (135 spe) away lu p'oJectio1., 1997) which have similar redshifts and are located more than $30\arcmin$ (135 kpc) away in projection. + It is therefore likely that the eraud-desigu spirals in NGC 5218 are driveu Noa massive large-scae bar. which is verified in the present work.," It is therefore likely that the grand-design spirals in NGC 5248 are driven by a massive large-scale bar, which is verified in the present work." +" Tle circumauclear ring of 'egions at a radius of 2"" (Ότο pc) (e.g. Elmeereen et al."," The circumnuclear ring of regions at a radius of $5\arcsec$ (375 pc) (e.g., Elmegreen et al." + 1997) also steeests the presence of a bar since rings are commonly associated with the dyuaimical resonalices o “a bar (e.tet?) review by Buta Combes 1996).," 1997) also suggests the presence of a bar since rings are commonly associated with the dynamical resonances of a bar (e.g., review by Buta Combes 1996)." + NGC 52[8 is classified as SAB(rs)be (de Vaucoileurs et al., NGC 5248 is classified as SAB(rs)bc (de Vaucouleurs et al. +" 1991: jereafter RCS) and has been »ostulated to Lave a weal. stellar bar with a1 ellipticity of QO.32 aud a semi-major axis of 22"" (1.6 spe) at a position angle (PA) of 110° (e.g.ο) Martin 1995)."," 1991; hereafter RC3) and has been postulated to have a weak stellar bar with an ellipticity of 0.32 and a semi-major axis of $22\arcsec$ (1.6 kpc) at a position angle (PA) of $110^\circ$ (e.g., Martin 1995)." + TUs ova feature is evident iu optical images (e.g.. Fig.," This oval feature is evident in optical images (e.g., Fig." + 1)., 1). + However. the exten all morplology of tle grald-desigu spirals in NGC 52[8 strongly suggests that the bar driving these spirals uust be significauly longer ane more nDiassive hau previously assumed.," However, the extent and morphology of the grand-design spirals in NGC 5248 strongly suggests that the bar driving these spirals must be significantly longer and more massive than previously assumed." + The two brig aler stelar spiral aruis |ave prominent cust alles oll heir ener (concave) sides (Fig., The two bright inner stellar spiral arms have prominent dust lanes on their inner (concave) sides (Fig. +" 1) out toa adius krT0"" (5 kpe).", 1) out to a radius $r \ge 70\arcsec$ (5 kpc). +" Such a dust la1e MO!‘phology is expected to exist ouly iuside the coοἱat]Ol) Fesmance (CR) of he arms. whe'e vou1@ stars which form when gas is coupressed by shocks. seeu as cust la105. Ceui overtake tlie patteἩ From his argument alone. we expect that tle CR of the spiral pattern in NGC 5218 is beyud 70""."," Such a dust lane morphology is expected to exist only inside the corotation resonance (CR) of the arms, where young stars which form when gas is compressed by shocks, seen as dust lanes, can overtake the pattern From this argument alone, we expect that the CR of the spiral pattern in NGC 5248 is beyond $70\arcsec$." + If the bar aud spirals in tus galaxy have the same pattern s»eed. he latter tus be djven by a stellar bar whose senmialajor axis is comparable iu size to tha of their common CR.," If the bar and spirals in this galaxy have the same pattern speed, the latter must be driven by a stellar bar whose semi-major axis is comparable in size to that of their common CR." + bars are expected to eud at or near CR based ou the stules «XE stellar orbits (Contopoulos Papayanunopoulos 1980). aid on the analysis of shapes of offset «ust anes within bars (Athanassoula 1992).," Large-scale bars are expected to end at or near CR based on the studies of stellar orbits (Contopoulos Papayannopoulos 1980), and on the analysis of shapes of offset dust lanes within bars (Athanassoula 1992)." + In order to test the existence of au extenced bar in NGC 52IS. we obtained a deep A-band ünage with a large field of view (§ 2).," In order to test the existence of an extended bar in NGC 5248, we obtained a deep $R$ -band image with a large field of view $\S$ 2)." + While this Letter focuses ou he observational aspects of the large-scale bar in NGC 2218 aud its consequences for galactie οναιMics in nearby aud high recshift e@alaxies. the subsequent paper (Jogee et al.," While this Letter focuses on the observational aspects of the large-scale bar in NGC 5248 and its consequences for galactic dynamics in nearby and high redshift galaxies, the subsequent paper (Jogee et al." + 2002. hereafter Paper II) ackclresses eas dyuaimiics iu," 2002, hereafter Paper II) addresses gas dynamics in" +We gratefully ackuowledge J. Poutanen for providing us his code and the anouvmos referee for his helpful comments.,We gratefully acknowledge J. Poutanen for providing us his code and the anonymous referee for his helpful comments. + POP. FII and LAL were supported by the Enropean Comission wider contract wmmber ERBFAIRA-CT9s8-0195 ( TAIR network “Accretion onto black holes. compact stars and protostars) and by the Italian Ministry for University aud Research (AIURST) uuder grant GALT," POP, FH and LM were supported by the European Commission under contract number ERBFMRX-CT98-0195 ( TMR network ""Accretion onto black holes, compact stars and protostars"") and by the Italian Ministry for University and Research (MURST) under grant COFIN98-02-154100." + and GCP were supported by the Ministry for University aud Research (AIURST) uuder eraut COFIN9O8-02-32., GM and GCP were supported by the Ministry for University and Research (MURST) under grant COFIN98-02-32. +observed the gradient.Ziroughoul the elliptical. we can still see the negative gradient. which becomes stecper farther in to the center.),"observed the gradient the elliptical, we can still see the negative gradient, which becomes steeper farther in to the center.)" + Fig., Fig. + 9 also demonstrates. as indicated above. that the mean metallicity of the stellar halo of the elliptical is much higher (~ a factor of 6) than that in the progenitor spiral in the outer halo regions.," 9 also demonstrates, as indicated above, that the mean metallicity of the stellar halo of the elliptical is much higher $\sim$ a factor of 6) than that in the progenitor spiral in the outer halo regions." + This is remarkably consistent with the LIST data for the NGC 5128 fields at 21 kpe and 381 kpe whose MDES are virtually indistinguishable (11100)., This is remarkably consistent with the HST data for the NGC 5128 fields at 21 kpc and 31 kpc whose MDFs are virtually indistinguishable (HH00). + We suggest. that. the near-zero metallicity gradient of the outer stellar halo is an observational test which can assess the validity of the merger scenario of elliptical galaxy formation., We suggest that the near-zero metallicity gradient of the outer stellar halo is an observational test which can assess the validity of the merger scenario of elliptical galaxy formation. + 1n Fig., In Fig. + LO we show the distribution of the halo stars on the ντm/L] diagram (radial velocity vs. metallicity) for he progenitor spirals and the elliptical., 10 we show the distribution of the halo stars on the $V_{\rm y}$ -[m/H] diagram (radial velocity vs. metallicity) for the progenitor spirals and the elliptical. + Onlv the elliptica 1o contains stars with both high projected (radial) velocity (V. 2 in our units. corresponding to 280 km 1) and high metallicity (m/H] > 0.6).," Only the elliptical halo contains stars with both high projected (radial) velocity $V_{\rm y}$ $\sim $ 2 in our units, corresponding to $\sim$ 280 km $^{-1}$ ) and high metallicity ([m/H] $>$ $-0.6$ )." + Some fraction of hese outer halo stars with rather high projected velocity also have large tangential velocities and thus high angular momenttun with respect to the elliptical., Some fraction of these outer halo stars with rather high projected velocity also have large tangential velocities and thus high angular momentum with respect to the elliptical. + The origin of hese halo stars with high angular momentum is closely associated with angular momentum transfer. from. inside ο outside. during major galaxy merging: orbital angular momentum: of the merging spirals is converted. into the intrinsic angular momentum of such outer halo stars.," The origin of these halo stars with high angular momentum is closely associated with angular momentum transfer, from inside to outside, during major galaxy merging; orbital angular momentum of the merging spirals is converted into the intrinsic angular momentum of such outer halo stars." + Dased on kinematics and spatial distribution. of the planetary nebula (PN) svstem in NGC 5128. Hui et al. (," Based on kinematics and spatial distribution of the planetary nebula (PN) system in NGC 5128, Hui et al. (" +1995) found a possible evidence of the PN's rotation increasing. with radius and discussed. the origin. of this elliptical. galaxy.,1995) found a possible evidence of the PN's rotation increasing with radius and discussed the origin of this elliptical galaxy. + Additional new velocity analyses are given by Peng et al. (, Additional new velocity analyses are given by Peng et al. ( +2002).,2002). + Although the necessary spectroscopic data to obtain kinematical properties of individual halo stars in NCC 5128 are bevond current observational capabilities. the results in Fie.," Although the necessary spectroscopic data to obtain kinematical properties of individual halo stars in NGC 5128 are beyond current observational capabilities, the results in Fig." + 10 suggest that. future such observations mav find a larger fraction of relatively metal-rich outer-halo stars with high angular momentum in NGC 512s.," 10 suggest that, future such observations may find a larger fraction of relatively metal-rich outer-halo stars with high angular momentum in NGC 5128." + ὃν comparing Fig., By comparing Fig. + 1 with Fig., 1 with Fig. + 11. we can clearlv see that the dilference. between the GC€ and field-star. NDEs in this merger model becomes much more conspicuous alter elliptical galaxy formation.," 11, we can clearly see that the difference between the GC and field-star MDFs in this merger model becomes much more conspicuous after elliptical galaxy formation." + This is essentially because, This is essentially because +model (he excitation of (his transition and cannot rely on it to determine the ortho:para ratio of II3CO in this source.,model the excitation of this transition and cannot rely on it to determine the ortho:para ratio of $_2$ CO in this source. +" Since our models of the 194—Ou, transition are likely the more reliable of the two para-IbCO lines. we find that our observations are not inconsistent with the LTE ortho:para ratio of 3:1. which we therefore assume throughout this paper."," Since our models of the $1_{01}-0_{00}$ transition are likely the more reliable of the two $_2$ CO lines, we find that our observations are not inconsistent with the LTE ortho:para ratio of 3:1, which we therefore assume throughout this paper." + Despite the uncertainties. our determined abundance agrees well wilh measured. values of the formaldehyde abundance relative (o water vapor in Solar System comets.," Despite the uncertainties, our determined abundance agrees well with measured values of the formaldehyde abundance relative to water vapor in Solar System comets." + If we take (LO)=(4-27)X10.* around IRC--10216. our peak formaldehyde abundance with respect to water is οςΟΠΗΟ)=(L.1d0.2)x107.," If we take $x({\rm H_2O})=(4-27) \times 10^{-7}$ around IRC+10216, our peak formaldehyde abundance with respect to water is $x({\rm H_2CO})/x({\rm H_2O})=(1.1\pm0.2)\times 10^{-2}$." + The fractional error on the relative abundance of formaldehyde {ο water vapor is much smaller than the error on either the waler vapor abundance or the formaldehyde abundance because the primary source of error in the absolute abundance measurements is the stellar mass loss rate. ancl (his alfects both absolute abundances similarly. so the error tends (to cancel out. allowing us to determine the relative abundance very precisely.," The fractional error on the relative abundance of formaldehyde to water vapor is much smaller than the error on either the water vapor abundance or the formaldehyde abundance because the primary source of error in the absolute abundance measurements is the stellar mass loss rate, and this affects both absolute abundances similarly, so the error tends to cancel out, allowing us to determine the relative abundance very precisely." + This compares well with the peak values measured [or Comet Lee Cr(Hl9CO)/r(1l590).=1x10 7) (Diveretal.2000).. Comet Hvakutake (ΟΙνο)—8xI0 7) (Biveretal.1999). and several comets observed by οἱal.(1992). Gr(IISCO)ταο)~5x10. 7).," This compares well with the peak values measured for Comet Lee $x({\rm H_2CO})/x({\rm H_2O})= +1\times 10^{-2}$ ) \citep{biv00}, Comet Hyakutake $x({\rm H_2CO})/x({\rm H_2O})=8\times 10^{-3}$ ) \citep{biv99} + and several comets observed by \citet{col92} + $x({\rm H_2CO})/x({\rm H_2O})\sim5\times 10^{-3}$ )." + While we do not know the identity of the carrier of U150. we can also use our photodissociation model to make some useful statements about possible carriers of the U150 line.," While we do not know the identity of the carrier of U150, we can also use our photodissociation model to make some useful statements about possible carriers of the U150 line." + The carrier of the U150 line is likely to be a product of the rich photochemistry in the cireumstellar envelope of IRC+10216., The carrier of the U150 line is likely to be a product of the rich photochemistry in the circumstellar envelope of IRC+10216. + The line has a high off-center/central-position ratio. comparable to or greater (han the oll-center/central-position ratio of the formaldehyde line in the 150 GlIz band. indicating that the carrier is at least as extended. as formaldehyde.," The line has a high off-center/central-position ratio, comparable to or greater than the off-center/central-position ratio of the formaldehyde line in the $150\,$ GHz band, indicating that the carrier is at least as extended as formaldehyde." + We can obtain additional information about the spatial distribution of the U150 line carrier by examining ils line shape in our central ancl off-center spectra., We can obtain additional information about the spatial distribution of the U150 line carrier by examining its line shape in our central and off-center spectra. +" The C150 line has a double-peaked prolile in our central position observations. indicating a resolved source. i.e. (he emission is much weer than the telescope beam (7PBW= 16"")."," The U150 line has a double-peaked profile in our central position observations, indicating a resolved source, i.e. the emission is much larger than the telescope beam $HPBW=16\arcsec$ )." + By contrast. the off-center line shape for U150 is relatively flat-topped. particularly compared to the ¢-Cyll> line. as would be expected or a source which is less extended than the ¢-Cylls line.," By contrast, the off-center line shape for U150 is relatively flat-topped, particularly compared to the $_3$ $_2$ line, as would be expected for a source which is less extended than the $_3$ $_2$ line." + This conclusion is supported. by the off-center/central-position ratio for the οσο line. which is larger than for the U150 ine.," This conclusion is supported by the off-center/central-position ratio for the $_3$ $_2$ line, which is larger than for the U150 line." + In addition. the existence of relatively bright emission in C150 so [ar from IRC+10216 indicates that the line originates in a relatively low-lving state which is easily excited even at the lower densities found bevond ~1400 AU from the star.," In addition, the existence of relatively bright emission in U150 so far from IRC+10216 indicates that the line originates in a relatively low-lying state which is easily excited even at the lower densities found beyond $\sim1400\,$ AU from the star." + A recent paper by Willaev(2004) has suggested that the water vapor and OII found, A recent paper by \citet{wil04} has suggested that the water vapor and OH found +The sequence (dashed line) crossing these stars is the same empirical ZAALS as above. but. shifted. by E(BWV) = We shall. refer το the more. reddened.— sequence as Bochum 9 candidate members.,"The sequence (dashed line) crossing these stars is the same empirical ZAMS as above, but shifted by $(B-V)$ = We shall refer to the more reddened sequence as Bochum 9 candidate members." + In. order to better understancl the nature of Bochum 9 we plotted the cluster, In order to better understand the nature of Bochum 9 we plotted the cluster +M5.107 erg +.,$\sim$$5\times$$ 10^{45}$ erg $^{-1}$. +" With a reverberation niass estimate Lor the SAIBLL in oof M—4»10""AL. (Ixaspi 22000) that luminosity suggests accretion in iis indecc near the Exldington rate. a conclusion consistent with the optical description of aas a Narrow Line QSO (Boroson and Green 1992. Ixaspi 22000). given that a high accretion ratio has been causally linked. with Narrow Line Sevlert 1. galaxies (ee Pounds anc Vaughan 2000 ancl references therein)."," With a reverberation mass estimate for the SMBH in of $M \sim 4 \times 10^{7}\Msun$ (Kaspi 2000) that luminosity suggests accretion in is indeed near the Eddington rate, a conclusion consistent with the optical description of as a Narrow Line QSO (Boroson and Green 1992, Kaspi 2000), given that a high accretion ratio has been causally linked with Narrow Line Seyfert 1 galaxies (eg Pounds and Vaughan 2000 and references therein)." + Lt may well be that energetic outflows are a signature of Edclineton-limited accretion in AGN., It may well be that energetic outflows are a signature of Eddington-limited accretion in AGN. + This might be the case for the bright Seyfert 1102220. which Alarkowitz al.(2006) have recently shown to exhibit a strongly. bluc-shifted Fe Ix absorption line indicating a highly ionised outflow at v0.1c.," This might be the case for the bright Seyfert 1 IC4329A, which Markowitz (2006) have recently shown to exhibit a strongly blue-shifted Fe K absorption line indicating a highly ionised outflow at $\sim$ 0.1c." + While relatively rare in the local universe such X-ray spectra could be common for luminous. higher redshift AGN. (," While relatively rare in the local universe such X-ray spectra could be common for luminous, higher redshift AGN. (" +1) A previous analysis of the 2001 oobservation of the bright quasar rreported evidence of a high velocity ionised outllow. with a mass and kinetic energy. comparable to the accretion mass and bolometric luminosity. respectively (P03). (,"1) A previous analysis of the 2001 observation of the bright quasar reported evidence of a high velocity ionised outflow, with a mass and kinetic energy comparable to the accretion mass and bolometric luminosity, respectively (P03). (" +2) This finding is now confirmed. with the previous uncertainty in the derived. velocity removed. by securing the identification of the main observed. absorption lines. (,"2) This finding is now confirmed, with the previous uncertainty in the derived velocity removed by securing the identification of the main observed absorption lines. (" +4) We suggest that fast. energetic outllows may. be a typical signature of type 1 AGN acereting at or close to the Iddington limit.,"4) We suggest that fast, energetic outflows may be a typical signature of type 1 AGN accreting at or close to the Eddington limit." + The results. reported. here are. based. on observations obtained with.XAZAZ-Neiwlon.. an ESA science mission with instruments ancl contributions cirectly funded. by ESA Alember States and the USA (NASA).," The results reported here are based on observations obtained with, an ESA science mission with instruments and contributions directly funded by ESA Member States and the USA (NASA)." + The authors wish to thank the SOC and SSC teams for organising the oobservations and initial cata reduction., The authors wish to thank the SOC and SSC teams for organising the observations and initial data reduction. + We also thank the anonymous referee for a careful reading of the text. and COonDslructive coninmients., We also thank the anonymous referee for a careful reading of the text and constructive comments. +the outer proton shell.,the outer proton shell. + This collision occurs at approximately the time £454; given above aud will generate a forward and a reverse shock., This collision occurs at approximately the time $t_{\rm collide}$ given above and will generate a forward and a reverse shock. + The characteristics of these shocks aud the resultant cussion depend ou the structure of the outer shell at the time of the collision., The characteristics of these shocks and the resultant emission depend on the structure of the outer shell at the time of the collision. + We will consider two linitiug approximations to this structure., We will consider two limiting approximations to this structure. + Tu the first approximation that we cousider. the outer shell is assumed to have relaxed to a self similar solution.," In the first approximation that we consider, the outer shell is assumed to have relaxed to a Blandford-McKee self similar solution." + Also. the outer shell is assumed to be hot (at least in the proton componet}. so that the enthalpy in the outer shell is mich larger than the rest mass energy deusity.," Also, the outer shell is assumed to be hot (at least in the proton component), so that the enthalpy in the outer shell is much larger than the rest mass energy density." + studied ummerically the evolution of external shocks aud showed that the Dlaudford-Mekee self similar solution is a good approximation once the shock has reached a radius greater than ~1.LOKdee. with the exact nuuber depending ou whether or not the reverse shock is relativistic.," \cite{kobpirsari} studied numerically the evolution of external shocks and showed that the Blandford-Mckee self similar solution is a good approximation once the shock has reached a radius greater than $\sim 1.4-1.9 r_{\rm dec}$, with the exact number depending on whether or not the reverse shock is relativistic." + Therefore. for reasonablc fireball parameters the collision between the inner aud outer shells may occur while the outer shell is still relaxing to the self similar solution.," Therefore, for reasonable fireball parameters the collision between the inner and outer shells may occur while the outer shell is still relaxing to the self similar solution." + A nunuerical solution of the evolution of the iuner aud outer shells would be needed to obtain the expected Heltcurves in this case., A numerical solution of the evolution of the inner and outer shells would be needed to obtain the expected lightcurves in this case. + The expected emission iu this first aproximation las been worked out in detail by and we craw on their results;, The expected emission in this first aproximation has been worked out in detail by \cite{pk} and we draw on their results. + When the iuuer cold shell collides with the outer hot shell a weak forward shock results., When the inner cold shell collides with the outer hot shell a weak forward shock results. + The effect on the cussion from the outer shell is a modest iucrease in the total hunuinositv and little change in the spectrum., The effect on the emission from the outer shell is a modest increase in the total luminosity and little change in the spectrum. + The reverse shock propagating into the immer shell is strong and iuildly relativistic., The reverse shock propagating into the inner shell is strong and mildly relativistic. + The characteristic frequency for the oe1issiou frou the iuner shell is This expression should be taken as somewhat approximate because a imuuerical study of the evolution of the reverse shock propagating iuto the neutron shell is needed for an accurate determination of the characteristic frequency., The characteristic frequency for the emission from the inner shell is This expression should be taken as somewhat approximate because a numerical study of the evolution of the reverse shock propagating into the neutron shell is needed for an accurate determination of the characteristic frequency. +" The flux at the characteristic frequeucy is larger by a factor ~(5,E,/E,ye? than the flux from the outer shell at the same frequency (Iuiar&Piran2000).", The flux at the characteristic frequency is larger by a factor $\sim(\gamma_n E_p/E_n)^{5/3}$ than the flux from the outer shell at the same frequency \citep{pk}. +. Tf the observed eunission fron the proton shell arose from the reverse shock in the proton shell (which iighlt occur if the emission from the forward shock occurs at too high a frequency to be observed by BATSE). then the characteristic frequency iu the first and second peaks is similar.," If the observed emission from the proton shell arose from the reverse shock in the proton shell (which might occur if the emission from the forward shock occurs at too high a frequency to be observed by BATSE), then the characteristic frequency in the first and second peaks is similar." + If. on the other hand. the dominant emission in the first peak arose from the forward shock propagating iuto the ISM. the first peak will have a uch higher average energy than the second peak.," If, on the other hand, the dominant emission in the first peak arose from the forward shock propagating into the ISM, the first peak will have a much higher average energy than the second peak." + The future CLAST iav therefore provide useful insights iuto this problem., The future GLAST may therefore provide useful insights into this problem. + The spectrum of ciuission from the imuer shell depends ou whether or not the typical post-shock electron cools within a dynamical timescale., The spectrum of emission from the inner shell depends on whether or not the typical post-shock electron cools within a dynamical timescale. +" The thermal Loreutz factor of an electron which just cools ou a lydrodvuamic timescale is elven by 544,=οlopημένα).©BCE,μὴτηωνsept)."," The thermal Lorentz factor of an electron which just cools on a hydrodynamic timescale is given by $\gamma_{e,c}=3m_e +c/(4\sigma_{\rm T} U_B \gamma_n t_{\rm hyd}) \approx 3(E_p/E_n)(1/n_{\rm +ISM}\gamma_{n,3}^3\epsilon_B t)$." +" Hore Cp is the maenetic field energy deusitv in the iuner neutron shell. στ is the Thomsou cross section. figa is the observed bydrodvuuuic timescale for the shell (approximately σσ), aud tis the observed time in seconds."," Here $U_B$ is the magnetic field energy density in the inner neutron shell, $\sigma_{\rm T}$ is the Thomson cross section, $t_{\rm hyd}$ is the observed hydrodynamic timescale for the shell (approximately $r/c \gamma_n^2$ ), and $t$ is the observed time in seconds." + Because the thermal Loreutz factor (oai) for the average clectron in the post-shocked. Πιο shell is typically of order a few huudred or higher. we see that 55;S56e diving the first few seconds.," Because the thermal Lorentz factor $\gamma_{e,{\rm therm}}$ ) for the average electron in the post-shocked inner shell is typically of order a few hundred or higher, we see that $\gamma_{e,c}\lesssim \gamma_{e,{\rm therm}}$ during the first few seconds." + This means that we may approximate the electrous as fast cooling., This means that we may approximate the electrons as fast cooling. + In this case the flux from the neutron shell is proportional tov for frequencies above the characteristic frequency., In this case the flux from the neutron shell is proportional to $\nu^{-p/2}$ for frequencies above the characteristic frequency. + Here p is the power Luv index characterizing the electron distribution in the shock (typically p~ 2.1)., Here $p$ is the power law index characterizing the electron distribution in the shock (typically $p\sim 2.4$ ). + Even though the characteristic frequency for the immer shell is low. siguificant cuuission can occur in the tens to huudreds of keV rauge if the iudex of the power law characterizing the post-shock electrou distribution is close to 2.," Even though the characteristic frequency for the inner shell is low, significant emission can occur in the tens to hundreds of keV range if the index of the power law characterizing the post-shock electron distribution is close to 2." +"mmethod and bbased methods is known and expected (see,e.g.,toSo masses). 'T","method and based methods is known and expected \citep[see, e.g., the discussion +in][concerning the relation of \FOF\ masses to \SO\ +masses]{Tinker2008, Lukic2009}." +he entering of the era of precision cosmology in the last couple of years made it possible to derive the mass function of gravitationally bound objects in cosmological simulations with unprecedented accuracy., The entering of the era of precision cosmology in the last couple of years made it possible to derive the mass function of gravitationally bound objects in cosmological simulations with unprecedented accuracy. + This led to an emergence of refined analytical formulae (cf. and it only appears natural to test whether or not our halo finder ccomplies with these prescriptions.," This led to an emergence of refined analytical formulae \citep[cf. ][]{Sheth1999, Jenkins2001, Reed2003, Warren2006, +Tinker2008} and it only appears natural to test whether or not our halo finder complies with these prescriptions." +" To this extent we are utilizing our best resolved simulation BB963hi of Set 2, cf."," To this extent we are utilizing our best resolved simulation B963hi of Set 2, cf." + Table and present in figure (i.e.12 à comparison 1)) ," Table \ref{tab:simulations}) ) and present in figure \ref{fig:hfcomp_mass_high} a comparison against the mass functions proposed by \citet{Press1974, Sheth1999, Jenkins2001, +Reed2003, Warren2006} and \citet{Tinker2008}." +In this respect it must be noted that the proposed theoretical mass functions are calibrated to mass functions utilizing different halo overdensities., In this respect it must be noted that the proposed theoretical mass functions are calibrated to mass functions utilizing different halo overdensities. +" The mass function of ? is based on halo catalogs applying an overdensity of A—178 (?),, and the ? and ? functions are formulated for overdensities of A=200."," The mass function of \citet{Sheth1999} is based on halo catalogs applying an overdensity of $\Delta = 178$ \citep{Tormen1998a}, , and the \citet{Reed2003} and \citet{Warren2006} functions are formulated for overdensities of $\Delta = 200$." +" ? provide various calibration and we use their equation B4 which is calibrated to a ACDM simulation and an So--halo finder with an overdensity of A—324, quite close to our value of A—340."," \citet{Jenkins2001} provide various calibration and we use their equation B4 which is calibrated to a $\Lambda$ CDM simulation and an -halo finder with an overdensity of $\Delta = 324$, quite close to our value of $\Delta = 340$." + The ? mass function explicitly includes the overdensity as a free parameter and as such we use the value of our catalog to produce the mass function., The \citet{Tinker2008} mass function explicitly includes the overdensity as a free parameter and as such we use the value of our catalog to produce the mass function. +" We find the ? formula to give an excellent description of the observed mass function and also the ? formula provides a good description, albeit overestimating the number of halos at intermediate masses, which might be due to the slightly wrong overdensity."," We find the \citet{Tinker2008} formula to give an excellent description of the observed mass function and also the \citet{Jenkins2001} formula provides a good description, albeit overestimating the number of halos at intermediate masses, which might be due to the slightly wrong overdensity." +" While the other formulas also provide an adequate description for the mass function at intermediate masses, they overestimate the number of halos at the high mass end."," While the other formulas also provide an adequate description for the mass function at intermediate masses, they overestimate the number of halos at the high mass end." + As has been eluded to above this isto be expected and can be understood by the different halo overdensities they have been calibrated to., As has been eluded to above this isto be expected and can be understood by the different halo overdensities they have been calibrated to. +" However, clearly the ? prescription does not provide a good description of the halo mass function in this case."," However, clearly the \citet{Press1974} prescription does not provide a good description of the halo mass function in this case." +" As the ? formula provides an excellent fit to our data, we refer the reader to their work for further discussions concerning the impact of the different overdensities used to define a halo."," As the \citet{Tinker2008} formula provides an excellent fit to our data, we refer the reader to their work for further discussions concerning the impact of the different overdensities used to define a halo." +" As our halo finder simultaneously finds field and sub-halos without the need to refine the parameters for the latter it appears mandatory to compare the derived subhalo mass function against results in the literature, too."," As our halo finder simultaneously finds field and sub-halos without the need to refine the parameters for the latter it appears mandatory to compare the derived subhalo mass function against results in the literature, too." +" To this extent, we identify the substructure of the most massive halo in B20 with our cross matching tool refsubsubsec:halohalocrosscomp))."," To this extent, we identify the substructure of the most massive halo in B20 with our cross matching tool \\ref{subsubsec:halohalocrosscomp}) )." +" We restrict ourselves here to only investigating this particular halo, as the particle resolution for the other available simulations is not sufficient to resolve the subhalo population adequately."," We restrict ourselves here to only investigating this particular halo, as the particle resolution for the other available simulations is not sufficient to resolve the subhalo population adequately." +" Also, we did use the 128-01-5-1.0-2.0 analysis to have a high sensitivity to very small halos (cf."," Also, we did use the 128-01-5-1.0-2.0 analysis to have a high sensitivity to very small halos (cf." + discussion of AHF'ss parameters in section 3))., discussion of s parameters in section \ref{sec:testing}) ). +" It has been found before (e.g.????7???7) that the subhalo mass function can be described with a functional fom Neup(>M)«Μα, with a=0.7...0.9."," It has been found before \citep[e.g.][]{Ghigna2000, Helmi2002, + DeLucia2004, Gao2004, vandenBosch2005, Diemand2007, Giocoli2008, + Springel2008} that the subhalo mass function can be described with a functional form $N_{\rm sub}(>M) \propto M^{-\alpha}$, with $\alpha = +0.7 \ldots 0.9$." + In figure 13 we show the cumulative mass function of the most massive halo in B20 and provide — as guide forthe eye — two power laws with those limiting slopes., In figure \ref{fig:hfcomp_subhalo_theory} we show the cumulative mass function of the most massive halo in B20 and provide – as guide forthe eye – two power laws with those limiting slopes. +" Additionally, we fitted a power law to the actual M), yielding a slope of a= 0.81."," Additionally, we fitted a power law to the actual $N_{\rm + sub}^{\rm AHF}(>M)$ , yielding a slope of $\alpha = 0.81$ ." + This test confirms NABE(Sthe, This test confirms the +in eight sub-volumes.,in eight sub-volumes. +" The average values of Cy, agree in the 1024* and 15367 simulations. and the small (£10%) variance among these sub-volumes suggests that the 1024* and 1536? simulations are converged."," The average values of $C_H$ agree in the $1024^3$ and $1536^3$ simulations, and the small $\pm10$ %) variance among these sub-volumes suggests that the $1024^3$ and $1536^3$ simulations are converged." + Over the redshift range 5<2<9 in the 1536 simulation. the clumpineg [actor is well fitted bv a power-law. represenüng a slow rise in clumping {ο lower τους. after the (urn-on of ionizing radiation.," Over the redshift range $5 < z < 9$ in the $1536^3$ simulation, the clumping factor is well fitted by a power-law, representing a slow rise in clumping to lower redshift, after the turn-on of ionizing radiation." + To study the effect of radiative heating from the ionizing background on filamentary structure. we ran a suite of mocderate-resoliution simulations with different ionizing backgrounds (see Table 2 for details).," To study the effect of radiative heating from the ionizing background on filamentary structure, we ran a suite of moderate-resolution simulations with different ionizing backgrounds (see Table 2 for details)." + The redshift al which the UV background is turned on affects the clumpine factor. causing it to drop and then recover at lower redshift.," The redshift at which the UV background is turned on affects the clumping factor, causing it to drop and then recover at lower redshift." + Pawliketal. (2009) altribute this effect tofiltering. where the photo-heating raises the cosmological Jeans nass. preventine further accretion onto low-mass halos and smoothing out small-scale density fluctuations.," Pawlik (2009) attribute this effect to, where the photo-heating raises the cosmological Jeans mass, preventing further accretion onto low-mass halos and smoothing out small-scale density fluctuations." +" The photoheating also heats the filaments we are focusing on. which lowers the hydrogen recombination rate coefficient, ajG3)xT.P. and causes the filaments to expand:— both of these effects reduce the chunping factor."," The photoheating also heats the filaments we are focusing on, which lowers the hydrogen recombination rate coefficient, $\alpha_H^{(B)} \propto T^{-0.845}$, and causes the filaments to expand; both of these effects reduce the clumping factor." + Without a UV. background. the clumpiug continues (o rise as (he filaments gravitationallv collapse.," Without a UV background, the clumping continues to rise as the filaments gravitationally collapse." + Pawlik etal. (2009) also claim (hat the clumping factor al z=6 is insensitive to when the background is turned on. as long as 1 is Curned on al 2>9.," Pawlik (2009) also claim that the clumping factor at $z=6$ is insensitive to when the background is turned on, as long as it is turned on at $z>9$." + When an ionizing background is introduced. photoheating acts as a positive feedback to reionization bv lowering the clumping factor and making it easier {ο stay lonized.," When an ionizing background is introduced, photoheating acts as a positive feedback to reionization by lowering the clumping factor and making it easier to stay ionized." + This same photoheating mechanism also suppresses star lormation in low-mass halos. which in turn lowers the ionizing photon production rate bv star-forming galaxies and acts as a negative feedback to reionization (Pawliketal. 2009).," This same photoheating mechanism also suppresses star formation in low-mass halos, which in turn lowers the ionizing photon production rate by star-forming galaxies and acts as a negative feedback to reionization (Pawlik 2009)." + These thermodynamic processes affect clumping and structure and emphasize (he importance of carefully modeling the strength of feedback processes ancl their elfects on Jeans mass., These thermodynamic processes affect clumping and structure and emphasize the importance of carefully modeling the strength of feedback processes and their effects on Jeans mass. + We have explored what happens when the ionizing radiation turned on earlier. especially during the interval 26—8 marking the transition [rom a neutral to fully ionized ICM.," We have explored what happens when the ionizing radiation turned on earlier, especially during the interval $z = 6-8$ marking the transition from a neutral to fully ionized IGM." + In a series of 5127 simulations. we explore the influence of turn-on of photoionizing radiation between redshifts 2=7 and z=9.," In a series of $512^3$ simulations, we explore the influence of turn-on of photoionizing radiation between redshifts $z = 7$ and $z = 9$." + Figure 4 shows Cj. computed for the moderate-resolution simulations via the density-field method and weighted byvolume.," Figure 4 shows $C_H$, computed for the moderate-resolution simulations via the density-field method and weighted byvolume." + We do not plot simulation, We do not plot simulation +The performance of our selection pipeline was checked by comparing it with the results of the SNLS real-time pipeline used to select spectroscopy targets.,The performance of our selection pipeline was checked by comparing it with the results of the SNLS real-time pipeline used to select spectroscopy targets. + A total of 340 supernovae were targeted during the period considered here including events as faint as i’=24.4., A total of 340 supernovae were targeted during the period considered here including events as faint as $i^\prime=24.4$. +" Of these, all but two were found on the 7’ stacked images. ("," Of these, all but two were found on the $i^\prime$ stacked images. (" +The two lost events were outside the reference images.),The two lost events were outside the reference images.) +" Of the 338 events, 295 passed our selection criteria."," Of the 338 events, 295 passed our selection criteria." + The loss of the 43 events was due to our time sampling criteria which is more restrictive than the real-time criteria., The loss of the 43 events was due to our time sampling criteria which is more restrictive than the real-time criteria. + Figure 6 shows the i’ Hubble diagram for the 221 events with host photometric redshifts <0.4.," Figure \ref{hubbleifig} + shows the $i^\prime$ Hubble diagram for the 221 events with host photometric redshifts $<0.4$." +" Events that are spectroscopically identified as SNIa or SNcc (5ΝΗ, SNIb, SNIc) are marked."," Events that are spectroscopically identified as SNIa or SNcc (SNII, SNIb, SNIc) are marked." + Also marked are photometrically identified SNIa as discussed in Sec. 4.., Also marked are photometrically identified SNIa as discussed in Sec. \ref{classificationsec}. + The spectroscopic SNIa’s fall mostly along the band of bright events centered approximately on i’~21.8+51og(z/0.3)., The spectroscopic SNIa's fall mostly along the band of bright events centered approximately on $i^\prime\sim21.8+5\log(z/0.3)$. + The spectroscopic SNcc's are generally fainter with i’>22.7+5log(z/0.3)., The spectroscopic SNcc's are generally fainter with $i^\prime>22.7+5\log(z/0.3)$. + The supernovae that we will use to measure rates have a wide range of redshifts up to z=0.4., The supernovae that we will use to measure rates have a wide range of redshifts up to $z=0.4$. +" In order to compare supernovae of differing z, we define an AB magnitude centered on 570nm in the supernova rest-frame by a simple dependent interpolation between 7’ and 7’: This gives ms7o(z=0.1)r' (A=626 nm) and ms79(z=0.35)=i’ (A= 769nm)."," In order to compare supernovae of differing $z$, we define an AB magnitude centered on $570\,nm$ in the supernova rest-frame by a simple redshift-dependent interpolation between $r^\prime$ and $i^\prime$: This gives $m_{570}(z=0.1)=r^\prime$ $\lambda=626\,nm$ ) and $m_{570}(z=0.35)=i^\prime$ $\lambda=769\,nm$ )." + We then define the quantity AMs570 to be proportional to the absolute magnitude taking into account the supernova distance but not host absorption: where The constant C=24.2 is chosen so that the spectroscopically confirmed SNIa are centered on AMs;o= 0., We then define the quantity $\Delta M_{570}$ to be proportional to the absolute magnitude taking into account the supernova distance but not host absorption: where The constant $C=24.2$ is chosen so that the spectroscopically confirmed SNIa are centered on $\Delta M_{570}=0$ . + Figure 7 shows AMs;o as a function of redshift., Figure \ref{m600fig} shows $\Delta M_{570}$ as a function of redshift. + The spectroscopically identified SNIa and SNcc are now separated horizontally with AMs579«0.75 dominated by SNIa and AMs;o>0.75 containing most spectroscopically-confirmed SNcc., The spectroscopically identified SNIa and SNcc are now separated horizontally with $\Delta M_{570}<0.75$ dominated by SNIa and $\Delta M_{570}>0.75$ containing most spectroscopically-confirmed SNcc. +" The characteristics ofthe events as a function of AM579,"," The characteristics ofthe events as a function of $\Delta M_{570}$ ," +"All photometric imagnitudes were imeasured in 3” diuneter apertures aud them corrected to 6"" diameter (near total) imaenitudes following the procedures of CCowie et (0199D).",All photometric magnitudes were measured in $3''$ diameter apertures and then corrected to $6''$ diameter (near total) magnitudes following the procedures of \markcite{cowie94}C Cowie et (1994). + SSerjeaut et ((1997) obtained deep ISOCAM observations of the IIDE. aud fiaukiug fields at 6.75 and yan. The AAussel et ((1999) reductious of the data produced a iain source list of 19 objects (70) aud a supplementary list of an additional 5l objects (30 for jan and Se for jn)., \markcite{s97}S Serjeant et (1997) obtained deep ISOCAM observations of the HDF and flanking fields at 6.75 and $\mu$ m. The \markcite{aussel99}A Aussel et (1999) reductions of the data produced a main source list of 49 objects $7\sigma$ ) and a supplementary list of an additional 51 objects $3\sigma$ for $\mu$ m and $5\sigma$ for $\mu$ m). +" Despite the large point spread funetion (15"" at jin). in most cases the optical or NIR identification of the ISOCAAL source was straightforward."," Despite the large point spread function $15''$ at $\mu$ m), in most cases the optical or NIR identification of the ISOCAM source was straightforward." + The redshifts for sources in the sample are in the rauge >=.078 to.=1.212 Guecian 2=0.585)., The redshifts for sources in the sample are in the range $z=0.078$ to $z=1.242$ (median $z=0.585$ ). + We used LRIS during a two night rum ou EKeck II iu March 1999 to obtain spectroscopic observations of a sub-sale of the GG sources in a strip region centered. ou the NDF., We used LRIS during a two night run on Keck II in March 1999 to obtain spectroscopic observations of a sub-sample of the GHz sources in a strip region centered on the HDF. + Although zthe WDF and flanking field region has been intensely studied by a number of groups (see CCohen et 11999 for a παν aud references}. most of the sources im our sample had not been previously observed due to their faint optical fluxes.," Although the HDF and flanking field region has been intensely studied by a number of groups (see \markcite{cohen99}C Cohen et 1999 for a summary and references), most of the sources in our sample had not been previously observed due to their faint optical fluxes." + We used 1.1” wide slits aud the 100 ! erating blazed atAA.. which gives a waveleusth resolution of ~12 aid a wavelength coverage of 1000AA.," We used $1.4''$ wide slits and the 400 $^{-1}$ grating blazed at, which gives a wavelength resolution of $\sim 12$ and a wavelength coverage of $\sim 4000$." +. The waveleueth range for each object depends ou the exact location of the slit iu the mask but is eenerallv between 1000 andAA., The wavelength range for each object depends on the exact location of the slit in the mask but is generally between $\sim4000$ and. + Three of the slit masks were constructed. at a position angle of 907. aud the remaining three were nearly identical versions coustructed at a position angle of 903.," Three of the slit masks were constructed at a position angle of $90^\circ$, and the remaining three were nearly identical versions constructed at a position angle of $-90^\circ$." + This procedure enabled us to obtain sufficient wavelength coverage for all the objects in our sample. Πιοπιαπο those that fell close to the edges of the masks.," This procedure enabled us to obtain sufficient wavelength coverage for all the objects in our sample, including those that fell close to the edges of the masks." + The observatious were hhr per slit mask. broken iuto three sets of nuuiuute exposures.," The observations were hr per slit mask, broken into three sets of minute exposures." + Three IIDF slit masks were observed per nieht., Three HDF slit masks were observed per night. + Some of the objects were in all of the slit masks aud heuce were observed for hlus (see Table 2))., Some of the objects were in all of the slit masks and hence were observed for hrs (see Table \ref{tab2}) ). +" Conditions were photometric with secing ~0.6%—0,7"" FWIIM both nights.", Conditions were photometric with seeing $\sim 0.6''-0.7''$ FWHM both nights. +" The objects were stepped along the slit bv 10"" in each direction. aud the sky backerounds were removed using the median of the images to avoid the difficult aud πιοσοκο problems of fat-ficlding LRIS data."," The objects were stepped along the slit by $10''$ in each direction, and the sky backgrounds were removed using the median of the images to avoid the difficult and time-consuming problems of flat-fielding LRIS data." + Details of the spectroscopic reduction procedures ean be found in CCowie et (1996)., Details of the spectroscopic reduction procedures can be found in \markcite{cowie96}C Cowie et (1996). + Iu Table 2 we list all the objects in the racio sample that fallin the LRIS strip region., In Table \ref{tab2} we list all the objects in the radio sample that fall in the LRIS strip region. + The cols are radio catalog uuniber from Table 1. I£A' muuag. £ nuuag. redshift. and exposure time for auv object targeted in our March 1999 spectroscopic urveyv.," The columns are radio catalog number from Table 1, $HK'$ mag, $I$ mag, redshift, and exposure time for any object targeted in our March 1999 spectroscopic survey." + Over an area ~58 απο”. 19 of the 37 radio sources now have secure redshift identifications: all are at :<1.9.," Over an area $\sim 58$ $^2$, 19 of the 37 radio sources now have secure redshift identifications; all are at $z\lesssim 1.3$." + Figure laa. b shows TIN’ versus vedshift aud £ versus redshift.," Figure \ref{figzhkandzi}a a, b shows $HK'$ versus redshift and $I$ versus redshift." + Spectroscopic redshifts are in general relatively straightforward to obtain for radio objects with IEA’<20., Spectroscopic redshifts are in general relatively straightforward to obtain for radio objects with $HK'\lesssim 20$. + We note that Waddinetou et ((1999) claim a redshift identification of +=L12 for object 30 based on a Lyra detection., We note that Waddington et (1999) claim a redshift identification of $z=4.42$ for object 30 based on a $\alpha$ detection. + However. the position of their detection is 1” away from the radio source position and counterpart optical galaxy. aud so an association with the radio source is not secure.," However, the position of their detection is $1''$ away from the radio source position and counterpart optical galaxy, and so an association with the radio source is not secure." + The radio source is detected im the nmüd-IR. which would sugeest 2<1.3. consistent with the redshift estimated using the millimetric redshift techuique described in L.," The radio source is detected in the mid-IR, which would suggest $z<1.3$, consistent with the redshift estimated using the millimetric redshift technique described in \ref{secze}." + However. we did not see auv strong 33727 feature iu our spectrum from 10009200AA.. which would sugeest 2>1.5.," However, we did not see any strong 3727 feature in our spectrum from $4000-9200$, which would suggest $z>1.5$." + Thus. the redshift of this object remains uncertain.," Thus, the redshift of this object remains uncertain." + Iu all of our slit-inasks (equivalent to a hlir integration) we also included the position of the brightest SCUBA source. IIDESS0.1. from the deep 432 map of tle ITIDE-proper by II985.," In all of our slit-masks (equivalent to a hr integration) we also included the position of the brightest SCUBA source, HDF850.1, from the deep $\mu$ m map of the HDF-proper by H98." + We centered our slit across the position of the uuu detection of IIDES50.1 reported by Downes et (19993. which also coincides with the GCIIz supplemental radio source 3651]|1226 (Richards et 11998).," We centered our slit across the position of the mm detection of HDF850.1 reported by Downes et (1999), which also coincides with the GHz supplemental radio source 3651+1226 (Richards et 1998)." + We oriented the slit such that it fell across both the arc-like feature 3-593.0 that is favored by Downes ct ((1999) as the optical counterpart to IIDESD0.1 aud the nearby red galaxy 3-586.0., We oriented the slit such that it fell across both the arc-like feature 3-593.0 that is favored by Downes et (1999) as the optical counterpart to HDF850.1 and the nearby red galaxy 3-586.0. + However. we were unable to determine a secure redshift for either source frou our spectroscopic data.," However, we were unable to determine a secure redshift for either source from our spectroscopic data." + Our SCUBA jigele map observations were flexibly scheduled in mostly excellent observing conditions duriug two ruis in April aud June 1999 for a total of five observing shifts., Our SCUBA jiggle map observations were flexibly scheduled in mostly excellent observing conditions during two runs in April and June 1999 for a total of five observing shifts. + The maps were dithered to prevent any regions of the sky from repeatedly falling ou bad bolometers., The maps were dithered to prevent any regions of the sky from repeatedly falling on bad bolometers. + The chop throw was fixed at a position angle of 90° so that the uceative beams would appear aarcsec on either side cast-awest of the positive beau., The chop throw was fixed at a position angle of $90^\circ$ so that the negative beams would appear arcsec on either side east-west of the positive beam. +" The data were reduced using beam weighted extraction. routines that included both the positive and negative portious of the chopped tages. thereby increasing the effective exposure ues,"," The data were reduced using beam weighted extraction routines that included both the positive and negative portions of the chopped images, thereby increasing the effective exposure times." +" Begular ""skvdips (LLiehtfoot et 11998) were obtained to measure the zenith atmospheric opacitics at 150. and pau. and the QGGIIz sky opacity was nonitored at all times to check for sky stabilitv."," Regular “skydips” \markcite{manual}L Lightfoot et 1998) were obtained to measure the zenith atmospheric opacities at 450 and $\mu$ m, and the GHz sky opacity was monitored at all times to check for sky stability." + The nedian pau optical depth for all nights together was 1.265., The median $\mu$ m optical depth for all nights together was 0.265. +" Poiutiug checks were performed every hour during he observatious on the blazars 0051050, L1181516. 9923|392. or 1308|326."," Pointing checks were performed every hour during the observations on the blazars 0954+685, 1418+546, 0923+392, or 1308+326." + The data were calibrated. using aarcsee diameter aperture nieasurements of the positive jun iun bean maps of the primary calibration source. Abus. and one of three secondary calibration sources. CRLGIS. IRC|10216. or OIT231.8.," The data were calibrated using arcsec diameter aperture measurements of the positive beam in beam maps of the primary calibration source, Mars, and one of three secondary calibration sources, CRL618, IRC+10216, or OH231.8." + The data were reduced m a standard aud consistent way using the dedicated SCUBA User Reduction Facility (SURF: JJeuness Lightfoot 1998)., The data were reduced in a standard and consistent way using the dedicated SCUBA User Reduction Facility (SURF; \markcite{surf}J Jenness Lightfoot 1998). + Due to the variation in the density of bolometer samples across the maps. there Is a rapid iucrease in the noise levels at the very edges.," Due to the variation in the density of bolometer samples across the maps, there is a rapid increase in the noise levels at the very edges." + We rave clipped the low exposure edges from our images., We have clipped the low exposure edges from our images. + We xeseut our SCUBA maps in Fie. 2.., We present our SCUBA maps in Fig. \ref{figmaps}. + We also re-reduced the archival IIDE-proper SCUBA data of II98 in order to make a consistent analysis with he present data., We also re-reduced the archival HDF-proper SCUBA data of H98 in order to make a consistent analysis with the present data. + We could ouly make use of the maps that were taken with a fixed RA chop pper cent of the data saluple}. which iucluded 31 hours with a aaresec cliop τον aud hhours with a aarcsec chop throw.," We could only make use of the maps that were taken with a fixed RA chop per cent of the data sample), which included 34 hours with a arcsec chop throw and hours with a arcsec chop throw." + We combined these data separately to form: two iudepenudoeut naps., We combined these data separately to form two independent maps. + In Table 1 we quote subiiillimeter fluxes determined youn the weighted average of nieasurements made in eac[um nap., In Table 1 we quote submillimeter fluxes determined from the weighted average of measurements made in each map. +enters the Hill sphere of the planet.,enters the Hill sphere of the planet. +" During the simulations, planetesimals are removed if they The choice for rg; comes from the fact that very eccentric orbits with perihelion distances smaller than 0.05 AU are hard to resolve without using a very small timestep, and will lead to non-physical behaviour."," During the simulations, planetesimals are removed if they The choice for $r_{\rm min}$ comes from the fact that very eccentric orbits with perihelion distances smaller than 0.05 AU are hard to resolve without using a very small timestep, and will lead to non-physical behaviour." +" Furthermore, bodies that come this close to the central star are likely to be evaporated."," Furthermore, bodies that come this close to the central star are likely to be evaporated." + An example of resonance capture in the simulations is illustrated in fig. 4.., An example of resonance capture in the simulations is illustrated in fig. \ref{fig:54_a_br}. + The figure shows a Neptune-mass planet being pushed artificially to migrate in from 30 AU at a rate of 7.3x10?AUΥΓ].," The figure shows a Neptune-mass planet being pushed artificially to migrate in from 30 AU at a rate of $7.3\times10^{-5}\rm \, AU\,yr^{-1}$." + A massless asteroid is orbiting the mass star at 13 AU on an initially circular orbit., A massless asteroid is orbiting the solar-mass star at 13 AU on an initially circular orbit. + The asteroid survives the passing of the 1:2 (j= 1) MMR but is eventually captured by the 3:4 (j2 3) MMR., The asteroid survives the passing of the 1:2 $j=1$ ) MMR but is eventually captured by the 3:4 $j=3$ ) MMR. +" For lower migration rates (or higher planet masses) the asteroid gets trapped in the 1:2 resonance already, while for higher migration rates (or lower planet masses) the asteroid only gets captured very close to the planet."," For lower migration rates (or higher planet masses) the asteroid gets trapped in the 1:2 resonance already, while for higher migration rates (or lower planet masses) the asteroid only gets captured very close to the planet." + Figure 5 shows the evolution of a massless body as it is dragged along in a migrating planet's 1:2 resonance., Figure \ref{fig:epumping} shows the evolution of a massless body as it is dragged along in a migrating planet's 1:2 resonance. +" The integration has been performed using two different integrators, to check the consistency of SYMBA for highly eccentric orbits."," The integration has been performed using two different integrators, to check the consistency of SyMBA for highly eccentric orbits." + The test particle is captured at {~0.13 Myr and eventually lost to the central star after about 0.32 Myr., The test particle is captured at $t\approx0.13$ Myr and eventually lost to the central star after about 0.32 Myr. +" During this time, the 10MyNep mass planet has travelled ~14 AU."," During this time, the $10M_{\rm Nep}$ mass planet has travelled $\sim14$ AU." +" The results of the SyMBA and Bulirsch-Stoer integrators are very similar, and in both cases the massless body is eventually lost to the central star when it reaches e~0.99."," The results of the SyMBA and Bulirsch-Stoer integrators are very similar, and in both cases the massless body is eventually lost to the central star when it reaches $e\approx0.99$." +" The expected increase in eccentricity, as predicted by eq."," The expected increase in eccentricity, as predicted by eq." + 14 is also plotted and seen to agree well with the simulations., \ref{eq:epump} is also plotted and seen to agree well with the simulations. + The discrepancy between eq., The discrepancy between eq. + 14 and the simulations towards higher e comes from the fact eq., \ref{eq:epump} and the simulations towards higher $e$ comes from the fact eq. + 14 is a first-order approximation., \ref{eq:epump} is a first-order approximation. + Figure 6aa shows the evolution of the planetesimal swarm as a function of time., Figure \ref{fig:all_BW}a a shows the evolution of the planetesimal swarm as a function of time. +" The left panels show eccentricity, the right panels inclination, and time passes from top to bottom."," The left panels show eccentricity, the right panels inclination, and time passes from top to bottom." + The large circle shows the location of the planet and the small circles represent massless planetesimals., The large circle shows the location of the planet and the small circles represent massless planetesimals. + Planetesimals above the solid lines are on a planet-crossing orbit., Planetesimals above the solid lines are on a planet-crossing orbit. +" The dotted lines show the 1:2 and 2:3 MMR, where the 1:2 MMR is furthest from the planet."," The dotted lines show the 1:2 and 2:3 MMR, where the 1:2 MMR is furthest from the planet." + The planet is 0.1Myep and migrating at a rate of 7.3x107?AUyr!.," The planet is $0.1M_{\rm Nep}$ and migrating at a rate of $7.3\times10^{-5}\rm \, AU\,yr^{-1}$." + The planetesimals start out between 10 and 15 AU with e=i0., The planetesimals start out between 10 and 15 AU with $e=i=0$. +" After 0.15 Myr (top panels), both resonances have reached the planetesimal population, and both appear unable to capture planetesimals."," After 0.15 Myr (top panels), both resonances have reached the planetesimal population, and both appear unable to capture planetesimals." + The passing of the resonances through the swarm of planetesimals is seen to have a very small effect on their orbital parameters., The passing of the resonances through the swarm of planetesimals is seen to have a very small effect on their orbital parameters. +" After 0.3 Myr the planet itself has migrated through the population of massless bodies, and has scattered most of them via direct encounters."," After 0.3 Myr the planet itself has migrated through the population of massless bodies, and has scattered most of them via direct encounters." +" Since the planetesimal orbits were not excited before the encounter, the relative velocity remained small, and the scattering events proved unable to get the planetesimal inclinations higher than a couple of degrees."," Since the planetesimal orbits were not excited before the encounter, the relative velocity remained small, and the scattering events proved unable to get the planetesimal inclinations higher than a couple of degrees." +"The resulting population, shown after 0.4 Myr in the bottom panels, is very similar to the one after 0.3 Myr, i.e., the planet has little effect on the bodies once it has migrated inside the population.","The resulting population, shown after 0.4 Myr in the bottom panels, is very similar to the one after 0.3 Myr, i.e., the planet has little effect on the bodies once it has migrated inside the population." +" During this simulation, of the planetesimals is accreted by the migrating planet."," During this simulation, of the planetesimals is accreted by the migrating planet." +"filly dominated by 3 -decavs (the most important ones being ος 7Si. 7Si(3 )""AL and οί )"" P. at the inner shells. whereas the outer envelope is dominated by 27"" ο. 29 S1, ure j ys. and ""N( j J Ar).","fully dominated by $\beta^+$ -decays (the most important ones being $^{28-30}$ $\beta^+$ $^{28-30}$ Si, $^{27}$ $\beta^+$ $^{27}$ Al, and $^{31}$ $\beta^+$ $^{31}$ P, at the inner shells, whereas the outer envelope is dominated by $^{29,30}$ $\beta^+$ $^{29,30}$ Si, $^{34m}$ $\beta^+$ $^{34}$ S, and $^{38}$ $\beta^+$ $^{38}$ Ar)." + At this stagec» of the evolution. the envelope shows dramatic changes in composition.," At this stage of the evolution, the envelope shows dramatic changes in composition." +" In particular. isotopes such as 77798, oH p, 2318 ΟΙ, 38558 AD or ""kN show a significant enhancement whereas 7""Si, 7°4S. το 7HE op SPA, ape elliciently destroved."," In particular, isotopes such as $^{28,29,30}$ Si, $^{30,31}$ P, $^{32-34}$ S, $^{35}$ Cl, $^{36,37}$ Ar or $^{38}$ K show a significant enhancement whereas $^{26}$ Si, $^{29-31}$ S, $^{27-29}$ P, $^{31-34}$ Cl, or $^{34}$ Ar are efficiently destroyed." + During the final stages of the outburst (Figs., During the final stages of the outburst (Figs. + 2 to 6. seventh panel). convection recedes from (he surface and the burning shell becomes detached from (the major part of the envelope. which is ultimately. ejected.," 2 to 6, seventh panel), convection recedes from the surface and the burning shell becomes detached from the major part of the envelope, which is ultimately ejected." +" When the envelope reaches a size of 107""10 cam. (he main nuclear path in the Si-Ca region is basically carried by 7""POs 75""sj; 72825109 premi A] BOSE, j yup. and “Clos y""$. with “POs y""Si being the dominant one within most of the envelope (again. contribution from "" C143. YS and K(9. y Ar ave important in the outer envelope)."," When the envelope reaches a size of $10^{10}$ cm, the main nuclear path in the Si-Ca region is basically carried by $^{28-30}$ $\beta^+$ $^{28-30}$ Si, $^{26,27}$ $\beta^+$ $^{26m,27}$ Al, $^{30,31}$ $\beta^+$ $^{30,31}$ P, and $^{33}$ $\beta^+$ $^{33}$ S, with $^{30}$ $\beta^+$ $^{30}$ Si being the dominant one within most of the envelope (again, contribution from $^{34m}$ $\beta^+$ $^{34}$ S and $^{38}$ $\beta^+$ $^{38}$ Ar are important in the outer envelope)." + Soon alter. when the envelope reaches a size of LO! em (Figs.," Soon after, when the envelope reaches a size of $10^{12}$ cm (Figs." + 2 to 6. eighth panel). most ol the © -unstable nuclei have already decaved.," 2 to 6, eighth panel), most of the $\beta^+$ -unstable nuclei have already decayed." +" Only (he medium-lived ones (7~ minutes). contribute vel to the energv production: “POs οι, ?""C1(63. YES. and IkK(4. y Ar."," Only the medium-lived ones $\tau \sim$ minutes), contribute yet to the energy production: $^{30}$ $\beta^+$ $^{30}$ Si, $^{34m}$ $\beta^+$ $^{34}$ S, and $^{38}$ $\beta^+$ $^{38}$ Ar." +" The mean composition of the ejecta in the Si-Ca mass region consists. for (lis particular model. mainlv of 7. 78i, 77S, and ! P. The most overproduced species with respect to solar are P and ""Si. with overproduction [actors (i.e.. ratios between mean mass fractions in the ejecta. over solar values) 1100 and 600. respectively."," The mean composition of the ejecta in the Si-Ca mass region consists, for this particular model, mainly of $^{28-30}$ Si, $^{32}$ S, and $^{31}$ P. The most overproduced species with respect to solar are $^{31}$ P and $^{30}$ Si, with overproduction factors (i.e., ratios between mean mass fractions in the ejecta over solar values) 1100 and 600, respectively." + 7S are overproduced by a factor ~ 100.," $^{32,33}$ S are overproduced by a factor $\sim$ 100." + In summary. nuclear activity in {je SiCa mass region is powered bv leakage from the NeNaMgAl region. where the activity is confined diring the early stages of the ourburst.," In summary, nuclear activity in the Si–Ca mass region is powered by leakage from the NeNa–MgAl region, where the activity is confined during the early stages of the ourburst." +" The main nuclear reaction that crives nueear aclivily towards heavier species bevond sulfur is Pips). through two different paths: either ""P(p.5) S(p.5) ?ClG44- 78 or ""P(p.5 σε P(p.5 )?> 5. Then. the nuclear flow is dramatically reduced by the slow ορ.) limiting the production of heavier isotopes in the S-Ca mass range."," The main nuclear reaction that drives nuclear activity towards heavier species beyond sulfur is $^{30}$ $\gamma$ ), through two different paths: either $^{30}$ $\gamma)^{31}$ $\gamma)^{32}$ $\beta+)^{32}$ S or $^{30}$ $\gamma)^{31}$ $\beta+)^{31}$ $\gamma)^{32}$ S. Then, the nuclear flow is dramatically reduced by the slow $^{32}$ $\gamma$ ) limiting the production of heavier isotopes in the S-Ca mass range." + The rates of the > ορ.) reactions have been discussed in José et al. (," The rates of the $^{26,27}$ $\gamma$ ) reactions have been discussed in José et al. (" +1999).,1999). + These reactions do not play a dominant role in (he path towards heavier species as photocdisinteeration of 7*P is effective (low Q-value) and. because the τσP lifetimes are small (< 1 5).," These reactions do not play a dominant role in the path towards heavier species as photodisintegration of $^{27}$ P is effective (low Q-value) and because the $^{27,28}$ P lifetimes are small $<$ 1 s)." + The 7SSip.sP reaction is the only significant. leak [rom the NeAl region towards heavier nuclei (Figure 1)., The $^{28}$ $\gamma)^{29}$ P reaction is the only significant leak from the Ne–Al region towards heavier nuclei (Figure 1). + Hence it is natural (o begin our analysis al (his point. referring for the discussion of rates in the NeAl chains to our previous paper (José et al.," Hence it is natural to begin our analysis at this point, referring for the discussion of rates in the Ne–Al chains to our previous paper (José et al." + 1999)., 1999). + Except for, Except for +"different approach, detected three main structures in Abell 85.","different approach, detected three main structures in Abell 85." + The two substructures (S; and S5) detected by Ramella et al. (, The two substructures $_{1}$ and $_{2}$ ) detected by Ramella et al. ( +2007) are close to the C2 and SB substructures reported by Bravo-Alfaro et al. (,2007) are close to the C2 and SB substructures reported by Bravo-Alfaro et al. ( +2009).,2009). + Figure 8 shows the substructure in Abell 85 obtained by our method., Figure \ref{f9} shows the substructure in Abell 85 obtained by our method. +" The substructure galaxies were those with ὃ>0599 and 6>6;99 for the M,«—20 (ECI) and M,«-19 (EC2) samples."," The substructure galaxies were those with $\delta>\delta_{g,99}$ and $\delta>\delta_{i,99}$ for the $M_{r}<-20$ (EC1) and $M_{r}<-19$ (EC2) samples." +" Note that in the EC1 and EC2 samples less substructure is measured when ὃς=ó,599."," Note that in the EC1 and EC2 samples less substructure is measured when $\delta_{c}=\delta_{g,99}$." + Only in the case of ECI are galaxies in substructure obtained in the central region of the cluster., Only in the case of EC1 are galaxies in substructure obtained in the central region of the cluster. +These galaxies are part of the C2 and S5 substructure detected by Bravo-Alfaro et al. (,These galaxies are part of the C2 and $_{2}$ substructure detected by Bravo-Alfaro et al. ( +2009) and Ramella et al. (,2009) and Ramella et al. ( +"2007), respectively.","2007), respectively." + The substructure measured by this method should thus be taken as a lower limit of the real value., The substructure measured by this method should thus be taken as a lower limit of the real value. + The situation is better when the galaxies in substructure are determined by ὅμοο.," The situation is better when the galaxies in substructure are determined by $\delta_{i,99}$." +" In this case, for the EC2 sample we obtain two groups of galaxies in substructures that correspond to the main groups of galaxies in substructure (C2 and SE) identified by (Bravo-Alfaroetal.2009) in this cluster."," In this case, for the EC2 sample we obtain two groups of galaxies in substructures that correspond to the main groups of galaxies in substructure (C2 and SE) identified by \cite{bravoalfaro09} in this cluster." + That we have not identified the other groups proposed by these authors might be related to the different galaxy population studied., That we have not identified the other groups proposed by these authors might be related to the different galaxy population studied. + Their observations are —2 magnitudes deeper than our data., Their observations are $\sim 2$ magnitudes deeper than our data. + Notice that we have not identified any galaxy from the substructure labeled F in Bravo-Alfaro et al. (, Notice that we have not identified any galaxy from the substructure labeled F in Bravo-Alfaro et al. ( +2009).,2009). +" Indeed, at the position of this group of galaxies there are no objects in our data (compare Fig."," Indeed, at the position of this group of galaxies there are no objects in our data (compare Fig." + 4 from Bravo-Alfaro et al., 4 from Bravo-Alfaro et al. + 2009 and our Fig., 2009 and our Fig. + 7)., 7). +" This could indicate that the galaxies of this substructure are fainter than M,——19 and they are not present in our galaxy sample.", This could indicate that the galaxies of this substructure are fainter than $M_{r}=-19$ and they are not present in our galaxy sample. +" As we have seen in previous sections, the completeness of the observations is important for the determination of the number of galaxies in substructure."," As we have seen in previous sections, the completeness of the observations is important for the determination of the number of galaxies in substructure." +" Indeed, variations in the abundance of dwarf galaxies within substructures have been previously observedas, for example, in the Hercules cluster (Sánnchez-Janssen et al."," Indeed, variations in the abundance of dwarf galaxies within substructures have been previously observedas, for example, in the Hercules cluster (Sánnchez-Janssen et al." + 2005)., 2005). + We would like also to note that no galaxies in substructure were obtained in Abell 85 for the case of EC2 with ὅροο.," We would like also to note that no galaxies in substructure were obtained in Abell 85 for the case of EC2 with $\delta<\delta_{g,99}$ ." + This might imply the variation of the 6 values from one cluster to another., This might imply the variation of the $\delta$ values from one cluster to another. + Some clusters might have galaxies with larger values of 6 that could bias 5g99 to larger values.," Some clusters might have galaxies with larger values of $\delta$ that could bias $\delta_{g,99}$ to larger values." + This is what happened for the EC2 sample; the value of 599 is so large that clusters like Abell 85 do not have galaxies in substructure according to this criterion.," This is what happened for the EC2 sample; the value of $\delta_{g,99}$ is so large that clusters like Abell 85 do not have galaxies in substructure according to this criterion." + This means that the galaxies in substructure selected in this way would be those with the highest values of ó and should be considered as a lower limit of galaxies in substructures., This means that the galaxies in substructure selected in this way would be those with the highest values of $\delta$ and should be considered as a lower limit of galaxies in substructures. +" The KS test revealed that radial and velocity distributions of galaxies brighter and fainter than M,=—22.0 were statistically different (at 99% C.L.).", The KS test revealed that radial and velocity distributions of galaxies brighter and fainter than $M_{r}=-22.0$ were statistically different (at $99\%$ C.L.). + This luminosity segregation was also observed in previous studies (see Biviano et al., This luminosity segregation was also observed in previous studies (see Biviano et al. + 2002)., 2002). +" In most of our clusters, galaxies brighter than M,=-22.0 are the first rank galaxies of the cluster (84% and 59% for EC! and EC2 respectively)."," In most of our clusters, galaxies brighter than $M_{r}=-22.0$ are the first rank galaxies of the cluster $\%$ and $\%$ for EC1 and EC2 respectively)." + Those bright galaxies are mostly located outside substructures., Those bright galaxies are mostly located outside substructures. + Only ~3—5% (at ECI and EC2) are located in substructures., Only $\approx 3-5\%$ (at EC1 and EC2) are located in substructures. +" Moreover, those bright galaxies located outside substructures are very clustered and show similar radial velocities to those of the mean cluster («η»*0.2 and «(v-νο/σε>0.5 for ECI and EC2)."," Moreover, those bright galaxies located outside substructures are very clustered and show similar radial velocities to those of the mean cluster $ \approx 0.2$ and $<(v-v_{c})/\sigma_{c}> \approx 0.5$ for EC1 and EC2)." +" Nevertheless, those galaxies with M,<--22.0 located in substructures are located in the outermost regions of the clusters («r/roog9>=1.05—1.42 for ECI and EC2 respectively)."," Nevertheless, those galaxies with $M_{r}<-22.0$ located in substructures are located in the outermost regions of the clusters $=1.05-1.42$ for EC1 and EC2 respectively)." +" The previous findings could indicate that those galaxies with M,«—22.0 and not in substructures would be mostly located at the bottom of the cluster potential.", The previous findings could indicate that those galaxies with $M_{r}<-22.0$ and not in substructures would be mostly located at the bottom of the cluster potential. +" In contrast, the small fraction of those bright galaxies located in substructures would be falling into the clusters associated with galaxy groups evolved in a merging process."," In contrast, the small fraction of those bright galaxies located in substructures would be falling into the clusters associated with galaxy groups evolved in a merging process." +" The origin of these bright galaxies (M,« —22.0) could be due to such accretion or merger processes (Governato et al.", The origin of these bright galaxies $M_{r}<-22.0$ ) could be due to such accretion or merger processes (Governato et al. + 2001; de Lucia et al., 2001; de Lucia et al. + 2007)., 2007). + Figure 9 shows the radial and velocity distributions of galaxies inside and outside substructures., Figure \ref{f7} shows the radial and velocity distributions of galaxies inside and outside substructures. + We have split the galaxy samples according to their u—r colours., We have split the galaxy samples according to their $u-r$ colours. + The red and relaxed galaxies are always located closer to the cluster centre than the blue and relaxed galaxy sample., The red and relaxed galaxies are always located closer to the cluster centre than the blue and relaxed galaxy sample. + Red galaxies outside substructures are always cooler than blue and relaxed ones., Red galaxies outside substructures are always cooler than blue and relaxed ones. + For galaxies in substructures it is also true than the red ones are cooler and are located closer to the cluster centre than the blue sample., For galaxies in substructures it is also true than the red ones are cooler and are located closer to the cluster centre than the blue sample. +" Nevertheless, galaxies outside substructures are basically inside 7299, in contrast to what happened for galaxies in substructures."," Nevertheless, galaxies outside substructures are basically inside $r_{200}$ , in contrast to what happened for galaxies in substructures." +" In earlier sections we saw that, in accordance with our selection criteria, our substructure galaxies are mainly located"," In earlier sections we saw that, in accordance with our selection criteria, our substructure galaxies are mainly located" +For this experiment. the images should be identical except for a known shift. defined to subpixel precision without introducing errors that are caused by the re-sampling needed for subpixel image shifting.,"For this experiment, the images should be identical except for a known shift, defined to subpixel precision without introducing errors that are caused by the re-sampling needed for subpixel image shifting." + We therefore start with a high-resolution image. degrade the resolution. shift it by a known number of whole high-resolution pixels. and then down-sample it to the SH image scale.," We therefore start with a high-resolution image, degrade the resolution, shift it by a known number of whole high-resolution pixels, and then down-sample it to the SH image scale." +" Specifically. we use a 2000x2000-pixel. high-quality SST G-band image with an image scale of O""004l/pixel. see Fig. là.."," Specifically, we use a $\times$ 2000-pixel, high-quality SST G-band image with an image scale of 041/pixel, see Fig. \ref{fig:GI}." + The image was recorded on 25 May 2003 by Mats Carlsson et from ITÀ in Oslo and corrected for atmospheric turbulence effects by use of Multi Frame Blind Deconvolution (Lófdahl2002).., The image was recorded on 25 May 2003 by Mats Carlsson et from ITA in Oslo and corrected for atmospheric turbulence effects by use of Multi Frame Blind Deconvolution \citep{lofdahl02multi-frame}. + We degraded it to 9.8 em hexagonal (edge to edge) subpupil resolution at 500 nm., We degraded it to 9.8 cm hexagonal (edge to edge) subpupil resolution at 500 nm. + This degraded image was shifted by integer steps from 0 to 20 times the high-resolution pixels. as well as in steps of 10 pixels from 30 to 60.," This degraded image was shifted by integer steps from 0 to 20 times the high-resolution pixels, as well as in steps of 10 pixels from 30 to 60." + The so degraded and shifted GIs were box-car compressed by a factor 10 to 200: 200 pixels of size OY441., The so degraded and shifted GIs were box-car compressed by a factor 10 to $\times$ 200 pixels of size 41. + This procedure gives images with known subpixel shifts. ὃν and ov. without any re-sampling. except for the compression.," This procedure gives images with known subpixel shifts, $\delta x$ and $\delta y$, without any re-sampling, except for the compression." + Figure Ib. shows a sample compressed image., Figure \ref{fig:degraded} shows a sample compressed image. + The data with 0-20 high-resolution pixel shifts were made to test subpixel accuracy. while the 30-60-pixel shifts are for testing linearity with larger shifts.," The data with 0–20 high-resolution pixel shifts were made to test subpixel accuracy, while the 30–60-pixel shifts are for testing linearity with larger shifts." + The diffraction limited resolution. ομι=1 at 500 nm. corresponds to >2 pixels.," The diffraction limited resolution, $\lambda/D_\text{sub}\approx1\arcsec$ at 500 nm, corresponds to $>2$ pixels." +" This means subpixel accuracy corresponds to super-resolution accuracy,", This means subpixel accuracy corresponds to super-resolution accuracy. + The resulting images had more contrast than the real data from our SH WFS. so some bias was added to change the RMS contrast to ~3% of the mean intensity.," The resulting images had more contrast than the real data from our SH WFS, so some bias was added to change the RMS contrast to $\sim$ of the mean intensity." + The resulting images were stored in two versions. with and without Gaussian noise with a standard deviation ofantsoplanatism.," The resulting images were stored in two versions, with and without Gaussian noise with a standard deviation of." +.. The digitization noise of a 12-bit camera is insignificant compared to the Gaussian noise but may be significant for an 8-bit camera., The digitization noise of a 12-bit camera is insignificant compared to the Gaussian noise but may be significant for an 8-bit camera. + We do not include the effects of digitization in our simulations., We do not include the effects of digitization in our simulations. + The 200x200-pixel FOV is much larger than the FOV of the SH WFS. which allows the use of many different. subfields in order to get better statistics.," The $\times$ 200-pixel FOV is much larger than the FOV of the SH WFS, which allows the use of many different subfields in order to get better statistics." + Centered on each of 17x17 σης positions. subimages. g. of size 16x16 or 24x24 pixels. were defined.," Centered on each of $\times$ 17 grid positions, subimages, $g$, of size $\times$ 16 or $\times$ 24 pixels, were defined." + The subimages defined in the unshifted reference image. ger were larger in order to accommodate a shift range limited to +8 pixels along each axis direction. except for CFF. which uses two images of equal size.," The subimages defined in the unshifted reference image, $g_\text{ref}$, were larger in order to accommodate a shift range limited to $\pm8$ pixels along each axis direction, except for CFF, which uses two images of equal size." + Note also that for CFF. the size of the correlation matrix is limited by the subimage size.," Note also that for CFF, the size of the correlation matrix is limited by the subimage size." + For 16 16-pixel subfields. this limits the range to £6 pixels (in reality to even less).," For $\times$ 16-pixel subfields, this limits the range to $\pm6$ pixels (in reality to even less)." + The different sizes of g. 16x16 and 24x24 pixels. have two purposes: 1) We want to see how a change in size affects some of the methods and 2) we will compare CFF using 24x24 pixels with the other methods using 16x16 pixels.," The different sizes of $g$, $\times$ 16 and $\times$ 24 pixels, have two purposes: 1) We want to see how a change in size affects some of the methods and 2) we will compare CFF using $\times$ 24 pixels with the other methods using $\times$ 16 pixels." + If the image geometry on the detector accommodates à 24x24-pixel gor. then it can also accommodate 24x24-pixel e subfields if no oversize reference image is needed.," If the image geometry on the detector accommodates a $\times$ 24-pixel $g_\text{ref}$, then it can also accommodate $\times$ 24-pixel $g$ subfields if no oversize reference image is needed." + We measured the shifts with each combination of CAs in 2.1 and IAs in 2.2.., We measured the shifts with each combination of CAs in \ref{sec:corr-algor} and IAs in \ref{sec:subpixel-interp}. + We do this with and without noise and with and without multiplying the reference image by 1:01. giving an approximate bias mismatch.," We do this with and without noise and with and without multiplying the reference image by 1.01, giving an approximate bias mismatch." + The bias mismatch sensitivity is investigated because it is known to be a problem with the ADF and ADF? methods., The bias mismatch sensitivity is investigated because it is known to be a problem with the ADF and $^2$ methods. +In general. isochrones assume the following prescription for initial helium: where Y is the initial helium. abundance of the star. Yp is the primordial helium abundance [rom big bang nucleosvnthesis. Z is the metallicity mass fraction of the star. and GNYAZ). is the slope derived by fitting a line from (he primordial values. (Zp.3p) (Simha&Steigman 2003).. to the solar values. (Z..Y3.)ez(0.018.0.272) (vanPinsonneault 2011).. vielding (AY/AZ).x 1.5.,"In general, isochrones assume the following prescription for initial helium: where $Y$ is the initial helium abundance of the star, $Y_{\rm{P}}$ is the primordial helium abundance from big bang nucleosynthesis, $Z$ is the metallicity mass fraction of the star, and $({\Delta}Y/{\Delta}Z)_{\odot}$ is the slope derived by fitting a line from the primordial values, $(Z_{\rm{P}}, Y_{\rm{P}}) = (0,0.249)$ \citep{2008JCAP...08..011S}, , to the solar values, $(Z_{\odot}, Y_{\odot}) \approx (0.018,0.272)$ \citep{2011arXiv1108.2273V}, yielding $({\Delta}Y/{\Delta}Z)_{\odot} \approx1.5$ ." + Some variation oceurs as some isochrones use the pre-WAIAP value Y»=0.235., Some variation occurs as some isochrones use the pre-WMAP value $Y_{P}=0.235$. + Equation (1)) is manilestly problematic., Equation \ref{EQ:Iisochrone}) ) is manifestly problematic. + There is no reason thal Y should be a single-parameter. deterministic function of Z: that such a function should be a first-order polynomial: or that AY/AZ should be a universal constant.," There is no reason that $Y$ should be a single-parameter, deterministic function of $Z$; that such a function should be a first-order polynomial; or that ${\Delta}Y/{\Delta}Z$ should be a universal constant." + Why is (he most abundant non-trivial element not generally incorporated as à varlable input into isochrones?, Why is the most abundant non-trivial element not generally incorporated as a variable input into isochrones? + It is siniply (oo difficult to measure: as the noble gas with (wo protons. it has the hiehest first ionization potential of auv element. 24.6 eV. For the purposes of this work. we define a helium-enhanced stellar population as being a stellar population with values of Y exceeding those predicted by Equation (1)).," It is simply too difficult to measure: as the noble gas with two protons, it has the highest first ionization potential of any element, 24.6 eV. For the purposes of this work, we define a helium-enhanced stellar population as being a stellar population with values of $Y$ exceeding those predicted by Equation \ref{EQ:Iisochrone}) )." + The effect. of helium. abundance on stellar evolution and thus inferred. ages can be significant. due to the higher mean molecular weight and lower initial central hvdrogen abundance accelerating the evolution of helinm-enhanced stars.," The effect of helium abundance on stellar evolution and thus inferred ages can be significant, due to the higher mean molecular weight and lower initial central hydrogen abundance accelerating the evolution of helium-enhanced stars." + Hence. applying standard isochrones to helium-enhanced populations leads one to overestimate photometric ages Franchetal. 2010)..," Hence, applying standard isochrones to helium-enhanced populations leads one to overestimate photometric ages \citep{2010ApJ...714.1072M}." + And further. as we will demonstrate. the opposite holds for spectroscopic determinations: ages will be underestimated.," And further, as we will demonstrate, the opposite holds for spectroscopic determinations: ages will be underestimated." + At fixed age and metallicitv. MSTO stars with hieher initial helium will be hotter aud more compact. and (hus bluer and dimmer.," At fixed age and metallicity, MSTO stars with higher initial helium will be hotter and more compact, and thus bluer and dimmer." + Their hieher temperatures nünic vounger ages on a οσο diagram. but their smaller sizes and thus lower luminosity vield a dimmer MSTO. mimicking older ages on à CMD.," Their higher temperatures mimic younger ages on a $\log{g}$ $T_{\rm{eff}}$ diagram, but their smaller sizes and thus lower luminosity yield a dimmer MSTO, mimicking older ages on a CMD." + On the SGD. the temperatures and bolometric Iuminosities become more similar. but not the surface eravilies. causing spectroscopic ages to be underestimated.," On the SGB, the temperatures and bolometric luminosities become more similar, but not the surface gravities, causing spectroscopic ages to be underestimated." + These ellects are easily discerned in Figure L.., These effects are easily discerned in Figure \ref{Fig:Dartmouth4}. + The assumption that AY/AZ is a constant has been demonstrated tobea spectacular [aure in GC's., The assumption that ${\Delta}$ ${\Delta}$ Z is a constant has been demonstrated tobea spectacular failure in GCs. + For example. w Cen. NGC 2808. and 47 Tuc have a strong diversity. of," For example, $\omega$ Cen, NGC 2808, and 47 Tuc have a strong diversity of" +that a ιαππι outcome of the eiission line radiation 1s frou jet sides moving in the wind.,that a maximum outcome of the emission line radiation is from jet sides moving in the wind. +" As a result of collision with the wind a cloud decelerates at a rate: Tere we used A, as the lower Πιτ of the iutegration because evolution of the jet at distances 2 data.","inferred by \cite{reddy09}, which also includes more recent high redshift points as well as a luminosity-dependent dust correction to the $z>2$ data." + We obtained the green long dashed line shown in Fig. 9.., We obtained the green long dashed line shown in Fig. \ref{fig:mdens}. +" Our results solve the discrepancy between the SMD and the integrated SFRD at z>2 (modulo the uncertainties affecting the z~2.1 redshift interval), especially when considering the dispersion caused by the inclusion of high mass 1/Vingx points from the other surveys."," Our results solve the discrepancy between the SMD and the integrated SFRD at $z>2$ (modulo the uncertainties affecting the $z\sim 2.1$ redshift interval), especially when considering the dispersion caused by the inclusion of high mass $1/V_{max}$ points from the other surveys." +" Consistency at high redshift was found by Mortlocketal.(2011) and Papovichetal.(2011),, the latter study being based on an independents analysis."," Consistency at high redshift was found by \cite{mortlock11} and \cite{papovich11}, the latter study being based on an independents analysis." +" Overall, our results support the notion that the SMD can be reasonably close to the integrated SFRD at z>2, mostly due to a steepening of the GSMF, although our results might be systematically too high because of the known overdensities in the small ERS field."," Overall, our results support the notion that the SMD can be reasonably close to the integrated SFRD at $z>2$, mostly due to a steepening of the GSMF, although our results might be systematically too high because of the known overdensities in the small ERS field." +" As mentioned, the higher values that we obtained than most previous studies is essentially due to the efficiency of WFC3 deep near-IR data to accurately recover the faint-end of the GSMF, especially at high redshift, which contributes significantly to the total SMD."," As mentioned, the higher values that we obtained than most previous studies is essentially due to the efficiency of WFC3 deep near-IR data to accurately recover the faint-end of the GSMF, especially at high redshift, which contributes significantly to the total SMD." +" However, the significant steepening in the faint-end slope presented in this work is insufficient to solve the disagreement at z<2, where the integrated SFRD exceeds the observed SMD by a factor of ~2—3, even when both of them are integrated down to low values of stellar mass / luminosity and adopting the SFRD computed by Reddy&Steidel(2009)."," However, the significant steepening in the faint-end slope presented in this work is insufficient to solve the disagreement at $z<2$, where the integrated SFRD exceeds the observed SMD by a factor of $\sim 2-3$, even when both of them are integrated down to low values of stellar mass / luminosity and adopting the SFRD computed by \cite{reddy09}." +". Their SFRD, although it is lower than that resulting from the best-fit relation of Hopkins&Beacom(2006) at z<2.5, is still unable to reconcile the two observables."," Their SFRD, although it is lower than that resulting from the best-fit relation of \cite{hopkins06} at $z<2.5$, is still unable to reconcile the two observables." +" The discrepancy is also not solved when our deep data, which allow a good control of the faint-end slope, are matched to the large surveys results to constrain the bright tail of the GSMF, and it gets even worse if one assumes that our mass density results are systematically too high owing to overdensities in the ERS field."," The discrepancy is also not solved when our deep data, which allow a good control of the faint-end slope, are matched to the large surveys results to constrain the bright tail of the GSMF, and it gets even worse if one assumes that our mass density results are systematically too high owing to overdensities in the ERS field." +" In Fig. 10,,"," In Fig. \ref{fig:mf_mod}," +" we compare our results with the predictions of semi-analytical models of galaxy formation and evolution, which follow the evolution of the baryonic component adopting an approximate description of the relevant physical processes (i.e. gas cooling, star formation, stellar feedback, black hole growth, and AGN feedback) and of their interplay with gravitational processes, linked to the assembly of the large-scale structure of the Universe."," we compare our results with the predictions of semi-analytical models of galaxy formation and evolution, which follow the evolution of the baryonic component adopting an approximate description of the relevant physical processes (i.e. gas cooling, star formation, stellar feedback, black hole growth, and AGN feedback) and of their interplay with gravitational processes, linked to the assembly of the large-scale structure of the Universe." + These “recipes” include a number of parameters that are usually fixed by comparing model predictions with a set of low-redshift observations., These “recipes” include a number of parameters that are usually fixed by comparing model predictions with a set of low-redshift observations. +" Despite their simplified approach, semi-analytical models have turned into a flexible and widely used tool to explore a broad range of specific physical assumptions, as well as the interplay between different physical processes."," Despite their simplified approach, semi-analytical models have turned into a flexible and widely used tool to explore a broad range of specific physical assumptions, as well as the interplay between different physical processes." +" We considered different, independently developed semi-analytical models: Menci (red dotted curves) updated to include the Reedetal.(2007) halo mass function, MORGANA (Monacoetal.2007,, as updated in LoFaroetal.2009,, blue long-dashed curves), Wangetal.(2008) (green dashed curves), and Somervilleetal.(2011) (orange dot-dashed curves)."," We considered different, independently developed semi-analytical models: \cite{menci06} (red dotted curves) updated to include the \cite{reed07} halo mass function, MORGANA \citealt{monaco07}, as updated in \citealt{lofaro09}, blue long-dashed curves), \cite{wang08} (green dashed curves), and \cite{somerville11} (orange dot-dashed curves)." + We refer to the original papers for a detailed description of the recipes adopted in the galaxy formation and evolution modelling., We refer to the original papers for a detailed description of the recipes adopted in the galaxy formation and evolution modelling. +" All three models of Wangetal.(2008),, Somervilleetal. (2011),, and MORGANA resolve galaxies with M.>10?Me, while the Mencietal.(2006) model has a lower mass limit of 10°Mo."," All three models of \cite{wang08}, \cite{somerville11}, , and MORGANA resolve galaxies with $M_* > 10^{9} M_\odot$, while the \cite{menci06} model has a lower mass limit of $10^8 M_\odot$." + The predicted stellar masses were convolved with a Gaussian error distribution on logM. (see Fig. 2)), The predicted stellar masses were convolved with a Gaussian error distribution on $M_*$ (see Fig. \ref{fig:errmass}) ) + to reproduce the observational uncertainties., to reproduce the observational uncertainties. + We refer the reader to Fontanot and Marchesinietal.(2009)for a detailed analysis of the effects of convolving the model predictions with observational errors., We refer the reader to \cite{fontanot09} and \cite{marchesini09} for a detailed analysis of the effects of convolving the model predictions with observational errors. + All stellar masses were converted to those for a Salpeter IMF., All stellar masses were converted to those for a Salpeter IMF. +Figure 5.,Figure 5. +" The XY and XZ projection of points (on the left) generated by the dynamical system defined by(5.34),, observed at time intervals At=1 starting from the initial condition (0.1,1.1,0.4), and points (on the right) generated by random sampling with the probability distribution(5.35).."," The XY and XZ projection of points (on the left) generated by the dynamical system defined by, observed at time intervals $\Delta t=1$ starting from the initial condition $(x,y,z)=(0.1,1.1,0.4)$ , and points (on the right) generated by random sampling with the probability distribution." + 20pt Comparing connected associated with the probability distribution with moments generated by the chaotic trajectory suggests that the two agree. (, 20pt Comparing connected associated with the probability distribution with moments generated by the chaotic trajectory suggests that the two agree. ( +see table 3).,see table 3). + 20pt 20pt, 20pt 20pt +But the relationship between P=O3;// aud the big beud tn (A) is derived assumiug that matter aud radiation are the ouly siguificant. coutributors to the density. at La the redshift of matter-radiation equality.,"But the relationship between $\Gamma = \Omega_M h$ and the big bend in $P(k)$ is derived assuming that matter and radiation are the only significant contributors to the density at $z_{eq}$, the redshift of matter-radiation equality." + Prior to σος the Universe is expandiug faster than the free-fall tine for matter perturbations. so growth is suppressed for fluctuations that are iuside the borizou earlier than z44.," Prior to $z_{eq}$, the Universe is expanding faster than the free-fall time for matter perturbations, so growth is suppressed for fluctuations that are inside the horizon earlier than $z_{eq}$." +" To allow for the possibility that dark energy contributes. 2,4 is found using +O. The horizon at z;4 is found using = Then the effective value of D is Eg=(1602kin/sec)/(H.0D.,)."," To allow for the possibility that dark energy contributes, $z_{eq}$ is found using = + + ) The horizon at $z_{eq}$ is found using = Then the effective value of $\Gamma$ is $\Geff = (1602\;\mbox{km/sec})/(H_\circ D_{eq})$." +" By finding the effective Pg al two different values for H«. which leads to two different values for Qj since μή is fixed by the measurement of 75. the standard D—QO3;// cau be replaced by a modified power law fuuctiou of /i which reduces to the standard frin except when the dark energy issignificant near 2,4."," By finding the effective $\Geff$ at two different values for $H_\circ$, which leads to two different values for $\Omega_R$ since $\Omega_R h^2$ is fixed by the measurement of $T_\circ$, the standard $\Gamma = \Omega_M h$ can be replaced by a modified power law function of $h$ which reduces to the standard form except when the dark energy issignificant near $z_{eq}$ ." +" Por example. in the track of models shown i Figure L. when ppg/p«za=0.138 at τες one has Qa,=0.2083. w=—1.098 and «=0.570."," For example, in the track of models shown in Figure \ref{fig:R-ell_a}, when $\rho_{DE}/\rho_{\gamma m} = 0.138$ at $z_{LS}$ one has $\Omega_M = 0.2983$, $w = -1.098$ and $w^\prime = 0.570$." + These values give w(z)—0.012 a 107. so the dark energy density grows faster than the matter «eusity but slower than the radiation deusity at high z.," These values give $w(z) = 0.042$ at $z >> 10^3$, so the dark energy density grows faster than the matter density but slower than the radiation density at high $z$." + For these parameters oue finds that Dg=0.171701 for bh=0.679373373 and Fog=0.188939 [or h=0.716102., For these parameters one finds that $\Geff = 0.171704$ for $h = 0.675373$ and $\Geff = 0.188939$ for $h = 0.746402$. +" Fitting a power law function of / gives Pog=0.2L990fh!P""i instead of the standard 0.20834.", Fitting a power law function of $h$ gives $\Geff \approx 0.2499 h^{0.95657}$ instead of the standard $0.2983 h$. +" For h=0.71 this is a dillerence which is quite sienilicant compared to the precision of the mean of the P's from the SDSS aud the 2dF. When finding X7. a weighted mean estimate for / is found using the EF. Hz and oy, priors."," For $h = 0.71$ this is a difference which is quite significant compared to the precision of the mean of the $\Gamma$ 's from the SDSS and the 2dF. When finding $\chi^2$, a weighted mean estimate for $h$ is found using the $\Gamma$, $H_\circ$ and $\omega_m$ priors." + This weighted mean minimizes the 4? contribution [roin these three priors. aud this minimum is added to the 4? from the Hubble diagram. CMB. and the BAO.," This weighted mean minimizes the $\chi^2$ contribution from these three priors, and this minimum is added to the $\chi^2$ from the Hubble diagram, CMB, and the BAO." + Therefore / becomes a third nuisance parameter., Therefore $h$ becomes a third nuisance parameter. + Then tin bo Mss asec OF ey A ua MTU . > ↓⊳∖⋜∥⇂≺⇂↩≺⊓∩↕∐↩∩∖⇁≺↵↓⋅⋜↕∐∖−⋅⇀−∖⊳∖↕∐≺↵≺⇂⋜⋃⋅," Then ) = _h ,h) )) + _M h^2 - _M)+ ((h - (h))] is added to the overall $\chi^2$ ." +↕⊆≺↵∐≺↵↥⋅∑≟⊽∖⇁∣⋈↵∢∙∩⋯≺↵⊳∖⊳∖↓∑≟∐∐∐∙⋜↕∐↕⋜↕↕↓⋅≺↵∢∙∩⋯∣∐∐⋜↕⋃∩∐⋅≤≥⋏⋃∐⋜↕⊳∖ H⋅⋅ ⋅ ↕∩↥∐∢↝↕⋅≺↵⋜↕⊳∖≺↵↕∩↕⊊≺↵≺↵↥↽≻↕∐≺↵≺↵∐⇀≺↵∢↝∏∖⇁≺↵↕↴∢↝↥∩⊳∖≺↵↕∩↕∐≺↵∩∣≽⊳∖≺↵↕," As thedark energy becomes significant at recombination, $\Omega_M$ has to increase to keep the effective $\Gamma$ close to the observed value." +⋅∖⇁≺↵≺⇂∖⇁⋜≹∐∐↵−∐⋅∖∖↽≺↵↕⋜↕↕⊆≺↵∐∐↵⊳∖⋜⋃∐≺↵∩⊽∶≓⊽⊔⋗∪↖∖⋅ , If we take the same $w = -1.098$ +We calculated the galaxy luminosity density field. to reconstruct the underlying mass distribution.,We calculated the galaxy luminosity density field to reconstruct the underlying mass distribution. + To determine superclusters (extended systems of galaxies) in the luminosity density field we created a set of deasity contours by choosing a density threshold and defite connected volumes above a certain density threshold as stperclusters., To determine superclusters (extended systems of galaxies) in the luminosity density field we created a set of density contours by choosing a density threshold and define connected volumes above a certain density threshold as superclusters. + In order to choose proper density levels to determine individual superclusters. we analysed the density field superclusters at a series of density levels.," In order to choose proper density levels to determine individual superclusters, we analysed the density field superclusters at a series of density levels." + As a result we used the density level D=5.0 (in units of mean density: mean luminosity dersity of our sample Is £i = 1526107 T5.) to determine individual superclusters., As a result we used the density level $D = 5.0$ (in units of mean density; mean luminosity density of our sample is $\ell_{\mathrm{mean}}$ = $\cdot10^{-2}$ $\frac{10^{10} h^{-2} L_\odot}{(\vmh)^3})$ to determine individual superclusters. + At this density level supercltsters in the richest chains of superclusters in the volume under study still form separate systems; at lower density levels they Join into huge percolating systems., At this density level superclusters in the richest chains of superclusters in the volume under study still form separate systems; at lower density levels they join into huge percolating systems. + At higher threshold density levels superclusters are smaller and their number decreases., At higher threshold density levels superclusters are smaller and their number decreases. + In our flux-limited catalogue the luninosity-dependent selection effects are the smallest at the distance interval 90 €Deom< 320Mpe.., In our flux-limited catalogue the luminosity-dependent selection effects are the smallest at the distance interval 90 $\le D_\mathrm{com} \le $ 320. + For the present study we chose superclusters of galaxies in this distance interval., For the present study we chose superclusters of galaxies in this distance interval. + There are 125 superclusters in the sanple., There are 125 superclusters in the sample. + Even the poorest systems in our sample contain several groups of galaxies., Even the poorest systems in our sample contain several groups of galaxies. + These systems can be compared with the Local supercluster containing one cluster of galaxies with outgoing filaments., These systems can be compared with the Local supercluster containing one cluster of galaxies with outgoing filaments. + In the Appendix AppendixA: we give the details of the calculations of galaxy luminosities and of the luminosity density field. as well as of the selection effects.," In the Appendix \ref{sec:DF} we give the details of the calculations of galaxy luminosities and of the luminosity density field, as well as of the selection effects." + The descriptior of the supercluster catalogues is given inL10., The description of the supercluster catalogues is given in. +. The superclusters can be characterised by the following physical parameters: the total weighted luminosity of galaxies in a supercluster. Ly. the volume Volume. the diameter Diameter. and the number of galaxies in superclusters. Ngal," The superclusters can be characterised by the following physical parameters: the total weighted luminosity of galaxies in a supercluster, $L_g$, the volume $Volume$, the diameter $Diameter$, and the number of galaxies in superclusters, $N_{\mbox{gal}}$." + The supercluster volume is calculated from the density field as the number of connected grid cells multiplied by the cell volume: where A is the grid cell length., The supercluster volume is calculated from the density field as the number of connected grid cells multiplied by the cell volume: where $\Delta$ is the grid cell length. +" The total luminosity of the superclusters L, is calculated as the sum of weighted galaxy luminosities: Here the Wy(d..)) 1s the distance-dependent weight of a galaxy (the ratio of the expected total luminosity to the luminosity within the visibility window).", The total luminosity of the superclusters $L_g$ is calculated as the sum of weighted galaxy luminosities: Here the $W_L(d_{\mathrm{gal}})$ is the distance-dependent weight of a galaxy (the ratio of the expected total luminosity to the luminosity within the visibility window). + We describe the calculation of weights in Appendix AppendixA:.., We describe the calculation of weights in Appendix \ref{sec:DF}. + The diameter of a supercluster is defined as the maximum distance between its galaxies., The diameter of a supercluster is defined as the maximum distance between its galaxies. + The distance of a supercluster is the distance to 1€s density maximum., The distance of a supercluster is the distance to it's density maximum. + The peak density Doeak Is that of the highest density peak within the supercluster., The peak density $D_{\mbox{peak}}$ is that of the highest density peak within the supercluster. + Usually the highest values of densities coincide with the richest cluster of galaxies in a supercluster., Usually the highest values of densities coincide with the richest cluster of galaxies in a supercluster. + For details we refer to L10., For details we refer to L10. +" The overall morphology of a supercluster is described by the shapefinders A, (planarity) and A> (filamentarity). and their ratio. Kj/K*. (the shape parameter)."," The overall morphology of a supercluster is described by the shapefinders $K_1$ (planarity) and $K_2$ (filamentarity), and their ratio, $K_1$ $K_2$ (the shape parameter)." + The shapefinders are calculated using the volume. area. and integrated mean curvature ofa supercluster: they contain information both about the sizes of superclusters and about their outer shape.," The shapefinders are calculated using the volume, area, and integrated mean curvature of a supercluster; they contain information both about the sizes of superclusters and about their outer shape." + Systems with different shapes and similar sizes have different shape parameters(?)., Systems with different shapes and similar sizes have different shape parameters. +. For the first time the shapefinders were applied in the studies of galaxy systems by who analysed the shapes of the PSCz superclusters., For the first time the shapefinders were applied in the studies of galaxy systems by who analysed the shapes of the PSCz superclusters. + We use the maximum value of the fourth Minkowski functional V3 (the clumpiness) to characterise the inner structure of the superclusters., We use the maximum value of the fourth Minkowski functional $V_3$ (the clumpiness) to characterise the inner structure of the superclusters. + The larger the value of Vi. the more complicated the inner morphology of a supercluster is: superclusters may be clumpy. and they also may have holes or tunnels in them (??)..The formulae for the Minkowski functionals and shapefinders are given in App.Appendix B:..," The larger the value of $V_3$, the more complicated the inner morphology of a supercluster is; superclusters may be clumpy, and they also may have holes or tunnels in them .The formulae for the Minkowski functionals and shapefinders are given in \ref{sec:MF}. ." +quasars.,quasars. + They interpret this relation as evidence for the preseuce of dust in the associate aabsorbers. which reddens the optical coutiuuuau.," They interpret this relation as evidence for the presence of dust in the associated absorbers, which reddens the optical continuum." + The gas and dust emission often trace cach other 2000).. sugeestingOO that he associated absorbers seen in both quasars aud radio galaxies probe the large eas aud dust reservoirs surrounding ACNs.," The gas and dust emission often trace each other , suggesting that the associated absorbers seen in both quasars and radio galaxies probe the large gas and dust reservoirs surrounding AGNs." + The presence of CO from these reservoirs imiplies that they contain processed material., The presence of CO from these reservoirs implies that they contain processed material. + This metal cussion is sonietinies also seen in cussion in extended haloes of1519.. aand citepiunax02.," This metal emission is sometimes also seen in emission in extended haloes of, and ." +vilü03... They max have been deposited bv previous nierecr events. or by starburst-driven superwinds at even higher redshifts 2003).," They may have been deposited by previous merger events, or by starburst-driven superwinds at even higher redshifts ." +". Indeed. discuss evidence that a superwind occurs ina 2=3.09 ""blob of ccluission Which also cimits strongly at subi waveleugtlis2001)."," Indeed, discuss evidence that a superwind occurs in a $z=3.09$ “blob” of emission which also emits strongly at submm wavelengths." +. Such objects nav be related ο HIzRCs. wwhen observe durmg a radio-quiet phase.," Such objects may be related to HzRGs, when observed during a radio-quiet phase." + To sunnarize. our observations of D3 J2330|3927 xovide further evidence that ITZRCis are massive galaxies. ocated in a dense. interacting environment.," To summarize, our observations of B3 J2330+3927 provide further evidence that HzRGs are massive galaxies, located in a dense, interacting environment." + Deep neur-IB imaging with Weck2002).. UST2001).. aud erouud-based adaptive optics shows that the host galaxies are often surrounded bv füuter clamps. like objects aud in D3 J2330|3926.," Deep near-IR imaging with Keck, HST, and ground-based adaptive optics shows that the host galaxies are often surrounded by fainter clumps, like objects and in B3 J2330+3926." + These clamps may well be couceutrations within the large eas/dust reservoir surroundiug the ACN. which will eventually merge with the massive central ealaxy hosting the ACN.," These clumps may well be concentrations within the large gas/dust reservoir surrounding the AGN, which will eventually merge with the massive central galaxy hosting the AGN." + Taving found evidence that the host ealaxy of D3 J2330|3927 is surrounded bv a luge gas reservoir. which has already been chemically enriched. it d8 of interest to estimate the ongoing star formation rate in this galaxy.," Having found evidence that the host galaxy of B3 J2330+3927 is surrounded by a large gas reservoir, which has already been chemically enriched, it is of interest to estimate the ongoing star formation rate in this galaxy." + We cannot use the rest-frame UV and optical cussion lines. because they are uainlv ionized bv the AGN. iud not bv massive stars.," We cannot use the rest-frame UV and optical emission lines, because they are mainly ionized by the AGN, and not by massive stars." + Similarly. the UV continuum cussion is Likely to be contaminated bv a scattered quasar component2001a).," Similarly, the UV continuum emission is likely to be contaminated by a scattered quasar component." +. We therefore determine au upper Inuuit to the elobal star formation rate of the cutive svstei using the far-IR (FIR) dust enission., We therefore determine an upper limit to the global star formation rate of the entire system using the far-IR (FIR) dust emission. +" We can cetermiune the total FIR ΠΠ λε inteerating the thermal spectra: vieldiug: where D aud ¢ are the Cóunnma aud Bienuanu ς functions. respectively,"," We can determine the total FIR luminosity by integrating the thermal spectrum: yielding: where $\Gamma$ and $\zeta$ are the Gamma and Riemann $\zeta$ functions, respectively." +" Substituting equation (3) aud e=hry/kTa.we fiud: For the values adopted in this paper. we fd: Tn 83.5. we have argued that the dust ciission probably consists of a ceutral compoucut near the ACN, and a spatially extended compoucut."," Substituting equation (3) and $x=h\nu_{\rm rest}/k T_{\rm d}$, we find: For the values adopted in this paper, we find: In 3.5, we have argued that the dust emission probably consists of a central component near the AGN, and a spatially extended component." + This would imply that the power source of the FIR cutission is a combination of direct heating by the AGN (heating the ceutral component) and w recently forme llassive stars il a starburst Cheating the extended component)., This would imply that the power source of the FIR emission is a combination of direct heating by the AGN (heating the central component) and by recently formed massive stars in a starburst (heating the extended component). + It is uulikelv that the AGN can power the dust emission out to several tens of kpe. while the detection of several companion objects iu the optical aud near-IR images suggests the presence of stars out to LO kpe.," It is unlikely that the AGN can power the dust emission out to several tens of kpc, while the detection of several companion objects in the optical and near-IR images suggests the presence of stars out to $\sim$ 40 kpc." + Following(2001).. we can then calculate the star formation rate where óygg is a function of the stellar mass function. and dyp is the fraction of the FIR cuiission heated by the starburst.," Following, we can then calculate the star formation rate where $\delta_{\rm MF}$ is a function of the stellar mass function, and $\delta_{\rm SB}$ is the fraction of the FIR emission heated by the starburst." + Asstumine conservatively ὄνῃι=1. we fined report star-formation rates up to 1500 AL.sr3 in the 2 other HzRGs where CO 3249)01 has been detected.," Assuming conservatively $\delta_{\rm MF}=1$, we find report star-formation rates up to 1500 ${\rm M}_{\odot}{\rm yr}^{-1}$ in the 2 other HzRGs where CO emission has been detected." + Because óup is likely to be sjenificautlv smaller than 1. our values are probably lower.," Because $\delta_{\rm SB}$ is likely to be significantly smaller than 1, our values are probably lower." + Nevertheless. they are still extremely ligh. indicating that we are witnessing a major starburst phase. possibly trigecred bv the interaction and/or mnereius of the different nearby companion objects seen iu the fy band nuage.," Nevertheless, they are still extremely high, indicating that we are witnessing a major starburst phase, possibly triggered by the interaction and/or merging of the different nearby companion objects seen in the $K-$ band image." + The main results from our multi-frequeucey. observations of D3 J2330|3927 are: e We detect the CO J=13 line with a full velocity width of ~500 aat the position of the AGN host galaxy., The main results from our multi-frequency observations of B3 J2330+3927 are: $\bullet$ We detect the CO $J=4-3$ line with a full velocity width of $\sim$ 500 at the position of the AGN host galaxy. +" The line is centered at 2=3.091, much closer to the ceutral velocity of the associated aabsorber in tthan to the systemic redshift determined from the liue."," The line is centered at $z=3.094$, much closer to the central velocity of the associated absorber in than to the systemic redshift determined from the line." + This strongly suggests the CO cinission and associated aabsorption both originate from the samc gas reservoir surrounding the WzRC., This strongly suggests the CO emission and associated absorption both originate from the same gas reservoir surrounding the HzRG. +are located in 47 Tuc.,are located in 47 Tuc. +" So far, ~800 ksee deep Chandra observations found X-ray pulses from only three of the nineteen 47 Tue millisecond pulsars (Cameronetal.2007)."," So far, $\sim 800$ ksec deep Chandra observations found X-ray pulses from only three of the nineteen 47 Tuc millisecond pulsars \citep{Cameron2007}." +. We used the archival HRC-S data (cf., We used the archival HRC-S data (cf. + Table 1)) to re-analyze these data in order to consistently determine their temporal emission properties., Table \ref{t:observations}) ) to re-analyze these data in order to consistently determine their temporal emission properties. + The ephemeris we used are summarized in Table 7.., The ephemeris we used are summarized in Table \ref{t:ephemeris}. +" X-ray pulses are reported for PSR JO024-7204D, PSR J0024-7204O and PSR J0024-7204R. PSR is a solitary pulsar spinning at a period of 5.35 ms."," X-ray pulses are reported for PSR J0024-7204D, PSR J0024-7204O and PSR J0024-7204R. PSR J0024-7204D is a solitary pulsar spinning at a period of 5.35 ms." + PSRs OO.R are in binaries (Camilo et al.," PSRs O,R are in short-period binaries (Camilo et al." + 2000) with a ~0.02 M.. companion., 2000) with a $\sim 0.02$ $_\odot$ companion. +" Their oorbit periods are 2.64 //33.26 h and 3.48 11.58 h, respectively."," Their orbit periods are 2.64 3.26 h and 3.48 1.58 h, respectively." +" For analyzing their temporal emission properties we selected all events from circular regions of radius 1 arcsec or 1.5 arcsec, centered on the pulsar position."," For analyzing their temporal emission properties we selected all events from circular regions of radius 1 arcsec or 1.5 arcsec, centered on the pulsar position." + The smaller selection radius was used for OO.R in order to minimize a possible flux contribution from neighboring sources located in the crowded cluster center (cf.," The smaller selection radius was used for O,R in order to minimize a possible flux contribution from neighboring sources located in the crowded cluster center (cf." + Figure 2))., Figure \ref{figure2}) ). + The baryeentered photon arrival times were coherently folded with the extrapolated to the epoch fp listed in Table 7.., The barycentered photon arrival times were coherently folded with the spin-period extrapolated to the epoch $t_0$ listed in Table \ref{t:ephemeris}. + The =;—-test (Buccheri De Jager 1989) was applied for n=1—10 harmonics in combination with the H-test (de Jager 1987) to determine the significance of the pulsed signal as a function of its harmonic content., The $z^2_n$ -test (Buccheri De Jager 1989) was applied for $n=1-10$ harmonics in combination with the H-test (de Jager 1987) to determine the significance of the pulsed signal as a function of its harmonic content. +" According to this tests the pulsations in PSR DD.R have the highest significance of 3.646, and 3.966 for n=2 harmonics whereas the pulsed signal in JOO24-72040 is found to have a significance of 4.84o for i1z3 harmonics."," According to this tests the pulsations in PSR D,R have the highest significance of $3.64\,\sigma$ , and $3.96\,\sigma$ for $n=2$ harmonics whereas the pulsed signal in J0024-7204O is found to have a significance of $4.84\sigma$ for $n=3$ harmonics." + The pulse profiles are shown in Figure 12.., The pulse profiles are shown in Figure \ref{figure12}. +" They all appear to be double peaked with a phase separation of 0.44+0.06, 0.50+0.02 and 0.4+0.04 for PSRs DD.O.R. The phase width of the two peaks are 0.42£0.1 (FWHMD and 0.25x0.15 (FWHM) for PSR DD. 0.15£0.04 (FWHM) and 0.27£0.02 (FWHM) for PSR OO and 0.2£0.06 (FWHM) and 0.32£0.05 (FWHM) for PSR J0024-7204R. For the fraction of pulsed photons we measured 60+15% for PSR J0024—7204 DD. 57415% for PSR J0024—7204 OO and 64+17% for PSR J0024—7204 RR using a bootstrap method (cf."," They all appear to be double peaked with a phase separation of $0.44\pm 0.06$, $0.50\pm 0.02$ and $0.4\pm 0.04$ for PSRs D,O,R. The phase width of the two peaks are $0.4\pm 0.1$ (FWHM) and $0.25\pm 0.15$ (FWHM) for PSR D, $0.15\pm 0.04$ (FWHM) and $0.27\pm 0.02$ (FWHM) for PSR O and $0.2\pm 0.06$ (FWHM) and $0.32\pm 0.05$ (FWHM) for PSR J0024-7204R. For the fraction of pulsed photons we measured $60\pm 15 \%$ for PSR $-$ D, $57\pm 15\%$ for PSR $-$ O and $64\pm 17 \%$ for PSR $-$ R using a bootstrap method (cf." + Becker Trümmper 1999; Swanepoel et al., Becker Trümmper 1999; Swanepoel et al. + 1996)., 1996). + Figure 13. shows the pulsar's X-ray profiles together with their corresponding radio profiles observed at 1400 MHz by Freire et al. (, Figure \ref{figure13} shows the pulsar's X-ray profiles together with their corresponding radio profiles observed at 1400 MHz by Freire et al. ( +2010. in prep.).,"2010, in prep.)." +" The 3.2 s frame time of the ACIS-S detector does not allow to search for coherent X-ray pulsations from the clusters"" millisecond pulsars.", The 3.2 s frame time of the ACIS-S detector does not allow to search for coherent X-ray pulsations from the clusters' millisecond pulsars. +" Most of the sources considered in this work, though, were in the focus of the ACIS-S for multiple times, permitting us to investigate their temporal behavior on longer time scales."," Most of the sources considered in this work, though, were in the focus of the ACIS-S for multiple times, permitting us to investigate their temporal behavior on longer time scales." + The length of the time scales in the various datasets is given by the time gaps between the different observations. e.g. hours to years.," The length of the time scales in the various datasets is given by the time gaps between the different observations, e.g. hours to years." + We checked the countingrates of all pulsars for variability (cf., We checked the countingrates of all pulsars for variability (cf. + Table 5))., Table \ref{t:xraydetections}) ). + Binary pulsars (cf., Binary pulsars (cf. + Table 3)) were tested on whether they show flux variability related to e.g. their orbital binary, Table \ref{t:ms-detected-basicproperties}) ) were tested on whether they show flux variability related to e.g. their orbital binary +of ANPs is mace feasible by the soft response of USA and the eood absolute timine.,of AXPs is made feasible by the soft response of USA and the good absolute timing. + Rotation-powered (radio) pulsars are also observed by USA to validate the time transfer between USA aud RNTE. aud to measure the radio to N-rav offset of the pulses.," Rotation-powered (radio) pulsars are also observed by USA to validate the time transfer between USA and RXTE, and to measure the radio to X-ray offset of the pulses." +" Cataclysinic variables (CVs) exhibit a wide range of timing phenomena.ιοπιοπας QPOs, X-rav trausicuts. and comples. light curves."," Cataclysmic variables (CVs) exhibit a wide range of timing phenomena,including QPOs, X-ray transients, and complex light curves." + While CVs are typically times fainter than LAINBs. their dvuamical time scales are ~LOOO tines longer.," While CVs are typically $\sim 100$ times fainter than LMXBs, their dynamical time scales are $\sim 1000$ times longer." + Moreover the magnetic CVs. which will be USAs prine targets amoung CVs are distiuguished by having the largest magnetic moments among known stellar populations. inchiding even magnuetars.," Moreover the magnetic CVs, which will be USA's prime targets among CVs are distinguished by having the largest magnetic moments among known stellar populations, including even magnetars." + Curiously. accretion-induced QPOs were predicted historically to result from this flow before they were observed.," Curiously, accretion-induced QPOs were predicted historically to result from this flow before they were observed." + The QPOs have been seeu repeatedly in optical waveleneths but never iu N-ravs. despite searches.," The QPOs have been seen repeatedly in optical wavelengths but never in X-rays, despite searches." + Highly correlated optical and X-ray Iuuninosity variations are predicted im current bydrodvuamic models (Wolff. Wood Tamura 1991) Finally. USA can exploit its ereat flexibility to observe targets of opportunity that are decined important by the science working eroup.," Highly correlated optical and X-ray luminosity variations are predicted in current hydrodynamic models (Wolff, Wood Imamura 1991) Finally, USA can exploit its great flexibility to observe targets of opportunity that are deemed important by the science working group." + Already. USA lias observed Aql X-1. the Rapid Burster. and X1630-172 during outbursts.," Already, USA has observed Aql X-1, the Rapid Burster, and X1630-472 during outbursts." + Of course. the accreting millisecond pulsar SAXJ1808.1-3658 would be of particular interest if it becomes active during the USA mission.," Of course, the accreting millisecond pulsar SAXJ1808.4-3658 would be of particular interest if it becomes active during the USA mission." + The detector (Table 1) consists of two iultivire constaut flow proportional counters equipped with a 5.0 pau λίαν window and an additional 1.9 gan thick aluninized Movlax heat shield., The detector (Table 1) consists of two multiwire constant flow proportional counters equipped with a 5.0 $\mu$ m Mylar window and an additional 1.9 $\mu$ m thick aluminized Mylar heat shield. + The detector is filled with a mixture of argon and nunethane (P-10) at a pressure of 16.1 psia (at room temperature)., The detector is filled with a mixture of argon and methane (P-10) at a pressure of 16.1 psia (at room temperature). + The detector interior contains an array of wires which provides two lavers of nime 2.8 cni square cells. cach containing oue anode wire. runing the leneth of the counter.," The detector interior contains an array of wires which provides two layers of nine 2.8 cm square cells, each containing one anode wire, running the length of the counter." + Au additional wire runs around the periphery ofthe array as part of tle cosmic ray. veto svsteun., An additional wire runs around the periphery of the array as part of the cosmic ray veto system. +"Moreover, comparing the pressurised virial masses of the cores with those estimated from the CO data reveals that SFO 75 and SFO 76 are both more than a factor of two more massive than the critical pressurised viral mass.","Moreover, comparing the pressurised virial masses of the cores with those estimated from the CO data reveals that SFO 75 and SFO 76 are both more than a factor of two more massive than the critical pressurised viral mass." + It is therefore likely that the exposure of these two cores to their respective HII regions has rendered them unstable against gravitational collapse., It is therefore likely that the exposure of these two cores to their respective HII regions has rendered them unstable against gravitational collapse. +" However, detailed hydrodynamical or radiative transfer modelling (e.g. ??)) of higher signal-to-noise molecular line data are needed to investigate the presence of collapse motions in these clouds."," However, detailed hydrodynamical or radiative transfer modelling (e.g. \citealt{thompson-white2004,deVries2005}) ) of higher signal-to-noise molecular line data are needed to investigate the presence of collapse motions in these clouds." +" Once a cloud has reached the cometary stage the shocks dissipate, however, the cloud’s mass continues to be slowly eroded away as the D-type ionisation front continues to propagate intoit (?))."," Once a cloud has reached the cometary stage the shocks dissipate, however, the cloud's mass continues to be slowly eroded away as the D-type ionisation front continues to propagate intoit \citealt{lefloch1994}) )." + In this situation the propagation of the ionisation front leads to a constant mass loss in the form of a photo-evaporated flow into the HII region (?))., In this situation the propagation of the ionisation front leads to a constant mass loss in the form of a photo-evaporated flow into the HII region \citealt{megeath1997}) ). +" The amount of material within the boundary of a cloud is finite, and thus the effect of the ionisation is to slowly erode the limited reservoir of material available for star formation."," The amount of material within the boundary of a cloud is finite, and thus the effect of the ionisation is to slowly erode the limited reservoir of material available for star formation." +" This mass loss eventually results in the total ionisation and dispersion of the cloud, and perhaps the disruption of ongoing star formation either by disrupting any molecular cores before the accretion phase has begun, or by exposing the protostar to the FUV radiation field before the accretion phase has finished."," This mass loss eventually results in the total ionisation and dispersion of the cloud, and perhaps the disruption of ongoing star formation either by disrupting any molecular cores before the accretion phase has begun, or by exposing the protostar to the FUV radiation field before the accretion phase has finished." +" Once the protostar has been exposed much of the surrounding envelope of molecular material becomes ionised, therefore limiting the possible size of the forming protostar (see ?))."," Once the protostar has been exposed much of the surrounding envelope of molecular material becomes ionised, therefore limiting the possible size of the forming protostar (see \citealt{whitworth2004}) )." +" Therefore the mass loss rate is an important parameter that can help determine the effect photoionisation has on current, and future star formation within BRCs, and in estimating their lifetime."," Therefore the mass loss rate is an important parameter that can help determine the effect photoionisation has on current, and future star formation within BRCs, and in estimating their lifetime." +" 'To evaluate the mass loss we use Equation 36 from which relates the mass loss (Mc; Myr~') to the ionising flux illuminating the cloud (Φ photons cm""? s~*), i.e. The globally averaged photon flux calculated in Section and the cloud radii presented in Paper I were used to estimate the mass loss rate for each cloud using Equation [IT]; these values are presented in along with an estimate for the lifetime of each cloud."," To evaluate the mass loss we use Equation 36 from \citet{lefloch1994} which relates the mass loss $_\odot$ $\rm{Myr}^{-1}$ ) to the ionising flux illuminating the cloud $\Phi$ photons $^{-2}$ $^{-1}$ ), i.e. The globally averaged photon flux calculated in Section \ref{sect:radio_analysis} and the cloud radii presented in Paper I were used to estimate the mass loss rate for each cloud using Equation \ref{eqn:mass_loss}; these values are presented in Table \ref{tbl:virial_mass} along with an estimate for the lifetime of each cloud." +" TableThe[I2] BRC mass loss rates range between ~ 12-59 Mc Myr}, corresponding to cloud lifetimes from as little as 6x10? yr to several Myr."," The BRC mass loss rates range between $\sim$ 12–59 $M_\odot$ $^{-1}$, corresponding to cloud lifetimes from as little as $6\times10^5$ yr to several Myr." + 'The accretion phase of protostar formation is known to last for several (?))., The accretion phase of protostar formation is known to last for several \citealt{andre2000}) ). +" Therefore any ongoing, or imminent, star formation within SFO 58, SFO 68, SFO 75 and SFO 76 will be unaffected by the ionisation and mass loss, especially SFO 68 where the star formation already appears to be well developed and unlikely to be affected by the mass loss experienced by the cloud."," Therefore any ongoing, or imminent, star formation within SFO 58, SFO 68, SFO 75 and SFO 76 will be unaffected by the ionisation and mass loss, especially SFO 68 where the star formation already appears to be well developed and unlikely to be affected by the mass loss experienced by the cloud." +" However, the future star formation within SFO 58 may be adversely affected as the ionisation front propagates into the cloud."," However, the future star formation within SFO 58 may be adversely affected as the ionisation front propagates into the cloud." +" Although there is no evidence of any current star formation taking place within either SFO 75 or SFO 76, we have shown these clouds are likely to be undergoing RDI as well as having sufficiently long lifetimes for RDI to be a viable method of triggered star formation."," Although there is no evidence of any current star formation taking place within either SFO 75 or SFO 76, we have shown these clouds are likely to be undergoing RDI as well as having sufficiently long lifetimes for RDI to be a viable method of triggered star formation." +" Direct evidence of whether star formation within these clouds has been triggered is not readily available, however, it is possible to investigate the probability that the star formation has been triggered by considering the circumstantial evidence."," Direct evidence of whether star formation within these clouds has been triggered is not readily available, however, it is possible to investigate the probability that the star formation has been triggered by considering the circumstantial evidence." +" It is interesting to note that there is strong evidence for the presence of ongoing star formation within the two clouds (SFO 58 and SFO 68) that fall into the post-pressure balance cloud category, such as the molecular outflows (see Section[4.1)), association with OH, H2O and methanol masers (??7,, i.e. SFO 68) and the possible association with an embedded UC HII region (Section [4], ie. SFO 58)."," It is interesting to note that there is strong evidence for the presence of ongoing star formation within the two clouds (SFO 58 and SFO 68) that fall into the post-pressure balance cloud category, such as the molecular outflows (see Section \ref{sect:co_analysis}) ), association with OH, $_2$ O and methanol masers \citealt{braz1989,macleod1992,caswell1995}, i.e. SFO 68) and the possible association with an embedded UC HII region (Section \ref{sect:uchii_region}, i.e. SFO 58)." +" Moreover, the association of the UC HII region with SFO 58 and of H3O and methanol masers with SFO 68 — which are respectively and almost exclusively associated with Class 0 protostars (?)) and high-mass star formation (?)) — lead us to conclude that the star formation within these two clouds is relatively recent, being no more than a few 105 years old."," Moreover, the association of the UC HII region with SFO 58 and of $_2$ O and methanol masers with SFO 68 — which are respectively and almost exclusively associated with Class 0 protostars \citealt{furuya2001}) ) and high-mass star formation \citealt{minier2003}) ) — lead us to conclude that the star formation within these two clouds is relatively recent, being no more than a few $^5$ years old." +" Contrary to the evidence of recent high-mass star formation within the post-pressure balanced clouds we find no evidence for any ongoing star formation within either of the two pre-pressure balance clouds (SFO 75 and SFO 76), short of the presence of the embedded IRAS point source."," Contrary to the evidence of recent high-mass star formation within the post-pressure balanced clouds we find no evidence for any ongoing star formation within either of the two pre-pressure balance clouds (SFO 75 and SFO 76), short of the presence of the embedded IRAS point source." +" If, as suggested by the RDI models (e.g. ??)) and observations (e.g. ?)), that rim morphologies represent an evolutionary sequence (see Figure [7)), we should expect to find clouds at similar stages of evolution to exhibit similar physical parameters, and furthermore, the star formation within clouds at different evolutionary states to be at different stages of development."," If, as suggested by the RDI models (e.g. \citealt{lefloch1994, vanhala1998}) ) and observations (e.g. \citealt{sugitani1991}) ), that rim morphologies represent an evolutionary sequence (see Figure \ref{fig:rim_classification}) ), we should expect to find clouds at similar stages of evolution to exhibit similar physical parameters, and furthermore, the star formation within clouds at different evolutionary states to be at different stages of development." + It is therefore useful to compare the observational results to the evolutionary sequence predicted by the models to investigate any differences in the star formation within clouds with different rim morphologies., It is therefore useful to compare the observational results to the evolutionary sequence predicted by the models to investigate any differences in the star formation within clouds with different rim morphologies. +" However, we must point out that the boundary conditions of where the clouds meet the larger-scale molecular material are very important and may affect the following analysis."," However, we must point out that the boundary conditions of where the clouds meet the larger-scale molecular material are very important and may affect the following analysis." + To emphasise the morphology of each rim a black curved line has been fitted (by eye) to the radio contours following the minimum gradient of the emission (see of Figures ??--??))., To emphasise the morphology of each rim a black curved line has been fitted (by eye) to the radio contours following the minimum gradient of the emission (see of Figures \ref{fig:co_sfo58}- \ref{fig:co_sfo76}) ). + The four clouds separate quite nicely into two morphological groups after comparison of the rim morphologies presented in Figure[7., The four clouds separate quite nicely into two morphological groups after comparison of the rim morphologies presented in Figure \ref{fig:rim_classification}. . + SFO 58 and SFO 68 are typical of a type A rim, SFO 58 and SFO 68 are typical of a type A rim +Equation (3)).,Equation \ref{form:conft}) ). + The last term in Equation (A4+)) is the homogeneous part., The last term in Equation \ref{eq:solut}) ) is the homogeneous part. + Here we do not assumepriori irrotationality of the velocity field. so we retain this term. (," Here we do not assume irrotationality of the velocity field, so we retain this term. (" +Though it does not contribute to the velocity divergence. because V-Fo= 0.),"Though it does not contribute to the velocity divergence, because $\nabla +\cdot \bmath{F} = 0$ .)" + The limit 2=0 corresponds Το)οxX.," The limit $\Omega \to 0$ corresponds to $\eta +\to \infty$." + Therefore. in the above equation we can neglect the terms v;/a and Ε/a. as well as a).," Therefore, in the above equation we can neglect the terms $\bfv_i/a$ and $\bmath{F}/a$, as well as $\eta_i$." + This yields From Equation CA2)) we have This vields in ¢A5)) In an (almost) empty universe //(/)=!/ Landa(t)=Fffy. hence {fa=Ly.," This yields From Equation \ref{eq:grav}) ) we have This yields in \ref{eq:solut_limit}) ) In an (almost) empty universe $H(t) = t^{-1}$ and $a(t) = t/t_0$, hence $H a = H_0$." +" Also. the general relation (5)) between © and the conformal time simplifies then to Q=te""."," Also, the general relation \ref{form:Omega of + eta}) ) between $\Omega$ and the conformal time simplifies then to $\Omega = 4 {\rm e}^{-\eta}$." +" Substituting this in Equation (A7)) we obtain Vv=LoGye""8."," Substituting this in Equation \ref{eq:div_v}) ) we obtain $\nabla \cdot \bfv = - H_0 6 \eta +{\rm e}^{-\eta} \delta$." + Comparing this equation with Equation (255). we identify the factor 67e. as the low-©. limit ofthe factor {(Q).," Comparing this equation with Equation \ref{form:f eta big}) ), we identify the factor $6 \eta {\rm e}^{-\eta}$ as the $\Omega$ limit of the factor $f(\Omega)$." + Hence. in agreement with the general linear theory prediction. Equation CI).," Hence, in agreement with the general linear theory prediction, Equation \ref{eq:linear}) )." + Now. we claim that in the limit (2.=0. solution (A5)) is also a solution of the general equation of motion (AL). forarbitrary 9.," Now, we claim that in the limit $\Omega \to 0$, solution \ref{eq:solut_limit}) ) is also a solution of the general equation of motion \ref{eq:motion}) ), $\delta$." + To prove this statement we have to demonstrate that in this limit. the non-linear term in equation CAT) is negligible.," To prove this statement we have to demonstrate that in this limit, the non-linear term in equation \ref{eq:motion}) ) is negligible." +" Substituting solution CA5)) in this term gives The amplitude of the second term on the RHS is of order Ll,μπινο~PagH7Oa6."," Substituting solution \ref{eq:solut_limit}) ) in this term gives The amplitude of the second term on the RHS is of order $H_0^{-2} \eta^2 +a\, g\, \nabla \cdot \bfg \sim H_0^{-2} \eta^2 a\, g\, H^2 \Omega a\, +\delta$." + The amplitude of the second term relative to the first is thus and inthe limit $2.-0 it tends to zero. (, The amplitude of the second term relative to the first is thus and in the limit $\Omega \to 0$ it tends to zero. ( +"Formally speaking. for arbitrary ¢20 and arbitrary 9. there always exists ;j, such that for all > ye""|8|& c)","Formally speaking, for arbitrary $\eps > 0$ and arbitrary $\delta$, there always exists $\eta_\eps$ such that for all $\eta > \eta_\eps$, $\eta^2 {\rm + e}^{-\eta} |\delta| < \eps$ .)" + Thus. in the limit Q*0 the non-linear term in the equation of motion becomes negligible. for arbitrary value of 6.," Thus, in the limit $\Omega \to 0$ the non-linear term in the equation of motion becomes negligible, for arbitrary value of $\delta$." + This is why in every matter-only. open universe. the velocitylensity relation evolves towards the linear one.," This is why in every matter-only, open universe, the velocity–density relation evolves towards the linear one." + Our aim here is to extend calculations of Section 5. for voids up to third order in the perturbation parameter ὦ (© is assumed to be large. but not infinitely large).," Our aim here is to extend calculations of Section \ref{sec:voids} for voids up to third order in the perturbation parameter $\phi$ $\phi$ is assumed to be large, but not infinitely large)." + We begin applying to Equation (1 19) the equality sinhó=coshó—exp(.ó) and expand this equation up to terms of the order cosh76.," We begin applying to Equation \ref{form:delta fi eta}) ) the equality $\sinh\phi = +\cosh\phi\, -\, \exp(-\phi)$ and expand this equation up to terms of the order $\cosh^{-2}\phi$." + Solving perturbatively the resulting equation for oO; we obtain where coshó» is given by Equation (373). 04 by (399) and the second term on the RHS of the above equation is a small correction.," Solving perturbatively the resulting equation for $\phi_3$ we obtain where $\cosh\phi_2$ is given by Equation \ref{eq:phi2_eta_arbitrary}) ), $\phi_1$ by \ref{eq:phi1_eta_arbitrary}) ) and the second term on the RHS of the above equation is a small correction." + This enables us to write Using the above equation in Equation (17)) yields (360). (B5)) (42, This enables us to write Using the above equation in Equation \ref{form:teta open}) ) yields \ref{eq:g_eta}) \ref{eq:Theta3_fin}) \ref{eq:Theta3_general}) +The leus equation (Equation 2)) is an implicit equation. in that the nuage position 0 is needed to evaluate the deflection @(0).,"The lens equation (Equation \ref{lensEQ}) ) is an implicit equation, in that the image position $\vec{\theta}$ is needed to evaluate the deflection $\vec{\alpha}(\vec{\theta})$." + For a eivenu source position } it is difficult to solve this iuplicit equation to obtain 0., For a given source position $\vec{\beta}$ it is difficult to solve this implicit equation to obtain $\vec{\theta}$. + Ou the other haud. if 0 is known J can he casily evaluated.," On the other hand, if $\vec{\theta}$ is known $\vec{\beta}$ can be easily evaluated." + This constitutes the basis of ray-traciue sinulatious of eravitational leusiug: start with an array of Tage positions and determine the source positions from which they cmereed., This constitutes the basis of ray-tracing simulations of gravitational lensing: start with an array of image positions and determine the source positions from which they emerged. + Sinple halo profiles. like the singular isothermal sphere (SIS). cau often produce analytical cross-sections.," Simple halo profiles, like the singular isothermal sphere (SIS), can often produce analytical cross-sections." + More colmplex mass profiles often have no simple analytical solution aud the cross-section has to be mmucrically conrputed using a ταν tracing simulation., More complex mass profiles often have no simple analytical solution and the cross-section has to be numerically computed using a ray tracing simulation. + In addition to the ability to compute lensing quautities for auyv arbitrary lass configuration. rav-traciug siuulatious have the advantage that they can casily include finite source effects which are not properly modeled im analytical solutions.," In addition to the ability to compute lensing quantities for any arbitrary mass configuration, ray-tracing simulations have the advantage that they can easily include finite source effects which are not properly modeled in analytical solutions." + Qur simulation males surface density maps as a matrix of LOO100 clemments aud solves the lens equation using the method described iu ?.., Our simulation makes surface density maps as a matrix of $400\times 400$ elements and solves the lens equation using the method described in \citet{Keeton:01}. + The image plane is divided to 180150 squares cach of which is divided iuto two triangles aud the correspoucding positions of cach vertex are found in the source plane., The image plane is divided to $180\times 180$ squares each of which is divided into two triangles and the corresponding positions of each vertex are found in the source plane. + The magnification is computed by defining a exid iu the source plane and calculating the umaege-plane area of triangles that have been mapped into each source position., The magnification is computed by defining a grid in the source plane and calculating the image-plane area of triangles that have been mapped into each source position. +" We asstune that the leus profiles iu the region of interest are welbapproxiuated by singular isotlermal profiles. where the three dimensional density profile for a spherical profile is where σι, is the hue of sight velocity dispersion of the stars in the ealactic disk or the ealaxics in a ealaxy cluster."," We assume that the lens profiles in the region of interest are well-approximated by singular isothermal profiles, where the three dimensional density profile for a spherical profile is where $\sigma_{\nu}$ is the line of sight velocity dispersion of the stars in the galactic disk or the galaxies in a galaxy cluster." + It is well known that this is not a eood approximation to halos produced in dark matter siuulatious (?7).. but the region that dominates the stroug lensing properties is typically dominated by barvonuic processes aud is enipircallv found to be close to isothermal (?)..," It is well known that this is not a good approximation to halos produced in dark matter simulations \citep{NFW:97}, but the region that dominates the strong lensing properties is typically dominated by baryonic processes and is empirically found to be close to isothermal \citep{Koopmans:09}." +" The dependence of the velocity dispersion on the redshift aud mass of the halo is eiven by ? as where and f, is a scaling parameter used to match the normalization from simulations.", The dependence of the velocity dispersion on the redshift and mass of the halo is given by \cite{Bryan:98} as where and $f_{\sigma}$ is a scaling parameter used to match the normalization from simulations. +" While the density profile may indecd scale roughly as 1/77 in the central regions of interest. the relationship between the normalization (νο, the velocity dispersion) and total halo mass is not clupirically calibrated and is a potential laree source of systematic uncertainty in this analysis."," While the density profile may indeed scale roughly as $1/r^2$ in the central regions of interest, the relationship between the normalization (i.e., the velocity dispersion) and total halo mass is not empirically calibrated and is a potential large source of systematic uncertainty in this analysis." + lutegratiug ptr) along the lne-of-sight produces the projected surface mass deusity The correspouding dimensionless surface mass deusity ls where we have defined the Eimsteiu deflection angle as The maenification for point sources leused by this mass profile is analytic. with (0)=|t(Ür).," Integrating $\rho(r)$ along the line-of-sight produces the projected surface mass density The corresponding dimensionless surface mass density is where we have defined the Einstein deflection angle as The magnification for point sources lensed by this mass profile is analytic, with $ \mu(\vec{\theta})=|\vec{\theta}|/(|\vec{\theta}|-\theta_E) $." + We calculate magnification for extended sources as the ratio of the area of combined images to the source area., We calculate magnification for extended sources as the ratio of the area of combined images to the source area. + This allows easy exploration of finite source effects and non-trivial lens distributions., This allows easy exploration of finite source effects and non-trivial lens distributions. +" The integral lensing cross-section Of2Εμ) is the area on the source plane inside which the macuification of a source is equal or larger than p,,;,.", The integral lensing cross-section $\sigma(\mu>\mu_{min})$ is the area on the source plane inside which the magnification of a source is equal or larger than $\mu_{min}$. + Throughout this work of)>Junin} and a(t) are used interchangeably., Throughout this work $\sigma(\mu>\mu_{min})$ and $\sigma(\mu)$ are used interchangeably. +" The cross-section for an SIS halo for fiji,2 is eiven analytically by Perrotta et al. (", The cross-section for an SIS halo for $\mu_{min}>2$ is given analytically by Perrotta et al. ( +2002) and at larec inaenifications our numerical results aeree with the analytic form to better than ,2002) and at large magnifications our numerical results agree with the analytic form to better than $\%$. +"The morphologv of the salaxies from observations (1) and the shape of dark matter halos frou, N-body simulations (2) both incicate that a considerable amount of ellipticity is prescut iu the lensing halos.", The morphology of the galaxies from observations \citep{Evans:09} and the shape of dark matter halos from N-body simulations \citep{Ludlow:10} both indicate that a considerable amount of ellipticity is present in the lensing halos. + Mauv studies previously (c.¢..2)) have introduced ellipticity iu the projected two-dimensional lensing potential o.," Many studies previously (e.g., \citet{Meneghetti:05}) ) have introduced ellipticity in the projected two-dimensional lensing potential $\phi$." + For analytical studics this has the advantage that the second derivatives of the potential directly eive the lensing quantities and lead to simple analytical expressions., For analytical studies this has the advantage that the second derivatives of the potential directly give the lensing quantities and lead to simple analytical expressions. + Towever for high values of ellipticity this iuplies dunmbbell shape density profiles which are uurealistic., However for high values of ellipticity this implies dumbbell shape density profiles which are unrealistic. + Simulations and observations both indicate ellipticity iu the distribution of mass. rather than in the poteutial resulting frou it.," Simulations and observations both indicate ellipticity in the distribution of mass, rather than in the potential resulting from it." + Iu our rav-traciug approach it is simple to introduce ellipticity iu the actual surface mass deusity., In our ray-tracing approach it is simple to introduce ellipticity in the actual surface mass density. + At each point defined by x and y on the two-dimensional plane with radius r=y|gy? we compute the SIS or NEW density using radius à defined as The axis ratios are now eiven bv δα=1ey., At each point defined by x and y on the two-dimensional plane with radius $r=\sqrt{x^2+y^2}$ we compute the SIS or NFW density using radius $r_e$ defined as The axis ratios are now given by $b/a=1-e_{\kappa}$. + The iupact of ellipticity can be clearly secu in Figure 2.., The impact of ellipticity can be clearly seen in Figure \ref{f2}. + Ellipticity increases the area of the source plane where strong lensing can occur., Ellipticity increases the area of the source plane where strong lensing can occur. + However. in the same figure we can see the effects of finite sources.," However, in the same figure we can see the effects of finite sources." +" The regious of high magnification become narrower as ellipticity Increases, so larger sources will tend to have smaller peak 1iaenificatious."," The regions of high magnification become narrower as ellipticity increases, so larger sources will tend to have smaller peak magnifications." + The interplay between ellipticity aud source size ids shown in Figure 3.., The interplay between ellipticity and source size is shown in Figure \ref{f3}. + Ellipticitv ecnerally leads to higher magnifications. but finite source sizes become more nuportant for higher cllipticities.," Ellipticity generally leads to higher magnifications, but finite source sizes become more important for higher ellipticities." + This discussion has assuned a fixed Einstein radius., This discussion has assumed a fixed Einstein radius. + The relevant factor is the ratio of the source size to the Eiusteiu racius: a given, The relevant factor is the ratio of the source size to the Einstein radius; a given +is (he best and only candidate in the entire observed simple for a CDM-consistent. dark-matter-dominatecd galaxy. with a well-constrained solution.,"is the best and only candidate in the entire observed sample for a CDM-consistent, dark-matter-dominated galaxy with a well-constrained solution." + The level of agreement is not perfect though. UGC 731 is consistent with aa =—0.8 slope at the 1.36 confidence level. with the confidence level decreasing (ο 1.τσ for an a=—1 slope. which is still only the upper limit of the range of slopes expected from the simulations.," The level of agreement is not perfect though, UGC 731 is consistent with a $\alpha = -0.8$ slope at the $1.3\sigma$ confidence level, with the confidence level decreasing to $1.7\sigma$ for an $\alpha = -1$ slope, which is still only the upper limit of the range of slopes expected from the simulations." + Once (he steep slope constraint is added to the HO4 constraints there are thus only 3 ealaxies left that. have a well-constrained fit consistent wilh a steep slope anc ACDAL, Once the steep slope constraint is added to the H04 constraints there are thus only 3 galaxies left that have a well-constrained fit consistent with a steep slope and $\Lambda$ CDM. + Of these 3 galaxies. 2 are of verv high surface brightness ancl are likely to be dominated by stars in the inner parts. leaving only one possible candidate with a well-constrained fit.," Of these 3 galaxies, 2 are of very high surface brightness and are likely to be dominated by stars in the inner parts, leaving only one possible candidate with a well-constrained CDM-compatible fit." + The large majority of the well-constrained fits strongly. prefer shallow slopes., The large majority of the well-constrained fits strongly prefer shallow slopes. + The 2o limit used here already indicates that for many galaxies it is difficult to adjust the fil parameters to get a CDM-compatible fit., The $\sigma$ limit used here already indicates that for many galaxies it is difficult to adjust the fit parameters to get a CDM-compatible fit. + Restrictive as this criterion is. it really only gives an upper limit to the true probability.," Restrictive as this criterion is, it really only gives an upper limit to the true probability." + While one has the Ireedom to adjust the parameters of an individual fit to test the likelihood of an hwvpothesis for one particular rotation curve. this becomes problematic when dealing with many fits.," While one has the freedom to adjust the parameters of an individual fit to test the likelihood of an hypothesis for one particular rotation curve, this becomes problematic when dealing with many fits." + If every. fit is individually. adjusted to fit a particular model. does that still constitute a proper test?," If every fit is individually adjusted to fit a particular model, does that still constitute a proper test?" + An analogue can perhaps be [οτι in some of the first supernova results (hat indicated the existence of a cosmological constant cileallviess))., An analogue can perhaps be found in some of the first supernova results that indicated the existence of a cosmological constant \\citealt{riess}) ). + The majority of the supernovae in that early work were each individually consistent within 20 with the non-eexistence of A., The majority of the supernovae in that early work were each individually consistent within $2\sigma$ with the existence of $\Lambda$. + Even though the data showed a svstematic trend. each measurement could have been corrected individually to. fit the no-X model.," Even though the data showed a systematic trend, each measurement could have been corrected individually to fit the $\Lambda$ model." + llowever. the joint result of these small inconsistencies has formed (he basis for the discovery of the effects of A on the expansion of the universe.," However, the joint result of these small inconsistencies has formed the basis for the discovery of the effects of $\Lambda$ on the expansion of the universe." + While it would be presumptuous to compare those results with the current. analysis. it does show that it is important to pay attention to the elobal conclusion (hat is forced upon us by the data.," While it would be presumptuous to compare those results with the current analysis, it does show that it is important to pay attention to the global conclusion that is forced upon us by the data." + One thing that is clear is Chat galaxies that are significantly consistent with ACDM in terms of their inferred central densities ancl the shapes of their rotation curves seem {ο be rare indeed., One thing that is clear is that galaxies that are significantly consistent with $\Lambda$ CDM in terms of their inferred central densities and the shapes of their rotation curves seem to be rare indeed. + I have investigated the claim bv HO4 that the majority of rotation curves of LSB galaxies are nol inconsistent with CDM., I have investigated the claim by H04 that the majority of rotation curves of LSB galaxies are not inconsistent with CDM. + I have shown that the method used is unable io distinguishe between shallow and steep slopes. even when these are obviously present and easily detectable.," I have shown that the method used is unable to distinguish between shallow and steep slopes, even when these are obviously present and easily detectable." + I illustrate this bv showing that with the HO4 method one would infer even, I illustrate this by showing that with the H04 method one would infer even +wwith much larger turbulent fractions than the similar mmeans in IC348 and L1448: 1.91--0.07 compared to 1.44--0.07 and 1.52+0.13.,with much larger turbulent fractions than the similar means in IC348 and L1448: $1.91\pm 0.07$ compared to $1.44\pm 0.07$ and $1.52\pm 0.13$. +" Therefore, for both populations, the IC348 linewidths are smaller than in1333,, even though both regions are close to stellar clusters."," Therefore, for both populations, the IC348 linewidths are smaller than in, even though both regions are close to stellar clusters." +" This is possibly (as noted in [Paper1)) because the IC348 IR cluster is old and no longer actively forming stars, so it affects its environs much less than the ccluster."," This is possibly (as noted in \citetalias{paper1}) ) because the IC348 IR cluster is old and no longer actively forming stars, so it affects its environs much less than the cluster." +" There is a wide range of clump iin L1448, which could be a result of a significant contribution to the llinewidth from molecular outflows."," There is a wide range of clump in L1448, which could be a result of a significant contribution to the linewidth from molecular outflows." + Many of the protostellar clumps in L1448 drive particularly strong flows (PaperII)., Many of the protostellar clumps in L1448 drive particularly strong flows \citepalias{paper3}. +". On dividing the clumps into protostellar and starless subsets (see 0.15 reffig:fturbyysource)), thereappearstolittledif erencebetweenthedist ribitiensof turbulent f ractionf orbothsourcety pesandclumppopulat ions."," On dividing the clumps into protostellar and starless subsets (see \\ref{fig:fturb_bysource}) ), there appears to little difference between the distributions of turbulent fraction for both source types and clump populations." +"Atthepeal oob jects,find (fup)=1.80.2 for starless clumps compared to 1.89+0.12we for protostars."," At the peak positions of the objects, we find $\langle f_\mathrm{turb} \rangle=1.8\pm0.2$ for starless clumps compared to $1.89\pm0.12$ for protostars." +" Similarly, (fip)=1.61£0.11 and 1.80+0.10 for starless and protostellar ssources respectively."," Similarly, $\langle f_\mathrm{turb} \rangle=1.61\pm0.11$ and $1.80\pm0.10$ for starless and protostellar sources respectively." + Further separation of the protostars into Class 0 and I clumps does not yield statistical differences between their average ((see reftab:fturbclfind and ))., Further separation of the protostars into Class 0 and I clumps does not yield statistical differences between their average (see \\ref{tab:fturbclfind} and \ref{tab:fturbgclumps}) ). +" Unfortunately, such simple averages do not provide the whole picture we can see in the distributions (in reffig:fturb,ysource))."," Unfortunately, such simple averages do not provide the whole picture we can see in the distributions (in \\ref{fig:fturb_bysource}) )." +"Forexample,ifthesmallbutsigni ficantpopulationo fhight sstarless cores were eliminated it would seem that protostars have marginally higher oon average."," For example, if the small but significant population of high starless cores were eliminated it would seem that protostars have marginally higher on average." +" However, the large uncertainties on the average ddo emphasize the need for larger samples of objects."," However, the large uncertainties on the average do emphasize the need for larger samples of objects." +" For the ppopulation (but not the ssources) most of the high pprotostars are Class 0, and all of the low CClass I, which is perhaps what we might expect if outflow power decreases from the Class 0 to I stage (Bontempsal.1996]; "," For the population (but not the sources) most of the high protostars are Class 0, and all of the low Class I, which is perhaps what we might expect if outflow power decreases from the Class 0 to I stage \citealt{bontemps96}; \citetalias{paper3}) )." +"Overall, there are few significant differenceset between the [II)).starless and protostellar distributions."," Overall, there are few significant differences between the starless and protostellar distributions." + We can draw interesting comparisons with the 1)) and ddistributions presented by Sep|KJTO7| (see reffig:fturbcomp;starl ).," We can draw interesting comparisons with the ) and distributions presented by \citetalias{hkirk07} + (see \\ref{fig:fturb_comp_starless} and \ref{fig:fturb_comp_proto}) )." +Ourdist ributionsareclosertotheC'8O distributions of than their N2H* results., Our distributions are closer to the $^{18}$ O distributions of \citetalias{hkirk07} than their $_2$ $^+$ results. +" The high levels of non-thermal motions, shown by some of our sources, are simply not present in N2H* data."," The high levels of non-thermal motions, shown by some of our sources, are simply not present in $_2$ $^+$ data." +" A striking contrast between the ddistributions is that many of our cores have high ((> 3.5), which are not seen for either protostars or starless cores by |KJTO7."," A striking contrast between the distributions is that many of our cores have high $\ge 3.5$ ), which are not seen for either protostars or starless cores by \citetalias{hkirk07}." +" In addition, many IKJTO7I starless cores have sub-thermal linewidths (furbi 1)."," In addition, many \citetalias{hkirk07} + starless cores have sub-thermal linewidths $<1$ )." +" T hesedif ferencesmaybepartlycausedbythespectralresolutiono f ourob ccompared to [KJTO07]'s kms)), rather than intrinsically different results."," These differences may be partly caused by the spectral resolution of our observations $\Delta v=0.15$ compared to \citetalias{hkirk07}' 's ), rather than intrinsically different results." +" Our slightly poorer resolution means we cannot probe as narrow linewidths and we possibly blend many of the separate components, noted in [KITO7!'s sspectra, into one."," Our slightly poorer resolution means we cannot probe as narrow linewidths and we possibly blend many of the separate components, noted in \citetalias{hkirk07}' 's spectra, into one." + Given the similarities it seems likely our, Given the similarities it seems likely our +‘This in turn could have triggered star formation. some of it dust. enshrouded. producing the bright knot and the CRB »rogenitor.,"This in turn could have triggered star formation, some of it dust enshrouded, producing the bright knot and the GRB progenitor." + Llowever. even prior to identification of the likely host. here were a number of reasons to doubt the very high redshift hypothesis.," However, even prior to identification of the likely host, there were a number of reasons to doubt the very high redshift hypothesis." + In. particular. the significant excess column density above the Galactic. foreground. inferred rom the X-rav spectrum.," In particular, the significant excess column density above the Galactic foreground, inferred from the X-ray spectrum." + At very high-z the rest-frame soft. N-ravs move out of the NIE. bandpass. so even igh columns in the host will produce. little attenuation (presumably exacerbated by the low metallicity at. carly cosmic times).," At very $z$ the rest-frame soft X-rays move out of the /XRT bandpass, so even high columns in the host will produce little attenuation (presumably exacerbated by the low metallicity at early cosmic times)." + For example. in the sample of 55 long-cluration bursts with redshifts considered by Cirupeetal. (2007).. none of those above z=2.7 showed such a high excess column as seen here.," For example, in the sample of 55 long-duration bursts with redshifts considered by \citet{Grupe07}, none of those above $z=2.7$ showed such a high excess column as seen here." + We should. caution. however. hat the reliability of column densities derived from evolving X-rav alterglow spectra has been questioned. by Butler&Ixocevski (2007).," We should caution, however, that the reliability of column densities derived from evolving X-ray afterglow spectra has been questioned by \citet{Butler07}." +. Phis could be particularly relevant if truly at high-: since time-dilation would mean the NRT was observing early in the rest-frame., This could be particularly relevant if truly at $z$ since time-dilation would mean the XRT was observing early in the rest-frame. + However. the faintness and redness of the afterglow in the nl. bands. and the fact that the spectral slope between the nll and N-rav. gxà0.4. also requires a strong spectral break. can all be explained most easilv if there is significant dust attenuation even in dy.," However, the faintness and redness of the afterglow in the nIR bands, and the fact that the spectral slope between the nIR and X-ray, $\beta_{KX}\approx0.4$, also requires a strong spectral break, can all be explained most easily if there is significant dust attenuation even in $K$." + We illustrate this further with the inset panel in Fig. 4..," We illustrate this further with the inset panel in Fig. \ref{SEDfigure}," + which shows a combined fit to the X-ray. and. nlli cata., which shows a combined fit to the X-ray and nIR data. + The model in this case is fixed at 2=2.8. and assumes SALC extinction law. metallicity and gas-to-dust. ratio.," The model in this case is fixed at $z=2.8$, and assumes SMC extinction law, metallicity and gas-to-dust ratio." + The unabsorbed spectrum is a £x&| power-law which breaks to Foxp°°, The unabsorbed spectrum is a $F_{\nu}\propto\nu^{-1}$ power-law which breaks to $F_{\nu}\propto\nu^{-0.5}$. + In fact this cooling break must be close to. or in the NICE band to provide a good simultaneous fit.," In fact this cooling break must be close to, or in the XRT band to provide a good simultaneous fit." + Alore generally. in Fig.," More generally, in Fig." + 6 we show how several constraints on the afterglow properties would vary. with assumed redshift., \ref{av} we show how several constraints on the afterglow properties would vary with assumed redshift. + For simplicity. and to reduce the number of free parameters. we assume here an SMC dust extinction law and eas-to-cdust ratio of ΑμEDVy)xLds107 atoms > (Bouchetetal.1985)..," For simplicity, and to reduce the number of free parameters, we assume here an SMC dust extinction law and gas-to-dust ratio of $N_{\rm H}/E(B-V)\approx4.4\times10^{22}$ atoms $^{-2}$ \citep{Bouchet}." + Phe solid line shows the rest-frame extinction required to produce JA=3.5 from an intrinsic P5x» afterglow spectrum. (equivalenttoJiANm1.e.g.Gorosabeletal. 2002).," The solid line shows the rest-frame extinction required to produce $J-K=3.5$ from an intrinsic $F_{\nu}\propto\nu^{-1}$ afterglow spectrum \citep[equivalent to $J-K\approx1.7$, e.g.][]{Gorosabel02}." +. In a rather moclel independent way. then. we can state that the alterelow should lic around this line or above it.," In a rather model independent way, then, we can state that the afterglow should lie around this line or above it." + The shaded region shows the foreground-subtracted ccolumn density (the le full range) derived by assuming the curvature of the X-ray. spectrum is due to absorption by heavy elements (althoughwecautionthatcolumnsinferredabsorption:Watsonetal.2007:Jakobsson 2006b).," The shaded region shows the foreground-subtracted column density (the $1\sigma$ full range) derived by assuming the curvature of the X-ray spectrum is due to absorption by heavy elements \citep[although we caution that columns inferred this +way usually exceed that measured directly from Ly$\alpha$ absorption;] +[]{Watson07,Jakobsson06b}." +. Lor consistenev we also assume SAIC metallicity here. so whilst the absolute scale may be wrong. the comparison of ely ancl Ny should be valid.," For consistency we also assume SMC metallicity here, so whilst the absolute scale may be wrong, the comparison of $A_V$ and $\nh$ should be valid." + Finally. the hatched region shows the results of moclel fitting to the combined X-ray and Ix-band data.," Finally, the hatched region shows the results of model fitting to the combined X-ray and K-band data." + Specifically. we extracted a NIE X-ray spectrum such that its observation log midpoint coincided with the time of the Ix bancl photometry.," Specifically, we extracted a /XRT X-ray spectrum such that its observation log midpoint coincided with the time of the K band photometry." + We fitted these together in count space (c.g.Starlineetal.2007) with mocels consisting of an absorbed power law or absorbed broken power law., We fitted these together in count space \citep[e.g.][]{Starling} with models consisting of an absorbed power law or absorbed broken power law. + A single, A single +bright emission lines of ionized iron and metals. (hat were later catalogued by Merrill (1951) and Cool et al. (,"bright emission lines of ionized iron and metals, that were later catalogued by Merrill (1951) and Cool et al. (" +2005).,2005). + The optical spectra of XX Oph are characterized by a hot continuum enussion Irom nebular material at blue wavelengths. [rom which molecular absorption bands of an AIG LII star emerge at red wavelengths (de Winter Thé 1990).," The optical spectra of XX Oph are characterized by a hot continuum emission from nebular material at blue wavelengths, from which molecular absorption bands of an M6 III star emerge at red wavelengths (de Winter Thé 1990)." + Spectral variability of XX Oph was studied by Goswami. Rao and Lambert (2001). and by Tarasov (2006) among others.," Spectral variability of XX Oph was studied by Goswami, Rao and Lambert (2001), and by Tarasov (2006) among others." + XX Oph has an unusual photometric variability., XX Oph has an unusual photometric variability. + Using Harvard collection οἱ photographic plates. Prager (1940) showed that the light curve of the star had over Ἱ-πιας deep aperiodic minima in the blue-photographic region. which could last for several vears and are reminiscent of obscurations in I CrD type of stars.," Using Harvard collection of photographic plates, Prager (1940) showed that the light curve of the star had over 1-mag deep aperiodic minima in the blue-photographic region, which could last for several years and are reminiscent of obscurations in R CrB type of stars." + The 1964-2010 visual light-curve collected by AAVSO shows a much lower degree of variabilitv. with just (wo minima occurring in 1967 and 2004 superimposed (o a steady linear decline from. m7g.=8.7 to Mip=O.2 mag.," The 1964-2010 visual light-curve collected by AAVSO shows a much lower degree of variability, with just two minima occurring in 1967 and 2004 superimposed to a steady linear decline from $m_{\rm vis}$ =8.7 to $m_{\rm vis}$ =9.2 mag." + No outburst has been recorded over the 1890-2010 monitored period., No outburst has been recorded over the 1890-2010 monitored period. + The spectrum of XX Oph presented in Figure 1 shows the highly popular regions of Ila. He/Nal and mulliplets 42 and 49 of Fell.," The spectrum of XX Oph presented in Figure 1 shows the highly popular regions of $\alpha$, He/NaI and multiplets 42 and 49 of FeII." + The emission lines are dominated by metals in their first stage of ionization., The emission lines are dominated by metals in their first stage of ionization. + Thev are very sharp and their heliocentric radial velocities are close to —37 kms +., They are very sharp and their heliocentric radial velocities are close to $-$ 37 km $^{-1}$. + Only Balmer lines present a complex. non-svmunetric profile wilh a radial velocity of —18 kms ! for the peak of the emission.," Only Balmer lines present a complex, non-symmetric profile with a radial velocity of $-$ 18 km $^{-1}$ for the peak of the emission." + Droad and blue shifted absorplions are visible for the strongest permitted lines of Fell. Crll. Till ancl Nal at radial velocities around —360 kins !.," Broad and blue shifted absorptions are visible for the strongest permitted lines of FeII, CrII, TiII and NaI at radial velocities around $-$ 360 km $^{-1}$." + Table 5 summarizes the mean velocities [or the photocenters of (he emission and absorption lines identified in Figure 1. which are similar {ο the values reported earlier by Merrill (1961).," Table 5 summarizes the mean velocities for the photocenters of the emission and absorption lines identified in Figure 1, which are similar to the values reported earlier by Merrill (1961)." + The values given for Ho. and IL3 refer to the velocity οἱ the sharp peak in their broad profile., The values given for $\alpha$ and $\beta$ refer to the velocity of the sharp peak in their broad profile. + The Ila profile of Figure 1 has no counterpart among those so far published. with the exception of the IL? profile for July 1996 presented by Goswami et al. (," The $\alpha$ profile of Figure 1 has no counterpart among those so far published, with the exception of the $\beta$ profile for July 1996 presented by Goswami et al. (" +2001) for which the,2001) for which the +"value for O, using the WALAPT value of f=0.702.",value for $\Omega_{b}$ using the WMAP7 value of $h=0.702$. + For reference we give our ficlucial values of each. parameter in ‘Table 1., For reference we give our fiducial values of each parameter in Table \ref{fidparams}. + Xs stated in the caption. most of these are taken from Table 1 in WALAPT. but others are assumptions based on ACDAL (e.g. uy=1 exactly).," As stated in the caption, most of these are taken from Table 1 in WMAP7, but others are assumptions based on $\Lambda CDM$ (e.g. $w_{0}=-1$ exactly)." + For cach published measurement. we also choose a category based on the tvpe of data and method. used to extract the cosmological parameter.," For each published measurement, we also choose a category based on the type of data and method used to extract the cosmological parameter." + Phere are obviously many cillerent possible choices of categorization possible and with cillerent coarseness., There are obviously many different possible choices of categorization possible and with different coarseness. + We choose the following 12 categories in order to have a reasonable number of measurements in each (the mean is 53): In Figure 1. we show a scatter. plot. of method vs xwameter for our dataset., We choose the following 12 categories in order to have a reasonable number of measurements in each (the mean is 53): In Figure \ref{methodvsparam} we show a scatter plot of method vs parameter for our dataset. +" We can see that. the mos »opular parameter/moethod. combination is Qa, measured using galaxv clusters. but that in general there is a fairly wide selection of method and parameter. with just over half (76 out of 144) of the combinations covered by at least one xublished abstract."," We can see that the most popular parameter/method combination is $\Omega_{M}$ measured using galaxy clusters, but that in general there is a fairly wide selection of method and parameter, with just over half (76 out of 144) of the combinations covered by at least one published abstract." + Our analysis is in two parts. the first being a study of general trends in the number of parameter measurements and popularity of dilferent methods by vear. as well as a looking at the measurement value vs vear for a subset of parameters (Sections 3.1 and 3.2).," Our analysis is in two parts, the first being a study of general trends in the number of parameter measurements and popularity of different methods by year, as well as a looking at the measurement value vs year for a subset of parameters (Sections 3.1 and 3.2)." + In the second. part (Sections 3.3 and 3.4). we compute the precision ancl accuracy of the measurements and see how these have varied with time.," In the second part (Sections 3.3 and 3.4), we compute the precision and accuracy of the measurements and see how these have varied with time." +he maximum: value. to south-east.,"the maximum value, to south-east." + Previous studies have excluded the inner 10 aresec from their studies (722))., Previous studies have excluded the inner $~$ arcsec from their studies ). + ound that NGXC221 can be best. profiled with a bulgedisk model (muss= 1.51) whileLOO found. misuse=4.00 plus disk., found that NGC221 can be best profiled with a bulge/disk model $n_{\rm bulge}=1.51$ ) whileH09 found $n_{\rm bulge}=4.00$ plus . +3. Comparison with thedata,"quark and becomes a non-leading baryon, but instead the intrinsic antidiquark behaves" +(the dashed lino). and the DAISL separation distributions with field-like and 75 per cent initial binary fractions (the dot-dashed and dotted lines. respectively).,"(the dashed line), and the DM91 separation distributions with field-like and 75 per cent initial binary fractions (the dot-dashed and dotted lines, respectively)." + The results shown in Fie., The results shown in Fig. + 3 are summarised in Table 2, \ref{bin_fracs} are summarised in Table \ref{bin_frac_table}. + For the various initial conditions. we show the binary raction as measured by our algorithm at MMyr. MMyE and MMyr.," For the various initial conditions, we show the binary fraction as measured by our algorithm at Myr, Myr and Myr." + When considering the evolution of the binary raction in dense. virialised. Plummer spheres. 2 noted hat the cluster. was too dense initially for the widest Xnaries observed. in the field to be bound. systems.," When considering the evolution of the binary fraction in dense, virialised Plummer spheres, \citet{Parker09a} noted that the cluster was too dense initially for the widest binaries observed in the field to be bound systems." + “This means that the initial binary [fraction in the clusters in. 2 with a LOO per cent primordial binary fraction actually ranslatecl into an initial value of 75 per cent for a DMO9I separation distribution., This means that the initial binary fraction in the clusters in \citet{Parker09a} with a 100 per cent primordial binary fraction actually translated into an initial value of 75 per cent for a DM91 separation distribution. + The fractal clusters presented. here are less dense than these Plummer spheres initially. and the calculated binary [fractions are all higher (although none are 100 per cent).," The fractal clusters presented here are less dense than these Plummer spheres initially, and the calculated binary fractions are all higher (although none are 100 per cent)." + For clusters with a moderate level of substructure (D= 2.0. an initial input binary fraction of 100 per cent. and separations drawn from the DALOL distribution. he measured. binary fraction at OALAIvr is S3 per cent. ligher than the 75 per cent initial binary fraction in a clense hummer sphere (?)..," For clusters with a moderate level of substructure $D = 2.0$ ), an initial input binary fraction of 100 per cent, and separations drawn from the DM91 distribution, the measured binary fraction at Myr is 83 per cent, higher than the 75 per cent initial binary fraction in a dense Plummer sphere \citep{Parker09a}." + This clleet is even. more pronounced for. the clusters with a binary fraction of 100 per cent and separations drawn rom the Ix95 distribution., This effect is even more pronounced for the clusters with a binary fraction of 100 per cent and separations drawn from the K95 distribution. + This distribution was derived to reconcile the observed. overabundance of wide binaries in voung clusters with the DAIOL field. distribution., This distribution was derived to reconcile the observed overabundance of wide binaries in young clusters with the DM91 field distribution. + Recently. 7? have suggested that a dynamical operator (which is a function of the cluster’s density) can be used to transform a Ix95 distribution to the field cistribution in a dense cluster.," Recently, \citet*{Marks11} have suggested that a dynamical operator (which is a function of the cluster's density) can be used to transform a K95 distribution to the field distribution in a dense cluster." + Llowever. the IxX95 cistribution saturates a dense cluster with wide binaries which are not physically bound. and it is cillicult to see how they could form in such an environment.," However, the K95 distribution saturates a dense cluster with wide binaries which are not physically bound, and it is difficult to see how they could form in such an environment." + 7. suggest this problem could be negated if the eluster formed in a more sparse environment. and then underwent cool collapse. which is exactly the scenario we propose here.," \citet{Marks11} suggest this problem could be negated if the cluster formed in a more sparse environment, and then underwent cool collapse, which is exactly the scenario we propose here." + llowever. the calculated initial binary fraction in all the clusters here is significantly lower than LOO per cent (the dashed lines in Fig. 3:," However, the calculated initial binary fraction in all the clusters here is significantly lower than 100 per cent (the dashed lines in Fig. \ref{bin_fracs};" + see also Table 2)). which indicates that very wide binaries cannot form in star forming regions: an alternative solution is that they form curing cluster dissolution. when two stars are simultaneously. ejected in he same cirection (e.g.?27)..," see also Table \ref{bin_frac_table}) ), which indicates that very wide binaries cannot form in star forming regions; an alternative solution is that they form during cluster dissolution, when two stars are simultaneously ejected in the same direction \citep[e.g.][]{Kouwenhoven10,Moeckel10}." + The initial and final binary fractions depend heavily on he level of substructure., The initial and final binary fractions depend heavily on the level of substructure. + Comparing the simulations with D=L6 (highly substructured). to those with 2=3.0 (uniform spheres). we see that the initial binary fraction is higher by 10 per cent for the uniform sphere (0.89. versus 79). and after. Myr the cilference is still significant. with a binary fraction of 0.66 for the DD=3.0 mocdel versus 51 for D=1.6 mocel.," Comparing the simulations with $D = 1.6$ (highly substructured), to those with $D = 3.0$ (uniform spheres), we see that the initial binary fraction is higher by 10 per cent for the uniform sphere (0.89 versus 0.79), and after Myr the difference is still significant, with a binary fraction of 0.66 for the $D = 3.0$ model versus 0.51 for $D = 1.6$ model." + Indeed. comparison of Figs.," Indeed, comparison of Figs." + 3fa) and 3(b) with the overall evolution of the cluster in Fig., \ref{binfrac1p6}~ and \ref{binfrac2p0} with the overall evolution of the cluster in Fig. + 2. shows that the vast majority of binary processing occurs before the cluster reaches its densest phase (alter 0.9MMyr)., \ref{cluster_evolve} shows that the vast majority of binary processing occurs before the cluster reaches its densest phase (after Myr). + This is due to pockets of localised density in the substructure. which dynamically. process the binary populations.," This is due to pockets of localised density in the substructure, which dynamically process the binary populations." + In the case of a cluster with almost no initial substructure (Fig. 3(0))).," In the case of a cluster with almost no initial substructure (Fig. \ref{binfrac3p0}) )," + we see that there is very little binary processing until the eluster has almost reached. its densest. phase at. collapse (note the sudden drop in binary fraction between 0.3 and MMyvr. which corresponds to the density peak in Fig. 2)).," we see that there is very little binary processing until the cluster has almost reached its densest phase at collapse (note the sudden drop in binary fraction between 0.3 and Myr, which corresponds to the density peak in Fig. \ref{cluster_evolve}) )." + The fact that dense substructure processes binaries to almost the same extent as the overall collapse of the cluster sugeests that substructurecd clusters in. virial equilibrium and those undergoing cxpansion would. also process any primordial binary population., The fact that dense substructure processes binaries to almost the same extent as the overall collapse of the cluster suggests that substructured clusters in virial equilibrium and those undergoing expansion would also process any primordial binary population. + ? and ? estimate that the binary fraction in the ONC is consistent with the field value. i.e. between 40 and 60 per cent. depending on the spectral tvpe of the primary.," \citet{Petr98} and \citet{Reipurth07} estimate that the binary fraction in the ONC is consistent with the field value, i.e. between 40 and 60 per cent, depending on the spectral type of the primary." + We note from Fig., We note from Fig. + 3. and Table 2. that dynamical processing reduces the overall binary fraction to such an extent that the initial binary fraction cannot be that of the field., \ref{bin_fracs} and Table \ref{bin_frac_table} that dynamical processing reduces the overall binary fraction to such an extent that the initial binary fraction cannot be that of the field. + Even in the smooth clusters. the binary fraction at AlAIvr is less than 40 per cent.," Even in the smooth clusters, the binary fraction at Myr is less than 40 per cent." + For the other initial conditions (22=1.6 or D= 2.0). the binary fraction in the ONC at MMsyr can be reproduced (within the uncertainties) ifthe initial binary fraction was 75 per cent or higher.," For the other initial conditions $D = 1.6$ or $D = 2.0$ ), the binary fraction in the ONC at Myr can be reproduced (within the uncertainties) if the initial binary fraction was 75 per cent or higher." +class of coherently emitting objects.,class of coherently emitting objects. + Search to detect additional bursts from the source in archival data sets were made. resulting in its re-detection for «2 minutes al 325 MIIz Giant metrewave radio telescope (GAIRT) observation in September 2003 (IIxinanetal.2006) and in March 2004 elal. 2007).," Search to detect additional bursts from the source in archival data sets were made, resulting in its re-detection for $\sim$ 2 minutes at 325 MHz Giant metrewave radio telescope (GMRT) observation in September 2003 \citep{HYMAN2006} and in March 2004 \citep{HYMAN2007}." +". At the last known epoch of emission detected in 2004. the source exhibited an unusually sleep spectrum with alpha = -—1343 (8 (»)o pj"") (Ivanetal.2007)."," At the last known epoch of emission detected in 2004, the source exhibited an unusually steep spectrum with alpha = $-$ $\pm$ 3 (S $\nu$ $\propto +\nu^{\alpha}$ ) \citep{HYMAN2007}." +. several theories have been proposed to explain the emission from GCRT J1745-3009 (see IIvimanetal.(2007) and references therein)., Several theories have been proposed to explain the emission from GCRT J1745-3009 (see \citet{HYMAN2007} and references therein). + These include nulling. (sulkarni&Phinnev 2005).. double (CIurollaetal.2005).. precessing (Zhu&Xu2006) and a transient white dwarl pulsar (Zhang&Gil2005).," These include nulling \citep{KULKARNI2005}, , double \citep{TUROLLA2005}, precessing \citep{ZHU2006} and a transient white dwarf pulsar \citep{ZHANG2005}." +. Also. Hallinanetal.(2007) suggested a nearby ultracool dwarf as ils progenitor.," Also, \citet{HALLINAN2007} suggested a nearby ultracool dwarf as its progenitor." + Unfortunately. non-detection of GCRT J1745—3009 αἱ frequencies other than 325 MlIz (kaplanetal.2003). hindered attempts to discover its progenitor.," Unfortunately, non-detection of GCRT $-$ 3009 at frequencies other than 325 MHz \citep{KAPLAN2008} hindered attempts to discover its progenitor." + Its brightness temperature in possible excess of the Compton limit suggests coherent processes such as electron exclotron maser enussion or plasma emission., Its brightness temperature in possible excess of the Compton limit suggests coherent processes such as electron cyclotron maser emission or plasma emission. + Notably. both of these mechanisms produce circeularly. polarized emission. motivating us to re-examine earlier detections of GCRT J1745—3009 in search of its signature.," Notably, both of these mechanisms produce circularly polarized emission, motivating us to re-examine earlier detections of GCRT $-$ 3009 in search of its signature." + We have reanalvzed the 325 MIIz GAMIRT data from September 2003. the detection with the highest signal to noise ratio per integration (ime available.," We have reanalyzed the 325 MHz GMRT data from September 2003, the detection with the highest signal to noise ratio per integration time available." + The subsequent sections are arranged as follows - in Sect., The subsequent sections are arranged as follows - in Sect. + 2 and 3 we describe our reanalvsis procedure ancl its results. respectively.," 2 and 3 we describe our reanalysis procedure and its results, respectively." + The interpretation of these results are presented in Sect., The interpretation of these results are presented in Sect. + 4d aud conclusions in Sect., 4 and conclusions in Sect. + 5., 5. + During the observations. the pointing center of the GAIRT antennas was 0.57 West οἱ GCRT J1745—3009 (hereafter GCRT).," During the observations, the pointing center of the GMRT antennas was $^{\circ}$ West of GCRT $-$ 3009 (hereafter GCRT)." + The unpolarizedcalibrator 3C43 was observed for, The unpolarizedcalibrator 3C48 was observed for +preferred to a combination of Ne. Ar and S abundances. since. for these two last elements. the abundances are not reliable when the excitation is extreme (MSBMO3/).,"preferred to a combination of Ne, Ar and S abundances, since, for these two last elements, the abundances are not reliable when the excitation is extreme /)." + For each Π/ region. we extract from the 7;5/-U/-Z photoionization model grid the 7yy/-U// plane. whose metallicity lies closest to the Ne/Ne./ of the II/ region.," For each / region, we extract from the $Z$ photoionization model grid the / plane, whose metallicity lies closest to the / of the / region." + The 2/ shows. for the 5 metallicities used in the photoionization model grid. the values taken by νο and III/ITJ/. The effect of increasing the metallicity of the atmosphere models (and consequently of the nebular gas) is clearly to increase the value of 7;4/ for a given II/II|/ ratio. as already pointed out in MSBMO3/. The observed values for the II/ regions are also plotted in the diagramm corresponding to their metallicities.," The / shows, for the 5 metallicities used in the photoionization model grid, the values taken by / and /. The effect of increasing the metallicity of the atmosphere models (and consequently of the nebular gas) is clearly to increase the value of / for a given / ratio, as already pointed out in /. The observed values for the / regions are also plotted in the diagramm corresponding to their metallicities." + All the observed values lie inside the grids., All the observed values lie inside the grids. + 2D-Interpolations are performed to determine Το and U/ for each II/ region., 2D-Interpolations are performed to determine / and / for each / region. + The Table ] presents the characteristics of the 42 Π/ regions used in this work: Ryy/. Ne/Ne./ (with a symbol corresponding to the grid used within the Z-Method. Sec. 4.2)). IIU/TI|/. IV/IIIJ/.," The Table \ref{tab:res} presents the characteristics of the 42 / regions used in this work: /, / (with a symbol corresponding to the grid used within the Z-Method, Sec. \ref{sec:met2}) ), /, /," + and the 7:47 and U/ obtained using the Z-Method., and the / and / obtained using the Z-Method. + The 7;4/ range from 34 to 50 kK. and y from -1.5 to 0.5. with mean values of 40.5 kK and -0.60. respectively.," The / range from 34 to 50 kK, and / from -1.5 to 0.5, with mean values of 40.5 kK and -0.60, respectively." + Such range for Τομ and U/ is in agreement with the results found by Evans&Dopita(1985)., Such range for / and / is in agreement with the results found by \citet{ED85}. + For the 3 sources for which two independent observations are available. the results obtained lead to a coherent determination of 7/7. while the values of U/ can differ by a factor up to 5.," For the 3 sources for which two independent observations are available, the results obtained lead to a coherent determination of /, while the values of / can differ by a factor up to 5." + The set of inferred values for Τωη/ and y versus the galactocentric radius Γιαν and the abundance ratio ./ are shown in Fig., The set of inferred values for / and / versus the galactocentric radius / and the abundance ratio / are shown in Fig. + 3 for the S-Method (Sec. 4.1)).," \ref{fig:res_1z} for the S-Method (Sec. \ref{sec:met1}) )," + and in Fig., and in Fig. + for the Z-Method (Sec. 4.2)).," \ref{fig:res_all} + for the Z-Method (Sec. \ref{sec:met2}) )." + Linear fit to the data are also presented in all the figures., Linear fit to the data are also presented in all the figures. + The results obtained for Το with S- and Z-Methods are very different (upper panels of Figs. 3--4))., The results obtained for / with S- and Z-Methods are very different (upper panels of Figs. \ref{fig:res_1z}- \ref{fig:res_all}) ). +" While S-Method leads to an increase (decrease) of Tyj/ with [δω ./). the use of the Z-Method leads to rather different results: no clear correlation is found to exist between 7Zj/ and [ιν while a correlation is present between 7,g/ and ./. The distribution of 7sy/ versus Ne/Ne./ obtained with the Z-Method can also be described as follows: 7.y/ increasing strongly with Ne/Ne./ for Ne/Ne./«1.2. and a quasi constant value (43 kK) for higher ./. coupled with a higher dispersion."," While S-Method leads to an increase (decrease) of / with / /), the use of the Z-Method leads to rather different results: no clear correlation is found to exist between / and / while a correlation is present between / and /. The distribution of / versus / obtained with the Z-Method can also be described as follows: / increasing strongly with / for $<1.2$, and a quasi constant value $\sim43$ kK) for higher /, coupled with a higher dispersion." + The dispersion of ./ with position in the Galaxy is relatively high (see the symbols dispersion along in the left panels of Fig. 4))., The dispersion of / with position in the Galaxy is relatively high (see the symbols dispersion along / in the left panels of Fig. \ref{fig:res_all}) ). + The absence of correlation betweenΚιν 7;4/ and obtained with Z-Method might be the result of this high R.4j/dispersion., The absence of correlation between / and / obtained with Z-Method might be the result of this high dispersion. + Note that for II/ regions with Raj Ray... the determination of is degenerate (Martín-Hernándezetal.2002a) and the errorsR4// are also important.," Note that for / regions with $<$ $_\odot$, the determination of / is degenerate \citep{PaperII} and the errors are also important." + Virtually no changes are observed for y from S- to Z-Method (lower panels of Figs. 3--4))., Virtually no changes are observed for / from S- to Z-Method (lower panels of Figs. \ref{fig:res_1z}- \ref{fig:res_all}) ). + This gives insights of the robustness of our results concerning U/ whatever the method used., This gives insights of the robustness of our results concerning / whatever the method used. + This can be understood as follows: the main effect of changing Z on the diagnostic diagrams 2/) is to shift horizontally II/TI]/ axis) the grids of models. while the determination of U/ is mainly dependent on the vertical position along the Νο; axis. which is not affected by the stellar metallicity.," This can be understood as follows: the main effect of changing $Z$ on the diagnostic diagrams /) is to shift horizontally / axis) the grids of models, while the determination of / is mainly dependent on the vertical position along the / axis, which is not affected by the stellar metallicity." + No clear correlation is found between U/ and but an inverse correlation between U/ and ./ Is presentR4/ (see Fig. 4..," No clear correlation is found between / and / but an inverse correlation between / and / is present (see Fig. \ref{fig:res_all}," + lower panels)., lower panels). + Fig., Fig. + 5 shows the distribution of 7.;;/ versus the III/II|/ excitation ratio., \ref{fig:teff_exne} shows the distribution of / versus the / excitation ratio. + The softening of the stellar emission when the metallicity increases (even 1f 7y)/ doesn't change) is enough to cover the whole observed range of ΠΙ/ (over 2.5 dex)., The softening of the stellar emission when the metallicity increases (even if / doesn't change) is enough to cover the whole observed range of / (over 2.5 dex). + This Fig., This Fig. + 5 illustrates one more time the illusion of determining 7;j/ from only one excitation diagnostic., \ref{fig:teff_exne} illustrates one more time the illusion of determining / from only one excitation diagnostic. +On the other hand. a global increase of 7;4/ with III/II|/ is also present (the hottest stars are associated with the most excited IV/ regions).,"On the other hand, a global increase of / with / is also present (the hottest stars are associated with the most excited / regions)." + The results presented in Sect., The results presented in Sect. + 5 are sensitive to the changes of the stellar SED with metallicity. for à given atmosphere," \ref{sec:results} are sensitive to the changes of the stellar SED with metallicity, for a given atmosphere" +First. the large widths aud suppressed strengths of the rotationally broadened lines make their detection cifficult.,"First, the large widths and suppressed strengths of the rotationally broadened lines make their detection difficult." + This may be able to account for the featureless spectra of a ος of isolated jeutron stars observed with audNewton. such as RSJ 1856-3751 (Braje Romani 2002: Zavlin Pavlov 2002).," This may be able to account for the featureless spectra of a number of isolated neutron stars observed with and, such as RXJ 1856–3754 (Braje Romani 2002; Zavlin Pavlov 2002)." + Correspoucinely. if narrow liue features are «etected. from rapidly ‘olating neutrou stars. e.g.. bursters. they could not have originated from the neutrou star surlacκ... tuless the etuissiou is ‘est‘icted to the rotational pole.," Correspondingly, if narrow line features are detected from rapidly rotating neutron stars, e.g., bursters, they could not have originated from the neutron star surface, unless the emission is restricted to the rotational pole." + Searches for lines ii such sources shotld ake into account these rel:uivistic effects., Searches for lines in such sources should take into account these relativistic effects. + Finally. the assinet‘y of the liue profiles introduces siguilieant syseimatic uncertalutiesuU in measuring the com)actness of aleulron star uslug gravitational recsifts.," Finally, the asymmetry of the line profiles introduces significant systematic uncertainties in measuring the compactness of a neutron star using gravitational redshifts." + As an exaiuple. Figure { shows that if lie »eak of the line is used in iueasuriug al apparent 'ecshüft. the resulti18oO compactuess of the neτο1 sar will je signilicautly overestimated even wlen the entire surface is emitting.," As an example, Figure 4 shows that if the peak of the line is used in measuring an apparent redshift, the resulting compactness of the neutron star will be significantly overestimated even when the entire surface is emitting." + For the inferred. spin [recuencies of bursters. in the abseuce of realistic models. systematic uncertainies cau be as laree as 1056. which are larger than the yA( accuracy recui to distinguish betwee1 the different ecuations of state (Prakash Lattimer 2000).," For the inferred spin frequencies of bursters, in the absence of realistic models, the systematic uncertainties can be as large as $10\%$, which are larger than the $5\%$ accuracy required to distinguish between the different equations of state (Prakash Lattimer 2000)." +"the infall divided by 0.18, the universal baryon fraction, Mh,12 is the halo mass in units of 1013 Mo, and e; is the fraction of gas entering the halo that reaches the galactic disk rather than being shock-heated and joining the halo.","the infall divided by 0.18, the universal baryon fraction, $M_{h,12}$ is the halo mass in units of $10^{12}$ $\msun$, and $\epsilon_{\rm in}$ is the fraction of gas entering the halo that reaches the galactic disk rather than being shock-heated and joining the halo." +" This is approximately given by where f(z) is a function that is linear in time and varies from unity at z=2.2 to 0.5 at z=1.° Inserting M, from equation for Me in equation (34)), we are able to evaluate the (46))expected velocity dispersion of gravitational instability-dominated galactic disks as a function of halo mass and redshift."," This is approximately given by where $f(z)$ is a function that is linear in time and varies from unity at $z=2.2$ to 0.5 at $z=1$ Inserting $\dot{M}_g$ from equation \ref{mdotgas}) ) for $\dot{M}_{\rm ext}$ in equation \ref{sigmaeq}) ), we are able to evaluate the expected velocity dispersion of gravitational instability-dominated galactic disks as a function of halo mass and redshift." + We do so in Figure 2.., We do so in Figure \ref{fig:halosigma}. . +" Examining the plot, we see that for a Milky Way-like halo (Mz,12=1, ?)) where o,>>o (so that the fy1 case applies), we predict a typical velocity dispersion of 10.7 km s-!."," Examining the plot, we see that for a Milky Way-like halo $M_{h,12} = 1$, \citealt{xue08a}) ) where $\sigma_* \gg \sigma$ (so that the $f_g=1$ case applies), we predict a typical velocity dispersion of $10.7$ km $^{-1}$." +" While this is very slightly higher than the value of ¢~8 km s! observed in typical Milky Way-like disks today (?,, ?,, and references therein), the agreement is quite good given our purely analytic model."," While this is very slightly higher than the value of $\sigma \simeq 8$ km $^{-1}$ observed in typical Milky Way-like disks today \citealt{blitz04}, \citealt{dib06a}, and references therein), the agreement is quite good given our purely analytic model." + Our results are quite similar to the numerical ones obtained by ? and ?.., Our results are quite similar to the numerical ones obtained by \citet{kim07} and \citet{agertz09a}. +" Moreover, as ? ppoint out, gravitationally-driven turbulence has the advantage that it can operate even in the outer H disk where there is very little star formation, so mechanisms such as supernovae that are invoked to explain turbulence in the inner disk (e.g.??) are unavailable."," Moreover, as \citeauthor{agertz09a} point out, gravitationally-driven turbulence has the advantage that it can operate even in the outer H disk where there is very little star formation, so mechanisms such as supernovae that are invoked to explain turbulence in the inner disk \citep[e.g.][]{de-avillez07a, joung09a} are unavailable." +" We also predict lower velocity dispersion in smaller halos, and this appears to be consistent with the somewhat lower H velocity dispersions seen indwarf galaxies (?7).."," We also predict lower velocity dispersion in smaller halos, and this appears to be consistent with the somewhat lower H velocity dispersions seen indwarf galaxies \citep{walter08a, chung09a}." +" Finally,1 however, we do note that there are alternative models to explain outer disk turbulence, including magnetorotational instability ?? and accretion of clumpy gas ?.."," Finally, however, we do note that there are alternative models to explain outer disk turbulence, including magnetorotational instability \citet{sellwood99a, piontek07a} and accretion of clumpy gas \citet{santillan07a}." + Within the same framework we are able to explain the large velocity dispersions of 20—80 km s! found in galactic disks found at redshifts ~1.5—3 , Within the same framework we are able to explain the large velocity dispersions of $20-80$ km $^{-1}$ found in galactic disks found at redshifts $\sim 1.5-3$ \citep{cresci09a}. +The observed galaxies likely correspond to ~10!? Mo (?)..halos., The observed galaxies likely correspond to $\sim 10^{12}$ $\msun$ halos. +" For redshifts in this range and f,~1/2, typical of galaxies at that redshift we predict typical velocity dispersions of 30—50 km (??)s-!, with fluctuations at the factor of ~1.5 level, corresponding to the expected factor of ~3 level variations in the accretion rates of halos at the same mass and redshift."," For redshifts in this range and $f_g \sim 1/2$, typical of galaxies at that redshift \citep{daddi09a, tacconi10a} we predict typical velocity dispersions of $30-50$ km $^{-1}$, with fluctuations at the factor of $\sim 1.5$ level, corresponding to the expected factor of $\sim 3$ level variations in the accretion rates of halos at the same mass and redshift." + This is in good agreement with the observations., This is in good agreement with the observations. + It is also instructive to compare the velocity dispersions we predict to the expected rotation velocities of galactic disks., It is also instructive to compare the velocity dispersions we predict to the expected rotation velocities of galactic disks. +" We compute the approximate virial velocity of a halo as a function of mass and redshift following the approximation given in Appendix A2 of ?,, and we take the maximum circular velocity to be 1.2 times this based on fitting the zero point of the Tully-Fisher relation (?).."," We compute the approximate virial velocity of a halo as a function of mass and redshift following the approximation given in Appendix A2 of \citet{dekel06a}, and we take the maximum circular velocity to be $1.2$ times this based on fitting the zero point of the Tully-Fisher relation \citep{dutton07a}." +" With this approximation, we plot Vinax/o in Figure 3.."," With this approximation, we plot $V_{\rm max}/\sigma$ in Figure \ref{fig:halovsigma}." + We see that accretion-driven turbulence naturally produces the transition from disks with Vinnax/o~5 found at redshifts =2 to disks with Viax/o~20—25 found today., We see that accretion-driven turbulence naturally produces the transition from disks with $V_{\rm max}/\sigma\sim 5$ found at redshifts $\ga 2$ to disks with $V_{\rm max}/\sigma \sim 20-25$ found today. +" Interestingly, we find that there is little dependence of Vaax/o on halo mass."," Interestingly, we find that there is little dependence of $V_{\rm max}/\sigma$ on halo mass." +" Instead, the primary dependence is in fj, the gas mass fraction; analytically, Vinax/oος91/35 "," Instead, the primary dependence is in $f_g$, the gas mass fraction; analytically, $V_{\rm max}/\sigma \propto f_g^{-1/3}$ ." +"Thus the most gas-dominated systems (or old galaxies that have c,>>c) have the largest Vaax/o, while gas-poor systems have smaller Vinax/o."," Thus the most gas-dominated systems (or old galaxies that have $\sigma_* \gg \sigma$ ) have the largest $V_{\rm max}/\sigma$, while gas-poor systems have smaller $V_{\rm max}/\sigma$." + This suggests that the range of Vinax/o seen for galaxies at z~2 by the SINS survey (?) represents a sequence in gas fraction., This suggests that the range of $V_{\rm max}/\sigma$ seen for galaxies at $z\sim 2$ by the SINS survey \citep{cresci09a} represents a sequence in gas fraction. +" The dispersion-dominated galaxies should on average be comparatively gas poor, while rotation-dominated ones should be gas rich."," The dispersion-dominated galaxies should on average be comparatively gas poor, while rotation-dominated ones should be gas rich." +" Of course fluctuations in accretion rate can also cause changes in c, so detecting this effect will require samples large enough for this noise source to be averaged out."," Of course fluctuations in accretion rate can also cause changes in $\sigma$, so detecting this effect will require samples large enough for this noise source to be averaged out." +" Nonetheless, it seems likely that data to test this prediction will become available in the next few years."," Nonetheless, it seems likely that data to test this prediction will become available in the next few years." +" It is particularly interesting to apply our models to the z~2—3 galaxies observed by ??,, ?,, 7,, ?,, and others, since these are thought to be examples of strongly gravitational instability-dominated disks."," It is particularly interesting to apply our models to the $z\sim 2-3$ galaxies observed by \citet{elmegreen04b, elmegreen05a}, \citet{genzel08a}, \citet{forster-schreiber09a}, \citet{cresci09a}, and others, since these are thought to be examples of strongly gravitational instability-dominated disks." +" We first note that, in the redshift range z—23 for halos of mass My,=1013 Mo, thought to be typical of the observed systems, the models shown in Figures 2 and 3 give x=81073—1.11072."," We first note that, in the redshift range $z=2-3$ for halos of mass $M_h = 10^{12}$ $\msun$, thought to be typical of the observed systems, the models shown in Figures \ref{fig:halosigma} and \ref{fig:halovsigma} give $\chi = 8\times 10^{-3} - 1.1\times 10^{-2}$." +" For these values of x and gas fractions f,— using equations (40)) and (42)) the ratio of star formation1/2, time to accretion time tgr/tace=1.8— 2.6, so the star formation rate is roughly 1/2—1/3 of the total accretion rate."," For these values of $\chi$ and gas fractions $f_g = 1/2$, using equations \ref{tacc}) ) and \ref{tsf}) ) the ratio of star formation time to accretion time $t_{\rm SF} / t_{\rm acc} = 1.8 - 2.6$ , so the star formation rate is roughly $1/2 - 1/3$ of the total accretion rate." +" Given the uncertainties in this model and thedispersion in expected accretion rates, for simplicity we can simply adopt M.~Mext."," Given the uncertainties in this model and thedispersion in expected accretion rates, for simplicity we can simply adopt $\dot{M}_* \approx \dot{M}_{\rm ext}$." +" Since the star formation rates are observed (and have typical values ~100 Mo ντ”1), we can plug them into our model in place of Mex in order to predict disk properties."," Since the star formation rates are observed (and have typical values $\sim 100$ $\msun$$^{-1}$ ), we can plug them into our model in place of $\dot{M}_{\rm ext}$ in order to predict disk properties." +" Doing so, we find that the redshift 2—3 disks should have velocity dispersions (from equation 34)) M.100=M,/100 Mo yr-!, independent of their wheremaximum rotation velocities Vinax."," Doing so, we find that the redshift $2-3$ disks should have velocity dispersions (from equation \ref{sigmaeq}) ) where $\dot{M}_{*,100} = \dot{M}_* / 100$ $\msun$ $^{-1}$, independent of their maximum rotation velocities $V_{\rm max}$ ." + Thus galaxies of similar star formation rate and gas fraction should have the same o independent of V4., Thus galaxies of similar star formation rate and gas fraction should have the same $\sigma$ independent of $V_{\rm max}$ . + The viscous accretion timescale required for the gas at theedge of one of these, The viscous accretion timescale required for the gas at theedge of one of these +terrestrial timescale(o...22).. detecting errors inthe Solar-System ephemeris (2)... ancl providing constraining limits on. or a detection of. low-Lrequeney GWs.,"terrestrial timescale\citep[e.g.,][]{pt96,2010arXiv1011.5285H}, detecting errors inthe Solar-System ephemeris \citep{2010ApJ...720L.201C}, and providing constraining limits on, or a detection of, low-frequency GWs." + Phe project has been ongoing since late 2004., The project has been ongoing since late 2004. + Observations of some of the PIUEX pulsars have been made at the Parkes observatory since 1994. albeit with less regularity and precision.," Observations of some of the PPTA pulsars have been made at the Parkes observatory since 1994, albeit with less regularity and precision." + Recent work (??777?7?7) has addressed the detectability of individual sources of GWs in pulsar timing residuals and shows that it is unlikely that current instrumentation will allow a detection.," Recent work \citep{2010MNRAS.407..669Y, 2010arXiv1005.5163B, 2010MNRAS.401.2372V, svv09, 2010arXiv1008.1782C} has addressed the detectability of individual sources of GWs in pulsar timing residuals and shows that it is unlikely that current instrumentation will allow a detection." + However. if the universe contains many such sources of GWs. these sources will form an isotropic stochastic eravitational-wave background (GWDB). 2.0 2..," However, if the universe contains many such sources of GWs, these sources will form an isotropic stochastic gravitational-wave background (GWB). \citet{saz78}, \citet{det79}," + ? and ? have deseribed how pulsar timing arrays (PPAs). such as the PPEA. can directly detect such a background of ~nullz frequeney GWs.," \citet{hd83} and \citet{jhlm05} have described how pulsar timing arrays (PTAs), such as the PPTA, can directly detect such a background of $\sim$ nHz frequency GWs." + For each. pulsar. this CWB would. cause ολ perturbations that are correlated between pulsar pairs in a quadrupolar fashion.," For each pulsar, this GWB would cause ToA perturbations that are correlated between pulsar pairs in a quadrupolar fashion." + This correlation. which cepends only on the angle between the pair of pulsars as shown in Figure 1 (2).. provides an unambiguous signature of the CWB.," This correlation, which depends only on the angle between the pair of pulsars as shown in Figure 1 \citep{hd83}, provides an unambiguous signature of the GWB." +" The functional form of this signature is given by: where =1cos6),)]2 and 8;; is the angle between pulsars 7 and j subtended at the observer (22).."," The functional form of this signature is given by: where $x=[1-\cos(\theta_{ij})] / 2$ and $\theta_{ij}$ is the angle between pulsars $i$ and $j$ subtended at the observer \citep{hd83, jhlm05}." + The function C(86;;) is independent of CGAY frequency. and. is) derived assuming GWs are described. by general relativity: other CAV modes are analysed in ? but are not considered. in this paper.," The function $\zeta(\theta_{ij})$ is independent of GW frequency, and is derived assuming GWs are described by general relativity; other GW modes are analysed in \citet{2008ApJ...685.1304L} but are not considered in this paper." + We believe that a first detection of the GWB is only possible via an unambiguous detection ofthis expected correlation., We believe that a first detection of the GWB is only possible via an unambiguous detection of this expected correlation. + In. view of the widespread. interest in such a detection. we have designed a detection procedure that can show this signature in an easily discernible and convincing manner.," In view of the widespread interest in such a detection, we have designed a detection procedure that can show this signature in an easily discernible and convincing manner." + Several techniques have already been proposed. in the literature to both limit (72777). and. detect (72). the CAVB.," Several techniques have already been proposed in the literature to both limit \citep{1983ApJ...265L..35R, ktr94, 1996PhRvD..53.3468T, lom02, jhv+06} and detect \citep{jhlm05, 2009PhRvD..79h4030A} the GWB." + However. these methods have not taken into account all the details of optimally treating pulsar timing data. or are restricted. to. particular observations.," However, these methods have not taken into account all the details of optimally treating pulsar timing data, or are restricted to particular observations." + Application of a Bayesian technique (7). is ongoing work. and our method is completely independent.," Application of a Bayesian technique \citep{2009MNRAS.395.1005V} is ongoing work, and our method is completely independent." + The lowest published limit for a CGWD caused by supermassive binary black holes (2) begins to constrain the parameters of galaxy evolution (e.g...2).. cosmic strings (e.e..2) and relic GAs from the Big Bang (e.g.7)..," The lowest published limit for a GWB caused by supermassive binary black holes \citep{jhv+06} begins to constrain the parameters of galaxy evolution \citep[e.g.,][]{2003ApJ...590..691W}, cosmic strings \citep[e.g.,][]{dv05} and relic GWs from the Big Bang \citep[e.g.,][]{mag00}." + Further improvements in sensitivity could. either enable detection of GWs or rule out most. proposed. models ofa GWD., Further improvements in sensitivity could either enable detection of GWs or rule out most proposed models of a GWB. + The GWB detection technique we present here is based on the method of ?.., The GWB detection technique we present here is based on the method of \citet{jhlm05}. + It improves on their technique in a number of wavs: Our technique is not optimal for bounding the GAB with these observations because the variation in S/N ratio otween pulsars is too large., It improves on their technique in a number of ways: Our technique is not optimal for bounding the GWB with these observations because the variation in S/N ratio between pulsars is too large. + This means that there are not enough significant cross power spectra to compensate. [or he low value of the average cross correlation., This means that there are not enough significant cross power spectra to compensate for the low value of the average cross correlation. + X tighter und. on the GAVB amplitude could. be obtained with hese observations using the amplitudes of the individual »ower spectra (similarto2).., A tighter bound on the GWB amplitude could be obtained with these observations using the amplitudes of the individual power spectra \citep[similar to][]{jhv+06}. + However. a detection algorithm cannot be based on the amplitudes of individual power spectra because there arc many unknown contributions to hose power spectra.," However, a detection algorithm cannot be based on the amplitudes of individual power spectra because there are many unknown contributions to those power spectra." + We discuss a number of issues that are common to both the 7. limit technique and any limit echnique based on measuring the CAVB-ineluced correlation oween pulsars., We discuss a number of issues that are common to both the \citet{jhv+06} limit technique and any limit technique based on measuring the GWB-induced correlation between pulsars. + Such issues include the estimation of power spectra when the sampling is irregular and the To. uncertainties are variable. and the ellects of fitting the imine model.," Such issues include the estimation of power spectra when the sampling is irregular and the ToA uncertainties are variable, and the effects of fitting the timing model." + In 2 we describe the observations and the analysis that ed to the timing residuals we use in this paper., In \ref{sec:obsns} we describe the observations and the analysis that led to the timing residuals we use in this paper. + 83. describes he theoretical background. ancl our method for making a detection of the isotropic stochastic CWD., \ref{sec:method} describes the theoretical background and our method for making a detection of the isotropic stochastic GWB. + &4. describes the results obtained. 85. deseribes their implications ancl the outstanding issues for GWD detection via pulsar timing. and 8&6 summarises our conclusions.," \ref{sec:res} describes the results obtained, \ref{sec:disc} describes their implications and the outstanding issues for GWB detection via pulsar timing, and \ref{sec:conc} summarises our conclusions." + The 20 pulsars used in this paper were observed. for ~ min to hh in each observation. depending on the hardware being used at the time.," The 20 pulsars used in this paper were observed for $\sim$ min to h in each observation, depending on the hardware being used at the time." +" Since 2005. the typical integration time on most pulsars is lhh. For each observation a mean pulse profile was formed using an ephemeris which ""folds"" the data at the apparent pulse period."," Since 2005, the typical integration time on most pulsars is $\sim$ h. For each observation a mean pulse profile was formed using an ephemeris which “folds” the data at the apparent pulse period." + Observations of cach pulsar were mace every few weeks (although there are some gaps of many months) and the observations span many vears. as shown in Table 1 and. Figure 2..," Observations of each pulsar were made every few weeks (although there are some gaps of many months) and the observations span many years, as shown in Table \ref{tbl:jorisData} and Figure \ref{fig:overlaps}. ." + The time shift. between a. standard: pulse profile ancl the observed profile is measured. using the technique described in ?.. as," The time shift between a standard pulse profile and the observed profile is measured using the technique described in \citet{tay92}, , as" +"""here are about 170 unidentified *5-rav sources in the third EGRET catalog. anc nearly. one third. of these sources [ie close to the Galactic plane b«D (Llartman et al.","There are about 170 unidentified $\gamma$ -ray sources in the third EGRET catalog, and nearly one third of these sources lie close to the Galactic plane $|b|<5^\circ$ (Hartman et al." + 1999)., 1999). + Alos of those unidentified sources in the Galactic plane can be icentified as οταν pulsars. possibly Ceminga-like pulsars which are radio quiet (Cheng Zhang 1998: Zhang. Zlang MCrene 2000).," Most of those unidentified sources in the Galactic plane can be identified as $\gamma$ -ray pulsars, possibly Geminga-like pulsars which are radio quiet (Cheng Zhang 1998; Zhang, Zhang Cheng 2000)." + For the medium and high latitude sources. it has been suggested that some of them are associated with the supernova remnants in the nearby Gould. Belt (Gehrels et al.," For the medium and high latitude sources, it has been suggested that some of them are associated with the supernova remnants in the nearby Gould Belt (Gehrels et al." + 2000: Grenier 2000)., 2000; Grenier 2000). + In. addition. Harding Zlane (2001) used the polar cap model (Daugherty Harding 19906) to investigate if s-rayv pulsars viewed at a large angle to the neutron star magnetic pole could. contribute to unidentified. EGRET sources in the medium [atitudes associated with the Gould. Belt.," In addition, Harding Zhang (2001) used the polar cap model (Daugherty Harding 1996) to investigate if $\gamma$ -ray pulsars viewed at a large angle to the neutron star magnetic pole could contribute to unidentified EGRET sources in the medium latitudes associated with the Gould Belt." + Pheir results suggest that at least some of racdio-quiet Could. Belt sources detected by EGRET could be such olf-beam >-rav pulsars., Their results suggest that at least some of radio-quiet Gould Belt sources detected by EGRET could be such off-beam $\gamma$ -ray pulsars. + At the same time. these 5-rav pulsars could produce wind nebulae through the interactions between relativistic wind particles with the interstellar medium. (1981).," At the same time, these $\gamma$ -ray pulsars could produce wind nebulae through the interactions between relativistic wind particles with the interstellar medium (ISM)." + “Phe pulsar wind nebulae will contribute to the production of non-pulsed. X-ray. emission by svnchrotron. processes (Chevalier 2000). and TeV photons through inverse Compton scattering (ICS)Aharonian. Atovan Ixifune LOOT).," The pulsar wind nebulae will contribute to the production of non-pulsed X-ray emission by synchrotron processes (Chevalier 2000), and TeV photons through inverse Compton scattering (ICS)(Aharonian, Atoyan Kifune 1997)." + These excess Ley photons have been detected. in some known pulsar. wind nebulae. such as the Crab. Vela. PSIU 1706-44. possibly CGeminga. (lxifune. et al.," These excess TeV photons have been detected in some known pulsar wind nebulae, such as the Crab, Vela, PSR 1706-44, possibly Geminga (Kifune et al." + 1995: Yoshikoshi et al., 1995; Yoshikoshi et al. + 1997: Aharonian οἱ al., 1997; Aharonian et al. + 1999: Lessard οἱ al., 1999; Lessard et al. + 2000)., 2000). + Therefore. if -- pulsars contribute to he unidentified: EGRET sources. possible TeV signals coulc|. be expected to be detected. in these EGRET sources.," Therefore, if $\gamma$ -ray pulsars contribute to the unidentified EGRET sources, possible TeV signals could be expected to be detected in these EGRET sources." + Several groups have searched for TeV signals in the error boxes o unidentified IEEGIUZE sources. for example. with the IECRA ATRODICG array (Aharonian et al.," Several groups have searched for TeV signals in the error boxes of unidentified EGRET sources, for example, with the HEGRA AIROBICC array (Aharonian et al." + 20022). and the Whipple Lom Camma-lItay Telescope.," 2002a), and the Whipple 10m Gamma-Ray Telescope." + No Toy source detection has been confirmed at Whipple. with only anupper limit TeV 1ux for about 20 ΓΙΟΤΕ sources determined at ~(36)0LLphotoncmsy l'(pogan Weekes 2004).," No TeV source detection has been confirmed at Whipple, with only anupper limit TeV flux for about 20 EGRET sources determined at $\sim (3-6)\times 10^{-11}\ +{\rm photon\ cm^{-2}\ s^{-1}}$ (Fegan Weekes 2004)." + Deep observations of the Cvenus region using IIECGILA (Aharonian ct al., Deep observations of the Cygnus region using HEGRA (Aharonian et al. + 2002b) showed an unidentified TeV source in the vicinity of Cygnus OD2 with an integral flux ο1Γον}--51070photonem?s. +. at the edge of the," 2002b) showed an unidentified TeV source in the vicinity of Cygnus OB2 with an integral flux $F(>1\ {\rm TeV})\sim 5\times +10^{-13}\ {\rm photon\ cm^{-2}\ s^{-1}}$ , at the edge of the" +"and for themodes, i.e. when n>n,, In this simulation, we take 400 segments in the x-direction, and 200 segments in the y direction.","and for the, i.e. when $ n > n_c$, In this simulation, we take 400 segments in the $x$ -direction, and 200 segments in the $y$ direction." +" When restricted to the middle half domain, the functions also provide the for the simulations on the middle half domain."," When restricted to the middle half domain, the functions also provide the for the simulations on the middle half domain." + The simulation results over the larger domain M are plotted inFigures 2 to 17.., The simulation results over the larger domain $\M$ are plotted inFigures \ref{f1.2} to \ref{f1.7e}. +" Figure 2 is the cone plot with isosurface of the initial state of the velocity field, and Figures 3 and 4 are the slice-plane plots of the initial state of dand v."," Figure \ref{f1.2} is the cone plot with isosurface of the initial state of the velocity field, and Figures \ref{f1.3} and \ref{f1.4} are the slice–plane plots of the initial state of $\phi$and $\psi$ ." +" Figures 5 to 9 are the contour plots of u, v, w, w and 6, respectively, on the plane z=—2,500m, att= 0."," Figures \ref{f1.4a} to \ref{f1.4e} are the contour plots of $u$, $v$, $w$, $\psi$ and $\phi$, respectively, on the plane $z=-2,500m$, at$t=0$ ." +" Figure 10 is the cone plot with isosurface of the velocity field at the finaltime t=T, and Figures 11and 12are the slice-plane plots of thestate of @ and w at the final time t= T."," Figure \ref{f1.5} is the cone plot with isosurface of the velocity field at the finaltime $t =T$, and Figures \ref{f1.6} and \ref{f1.7} are the slice–plane plots of thestate of $\phi$ and $\psi$ at the final time $t = T$ ." +" Figures 13to 17 are the contour plots of u, v, w, w and $, respectively, on the plane z= —2,500m, att— T."," Figures \ref{f1.7a} to \ref{f1.7e} are the contour plots of $u$ , $v$ , $w$ , $\psi$ and $\phi$ , respectively, on the plane $z=-2,500m$ , at$t=T$ ." +than we have assumed in our mocelling (Gaskell 1984).,than we have assumed in our modelling \citep{gaskell}. +. The presence of FIHILs in the spectra of the majority. of active galaxies has led to a number ofstudies on their nature. kinematies and location in AGN (e.g. see Alullaneyctal. 2009)).," The presence of FHILs in the spectra of the majority of active galaxies has led to a number of studies on their nature, kinematics and location in AGN (e.g. see \citealt{mullaney}) )." + One of the most credible suggestions for the origin ol the FLILL emission is the inner torus wall (see Muravama&Taniguchi1905 and Nagaoetal. 2001))., One of the most credible suggestions for the origin of the FHIL emission is the inner torus wall (see \citealt{murayama2} and \citealt{nagao1}) ). +" The ΤΕΙ, emission is rich in iron lines. which can be enhanced (relative to the classical NLR) by the evaporation of dust. erains in the inner torus wall. releasing the iron locked up in the erains (Pier&Voit1995)."," The FHIL emission is rich in iron lines, which can be enhanced (relative to the classical NLR) by the evaporation of dust grains in the inner torus wall, releasing the iron locked up in the grains \citep{pier}." +".. Moreover. studies of molecular emission [from the cireum-nuclear molecular. clouds. of the centres of the Milky Way and other galaxies (hypothetically the torus) reveal densities in the range ng» ~ 107"" em (c.g. Paglioneetal. 1998)). similiar to the densities deduced for the FIILLs."," Moreover, studies of molecular emission from the circum-nuclear molecular clouds of the centres of the Milky Way and other galaxies (hypothetically the torus) reveal densities in the range ${_{H2}}$ $\sim$ $^{5-6}$ $^{-3}$ (e.g. \citealt{pag}) ), similiar to the densities deduced for the FHILs." + In the case of QT131|16. our results are consistent with the idea that the FLILLs are emitted by the far wall of the torus. observed. with our line of sight at a relatively large angle to the torus axis.," In the case of Q1131+16, our results are consistent with the idea that the FHILs are emitted by the $\it{far}$ $\it{wall}$ of the torus, observed with our line of sight at a relatively large angle to the torus axis." + We emphasise that such a geometry is Consistent with the relatively narrow line widths and small velocity shifts of the FILL. since the circular velocities associated with the torus and any out-ol-the-plane gas motions would then be directed close to perpendicular to the line of sight.," We emphasise that such a geometry is consistent with the relatively narrow line widths and small velocity shifts of the FHIL, since the circular velocities associated with the torus and any out-of-the-plane gas motions would then be directed close to perpendicular to the line of sight." + In this case. our results imply that the torus is dynamically cold. with velocity. dispersion that is small relative to its circular. velocity.," In this case, our results imply that the torus is dynamically cold, with velocity dispersion that is small relative to its circular velocity." + Lt is dillicult to entirely rule out the idea that the ELILEs are emitted by an infalling molecular cloud. or a clump of the torus which has broken off from the rest of the torus and is falling towards the AGN.," It is difficult to entirely rule out the idea that the FHILs are emitted by an infalling molecular cloud, or a clump of the torus which has broken off from the rest of the torus and is falling towards the AGN." + However. in such cases we might expect to see a larger velocity shift between the ELILE emission lines and the host galaxy rest-frame. unless the cloud happens to be falling perpendicular to the line of sight.," However, in such cases we might expect to see a larger velocity shift between the FHIL emission lines and the host galaxy rest-frame, unless the cloud happens to be falling perpendicular to the line of sight." + Therefore the FLILL emission is most likely to originate from the inner torus wall of the AGN. supporting the original suggestion of Muravama&Taniguchi(1908) and Nagaoetal.(2001).," Therefore the FHIL emission is most likely to originate from the inner torus wall of the AGN, supporting the original suggestion of \citet{murayama2} and \citet{nagao1}." +. The idea that the FILL region is located in the torus can be further investigated by determining its radial distance from the AGN (rg)., The idea that the FHIL region is located in the torus can be further investigated by determining its radial distance from the AGN $r_H$ ). + First we estimate rg based on the spatial information eiven in and the parameters determined in 4.1.," First we estimate $r_H$ based on the spatial information given in $\oint$ 3.1, and the parameters determined in $\oint$ 4.1." + The ionising 9.1.luminosity (τον) of the illuminating source is related to the racial distance of the emission region [roni the ionising source (r) and the ionisation parameter (UW). by: where ng is the hydrogen density. (iv). is the mean ionising.e. photon.. and e is. the speed of ENlight.," The ionising luminosity $L_{ION}$ ) of the illuminating source is related to the radial distance of the emission region from the ionising source (r) and the ionisation parameter (U), by: where $n_{H}$ is the hydrogen density, $\left \langle h\nu \right \rangle_{ion}$ is the mean ionising photon, and c is the speed of light." + EThen. solving for the radial distance of the low ionisationdensity region. we get:," Then, solving for the radial distance of the low ionisation/density region, we get:" + , +0.511 a) IIubble Space Telescope WEPC? image of TRAS 08572|3915.,0.3in a) Hubble Space Telescope WFPC2 image of IRAS 08572+3915. + b) CO(L5» 0) contours of the merecr superimposed ou a three-color composite NICMOS nnaege (due-1.1 imi. green = 1.6 jan. red22.2 pmuj.," b) $1\to0$ ) contours of the merger superimposed on a three-color composite NICMOS image (blue=1.1 $\mu$ m, green = 1.6 $\mu$ m, red=2.2 $\mu$ m)." +" The CO contours are plotted as3056...1056...DOT... 6086... TOC. SUE. Ορ, and the peak flux of 8.1 Jy kan lj camD."," The CO contours are plotted as, and the peak flux of 8.4 Jy km $^{-1}$ $^{-1}$." +" The CO enission is unresolved. with a beam FWIIM of 271«178 at a position auele of 77.9""."," The CO emission is unresolved, with a beam FWHM of $2\farcs4\times1\farcs8$ at a position angle of $^{\rm o}$." + The appareut northwest extension of CO emission may be au artifact., The apparent northwest extension of CO emission may be an artifact. + The »0) spectra of the NW nucleus is also shown., The $\to$ 0) spectrum of the NW nucleus is also shown. + For voth mages. north is up aud east is to the left.," For both images, north is up and east is to the left." + a) Uublie Space Telescope WEPC2 image of TRAS 121121.0305., a) Hubble Space Telescope WFPC2 image of IRAS 12112+0305. + bj) CO(L» 0) coitours of the merger superimposed on a three-color composite NICMOS Mnage {due-il.l gan. green = 1.6 gan. red=2.2 jan).," b) $1\to0$ ) contours of the merger superimposed on a three-color composite NICMOS image (blue=1.1 $\mu$ m, green = 1.6 $\mu$ m, red=2.2 $\mu$ m)." +" The CO coutours are plotted as.. 50%.. 6054.TUA. sO%.. 90%... acd the peak flux of 21.7 Jy ans! ο,"," The CO contours are plotted as, , and the peak flux of 24.7 Jy km $^{-1}$ $^{-1}$." +" The CO emission for cach nucleus is unresolved. with a beam EWIIM of 277«179 at a position angle of οσο, "," The CO emission for each nucleus is unresolved, with a beam FWHM of $2\farcs7\times1\farcs9$ at a position angle of $^{\rm o}$." +The > 0) spectra of the SW and NE progenitors are also shown., The $\to0$ ) spectra of the SW and NE progenitors are also shown. + For both nuages. north is up aud east is to the left.," For both images, north is up and east is to the left." + a) IIubble Space Telescope WFPC?2 image of Ak 163, a) Hubble Space Telescope WFPC2 image of Mrk 463. + by COL» 0) contours of the merecr superimposed on a three-color composite NICMOS image (1due-1.l juu. ercen = 1.6 qun. red=2.07 jan).," b) $1\to0$ ) contours of the merger superimposed on a three-color composite NICMOS image (blue=1.1 $\mu$ m, green = 1.6 $\mu$ m, red=2.07 $\mu$ m)." + The 2;02 0mission is unresolved for Mrk 163E (the speckle pattern is au artifact «of the NICMOS PSF). while Mrk. L63W is clearly resolved.," The $\mu$ m emission is unresolved for Mrk 463E (the speckle pattern is an artifact of the NICMOS PSF), while Mrk 463W is clearly resolved." +" The CÓ contours are plotted as5056. ον,TAM.SUI. ο. and the peal flux of 6.1 Jv lan 11 +."," The CO contours are plotted as, , and the peak flux of 6.4 Jy km $^{-1}$ $^{-1}$." + The CO emission is unresolved. with a beam FEWITM of 277<272 at a position angle of -61.9°.," The CO emission is unresolved, with a beam FWHM of $2\farcs7\times2\farcs2$ at a position angle of $^{\rm o}$." + The »0) spectruui of the E nucleus is also shown., The $\to$ 0) spectrum of the E nucleus is also shown. + For both images. north is up aud cast is to the left.," For both images, north is up and east is to the left." + My16 VS. yg22 color-color diagram for the five ULIGs: data for the nuclei of Arp 220 are also plotted., $m_{1.1-1.6}$ vs. $m_{1.6-2.2}$ color-color diagram for the five ULIGs; data for the nuclei of Arp 220 are also plotted. + Fluxes are measured ina 1711 diameter aperture centered on cach nucleus., Fluxes are measured in a $1\farcs1$ diameter aperture centered on each nucleus. + The locus for the evolution of au instantancous starburst with a Salpeter IMF is also shown., The locus for the evolution of an instantaneous starburst with a Salpeter IMF is also shown. + The typical colors of optical PC QSOs are shown plotted with variable percentages of 2.2 gan emission due to wari dust., The typical colors of optical PG QSOs are shown plotted with variable percentages of 2.2 $\mu$ m emission due to warm dust. + Lastly a reddening vector based on the extinction curve of Ricke Lebofskv (1985) modified at the shortest waveleneths is shown for two cases - a foreground screen of dust and a modeliu which the dust is uniforiulv mixed with the οΓιο sources.," Lastly, a reddening vector based on the extinction curve of Rieke Lebofsky (1985) modified at the shortest wavelengths is shown for two cases - a foreground screen of dust and a modelin which the dust is uniformly mixed with the emitting sources." +Adapted from Scoville et al (2000).,Adapted from Scoville et al (2000). +range of sino. which drastically simplifies the subsequent analysis.,"range of $\sin\,\phi$, which drastically simplifies the subsequent analysis." + We also replace a polyuouial expausion for limbshift with the more sophisticated model from (Hathaway1996):: ESSEPECL rhol).{9) where P? are shifted Legendre polynomials orthogonal on [0.1]. p is the central augle A). and 9; are free fitting coellicients.," We also replace a polynomial expansion for limbshift with the more sophisticated model from \citep{hat1}: _i ), where $P_k^*$ are shifted Legendre polynomials orthogonal on $[0,1]$, $\rho$ is the central angle $\cos\,\rho=\cos\,\phi\,\cos\,\lambda$ ), and $\beta_i$ are free fitting coefficients." + Thus. the new model. which more faithfully represeuts the observed. velocity field is We carried over the ABC terms of differential rotation (rather than using Ciegenbauer polynomials) to simplify subsequent transformations.," Thus, the new model, which more faithfully represents the observed velocity field is We carried over the $ABC$ terms of differential rotation (rather than using Gegenbauer polynomials) to simplify subsequent transformations." + Our task is now to recompute the observed parameters of the velocity field using the published ABCDEF parameters., Our task is now to recompute the observed parameters of the velocity field using the published $ABCDEF$ parameters. + The fitting procedure is a linear least-squares problem aud the trausformatiou problem cau be expressed in matrix uotation = Tright]]X+ ¢.(7) where A is the matrix of ciffereutial rotation (tlie ABC terms). ® is the matrix of the symmetric stretch (the DEF terms). is the matrix of the new meridional flow aud limb shift terms. X is the vector of free parameters of the old model. x is the vector of [ree parameters of the new moclel. aud € is raudom noise.," The fitting procedure is a linear least-squares problem and the transformation problem can be expressed in matrix notation = + , where ${\bf \Lambda}$ is the matrix of differential rotation (the $ABC$ terms), ${\bf \Phi}$ is the matrix of the symmetric stretch (the $DEF$ terms), is the matrix of the new meridional flow and limb shift terms, ${\bf \tilde x}$ is the vector of free parameters of the old model, ${\bf \bar x}$ is the vector of free parameters of the new model, and ${\bf \epsilon}$ is random noise." + It can be shown that in a least-squares solution.X..(8) where T!=(PUT)UE is the pseudoinverse of T.," It can be shown that in a least-squares solution, where ${\bf T}^\dagger=({\bf T}^{\rm T}{\bf T})^{-1}{\bf T}^{\rm T}$ is the pseudoinverse of ${\bf T}$." + The matrix aud inner vector products here are calculated through integratiou of the element products over the visible disk with the cos6 weieht.," The matrix and inner vector products here are calculated through integration of the element products over the visible disk with the $\cos\,b$ weight." + The iuuer products of the new model terms and the ABC terms are all zero (in other terms. these fuuctions are orthogonal).," The inner products of the new model terms and the $ABC$ terms are all zero (in other terms, these functions are orthogonal)." + Therefore. the ABC coelficieuts remain unchanged in this transformation. aud the new parameters depeud only onthe DEF coellicients.," Therefore, the $ABC$ coefficients remain unchanged in this transformation, and the new parameters depend only onthe $DEF$ coefficients." + After some toil with inteeratione aud matrix Inversion. one obtains," After some toil with integration and matrix inversion, one obtains" +As discussed. in. Appendix (X. dt ds important to consider not onlv the completeness of the sample but also its contamination bv spurious sources arising from. noise peaks. especially when the counts are extended: past. the completeness limit.,"As discussed in Appendix A, it is important to consider not only the completeness of the sample but also its contamination by spurious sources arising from noise peaks, especially when the counts are extended past the completeness limit." + Lowe define the noise fraction as the fraction of false objects per magnitude bin. we may proceed with an incomplete sample only if the noise fraction brighter than our limiting magnitude is small.," If we define the noise fraction as the fraction of false objects per magnitude bin, we may proceed with an incomplete sample only if the noise fraction brighter than our limiting magnitude is small." + To estimate this we used the same pure noise image discussed: above. aud measured the magnitudes in 500 randomly placed apertures.," To estimate this we used the same pure noise image discussed above, and measured the magnitudes in 500 randomly placed apertures." +" ‘Table 2 shows the resulting distribution of magnitudes. with only of ""detections. falling below the 47=24 cutoll."," Table 2 shows the resulting distribution of magnitudes, with only of `detections' falling below the $H=24$ cutoff." + This should be considered. as an upper limit. since the detection in our sample is performed in the deeper Z-band image.," This should be considered as an upper limit, since the detection in our sample is performed in the deeper $I$ -band image." + Moreover. contamination. if it is left. unaccounted for. will tend to reduce the lensing signal.," Moreover, contamination, if it is left unaccounted for, will tend to reduce the lensing signal." + We therefore conservatively ignore this small ellect in our analysis., We therefore conservatively ignore this small effect in our analysis. + An essential precursor in examining a possible depletion elect in Abell 2219 is the location of the lensing and unlensecl population of galaxies. the latter of which is. of course. dominated for such a low redshift svstem by cluster members.," An essential precursor in examining a possible depletion effect in Abell 2219 is the location of the lensing and unlensed population of galaxies, the latter of which is, of course, dominated for such a low redshift system by cluster members." + The sequence of cluster galaxies is clearly visible on the 4.ff colour magnitude diagram shown in Fig. 4.., The sequence of cluster galaxies is clearly visible on the $I-H$ colour magnitude diagram shown in Fig. \ref{fig-colmag}. +" Taking into account known members and photometric errors. cluster galaxies can be optimally excised. according to the relation We can divide the remaining population of field ealaxies into ""red and ""blue (unlensed) field populations. adding the ""urther constraint that IS 0.5., Combining the present $_2$ S/HDS upper limit (Table \ref{table3}) ) with the $_2$ S value found by \citet[HDS/H$_2$S$\sim 0.1$]{vandishoeck95} gives: $_2$ S) $\geq$ 0.5. + It seems hence that while methanol aud hydrogen sulfide are consistent with the hypothesis of the random distribution ol D's and formation on the grain surfaces. formaldehyde is definitively off.," It seems hence that while methanol and hydrogen sulfide are consistent with the hypothesis of the random distribution of D's and formation on the grain surfaces, formaldehyde is definitively off." + The use of the F [actors has the ereal advantage to highlighüng what chemical mechanism is responsible for the observed deuteration (Roclgers&Charnley2002).. but obviously overlooks the details of We computed in Table 3. thecolumn densities for the IIDS molecule.," The use of the F factors has the great advantage to highlighting what chemical mechanism is responsible for the observed deuteration \citep{rodgers02}, but obviously overlooks the details of We computed in Table \ref{table3} thecolumn densities for the HDS molecule." + Assuming that the IIDS/1I5S is around1054.. the value found for formaldehyde and other molecules presenting a large degree of deuteration. one would obtain [1ος abundances in the range (0.2 - 2) x ," Assuming that the $_2$ S is around, the value found for formaldehyde and other molecules presenting a large degree of deuteration, one would obtain $_2$ S abundances in the range (0.2 - 2) $\times$ " +2008).,. +. The typical number. width and spatial distribution of long strings or string loops in a given field of view are also all governed by the concordance cosmological model.," The typical number, width and spatial distribution of long strings or string loops in a given field of view are also all governed by the concordance cosmological model." + Our30 simulations of the CMB signal are built as a superposition of a unique realistic string signal simulation borrowed fromwith 30 simulations of the Gaussian correlated noise., Our$30$ simulations of the CMB signal are built as a superposition of a unique realistic string signal simulation borrowed fromwith $30$ simulations of the Gaussian correlated noise. + Thestring tension p. a dimensionless number related to the mass per unit length of string. is up to some extent a free parameter of the model.," Thestring tension $\rho$, a dimensionless number related to the mass per unit length of string, is up to some extent a free parameter of the model." + This tension sets the overall amplitude of the signal and needs to be evaluated from observations., This tension sets the overall amplitude of the signal and needs to be evaluated from observations. + For the sake of the present analvsis. we only study the string signal forone realistic value p=3.2«107. which technically fixes the SNR of the observed string signal buried in the astrophysical noise.," For the sake of the present analysis, we only study the string signal forone realistic value $\rho=3.2\times10^{-8}$, which technically fixes the SNR of the observed string signal buried in the astrophysical noise." + This value is assessed prior to any signal reconstruction. by fitting the power spectrum of the data to the sum of the power spectra of the signa and noise on the frequencies probed2008).," This value is assessed prior to any signal reconstruction, by fitting the power spectrum of the data to the sum of the power spectra of the signal and noise on the frequencies probed." +. This estimation may be considered as very precise at the tension of interest and is not to be considered as a significant source of error in the subsequent reconstruction., This estimation may be considered as very precise at the tension of interest and is not to be considered as a significant source of error in the subsequent reconstruction. + In thiscontext. preliminary analysis of 16 independen realistic simulations of a string signal. also from(2008).. allows one to show that the random process from which the string signal arises is well modelled by GGD's in wavele space2008).," In thiscontext, preliminary analysis of $16$ independent realistic simulations of a string signal, also from, allows one to show that the random process from which the string signal arises is well modelled by GGD's in wavelet space." +. We consideraredundantsteerable wavelet basis V. with 6 scales j (1xj: 6) including low pass and high pass axisymmetricfilters. andfour intermediate scales detining steerable wavelets with 6basis orientations q (1i.," The weight $T^{(ij)}$ is required to satisfy the nulling condition \ref{eq:nc}) ) in its discretized form, for all $j>i$." + Here. y; and y; shouldbe chosen such that they represent well the distance to redshift bins / and Κ.," Here, $\chi_i$ and $\chi_k$ shouldbe chosen such that they represent well the distance to redshift bins $i$ and $k$." + In this paper we choose them to be the distances corresponding to the median redshift of the bin., In this paper we choose them to be the distances corresponding to the median redshift of the bin. + The summation over index k runs from /+I rather than / since we consider only bispectrum measures withij>/ and &>i to avoid [Land GIL systematies., The summation over index $k$ runs from $i+1$ rather than $i$ since we consider only bispectrum measures with $j > i$ and $k > i$ to avoid III and GII systematics. +" In this case B.d in (17)) can be written as a sum of BerBeo and BLky, and yun can be expressed as Suppose one has infinitely many redshift bins. then the lensing signal in bin & caused by the matter inhomogeneity in bin i gs exactly proportional to χα. which means BoΕ/Α""if).0) can be written. as a product ofc 1=q;/y; and some function of the parameters other than y;: Then we have This suggests that only the GGG contribution ts left in the nulled measure Y. the GGI contribution has been “nulled"," In this case $B^{(ijk)}_{\textrm{obs}}$ in \ref{eq:Yij}) ) can be written as a sum of $B^{(ijk)}_{\textrm{GGG}}$ and $B^{(ijk)}_{\textrm{GGI}}$, and $Y^{(ij)}$ can be expressed as Suppose one has infinitely many redshift bins, then the lensing signal in bin $k$ caused by the matter inhomogeneity in bin $i$ is exactly proportional to $1-\chi_i/\chi_k$ , which means $B^{(ijk)}_{\textrm{GGI}}({\ell}_1,{\ell}_2,{\ell}_3)$ can be written as a product of $1-\chi_i/\chi_k$ and some function of the parameters other than $\chi_k$ : Then we have This suggests that only the GGG contribution is left in the nulled measure $Y^{(ij)}$ , the GGI contribution has been “nulled" +(from Falco et al.,(from Falco et al. + 1996) while varving absolute position ou the chip to minimize the residuals of the image miuus the model using a linear least-squares ft., 1996) while varying absolute position on the chip to minimize the residuals of the image minus the model using a linear least-squares fit. + Usine the relative positions measured by UST (Rix ct al., Using the relative positions measured by HST (Rix et al. + 1992) changed the flux ratios bv an amount much smaller than the error bars., 1992) changed the flux ratios by an amount much smaller than the error bars. + The resulting fluxes are shown in Table 2.., The resulting fluxes are shown in Table \ref{tab1}. +" Figure lL shows the suuuued tage from both bands aud both nights. smoothed with a 0.25"" boxcar to eliminate noise."," Figure 1 shows the summed image from both bands and both nights, smoothed with a $\arcsec$ boxcar to eliminate noise." + The leus galaxy is uudetected: neither is there auy evideuce of a fifth lensed QSO image., The lens galaxy is undetected; neither is there any evidence of a fifth lensed QSO image. +" For comparison to models. the fraction of the total Einstein Cross flux contained in cach image was computed. hereafter referred to as the ""fux ratio: ic. if all four nuages have the same fux. then the flux ratio is 1/1 for cach image."," For comparison to models, the fraction of the total Einstein Cross flux contained in each image was computed, hereafter referred to as the “flux ratio""; i.e. if all four images have the same flux, then the flux ratio is 1/4 for each image." + As inentioned above. the pointing errors resulting frou dithering can lead to a broadening of the PSF for long observations ou faint sources. such as those prescuted here.," As mentioned above, the pointing errors resulting from dithering can lead to a broadening of the PSF for long observations on faint sources, such as those presented here." + A stellar PSF (corrected for pointing errors) was convolved with a gaussian. varvine the FWIIMD until the best fit was obtained for each muaege.," A stellar PSF (corrected for pointing errors) was convolved with a gaussian, varying the FWHM until the best fit was obtained for each image." + The typical FWIAL varies between 3 aud 5 pixels (see Table 2)). but the flux ratio of cach dmage on cach night in cach waveband varies by ouly if the EWIINE is chaueed from 3 to 5 pixels (0725 to 071).," The typical FWHM varies between 3 and 5 pixels (see Table \ref{tab1}) ), but the flux ratio of each image on each night in each waveband varies by only if the FWHM is changed from 3 to 5 pixels $0\farcs25$ to $0\farcs4$ )." + This demonstrates that the flux ratios are rather insensitive to the gaussian FWIAL, This demonstrates that the flux ratios are rather insensitive to the gaussian FWHM. + The absolute fluxes. however. are quite scusitive to the asstuued EWIIM.," The absolute fluxes, however, are quite sensitive to the assumed FWHM." + Fortunately. the aremuent for microleusiug depends oulv ou the relative flux ratios.," Fortunately, the argument for microlensing depends only on the relative flux ratios." + A Monte Carlo technique was used to compute the error bars ou the fluxes., A Monte Carlo technique was used to compute the error bars on the fluxes. + Duriug these observations the LNS chip exhibited pattern noise which prevented a direct measurement of the error bars frou photon counting statistics., During these observations the LWS chip exhibited pattern noise which prevented a direct measurement of the error bars from photon counting statistics. + Iustead. the best-fit 1uodel of the four images was added back iun at various points on the chip to create simulated images.," Instead, the best-fit model of the four images was added back in at various points on the chip to create simulated images." + The simulated images were run through the entire reduction procedure. measuring the position. eaussian EWIIM. and fuses of the four images.," The simulated images were run through the entire reduction procedure, measuring the position, gaussian FWHM, and fluxes of the four images." + This was repeated —100 times to compute the standard deviation of the image fluxes. flux ratios. PWHAL aud position.," This was repeated $\sim$ 100 times to compute the standard deviation of the image fluxes, flux ratios, FWHM, and position." + The error bars ou the flux ratios are typically about a factor of 2 ereater than what one would infer from shot-nolse statistics only., The error bars on the flux ratios are typically about a factor of 2 greater than what one would infer from shot-noise statistics only. + Thus. only the Moute Carlo error bars are reported in this paper (Table 2:: L-sigmia error bars are alwavs quoted).," Thus, only the Monte Carlo error bars are reported in this paper (Table \ref{tab1}; 1-sigma error bars are always quoted)." + The error bars on the absolute flux are quite large. mostly due to the munecertainty in the poiut spread fuuction.," The error bars on the absolute flux are quite large, mostly due to the uncertainty in the point spread function." + The error bars ou the iieasured. FWIAL are reported in Table 2:: this is the PWHAT eaussian which was couvolved with the stellar PSF to approximate the QSO PSF., The error bars on the measured FWHM are reported in Table \ref{tab1}; this is the FWHM gaussian which was convolved with the stellar PSF to approximate the QSO PSF. + The fux ratios measured ou both nights aud iu both bands are consistent with being coustaut with tine and with waveleneth. as shown in Figure 2.," The flux ratios measured on both nights and in both bands are consistent with being constant with time and with wavelength, as shown in Figure 2." + Auv disagereeimoeut between the measurements are consistent with raudon errors causing the differences: there is no need to invoke variabilitv iu the flux ratios with time or between the two bauds. nor anv need to fud svsteniatiec errors to explain the differences.," Any disagreement between the measurements are consistent with random errors causing the differences; there is no need to invoke variability in the flux ratios with time or between the two bands, nor any need to find systematic errors to explain the differences." + 2uuu Table 3 compares the mid-infrared flux ratios (averaged from both nights aud both bands) to the flux ratios in other wave bands., 2mm Table \ref{tab2} compares the mid-infrared flux ratios (averaged from both nights and both bands) to the flux ratios in other wave bands. + The V baud magnitudes are frou the OGLE monitoring data ou the dates closest to the IKeck observations (available on their website: Woznnuiak et al., The V band magnitudes are from the OGLE monitoring data on the dates closest to the Keck observations (available on their website; Woźnniak et al. + 2000); this data was corrected for extinction as described iu the Appeudix., 2000); this data was corrected for extinction as described in the Appendix. + The VLA radio data are from Falco et al. (, The VLA radio data are from Falco et al. ( +1996) which were taken in 1995.,1996) which were taken in 1995. + The CTI] ratios are, The CIII] ratios are +"calculated by where d;(z) is the luminosity distance at redshift, z, I is the photon index and S(e;,€2) is the observed energy flux between the energies ει and e».","calculated by where $d_L(z)$ is the luminosity distance at redshift, $z$, $\Gamma$ is the photon index and $S(\epsilon_1,\epsilon_2)$ is the observed energy flux between the energies $\epsilon_1$ and $\epsilon_2$." +" The energy flux is given from the photon flux F,, which is in the unit of photons/cm?/s, above €1 by Radio luminosity is also calculated in the same manner."," The energy flux is given from the photon flux $F_\gamma$ , which is in the unit of $^2$ /s, above $\epsilon_1$ by Radio luminosity is also calculated in the same manner." + Figure 1 shows the 5 GHz and 0.1-10 GeV luminosity relation ofFermi gamma-ray loud radio galaxies., Figure \ref{fig:lrlg} shows the 5 GHz and 0.1-10 GeV luminosity relation of gamma-ray loud radio galaxies. +" Square and triangle data represents FRI and FRII radio galaxies, respectively."," Square and triangle data represents FRI and FRII radio galaxies, respectively." + The solid line shows the fitting line to all the data., The solid line shows the fitting line to all the data. + The function is given by where errors show |-σ uncertainties., The function is given by where errors show $\sigma$ uncertainties. +" In the case of blazars, the slope of the correlation between L,(> 100MeV), luminosity above 100 MeV, and radio luminosity at 20 GHz is 1.074:0.05 (Ghirlandaetal.2010b)."," In the case of blazars, the slope of the correlation between $L_\gamma(>100 {\rm MeV})$ , luminosity above 100 MeV, and radio luminosity at 20 GHz is $1.07\pm0.05$ \citep{ghi10b}." +. The correlation slopes of gamma-ray loud radio galaxies are similar to that of blazars., The correlation slopes of gamma-ray loud radio galaxies are similar to that of blazars. + This may indicate that emission mechanism is similar in gamma-ray loud radio galaxies and blazars., This may indicate that emission mechanism is similar in gamma-ray loud radio galaxies and blazars. + We need to examine whether the correlation between the radio and gamma-ray luminosities is true or not., We need to examine whether the correlation between the radio and gamma-ray luminosities is true or not. +" In the flux limited observations, the luminosities of samples are strongly correlated with redshifts."," In the flux limited observations, the luminosities of samples are strongly correlated with redshifts." + This might result in a spurious luminosity correlation., This might result in a spurious luminosity correlation. +" As in previous works on blazar samples (Padovani1992;Zhangetal.2001;Ghirlandaetal. 2010b), we perform a partial correlation analysis to test the correlation between the radio and gamma-ray luminosities excluding the redshift dependence (see the Appendix for details)."," As in previous works on blazar samples \citep{pad92,zha01,ghi10b}, we perform a partial correlation analysis to test the correlation between the radio and gamma-ray luminosities excluding the redshift dependence (see the Appendix for details)." +" First, we calculatethe Spearman rank-order correlation coefficients (seee.g.Pressetal.1992)."," First, we calculatethe Spearman rank-order correlation coefficients \citep[see e.g.][]{nr92}." +". The correlation coefficient is 0.993, 0.993, 0.979 between and log;g between and redshift, and logigLscuzbetween L4,and redshift, log;oLsguz;respectively."," The correlation coefficient is 0.993, 0.993, 0.979 between $\log_{10}L_{\rm 5 GHz}$ and $\log_{10}L_\gamma$, between $\log_{10}L_{\rm 5 GHz}$ and redshift, and between $\log_{10}L_\gamma$ and redshift, respectively." +" Then, the partial correlation log;oL.,coefficient becomes 0.866 with chance probability 1.65x1079."," Then, the partial correlation coefficient becomes 0.866 with chance probability $1.65\times10^{-6}$." +" Therefore, we conclude that there is a correlation between the radio and gamma-ray luminosities of gamma-ray loud radio galaxies."," Therefore, we conclude that there is a correlation between the radio and gamma-ray luminosities of gamma-ray loud radio galaxies." +" In this section, we derive the GLF of gamma-ray loud radio galaxies, "," In this section, we derive the GLF of gamma-ray loud radio galaxies, $\rho_\gamma(L_\gamma,z)$." +"There is a correlation between the radio and gamma-ray p,(L,,z).luminosities as Equation 5..", There is a correlation between the radio and gamma-ray luminosities as Equation \ref{eq:lrlg}. . +" With this correlation, we develop the GLF by using the RLF of radio galaxies, p,(L,,z), with radio luminosity, L,."," With this correlation, we develop the GLF by using the RLF of radio galaxies, $\rho_r(L_r,z)$, with radio luminosity, $L_r$." + The GLF is given as where & is a normalization factor., The GLF is given as where $\kappa$ is a normalization factor. + We use the 151 MHz RLF (Willottetal.2001)., We use the 151 MHz RLF \citep{wil01}. +". Since they presented the formula of FRI and FRII RLFS separately, we combined them as in their paper because it is difficult to analyze each population separately with our limited number of "," Since they presented the formula of FRI and FRII RLFs separately, we combined them as in their paper because it is difficult to analyze each population separately with our limited number of samples." +"Moreover, since the cosmological parametersin Willottsamples.etal.(2001) are Qy2Q4=0 and /z 0.5, we also convert the RLF tothe standard cosmology adopted inthis study."," Moreover, since the cosmological parametersin \citet{wil01} are $\Omega_M=\Omega_\Lambda=0$ and $h=0.5$ , we also convert the RLF tothe standard cosmology adopted inthis study." + The RLF is given by, The RLF is given by +arc in normalized form.,arc in normalized form. + Now we cousider the effect of a phase gradient Vo in the screen., Now we consider the effect of a phase gradient $\nabla \phi_*$ in the screen. + It will tilt the angular spectra seen by the observer by an augle 0.=Vo./2h., It will tilt the angular spectrum seen by the observer by an angle $\theta_* = \nabla \phi_*/2k$. + If the eracicut is perpendicular to the velocity then it will have no effect ou the arc., If the gradient is perpendicular to the velocity then it will have no effect on the arc. + Thus we consider oulv the eradicut in the direction of the velocity., Thus we consider only the gradient in the direction of the velocity. + The group σαν is given by το)=PfeOV in uondsporsive (top sign) and dispersive (bottoni sign)o. cases., The group delay is given by $\tau_g (\theta ) = z\theta^2/c \mp z\theta\nabla\phi_*/\omega$ in nondispersive (top sign) and dispersive (bottom sign) cases. + The differeutial Doppler between au uuscattered wave arriving at auele 0. and a scattered wave arriving at angle 6.|90 is uuchaused bv the phase eracdieut., The differential Doppler between an unscattered wave arriving at angle $\theta_*$ and a scattered wave arriving at angle $\theta_* + \delta\theta$ is unchanged by the phase gradient. + The differential delay is more conrplex., The differential delay is more complex. + Iu the uon-dispersive case we lave ὅτι2607 fe. ie. the ares are unaffected by a pliase gradient. at least to first order.," In the non-dispersive case we have $\delta\tau_d = z\delta\theta^2/c$ , i.e. the arcs are unaffected by a phase gradient, at least to first order." +" However iu the dispersive case we have 67)=(007| 10,60)/c.", However in the dispersive case we have $\delta\tau_d = z(\delta\theta^2 + 4\theta_*\delta\theta)/c$ . + Putting this in nonualized form we have àzu/Ta=(faffag|20/04?(20./04Y?., Putting this in normalized form we have $\delta\tau_d/\tau_{d0} = (\delta f_d/f_{d0} + 2\theta_* /\theta_0)^2 - (2\theta_* /\theta_0)^2$. +" The apex of the arc is shifted in Doppler by (20.—/05)fy aud in delav by (20,/04)?tay.", The apex of the arc is shifted in Doppler by $(2\theta_* /\theta_0) f_{d0}$ and in delay by $(2\theta_* /\theta_0)^2 \tau_{d0}$. + Thus. if the phase gradient shifts he entire aneular spectimm by an amount comparable with the rms scattering angle (y. then the shift iu the apex of the parabola should be detectable in a dispersive nedimm.," Thus, if the phase gradient shifts the entire angular spectrum by an amount comparable with the rms scattering angle $\theta_0$, then the shift in the apex of the parabola should be detectable in a dispersive medium." + This analysis shows why tilted arcs are observed in dispersive cases and not m uou-dispersive cases., This analysis shows why tilted arcs are observed in dispersive cases and not in non-dispersive cases. + It also agrees with carlicr rough analyses of the slope of ited structures in the cdvnamic spectrum (Shishov 197I: Tewish 1980: Capta et al., It also agrees with earlier rough analyses of the slope of tilted structures in the dynamic spectrum (Shishov 1974; Hewish 1980; Gupta et al. + 1991)., 1994). + Wowever. it is difficult o use these expressions quantitatively to estimate the electron density eradicuts in the IISM because the ares are not always very clistinet (as in the case simulated).," However, it is difficult to use these expressions quantitatively to estimate the electron density gradients in the IISM because the arcs are not always very distinct (as in the case simulated)." + To do this one would ueed to model the eutire secondary spectrin iucludiug the effects of eradieuts both parallel and perpendicular to the velocity., To do this one would need to model the entire secondary spectrum including the effects of gradients both parallel and perpendicular to the velocity. + The simulated electric ποια £Or.ο.£f) allows one to calculate the pulse Poryt)=[FeEley.F2 at cach pixel.," The simulated electric field $E(x, y, f)$ allows one to calculate the pulse $I(x, y, t) = |F_\text{f} \{E(x, y, f)\}|^2$ at each pixel." + Were Fg is the Fourier transform operating on coordinate f. Thus the simulation provides a direct calculation of the pulse shape. including the arrival time variations.," Here $F_\text{f}$ is the Fourier transform operating on coordinate f. Thus the simulation provides a direct calculation of the pulse shape, including the arrival time variations." + Iu the simulation the mean clectron density over the simmlation window is zero. but at any given position there is “dispersion delay aud it fluctuates with position.," In the simulation the mean electron density over the simulation window is zero, but at any given position there is “dispersion delay” and it fluctuates with position." + Iu addition the pulse shape chanees on both the diffractive aud refractive scales., In addition the pulse shape changes on both the diffractive and refractive scales. + This is shown in Figure 10., This is shown in Figure 10. + Tere the pulse power is shown ou a scale over a lO dB dynamic range., Here the pulse power is shown on a $\log_{10}$ scale over a 40 dB dynamic range. + The phase screen logyydelay at fo is overplotted ou Figure 10 as a white line., The phase screen delay at $f_0$ is overplotted on Figure 10 as a white line. + The screen delay is taken as the eroup delay of the phase screen. which is the negative of the phase delay for aplasia.," The screen delay is taken as the group delay of the phase screen, which is the negative of the phase delay for a plasma." + In the top panel one can see that the peak of the pulse power tracks the slow variation due to dispersion measure., In the top panel one can see that the peak of the pulse power tracks the slow variation due to dispersion measure. + In the bottom panel oue cau see the iimch fuer scale variation ue to diffractive and refractive scattering., In the bottom panel one can see the much finer scale variation due to diffractive and refractive scattering. + The average pulse shape would be dominated by the ispersion nieasure variatious., The average pulse shape would be dominated by the dispersion measure variations. + However the scattered pulses can be aligned with respect to the dispersion delay in the screen itself., However the scattered pulses can be aligned with respect to the dispersion delay in the screen itself. + With this aliguiment all the delay variatious are duc to propagation from the screen to the observer., With this alignment all the delay variations are due to propagation from the screen to the observer. + The average pulse-shape. which is the expected nasi-exponcutial. is shown in Figure Ll.," The average pulse-shape, which is the expected quasi-exponential, is shown in Figure 11." + Note that this figure las a log ordinate. so au expoucutial pulse would rop linearly with delay.," Note that this figure has a log ordinate, so an exponential pulse would drop linearly with delay." + In order to display the leading edee of the pulse with low sidelobes we used a Blackman window in the Fourier transform for this display., In order to display the leading edge of the pulse with low sidelobes we used a Blackman window in the Fourier transform for this display. + One can see that the pulse tail does not drop nearly as fast as the exponential. which would be characteristic of a Gaussian angular spectrum.," One can see that the pulse tail does not drop nearly as fast as the exponential, which would be characteristic of a Gaussian angular spectrum." + This is because the actual aneular spectrmm falls more slowly than a Catssian at laree angles., This is because the actual angular spectrum falls more slowly than a Gaussian at large angles. +" It is casily shown that at high angles Boyx01012, so F(t)wt001297,"," It is easily shown that at high angles $B(\theta) \propto \theta^{-(\alpha+2)}$, so $I(t) \propto t^{-(\alpha+2)/2}$." + The asviiptotic diffractive theory is overplotted as a dashed line., The asymptotic diffractive theory is overplotted as a dashed line. + The theoretical curve was scaled up by a factor of 1.5 to allow for rounding of the peak by the Blackman window., The theoretical curve was scaled up by a factor of 1.5 to allow for rounding of the peak by the Blackman window. + It is clear that the long term average. when corrected for dispersion measure fluctuations. agrees very well with the siuple diffractive theory.," It is clear that the long term average, when corrected for dispersion measure fluctuations, agrees very well with the simple diffractive theory." + The dittractive effect. is uot to spread cach pulse iuto a quasi-exponcutial. rather to break the pulse inte subpulses.," The diffractive effect is not to spread each pulse into a quasi-exponential, rather to break the pulse into subpulses." + This is shown iu a very expanded view in Figure 12., This is shown in a very expanded view in Figure 12. + It is ouly the superposition of all the pulses that is a continuous quasi-exponenutial., It is only the superposition of all the pulses that is a continuous quasi-exponential. + The width of the fraeiieuts of cach pulse appears to be the resolution of the Fourier transform i.c. the inverse of the bandwidth., The width of the fragments of each pulse appears to be the resolution of the Fourier transform i.e. the inverse of the bandwidth. + One never observes such breakup of the pulse shape iu pulsars because the intrinsic pulse width is always wach larger than the inverse of the baudwidth., One never observes such breakup of the pulse shape in pulsars because the intrinsic pulse width is always much larger than the inverse of the bandwidth. + It might be observable i giaut pulses with coherent de-dispersiou (e.g. ITonkius et al.," It might be observable in giant pulses with coherent de-dispersion (e.g. Hankins et al.," + 2003)., 2003). + Diffactive scattering also causes the ceutroid of the pulse to shift. aud this effect is observable.," Diffractive scattering also causes the centroid of the pulse to shift, and this effect is observable." + Indeed it may be au iuportaut source of tinüng noise Óu some pulsars (Foster Cordes 1990)., Indeed it may be an important source of timing noise in some pulsars (Foster Cordes 1990). + The ceutroid is shown iu the top panel of Figure 13 with the phase screen delay marked as a black line., The centroid is shown in the top panel of Figure 13 with the phase screen delay marked as a black line. + One can see that the centroid of the pulse oes not follow the screen delay as well in regious of high eracdieut in screen delay., One can see that the centroid of the pulse does not follow the screen delay as well in regions of high gradient in screen delay. + This difference is πιο weaker in the non-dispersive case. Which is shown in the lower panel.," This difference is much weaker in the non-dispersive case, which is shown in the lower panel." + Here. of course. the screen delay plotted is the phase delay aud it has the opposite sign of the eroup clay in the upper panel.," Here, of course, the screen delay plotted is the phase delay and it has the opposite sign of the group delay in the upper panel." + Clearly a steep gradient iu ‘ther case leads to increased refraction but the effect of this refraction on the delav is much ercater in the ISPCLSIVE case., Clearly a steep gradient in either case leads to increased refraction but the effect of this refraction on the delay is much greater in the dispersive case. + It las been known for some time that scattering ‘auses fluctuation in pulse arrival times. and that this Huctuation is anticorrelated with pulse power.," It has been known for some time that scattering causes fluctuation in pulse arrival times, and that this fluctuation is anticorrelated with pulse power." + This ins been discussed theoretically (Blandford Narayan 1985) aud observed (Lestrade et al., This has been discussed theoretically (Blandford Narayan 1985) and observed (Lestrade et al. + 1998)., 1998). + Theory aud jbservations were discussed iu terms of a refractive nechanisin applied to observations which were averaged wer many diffractive time scales., Theory and observations were discussed in terms of a refractive mechanism applied to observations which were averaged over many diffractive time scales. + The auti-correlation also exists at diffractive scales. as cau be seen in Figure ll panels a and b. Here the first 50 rg of the simulation shown iu Figure 13 have been expanded to show the diffractive structure.," The anti-correlation also exists at diffractive scales, as can be seen in Figure 14 panels a and b. Here the first 50 $r_\text{f}$ of the simulation shown in Figure 13 have been expanded to show the diffractive structure." + The centroid corrected for the screen delay. 7; is shown in the top panel., The centroid corrected for the screen delay $T_c$ is shown in the top panel. + In the middle panel we show the total pulse fiux density Pr., In the middle panel we show the total pulse flux density $P_T$. + The auti-correlation is evident both at δε=(0.22rg and at σος=S4re., The anti-correlation is evident both at $s_\text{dif} = 0.22 r_\text{f}$ and at $s_\text{ref} = 5.5 r_\text{f}$. + The correlation is siguificantlv higher between T; aud 1/Pp as appareut in Figure lle., The correlation is significantly higher between $T_c$ and $1/\sqrt{P_T}$ as apparent in Figure 14c. + Here the raw cross correlation is73%.. aud it rises to if both series are lowpass filtered to remove all scales larger than the refractive scale.," Here the raw cross correlation is, and it rises to if both series are lowpass filtered to remove all scales larger than the refractive scale." + The anti-correlation between TOA aud flux at the, The anti-correlation between TOA and flux at the +The constituents of intracluster space can tell us a great. deal about the history οἱ ealaxies and clusters.,The constituents of intracluster space can tell us a great deal about the history of galaxies and clusters. + As a cluster forms. tidal interactions between galaxies and with the cluster potential alfect the internal structure of galaxies. altering both their morphological and photometric properties (Butcher&Oemler1973:Dressler1930:Gotoetal.2003:Co-endaοἱal.2006.andmany others).," As a cluster forms, tidal interactions between galaxies and with the cluster potential affect the internal structure of galaxies, altering both their morphological and photometric properties \citep[][and many others]{butcher1978, +dressler1980, goto2003, coenda2006}." +.. At the same. these interactions also liberate material into itergalactic space. (hus creatine a fossil record of the encounters.," At the same, these interactions also liberate material into intergalactic space, thus creating a fossil record of the encounters." + By studying the composition. distribution. and kinematics of these orphaned objects. we can examine the physics of tidal stripping. the distribution of matter in and around galaxies. and (he initial conditions and history of cluster formation (Merritt.1934:Westetal.1995:1993:Sommer-Larsen.Romeo.&Portinari2005.andmanyothers )..," By studying the composition, distribution, and kinematics of these orphaned objects, we can examine the physics of tidal stripping, the distribution of matter in and around galaxies, and the initial conditions and history of cluster formation \citep[][and many others]{merritt1984, west95, gregg1998, +sommer2005}." + Intracluster globular clusters (GCs) are an especially useful probe of these processes (Westetal.1995)., Intracluster globular clusters (IGCs) are an especially useful probe of these processes \citep{west95}. +. As a globular cluster evolves. it preserves information about the time ol its creation. the chemistry of the gas out of which it lormecl. ancl even the gravitational forces to which it has been exposed (seeAshman&Zepf1905.andreferences(herein)..," As a globular cluster evolves, it preserves information about the time of its creation, the chemistry of the gas out of which it formed, and even the gravitational forces to which it has been exposed \citep[see][and references +therein]{ashman98}." + Consequently. a laree sample of IGCs can be used to trace the history of galaxy interactions and constrain both the epoch of cluster Formation and the svstem/’s dvnanmical history.," Consequently, a large sample of IGCs can be used to trace the history of galaxy interactions and constrain both the epoch of cluster formation and the system's dynamical history." + Unfortunately. collecting aud measuring a laree sample of intracluster elobular clusters is difficult.," Unfortunately, collecting and measuring a large sample of intracluster globular clusters is difficult." + Globular clusters in the halos of galaxies are routinely identified. as an excess of point sources above the background. and searches for such objects have been conducted," Globular clusters in the halos of galaxies are routinely identified as an excess of point sources above the background, and searches for such objects have been conducted" +"There is one possibility for (h(p2,vWiNOxaj nunelv (0.0.0).","There is one possibility for $(h^q(\P^2,V))_{q=0}^2=(h^i(X,\O_X))_{i=1}^3$, namely $(0,0,0)$." + By Leuuua 13. we kuow that e4(V)1.," By Lemma \ref{first_chern} we know that $c_1(V)\leq +-3$, and by Lemma \ref{kollar} we know that $h^q(\P^2,V(k))=0$ for $k\geq 1$ and $q\geq 1$." + We will describe here an example whose fibres are products of elliptic curves: in Section 9 we will describe an example whose fbres are Jacobiaus of eeuus two curves., We will describe here an example whose fibres are products of elliptic curves; in Section 9 we will describe an example whose fibres are Jacobians of genus two curves. + Both examples will have V2Qoo(.12.1Qu( 2)., Both examples will have $V\cong\O_{\P^2}(-1)\oplus\O_{\P^2}(-2)$ . +independent of angle. (he model distribution is important in determining the flux only because of occultation of parts of the distribution by the Earth.,"independent of angle, the model distribution is important in determining the flux only because of occultation of parts of the distribution by the Earth." +" As noted above. I required the inner 60"" of Galactic longitude to be visible in each pointing. but on average a considerable additional amount of the plane is also included."," As noted above, I required the inner $^{\rm{o}}$ of Galactic longitude to be visible in each pointing, but on average a considerable additional amount of the plane is also included." + A certain amount of this high-longitude plane emission also appears in the background intervals. however. ancl is subtracted olf.," A certain amount of this high-longitude plane emission also appears in the background intervals, however, and is subtracted off." + Adding the GRIS best-lit value of 5.4 keV for the Galactic line width in equadrature with Προος insirumental resolution would give a 6.78 keV width., Adding the GRIS best-fit value of 5.4 keV for the Galactic line width in quadrature with s instrumental resolution would give a 6.78 keV width. + Fixing the width at that value for the fit [rom 1790.1825 keV causes A7 to increase by 17.3 to 44.0 (now with 31 degrees of freedom)., Fixing the width at that value for the fit from 1790–1825 keV causes $\chi^{2}$ to increase by 17.3 to 44.0 (now with 31 degrees of freedom). + The probabilitw of AILESSTss result being consistent with the GRIS best fit is then 4x10.? for one parameter of interest., The probability of s result being consistent with the GRIS best fit is then $\times 10^{-5}$ for one parameter of interest. + The RHESSI value for the Galactic lines width is only marginally consistent with zero., The RHESSI value for the Galactic line's width is only marginally consistent with zero. + It is expected. however. that the interstellar wwill share in Galactic rotation and display appropriate Doppler shifts (Skibo&Ramaty1991:Gehrels&Chen 1996).," It is expected, however, that the interstellar will share in Galactic rotation and display appropriate Doppler shifts \citep{Sk91,Ge96}." +. Gehrels&Chen(1996). combined a three-dimensional mocel ddistiibution derived from COMPTEL data with a Galactic rotation model to produce a map of the radial velocity. versus Galactic longitude (integrated over Galactic latitude ancl line of sight)., \citet{Ge96} combined a three-dimensional model distribution derived from COMPTEL data with a Galactic rotation model to produce a map of the radial velocity versus Galactic longitude (integrated over Galactic latitude and line of sight). + This map has a Galactic bulge component with velocities up to ~75 km/s and spiral arm components with velocities up to ~150 km/s. Although an integration of this map over the inner Galaxy has not been published. [rom the slices shown at different longitudes il appears (hat a integrated FWIIM of not more than 150 kin/s or about 0.9 keV would be obtained.," This map has a Galactic bulge component with velocities up to $\sim$ 75 km/s and spiral arm components with velocities up to $\sim$ 150 km/s. Although an integration of this map over the inner Galaxy has not been published, from the slices shown at different longitudes it appears that a integrated FWHM of not more than 150 km/s or about 0.9 keV would be obtained." + This is within lo of our result., This is within $\sigma$ of our result. + Additional broadening due to more local motions of the A]l--bearing gas or dust is possible. and of course the most recentlv-created portion of the ccan be (traveling near its birth velocity in supernovae. etc..," Additional broadening due to more local motions of the -bearing gas or dust is possible, and of course the most recently-created portion of the can be traveling near its birth velocity in supernovae, etc.," + even if (Bis portion is small., even if this portion is small. + RIHESSFss (lux value of (5.7120.54)x10 iis comparable to previous measurements., s flux value of $(5.71 \pm 0.54)$ is comparable to previous measurements. + A value of ~4x10 | was considered Consistent with the existing ensemble of data sets at the time by Diehl&Timmes(1997)., A value of $\sim 4$ $^{-1}$ was considered consistent with the existing ensemble of data sets at the time by \citet{Di97}. +. For a uniform distribution in the plane. this would imply. about 1.4 rad lor RILESSTss ellective field of view (including the effect of subtracted flux in the backeroundex pointings).," For a uniform distribution in the plane, this would imply about 1.4 rad for s effective field of view (including the effect of subtracted flux in the background pointings)." +ej Realistic distributions fall off with loneitude.ex however. and would require an even lareer effective field of view. Navaetal.(1998).," Realistic distributions fall off with longitude, however, and would require an even larger effective field of view. \citet{Na98}," +. however. using the GRIS data. found higher fluxes per radian. with the value depending on the model used ancl raneine," however, using the GRIS data, found higher fluxes per radian, with the value depending on the model used and ranging" +in the optcial spectrum of GRB 990510 (CovinoaL... 1999. WijersaL... 1999).,"in the optcial spectrum of GRB 990510 (Covino, 1999, Wijers, 1999)." + In this case. it is well-known that the syuchrotron peak frequency η is given by (Waxinau 19972) where E54 is the explosion energy in units of 107*erg. {μου is the time of observations iu units ol days alter the beeinnine of the afterglow. aud ~ is the initial bulk Lorentz factor before the inertia of the swept-up matter begius slowdown.," In this case, it is well–known that the synchrotron peak frequency $\nu_m$ is given by (Waxman 1997a) where $E_{53}$ is the explosion energy in units of $10^{53}\; erg$, $t_{day}$ is the time of observations in units of days after the beginning of the afterglow, and $\gamma$ is the initial bulk Lorentz factor before the inertia of the swept–up matter begins slowdown." + Usiug Eq. 2..," Using Eq. \ref{td}," + it is convenient to rewrite this as a function of the time-delay /4: As an exaiple. for the time-delays discussed above. ten minutes after the beginuing of the alterglow we expect the peakIrequeucy to be νι=22keV. for the disk ISM. 250eV for the halo. aud 1eV for the IGM.," it is convenient to rewrite this as a function of the time–delay $t_d$: As an example, for the time–delays discussed above, ten minutes after the beginning of the afterglow we expect the peakfrequency to be $h \nu_m = 22 \; keV $ for the disk ISM, $250 \; eV$ for the halo, and $1\; eV$ for the IGM." +" On the other hand. the intensity at 74, 1s independent of the bulk Lorenz factor. (Waxuiau 1997): but is a reasonably steep function of the environmental density."," On the other hand, the intensity at $\nu_m$ is independent of the bulk Lorenz factor (Waxman 1997b): but is a reasonably steep function of the environmental density." + Eq. 2..5..6 ," Eq. \ref{td}, \ref{num}," +allow the simultaneous solution for the three uuknown parameters E. i aud 5. which are the ouly ones potentially varyingby several orders of magnitude.," \ref{fnum} allow the simultaneous solution for the three unknown parameters $E$, $n$ and $\gamma$, which are the only ones potentially varyingby several orders of magnitude." + Du this way. we can lift the degeneracy present in the factor 5.," In this way, we can lift the degeneracy present in the factor $n\gamma^8$." + Basically. given a time-delay. a time {ων after the new peakwe may locate the afterglow peak at a frequency given by Eq. 5.. ," Basically, given a time–delay, a time $t_{day}$ after the new peakwe may locate the afterglow peak at a frequency given by Eq. \ref{num}, ," +and then the afterglow inteusity (Eq. 6)), and then the afterglow intensity (Eq. \ref{fnum}) ) + will establish whether the üne-delay is given a much sinaller. value of à or to a mareinally sinaller value of 7., will establish whether the time–delay is given a much smaller value of $n$ or to a marginally smaller value of $\gamma$. +" La bands like he X-ray. if the time-delay is due ton«Lem7"". we basically do not expect auy detectable fIux. which might however be detectable iu the optical/UV. while the afterglow is certainly. detectable in the optical i£ a smaller value of + accounts for the time-delay."," In bands like the X–ray, if the time–delay is due to $n \ll 1\; cm^{-3}$, we basically do not expect any detectable flux, which might however be detectable in the optical/UV, while the afterglow is certainly detectable in the optical if a smaller value of $\gamma$ accounts for the time–delay." + For this reason. experiments like SWIFT. which will provide simultaneous coverage in both optical/UV. and in the X-ray. are of undamental importauce to iuterpret time-delays.," For this reason, experiments like SWIFT, which will provide simultaneous coverage in both optical/UV and in the X–ray, are of fundamental importance to interpret time–delays." + Another interesting application of Eq., Another interesting application of Eq. + 1 occurs for the opposite case. in which the surrounding material is that of a pre-existing wind from the progenitor system.," 1 occurs for the opposite case, in which the surrounding material is that of a pre–existing wind from the progenitor system." +" In this case. using mnes. L find From this it can be seen that ouly exceediuglv short bursts. Ze... those lasting less tla agiti>820.03. s. can display.a break in. the X-rayr ejission:"" all other bursts (45e... the near"," In this case, using $n = \dot{M}/4\pi r^2 m_p +v_\infty$ , I find From this it can be seen that only exceedingly short bursts, , those lasting less than $R_{ag}/\gamma^2 c \approx 0.03\; s$ , can displaya break in the X–ray emission: all other bursts , the near" +the dominant charge delivery mechanisms are starlightinduced photoelectric emission and sticking collisions of gas-phase electrons.,the dominant charge delivery mechanisms are starlight-induced photoelectric emission and sticking collisions of gas-phase electrons. + Bulk. neutral silicates are. good insulators. with a full valence band. and empty conductionband.," Bulk, neutral silicates are good insulators, with a full valence band and empty conductionband." + Observations of the 9.7yam band. profile indicate that interstellar silicates are predominantly amorphous (Li Draine 2001: Ixemper. Vyiend. Tielens 2004: Li. Zhao. Li 2007).," Observations of the $9.7 \ \micron$ band profile indicate that interstellar silicates are predominantly amorphous (Li Draine 2001; Kemper, Vriend, Tielens 2004; Li, Zhao, Li 2007)." + In amorphous materials. localized energy states Clraps appear in the tails of the conduction and. valence bands.," In amorphous materials, localized energy states (`traps') appear in the tails of the conduction and valence bands." + )For any realistic interstellar erain. there are also localized. states associated with impurity atoms.," For any realistic interstellar grain, there are also localized states associated with impurity atoms." + Electrons and holes can hop from site to site with assistance from a phonon (c.g.. Mott Davis 1971: Blaise 2001). so no grain is perfectly insulating.," Electrons and holes can hop from site to site with assistance from a phonon (e.g., Mott Davis 1971; Blaise 2001), so no grain is perfectly insulating." + The rate at which an electron hops from site / to site j is typically approximated as =v οκρίς 2505/ídi)expt((, The rate at which an electron hops from site $i$ to site $j$ is typically approximated as = (-2 / ) ) (Ambegaokar et al. + da) ↿∖⇀∖⊔↓∣⋊⋅⋏∙, 1971; Mady et al. +≟⋜⋯↳⋜⊔⋅∢⊾↿⋜↧↓⊳↓≤⋗⊤↓∶↳∖↓⋯⇂∙∖⇁⋖⊾↿⋜↧↓⊳⇉∪∪⊤⊐⊳∖∖⊽↓∐⋅↓⋅⋖⋅ ∕∕↴⋅↥∆∿↓∪↓⊽⋝≱∖⊥⊲↓⊳∖⇂↓↕⋖⋅↓≻↓↕∪⊔∪⊔∐⋅⋖⋅⊏↥⋯⋅⊔≼∙∙∖⇁↿∖≧↓⋅⋯," 2007), where $\nu_{\mathrm{ph}} \sim 10^{13} \ \mathrm{s}^{-1}$ is the phonon frequency (Brucato et al." +∙⋜∐∪⋖⋅↿ ⋜↧↓⊳⇉∪∪⇉∃⊳∣⋮∣∕⊲↓⊳∖↿↥⋖⋅∠⇂⊲↓⊳∖⇂⋜⋯≼∙⋖⋅∣⋡∢⋅↥∖∖⊽⋖⋅⋖⋅⊔⊳∖⊲↓↿∢⊾⊳∖∣⊽⋜⋯∠⇂∙∣∎⊳↙∣∡⊽⊲↓⊳∖ ↿↓↥⋖⋅∢⋅⇂⋖⋅≼∙⇂↓⋅∪⊔↓∪≼⇍⋜↧∐∠⋜∐⊲↓∪↓↕↓∢⊾⊔⋏∙≟↿↓↕⊳⊓⊽∣⋅∕∶⊔↓⋜∟∖↕∆⋅∕∆⋅∣⊳↖∏⊳∆⋅∣ ⋠↓⋡∖↥⇂↥⋖⋅⋖⋅↥∢⋅≼∙∣↓⋅∪⊔∢⋅⊔⋖⋅↓⋅⋏∙≟∙∖⇁∖∖⊽↓⊔⋅⊔↓⋯↛⋜↧∐∠⋖⊾∠⇂⋜∐⊳∖⊀↓↿⋖⋅∣⊽⊳⋜⋃⊔⊔↕⇂⊲↓⊳∖↿↓∐⊾ dust temperature.," 2002), $r_{ij}$ is the distance between sites $i$ and $j$, $d_{\psi}$ is the electron localization length, $W_{i \rightarrow j} = \max[E_j - E_i, 0]$, $E_i$ is the electron energy when localized at site $i$, and $T_{\mathrm{d}}$ is the dust temperature." + A completely rigorous treatment of the grain electric dipole moment would include following the charges as they hop among traps., A completely rigorous treatment of the grain electric dipole moment would include following the charges as they hop among traps. + However. this approach is not feasible.," However, this approach is not feasible." + First. the quantities appearing in equation (9)). namely d. and the trap energy distribution. are poorly known.," First, the quantities appearing in equation \ref{eq:R_hop}) ), namely $d_{\psi}$ and the trap energy distribution, are poorly known." + Second. even for tight binding at traps (e.g. ερ=2 A). there are tvpically numerous neighboring traps for which the hopping time is orders of magnitude smaller than the time between discrete charging events (which itself is orders of magnitude smaller than the clisalignment time).," Second, even for tight binding at traps (e.g., $d_{\psi} \approx 2 \ \mathrm{\AA}$ ), there are typically numerous neighboring traps for which the hopping time is orders of magnitude smaller than the time between discrete charging events (which itself is orders of magnitude smaller than the disalignment time)." + This is true even when a charge is well-Iocalized within the vicinity of à particularly deep trap., This is true even when a charge is well-localized within the vicinity of a particularly deep trap. + Civen the large clisparity in time-scales. the CPU time for a simulation that follows hopping in detail is prohibitive.," Given the large disparity in time-scales, the CPU time for a simulation that follows hopping in detail is prohibitive." + Fortunately. a few simple. plausible idealizations are available and do not strain computational resources.," Fortunately, a few simple, plausible idealizations are available and do not strain computational resources." + We will consider the following 4 moclels: Lach time a charge arrives at the erain (either an electron from the gas or a hole left following photoemission). it remains at its arrival point forever.," We will consider the following 4 models: Each time a charge arrives at the grain (either an electron from the gas or a hole left following photoemission), it remains at its arrival point forever." +" The full hopping mocel simplifies to this case when d,.:OQ. if the tvpical distance between traps is much less than the grain size."," The full hopping model simplifies to this case when $d_{\psi} \rightarrow 0$, if the typical distance between traps is much less than the grain size." + This idealization is also reasonable if (a) the typical distance betweendeep traps is much less than the grain size and (b) the deep traps effectively retain charges in. their immediate vicinity., This idealization is also reasonable if (a) the typical distance between traps is much less than the grain size and (b) the deep traps effectively retain charges in their immediate vicinity. +" That is. a charge is unlikely to leave the ""sphere of influence’ of a deep trap before recombining."," That is, a charge is unlikely to leave the `sphere of influence' of a deep trap before recombining." + The excess charge on the grain is completely delocalized., The excess charge on the grain is completely delocalized. + For a homogeneous. spherical erain. the electric dipole moment p vanishes in this case.," For a homogeneous, spherical grain, the electric dipole moment $\bmath{p}$ vanishes in this case." + For non-spherical shapes. pxZ. the net charge on the erain (in units of the proton charge).," For non-spherical shapes, $p \propto Z$, the net charge on the grain (in units of the proton charge)." + Vhis model is probably not suitable for interstellar grains. since we expect Z to be less than the total number of deep traps in the grain.," This model is probably not suitable for interstellar grains, since we expect $Z$ to be less than the total number of deep traps in the grain." + Still. it is useful to consider this case. to Constrain the range of possible Οἱcones.," Still, it is useful to consider this case, to constrain the range of possible outcomes." + Some number of deep traps are located at. random. positions within the erain., Some number of deep traps are located at random positions within the grain. + When a charge arrives. it immediately moves to the nearest. available trap (either occupying it or recombining with a resident charge of the opposite sign).," When a charge arrives, it immediately moves to the nearest available trap (either occupying it or recombining with a resident charge of the opposite sign)." + This model approaches case (1) as the number density of deep traps increases., This model approaches case (1) as the number density of deep traps increases. + Same as (3). except that a charge executes a random walk through the grain. with some tvpical step size ancl frequcney. until it comes close to an available deep trap. where it gets stuck.," Same as (3), except that a charge executes a random walk through the grain, with some typical step size and frequency, until it comes close to an available deep trap, where it gets stuck." + We assume that any acdsorbates present on the grain surface are sullicienthy clilute that there is no associated. enhancement in conductivity along the surface., We assume that any adsorbates present on the grain surface are sufficiently dilute that there is no associated enhancement in conductivity along the surface. + The trajectories of charged particles in the vicinity of a grain with non-vanishing electric dipole moment p ciller [rom those for the p=0 case., The trajectories of charged particles in the vicinity of a grain with non-vanishing electric dipole moment $\bmath{p}$ differ from those for the $\bmath{p} = 0$ case. + The distribution of arrival sites on the grain surface is such as to reduce p=|p|., The distribution of arrival sites on the grain surface is such as to reduce $p = |\bmath{p}|$. + Excep [or model (2) in 83.1.. this elfect is critical for limiting p.," Except for model (2) in \ref{sec:idealizations}, this effect is critical for limiting $p$." + Llowever. it is extremely. difficult to treat for non-spherica erain shapes.," However, it is extremely difficult to treat for non-spherical grain shapes." + Fhus. we will always treat the grain as a sphere when computing collisional charging rates and the arriva sites of colliding particles.," Thus, we will always treat the grain as a sphere when computing collisional charging rates and the arrival sites of colliding particles." + For further simplification in these calculations. we also neglect the motion of the grain with respect to the gas.," For further simplification in these calculations, we also neglect the motion of the grain with respect to the gas." +" Even though the erain’s speed is assume to be roughly the sound speed of the gas. the speed of the light electrons is greater by a factor z(mym,yhee (my anc my are the proton and electron. mass. respectively)."," Even though the grain's speed is assumed to be roughly the sound speed of the gas, the speed of the light electrons is greater by a factor $\approx (m_p/m_e)^{1/2}$ $m_p$ and $m_e$ are the proton and electron mass, respectively)." + Thus. we do not expect this assumption to introduce serious error for electron collisional charging.," Thus, we do not expect this assumption to introduce serious error for electron collisional charging." + In addition. we neglect ion collisional charging. which is dominated: by photoelectric emission.," In addition, we neglect ion collisional charging, which is dominated by photoelectric emission." + These simplifications are justified in Appendix A.., These simplifications are justified in Appendix \ref{app:drift}. . + Fora grain at rest with respect to the gas. the collisional charging rate is given by ?p where n is the number density of the colliding particles. sis the sticking cocllicient (ic. the probability. that. the particle sticks to the grain following a collision). m is the mass of colliding particle. and 42 accounts for deviations of the collision cross section from the geometric cross section.," For a grain at rest with respect to the gas, the collisional charging rate is given by R = a^2 n s ( where $n$ is the number density of the colliding particles, $s$ is the sticking coefficient (i.e., the probability that the particle sticks to the grain following a collision), $m$ is the mass of colliding particle, and $\tilde{R}$ accounts for deviations of the collision cross section from the geometric cross section." + For the relatively [ge grains under consideration here. we adopt sz1/2 (Weingartner Draine 2001. hereafter WDOLD.," For the relatively large grains under consideration here, we adopt $s \approx 1/2$ (Weingartner Draine 2001, hereafter WD01)." +" Draine Sutin (1987) provided expressions for ""n [or a charged. conducting sphere. including the polarization of the grain by the charged gas-phase particle."," Draine Sutin (1987) provided expressions for $\tilde{R}$ for a charged, conducting sphere, including the polarization of the grain by the charged gas-phase particle." +" Phe effect of polarization decreases with grain size (as long as Z5, does not approach zero). and can be reasonably neglected. whenac.l qmm."," The effect of polarization decreases with grain size (as long as $T_{\mathrm{gas}}$ does not approach zero), and can be reasonably neglected when$a \ge 0.1 \ \micron$ ." + Consider a spherical grain with radius e centered at the origin., Consider a spherical grain with radius $a$ centered at the origin. + Xpproximate the charge cistribution within the grain as à point charge Q and point dipolep2 (p>0) located at the origin., Approximate the charge distribution within the grain as a point charge $Q$ and point dipole$p \bmath{\hat{z}}$ $p>0$) located at the origin. + In spherical coordinates (η. 8.0). the electric force on a point charge q is," In spherical coordinates $(r, \theta, \phi)$ , the electric force on a point charge $q$ is" +With the unique database from MDI/SOUO in the interval from September 1996 to February 2010. which embodies the entire Solar Cycle 23. we analyze the evelie variations of quiet Sun's magnetic flux aud Sun'ss sinall-scale magnetic elements.,"With the unique database from MDI/SOHO in the interval from September 1996 to February 2010, which embodies the entire Solar Cycle 23, we analyze the cyclic variations of quiet Sun's magnetic flux and s small-scale magnetic elements." + The «quiet regions contributed (0.94—1.44)x107* Mx flux [rom approximately the solar minimun to maximum in Cvele 23., The quiet regions contributed $(0.94-1.44) \times 10^{23}$ Mx flux from approximately the solar minimum to maximum in Cycle 23. + The fractional area of quiet regions decreased from the evele minimum to maximum by a factor of 1.2. but their total flux increased by a factor of 1.53.," The fractional area of quiet regions decreased from the cycle minimum to maximum by a factor of 1.2, but their total flux increased by a factor of 1.53." + The quiet regions dominate Sun's magnetic flix over duration of the evcle., The quiet regions dominate Sun's magnetic flux over duration of the cycle. + Furthermore. the ratio of the quiet region magnetic flux to the Sun's total [lux can be used to describe the course of solar cvele. just as sunspots.," Furthermore, the ratio of the quiet region magnetic flux to the Sun's total flux can be used to describe the course of solar cycle, just as sunspots." + The maximum flix occupation of «quiet regions marks the minima of solar cvcle., The maximum flux occupation of quiet regions marks the minima of solar cycle. + The flux occupation on the quiet Sun had been larger than lor 28 continuous months from July 2007 to October 2009. which seems to equally characterize the grand minima of Cycles 23 and 24.," The flux occupation on the quiet Sun had been larger than for 28 continuous months from July 2007 to October 2009, which seems to equally characterize the grand minima of Cycles 23 and 24." + With increasing magnetic flux per element (he number and total flux of the Sun's small- magnetic elements follow no-correlation. anti-correlation aud correlation changes with sunspots.," With increasing magnetic flux per element the number and total flux of the Sun's small-scale magnetic elements follow no-correlation, anti-correlation and correlation changes with sunspots." + The anti-correlated component. covering the flux range of (2.9 - 32.0)xLOY Mx. occupies of total elements and of flux on the quiet Sun.," The anti-correlated component, covering the flux range of (2.9 - $\times 10^{18}$ Mx, occupies of total elements and of flux on the quiet Sun." + However. the stronger magnetic elements with [lux larger than 4.3x10 Mx dominate the quiet Sun magnetic flux and follow closely the sunspot cvele.," However, the stronger magnetic elements with flux larger than $\times 10^{19}$ Mx dominate the quiet Sun magnetic flux and follow closely the sunspot cycle." + The definitively iclentifiecl anti-correlated component of the small-scale magnetic elements seenis (o offer an interpretation on the puzzling observations of anti-correlation variation of many (vpes of small-scale activity. wilh the solar evele. e.g. the network bright points. el 10830 cldark points and coronal X-ray bright points.," The definitively identified anti-correlated component of the small-scale magnetic elements seems to offer an interpretation on the puzzling observations of anti-correlation variation of many types of small-scale activity with the solar cycle, e.g., the network bright points, HeI 10830 dark points and coronal X-ray bright points." + It is speculated that the anti-correlated small-scale magnetic elements are products οἱ some local turbulent dynamo or dvnamos Chat is modulated to be anti-phasecl with the elohal mean-field dynamo., It is speculated that the anti-correlated small-scale magnetic elements are products of some local turbulent dynamo or dynamos that is modulated to be anti-phased with the global mean-field dynamo. + The authors are grateful to Dean-Yi Chou. Sara Martin and Jie Jiang for their valuable suggestions and discussions.," The authors are grateful to Dean-Yi Chou, Sara Martin and Jie Jiang for their valuable suggestions and discussions." + We appreciate the instructive adyice ancl valuable suggestions of the anonvanous referee. by which the paper has been significantly improved.," We appreciate the instructive advice and valuable suggestions of the anonymous referee, by which the paper has been significantly improved." + The work is supported bv the National Natural Science Foundation of China (10873020. 11003024. 40974112. 40731056. 10973019. 408901GI. 10921303. 11025315). and the National Basic Research. Program of China (G201ICD811403).," The work is supported by the National Natural Science Foundation of China (10873020, 11003024, 40974112, 40731056, 10973019, 40890161, 10921303, 11025315), and the National Basic Research Program of China (G2011CB811403)." +oL au absorption line. sharp ail deep lines contain more RV information than broad aud shallow lines.,"of an absorption line, sharp and deep lines contain more RV information than broad and shallow lines." + Mathematically. the slope is the derivative of flux as a function of optical frequency. ie. dod».," Mathematically, the slope is the derivative of flux as a function of optical frequency, i.e., $dS_0/d\nu$." + The power spectrum o| dSofdr is obtained by Fourier trausforim., The power spectrum of $dS_0/d\nu$ is obtained by Fourier transform. + According to properties of Fourier transform. JF[dSu/dv]=(ipτσ[Su]. where F manifests Fourier transform. 7 is the unit of imaginary number aud p is he representation of v/c in Fourier space.," According to properties of Fourier transform, $\mathcal{F}[dS_0/d\nu]=(i\rho)\cdot \mathcal{F}[S_0]$, where $\mathcal{F}$ manifests Fourier transform, $i$ is the unit of imaginary number and $\rho$ is the representation of $\nu/c$ in Fourier space." + We plot Z(|dSu/dr] in Fig., We plot $\mathcal{F}([dS_0/d\nu]$ in Fig. + [. as well as the spectral response function (SRF). which is [LSF].," \ref{fig:Rho_Power_PSF} as well as the spectral response function (SRF), which is $\mathcal{F}[LSF]$ ." + SRF at R=2.000 drops drastically toward lieh 5yatial requency (high. p value) such that it misses most of the RV information contaiued in stellar spectrum.," SRF at $R=5,000$ drops drastically toward high spatial frequency (high $\rho$ value) such that it misses most of the RV information contained in stellar spectrum." + As A increases. SRE gradually increases. towau« high p where the bulk of RV. infornation is stored.," As $R$ increases, SRF gradually increases toward high $\rho$ where the bulk of RV information is stored." + A spectrograph with 42 of ~100.000 is capable of uearly completely extracting RV infor:ration.," A spectrograph with $R$ of $\sim$ 100,000 is capable of nearly completely extracting RV information." + Unlike DE. DFDI can shift FldSy/dr] by an amount determined by the OPD of the intererometer (?)..," Unlike DE, DFDI can shift $\mathcal{F}[dS_0/d\nu]$ by an amount determined by the OPD of the interferometer \citep{Erskine2003}." + For example. Fig.," For example, Fig." + | also shows the )Ower spectrum of FeldSy/dv] of a ringiug spectrum obtained with a DEDI instrument with a 20 tun optical delay. which shifts JF[dSu/v] by 20 maim.," \ref{fig:Rho_Power_PSF} also shows the power spectrum of $\mathcal{F}([dS_0/d\nu]$ of a fringing spectrum obtained with a DFDI instrument with a 20 mm optical delay, which shifts $\mathcal{F}[dS_0/\nu]$ by 20 mm." + In this case. RV information has been shifted [rom the original high. spatia frequencies to low spatial [frequencies which cau be resolved by a spectrograph with a low or mediun Ain DEDI.," In this case, RV information has been shifted from the original high spatial frequencies to low spatial frequencies which can be resolved by a spectrograph with a low or medium $R$ in DFDI." + Iu the DE methocl. au efficient way based ou a spectral quality factor (Q) was introduced by ? to calculate the fuidamental uncertaiuly in the Doppler measturemeuts.," In the DE method, an efficient way based on a spectral quality factor $Q$ ) was introduced by \citet{Bouchy2001} to calculate the fundamental uncertainty in the Doppler measurements." + The (Q (actor is a measure of spectral profie information witlin a given waveleneth region. cousidered for Doppler Dnieasurenients., The $Q$ factor is a measure of spectral profile information within a given wavelength region considered for Doppler measurements. + Here we ¢levelop a similar 1jethod. to calculate Q values for the DEDI methocl., Here we develop a similar method to calculate $Q$ values for the DFDI method. + [ustead of representing tle spetral line prolie information iu the DE method. the Q [actor in our DFDI method represents stellar fringe profile information.," Instead of representing the spetral line profile information in the DE method, the $Q$ factor in our DFDI method represents stellar fringe profile information." + We use high resolution (0.005 sspacing) syuhetic stellar spectra generale by PHOENIX code(??) because observed spectra of low mass stars do not have high. enough resolution aud. broad. effective temperature coverage.," We use high resolution (0.005 spacing) synthetic stellar spectra generated by PHOENIX \citep{Hauschildt1999,Allard2001} + because observed spectra of low mass stars do not have high enough resolution and broad effective temperature coverage." + ὃς have coiclucted several coiiparisous between syuthetic specra generated by PHOENIX and the observed spectra., \citet{Reiners2010} have conducted several comparisons between synthetic spectra generated by PHOENIX and the observed spectra. + They concluded. that he syuthetic specra are accurate enough for RV 1ueasttremen uncertainty calculation., They concluded that the synthetic spectra are accurate enough for RV measurement uncertainty calculation. + We used svuthetic stellar spectra of solar abuudauce with Tey rangiug rom 21001 to 3100Ix. (correspoticing spectral type f‘on M9V to LV) and a surface [n]eravity logg of L5., We used synthetic stellar spectra of solar abundance with $T_{\rm{eff}}$ ranging from 2400K to 3100K (corresponding spectral type from M9V to M4V) and a surface gravity $\log g$ of 4.5. + The Q lacor is Calculated for a series of 10 unm spectral slices roin SOO niu to 1350 nm., The $Q$ factor is calculated for a series of 10 nm spectral slices from 800 nm to 1350 nm. + We artificially bro:«leni spectra with Vsiu from 0 knes Lto I0 kmsi asstnilg a limb cdarkeniug index of 0.6. wuch is a typica value for an M dwarl.," We artificially broaden spectra with $V +\sin{i}$ from 0 $\rm{km\cdot s}^{-1}$ to 10 $\rm{km\cdot s}^{-1}$ assuming a limb darkening index of 0.6, which is a typical value for an M dwarf." + We convolve the rotatioual broadening profile with each spectral slice of LO nim to obtain a 'otatioually-b'oadened spectruu., We convolve the rotational broadening profile with each spectral slice of 10 nm to obtain a rotationally-broadened spectrum. + We asstime a Ciaussiau LSF wich is deterinied by spectral resolution /? (Equatior (3)))., We assume a Gaussian LSF which is determined by spectral resolution $R$ (Equation \ref{eq:LSF}) )). + After artificial rotational broacdeniug aud LSF convolution. we rebin each spectral slice according to [.2 pixels per resolutionelement (according to the optical desigu of IRET by 2)) to generate the final 2D üunage on a detector based «i which we compute the ( factor.," After artificial rotational broadening and LSF convolution, we rebin each spectral slice according to 4.2 pixels per resolutionelement (according to the optical design of IRET by \citet{Zhao2010}) ) to generate the final 2D image on a detector based on which we compute the $Q$ factor." +We have so far demonstrated that PCA is an effective method for determining the parameter behavior with redshift.,We have so far demonstrated that PCA is an effective method for determining the parameter behavior with redshift. +" It provides a considerable reduction in the initial parameter space dimensionality, without introducing any hypothesis about the energy content, cosmological model, or underlying gravity theory."," It provides a considerable reduction in the initial parameter space dimensionality, without introducing any hypothesis about the energy content, cosmological model, or underlying gravity theory." +" The reconstruction relies on the assumption of a homogeneous and isotropic Universe, described by a FRW metric."," The reconstruction relies on the assumption of a homogeneous and isotropic Universe, described by a FRW metric." + The simulated data set used, The simulated data set used +CGrindlav 2001). although in the latter case the long period is sullicientIy stable that it has been suggested (Chou&Grindlay2001). that. N1820-30 could. be a triple system.,"Grindlay 2001), although in the latter case the long period is sufficiently stable that it has been suggested \cite{chg} that X1820-30 could be a triple system." + Most of these mocdulations are rather dillerent from. those exhibited by SAIC X-I. Her X-1 and LAC. X-4 in that they are much lower amplitude and do not appear to be due to varving obscuration.," Most of these modulations are rather different from those exhibited by SMC X-1, Her X-1 and LMC X-4 in that they are much lower amplitude and do not appear to be due to varying obscuration." + It has been customary to also interpre hese superorbital periods as due to a precessing. possibA warped aceretion disc. with the lower amplitudes due to ower inclinations.," It has been customary to also interpret these superorbital periods as due to a precessing, possibly warped accretion disc, with the lower amplitudes due to lower inclinations." + Clearly the detailed investigation of these Iong-period henomena is an observational challenge in that it realA requires regular. svstematic monitoring of the X-ray. Lux. oeferably with a single instrument in each energy range.," Clearly the detailed investigation of these long-period phenomena is an observational challenge in that it really requires regular, systematic monitoring of the X-ray flux, preferably with a single instrument in each energy range." + In he energy range 1.3 - 12.1 keV. the ΗΝΤΙ All-Sky Monitor (ASM) provides a continuous dataset. of all bright. X-ray sources. that has been continuously. compiled over a period of more than six vears.," In the energy range 1.3 - 12.1 keV, the RXTE All-Sky Monitor (ASM) provides a continuous dataset of all bright X-ray sources, that has been continuously compiled over a period of more than six years." + Up to energies of 1 MeV. the Burst And Transient Source Experiment (D.NTSIS) has provided a continuous dataset over a period of almost a decade.," Up to energies of 1 MeV, the Burst And Transient Source Experiment (BATSE) has provided a continuous dataset over a period of almost a decade." + The advent of such long-term continuous datasets has mace the work we describe here possible., The advent of such long-term continuous datasets has made the work we describe here possible. + This paper is the first in a series that examines the nature ancl properties of these superorbital variations., This paper is the first in a series that examines the nature and properties of these superorbital variations. + SAIC N-1: is à massive X-ray binary svstem consisting of a ο + 0.1 M. neutron star (an X-ray pulsar) and a high mass (17.2 + 0.6 AL.) BOL optical companion. known as Sk 60 (Revnolds et al 1993).," SMC X-1 is a massive X-ray binary system consisting of a 1.6 $\pm$ 0.1 $_\odot$ neutron star (an X-ray pulsar) and a high mass (17.2 $\pm$ 0.6 $_\odot$ ) B0 I optical companion, known as Sk 160 (Reynolds et al 1993)." + Ehe spin period of the pulsar is ).71s and the orbital period of the svstem is 3.89 clavs. and its orbital period is decaving on a timescale of 10 vears (sec vevnolds et al. (," The spin period of the pulsar is 0.71 s and the orbital period of the system is 3.89 days, and its orbital period is decaying on a timescale of $10^5$ years (see Reynolds et al. (" +1993) and references therein).,1993) and references therein). + SMC X-1 also las à superorbital period of approximately 60 days believed o be the consequence of a precessing. warped. accretion disk (sce Wojdowski at al. (," SMC X-1 also has a superorbital period of approximately 60 days believed to be the consequence of a precessing, warped, accretion disk (see Wojdowski at al. (" +1998) ancl references therein).,1998) and references therein). + This disk is presumed to periodically occult the X-rays from the central source. thereby creating a modulation in the X-ray ighteurve in a manner analogous to that of Her X-1.," This disk is presumed to periodically occult the X-rays from the central source, thereby creating a modulation in the X-ray lightcurve in a manner analogous to that of Her X-1." + A comprehensive X-ray. investigation of the SMC. svstem has been presented. by. Wojdowski et al (1998) which examines all of the available cata up to JD 24450660 (carly 1998)., A comprehensive X-ray investigation of the SMC X-1 system has been presented by Wojdowski et al \shortcite{woj} which examines all of the available data up to JD 24450660 (early 1998). + As well as showing a superorbital period of 60 davs. they demonstrate that the X-ray source has been continously active for at least the last 30 vears and that the mass transfer rate to the neutron star has been roughly constant over this time.," As well as showing a superorbital period of $\sim$ 60 days, they demonstrate that the X-ray source has been continously active for at least the last 30 years and that the mass transfer rate to the neutron star has been roughly constant over this time." + The latter is inferred. from the [ασ that the pulsar has been steadily spinning-up on a timescale of hundreds: of wears., The latter is inferred from the fact that the pulsar has been steadily spinning-up on a timescale of hundreds of years. + Based on the placement of pulse and. eclipse profiles within the superorbital evele. it was suggested that the luminosity and spectrum during the (orbital) eclipses are unatlectec by the lone evele.," Based on the placement of pulse and eclipse profiles within the superorbital cycle, it was suggested that the luminosity and spectrum during the (orbital) eclipses are unaffected by the long cycle." + Howas thus argued that no intrinsic source variation could. be responsible for the 60 day modulation. since the superorbital variation was present only in the out-of-eclipse data.," It was thus argued that no intrinsic source variation could be responsible for the 60 day modulation, since the superorbital variation was present only in the out-of-eclipse data." + Periodic occultation of the pulsar by the rim of a warped accretion disk. precessing under the gravity of the giant. companion was shown to be consistent with the observations.," Periodic occultation of the pulsar by the rim of a warped accretion disk, precessing under the gravity of the giant companion was shown to be consistent with the observations." + However. whilst confirming the presence of. the superorbital modulation. Wojdowski et al also. noted that it was not steady. but. appeared. to. vary between 50 and 60 days.," However, whilst confirming the presence of the superorbital modulation, Wojdowski et al also noted that it was not steady, but appeared to vary between 50 and 60 days." + The identification of pointings with phase in the superorbital evele could. therefore not. be mace independently of the pointed lighteurves themselves., The identification of pointings with phase in the superorbital cycle could therefore not be made independently of the pointed lightcurves themselves. + Insteacl. timing in the superorbital evele was performed. by creating a consistent scenario. then fitting the pointings to that scenario.," Instead, timing in the superorbital cycle was performed by creating a consistent scenario, then fitting the pointings to that scenario." + We therefore believe that the elimination of intrinsic Luminosity variation is open to question., We therefore believe that the elimination of intrinsic luminosity variation is open to question. + In this work we present the results of an analysis of both ASAT and. BATSE data that allows the variation in the third. period to be followed continuously over more than a decade., In this work we present the results of an analysis of both ASM and BATSE data that allows the variation in the third period to be followed continuously over more than a decade. + We also extend the timeline of observations by 53 vears since. Wojdowski et al (1998)... which allows us to see that the variation of the third. period. might. itself. be periodic. as suggested by Ribo et al (2001).," We also extend the timeline of observations by 3 years since Wojdowski et al \shortcite{woj}, which allows us to see that the variation of the third period might itself be periodic, as suggested by Ribo et al (2001)." + We show that this variation in the long period must be due to interaction of modes in à warped. precessing aceretion disk.," We show that this variation in the long period must be due to interaction of modes in a warped, precessing accretion disk." + Launched in 1996. the Rossi A-Rayv ‘Timing LExplorer (RATE) carries an All Sky Monitor. (ASAI). which gives continuous coverage of the entire sky.," Launched in 1996, the Rossi X-Ray Timing Explorer (RXTE) carries an All Sky Monitor (ASM), which gives continuous coverage of the entire sky." +" Typically 5-10 readings - called ""ebwells - are taken of cach of a List of sources per day. lasting about 90 seconds per cbwell."," Typically 5-10 readings - called “dwells” - are taken of each of a list of sources per day, lasting about 90 seconds per dwell." + Piming information is provided to within a thousandth of a day. as well as crude spectral information.," Timing information is provided to within a thousandth of a day, as well as crude spectral information." + The SM is sensitive to photon energies between 1.3 and 12.1 keV. broken into three energy channels (1.3-3.0 keV. 3.0-5.0 keV and 5.0-12.1 keV).," The ASM is sensitive to photon energies between 1.3 and 12.1 keV, broken into three energy channels (1.3-3.0 keV, 3.0-5.0 keV and 5.0-12.1 keV)." + AX total of 6.1 vears of data (AIJD 50083-52312) from the ASAT were used in our analysis., A total of 6.1 years of data (MJD 50083-52312) from the ASM were used in our analysis. + Since the X-ray flux of SAIC XN-l varies by a factor of 210 over the 40-60 day high-low, Since the X-ray flux of SMC X-1 varies by a factor of $>$ 10 over the 40-60 day high-low +(Schlegeletal.1998).,\citep[]{schlegel1998}. +" The geometric mean composite spectra for the non-absorber. sets were generated in exactly the same way, using the redshift of the corresponding DLA in each case for equation 1.."," The geometric mean composite spectra for the non-absorber sets were generated in exactly the same way, using the redshift of the corresponding DLA in each case for equation \ref{pixel_number}." +" Note that we use in each case the spectra delivered by the DR7 pipeline, which includes the latest version of the spectrophotometric calibration."," Note that we use in each case the spectra delivered by the DR7 pipeline, which includes the latest version of the spectrophotometric calibration." +" The advantage of thegeometric mean is that it yields a meaningful average of the extinction at each wavelength by essentially averaging optical Note that our method does not rely upon any interpolation of the original spectra - at the price of sacrificing spectral resolution, because we bin together flux values that may reside in the DLA restframe separated by 1/2 of a pixel at the extreme."," The advantage of the mean is that it yields a meaningful average of the extinction at each wavelength by essentially averaging optical Note that our method does not rely upon any interpolation of the original spectra - at the price of sacrificing spectral resolution, because we bin together flux values that may reside in the DLA restframe separated by 1/2 of a pixel at the extreme." +" We have tested the effects of this by comparison of the resulting composite spectra to two cases of a more refined treatment: I. rebinning each spectrum after deredshifting it, and II."," We have tested the effects of this by comparison of the resulting composite spectra to two cases of a more refined treatment: I. rebinning each spectrum after deredshifting it, and II." + computing the weighted average of the flux values of the two pixels in the original spectra that always straddle one wavelength element in the new DLA restframe grid., computing the weighted average of the flux values of the two pixels in the original spectra that always straddle one wavelength element in the new DLA restframe grid. +" As expected, the differences over large wavelength ranges are negligible, and manifest themselves to a noticable degree only on a two to three pixel scale."," As expected, the differences over large wavelength ranges are negligible, and manifest themselves to a noticable degree only on a two to three pixel scale." +" Hence, we believe our method, being as close as possible to the data, is robust enough not to have to rely on the intricacies of interpolation as in case I. Because we have to throw out pixels with fluxes f,< 0.0, method II from above results in having to flag out twice as many datapoints, which is therefore deemed less acceptable despite the higher spectral Figure 3 shows the number of spectra contributing to each wavelength bin for the construction of the composite spectra in the DLA restframe."," Hence, we believe our method, being as close as possible to the data, is robust enough not to have to rely on the intricacies of interpolation as in case I. Because we have to throw out pixels with fluxes $_{\lambda} \leq$ 0.0, method II from above results in having to flag out twice as many datapoints, which is therefore deemed less acceptable despite the higher spectral Figure \ref{number_contributing}{ shows the number of spectra contributing to each wavelength bin for the construction of the composite spectra in the DLA restframe." + It also highlights to which location in these spectra the observed central wavelength of the i band (7481 À)) is shifted in the DLA frames., It also highlights to which location in these spectra the observed central wavelength of the $i$ band (7481 ) is shifted in the DLA frames. +" Furthermore we have indicated the average brightness of the QSOs contributing at each wavelength, and the average DLA absorber redshift."," Furthermore we have indicated the average brightness of the QSOs contributing at each wavelength, and the average DLA absorber redshift." +" Note that the region covered by the bulk of the spectra extends from ~1400 to ~2300À,, and exhibits fairly constant values of the mean brightness and absorber redshifts."," Note that the region covered by the bulk of the spectra extends from $\sim$ 1400 to $\sim$ 2300, and exhibits fairly constant values of the mean brightness and absorber redshifts." +" The need for staying redward of the Lyman α emission, and the decreasing high (restframe) wavelength with increasing redshift of each QSO, result of course in fewer spectra contributing to the composite towards the edges of the wavelength regime covered by our samples."," The need for staying redward of the Lyman $\alpha$ emission, and the decreasing high (restframe) wavelength with increasing redshift of each QSO, result of course in fewer spectra contributing to the composite towards the edges of the wavelength regime covered by our samples." +" Hence, these spectral areas carry less weight due to their increased noise/scatter in the reddening analyses (as detailed in"," Hence, these spectral areas carry less weight due to their increased noise/scatter in the reddening analyses (as detailed in" +calculations we carry out. with special attention for the computation of the spectra of protons and. electrons. the magnetic field amplification and the radiation processes that we include.,"calculations we carry out, with special attention for the computation of the spectra of protons and electrons, the magnetic field amplification and the radiation processes that we include." + The dvnamics of the shock region is dominated by accelerated: protons. while electrons are accelerated in the shock environment generated by protons.," The dynamics of the shock region is dominated by accelerated protons, while electrons are accelerated in the shock environment generated by protons." + In. this sense he non-linearity of the problemi is [limited to the proton component. which also generates the local magnetic field by exciting a streaming instability.," In this sense the non-linearity of the problem is limited to the proton component, which also generates the local magnetic field by exciting a streaming instability." + Phe spectrum of accelerated ootons is computed. using the method of Amato&Blasi (2005)., The spectrum of accelerated protons is computed using the method of \cite{amato05}. +. The acceleration time in the presence of a precursor was determined by Blasietal.(2007)... ancl we adopt. that calculation.," The acceleration time in the presence of a precursor was determined by \cite{cap07}, and we adopt that calculation." + Lt was found there (and later confirmed for the xwameters o£ RX J1713.7-3946 by Ellison (2008))) that the »ecursor reduces the maximum energy compared with the naive prediction of the test-particle theory with the same value of the magnetic field upstream of the subshock., It was found there (and later confirmed for the parameters of RX J1713.7-3946 by \cite{vladi}) ) that the precursor reduces the maximum energy compared with the naive prediction of the test-particle theory with the same value of the magnetic field upstream of the subshock. + The maximum momentum is first caleulatecl using as a condition the equality between the acceleration time and the age of the SNR., The maximum momentum is first calculated using as a condition the equality between the acceleration time and the age of the SNR. + However we also illustrate our results in the case in which the maximum momentum. is determined by the finite size of the accelerator., However we also illustrate our results in the case in which the maximum momentum is determined by the finite size of the accelerator. + Phe cüffusion coellicient is chosen to be Bohm-like in the magnetic field &enerated through streaming instability (see 2.2))., The diffusion coefficient is chosen to be Bohm-like in the magnetic field generated through streaming instability (see \ref{sec:dyn}) ). + Since the magnetic field depends on the location in the precursor. the dilfusion coefficient is also a function of space: δρ.)=(13)pc? (cDBGr)).," Since the magnetic field depends on the location in the precursor, the diffusion coefficient is also a function of space: $D(p,x)=(1/3) p c^2/(e B(x))$ ." + The two conditions mentioned. above reacl: where a< Lis the fraction of the shell radius Gs v4) where the escape of particles at pppauax OCCULS.," The two conditions mentioned above read: where $\alpha<1$ is the fraction of the shell radius $R_{SNR}$ ) where the escape of particles at $p\sim p_{p,\rm max}$ occurs." + Although the basic structure of the calculation is the same proposed by Amato&Blasi(2005) and Amato&Blasi (2006).. the crucial new aspect taken into account here is the dvnaniuecal reaction of the self-generated magnetic field.," Although the basic structure of the calculation is the same proposed by \cite{amato05} and \cite{amato06}, the crucial new aspect taken into account here is the dynamical reaction of the self-generated magnetic field." + We introduce this effect following the treatment of Capriolictal.(2008a) ancl Capriolictal.(2008b):: the conservation equations at the shock and in the precursor ave modified so as to include the magnetic contribution., We introduce this effect following the treatment of \cite{cap08} and \cite{long}: the conservation equations at the shock and in the precursor are modified so as to include the magnetic contribution. + The compression factor at. the subshock. Av... ancl the total compression factor. {ζω are deeply allected by this change. in that the ratio Ryu/1.55 (the compression factor in the precursor). decreases when he amplified magnetic field. contributes a pressure which is comparable1 with the pressure of the thermal gas upstream.," The compression factor at the subshock, $R_{sub}$, and the total compression factor, $R_{tot}$, are deeply affected by this change, in that the ratio $R_{tot}/R_{sub}$ (the compression factor in the precursor), decreases when the amplified magnetic field contributes a pressure which is comparable with the pressure of the thermal gas upstream." + In turn this reflects in spectra of accelerated particles which are closer to power laws. though a concavity remains visible 2OOSbD).. as we discuss below.," In turn this reflects in spectra of accelerated particles which are closer to power laws, though a concavity remains visible \cite[]{long}, as we discuss below." + The normalization of the proton spectrum is an output of our non linear calculation. once a recipe for injection has been established.," The normalization of the proton spectrum is an output of our non linear calculation, once a recipe for injection has been established." + Following Blasietal. (2005)... particles are injected immediately. downstream of the subshock.," Following \cite{bgv05}, , particles are injected immediately downstream of the subshock." + The fraction of gas particles crossing the shock from downstream lo upstream. ting. Can be written as l]lere £~2.dis defined. by the relation ping=£pure: where poe is the momentum. of the thermal particles downstream.," The fraction of gas particles crossing the shock from downstream to upstream, $\eta_{\rm inj}$, can be written as Here $\xi\sim 2-4$ is defined by the relation $p_{\rm inj}=\xi \, p_{\rm +th,2}$ , where $p_{\rm th,2}$ is the momentum of the thermal particles downstream." + £ parametrizes the poorly known microphysics of the injection process. but. one should stress that pis is an output of the problem: as a result. theinjection elliciency is alPected by the dynamical reaction exerted. by 16 accelerated. particles and by the anplifiecl magnetic field.," $\xi$ parametrizes the poorly known microphysics of the injection process, but one should stress that $p_{\rm th,2}$ is an output of the problem: as a result, theinjection efficiency is affected by the dynamical reaction exerted by the accelerated particles and by the amplified magnetic field." + The spectrum of accelerated electrons at. the shock. fot(p). ds easy to calculate for. pPoauas WHE pean re maximum electron momentum.," The spectrum of accelerated electrons at the shock, $f_{e,0}(p)$, is easy to calculate for $p\ll p_{e,\rm max}$, with $p_{e,\rm max}$ the maximum electron momentum." + In fact the slope of the ectron spectrum. at given momentum p is the same as 16 slope of the proton spectrum at the same momentum. esuming that both electrons and. protons experience the same diffusion coefficient.," In fact the slope of the electron spectrum at given momentum $p$ is the same as the slope of the proton spectrum at the same momentum, assuming that both electrons and protons experience the same diffusion coefficient." + The relative normalization of le wo spectra ds unconstrainedpriori while the normalization of the proton spectrum. às stressed: above. is an output of our non linear calculation.," The relative normalization of the two spectra is unconstrained, while the normalization of the proton spectrum, as stressed above, is an output of our non linear calculation." + The maximum energv of electrons. is determined by equating the acceleration time with the minimum between the time for energv losses and the age of the remnant., The maximum energy of electrons is determined by equating the acceleration time with the minimum between the time for energy losses and the age of the remnant. + The loss time of electrons over a evele of shock crossing needs to be weighed by the residence times upstream and. downstream. therefore the condition for the maximum momentum. in the loss dominated case. can be written as: where τι denotes the loss time. and the indexes 71 and 73 refer to quantities measured upstream and downstream respectively.," The loss time of electrons over a cycle of shock crossing needs to be weighed by the residence times upstream and downstream, therefore the condition for the maximum momentum, in the loss dominated case, can be written as: where $\tau_l$ denotes the loss time, and the indexes “1” and “2” refer to quantities measured upstream and downstream respectively." + The residence times in the context of non linear theory of. particle acceleration can be written. explicitely (from Eqs. (, The residence times in the context of non linear theory of particle acceleration can be written explicitely (from Eqs. ( +25) ancl (26) of Blasietal. (2007))).,25) and (26) of \cite{cap07}) ). + Eq. (3)), Eq. \ref{eq:pemax}) ) + cannot be solved for piaua analytically. contrary to the case of acceleration in the test. particle regime.," cannot be solved for $p_{e,\rm max}$ analytically, contrary to the case of acceleration in the test particle regime." + The numerical solution is however easy to obtain with standard techniques., The numerical solution is however easy to obtain with standard techniques. + When only svnchroton losses are important. we can provide an approximate expression for the solution of Eq (3) ," When only synchroton losses are important, we can provide an approximate expression for the solution of Eq. \ref{eq:pemax}) )." +We use the function Ημ) defined. as. the mean plasma velocity that a particle with momentum. p experiences in the precursor region (see Eq. (, We use the function $u_p(p)$ defined as the mean plasma velocity that a particle with momentum $p$ experiences in the precursor region (see Eq. ( +8) in Amato&Blasi (2005))).,8) in \cite{amato05}) ). +" The function C,(p)—αρ]πω issuch that (η)<1 for any momentum.", The function $U_p(p)\equiv u_p(p)/u_0$ issuch that $U_p(p)< 1$ for any momentum. + The electron maximum momentum can then be written in an implicit way as: where ry is the classical electron radius., The electron maximum momentum can then be written in an implicit way as: where $r_0$ is the classical electron radius. + One may notice that Eq. (4)), One may notice that Eq. \ref{eq:pmax_e_2}) ) + reduces to the Iq. (, reduces to the Eq. ( +"11) of Berezhko(2006) if one poses C,=1.",11) of \cite{ber06} if one poses $U_p=1$. + leq. (4)), Eq. \ref{eq:pmax_e_2}) ) + leads to an error of less than 107 with respect to Eq. (3)) (, leads to an error of less than $10\%$ with respect to Eq. \ref{eq:pemax}) ) ( +but we stress that the results presented in this work are all obtained: using I5q. (3}}).,but we stress that the results presented in this work are all obtained using Eq. \ref{eq:pemax}) )). + The spectrum of electrons at energies around and above Poanas: Hamely the shape of the cutoll is harder to calculate in the context of a fully non linear calculation.," The spectrum of electrons at energies around and above $p_{e,\rm max}$, namely the shape of the cutoff is harder to calculate in the context of a fully non linear calculation." + In the test particle case ancl for strong shocks the solutionhas been calculated by Zirakashyili&Aharonian(2007).. Since the spectra we find for electrons at p 0.8$ ) clusters while the younger population contains a mixture of colors." + In the ease of NGC 3627 (analvzed below in Section 5). we indeed find that the form of our cluster formation rate is unimportant. aud (hat (he 2-parameter star formation rate [its the data as well as a more sophisticated function.," In the case of NGC 3627 (analyzed below in Section 5), we indeed find that the form of our cluster formation rate is unimportant, and that the 2-parameter star formation rate fits the data as well as a more sophisticated function." + We also created svnthetic CMBRDs using a variety of metallicity enrichment laws (with the same current metallicity). all of which produced similarly-good fits to the data.," We also created synthetic CMRDs using a variety of metallicity enrichment laws (with the same current metallicity), all of which produced similarly-good fits to the data." + We therefore characterize the cluster formation history with four parameters: cluster formation rates al voung and ancient ages. an age-metallieitv relation. and scatter around the age-metallicitv relation.," We therefore characterize the cluster formation history with four parameters: cluster formation rates at young and ancient ages, an age-metallicity relation, and scatter around the age-metallicity relation." + However. while all of these ingredients are necessary to produce a svnthetic CMBD. the only parameter (hat significantly affects the. CAIRD is the recent cluster formation rate.," However, while all of these ingredients are necessary to produce a synthetic CMRD, the only parameter that significantly affects the CMRD is the recent cluster formation rate." +a mass SAL.xAfpy=0.5 and provides fray—6.13 and ο’~7.72: the latter value indicates an average BLR column density Ny=107em-. consistent with expectations from phototonization models.," The empirical calibration performed by M08, and adopted by N09, assumed $\gamma=0.5$ and provides $\frad\simeq 6.13$ and $g^\prime\simeq 7.72$; the latter value indicates an average BLR column density $\NH=\ten{23}\CM\2$, consistent with expectations from photoionization models." + The column density of the BLR clouds sets the relative importance of the gravitational force (which depends on cloud mass) and the radiative force (which is independent of mass), The column density of the BLR clouds sets the relative importance of the gravitational force (which depends on cloud mass) and the radiative force (which is independent of mass). + Therefore it is the most critical parameter for the radiation pressure correction and we can outline its effects by writing: where No; is iin units of 2., Therefore it is the most critical parameter for the radiation pressure correction and we can outline its effects by writing: where $\NHn$ is in units of . +. The Eddington ratios with and without radiation pressure correction are therefore: where iis the Eddingtonluminosity fora 1 oobject., The Eddington ratios with and without radiation pressure correction are therefore: where is the Eddingtonluminosity for a 1 object. + The observed distribution of Eddington ratios in the, The observed distribution of Eddington ratios in the +periods between 100 and 1500 clavs with a step size of 0.1 days.,periods between 100 and 1500 days with a step size of 0.1 days. + For each period (he sum of the squared residuals was computed. and the period with the smallest value of that sum. 1154.5 days. was identilied as (he preliminary value of the orbital period.," For each period the sum of the squared residuals was computed, and the period with the smallest value of that sum, 1154.5 days, was identified as the preliminary value of the orbital period." + We note that a phase plot of our velocities. determined with the previously suggested orbital period of 304 days (CutlerPereiraetal. 1999).. shows that both maximum and minimum velocities occur al (he same phases.," We note that a phase plot of our velocities, determined with the previously suggested orbital period of 304 days \citep{cetal86, +petal99}, shows that both maximum and minimum velocities occur at the same phases." + Thus. the 304-day period is clearly excluded.," Thus, the 304-day period is clearly excluded." + speculated that the 304 day period was in fact an artifact of the strong L/L torque noise in the pulsars spin behavior., \citet{cr97} speculated that the 304 day period was in fact an artifact of the strong 1/f torque noise in the pulsar's spin behavior. + Adopting the 1154.5-dav. period ancl unit weight for all velocities. initial orbital elements were computed wilh BISP. a computer program that implements a slightly modified version ol the Wilsing-Russell method (Wolleetal.1967).," Adopting the 1154.5-day period and unit weight for all velocities, initial orbital elements were computed with BISP, a computer program that implements a slightly modified version of the Wilsing-Russell method \citep{whs67}." +. The orbit. was then refined. with SDI (Barkeretal.1967).. a program thal uses dillerential corrections.," The orbit was then refined with SB1 \citep{bel67}, a program that uses differential corrections." + The best fitting period is 1160.3 d or 3.18 vr., The best fitting period is 1160.8 d or 3.18 yr. + Because of the relatively low orbital eccentricitv of 0.101. & 0.022. we computed a circular-orbit solution with SBIC (D. Barlow 1993. private communication). which also uses differential corrections.," Because of the relatively low orbital eccentricity of 0.101 $\pm$ 0.022, we computed a circular-orbit solution with SB1C (D. Barlow 1998, private communication), which also uses differential corrections." + The tests of Lucy&Sweenev(1971). indicate that the eccentric solution is to be preferred., The tests of \citet{ls71} indicate that the eccentric solution is to be preferred. + Orbital phases for the observations and. velocity residuals to (his final solution are given in Table 1., Orbital phases for the observations and velocity residuals to this final solution are given in Table 1. + lu Figure 1 the velocities and computed velocity curve are compared. where zero phase is a time of periastron passage.," In Figure 1 the velocities and computed velocity curve are compared, where zero phase is a time of periastron passage." + The period of 3.13 vears has resulted in large phase gaps since only 1.5 orbital periods have been covered., The period of 3.18 years has resulted in large phase gaps since only 1.5 orbital periods have been covered. + Nevertheless. the elements. listed in Table 2. are reasonably well determined.," Nevertheless, the elements, listed in Table 2, are reasonably well determined." + The mass function. which is the minimum mass of (he unseen star. is quite large. 0.371... and thus consistent with the secondary being a neutron star.," The mass function, which is the minimum mass of the unseen star, is quite large, $M_{\sun}$, and thus consistent with the secondary being a neutron star." + The center-of-mass velocity of —177 kms ‘is within the range of emission line velocities of —120 to —370 km ! that Chakrabartyetal.(1998) found for this svstem., The center-of-mass velocity of $-$ 177 km $^{-1}$ is within the range of emission line velocities of $-$ 120 to $-$ 370 km $^{-1}$ that \citet{cvkl98} found for this system. + The standard error of an individual velocity is 0.85 | which is in good agreement with uncertainties derived in our work on other sviubiotie svstemis (Fekeletal.2000)., The standard error of an individual velocity is 0.85 $^{-1}$ which is in good agreement with uncertainties derived in our work on other S-type symbiotic systems \citep{fetal00}. +. V2116 Oph is classilied as a variable X-ray source. not a late-tvpe variable star. in the GCVS and there is no indication of intrinsic velocity variation in (he M III star.," V2116 Oph is classified as a variable X-ray source, not a late-type variable star, in the GCVS and there is no indication of intrinsic velocity variation in the M III star." + The orbital elements presented here supersede (he preliminary results of IHinkleetal.(2003)., The orbital elements presented here supersede the preliminary results of \citet{hetal03}. +. The ephemeris lor a possible eclipse of the neutron star is where E is the integer number of 1161-daxy. eveles after the given time of conjunction., The ephemeris for a possible eclipse of the neutron star is where E is the integer number of 1161-day cycles after the given time of conjunction. + This ephemeris predicts an upcoming mid-eclipse on local date 2008 March 31., This ephemeris predicts an upcoming mid-eclipse on local date 2008 March 31. +isted in Paper LH. but our WIIT. ZI-band image 33) also revealed a fainter object 1.4 aresee closer ο the racio central Component whose position is given in Tale 3.,"listed in Paper II, but our WHT $R$ -band image 3) also revealed a fainter object 1.4 arcsec closer to the radio central component whose position is given in Table 3." + 1 real. his is the more likely identification.," If real, this is the more likely identification." + The revise position of he object discussed in Paper His 17 48 12.95 |67 03 55.6 31950). the old. position was in error. presumably. due to he low signal:noisee of the detection.," The revised position of the object discussed in Paper II is 17 48 12.95 +67 03 55.6 (B1950), the old position was in error, presumably due to the low signal:noise of the detection." + The identification given in Pape coll is incorrect: the true identification is a faint. diffuse galaxy located between the racio hotspots. ringed in 33.," The identification given in Paper II is incorrect; the true identification is a faint, diffuse galaxy located between the radio hotspots, ringed in 3." + As discussed further in Paper IV. despite the additional racio imaging presented in 1. the nature of this racio source and its identification continues to elude us.," As discussed further in Paper IV, despite the additional radio imaging presented in 1, the nature of this radio source and its identification continues to elude us." +" Phe fairly compact source detected at 5CLΖ in Paper I now appears as just apart. perhaps a hotspot. ofa larger. zz30"" rraclio source in OUE 20cni ma»"," The fairly compact source detected at 5GHz in Paper I now appears as just a part, perhaps a hotspot, of a larger, $\approx 30$ radio source in our 20cm map." +" Spectra taken through objects a. dq"" and bU of 44 showed that all three were probably stars."," Spectra taken through objects `a', `F' and `b' of 4 showed that all three were probably stars." + The most Like‘Ly identification at present is object c. which is unfortunaely very close to star E," The most likely identification at present is object `c', which is unfortunately very close to star `F'." + Consequently the magnitude of this object is very uncertain. but we estimate /?zzz23.6 ina diameter aperture.," Consequently the magnitude of this object is very uncertain, but we estimate $R \approx 23.6$ in a $^{''}$ diameter aperture." + The original identification of this object in Paper LL was an H=21.1 galaxy 3 aresee from line joining the midpoint of the radio hotspots Ca in 2)., The original identification of this object in Paper II was an $R=21.1$ galaxy 3 arcsec from line joining the midpoint of the radio hotspots (`a' in 2). + The spectroscopy of Paper IV shows that the true identification is on the axis. and that ca ds foreground. and. possibly lensing the racio enission.," The spectroscopy of Paper IV shows that the true identification is on the axis, and that `a' is foreground, and possibly lensing the radio emission." + There is a 30 detection ofa possible identification. 4.5 aresec NW from the mid-point of the radio hotspots 53).," There is a $3\sigma$ detection of a possible identification, 4.5 arcsec NW from the mid-point of the radio hotspots 3)." + Another new identification. faintly visible in both ff 22) and / 33)," Another new identification, faintly visible in both $H$ 2) and $R$ 3)." + otter known as the quasar E18211643. this object is one of the most luminous raclio-quict quasars (OO) known with," Better known as the quasar E1821+643, this object is one of the most luminous radio-quiet quasars (RQQ) known with" +photometric data of SN 2002ap collected frou literature.,photometric data of SN 2002ap collected from literature. + The agreement is satisfactory (note that the tabulated helt curve data in Foley et al. (, The agreement is satisfactory (note that the tabulated light curve data in Foley et al. ( +2003) already. coutain the reddening correction - this was removed before plotting in Fig.3).,2003) already contain the reddening correction - this was removed before plotting in Fig.3). + As usual. the phase is referenced to the moment of Banaxinuun. which was determined as JD 2152311.5 (uote that it is 2 davs less than the oue eiven bv Cal-Yiinctal. 2002).," As usual, the phase is referenced to the moment of $B$ -maximum, which was determined as JD 2452311.5 (note that it is 2 days less than the one given by \cite{galy}) )." + The bolometric light cuwe was constructed after combining all available optical aud ucar-IR ucasuremenuts collected from the literature., The bolometric light curve was constructed after combining all available optical and near-IR measurements collected from the literature. + After dereddening with E(D1T)=0.09 inae (see next section). the magnitudes were converted iuto monochromatic fluxes using the calibration of Dessell.2001.," After dereddening with $E(B-V)=0.09$ mag (see next section), the magnitudes were converted into monochromatic fluxes using the calibration of \cite{bess}." +.. The ueiu-IR. coutiibutiou was estimated from the 11ν data of Yoshiietal.2003.. wlile contribution from other vais were neglected.," The near-IR contribution was estimated from the $JHK$ data of \cite{yosh}, while contribution from other bands were neglected." + Then. the bolometric fluxes were calculated by integrating the monochromatic fluxes with a simple trapezoidal rule.," Then, the bolometric fluxes were calculated by integrating the monochromatic fluxes with a simple trapezoidal rule." +" This resulted im the ""observed"" bolometric flux as a function of time.", This resulted in the “observed” bolometric flux as a function of time. + Finally. the absolute bolometric magnitudes have been determined applying the true distance modulus 29.13 mae derived in this paper (see Sect.1).," Finally, the absolute bolometric magnitudes have been determined applying the true distance modulus $\mu_0 = 29.13$ mag derived in this paper (see Sect.4)." + The absolute bolometric magnitudes lave been compared with those derived dy Yoshiietal.2003., The absolute bolometric magnitudes have been compared with those derived by \cite{yosh}. +. Because Yoshii ct al., Because Yoshii et al. + applied py=29.5 mag as distance modulus. their data were corrected to match the slightly lower distance modulus used above.," applied $\mu_0 = 29.5$ mag as distance modulus, their data were corrected to match the slightly lower distance modulus used above." + After correcting for this difference. the two bolometric light curves shower ταν eood aereenient.," After correcting for this difference, the two bolometric light curves showed very good agreement." + Thus. it is concluded. that the various determinations of the CVOZR bolometzc light curve of SN. 2002ap have led to consistent results. iux the source of the main uucertaimty of the bolometric light curve is the true distance modulus of the SN.," Thus, it is concluded that the various determinations of the $UVOIR$ bolometric light curve of SN 2002ap have led to consistent results, and the source of the main uncertainty of the bolometric light curve is the true distance modulus of the SN." + The bolometric lieht curve of SNe can be cescribec analytically by the simple model of Coutardoetal.2000., The bolometric light curve of SNe can be described analytically by the simple model of \cite{contardo}. +. Iu this model the light curve has the form Note that we applied only onc gaussian component. because the bolometric light curve of SN 2002ap docs not show significant bump on the descending brauch.," In this model the light curve has the form Note that we applied only one gaussian component, because the bolometric light curve of SN 2002ap does not show significant bump on the descending branch." +" The light curve parameters were determine via least-squares fitting as HP13.52£0.1. fj=310.£05. fo297.950.02. >=0,0172+0.0005. a)=15.565800001. 05=3.1677£0.0002. gy=1.1681270.2."," The light curve parameters were determined via least-squares fitting as $m_0 = 13.82 \pm 0.1$, $t_0 = 310.0 \pm 0.5$, $t_2 = 297.95 \pm 0.02$ , $\gamma = 0.0172 \pm 0.0005$, $\sigma_0 = 18.3658 \pm 0.0004$, $\sigma_2 = 3.1677 \pm 0.0002$ , $g_0 = 1.4684 \pm 0.2$." + Among these. the nost interesting parameter is the ate-time decline rate 5 that is physically linked to the Co-Fe ecav and the radiation transport in the expanding SN ejecta.," Among these, the most interesting parameter is the late-time decline rate $\gamma$ that is physically linked to the Co-Fe decay and the radiation transport in the expanding SN ejecta." + The value derived above. y=0.017 mag/dav is iu good aerecineut with the oue published by Pandeyetal.2002 (0.0199+0.000L).," The value derived above, $\gamma = 0.017$ mag/day is in good agreement with the one published by \cite{pande} $0.0199 \pm 0.0004$ )." +" Tn Fie. we plot the ""observed bolometric heht curve (Gnpj=My| μυ) together with the analytic model given above aud theexpected decline rates due to the Ni-Co-Fe radioactive decay.", In Fig.4 we plot the “observed” bolometric light curve $m_{bol} = M_{bol} + \mu_0$ ) together with the analytic model given above and theexpected decline rates due to the Ni-Co-Fe radioactive decay. + As ποσα in Fie.Ll. the decline of SN 2002ap is significantly faster than jo. C'o-Fe radioactive decline rate (7=0.0098 inag/dav). as also noted by Pandeyetal.2002 and Yoshiietal.2003.," As seen in Fig.4, the decline of SN 2002ap is significantly faster than the Co-Fe radioactive decline rate $\tau = 0.0098$ mag/day), as also noted by \cite{pande} and \cite{yosh}." +. They explained this as a leakage of + photous from the atmosphere. indicating a transparcut. less massive ejecta.," They explained this as a leakage of $\gamma-$ photons from the atmosphere, indicating a transparent, less massive ejecta." + Our new late-time photometry fully supports these conclusious., Our new late-time photometry fully supports these conclusions. + The connection between the plivsical state of the expanding atmosphere aud the bolometric light curve is analyzed further in Section L., The connection between the physical state of the expanding atmosphere and the bolometric light curve is analyzed further in Section 4. + The spectroscopic observations were carried out at David Duulap Observatory (DDO) between the 2ud aud 25th February. 2002 (f = 3 to |20 days). with the Casscerain spectroeraph attached to the 71 telescope.," The spectroscopic observations were carried out at David Dunlap Observatory (DDO) between the 2nd and 25th February, 2002 $t$ = $-3$ to $+20$ days), with the Cassegrain spectrograph attached to the 74"" telescope." + Two differeut setups have been applied: the 100 lines/mun erating was used for the low dispersion observations. while the 1500 lunesπα erating was selected for obtaining high resolution spectra.," Two different setups have been applied: the 100 lines/mm grating was used for the low dispersion observations, while the 1800 lines/mm grating was selected for obtaining high resolution spectra." + The reciprocal dispersion was 3.60 A/pixcl aud 0.2 A/pixel. respectively.," The reciprocal dispersion was 3.60 /pixel and 0.2 /pixel, respectively." + The low-resolution spectra extended from10060 to 7500. Α.. while the high- spectrum was centered on Na D and covered a 200 A--wide spectral interval.," The low-resolution spectra extended from4000 to 7500 , while the high-resolution spectrum was centered on Na D and covered a 200 -wide spectral interval." + The slit width was 306, The slit width was 306 +polarization observations mapping the plane-ol-the-sky component of the magnetic field) need also be incorporated in the analysis and interpretation of the observations.,polarization observations mapping the plane-of-the-sky component of the magnetic field) need also be incorporated in the analysis and interpretation of the observations. +" CIITIÓO also comment on the wav they derived the uncertainty on the envelope mean D-field: ""Moreover. CLUE did. not average the four envelope results for. cach cloud and obtain the uncertainty by. error. propagation: they synthesized a toroidal beam to sample the envelopes and obtained the uncertainties directly [rom the single envelope Bros measurement for each cloud"," CHT10 also comment on the way they derived the uncertainty on the envelope mean $B$ -field: “Moreover, CHT did not average the four envelope results for each cloud and obtain the uncertainty by error propagation; they synthesized a toroidal beam to sample the envelopes and obtained the uncertainties directly from the single envelope $B_{\rm LOS}$ measurement for each cloud.”" + The implication here is that the toroidal beam synthesis method adopted. by CLIEFO9. automatically returns the correct error of measurement. and that this error is cillerent rom the value obtained hy error propagation.," The implication here is that the toroidal beam synthesis method adopted by CHT09 automatically returns the correct error of measurement, and that this error is different from the value obtained by error propagation." + The second part of this claim can be refuted directly and quantitativeA he error quoted in CLIETO9 is almost exactly. the same as he uncertainty calculated using error propagation uncer the assumption of no D-[eld variation in the envelope it is for his reason that. CITPIO are now arguing against —envelope D-lield variations., The second part of this claim can be refuted directly and quantitatively: the error quoted in CHT09 is almost exactly the same as the uncertainty calculated using error propagation under the assumption of no $B$ -field variation in the envelope – it is for this reason that CHT10 are now arguing against envelope $B$ -field variations. + The reason for which this is the case. anc for which he first part of the CLUE. claim. is incorrect. can be seen immecdiatelv as follows.," The reason for which this is the case, and for which the first part of the CHT claim is incorrect, can be seen immediately as follows." + The CIETO9. method. of toroidal »ani synthesis consists of a [it of that best describes the data from all four beams., The CHT09 method of toroidal beam synthesis consists of a fit of that best describes the data from all four beams. + The uncertainty associated with this value is obtained from the error in the fit., The uncertainty associated with this value is obtained from the error in the fit. + Llowever. the uncertainty in this single-value fit isstrains’. ~," However, the uncertainty in this single-value fit is. “" +"Svuthesizing” the toroidal bean in the CLEEOO manner aces constraints. (and. decreases the ""synthesized? error) without allowing for field variation.",Synthesizing” the toroidal beam in the CHT09 manner adds constraints (and decreases the “synthesized” error) without allowing for field variation. + By contrast. in a true toroidal beam. the addition of observed area would induce additional noise in the observations and increase the uncertainty in the elobal fitdataset.," By contrast, in a true toroidal beam, the addition of observed area would induce additional noise in the observations and increase the uncertainty in the global fit." + The cillerence in derived. uncertainty if one allows or a priori rejects intrinsic spread in the envelope. D-field is thus exactly the same in the error propagation anc “toroidal beam synthesis? methods a result that is also verified by calculating the associated uncertainties in the two cases., The difference in derived uncertainty if one allows or a priori rejects intrinsic spread in the envelope $B$ -field is thus exactly the same in the error propagation and “toroidal beam synthesis” methods – a result that is also verified by calculating the associated uncertainties in the two cases. + The problem with this argument is two-Llolel., The problem with this argument is two-fold. + First. there is a fundamental dillerence between the specilic geometry of an observed. cloud ancl the basic physical processes that determine the properties. including the appearance. of the cloud.," First, there is a fundamental difference between the specific geometry of an observed cloud and the basic physical processes that determine the properties, including the appearance, of the cloud." + “Phe former can alter the observable quantities due to line-of-1ght. ellects anc additional noise due to intrinsic spread of the quantity being measured. (ancl this is what Figs., The former can alter the observable quantities due to line-of-sight effects and additional noise due to intrinsic spread of the quantity being measured (and this is what Figs. + la and 1b in M'TOO were designed to demonstrate). without allecting the nature of the underline physical processes that govern the evolution of the cloud.," 1a and 1b in MT09 were designed to demonstrate), without affecting the nature of the underlying physical processes that govern the evolution of the cloud." + As a result.model that can be safely. rejected. using such observable quantities without accounting for the possibility of more complex geometry.," As a result, that can be safely rejected using such observable quantities without accounting for the possibility of more complex geometry." + The logic of the argument. should. be as follows: “A model with simple geometry and physics X cannot describe mv. data of a physical system., The logic of the argument should be as follows: “A model with simple geometry and physics X cannot describe my data of a physical system. + Hence. if physics X is correct. the geometry of my. physical system is not simple.”," Hence, if physics X is correct, the geometry of my physical system is not simple.”" + This brings us back to the necessity. ofspread in order for the CIETOO analysis to be permissible., This brings us back to the necessity of in order for the CHT09 analysis to be permissible. +" En the svmbolic language used above. this would be equivalent to the following permissible (but. incorrect) argument: 7L have proven that the geometry of mv system is simple"" (in the CIITOO case. 7L haverejected the possibility of spread”). "," In the symbolic language used above, this would be equivalent to the following permissible (but incorrect) argument: “I have proven that the geometry of my system is simple” (in the CHT09 case, “I have the possibility of spread”). “" +7 model with simple gcometry and. physics X cannot describe my data: hence. physics X does not describe my physical system!,"A model with simple geometry and physics X cannot describe my data; hence, physics X does not describe my physical system”!" + As we discussed in reftest.. CLEEO9 not only do not reject spread in the envelope D-lield (Le. not only do they not show that the geometry of the system is simple). but in fact their own test shows that spread in the envelope D-values is prefered. (ie. a complex geometry ds. independently. a better. description. of their physical systems).," As we discussed in \\ref{test}, CHT09 not only do not reject spread in the envelope $B$ -field (i.e. not only do they not show that the geometry of the system is simple), but in fact their own test shows that spread in the envelope $B$ -values is prefered (i.e. a complex geometry is, independently, a better description of their physical systems)." + In refmaps owe also presented independent: evidence. (base on intensity maps tracing the column density) that the ecometry of these svstems. contrary to the CITPOO. ane ΟΥΓΟassumplions. is complex.," In \\ref{maps} we also presented independent evidence (based on intensity maps tracing the column density) that the geometry of these systems, contrary to the CHT09 and CHT10, is complex." + The second. problem with the CLUTPIO argumen discussed in this section is that the assumption of uniform magnetic field in the envelope. (in both magnitude: anc direction) is not consistently used by CLET09 throughout the observations. thereby enhancing the internal contradictions oftheir analysis.," The second problem with the CHT10 argument discussed in this section is that the assumption of uniform magnetic field in the envelope (in both magnitude and direction) is not consistently used by CHT09 throughout the observations, thereby enhancing the internal contradictions of their analysis." + For example. this assumption was not usec in designing the observations: Lf CIITOO really believed. or expected that a single value of the magnetic field strength could characterize each cloud envelope. then there would be no need to observe four envelope positions in cach cloud.," For example, this assumption was not used in designing the observations: If CHT09 really believed or expected that a single value of the magnetic field strength could characterize each cloud envelope, then there would be no need to observe four envelope positions in each cloud." + One position would be enough. and at that. position they could have spent at least four times as much actual Zeeman integration time (in [aet substantially more since the various overheads would. also be reduced). increasing the likelihood ofa -fielcl detection.," One position would be enough, and at that position they could have spent at least four times as much actual Zeeman integration time (in fact substantially more since the various overheads would also be reduced), increasing the likelihood of a $B$ -field detection." + Similarly. in L1544 in which obtain a detection in one of the envelope positions: if they hac been consistently using the assumption of a single B-lield value in the envelope. they could have used that detection to obtain an actual measurement of /? for this," Similarly, in L1544 in which obtain a detection in one of the envelope positions: if they had been consistently using the assumption of a single $B$ -field value in the envelope, they could have used that detection to obtain an actual measurement of $R$ for this" +for the second pulse.,for the second pulse. + Other parameters also need to change in order to fit the observed light curve., Other parameters also need to change in order to fit the observed light curve. + The simulation in Fig., The simulation in Fig. + 6 is remarkably similar to the observations., \ref{fig_com} is remarkably similar to the observations. +" Our results indicate that the two radio emission regions producing the two pulses are very close, which would be consistent with the nature of the cone radiation of ECMI."," Our results indicate that the two radio emission regions producing the two pulses are very close, which would be consistent with the nature of the cone radiation of ECMI." + An important feature is that the radio pulses would repeat with the rotation period of the UCD., An important feature is that the radio pulses would repeat with the rotation period of the UCD. +" In the case of TVLM 513, the period is ~1.96 hrs."," In the case of TVLM 513, the period is $\sim$ 1.96 hrs." +" Moreover, we note that the decay time of the pulses in some observations is longer than our simulation."," Moreover, we note that the decay time of the pulses in some observations is longer than our simulation." + This is possibly due to the deformation of the radio-emitting region as fast rotation of the dwarf can cause the shape of the emitting region to vary from an almost symmetric circle to an asymmetric ellipse with a tail., This is possibly due to the deformation of the radio-emitting region as fast rotation of the dwarf can cause the shape of the emitting region to vary from an almost symmetric circle to an asymmetric ellipse with a tail. + Our results show that rotation coupled with the ECMI mechanism can account for the flux density and polarization of the radio pulses from TVLM 513 successfully., Our results show that rotation coupled with the ECMI mechanism can account for the flux density and polarization of the radio pulses from TVLM 513 successfully. + We can not exclude the possibility that the depolarization of ECMI could be due to radiation transfer of the emission in a neutral atmosphere with lower fractional ionization or that inhomogeneous dust clouds (?) could have an effect on the quiescent emission and the unpolarized components., We can not exclude the possibility that the depolarization of ECMI could be due to radiation transfer of the emission in a neutral atmosphere with lower fractional ionization or that inhomogeneous dust clouds \citep{Littlefair08} could have an effect on the quiescent emission and the unpolarized components. +" ? suggested that the depolarization or mode conversion of the X-mode emission occurs in a density cavity, as mode conversion of terrestrial kilometric radiation (TKR) from X-mode to R-mode in the emitting density cavity (Ergun et al."," \citet{Hallinan06} suggested that the depolarization or mode conversion of the $X$ -mode emission occurs in a density cavity, as mode conversion of terrestrial kilometric radiation (TKR) from $X$ -mode to $R$ -mode in the emitting density cavity (Ergun et al." + 2000) may account for escape of maser emission without re-absorption at higher harmonics of the emission frequency., 2000) may account for escape of maser emission without re-absorption at higher harmonics of the emission frequency. +line shape. several wind models can be fitted to the observed line profiles (here we chose as typical values for model M2 VinaxSJ=Vus0.5ςQI ).,"line shape, several wind models can be fitted to the observed line profiles (here we chose as typical values for model M2 $\rm{v}_{max}^{eq}=V_{rot}=0.5~\rm{v}_{max}^{po}$ )." + From Figs., From Figs. + + and 5.. we note that our simple model is able to reproduce the diversity of the BAL profiles observed in a real sample of objects quite well.," \ref{fite1} and \ref{fite2}, we note that our simple model is able to reproduce the diversity of the BAL profiles observed in a real sample of objects quite well." + Interestingly enough. in order to be able to fit the profiles with MCRT. we must shift the whole simulated line profile with respect to the emission peak. usually used for redshift determination.," Interestingly enough, in order to be able to fit the profiles with MCRT, we must shift the whole simulated line profile with respect to the emission peak, usually used for redshift determination." + This shift is needed to center the underlying emission component of the profile on the zero velocity., This shift is needed to center the underlying emission component of the profile on the zero velocity. + Indeed. when dealing with resonant scattering. an absorption trough extending over the velocity range [-Vinax. 0] produces an emission feature extending from —Vjyax to tVia," Indeed, when dealing with resonant scattering, an absorption trough extending over the velocity range $-\rm{v}_{max}$, 0] produces an emission feature extending from $-\rm{v}_{max}$ to $+\rm{v}_{max}$." + The redshift of the quasar determined from the center of the underlying emission line is given in the second column of Table 2.., The redshift of the quasar determined from the center of the underlying emission line is given in the second column of Table \ref{tabfit}. + From the fitting procedure. one of the major parameters that control the line profile in this type of wind remains the viewing angle i. which plays a crucial role in the shape of the absorptio part of the line by controlling the relative contribution of the equatorial and polar components (when both are required).," From the fitting procedure, one of the major parameters that control the line profile in this type of wind remains the viewing angle $i$, which plays a crucial role in the shape of the absorption part of the line by controlling the relative contribution of the equatorial and polar components (when both are required)." + Thus when a line profile exhibits a sharp. deep absorptio trough superimposed on a shallower high-velocity absorptio component. the quasar is probably viewed along a line of sight. such as the dense equatorial wind seen nearly edge-o (e.g. QI4134+117).," Thus when a line profile exhibits a sharp, deep absorption trough superimposed on a shallower high-velocity absorption component, the quasar is probably viewed along a line of sight, such as the dense equatorial wind seen nearly edge-on (e.g. Q1413+117)." + However. it should be kept in mind that an edge-on disk does not necessarily produce à completely black absorption trough. even for the highest optical depths (cf.," However, it should be kept in mind that an edge-on disk does not necessarily produce a completely black absorption trough, even for the highest optical depths (cf." + Table 2)). since photons scattered to the observer may not be completely reabsorbed by the disk then filling in the absorption trough.," Table \ref{tabfit}) ), since photons scattered to the observer may not be completely reabsorbed by the disk then filling in the absorption trough." + This agrees with what 1s usually observed among the Korista et al. (1993)), This agrees with what is usually observed among the Korista et al. \cite{ko93}) ) + spectra and has already been pointed out by Lee Blandford (1997)) or Arav et al. (2007..," spectra and has already been pointed out by Lee Blandford \cite{le97}) ) or Arav et al. \cite{ar07}," + and references therein)., and references therein). + Finally in all modeled profiles. we need to allow for the creation of photons inside the wind (a fraction f.>0 relative to the continuum intensity).," Finally in all modeled profiles, we need to allow for the creation of photons inside the wind (a fraction $f_e > 0$ relative to the continuum intensity)." + This intrinsic emission produces stronger emission peaks than in the case of a purely resonant scattering wind., This intrinsic emission produces stronger emission peaks than in the case of a purely resonant scattering wind. + We showed that a simple two-component equatorialt+polar wind model is able to reproduce a variety of BAL profiles. ranging from detached absorption troughs to P. Cyeni-type profiles.," We showed that a simple two-component equatorial+polar wind model is able to reproduce a variety of BAL profiles, ranging from detached absorption troughs to P Cygni-type profiles." + The solutions of the fits are not unique and several models with different geometries and/or physical properties can equally reproduce the observed spectra., The solutions of the fits are not unique and several models with different geometries and/or physical properties can equally reproduce the observed spectra. + In accordance with previous studies (e.g. Hamann et al. 1993)).," In accordance with previous studies (e.g. Hamann et al. \cite{ha93}) )," + this demonstrates that a unique physical characterization of the outflow cannot be derived from line profile fitting., this demonstrates that a unique physical characterization of the outflow cannot be derived from line profile fitting. + While detailed information on the geometry of the outflows cannot be derived. we nevertheless reached some interesting conclusions.," While detailed information on the geometry of the outflows cannot be derived, we nevertheless reached some interesting conclusions." + First. in some objects. it is necessary to include both the equatorial and the polar absorption regions.," First, in some objects, it is necessary to include both the equatorial and the polar absorption regions." + This is indeed the case for objects like QI413+117. Q1333+2840. but also Q12354+1453 or Q08424+3431. where the polar component allows reproduction of the shallow absorption trough observed at higher velocities and where the lower velocity equatorial component ts needed to reabsorb the emission from the polar wind.," This is indeed the case for objects like Q1413+117, Q1333+2840, but also Q1235+1453 or Q0842+3431, where the polar component allows reproduction of the shallow absorption trough observed at higher velocities and where the lower velocity equatorial component is needed to reabsorb the emission from the polar wind." + In other objects (the prototype in our sample being Q0019+0107). the polar component is not necessary and the profiles can be fitted with only a rapidly rotating equatorial wind seen nearly edge-on.," In other objects (the prototype in our sample being Q0019+0107), the polar component is not necessary and the profiles can be fitted with only a rapidly rotating equatorial wind seen nearly edge-on." + In this particular case. there is à strong degeneracy between the model parameters. as also suggested by similar profiles having been computed in the framework of other wind models (e.g. Proga 2003.. Proga Kallman 2004)).," In this particular case, there is a strong degeneracy between the model parameters, as also suggested by similar profiles having been computed in the framework of other wind models (e.g. Proga \cite{pr03}, Proga Kallman \cite{pr04}) )." + Interestingly. in many of the fitted spectra. the viewing angle to the wind axis 1s found to be high. suggesting that BAL quasars are essentially observed when the optically thick equatorial wind blocks the direct view to the continuum source.," Interestingly, in many of the fitted spectra, the viewing angle to the wind axis is found to be high, suggesting that BAL quasars are essentially observed when the optically thick equatorial wind blocks the direct view to the continuum source." + This agrees with the high inclination generally inferred to account for the spectropolarimetric properties of BAL QSOs (Schmidt Hines 1999.. Ogle et al. 1999)).," This agrees with the high inclination generally inferred to account for the spectropolarimetric properties of BAL QSOs (Schmidt Hines \cite{sc99}, Ogle et al. \cite{og99}) )." + In this case. the polar wind could play the role of the extended scattering region at the origin of the polarization.," In this case, the polar wind could play the role of the extended scattering region at the origin of the polarization." + We also showed that. when the profile is constituted of a single deep absorption trough and a quasi-symmetric emission peak (e.g. Q0041-4023). the line can be produced in à two-component wind seen at low inclination (see the bottom right panel of Fig. 5)).," We also showed that, when the profile is constituted of a single deep absorption trough and a quasi-symmetric emission peak (e.g. Q0041-4023), the line can be produced in a two-component wind seen at low inclination (see the bottom right panel of Fig. \ref{fite2}) )." + This result underlines that some BAL troughs can be observed as the result of a polar outflow m à two-component wind with a large covering factor., This result underlines that some BAL troughs can be observed as the result of a polar outflow in a two-component wind with a large covering factor. + As mentioned in the introduction. a growing number of radio observations of BAL QSOs provide evidence for such two-component wind models. while recent hydrodynamical simulations show that a stable two-component wind can result from the flow around a black hole and its accretion disk (e.g. Proga 2007)).," As mentioned in the introduction, a growing number of radio observations of BAL QSOs provide evidence for such two-component wind models, while recent hydrodynamical simulations show that a stable two-component wind can result from the flow around a black hole and its accretion disk (e.g. Proga \cite{pr07}) )." + This model appears challenging for the unification by orientation scheme of BAL and non-BAL quasars (e.g. Tumshek 1984a.. Hamann et al. 1993))," This model appears challenging for the unification by orientation scheme of BAL and non-BAL quasars (e.g. Turnshek \cite{tu84a}, , Hamann et al. \cite{ha93}) )" + because of there is an absorption component at every viewing angle (cf., because of there is an absorption component at every viewing angle (cf. + panel E of Fig. 2))., panel E of Fig. \ref{param}) ). + However. that the polar component can be omitted in some cases (e.g. QO019+0107) supports the existence of a class of objects in which only a fraction of the continuum source is covered by the BAL material.," However, that the polar component can be omitted in some cases (e.g. Q0019+0107) supports the existence of a class of objects in which only a fraction of the continuum source is covered by the BAL material." + All in all. the observations suggest that BAL outflows can have a wide range of covering factors.," All in all, the observations suggest that BAL outflows can have a wide range of covering factors." + In our study we decided to use a simple radially expanding wind model with an equatorial and a polar component., In our study we decided to use a simple radially expanding wind model with an equatorial and a polar component. + This type of wind can account for most characteristics of the resonance line profiles observed in the spectra of BAL QSOs., This type of wind can account for most characteristics of the resonance line profiles observed in the spectra of BAL QSOs. + However. we were not able to fit the line shape of the P Cygnr-type quasar prototype PHL5200.," However, we were not able to fit the line shape of the P Cygni-type quasar prototype PHL5200." + This indicates that the model used does not include all the ingredients needed., This indicates that the model used does not include all the ingredients needed. + Indeed. the model cannot reproduce the very sharp transition observed between the absorption and the emission components in the profile of PHL5200 (Turnshek et al. 1988)).," Indeed, the model cannot reproduce the very sharp transition observed between the absorption and the emission components in the profile of PHL5200 (Turnshek et al. \cite{tuetal88}) )." + Such a sharp transition at zero velocity could in turn be produced in à wind launched from the disk itself., Such a sharp transition at zero velocity could in turn be produced in a wind launched from the disk itself. + In that type of model. which exhibits large-scale properties similar to those ofthe model considered in the present study. the wind is launched from," In that type of model, which exhibits large-scale properties similar to those ofthe model considered in the present study, the wind is launched from" +↑↕∐∖∐∪↴∖↴↑∶↴∙⊾⋜↧↕⋜↧⊼↕↸∖↴∖↴∪↕≯↕∪∐∶↴∙⊾⊣⊔∐⋅⋜↧↑↕∪∐↷↴≓ ↥⋅⋜↧∙↖⇁↴∏∐⋅↴∖↴↑↴∖↴⋖≼∶↕⊰↕≧↴∖↴⋟∐⋜↧↖⇁↸∖↕↸∖≼↧↑,"$\gamma$ \citep{fjm+03,fdm+03,chg04,fls+06,sgb+06}." +∪↑∐↸∖∶↴∙⊾↸∖∐↸∖↥⋅⋜↧↕↸⊳∪∐↴∖↴↸∖∐↴∖↴∏↴∖↴↑∐⋜↧↑ ↑∐↸∖⋅↖↽⋜∐⋅↸∖↕≯⋜, $z\lesssim 0.2$ $Z\sim 0.1-0.5$ $_\odot$ \citep{sgb+06}. +↧↕∐↑⋜⋯≼↧∐⋯∖∙↽∕∏∐↴∖↴∐⋜↧↴∖↴↴⋈∖↸∖∐↕∐↑↸∖∏∐⋅↸∖↑↸∖≺ ↸∖↖⇁↕≼∐∖∐↸⊳↸∖↕⋟∪↥⋅↕∐↑↸∖↕↴∖↴↸∖↴∖↴↑⋜∐⋅↕≯∪↥⋅⋯⋜↧↑↕∪∐⋜↧↸⊳↑↕↖⇁↕↑⋅↖↽∙⋜↧↴∖↴↖↖⇁↸∖∐⋜↧↴∖↴ ↕∪↖↖↽∐∐∖↑⋜↧∐↕↸⊳↕↑⋅↖↽⋜⋯≼↧↴∖↴↑↸∖∐⋜∐⋅⋯⋜↧↴∖↴↴∖↴≺⋮↖⇁∐↴⋝∪↸∖↑⋜↧↕∙⊇∩∩∶≩⇍ 200<0.2 Z—OL0.5 ή. (Staneketal.2006)., $_\odot$ $E\sim 10^{51}$ $z\sim 0.5-1$ \citep{fls+06}. +. Z.. E~10°! 2~0.5.1. 522) Z—0.05.0.5 Z. OURstudiesDergeretal.m2006b:Prochaska2006)). (MacFadyeu&Woosley1," $z>2$ $Z\sim 0.05-0.5$ $_\odot$ \citealt{bpc+06,pro06}) \citep{mw99}, \citep{hfw+03}." +"999).. (Heeeretal.2003).. 2>a ""n(Dergeretal.2006a).. Erbetal.20063)."," $z>6$ \citep{bcc+06}. \citealt{esp+06}) \citep{mw99,hfw+03}." +where Cy is the normalisation constant. oro and (ui are free parameters.,"where $\mathcal{C}_0$ is the normalisation constant, $x_0$ and $a_0$ are free parameters." + Another trial function that we considered was the Gauss function representing normal cistribution where wy and (e are free parameters., Another trial function that we considered was the Gauss function representing normal distribution where $x_0$ and $\sigma$ are free parameters. + We also tried the lognormal clistribution (suggested by Lorimeretal. (2006))). where wry and 0 are free parameters of period. probability clistribution function whose logarithm is normally distributed.," We also tried the log–normal distribution (suggested by \citet{lorimer06}) ), where $x_0$ and $\sigma$ are free parameters of period probability distribution function whose logarithm is normally distributed." + The opening angle (radius) of the pulsar beam can be calculated from the pulsewidth Wo if à and 3 angles are known. either from. the polarisation data (Manchester.&Taylor1977). or from the width of the core component (using Eq. (29))," The opening angle (radius) of the pulsar beam can be calculated from the pulse–width $W$ if $\alpha$ and $\beta$ angles are known, either from the polarisation data \citep{mt77} or from the width of the core component (using Eq. \ref{eq.w.core}) )" + taken from Rankin (1990: hereafter 29023). or both.," taken from Rankin (1990; hereafter \citet{r90}) )), or both." + Inverting Eq. (1)), Inverting Eq. \ref{eq.w.gil81}) ) + one obtains the opening angle p as à function of a. 3 and VM (Gibetal.1984) Lyne&Manchester(1988). were the first who applied this equation to a large number of LO per cent pulsewidth data M5 measured at 408 MlISE.," one obtains the opening angle $\rho$ as a function of $\alpha$, $\beta$ and $W$ \citep{gil84} + \citet{lm88} were the first who applied this equation to a large number of 10 per cent pulse–width data $W_{10}$ measured at 408 MHz." +" ""μον argued that. pjo(408 Allg) =67.5.07, whieh scaled to the 14 GllIz was ους (1990) reanalysed the same sample of data and argued that Rankin(1993a) analysecl a Large sample of pulsewidths cata taken at dillerent frequencies in different world racio observatories over a period of several vears."," They argued that $\rho_{10}$ (408 MHz) $\approx 6^{\circ}.5 P^{-1/3}$, which scaled to the 1.4 GHz was Biggs (1990) reanalysed the same sample of data and argued that \citet{r93a} analysed a large sample of pulse--widths data taken at different frequencies in different world radio observatories over a period of several years." + She has interpolated all available data to frequeney of about 1 Cllz and divided them into different profile classes (according to Rankin (1983)))., She has interpolated all available data to frequency of about 1 GHz and divided them into different profile classes (according to \citet{r83}) ). + In each class she obtained a bimodal xPU? opening angle distribution., In each class she obtained a bimodal $\propto P^{-1/2}$ opening angle distribution. +" ""This result. clearly indicated that pulsar beams consist one or (wo coaxial cones centred on the magnetic axis. with the opening angle p of cach cone following P0L? period dependence."," This result clearly indicated that pulsar beams consist one or two coaxial cones centred on the magnetic axis, with the opening angle $\rho$ of each cone following $P^{-1/2}$ period dependence." + Gil. Kijak Seiracakis (1998: GIX893) and. Wramerctal.(1904) have confirmed this result. at. frequeney 1.4. Cllz. using data obtained with the Elfelsberg 100. mi racdiotelescopoe.," Gil, Kijak Seiradakis (1993; GKS93) and \citet{k94} have confirmed this result at frequency 1.4 GHz, using data obtained with the Effelsberg 100 m radiotelescope." + Instead. of dividing pulsars into cillerent classes to reveal the bimodal 2 distribution of p. CUXS93 performed a careful error analysis4° and rejected all cata subject to large errors (broadening the apparent distribution).," Instead of dividing pulsars into different classes to reveal the bimodal $P^{-1/2}$ distribution of $\rho$, \citet{gks93} performed a careful error analysis and rejected all data subject to large errors (broadening the apparent distribution)." + As a result they obtained that for given period P. the opening angle p can have two possible values: (sce Fig.," As a result they obtained that for given period $P$, the opening angle $\rho$ can have two possible values: (see Fig." + 2 in GIN 893))., 2 in \citet{gks93}) ). + Ixrameretal.(1994). obtained exactly the same result. using an independent. method. for both the pulsewidth measurements and. error. analysis.," \citet{k94} obtained exactly the same result, using an independent method for both the pulse–width measurements and error analysis." + Ixamüning Lie, Examining Fig. + 2 in ο we can notice that the inner cone with p=4.9P1/2 seems to be preferred at shorter periods P?«0.7 s. while the outer cone with p=6321/2 dominates at longer periods £2?71.2 s. However. the exact model of transition between cones is not known.," 2 in \citet{gks93} we can notice that the inner cone with $\rho=4^{\circ}.9\;P^{-1/2}$ seems to be preferred at shorter periods $P<0.7$ s, while the outer cone with $\rho=6^{\circ}.3\;P^{-1/2}$ dominates at longer periods $P>1.2$ s. However, the exact model of transition between cones is not known." + This observational feature is crucial. and it has to be taken into account in the statistical analysis to calculate. the pulsewidth in the svnthetic population.," This observational feature is crucial, and it has to be taken into account in the statistical analysis to calculate the pulse–width in the synthetic population." + We use Iq. (15)), We use Eq. \ref{eq.rho.gks}) ) + in two model a) based on Fig., in two model a) based on Fig. +" 2 in GINS93. we established the period value P=0.7 s below which the inner cone (47.922). and above this value the outer cone (67.3PE72), is always b) like in case a) but below period P?=0.7 s there is a 20 per cent chance to choose the outer cone and an SO per cent chance for the inner ]t is worth noting that Iq. (15))"," 2 in \citet{gks93} we established the period value $P=0.7$ s below which the inner cone $4^{\circ}.9\;P^{-1/2}$ ), and above this value the outer cone $6^{\circ}.3\;P^{-1/2}$ ), is always b) like in case a) but below period $P=0.7$ s there is a 20 per cent chance to choose the outer cone and an 80 per cent chance for the inner It is worth noting that Eq. \ref{eq.rho.gks}) )" + was derived by CGINS93 by means of geometrical analysis of a large number of conal profiles., was derived by GKS93 by means of geometrical analysis of a large number of conal profiles. + We believe that it describes well the low intensity pulse-width measurements used in this paper., We believe that it describes well the low intensity pulse-width measurements used in this paper. + At the time of writing the manuscript of this paper there were 1520 normal pulsars (with. periods longer than 20 ms) known., At the time of writing the manuscript of this paper there were 1520 normal pulsars (with periods longer than 20 ms) known. + In nearly 3 per cent of them the so-called interpulse (1) emission could be identified. by which we understand eatures separated by about 180 (possible deviation could amount to about 40 per cent) from the main pulse (MI).," In nearly 3 per cent of them the so-called interpulse (IP) emission could be identified, by which we understand features separated by about $^{\circ}$ (possible deviation could amount to about 40 per cent) from the main pulse (MP)." + The canonical lighthouse pulsar model naturally predicts he occurrence of interpulses., The canonical lighthouse pulsar model naturally predicts the occurrence of interpulses. + In this model two beams are collimated along the open lines of dipolar magnetic field., In this model two beams are collimated along the open lines of dipolar magnetic field. + When the inclination angle az90° (almost orthogonal rotator) the observer can detect both beams. associated with two opposite magnetic poles.," When the inclination angle $\alpha\approx90^{\circ}$ (almost orthogonal rotator) the observer can detect both beams, associated with two opposite magnetic poles." + This is the so-called doublepole interpulse model (hereafter DPLP)., This is the so-called double--pole interpulse model (hereafter DP–IP). + In this case both pulse components are clearly separated (by about 1807 of longitude) and there is not anv kind. of low level emission between them., In this case both pulse components are clearly separated (by about $^{\circ}$ of longitude) and there is not any kind of low level emission between them. + Duty eveles of cach component are small. typically several per cent. of the pulsar period.," Duty cycles of each component are small, typically several per cent of the pulsar period." + Another possibility. of generating the interpulse is described by the so-called singlepole model (SPLP hereafter)., Another possibility of generating the interpulse is described by the so-called single–pole model (SP–IP hereafter). + This model requires a small inclination angle a (almost aligned rotator)., This model requires a small inclination angle $\alpha$ (almost aligned rotator). + In the SPLP case pulsewidths are much broader than in DPIP model. to the extent that they often fill the entire or most of the pulsar period. (3607).," In the SP–IP case pulse–widths are much broader than in DP–IP model, to the extent that they often fill the entire or most of the pulsar period $^{\circ}$ )." + Even if both components are separated. usually there is a low intensity bridge. of emission. between them.," Even if both components are separated, usually there is a low intensity bridge of emission between them." + The first. version of this moclel (Rickett&Lyne (1968))) assumes that MP. and LP occur when the observer's lineofsight cuts the wide hollow cone of radiation twice (ML77) at a distance of about 1807. of ongitude (Fig., The first version of this model \citet{rl68}) ) assumes that MP and IP occur when the observer's line–of–sight cuts the wide hollow cone of radiation twice (ML77) at a distance of about $^{\circ}$ of longitude (Fig. + C1 (Appendix ?? inthe online materials))., \ref{Fig.C1} (Appendix \ref{sec.appendix.figures} in the on–line materials)). + In the other version of SPLP model (Fig., In the other version of SP–IP model (Fig. + C2. (Appenclix ?? in the online materials)) the lineofsight stavs in à pulsar xam for the entire pulsar period and ALP and LP correspond o cuts through two nested. conical beams or through the arrangement of the core beam surrounded by the cone, \ref{Fig.C2} (Appendix \ref{sec.appendix.figures} in the on–line materials)) the line–of–sight stays in a pulsar beam for the entire pulsar period and MP and IP correspond to cuts through two nested conical beams or through the arrangement of the core beam surrounded by the cone +reionizalion gradually proceeds to the highest density regions.,reionization gradually proceeds to the highest density regions. + More recently. studies based on numerical simulations (e.g.. lliev et al 2006) have concluded that reionization proceeds [rom the highest densitv regions. where the ionizing photon production is stronely concentrated. to the lowest clensity regions.," More recently, studies based on numerical simulations (e.g., Iliev et al 2006) have concluded that reionization proceeds from the highest density regions, where the ionizing photon production is strongly concentrated, to the lowest density regions." + In this picture. the clustering of ionizing sources is more important than the density. variations in intergalactic gas.," In this picture, the clustering of ionizing sources is more important than the density variations in intergalactic gas." +" Fortunately. whether reionization proceeds “inside out or ""outside in.” (he ionized interlace will approximately follow (he cosmic density field."," Fortunately, whether reionization proceeds “inside out” or “outside in,” the neutral-ionized interface will approximately follow the cosmic density field." + This reduces the problem to the well-studied case of the genus number of the galaxy distribution in the linear (or nearly linear) regime., This reduces the problem to the well-studied case of the genus number of the galaxy distribution in the linear (or nearly linear) regime. + Because the genus curve of the densitv field is itself svmuimetric lor gaussian random phase initial conditions. we expect the genus number of the neutral-ionized interlace to behave similarly with volume ionized fraction in either scenario.," Because the genus curve of the density field is itself symmetric for gaussian random phase initial conditions, we expect the genus number of the neutral-ionized interface to behave similarly with volume ionized fraction in either scenario." + In (hie central phases of reionization. the 3D genus number of the interlace will become positive. rellecting the transition to a multiply-connected topology for both the ionized and neutral phases of the IGM.," In the central phases of reionization, the 3D genus number of the interface will become positive, reflecting the transition to a multiply-connected topology for both the ionized and neutral phases of the IGM." +" The amplitucle of the neutral-ionized interlace genus number can be estimated from two characteristic lengths: The typical bubble size (7j). and the effective smoothing scale A, of the observations."," The amplitude of the neutral-ionized interface genus number can be estimated from two characteristic lengths: The typical bubble size $\langle r_b \rangle$, and the effective smoothing scale $\lambda_s$ of the observations." +" For egalaxv (ests. radiative tranfer implies a line-o[-sight smoothing with A,e1.2pMpc."," For galaxy tests, radiative tranfer implies a line-of-sight smoothing with $\lambda_s \approx 1.2 \pMpc$." + The requirements discussed in section 3. suggest a comparable smoothing length should be applied in the transverse directions., The requirements discussed in section \ref{lya_req} suggest a comparable smoothing length should be applied in the transverse directions. +" Then the expected genus number density becomes ~(2x)7A,e10PAMpe7 (see. eg. eq."," Then the expected genus number density becomes $\sim (2\pi)^{-2} \lambda_s^{-3} \sim +10^{-5} \cMpc^{-3}$ (see, e.g., eq." + 8 of Rhoads. Gott. Postman. 1994).," 8 of Rhoads, Gott, Postman 1994)." + Since modern narrowband survevs with hall-cegree cameras cover volumes ~I07eMpc per field. a ssurvev of a few contiguous fields should contain enough volume for an interesting measurement of the neutral-ionized interface genus number.," Since modern narrowband surveys with half-degree cameras cover volumes $\sim 10^5 \cMpc^{3}$ per field, a survey of a few contiguous fields should contain enough volume for an interesting measurement of the neutral-ionized interface genus number." + If (7j)2Ax. we would need to substitute (7) for As in our estimated genus number density.," If $\langle r_b \rangle \gg \lambda_s$, we would need to substitute $\langle r_b \rangle$ for $\lambda_s$ in our estimated genus number density." + A sketch of the expected genus evolution is shown in figure 2.., A sketch of the expected genus evolution is shown in figure \ref{gen_cartoon}. + A detailed prediction for the magnitude of the genus number aud its evolution with redshift depends on the many unknown details of the reionization process (feedback effects. possible dependence of the escape fraction on galaxy mass. etc). so we do not attempt a detailed analvtical treatment here.," A detailed prediction for the magnitude of the genus number and its evolution with redshift depends on the many unknown details of the reionization process (feedback effects, possible dependence of the escape fraction on galaxy mass, etc), so we do not attempt a detailed analytical treatment here." + The best wav to make model the genus number in (his phase will be genus curve “neasuvelments in reionization simulations. preferablv coupled with a realistic algorithin for assigning goalaxies (ο dark matter halos.," The best way to make model the genus number in this phase will be genus curve “measurements” in reionization simulations, preferably coupled with a realistic algorithm for assigning galaxies to dark matter halos." +"v, We assume that the pairs have similar line-of-sight velocity differences as the seven elliptical-elliptical mergers discussed in Combes et ((1995).",$v_c$ we assume that the pairs have similar line-of-sight velocity differences as the seven elliptical-elliptical mergers discussed in Combes et (1995). +" The mean velocity difference of the Combes et ppairs Av=296+91 (with. the error. determined by the jackknife method). implying v,=/3Ar258134158 Που an isotropic velocity distribution."," The mean velocity difference of the Combes et pairs $\Delta v = 296 \pm 91$ (with the error determined by the jackknife method), implying $v_c = \sqrt{3} \Delta v = 513 \pm 158$ for an isotropic velocity distribution." + The median mass of the companions is (7+3)«10? M... where we used M/Ljg=4.6 in Solar units to convert luminosity to mass (van der Marel 1991) and assumed z20.10+0.02.," The median mass of the companions is $(7 \pm 3) \times 10^{10}\,M_{\odot}$ , where we used $M/L_R = 4.6$ in Solar units to convert luminosity to mass (van der Marel 1991) and assumed $z=0.10\pm 0.02$." + Taking InA—2 (following Dubinski et 11999 and Patton et 22000) we obtain 7j.=0.42:0.2 GGyr., Taking $\ln \Lambda \sim 2$ (following Dubinski et 1999 and Patton et 2000) we obtain $T_{\rm fric} = 0.4 \pm 0.2$ Gyr. +" With f£,=19/1220.1640.03 we obtain R=0.440.2 GGyr!.", With $f_m = 19/122 = 0.16 \pm 0.03$ we obtain $R = 0.4 \pm 0.2$ $^{-1}$. + The effect of the mergers on the mass evolution of red galaxies not only depends on the merger rate but also on the mass change resulting from individual mergers., The effect of the mergers on the mass evolution of red galaxies not only depends on the merger rate but also on the mass change resulting from individual mergers. +" The mass aceretion rate can be approximated by with M/M|, the median mass ratio of the mergers.", The mass accretion rate can be approximated by with $\overline{M_2/M_1}$ the median mass ratio of the mergers. + As shown ins refobservedmerge.see this ratio is approximately 0.23., As shown in \\ref{observedmerge.sec} this ratio is approximately 0.23. +" With Ry,20.4 we obtain AM/M=0.09+0.04 GGyr|. i.e. merging increases the masses of galaxies on the red sequence by ~10 For comparison to other studies it is also of interest toconsider the major merger fraction within a projected separation of kkpe."," With $R_{\rm m} = 0.4$ we obtain $\Delta M/M = 0.09 +\pm 0.04$ $^{-1}$, i.e., merging increases the masses of galaxies on the red sequence by $\sim 10$ For comparison to other studies it is also of interest toconsider the major merger fraction within a projected separation of kpc." + There are seven red pairs with luminosity ratio >0.3 and projected separation <11. corresponding to a fraction of 0.06+0.02.," There are seven red pairs with luminosity ratio $>0.3$ and projected separation $<11\arcsec$, corresponding to a fraction of $0.06\pm 0.02$." + It should be stressed that this number refers to mergers within the red sequence. not to the merger fraction within the full sample of R<17 galaxies.," It should be stressed that this number refers to mergers within the red sequence, not to the merger fraction within the full sample of $R<17$ galaxies." +" The colors of the well-separated pairs show that red galaxies ""prefer"" to merge with other red galaxies.", The colors of the well-separated pairs show that red galaxies “prefer” to merge with other red galaxies. + We have not examined the prevalence of mergers among luminous blue galaxies. but as discussed in «ΕΕ the stellar populations of ellipticals rule out widespread major mergers among this population.," We have not examined the prevalence of mergers among luminous blue galaxies, but as discussed in 1 the stellar populations of ellipticals rule out widespread major mergers among this population." + Therefore. the major merger rate in the full sample of red and blue galaxies is presumably much lower than that within the restricted sample of red galaxies.," Therefore, the major merger rate in the full sample of red and blue galaxies is presumably much lower than that within the restricted sample of red galaxies." + À very rough estimate of the merger fraction in the full sample ts0.06Λι/Mou~0.02. 1n reasonable agreement with previous studies of close pairs (see. e.g.. 2002. Lin et 22004. and references therein).," A very rough estimate of the merger fraction in the full sample is$0.06 \times +N_{\rm red}/N_{\rm total} \sim 0.02$, in reasonable agreement with previous studies of close pairs (see, e.g., 2002, Lin et 2004, and references therein)." + At redshifts z«I. the observed evolution of the luminosity function of red galaxies reflects passive evolution of the stellar populations and possible changes in the underlying mass function.," At redshifts $z<1$, the observed evolution of the luminosity function of red galaxies reflects passive evolution of the stellar populations and possible changes in the underlying mass function." + As discussed in. e.g.. MeIntosh et ((2005) these changes can be due to mergers. galaxies entering the red sample due to changes in their star formation rate. or other effects.," As discussed in, e.g., McIntosh et (2005) these changes can be due to mergers, galaxies entering the red sample due to changes in their star formation rate, or other effects." + The best available constraints on the evolution of the luminosity function of red galaxies were derived by (2004). using the COMBO-17 survey.," The best available constraints on the evolution of the luminosity function of red galaxies were derived by (2004), using the COMBO-17 survey." + They find that the luminosity density of luminous red galaxies is approximately constant out to z~I. which is surprising given the expected evolution of a factor of 3—4 in the M/L ratios of the galaxies (e.g.. 1998a. Treu et 22005. van der Wel et 22005).," They find that the luminosity density of luminous red galaxies is approximately constant out to $z\sim 1$, which is surprising given the expected evolution of a factor of $3-4$ in the $M/L$ ratios of the galaxies (e.g., 1998a, Treu et 2005, van der Wel et 2005)." + A possible explanation ts that the underlying stellar mass density evolves as well. compensating for passive evolution of the stellar populations 2004).," A possible explanation is that the underlying stellar mass density evolves as well, compensating for passive evolution of the stellar populations 2004)." + We first determine the effect of the observed red mergers only. i.e.. the pair.," We first determine the effect of the observed red mergers only, i.e., the pair." + Dry mergers have no effect on the total luminosity density. but they have a strong effect on the luminosity density of galaxies brighter than a fixed magnitude.," Dry mergers have no effect on the total luminosity density, but they have a strong effect on the luminosity density of galaxies brighter than a fixed magnitude." + The effect of a single generation of mergers can be approximated by with (2) the luminosity density of luminous galaxies before the mergers and 0) the luminosity density after the mergers., The effect of a single generation of mergers can be approximated by with $j(z)$ the luminosity density of luminous galaxies before the mergers and $j(0)$ the luminosity density after the mergers. +" For fj,20.52 and (£2/£L,)=0.3 we find /(z)=0.88/00)."," For $f_{\rm m}=0.52$ and $\langle L_2 / L_1 \rangle = 0.3$ we find $j(z) \approx 0.88 +j(0)$." + We use Monte Carlo simulations to test this approximation for a fiducial luminosity function with a=—0.6 and M.=-19.9 2004)., We use Monte Carlo simulations to test this approximation for a fiducial luminosity function with $\alpha = -0.6$ and $M_* = -19.9$ 2004). + The luminosity function is evolved backward in time by breaking galaxies into pieces with luminosity ratio 0.3., The luminosity function is evolved backward in time by breaking galaxies into pieces with luminosity ratio 0.3. + Calculating the luminosity density for M<—19 gives j(z)20.89(0). in very good agreement with the simple estimate given above.," Calculating the luminosity density for $M<-19$ gives $j(z) = 0.89 j(0)$, in very good agreement with the simple estimate given above." + The conclusion ts that the effect of the observed mergers and remnants on the luminosity density of bright galaxies is small. of order Theobserved interactions only probe a relatively short period of at most a few Gyr.," The conclusion is that the effect of the observed mergers and remnants on the luminosity density of bright galaxies is small, of order Theobserved interactions only probe a relatively short period of at most a few Gyr." +" In order to extrapolate the effect of the mergers back in time we assume the following: 1) the mass accretion rate at z20.1 is AM/M20.090.04 GGyr (see refrate.sec)): 2) the change in luminosity density due to mergers is proportional to the accreted luminosity: 3) all red galaxies are equally likely to undergo mergers: and 4) the mass accretion rate evolves as (1+2)"".", In order to extrapolate the effect of the mergers back in time we assume the following: 1) the mass accretion rate at $z=0.1$ is $\Delta M/M= 0.09 \pm 0.04$ $^{-1}$ (see \\ref{rate.sec}) ); 2) the change in luminosity density due to mergers is proportional to the accreted luminosity; 3) all red galaxies are equally likely to undergo mergers; and 4) the mass accretion rate evolves as $(1+z)^m$. + The value of i is treated as a free parameter: observational constraints on the evolution of the merger rate may not be quite consistent (see. e.g.. Patton et 22002. Concelice et 22003. Lin et 22004). and no studies have specifically considered the evolution of the pair fraction among galaxies on the red sequence.," The value of $m$ is treated as a free parameter: observational constraints on the evolution of the merger rate may not be quite consistent (see, e.g., Patton et 2002, Concelice et 2003, Lin et 2004), and no studies have specifically considered the evolution of the pair fraction among galaxies on the red sequence." + The dashed lines in refjevo.plot show the predicted merger-driven evolution of the luminosity density of bright red. galaxies with these assumptions. for three values of a.," The dashed lines in \\ref{jevo.plot} show the predicted merger-driven evolution of the luminosity density of bright red galaxies with these assumptions, for three values of $m$." + The model with mm20 has a constant accretion rate. and in the model with m=1.5 the accretion rate is 3« higher at z21 than it is at z=0.," The model with $m=0$ has a constant accretion rate, and in the model with $m=1.5$ the accretion rate is $3\times$ higher at $z=1$ than it is at $z=0$." +" The dotted lines show the evolution of the W/L, ratio of field early-type galaxies. as measured by van der Wel et ((2005)."," The dotted lines show the evolution of the $M/L_B$ ratio of field early-type galaxies, as measured by van der Wel et (2005)." + These authors find AInM/Lg=(71.204:0.18)z for galaxies with M>2«10!.. (appropriate for our sample). which is consistent. with the independent measurement by Treu et ((2005).," These authors find $\Delta \ln M/L_B = (-1.20 \pm 0.18) z$ for galaxies with $M>2\times 10^{11}\,M_{\odot}$ (appropriate for our sample), which is consistent with the independent measurement by Treu et (2005)." + The solid line shows the predicted evolution of jp when both mergers and M/L evolution are taken into account., The solid line shows the predicted evolution of $j_B$ when both mergers and $M/L$ evolution are taken into account. + Grey bands indicate the combined uncertainties in AInM/Lj and the merger rate., Grey bands indicate the combined uncertainties in $\Delta \ln M/L_B$ and the merger rate. + The predicted evolution of jj depends rather strongly on the assumed evolution of the mass accretion rate: itis positive for a non-evolving accretion rate. constant for m= |. and negative for i> I.," The predicted evolution of $j_B$ depends rather strongly on the assumed evolution of the mass accretion rate: itis positive for a non-evolving accretion rate, constant for $m=1$ , and negative for $m>1$ ." + Solid points show the luminosity density in luminous red galaxies as measured by (2004) (their 55)., Solid points show the luminosity density in luminous red galaxies as measured by (2004) (their 5). + As discussed extensively by these authors the data are inconsistent with passive evolution alone (dotted curves)., As discussed extensively by these authors the data are inconsistent with passive evolution alone (dotted curves). + However. as can be seen in," However, as can be seen in" +outward transport (Ciesla2009) if Iris was created in an inner-nebula shock (unless Jupiter vad migrated inside of 2 AU and was closer to the Sun than Iris when Iris formed. 2011))).,outward transport \citep{cie09} if Iris was created in an inner-nebula shock (unless Jupiter had migrated inside of 2 AU and was closer to the Sun than Iris when Iris formed \citep{wal11}) ). + Iris likely formed in an event prior to Jupiters formation. such as in an inner-nebula spiral shock that existed before Jupiter opened a gap in the disk 2005).," Iris likely formed in an event prior to Jupiter's formation, such as in an inner-nebula spiral shock that existed before Jupiter opened a gap in the disk \citep{bol05}." +. Therefore. our measurements set a constraint on the Formation time of Jupiter of al east 3 Myr alter CAI formation making it unlikely that Jupiter formed early (e.g.. by disk instability (Boss 2001))).," Therefore, our measurements set a constraint on the formation time of Jupiter of at least 3 Myr after CAI formation making it unlikely that Jupiter formed early (e.g., by disk instability \citep{bos01}) )." + Ow constraint on (he formation lime of Jupiter is consistent with arguments based on the requirement to accrete asteroids (wilh constituent racdiometric-dated chondrules ancl CAIs) before Jupiter grows large enough to inhibit accretion (>3 5 Myr. Seott(2006))).," Our constraint on the formation time of Jupiter is consistent with arguments based on the requirement to accrete asteroids (with constituent radiometric-dated chondrules and CAIs) before Jupiter grows large enough to inhibit accretion $>$ 3–5 Myr, \citet{sco06}) )." + Jupiter was estimated (o form 23.2 Myr after the onset of planetesimal fragmentation in the main belt by Bottkeetal.(2005).. also consistent with the oulwarel transport οἱ Tris.," Jupiter was estimated to form $\sim$ 3.3 Myr after the onset of planetesimal fragmentation in the main belt by \citet{bot05}, also consistent with the outward transport of Iris." + The formation of chondrules in planetesimal bow shocks caused by Jovian resonances (Weidenschillingetal.1998) requires Jupiter to form ~1 Myr after CAIs. a scenario which is disallowed by our measurements.," The formation of chondrules in planetesimal bow shocks caused by Jovian resonances \citep{wei98} requires Jupiter to form $\sim$ 1 Myr after CAIs, a scenario which is disallowed by our measurements." + This work was supported by NASA erant NNNOTAMG2G (GRILL) and NNNOTAAIGTG (A.J.W.)., This work was supported by NASA grant NNX07AM62G (G.R.H.) and NNX07AM67G (A.J.W.). + The operations of the Advanced Light Source and National Center for Electron Microscopy αἱ Lawrence Derkelev National Laboratory are supported by the Director. Ollice of Science. Ollice of Basic Energy. Sciences. U.S. Deparinent. of ποιον under contract number DE-AC02-05C1111231.," The operations of the Advanced Light Source and National Center for Electron Microscopy at Lawrence Berkeley National Laboratory are supported by the Director, Office of Science, Office of Basic Energy Sciences, U.S. Department of Energy under contract number DE-AC02-05CH11231." + The authors thank the anonymous reviewer for helpful suggestions., The authors thank the anonymous reviewer for helpful suggestions. + Tris was named by Laura. Westphal., Iris was named by Laura Westphal. +We consider a satellite galaxy placed in a circular. orbit within a spherical host potential.,We consider a satellite galaxy placed in a circular orbit within a spherical host potential. + Effects of civinamical friction are neglected., Effects of dynamical friction are neglected. + We consider a frame which rotates at the same rate as the satellite orbits., We consider a frame which rotates at the same rate as the satellite orbits. + The gravitational force (per unit mass) at a position υπ from the centre of the host potential is where AZ/(d) is the mass of the host contained. within racius c and a hat indicates a unit. vector., The gravitational force (per unit mass) at a position $\mathbf{r^\prime}$ from the centre of the host potential is where $M^\prime(d)$ is the mass of the host contained within radius $d$ and a hat indicates a unit vector. + ln addition. in this rotating frame. the particle experiences a fictitious force of where Q is à vector with magnitude equal to the angular frequeney of the satellite orbit. and normal to the orbital plane. v is the velocity of the particle.," In addition, in this rotating frame, the particle experiences a fictitious force of where $\mathbf{\Omega}$ is a vector with magnitude equal to the angular frequency of the satellite orbit, and normal to the orbital plane, ${\bf v}$ is the velocity of the particle." + For the circular orbit considered. The centrifugal force here will act to cancel the mean &ravitational force on the satellite since Ato any point in the satellite. we are. therefore. Left with a tidal force (i.c. the gravitational force minus this mean gravitational force) which has a quadrupole form. the Coriolis force and an internal force due to the mass of the satellite itself.," For the circular orbit considered, The centrifugal force here will act to cancel the mean gravitational force on the satellite since At any point in the satellite, we are therefore left with a tidal force (i.e. the gravitational force minus this mean gravitational force) which has a quadrupole form, the Coriolis force and an internal force due to the mass of the satellite itself." + Vhis latter will be ignored since it exerts no torque on the particle., This latter will be ignored since it exerts no torque on the particle. + We consider a particle orbitting within the satellite., We consider a particle orbitting within the satellite. + Let the satellite centre be at vr’. and the particle be at d.," Let the satellite centre be at ${\bf r}^\prime$ , and the particle be at ${\bf d}$." + The orbital position of the particle relative to the satellite centre isr-—dx., The orbital position of the particle relative to the satellite centre is ${\bf r}={\bf d} - {\bf r}^\prime$. + We are interested in the angular momentuni of the particle around the satellite centre anc so wish to compute the torque exerted. on the particle relative to this centre: Considering just the tidal part. of the above. the magnitude of the tidal torque is where @ is the between r and α΄. and. 3 is the angle between r and d.," We are interested in the angular momentum of the particle around the satellite centre and so wish to compute the torque exerted on the particle relative to this centre: Considering just the tidal part of the above, the magnitude of the tidal torque is where $\theta$ is the between ${\bf r}$ and ${\bf r}^\prime$ and $\beta$ is the angle between ${\bf r}$ and ${\bf d}$." + Defining (οο. Cada=2 for a point mass). we can write which is the usual linearapproximation for the tidal field. valid providing r«r.," Defining (e.g. $c_{\rm tidal}=-2$ for a point mass), we can write which is the usual linearapproximation for the tidal field, valid providing $r\ll r^\prime$." + Vherelore. Ifa is the angle between r/ and d. then and 3-506a.," Therefore, If $\alpha$ is the angle between ${\bf r}^\prime$ and ${\bf d}$, then and $\beta = \pi-\theta-\alpha$." + We also have Combining these results. we find ⊾↔⊔∣⋡⋡∖∣↓⋯⊔⊔⋏∙≟⇂∪↓⋅↙∣⋜⋃∐⇂⋖⋅⇀∖↓≻⋜⋃∐⊔⊔⋏∙≟⋜↧⊳∖⋜↧⊳∖≺⋅↓⋅⊓⋅⊳∖↓⊔∣⋮∣⋮∖∖⇁≺⋅ lind The first term in this expression shows the quadrupole nature of the tidal torque.," We also have Combining these results, we find Substituting for $d$ and expanding as a series in $r/r^\prime$ we find The first term in this expression shows the quadrupole nature of the tidal torque." + Note that the tical torque depends on Crd as expected. but there is an additional contribution (i.c. we have E.644 rather than just ο) which arises [rom the fact that. even if there is no gradient in the gravitational force as a function of distance from the host centre. there is still a dillerence in the forces acting at the satellite centre and at the position of the particle. which acts as a tidal field.," Note that the tidal torque depends on $c_{\rm +tidal}$ as expected, but there is an additional contribution (i.e. we have $1-c_{\rm tidal}$ rather than just $-c_{\rm tidal}$ ) which arises from the fact that, even if there is no gradient in the gravitational force as a function of distance from the host centre, there is still a difference in the forces acting at the satellite centre and at the position of the particle, which acts as a tidal field." + We will ignore higher order terms from now on., We will ignore higher order terms from now on. + We now wish to [ind the change in the angular momentum. of the particle as it moves around. its orbit in the satellite galaxy., We now wish to find the change in the angular momentum of the particle as it moves around its orbit in the satellite galaxy. + Note that the tidal torque always acts normal to the plane containing r' and r., Note that the tidal torque always acts normal to the plane containing ${\bf r}^\prime$ and ${\bf r}$ . + The change in angular momentum around the orbit is given simply by Writing dé=dy/x where \ is an angle measured around the orbit. and. using the fact that X=ju£r(4Y where jo=resinó isthe unperturbed angular momentunm of the particle. we have For an orbitin a plane whose normal makes an angle £ with r/. we have where we have chosen x to coincide with 6for the case £— 2/2.," The change in angular momentum around the orbit is given simply by Writing $\d t = \d \chi / \dot{\chi}$ where $\chi$ is an angle measured around the orbit, and using the fact that $\dot{\chi} = +j_0/r(\chi)^2$, where $j_0=rv\sin\phi$ isthe unperturbed angular momentum of the particle, we have For an orbitin a plane whose normal makes an angle $\xi$ with ${\bf r}^\prime$ , we have where we have chosen $\chi$ to coincide with $\theta$for the case $\xi=\pi/2$ ." + Thus, Thus +scattering cross section. with the inclusion of the double scattering terms see also (1997).,"scattering cross section, with the inclusion of the double scattering terms see also ." +. We assume (hat the quarks form a degenerate Fermi gas. with the particle number densitv 7 given by where E=(p?+i2)! ds(he quark kinetic energy and /([E(p)—ji=1/(exp[enn+1) is the Fermi-Dirac distribution funetion1963).," We assume that the quarks form a degenerate Fermi gas, with the particle number density $n$ given by where $E=\left( p^{2}+m^{2}\right) ^{1/2}$ is the quark kinetic energy and $% +f(\left[ E(p)-\mu \right] =1/\left( \exp \left[ \frac{E(p)-\mu }{T}\right] ++1\right) is the Fermi-Dirac distribution function." +. In order to estimate the importance of the LPAI effect on the bremsstrahlung emissivity of quark matter we have to estimate 7. the average (me between two collisions.," In order to estimate the importance of the LPM effect on the bremsstrahlung emissivity of quark matter we have to estimate $\tau $, the average time between two collisions." +" In the case of the interaction of two quarks. denoted 1 and 2. the average time can be obtained from where The kinematic invariant s is given by s=2(my,+Py)Bspypscosϱ)1993).."," In the case of the interaction of two quarks, denoted 1 and 2, the average time can be obtained from where The kinematic invariant $s$ is given by $s=2\left( +m_{eff}^{2}+E_{1}E_{2}-p_{1}p_{2}\cos \theta \right) $." + Dv assuning Chat quarks are ultrarelativistic. wilh ἐν=p. the average collision time can be approximated by (he following analvtic representation: ∖∖⊽↥↥≼↲↕⋅≼↲∠∕⊋⋖⋡⊳∶⇄⋝↕⋟∖⊽⊔∐↲↕↽≻∪↥∡∖↽↥∪≸≟≀↧↴↕⋅∐∐∐↓↓⋟∏∐≺∢∐∪∐≼⇂≼↲⇂," By assuming that quarks are ultrarelativistic, with $E=p$, the average collision time can be approximated by the following analytic representation: where $Li_{2}(z)$ is the polylogarithm function defined as }$." +∎∐∐↲≺⇂≀↧↪∖⊽∠∣⋟∣∣≼⋡⊳∶↕⋝∶∕↽∖⋮↓ ↴∏∐↲∖↽≀↧↴∏≀↧↴∐∪∐∪↓⋟⊔∐↲≺∢∪∐↕⋟∖⊽↕∪∐∐∐∐↲≀↧↪∖⊽≀↕↴↓⋟∏∐≺∢∐∪∐∪↓⋟⊔∐↲≺⇂∏≀↕↴↕⋅↳↽∐∏∐↓∣↽≻≼↲↕⋅≼⇂≼↲∐⋟∖⊽∐⋡∖↽↕⋟∖⇁↕↽≻↕⋅≼↲⋟∖⇁≼↲∐∩↲≺⇂⋅ for different values of the temperature. in Fig.," The variation of the collision time as a function of the quark number density is presented, for different values of the temperature, in Fig." + 2., 2. + In (he fraanework of our model aud for the range of temperatures considered. the collision (ime Is amost independentof 7.," In the framework of our model and for the range of temperatures considered, the collision time is almost independentof $T$." + As expected. 7 decreases with increasing densitv.," As expected, $\tau $ decreases with increasing density." + To calculate 7 we have assumed again that the test quarks. moving in (he dense medium. have energies. of. the same order as the Fermi. energy. E422Epzpeπό(870i)1/3 .," To calculate $\tau $ we have assumed again that the test quarks, moving in the dense medium, have energies of the same order as the Fermi energy, $E_{1}\approx E_{F}\approx p_{F}\approx +\left( \pi ^{2}n_{b}\right) ^{1/3}$ ." + A rough estimate, A rough estimate + A rough estimate., A rough estimate +"Most cosmological CMB analyses are based on Monte Carlo simulations, which in most cases is the only straightforward method of taking into account such world nuisances as non-uniformly distributed noise, non-Gaussian beam profiles and complex Galactic cuts.","Most cosmological CMB analyses are based on Monte Carlo simulations, which in most cases is the only straightforward method of taking into account such real-world nuisances as non-uniformly distributed noise, non-Gaussian beam profiles and complex Galactic cuts." +" If the ILC cleaned map is to be used for such purposes, one must be able to construct a Monte Carlo ensemble that reproduces the detailed properties of the observed map."," If the ILC cleaned map is to be used for such purposes, one must be able to construct a Monte Carlo ensemble that reproduces the detailed properties of the observed map." +" In this section, we first discuss how to produce such an ensemble, and then we take advantage of the simulations to study the properties of the ILC method itself."," In this section, we first discuss how to produce such an ensemble, and then we take advantage of the simulations to study the properties of the ILC method itself." +" Monte Carlo simulation of the ILC map amounts simply to producing a set of k base frequency maps with similar properties to the observed data, which are then processed through the ILC pipeline."," Monte Carlo simulation of the ILC map amounts simply to producing a set of $k$ base frequency maps with similar properties to the observed data, which are then processed through the ILC pipeline." +" The ILC pipeline may then in many respects be regarded simply as one among many statistics we apply to our maps - the crucial part is not the ILC pipeline in itself, but the construction of the base maps."," The ILC pipeline may then in many respects be regarded simply as one among many statistics we apply to our maps – the crucial part is not the ILC pipeline in itself, but the construction of the base maps." +" The only difference from main-stream simulation is that we in this case foregrounds to thesimulations, rather than them from theobservations."," The only difference from main-stream simulation is that we in this case foregrounds to the, rather than them from the." + 'The simulation process may be written in the following algorithmicform*:: The only subtle point in this prescription is how to handle foregrounds., The simulation process may be written in the following algorithmic: The only subtle point in this prescription is how to handle foregrounds. +" Ideally we would like to have a perfect full-sky, noiseless foreground template at each frequency and for each significant foreground free-free, synchrotron and dust), but unfortunately, no (e.g.,such templates are available."," Ideally we would like to have a perfect full-sky, noiseless foreground template at each frequency and for each significant foreground (e.g., free-free, synchrotron and dust), but unfortunately, no such templates are available." + We are therefore left with a choice between two options., We are therefore left with a choice between two options. +" First, we may use the Finkbeiner and Haslam templates (Haslametal.1982;Finkbeiner2004;Finkbeineretal.1999) for synchrotron, free-free and dustemission?, together with the channel specific weights listed in Table 3 of Bennettetal.(2003b).."," First, we may use the Finkbeiner and Haslam templates \citep{haslam:1982,fink:2004,fink:1999} for synchrotron, free-free and dust, together with the channel specific weights listed in Table 3 of \citet{bennett:2003b}." +" The channel specific weights are estimated through direct fits to the observed data, and are therefore"," The channel specific weights are estimated through direct fits to the observed data, and are therefore" +have been retricv¢xd by us from the open Isaac Newton Croup Archive. which is maintained as a part of the CASU Astromomical Data Centre at the Institute of Astronomy. Camvideo.,"have been retrieved by us from the open Isaac Newton Group Archive, which is maintained as a part of the CASU Astronomical Data Centre at the Institute of Astronomy, Cambridge." +" NGC 77123 was observed in two positions of the SATRON lenslet array 337&41"" in size centered outo the opposite sides relative to the galactic uucleus.", NGC 7743 was observed in two positions of the SAURON lenslet array $33\arcsec \times 41\arcsec$ in size centered onto the opposite sides relative to the galactic nucleus. + The resulting ceutra part of the galaxy observed was 535°.ffνΠΩ (sce Fig. 1)), The resulting central part of the galaxy observed was $35\arcsec \times 50\arcsec$ (see Fig. \ref{fig_r_slits_sau}) ) + with 07991 suupliug., with 94 sampling. + For our allaVsis we lave 1wed the scientificready spectral data cubes which have been preseuted earlier by Sil'ehienko&Chilinearian (2011)., For our analysis we have used the scientific-ready spectral data cubes which have been presented earlier by \citet{SilchenkoChilingarian2011}. +. The data cubes were fitted with the ULvSS software package in the παλιο manner as the lone-slit data described above., The data cubes were fitted with the ULySS software package in the same manner as the long-slit data described above. + The model of the LSF constructed from the wilight «kv spectra was taken iuto account., The model of the LSF constructed from the twilight sky spectra was taken into account. + Because of the relatively k»v SYN ratio of the cussion lines we fitted simniltauecously aud TIT] cussion line profiles by assuming that their velocities[0 are the sale: the line widths iud iuteusities were free paranueters, Because of the relatively low $S/N$ ratio of the emission lines we fitted simultaneously and III] emission line profiles by assuming that their velocities are the same; the line widths and intensities were free parameters. + The uaps were smeoothed by a Gaussian with FTETAL=1.5 pixels., The maps were smoothed by a Gaussian with $FWHM = 1.5$ pixels. +" The resulting maps are preseuted in FElg. ον,", The resulting maps are presented in Fig. \ref{fig_sauron_results}. + Radial variatious of the (ond σ derived frou our lone-slt data (Fig. 2)), Radial variations of the $v$ and $\sigma$ derived from our long-slit data (Fig. \ref{fig_longslit_results}) ) + show a goo agreement with the SAURON aps over the ealaxy central region (Fig. 3))., show a good agreement with the SAURON maps over the galaxy central region (Fig. \ref{fig_sauron_results}) ). +" The line-of-sight velocity curve at the PA=313° Qvhlich corresponds to the kinciaical major axis. see below) las a sharp simall-auuplitude iuterual masini at the Rox2"" (190 pc)."," The line-of-sight velocity curve at the $PA=313\degr$ (which corresponds to the kinematical major axis, see below) has a sharp small-amplitude internal maximum at the $R\approx 2\arcsec$ (190 pc)." + A ]lueger radi the rotation velocity rises continuously up to ARxGO” (5.5 kpc)., At larger radii the rotation velocity rises continuously up to $R\approx 60\arcsec$ (5.5 kpc). + The apparent auμίας of tje stellar rotation velocity is about 160kus1, The apparent amplitude of the stellar rotation velocity is about $160\km$. + We have assunied a purely Gaussian shape of the LOSVD and ignored the contribution of the δη aud fy 1noneuts. because the value of the iutrinsic velocity dispersion Is coniparable to the width of the LSF ίσεςςc65s 1j," We have assumed a purely Gaussian shape of the LOSVD and ignored the contribution of the $h_3$ and $h_4$ moments, because the value of the intrinsic velocity dispersion is comparable to the width of the LSF $\sigma_{LSF}\approx65\km$ )." +" The v profiles along differcut Pets are sliehtly differeut: the cross-sections along tιο PA=3137 and 358"" reveal a peak of SOlaus+ achieved in the uucleus. while along the bar (PA= 2687) a ceutral plateau has appeared."," The $\sigma$ profiles along different $PAs$ are slightly different: the cross-sections along the $PA = 313\degr$ and $358\degr$ reveal a peak of $80\km$ achieved in the nucleus, while along the bar $PA=268\degr$ ) a central plateau has appeared." + A complex surface distriution of the o is confirmed by the SAURON maps (Fig.T 3)):, A complex surface distribution of the $\sigma$ is confirmed by the SAURON maps (Fig. \ref{fig_sauron_results}) ): + iu the central region GR to R225"" (2.3 kpc)."," First of all, it follows from the tilted-ring analysis of the SAURON velocity field \citep[for the method description, see][]{Moiseev2004} that radial variations of the kinematical major-axis $PA$ demonstrate very small deviations $1$ $2\degr$ ) from the mean $PA_{star}$ (cited above) up to $R=25$ (2.3 kpc)." + Such a Xceture would have been iupossible if the bar significawlv distorts the velocity field we should observe a turn of the PA along the radius j)ecause the bar poential contribution decreases with he distance frou fje center. while iu the verv center he rotation of the bulge dominates the lue-of-sight velocity field.," Such a picture would have been impossible if the bar significantly distorts the velocity field – we should observe a turn of the $PA$ along the radius because the bar potential contribution decreases with the distance from the center, while in the very center the rotation of the bulge dominates the line-of-sight velocity field." + On t1ο other haud. we» tried to search or the orieutation parameters excludiug the bar. area and using only the clemeuts with Π> 302.8 ης].," On the other hand, we tried to search for the orientation parameters excluding the bar, area and using only the elements with $R> 30$ (2.8 kpc)." + This fit returus the value of P4; roughly equal to he estimates given above. but the inclnation cannot be confidently determunect i this fit.," This fit returns the value of $PA_{star}$ roughly equal to the estimates given above, but the inclination cannot be confidently determined in this fit." + Racial variations of the stellar population parameters derived. for NGC 7713 from our long-slit data those of the SSP-equivaleut age aud metallicity are Given iu Fie., Radial variations of the stellar population parameters derived for NGC 7743 from our long-slit data – those of the SSP-equivalent age and metallicity – are given in Fig. + 2 together with the other radial profiles.," \ref{fig_longslit_results} + together with the other radial profiles." + The stellar nucleus of NCC 7713 has appeared o be chemically and evolutionarily decoupled: the mean stellar age in the nucleus is only 1 Cr. the metality is 1.5 times above solar.," The stellar nucleus of NGC 7743 has appeared to be chemically and evolutionarily decoupled: the mean stellar age in the nucleus is only 1 Gyr, the metallity is 1.5 times above solar." + Devoud the uncleus. meallicity drops to subsolar values. aud the age stabilizes :uo about 2.5 Civ.," Beyond the nucleus, metallicity drops to subsolar values, and the age stabilizes at about 2.5 Gyr." +" We suppose that our measurenieuts a πιου30"" (i.c. 1.92.8 kpc) relate mainly to the bulee aud bar of NGC TTI3. based on its surface briglness distributiou (Erwinetal. 2008).."," We suppose that our measurements at $R<20\arcsec -30\arcsec$ (i.e. 1.9–2.8 kpc) relate mainly to the bulge and bar of NGC 7743, based on its surface brightness distribution \citep{Erwin2008}. ." +"Thommes. E. W., Duncan. M. J.. Levison. Η. 22002.AJ.. 123. 2862 Touboul. M.. Kleine. T.. Bourdon. B.. Palme. H.. Wieler. 22007,Nature.. 450. 1206 Tsiganis. Κ.. Gomes. R.. Morbidelli. Α.. Levison, H. 22005.Naturc.. 435, 459 Walsh. K.. Morbidelli, A.. Raymond. S.. O’Brien. D. and Avi. M. 2010.","Thommes, E. W., Duncan, M. J., Levison, H. 2002, 123, 2862 Touboul, M., Kleine, T., Bourdon, B., Palme, H., Wieler, 2007, 450, 1206 Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H. 2005, 435, 459 Walsh, K., Morbidelli, A., Raymond, S., O'Brien, D. and Avi, M. 2010." +" DPS abstract, Wetherill, G. 11967,Res... 72, 2429 Wetherill, G. 11992, Icarus, 100, 307 Wisdom. J.. Holman. 11991.AJ.. 102. 1528"," DPS abstract, Wetherill, G. 1967, 72, 2429 Wetherill, G. 1992, Icarus, 100, 307 Wisdom, J., Holman, 1991, 102, 1528" +"(Charlot Fall 1993) and therefore EW, ~ sodA..",(Charlot Fall 1993) and therefore $_o$ $\sim$ 800. +" Object 2218 has an EW, 310A. οi= 1:21. — 0.21. is undetected in 6. aud is therefore a good Lyima- a candidate."," Object 2218 has an $_o$ $\sim$ 340, $g-i$ = 4.21 $\pm$ 0.21, is undetected in $u$ , and is therefore a good Lyman $\alpha$ candidate." +" We also find one extremely high EW, (~ 1100 Aj) faint object (113) which is not detected in « and may be a high redshift Lyman o cmitter as well.", We also find one extremely high $_o$ $\sim$ 1100 ) faint object (413) which is not detected in $u$ and may be a high redshift Lyman $\alpha$ emitter as well. +" This object is detected in the ou-baud aud g ( — 27.25 + 0.36). but not in ἐν,"," This object is detected in the on-band and $g$ ( = 27.25 $\pm$ 0.36), but not in $i$." + Assumine ο~ 1.5 for Lyman a galaxies at 2=3.2. the expected / magnitude would be 25.8. just at our [ 6 detection limit.," Assuming $g-i \sim$ 1.5 for Lyman $\alpha$ galaxies at $z= 3.2$, the expected $i$ magnitude would be 25.8, just at our 4 $\sigma$ detection limit." + We camnot rule out the possibility that object 1123 is a dwarf uudoereoius lmassive starburst with a rest-frame [OTT] EW ~ sodA.. but it is more likely that it is backeround Lyman à euütter and we exclude it from our [OTL eiiissiou-line candidates.," We cannot rule out the possibility that object 413 is a dwarf undergoing massive starburst with a rest-frame [OII] EW $\sim$ 800, but it is more likely that it is background Lyman $\alpha$ emitter and we exclude it from our [OII] emission-line candidates." + We do uot fud anv other Lyinan a candidates above the lo cutoff., We do not find any other Lyman $\alpha$ candidates above the $\sigma$ cutoff. + Gravitational lensing by the cluster poteutial is expected to increase. not decrease. the number of detected Lui a galaxies as the effect of Ihuninositv amplification factor should dominate over angular scattering by the leus ou the observed high redshiff backeround galaxy number counts (Broadhurst. Tavlor Peacock 1995).," Gravitational lensing by the cluster potential is expected to increase, not decrease, the number of detected Lyman $\alpha$ galaxies as the effect of luminosity amplification factor should dominate over angular scattering by the lens on the observed high redshift background galaxy number counts (Broadhurst, Taylor Peacock 1995)." + A lensing model would be needed to determine the significance of the low ummber of Lyinan a caucdidates towards the cluster core., A lensing model would be needed to determine the significance of the low number of Lyman $\alpha$ candidates towards the cluster core. + However. the low umber we find is uot obviously iu conflict with the populations described by Rhoads ct al. (," However, the low number we find is not obviously in conflict with the populations described by Rhoads et al. (" +2000) aud Un et al. (,2000) and Hu et al. ( +1998).,1998). + We have detected 66 [OTT enisson-line. candidates in the MS1512.113617 field with excess ou-baucd fiuxes ercater than [| σ and gi <2., We have detected 66 [OII] emission-line candidates in the MS1512.4+3647 field with excess on-band fluxes greater than 4 $\sigma$ and $g-i$ $<$ 2.0. + In Table lL we eive the positions. colors. and fluxes of the enüssion-line candidates.," In Table 4, we give the positions, colors, and fluxes of the emission-line candidates." + In Figure 6. we plot the observed [OT] integrated line flux agains the contiuuuu fux for all detections above the 3 σ evel.," In Figure 6, we plot the observed [OII] integrated line flux against the continuum flux for all detections above the 3 $\sigma$ level." + The red iuterlopers are plotted as triangles. aud he galaxies with spiral aud ireeular colors are plotted as circles aud stars respectively.," The red interlopers are plotted as triangles, and the galaxies with spiral and irregular colors are plotted as circles and stars respectively." + Objects with y/—/ photomeric errors 9 0.5 are plotted as open squares., Objects with $g-i$ photometric errors $>$ 0.5 are plotted as open squares. + The vertical solid lines are lines of coustaut equivaleut width., The vertical solid lines are lines of constant equivalent width. + Contours of constant sumuued fiux show where the data are aid complete., Contours of constant summed flux show where the data are and complete. + The upper dashed line is the Lo cuoff. below which objects are excluded. from our sample (sce Figure 2). iux the lower dashed line is the 3 σ cutoff.," The upper dashed line is the 4 $\sigma$ cutoff, below which objects are excluded from our sample (see Figure 2), and the lower dashed line is the 3 $\sigma$ cutoff." +" All of the lo [OT] EW >100A Cluission-lne caucicates werο visually inspectcc ancl ford to be spatially exteuclec and significantly detected in at least oue broad-band ππασο, therefore they are unlikely to be spurious noise detections."," All of the 4 $\sigma$ [OII] EW $> 100$ emission-line candidates were visually inspected and found to be spatially extended and significantly detected in at least one broad-band image, therefore they are unlikely to be spurious noise detections." +" We do not detect chvarts above the Lo cutoff with star-formation rates below 0.13 AL 1H (ΤονΕΙΟΠΙ 0."," We will show below that, for a low-energy jet to be able to break out of the star in a time shorter than the precursor duration, it must have a moderately high asymptotic Lorentz factor, $\eta= L/\dot{M}c^2\ga 10$ ." + The asviuptotic Lorentz factor of this weak precursor jet can. however. be lower than that «f the typical main GRB ejecta. which are characterized by 42LOO. aud lis could account for the softer spectrum of the precursor compared to the main burst.," The asymptotic Lorentz factor of this weak precursor jet can, however, be lower than that of the typical main GRB ejecta, which are characterized by $\eta>100$, and this could account for the softer spectrum of the precursor compared to the main burst." + Phenomenological relations vetween the enerev (or buuinositv) aud the spectrum of he burst have been found by e.g. Amati et al. (, Phenomenological relations between the energy (or luminosity) and the spectrum of the burst have been found by e.g. Amati et al. ( +2002) and Yonetoku et al. (,2002) and Yonetoku et al. ( +2001). in which a lower cnereyv (or 1unuinositv) burst tends to have a lower peak euerex. heuce a softer spectrun.,"2004), in which a lower energy (or luminosity) burst tends to have a lower peak energy, hence a softer spectrum." + The jet head velocity is given by the longitudinal balance between the jet thrust aud the ram pressure of material ahead of it Rees 2001: Matzner 2003) where 0; is the opeuing angle of the jet while propagating inside the star. whose value will be derived below. aud p is the stellar deusity at radius r.," The jet head velocity is given by the longitudinal balance between the jet thrust and the ram pressure of material ahead of it Rees 2001; Matzner 2003) where $\theta_j$ is the opening angle of the jet while propagating inside the star, whose value will be derived below, and $\rho$ is the stellar density at radius $r$." + The presupernova density profile is assumed to be roughly described by pxr? out to the edge of the Πο core at 10Hon (MacFadyeu et al., The presupernova density profile is assumed to be roughly described by $\rho\propto r^{-3}$ out to the edge of the He core at $r=10^{11}{\rm cm}$ (MacFadyen et al. + 2001). at which point we take the deusity to be p=Leon.7.," 2001), at which point we take the density to be $\rho=1\, +{\rm g cm^{-3}}$." + The total time takeu by the jet head to move from the interior of the star to the surface is where à& Lis an inteerating factor over r (discussed after Eq.(10))., The total time taken by the jet head to move from the interior of the star to the surface is where $\alpha>1$ is an integrating factor over $r$ (discussed after Eq.(10)). +" While thejet is propagating inside the star with a sub-relativistic νο""itv. a significant fraction of ihejet “waste” enerev is pumped into the cocoon smronuding advancingjet."," While the jet is propagating inside the star with a sub-relativistic velocity, a significant fraction of jet “waste” energy is pumped into the cocoon surrounding the advancing jet." + Theiu theuushocked jet moving |with D;2» presseLis ow constrained transverse directionwv the of the cocoon. so that it ects collimated audbecomes more peuetrating.," The unshocked jet moving with $\Gamma_j\gg1$ is now constrained in the transverse direction by the pressure of the cocoon, so that it gets collimated and becomes more penetrating." + The opening augle 0 of the uushocked ofjet is determined by the balauce between the pressure the, The opening angle $\theta$ of the unshocked jet is determined by the balance between the pressure of the +111 luminosity of the galaxy.,IR luminosity of the galaxy. + Pheon observations of NGC 6810. lack the spatial resolution necessary to cleanly separate diffuse from point-like X-ray emission. but a reasonable approximation is to use the total estimated soft thermal X-ray luminosity as a proxy for the truly diffuse emission.," The observations of NGC 6810 lack the spatial resolution necessary to cleanly separate diffuse from point-like X-ray emission, but a reasonable approximation is to use the total estimated soft thermal X-ray luminosity as a proxy for the truly diffuse emission." + The logarithm of the ratio of the thermal X-ray flux to the FIR tux is ~3.8 to -3.6 for NGC GS1O (sec ‘Tables 2. and 3))., The logarithm of the ratio of the thermal X-ray flux to the FIR flux is $\sim -3.8$ to -3.6 for NGC 6810 (see Tables \ref{tab:fits} and \ref{tab:n6810}) ). + Again these numbers are consistent with local starbursts with superwinds. where the log of the soft dilfuse X-ray πας to the FIR flux is 3.660.2 (Strickland 2004)..," Again these numbers are consistent with local starbursts with superwinds, where the log of the soft diffuse X-ray flux to the FIR flux is $-3.6\pm{0.2}$ \citep{strickland_brazil}." + The soft X-ray luminosity. X-ray/ELli luminosity ratio and LRAS to flux ratio of NGC 6810 are extremely similar to those of NGC 1511. another starburst galaxy with a probable wind observed. with (Dahlemetal.2003).," The soft X-ray luminosity, X-ray/FIR luminosity ratio and IRAS to flux ratio of NGC 6810 are extremely similar to those of NGC 1511, another starburst galaxy with a probable wind observed with \citep{dahlem03}." +. This is despite their baryonic masses cilfering bv close to an order of magnitude., This is despite their baryonic masses differing by close to an order of magnitude. + I illustrates how stronely correlated the soft N-ray and EL properties of star orming galaxies are. ancl (contrary to naivve expectation) iow little ellect large ealactic mass appears to have on starburst-driven superwinds.," It illustrates how strongly correlated the soft X-ray and FIR properties of star forming galaxies are, and (contrary to naïvve expectation) how little effect large galactic mass appears to have on starburst-driven superwinds." + Galaxy. mass does appears to xav a role in determining the critical star formation rate »er unit disk area for creation of radio (and presumably hot eas) halos around spiral galaxies (Dahlemetal.2006).. but or a galaxy ofthe mass and size of NGC 6810 the transition oetween galaxies with and without radio halos occurs at a mean star formation rate per unit area approximately two orders of magnitude lower than that found in NGC 6810.," Galaxy mass does appears to play a role in determining the critical star formation rate per unit disk area for creation of radio (and presumably hot gas) halos around spiral galaxies \citep{dahlem06}, but for a galaxy of the mass and size of NGC 6810 the transition between galaxies with and without radio halos occurs at a mean star formation rate per unit area approximately two orders of magnitude lower than that found in NGC 6810." + Vhe X-ray emission not associated with the thermal components the hard X-ray emission and the power law component. all presumably. from. compact. objects) is also at the level we would expect from. purely stellar. processes with no additional AGN contribution required.," The X-ray emission not associated with the thermal components the hard X-ray emission and the power law component, all presumably from compact objects) is also at the level we would expect from purely stellar processes with no additional AGN contribution required." + Colbertetal.(2004) found an empirical relationship for the X-ray point source Luminosity of galaxies from both voung and old stellar populations., \citet{colbert04} found an empirical relationship for the X-ray point source luminosity of galaxies from both young and old stellar populations. + Given the stellar mass of NGC 6810 (CNS101ALY. see Table 33) we would expect the point source X-rav. luminosity from the old stellar population to be Lxp~110eres+ dn the E=03 8.0 keV energy band.," Given the stellar mass of NGC 6810 $\sim 8 \times 10^{10} \Msol$, see Table \ref{tab:n6810}) ) we would expect the point source X-ray luminosity from the old stellar population to be $L_{\rm XP, old} \sim +1.4 \times 10^{40} \ergps$ in the $E=0.3$ – 8.0 keV energy band." + The expected. X-ray emission from point sources associated with ongoing star formation is Lxo5.7107ores (we have corrected for the dillerent IMS used in the the SE3 rate given in Table 3. and Colbertοἱal. (200433).," The expected X-ray emission from point sources associated with ongoing star formation is $L_{\rm XP, old} \sim 5.7 \times 10^{39} \ergps$ (we have corrected for the different IMFs used in the the SF rate given in Table \ref{tab:n6810} and \citet{colbert04}) )." + The total predicted X-ray point source luminosity of2.10!ergs is 2.5 times larger than the luminosity of the power law component in NGC 6810. but this. is within the level of scatter expected from the Colbertctal. relationship.," The total predicted X-ray point source luminosity of $\sim 2 \times 10^{40} \ergps$ is 2.5 times larger than the luminosity of the power law component in NGC 6810, but this is within the level of scatter expected from the \citeauthor{colbert04} relationship." + The above mentioned galactic propertics ancl the lack of any sien of AGN activity in the 0.5. 10 keV energy band cast doubt on the classification of NGC 6810 as a Sevfert 2 ealaxy., The above mentioned galactic properties and the lack of any sign of AGN activity in the 0.5 – 10 keV energy band cast doubt on the classification of NGC 6810 as a Seyfert 2 galaxy. + Phe original classification of NGC 6810 as a Sevlert 2 galaxy is due to Ixirhakos&Steiner(1990b).. based on follow-up optical spectroscopy of LRAS sources near to or within the LIEXO-1 hard. X-ray error boxes of previously unidentified: N-ray sources (Woodetal.1984:Wirhakos&Stei," The original classification of NGC 6810 as a Seyfert 2 galaxy is due to \citet{kirhakos90b}, based on follow-up optical spectroscopy of IRAS sources near to or within the HEAO-1 hard X-ray error boxes of previously unidentified X-ray sources \citep{wood84,kirhakos90a}." +ner 19902).. Wirhakos&Steiner identified NGC 6810 as the counterpart to the LIEAXO-1 source 1111930-589. even though NGC 6810 Lies outside theconfidence error box of this source.," \citeauthor{kirhakos90b} identified NGC 6810 as the counterpart to the HEAO-1 source 1H1930-589, even though NGC 6810 lies outside theconfidence error box of this source." + This X-ray source had à i=2 10 keV N-rayv lux of fx~(2.01L12 : ↓∪⋖⋅↓⋅⋏∙≟⊳∖≼∼⊔↓⊳∖∖⋎↓⊔≼∼↓↥∖∖⋎∪⊔↓∠⇂≼⇍∪↓⋅↓⋅∢⊾≱∖↓≻∪⊔∠⇂↿∪⋜↧⊾↔∢⋅∙∖⇁⇂∢⋅↓⋅↥− ⇉−↓∐⊊⋖⋅↓⇂⇂↓↕↓↕↓↕∢⋟≻↕⇂∙∖⇁∢≱⇂⋅∠↽∖∿↿∖↓⋅↖∖∶∶∪⋅∶∫≻⊐↓∪⊔⋖⋅↓⋅⋏∙≟⊳∖↓⊀↓⇂⋅↥↓⊔⋅ ⋡∖∪⊔↓⋅≼∙⋖⋅∐⋖⊾⋡∖⋜⊔⇂↓↥⋖⊾∠⇂⋠↓⋡∖∣⋜⋃⊔↛⋖⋅∪⇂⋅↓∖⊽≺∶≺⊲≼≨↖∖↓∪⊳↓∖⊽≺," This X-ray source had a $E=2$ – 10 keV X-ray flux of $f_{\rm X} \sim (2.0\pm{0.3}) +\times 10^{-11} \ergps \pcmsq$ , which would correspond to a luminosity of $L_{\rm X} \sim (1.8\pm{0.3}) \times 10^{42} +\ergps$ if the source lies at the distance of NGC 6810." +∶≺⊲≼≨↖∖↓∪⋜↧↓⊳∖∪ satisfied their optical spectroscopic criteria for classification asan AGN: cLU and/or FWHUAL( Oui] or Lla)) E300kms1. although just barely as only the Oru] line width satisfies their criterion (see Table 3)).," NGC 6810 also satisfied their optical spectroscopic criteria for classification as an AGN: $\ge 1.0$ and/or FWHM ( ] or ) $\ge 300 \kmps$, although just barely as only the ] line width satisfies their criterion (see Table \ref{tab:n6810}) )." + A Om line width this large would. be unusual. in a normal galaxy. but not in a starburst galaxy with a superwind. where the velocity of warm ionized gas typically reaches 200—600 knis (Leckmanctal.1990:AXdelbergeretal.2003).," A ] line width this large would be unusual in a normal galaxy, but not in a starburst galaxy with a superwind, where the velocity of warm ionized gas typically reaches 200 – $600 \kmps$ \citep{ham90,adelberger03}." +. Indeed Coceatoetal.(2004) specifically discuss the large line width in NGC 6810 in terms of a possible outflow., Indeed \citet{coccato04} specifically discuss the large line width in NGC 6810 in terms of a possible outflow. + Ixewlevctal.(2001) apply a variety of galaxy classification methocls based on optical line Huxes to LRAS galaxies in the southern hemisphere., \citet{kewley01} apply a variety of galaxy classification methods based on optical line fluxes to IRAS galaxies in the southern hemisphere. + Of the eight. methods they apply to NGC 6810 they classify it as a galaxy six times. with one method. giving ambiguous results and one method vielding a classification of extreme starburst borderline LINER.," Of the eight methods they apply to NGC 6810 they classify it as a galaxy six times, with one method giving ambiguous results and one method yielding a classification of extreme starburst / borderline LINER." + Forbes&Norris(1998) also suggest the NGC 6810 may have been miscelassified as being a Seyfert 2 galaxy. based on its starburst-like radio properties and unpublished optical spectra.," \citet{forbes98} also suggest the NGC 6810 may have been misclassified as being a Seyfert 2 galaxy, based on its starburst-like radio properties and unpublished optical spectra." + However they also point out. that. several Sevlert galaxies with nuclear star formation have radio and LR. properties dominated by the star formation despite being bona fide Sevfert 2 galaxies., However they also point out that several Seyfert galaxies with nuclear star formation have radio and IR properties dominated by the star formation despite being bona fide Seyfert 2 galaxies. + As we have discussed. the hard. N-rav. spectrum. and luminosity of NGC 6810 are inconsistent with a Sevlert 2 classification., As we have discussed the hard X-ray spectrum and luminosity of NGC 6810 are inconsistent with a Seyfert 2 classification. + Phe identification of NGC 6810 with 1111030-58O is most probably spurious., The identification of NGC 6810 with 1H1930-589 is most probably spurious. + Phat NGC 0510 had a significantly higher X-ray luminosity in the early 1980s is à less likely alternative. as there is no other evidence of NGC 0510 ever being a luminous hare X-ray. source (Wardet(1978) place a 3e upper limit on the £=2. 10 keV luminosity of NGC 6810 of Lx<6«107eres| base on6 data). nor would the optical classification of the ealaxy suggest ib to be. or have recently. been. a Sevylor galaxy.," That NGC 6810 had a significantly higher X-ray luminosity in the early 1980's is a less likely alternative, as there is no other evidence of NGC 6810 ever being a luminous hard X-ray source \citet{ward78} place a $3\sigma$ upper limit on the $E=2$ – 10 keV luminosity of NGC 6810 of $L_{\rm X} < 6 \times 10^{42} \ergps$ based on data), nor would the optical classification of the galaxy suggest it to be, or have recently been, a Seyfert galaxy." + The possibility remains that either a low luminosity AGN. or a more luminous but very heavily obscured AGN. is present in NGC 6810.," The possibility remains that either a low luminosity AGN, or a more luminous but very heavily obscured AGN, is present in NGC 6810." + Deep observations with the Llare X-ray Detector (LIND) onSuzaku would be needed to rule the second possibility out. but at present we conclude tha NGC 6810 does not deserve classification as an active galaxy.," Deep observations with the Hard X-ray Detector (HXD) on would be needed to rule the second possibility out, but at present we conclude that NGC 6810 does not deserve classification as an active galaxy." + ltadio continuum. observations of NGC 6810. would oller another method of searching for a low luminosity ACN. in addition to constraining the location of recent. SN activity within the clisk.," Radio continuum observations of NGC 6810 would offer another method of searching for a low luminosity AGN, in addition to constraining the location of recent SN activity within the disk." + There is one respect in which the outflow from NGC 6810 may be less than typical. in that the wind appears to originate not in à compact (0Ss1 kpe) nuclear starburst (as seen in “classic” superwind galaxies such as NCC 253. AIS2 and NGC 3079). but to have a large r 6.5-kpc radius base.," There is one respect in which the outflow from NGC 6810 may be less than typical, in that the wind appears to originate not in a compact $r\la 1$ kpc) nuclear starburst (as seen in “classic” superwind galaxies such as NGC 253, M82 and NGC 3079), but to have a large $r \sim 6.5$ -kpc radius base." + Such vclisk-wicle” superwinds are less common han the nuclear superwinds. although there are à handful of previously known examples such as NGC 4666 (Dahlemetal.1997). and. NOC 5775 (Tüllmanunctal.2006).," Such “disk-wide” superwinds are less common than the nuclear superwinds, although there are a handful of previously known examples such as NGC 4666 \citep{dahlem97_n4666} and NGC 5775 \citep{tullmann06}." +. The owe radius of a superwind appears to match the region of active star-Formation (seee.g.Strickland 2004).. and as we have mentioned earlier may be related to stellar bars (for unknown reasons).," The base radius of a superwind appears to match the region of active star-formation \citep[see \eg][]{strickland_brazil}, , and as we have mentioned earlier may be related to stellar bars (for unknown reasons)." + Indeed. one of the greatest. current weaknesses of numerical models of superwinds is their failure ο produce a wind base racius equal to the radius of the star," Indeed, one of the greatest current weaknesses of numerical models of superwinds is their failure to produce a wind base radius equal to the radius of the star" +3.,. + In particular. we neglect photometric redshift errors. use only a limited range and number of (-bins. and adopt a power-law intrinsic-shear alignment model with a form described by (36) in JSO8 and a slope of 0.1.," In particular, we neglect photometric redshift errors, use only a limited range and number of $\ell$ -bins, and adopt a power-law intrinsic-shear alignment model with a form described by (36) in JS08 and a slope of 0.4." + We have contirmed the consistency between our power spectrum and bispectrum codes with those used in(2010)., We have confirmed the consistency between our power spectrum and bispectrum codes with those used in. + Our power spectrum code agrees also with iCosmo2008)., Our power spectrum code agrees also with iCosmo. + Figure shows the resulting constraint ellipses after nulling from the cosmic shear power spectrum analysis. the bispectrum analysis. and the two combined.," Figure shows the resulting constraint ellipses after nulling from the cosmic shear power spectrum analysis, the bispectrum analysis, and the two combined." + To show how much information is lost during the nulling process. we overplot the original two- and three-point combined constraints on top of the nulled constraint ellipses in7. but center them on the corresponding nulled constraints by subtracting the bias difference before and after nulling.," To show how much information is lost during the nulling process, we overplot the original two- and three-point combined constraints on top of the nulled constraint ellipses in, but center them on the corresponding nulled constraints by subtracting the bias difference before and after nulling." + The information content in terms of FoM for each parameter pair is presented in2., The information content in terms of FoM for each parameter pair is presented in. + One sees that the amount of information contained. in bispectrum measures and power spectrum measures are indeed comparable., One sees that the amount of information contained in bispectrum measures and power spectrum measures are indeed comparable. + With bispectrum information added. typically three times better constraints in terms of FoM are achieved. both before and after nulling.," With bispectrum information added, typically three times better constraints in terms of FoM are achieved, both before and after nulling." + This factor is smaller than the result in TJO4. although the same angular frequency range and the same set of 7 cosmological parameters are chosen for both studies.," This factor is smaller than the result in TJ04, although the same angular frequency range and the same set of 7 cosmological parameters are chosen for both studies." + However a direct comparison is prohibited by different fiducial values adopted and different survey specification., However a direct comparison is prohibited by different fiducial values adopted and different survey specification. + Through the nulling procedure. around % of the original information in terms of FoM is preserved in the two-point case. and around 20% in the three-point case.," Through the nulling procedure, around $\,\%$ of the original information in terms of FoM is preserved in the two-point case, and around $\,\%$ in the three-point case." + It is a bit higher in the three-point case. in accordance to the fact that a roughly N-2 compression is involved in the three-point case and a N->N.! one in the two-point case. while this fact is due to the summation over one redshift bin index during the nulling procedure (the same trend is evident in 5).," It is a bit higher in the three-point case, in accordance to the fact that a roughly ${N_z}^3 \rightarrow {N_z}^2$ compression is involved in the three-point case and a ${N_z}^2 \rightarrow {N_z}^1$ one in the two-point case, while this fact is due to the summation over one redshift bin index during the nulling procedure (the same trend is evident in $\,$ )." + The information loss is considerable. but it Is a price to pay for a model-independent method.," The information loss is considerable, but it is a price to pay for a model-independent method." + As we have discussed in the previous subsection. the difference between the information loss through the nulling and the unconditioned compression procedures represents the inevitable loss of information through nulling.," As we have discussed in the previous subsection, the difference between the information loss through the nulling and the unconditioned compression procedures represents the inevitable loss of information through nulling." + However. this difference is less than 50% in the considered three-point case.," However, this difference is less than $\,\%$ in the considered three-point case." + The other information loss is due to the simplifications we adopted in this study. including using only the first-order weights. and discarding the measures with two or three equal redshift bins.," The other information loss is due to the simplifications we adopted in this study, including using only the first-order weights, and discarding the measures with two or three equal redshift bins." + A further detailed consideration of these aspects can regain part of the lost information., A further detailed consideration of these aspects can regain part of the lost information. + Another simplification we have made in the three-point case Is to use only triangles with three different angular frequencies., Another simplification we have made in the three-point case is to use only triangles with three different angular frequencies. + This reduces both the original and the nulled information contained in the three-point measures., This reduces both the original and the nulled information contained in the three-point measures. + However. this simplification can be easily removed with a careful distinetion of all cases.," However, this simplification can be easily removed with a careful distinction of all cases." +" Also notice that. the dependerce of number of possible bispectrum modes. Le. triangles. on the maximum angular frequency £i, is roughly {Sas While that of power spectrum modes is roughly (/,,.."," Also notice that, the dependence of number of possible bispectrum modes, i.e. triangles, on the maximum angular frequency $\ell_{\rm max}$ is roughly $\ell_{\rm max}^3$, while that of power spectrum modes is roughly $\ell_{\rm max}^1$." +" For this study Gna,=3000 is chosen.", For this study $\ell_{\rm max}=3000$ is chosen. + If reliable information on smaller angular scales can be obtained. the three-point statistics will possibly give us more information than the two-point statistics.," If reliable information on smaller angular scales can be obtained, the three-point statistics will possibly give us more information than the two-point statistics." + In this study we developed a method to control the intrinsic-shear alignmet in three-point cosmic shear statistics by generalizing the nulling technique., In this study we developed a method to control the intrinsic-shear alignment in three-point cosmic shear statistics by generalizing the nulling technique. + We showed that the generalization of the nulling technique to three-point statistics is quite natural. providing a model-independent method to reduce the intrinsic-shear alignment signals (GGI and GID) in comparison to the lensing GGG signal.," We showed that the generalization of the nulling technique to three-point statistics is quite natural, providing a model-independent method to reduce the intrinsic-shear alignment signals (GGI and GII) in comparison to the lensing GGG signal." + To test the performance of the nulling technique. we assumed a fictitious survey with a setup typical of future multicolor imaging surveys. and applied the nulling technique to the nodeled bispectra with intrinsic-shear alignment contamiation.," To test the performance of the nulling technique, we assumed a fictitious survey with a setup typical of future multicolor imaging surveys, and applied the nulling technique to the modeled bispectra with intrinsic-shear alignment contamination." + The lensing bispectra (GGG) was computed based ¢n perturbation theory. while the GGI signal was modeled by a simple power-law toy model.," The lensing bispectra (GGG) was computed based on perturbation theory, while the GGI signal was modeled by a simple power-law toy model." + We focused on the reduction of the GGI contaminant. since GH can be removed simply by not considering tomographic bispectra with two or three equal redshift bins.," We focused on the reduction of the GGI contaminant, since GII can be removed simply by not considering tomographic bispectra with two or three equal redshift bins." + The reduction. of the intrinsic-shear alignment contamination at the three-point level by the nulling technique was demonstrated both in terms of the GGI/GGG ratio. and in terms of biases on cosmological parameters in the context of an extended Fisher matrix study.," The reduction of the intrinsic-shear alignment contamination at the three-point level by the nulling technique was demonstrated both in terms of the GGI/GGG ratio, and in terms of biases on cosmological parameters in the context of an extended Fisher matrix study." + In terms of the GGI/GGG ratio. a factor of 10 suppression is achieved after nulling over all angular scales.," In terms of the GGI/GGG ratio, a factor of 10 suppression is achieved after nulling over all angular scales." + Correspondingly. the biases on cosmological parameters are reduced to be less than or comparable to the original statistical errors.," Correspondingly, the biases on cosmological parameters are reduced to be less than or comparable to the original statistical errors." + We studied the performance of the nulling technique when 5. 10. 15. or 20 redshift bins are available. and found that the performance on bias reduction. rather than how much information is preserved," We studied the performance of the nulling technique when 5, 10, 15, or 20 redshift bins are available, and found that the performance on bias reduction, rather than how much information is preserved" +et al.,et al. + 2001). the molecular gas masses derived from CO observations are within a [actor of three of that now expected.," 2001), the molecular gas masses derived from CO observations are within a factor of three of that now expected." + Lhe mass of molecular gas appears to correlate ost with the optical emission. line. luminosity indicating hat the molecular gas observed is warmed [rom a lower emperature., The mass of molecular gas appears to correlate best with the optical emission line luminosity indicating that the molecular gas observed is warmed from a lower temperature. + The rapid progress in this field has been xossible due to the selection of massive cooling lows from he ROSATLT All-Skv. Survey (see Crawford. et al., The rapid progress in this field has been possible due to the selection of massive cooling flows from the ROSAT All-Sky Survey (see Crawford et al. + 1999). ew of which were known before 1990.," 1999), few of which were known before 1990." +" Lo provide a direct comparison of the ‘hot’ (1000.2500 Ix) and ""cool. (30. Ix) molecular gas components requires near-infrared spectra of he svstems that have been searched for CO.", To provide a direct comparison of the `hot' (1000–2500 K) and `cool' (30 K) molecular gas components requires near-infrared spectra of the systems that have been searched for CO. + In this paper we present the spectra and analysis for a systematic search for near-infrared. hydrogen. molecular ines in à complete sample of strong optical emission line emitting central galaxies drawn [rom Crewford et al. (, In this paper we present the spectra and analysis for a systematic search for near-infrared hydrogen molecular lines in a complete sample of strong optical emission line emitting central galaxies drawn from Crawford et al. ( +1999).,1999). + An a Εαν limit of >3.10I erg 7s. | was adopted o ensure moderately bright lines and a redshift range of 1.03 to 0.3 to cover at least one Le? line in the IEx-band., An ${H\alpha}$ flux limit of $>3\times10^{-15}$ erg $^{-2}$ $^{-1}$ was adopted to ensure moderately bright lines and a redshift range of 0.03 to 0.3 to cover at least one 2 line in the K-band. + This selection produces a sample of LS objects reachable with UBIRD (one. 2146. is above the declination limit of 60°).," This selection produces a sample of 18 objects reachable with UKIRT (one, A2146, is above the declination limit of $^\circ$ )." + Of this sample. only one object. A478. has not been observed in this study but it has a published spectrum (Jalle. Bremer van def Werf 2001).," Of this sample, only one object, A478, has not been observed in this study but it has a published spectrum (Jaffe, Bremer van def Werf 2001)." + We also include seven weaker ine emitting or lower redshift objects from Crawford et al. , We also include seven weaker line emitting or lower redshift objects from Crawford et al. ( +999) to fully sample any potential range in recombination ines to molecular line ratios. seven non-BCS central cluster galaxies with strong optical emission lines drawn from the icerature (e.g. NGC 1275. A2597 and PIS 191). and one control object with no lines (A2029) eiving a total sample of 32 spectra.,"1999) to fully sample any potential range in recombination lines to molecular line ratios, seven non-BCS central cluster galaxies with strong optical emission lines drawn from the literature (e.g. NGC 1275, A2597 and PKS $-$ 191), and one control object with no lines (A2029) giving a total sample of 32 spectra." + We also extend our spectral coverage o Fell] in the majority of our targets making this the first comprehensive study of this line in central cluster ealaxies., We also extend our spectral coverage to [FeII] in the majority of our targets making this the first comprehensive study of this line in central cluster galaxies. + Throughout we assume QO=| and 5Okkmss + +., Throughout we assume $\Omega_0=1$ and $H_0 = 50$ $^{-1}$ $^{-1}$. + The observations presented in this paper were taken with the CGS4 spectrograph on the United. Ixingdonm: Infrared Telescope. CUIKIICE) in September 1999. and March 2000. as shown in the observing log in Table 1.," The observations presented in this paper were taken with the CGS4 spectrograph on the United Kingdom Infrared Telescope (UKIRT) in September 1999 and March 2000, as shown in the observing log in Table 1." + The 256 loSh array. 40 [fmm grating and 300 mm focal length camera were used giving a spatial scale of 0:01 aresec per pixel.," The $\times$ 256 InSb array, 40 l/mm grating and 300 mm focal length camera were used giving a spatial scale of 0.61 arcsec per pixel." + With a 2-pixel (1.227) wide slit this set-up achieves spectral resolutions of SSO and 570 km | PWLIAL in the LE and Ix-bands respectively., With a 2-pixel $''$ ) wide slit this set-up achieves spectral resolutions of 880 and 570 km $^{-1}$ FWHM in the H- and K-bands respectively. + In. all but two observations. the slit was oriented. at. a position angle. of O degrees (north-south).," In all but two observations, the slit was oriented at a position angle of 0 degrees (north-south)." + Phe NDSTADBRI mode was used along with the conventional object-sky-skv-object nodding pattern., The NDSTARE mode was used along with the conventional object-sky-sky-object nodding pattern. + Atmospheric absorption features were removed. by ratioing with main sequence E stars and the spectra were calibrated against photometric standards., Atmospheric absorption features were removed by ratioing with main sequence F stars and the spectra were calibrated against photometric standards. + We add in one short. archival observation (A262. a CO detection mace after our March 2000 run) which used the 75 L/mm grating with a I-pixel (0.617) slit ata position angle of 2.07.," We add in one short, archival observation (A262, a CO detection made after our March 2000 run) which used the 75 l/mm grating with a 1-pixel $''$ ) slit at a position angle of $^\circ$." + The spectra. were reduced: using version V1.3-0. of the Portable €C6GS4 Data Reduction package available through Starlink., The spectra were reduced using version V1.3-0 of the Portable CGS4 Data Reduction package available through Starlink. + The individual Ix- ancl H- band spectra are presented. in Figures | and 2 respectively in the order they appear in ‘Table 1., The individual K- and H- band spectra are presented in Figures 1 and 2 respectively in the order they appear in Table 1. + Phe line Huxes are summarised in Table 2 in RA orcler., The line fluxes are summarised in Table 2 in RA order. + Several of the observations show significant extent or velocity structure or were selected from the literature. so we discuss these individually here: Selected as X-ray Luminous radio galaxy by Perlman οἱ ((1998) but it is a central cluster galaxy.," Several of the observations show significant extent or velocity structure or were selected from the literature, so we discuss these individually here: Selected as X-ray luminous radio galaxy by Perlman et (1998) but it is a central cluster galaxy." + This galaxy was incluced in this study on the basis of a published spectrum and not on X-rav Dux. (which is below 10.7 ere em7 10. 24 keV)., This galaxy was included in this study on the basis of a published spectrum and not on X-ray flux (which is below $\times 10^{-12}$ erg $^{-2}$ $^{-1}$ 0.1–2.4 keV). + This svstem has1/57 narrow band imaging withΑΙΟΛΟΣ (Donahue et 22000) that shows extended: emission., This system has narrow band imaging with (Donahue et 2000) that shows extended emission. + Our COGS4 spectrum. does not sample the IZ-W. extension highlighted by Donahue et ((2000) but shows significant extent in both Pao and 1-0 S(1) and. 8(3) over 5 pixels (3.0) or 8 kpe to the North. consistent with the457 data.," Our CGS4 spectrum does not sample the E-W extension highlighted by Donahue et (2000) but shows significant extent in both $\alpha$ and 1-0 S(1) and S(3) over 5 pixels $''$ ) or 8 kpc to the North, consistent with the data." + See section 4.4 for further cliscussion., See section 4.4 for further discussion. + This svstem is highlv anomalous in virtually every waveband so far observed and the NER is no exception., This system is highly anomalous in virtually every waveband so far observed and the NIR is no exception. + A strong. velocitv-olfset CO detection is made in this eluster (Edge 2001) and the optical morphology of the central galaxy is very peculiar in a recent LIST snapshot with an infalling galaxy apparently. being disrupted (Baver-Ixim et 22002).," A strong, velocity-offset CO detection is made in this cluster (Edge 2001) and the optical morphology of the central galaxy is very peculiar in a recent HST snapshot with an infalling galaxy apparently being disrupted (Bayer-Kim et 2002)." + We mace an acditional. COS4 observation ocover the region of this infalling ealaxy but made no significant detection of any H» lines although Paa was extended over 4 pixels (2.47) or 6 kpe to the North., We made an additional CGS4 observation tocover the region of this infalling galaxy but made no significant detection of any $_2$ lines although $\alpha$ was extended over 4 pixels $''$ ) or 6 kpc to the North. + The ack of NUR LI» emission is surprising given the strength of 1e CO line., The lack of NIR $_2$ emission is surprising given the strength of the CO line. + This could be an indication that the mechanism xciting the molecular gas in RAJOS21|07 is different from ju behind the majority of the other detections presented ore., This could be an indication that the mechanism exciting the molecular gas in RXJ0821+07 is different from that behind the majority of the other detections presented here. + The central galaxy in this cluster contains à very μαrong [lat spectrum radio source so it is possible that the ul(3) line is blended with ΙΝΕ., The central galaxy in this cluster contains a very strong flat spectrum radio source so it is possible that the S(3) line is blended with [SiVI]. + At the resolution used in js work it is not possible to determine the contribution of cach line., At the resolution used in this work it is not possible to determine the contribution of each line. + This cluster was included in this study on the basis ofits known cooling Dow (lwasawa et al., This cluster was included in this study on the basis of its known cooling flow (Iwasawa et al. + 1999) and does not fall above the X-ray flux limit of the BCS and hence not in the Crawford ct al. (, 1999) and does not fall above the X-ray flux limit of the BCS and hence not in the Crawford et al. ( +1999) sample.,1999) sample. + This system is one of the strongest optical line emitters in the sample., This system is one of the strongest optical line emitters in the sample. + Both the Pao. ancl Ls lines are extended to the south by 4 pixels (2.47) or 8 kpe (see section 1.4)., Both the $\alpha$ and $_2$ lines are extended to the south by 4 pixels $''$ ) or 8 kpc (see section 4.4). + The Pao and LH» lines are also extended to the south by 5 pixels (3.07) in this system but show also a velocity shift of | 200300 km ., The $\alpha$ and $_2$ lines are also extended to the south by 5 pixels $''$ ) in this system but show also a velocity shift of $+$ 200–300 km $^{-1}$ . +" ""Phe Foll] for this source is particularly strong (see Section 4.2).", The [FeII] for this source is particularly strong (see Section 4.2). +contribute correspondingly little to the disk-intcerated properties of the planet.,contribute correspondingly little to the disk-integrated properties of the planet. + The are larder to obtai- requiring shorter integration times aud therefore a larger telescope. all other things beiug equal.," The are harder to obtain, requiring shorter integration times and therefore a larger telescope, all other things being equal." + Ou the other hand. variability measurements are more robust to contanination from exo-zodiacal light.," On the other hand, variability measurements are more robust to contamination from exo-zodiacal light." + We lave shown that modern Earth regardless of viewing angle exhibits photometric variability at all waveleneths (RAIS variability within a factor of 2 for all wavebauds). while Snowball Earth varies 7 times more at short wavelengths than at lone wavelengths.," We have shown that modern Earth —regardless of viewing angle— exhibits photometric variability at all wavelengths (RMS variability within a factor of 2 for all wavebands), while Snowball Earth varies 7 times more at short wavelengths than at long wavelengths." + A more subtle analysis of the time variability may even allow us to distinguish between the equatorial aud polar viewing ecouetrics of Earth. because clouds play a larger role at micd-latitudes.," A more subtle analysis of the time variability may even allow us to distinguish between the equatorial and polar viewing geometries of Earth, because clouds play a larger role at mid-latitudes." + Frou an equatorial vantage point. the cominaut cigencolor is red. followed by blue: for the polar geometrics. the ordering of the red aud blue eigencolors is flipped. or there is a single dominant ervey cigencolor.," From an equatorial vantage point, the dominant eigencolor is red, followed by blue; for the polar geometries, the ordering of the red and blue eigencolors is flipped, or there is a single dominant grey eigencolor." + If the planets radius can be estimated. then its albedo can be put on an absolute scale aud one cau estimate it» Bond albedo.," If the planet's radius can be estimated, then its albedo can be put on an absolute scale and one can estimate its Bond albedo." + Transiting planets lave ταν well characterized radii. but nearby earth analogs will almost certainly be transiting.," Transiting planets have very well characterized radii, but nearby earth analogs will almost certainly be transiting." + Tustead. a radius estimate will require an additional large space iission: cither an infrared high-coutrast miagiue telescope. or a space based astrometry mnüssou.," Instead, a radius estimate will require an additional large space mission: either an infrared high-contrast imaging telescope, or a space based astrometry mission." + Iu the first case. thermal aud reflected photometry can be combined to estimate the planct’s radius.," In the first case, thermal and reflected photometry can be combined to estimate the planet's radius." + If thermal photometry is obtained at a varicty of pliases. then the efficiency of heat transport to the planets niglit-side may be estimated (Cowan&Ago 2011b).. and the svstematic mucertainty will be ~2% due to the unkown efficiency of latitudinal heat transport (Cowan&Ασοι2011a).," If thermal photometry is obtained at a variety of phases, then the efficiency of heat transport to the planet's night-side may be estimated \citep{Cowan_2011b}, and the systematic uncertainty will be $\sim2$ due to the unkown efficiency of latitudinal heat transport \citep{Cowan_2011}." +. The mncertainty in the radius will therefore likely be dominated bv the known uncertainties in thermal aud reflected photometry., The uncertainty in the radius will therefore likely be dominated by the —known— uncertainties in thermal and reflected photometry. + Tn the secoud case. the stars astrometric wobble orovides a niass 1ieasureiment for the planct: by assumine a plauetary density. oue can estimate the plauet's radius.," In the second case, the star's astrometric wobble provides a mass measurement for the planet; by assuming a planetary density, one can estimate the planet's radius." + The dominant source of uncertainty here is the plauct’s coluposition: eivoen a nis. a planets radius may vary w (ce.Charbouneanetal.2009:Datalha2011).. leading to absolute albedo estimates onlv valid o within a factor of 2.," The dominant source of uncertainty here is the planet's composition: given a mass, a planet's radius may vary by \citep[eg,][]{Charbonneau_2009, Batalha_2011}, leading to absolute albedo estimates only valid to within a factor of 2." + Trausitius planet survevs will ikelv reduce these svstematic uucertaiuties by providing an enipirdical mass-racdius relation for planets across a wide range of masses., Transiting planet surveys will likely reduce these systematic uncertainties by providing an empirical mass-radius relation for planets across a wide range of masses. + It is not clear to what extent he nüssou (eg.Doruckietal.2011) will iclp define the mass-radius relation: although the vast uajoritv of caudidates are likely to be auets (Morton&Joluson2011).. most will not have nass estimates.," It is not clear to what extent the mission \citep[eg,][]{Borucki_2011} will help define the mass-radius relation: although the vast majority of candidates are likely to be planets \citep{Morton_2011}, most will not have mass estimates." + The smaller. and better characterized. radius uncertainty would therefore most Likely come from colmbining optical aud infrared photometry. rather thu YOU à luass nieasurenment.," The smaller, and better characterized, radius uncertainty would therefore most likely come from combining optical and infrared photometry, rather than from a mass measurement." + The would allow us to better distinguish )etween the equatorial (Ap~0.3) and polar (lp~1) EPOXI observations. or between a snowball plauet (Ap~ 0.7) and a temperate one.," The would allow us to better distinguish between the equatorial $A_{B}\approx 0.3$ ) and polar $A_{B}\approx 0.4$ ) EPOXI observations, or between a snowball planet $A_{B}\approx 0.7$ ) and a temperate one." + Iu ecueral. tliis quautity would be very useful iu determining a plauet'* energv »aidget aud would go a long way towards coustrainiug its rabitability.," In general, this quantity would be very useful in determining a planet's energy budget and would go a long way towards constraining its habitability." + This work was supported bv the NASA Discovery Program., This work was supported by the NASA Discovery Program. + We thauk D.S. Abbot aud R.T. Pierrelinnibert or providing us with cloud maps of snowball Earth., We thank D.S. Abbot and R.T. Pierrehumbert for providing us with cloud maps of snowball Earth. + aacknowledges iuauv useful discussions witli S.C. Warren about snowball Earth. and thauks W. Sullivan for encouraging him to complete his astrobiology research rotation.," acknowledges many useful discussions with S.G. Warren about snowball Earth, and thanks W. Sullivan for encouraging him to complete his astrobiology research rotation." + iis supported bv a National Scicuce Foundation Career Grant., is supported by a National Science Foundation Career Grant. +Almost without exception. models of geometrically thin accretion disks that are used to predict radiation spectra in order to compare with observation are based on the alpha prescription introduced by Shakura&Sunvaev(1973).,"Almost without exception, models of geometrically thin accretion disks that are used to predict radiation spectra in order to compare with observation are based on the alpha prescription introduced by \citet{sha73}." +. This prescription enables one to compute the radial distribution of surface deisjtv in the disk., This prescription enables one to compute the radial distribution of surface density in the disk. + When this is combined with additional assumptions about the vertical distribution of dissipation. complete models of the vertical structure at each radius and the loca radiation spectrum can be computed.," When this is combined with additional assumptions about the vertical distribution of dissipation, complete models of the vertical structure at each radius and the local radiation spectrum can be computed." + In black hole accretion disks. for example. (he most detailed of such models so far are those of IIubenyetal.(2001) for superniassive black holes. Davisοἱal.(2005).5n) for stellar mass black holes. and Hui.Ixrolik.&IIubenv(2005)- for intermediate mass black holes.," In black hole accretion disks, for example, the most detailed of such models so far are those of \citet{hub01} for supermassive black holes, \citet{dav05} + for stellar mass black holes, and \cite{hui05} for intermediate mass black holes." + The models fully account [or relativistic effects. and include a detailed non-LTE treatment of level populations of hydrogen. helium. and abundant metals.," The models fully account for relativistic effects, and include a detailed non-LTE treatment of level populations of hydrogen, helium, and abundant metals." + Continuum opacities due to bound-free and. [ree-Iree. (ransilions. as well as Comptonization. are included.," Continuum opacities due to bound-free and free-free transitions, as well as Comptonization, are included." + In spite of this level of sophistication. the models are limited by other assumptions: the disk is assumed to be stationary. (he alpha-prescription is used (o calulate the radial distribution of surface densitv. a no-torque inner boundary. condition is assumed. (he vertical structure al each radius is assumed to depend only on height ancl is symmetric about the midplane. the vertical distribution of dissipation per unit mass is assunied to be constant. ancl (he disk is assumed to be supported vertically against the tidal field of the black hole by just eas ancl raciation pressure.," In spite of this level of sophistication, the models are limited by other assumptions: the disk is assumed to be stationary, the alpha-prescription is used to calulate the radial distribution of surface density, a no-torque inner boundary condition is assumed, the vertical structure at each radius is assumed to depend only on height and is symmetric about the midplane, the vertical distribution of dissipation per unit mass is assumed to be constant, and the disk is assumed to be supported vertically against the tidal field of the black hole by just gas and radiation pressure." + It is now widelv believed that the anomalous stress in accretion disks is a result of sustained magnetolivdrodvnamical turbulence which is akin to that seen in the nonlinear development of (he magnetorotational instability. or MRI (Balbus&Tawlev1998).," It is now widely believed that the anomalous stress in accretion disks is a result of sustained magnetohydrodynamical turbulence which is akin to that seen in the nonlinear development of the magnetorotational instability, or MRI \citep{bal98}." +. In principle. shearing box simulations ol this turbulence which incorporate (he vertical tidal field of the central mass (Brandlenburgetal.1995:Stone1996:Miller&2000) can be used to build models of tje vertical structure of accretion disks that are free of the ad hoc assumptions that plague existing models.," In principle, shearing box simulations of this turbulence which incorporate the vertical tidal field of the central mass \citep{bra95, sto96, mil00} can be used to build models of the vertical structure of accretion disks that are free of the ad hoc assumptions that plague existing models." + The most recent of these simulations (TurnerIxrolik.&Stone2005). are particularly useful lor (his purpose as they evolve (he equations of radiation magnetohvdrodyvnanmices ancl have sell-consistent thermocdwvnanmics.," The most recent of these simulations \citep{tur04,hir05} are particularly useful for this purpose as they evolve the equations of radiation magnetohydrodynamics and have self-consistent thermodynamics." + While much of the dissipation of (he turbulence in (hese simulations is numerical and happens on the grid scale. one hopes that this still mocks up the microscopic dissipation occuring al (the smallest scales of the turbulent. cascade. and in any case provides a better handle," While much of the dissipation of the turbulence in these simulations is numerical and happens on the grid scale, one hopes that this still mocks up the microscopic dissipation occuring at the smallest scales of the turbulent cascade, and in any case provides a better handle" +regions is 2025 Ix. significantly brighter than typical ecemission features.,"regions is 20–25 K, significantly brighter than typical emission features." + A field containing wavas observed by A.J. Walker on LOOT Apr 30. as part of a wide-ield Lla survey of the Southern Galactic Plane being carried out at Siding Spring Observatory (2)..," A field containing was observed by A.J. Walker on 1997 Apr 30, as part of a wide-field $\alpha$ survey of the Southern Galactic Plane being carried out at Siding Spring Observatory \cite{bbw98}." + Three 10 min exposures were mace with a 400 mm. f/4.5 Nikkor-Q lens. through a filter centred at 657.0 nm with a width of 1.5 nm.," Three 10 min exposures were made with a 400 mm, f/4.5 Nikkor-Q lens, through a filter centred at 657.0 nm with a width of 1.5 nm." + The detector was a 2048 CCD with a resolution of ., The detector was a $\times$ 2048 CCD with a resolution of $^{-1}$. + The images were bias and dark subtracted. Hat-Hielded and then combined with a median filter.," The images were bias and dark subtracted, flat-fielded and then combined with a median filter." + final image. without continuum subtraction. is shown in Fig (a)," A final image, without continuum subtraction, is shown in Fig 7(a)." + ROW SO is clearly delineated in Ho. having a similar are-like appearance to its radio morphology.," RCW 80 is clearly delineated in $\alpha$, having a similar arc-like appearance to its radio morphology." + As in the radio. LID 119796 is visible at the centre of this region.," As in the radio, HD 119796 is visible at the centre of this region." + No Ila emission from the SNR or from the column to its north is apparent., No $\alpha$ emission from the SNR or from the column to its north is apparent. +" The open cluster NGC 5281 is visible in the remnants interior. at RA (J2000) 1346""30. Dee (12000) 62°55."," The open cluster NGC 5281 is visible in the remnant's interior, at RA (J2000) $13^{\rm h}46^{\rm +m}30^{\rm s}$, Dec (J2000) $-62\degr55\arcmin$." + [ts distance has been estimated to be 1.3 kpe (7).., Its distance has been estimated to be 1.3 kpc \cite{mv73}. + wwas observed by the PPosition Sensitive Proportional Counter (PSPC) in 1992 Aug for 3931 sec: the data are now available from the ppublic archive., was observed by the Position Sensitive Proportional Counter (PSPC) in 1992 Aug for 3931 sec; the data are now available from the public archive. + In the energy range 0.1.0.4 keV. only a slight enhancement above the background is seen towards the SNR.," In the energy range 0.1–0.4 keV, only a slight enhancement above the background is seen towards the SNR." + However in Fig T(b) is shown emission in the range OA24 keV. where the compact X-ray source. IWOA J1346.56255. (White. Clommi& Angelini 19942.b)) can be seen near the remnants centre. and weak cilluse emission can be associated with the rest of the SNR.," However in Fig 7(b) is shown emission in the range 0.4–2.4 keV, where the compact X-ray source 1WGA J1346.5–6255 (White, Giommi Angelini \nocite{wga94a,wga94b}) ) can be seen near the remnant's centre, and weak diffuse emission can be associated with the rest of the SNR." + No significant emission can be seen along the column or from RCW 50., No significant emission can be seen along the column or from RCW 80. + AnHUS 60 fam image of the region. processed. with the LURES algorithm: (?2).. is shown in Fie Tle).," An 60 $\mu$ m image of the region, processed with the HIRES algorithm \cite{afm90}, is shown in Fig 7(c)." + Strong. Lk emission is coincident. with ROW SO and with LID 119796 (= IRAS 134366220). but. no obvious emission can be associated with the SNR. or with the column to its north.," Strong IR emission is coincident with RCW 80 and with HD 119796 $=$ IRAS 13436–6220), but no obvious emission can be associated with the SNR or with the column to its north." + The point source on the north-western edge of the SNR is IRAS 134286232., The point source on the north-western edge of the SNR is IRAS 13428–6232. +upper level of constraints from cluster observations aud weak leusine (for a recent compilation of experiucutal results see table 5 of Teeiarketal.2001)).,upper level of constraints from cluster observations and weak lensing (for a recent compilation of experimental results see table 5 of \citealt{Tegmark:2003ud}) ). + Future large aneular scale SZ surveys such as SPT promise to measure the cluster abundance as a function of mass and redshift. which will offer the possibility of constraining the matter density aud the equation of state of the dark cucrey.," Future large angular scale SZ surveys such as SPT promise to measure the cluster abundance as a function of mass and redshift, which will offer the possibility of constraining the matter density and the equation of state of the dark energy." +" Finally, related effects are produced by the scattering of CAIB photons off electrous moving as a result of the structure formation process."," Finally, related effects are produced by the scattering of CMB photons off electrons moving as a result of the structure formation process." + This process. also known as the kinetic Suuvaev-Zeldovich effect when applied. to clusters of galaxies (Sunvaev&Zoldovich 1980).. leads to hot or cold spots. depending on whether the ionized barvous move toward or away from the observer.," This process, also known as the kinetic Sunyaev-Zel'dovich effect when applied to clusters of galaxies \citep{Sunyaev:1980nv}, leads to hot or cold spots, depending on whether the ionized baryons move toward or away from the observer." + The frequency dependence of the plotons is left nuchaneed. except for tiny relativistic corrections.," The frequency dependence of the photons is left unchanged, except for tiny relativistic corrections." + These “Doppler” induced anisotropics are the only known wav to measure the Ligh redshift large scale velocity field.," These “Doppler"" induced anisotropies are the only known way to measure the high redshift large scale velocity field." + Although our simulations account for each of these effects. our focus in this paper will be ou the part of the Doppler effect generated during the epoch of relonization.," Although our simulations account for each of these effects, our focus in this paper will be on the part of the Doppler effect generated during the epoch of reionization." + This epoch is currently not well uuderstood observatioually., This epoch is currently not well understood observationally. +" The first vear release of the WALIAP data hinted at a laree optical depth owing to reiouization. r,;=0.17£0.05 (Sperecletal.2003).. through measurement of the ""reiouization bump (Zaldariaga1997)— in the temperature polarization cross correlation (lIxXogutetal 20035."," The first year release of the WMAP data hinted at a large optical depth owing to reionization, $\tau_{ri} =0.17 \pm 0.05$ \citep{Spergel:2003cb}, through measurement of the “reionization bump” \citep{Zaldarriaga:1996ke} in the temperature polarization cross correlation \citep{Kogut:2003et}." +" WALAP places only a weak constraint ou the relative height of the acoustic oscillation peaks. so these data alone are not sufücieut for constraining Tj. because it is stronely degenerate with the tilt of scalar fluctuations ος and the Darvon density paraleter aw,=Q,0°."," WMAP places only a weak constraint on the relative height of the acoustic oscillation peaks, so these data alone are not sufficient for constraining $\tau_{ri}$, because it is strongly degenerate with the tilt of scalar fluctuations $n_s$ and the baryon density parameter $\omega_b=\Omega_b +h^2$." + Ta combination with smaller scale CMD measurements. the data can be described by homogencous rejonization of the universe taking place at redshift 72LL43. or a Thomson scattering optical depth τιz0.13£0.02 (see ce. Reacdheadetal.2001:Boundetal. 2003)).," In combination with smaller scale CMB measurements, the data can be described by homogeneous reionization of the universe taking place at redshift $z \simeq 14 \pm 3$, or a Thomson scattering optical depth $\tau_{ri} \simeq 0.13 \pm 0.02$ (see e.g. \citealt{Readhead:2004gy,Bond:2003ur}) )." +" This estimate is also robust to the addition of other datasets to the analysis. such as the SDSS ealaxy clustering survev (Teemarketal.2001) (Ti=0.121 0022) or the Lyman alpha forest (Seljaletal2001) (7,=0.133 H2),"," This estimate is also robust to the addition of other datasets to the analysis, such as the SDSS galaxy clustering survey \citep{Tegmark:2003ud} $\tau_{ri} =0.124_{-0.057}^{+0.083}$ ) or the Lyman alpha forest \citep{Seljak:2004xh} $\tau_{ri} = +0.133_{-0.045}^{+0.052}$ )." + Since the laree scale polarization measurements are sensitive ouly to the line-of-sight integrated free electrou density. they do me require the time evolution of the ionized fraction to be a simple step function.," Since the large scale polarization measurements are sensitive only to the line-of-sight integrated free electron density, they do not require the time evolution of the ionized fraction to be a simple step function." + Observations of the evolution of the Lya optical depth in the absorption spectra of the highest redshift quasars at +6 when combined with the CMD coustraiuts favor a 1nore coniplicated ionization history.," Observations of the evolution of the $\alpha$ optical depth in the absorption spectra of the highest redshift quasars at $z +\simeq 6$ when combined with the CMB constraints favor a more complicated ionization history." + The observations show a distinct Comn-Petersou trough (Cama&Peterson1965) and poiut to a rapidly evolviug neutral fraction indicative of the final stages of reionization (Beckeretal. 01)...," The observations show a distinct Gunn-Peterson trough \citep{Gunn:1965hd} and point to a rapidly evolving neutral fraction indicative of the final stages of reionization \citep{Becker:2001ee,Fan:2001ff,White:2003sc,Fan:2004bn}." + Recently. there has also been an interpretation of the relatively high. temperature of the Lya forest at οτι Las evidence of au order unity change iu the ionized fraction at +10 (Theunsetal.2002:Thi&Uaiman 2003).. although this depends ou the properties 6 We II reionization (Sokasianetal.2002)..," Recently, there has also been an interpretation of the relatively high temperature of the $\alpha$ forest at $z\simeq 2-4$ as evidence of an order unity change in the ionized fraction at $z<10$ \citep{Theuns:2002yc,Hui:2003hn}, although this depends on the properties of He II reionization \citep{Sokasian:2002jw}." + Numerical sinulatious of the star formation epoch have shown that a first eeneration of low ποτάΠοτν (Population III) sources can survive negative feedback roni the UV background they produce if shielded iu nassive halos for some time (Schaerer2003:Brounetal.2002)..," Numerical simulations of the star formation epoch have shown that a first generation of low metallicity (Population III) sources can survive negative feedback from the UV background they produce if shielded in massive halos for some time \citep{Schaerer:2002yr,Bromm:2001ag}." + I£ they are heavy. these stars could produce au order of magnitude more louizinge photons per barvous han “normal” stars.," If they are heavy, these stars could produce an order of magnitude more ionizing photons per baryons than “normal” stars." + Besides a more complex temporal vchavior. the ionization fraction could have spatial variations: it could be “patchy” for a period of time while relonization is not complete.," Besides a more complex temporal behavior, the ionization fraction could have spatial variations; it could be “patchy"" for a period of time while reionization is not complete." + Naturally. we would like to ave an observable that sheds light on the duration aud structure of the reionization epoc[u," Naturally, we would like to have an observable that sheds light on the duration and structure of the reionization epoch." +m The shape of the large scale polarization signal iu he CMB could be used to constrain the evolution of the ionization fraction. without resorting to information from secondary anisotropies (Zalcdarriaga1997:Πα&older2003)..," The shape of the large scale polarization signal in the CMB could be used to constrain the evolution of the ionization fraction, without resorting to information from secondary anisotropies \citep{Zaldarriaga:1996ke,Hu:2003gh}." + Tlowever. these scales are affected by sample variance limitations. so the available information is rather limited.," However, these scales are affected by sample variance limitations, so the available information is rather limited." + Moreover. before such au approach can be successful. issues of foreground removal necd to be clarified (Bennettetal.2003:deOliveira-Costaetal.200L)..," Moreover, before such an approach can be successful, issues of foreground removal need to be clarified \citep{Bennett:2003ca,deOliveira-Costa:2003pu}." + Tn any event. large scale polarization lmucasturements will not vield information about the morphology of reionization. as this is confined to sub-degree scales.," In any event, large scale polarization measurements will not yield information about the morphology of reionization, as this is confined to sub-degree scales." + Several analytical iiodoels for pateliv reionization have been presented in the literature., Several analytical models for patchy reionization have been presented in the literature. + They vary siguificautlv in the assumed size aud time evolution of splerically shaped bubbles. aud whether the ionized regious are correlated (I&noxotal.1998:Sautoset2003). or not (τὰnov&Iu1998)..," They vary significantly in the assumed size and time evolution of spherically shaped bubbles, and whether the ionized regions are correlated \citep{Knox:1998fp,Santos:2003jb} or not \citep{Gruzinov:1998un}." + Some models emiplov a prescriptio1 for correlaing the ionizing sotrees by sine the bias that can be caculated for the dark matter halos in which they prestunably reside (Sautosetal.2003).., Some models employ a prescription for correlating the ionizing sources by using the bias that can be calculated for the dark matter halos in which they presumably reside \citep{Santos:2003jb}. + All authors agree that on scales below I. where the primordial CAIB signal falls rapidly owing to photon diffusion. the Doppler effect induced by patchiness could contribute chough to use it as a tool to study the relonization epoch.," All authors agree that on scales below $4'$, where the primordial CMB signal falls rapidly owing to photon diffusion, the Doppler effect induced by patchiness could contribute enough to use it as a tool to study the reionization epoch." + Modeling patchy reionization more accurately requires he use of nunerical simulations to incorporate effects of non-linear clustering and radiative trausfer., Modeling patchy reionization more accurately requires the use of numerical simulations to incorporate effects of non-linear clustering and radiative transfer. + The norpholoey of the ionized regions depends scusitively ou the star formation model (sec e.g. the reionization study companion by Barkana&Loch 2001)). source xoperties. feedback processes. aud radiative trauster (these effects lave for exiuuple. been modeled in Àbel2003:Sokasiauetal.2003. 2001).," The morphology of the ionized regions depends sensitively on the star formation model (see e.g. the reionization study companion by \citealt{Barkana:2000fd}) ), source properties, feedback processes, and radiative transfer (these effects have for example been modeled in \citealt{Abel:2001qs,Gnedin:2000gr,Ciardi:2003ia,Sokasian:2003au, +Sokasian:2004au}) )." + These simulations lve even us evidence that reionization was ich ess homogeneous than previously thought (Miralda-Escudéetal.1998:Barkana&Loch 2001)..," These simulations have given us evidence that reionization was much less homogeneous than previously thought \citep{Miralda-Escude:1998qs,Barkana:2000fd}." + Reionization ends to proceed from high to low density regious (Sokasianetal.2003.2001:πανί2003) and reconibinations seem to play a role subdominant to aree scale bias.," Reionization tends to proceed from high to low density regions \citep{Sokasian:2003au,Sokasian:2004au,Ciardi:2003ia} and recombinations seem to play a role subdominant to large scale bias." + Strónuusren spheres of uciglibormg xotogalaxies overlap. auc overdeusities will harbor large ionized regions.," Strömmgren spheres of neighboring protogalaxies overlap, and overdensities will harbor large ionized regions." + Because III regions extend to larger radi than the correlation leugth of galaxies. building au analytic model solely ou local galaxy properties appears to be difficult.," Because HII regions extend to larger radii than the correlation length of galaxies, building an analytic model solely on local galaxy properties appears to be difficult." + Besides uucertainties over the physics in current radiative transfer calculations of reionization. memory and CPU requirements pose a serious limitation. so that these simulations have so far only been performed as a post-processing step on scales of up to LO Mpc/h.," Besides uncertainties over the physics in current radiative transfer calculations of reionization, memory and CPU requirements pose a serious limitation, so that these simulations have so far only been performed as a post-processing step on scales of up to 10 Mpc/h," +describe our initial conditions: we present our results and discussion in Sections 3.. 4 and 5.. and we conclude in Section 6..,"describe our initial conditions; we present our results and discussion in Sections \ref{results}, , \ref{ONCoriginal} and \ref{discussion}, and we conclude in Section \ref{conclude}." + The simulated star clusters have masses 107 10* MM. and a range of half-mass radii of 0.1. 0.2. 0.4 ancl ppc.," The simulated star clusters have masses $\sim 10^2$ – $10^3$ $_\odot$ and a range of half-mass radii of 0.1, 0.2, 0.4 and pc." + This means we can simulate clusters with a range of densities [rom 50MM. pe* to ~107 MM. ' covering almost the complete range of probable initial cluster densities., This means we can simulate clusters with a range of densities from $\sim 50$ $_\odot$ $^{-3}$ to $\sim 10^5$ $_\odot$ $^{-3}$ covering almost the complete range of probable initial cluster densities. + We summarise the properties of the clusters that we simulate in ‘Table 1.., We summarise the properties of the clusters that we simulate in Table \ref{table}. . + For each set of initial conditions we run an ensemble of at least LO simulations which are identical apart from the random number seed used to initialise the positions. masses and binary properties.," For each set of initial conditions we run an ensemble of at least $10$ simulations which are identical apart from the random number seed used to initialise the positions, masses and binary properties." + Our clusters are set-up as initially virialised Plummer spheres. (7) according to the prescription of ?.., Our clusters are set-up as initially virialised Plummer spheres \citep{Plummer11} according to the prescription of \citet*{Aarseth74}. + The Plummer sphere provides the positions ancl velocities of the centres of mass of systems which may be single or binary πμο..., The Plummer sphere provides the positions and velocities of the centres of mass of systems – which may be single or binary systems. +" To create a stellar system. the mass of the primary star is chosen randomly from a? ME of the form where my = O.1MM.. my, = 0.5MM.. and m» = SOAMAL.."," To create a stellar system, the mass of the primary star is chosen randomly from a \citet{Kroupa02} IMF of the form where $m_0$ = $_\odot$, $m_1$ = $_\odot$, and $m_2$ = $_\odot$." + For simplicity we do not include brown cdwarfs (BDs) in our simulations., For simplicity we do not include brown dwarfs (BDs) in our simulations. + Ehe cllect of dvnamical processing on BDs in clusters will be studied in a future paper (for the results of recent observations of BDs in Orion see ?:: and for existing theoretical work see ? and 7))., The effect of dynamical processing on BDs in clusters will be studied in a future paper (for the results of recent observations of BDs in Orion see \citealt{Maxted08}; and for existing theoretical work see \citealt{Kroupa03} and \citealt{Thies08}) ). + We then assign à secondary to the system depending on the binary. fraction associated with the primary mass., We then assign a secondary to the system depending on the binary fraction associated with the primary mass. + For a field-like binary fraction we divide primaries into four groups., For a field-like binary fraction we divide primaries into four groups. + Primary masses in the range 0.08 0.47 are Al-clwarls. with a binary fraction of 0.42 (0)2)...," Primary masses in the range 0.08 $\leq M/{\rm M}_\odot~<$ 0.47 are M-dwarfs, with a binary fraction of 0.42 \citep{Fischer92}." + IX-dwarfs have masses in the range O47 xΑΝ. < 0SE and binary fraction of 0.45 (7) and €i-chvarls have masses [rom 0.84 x:AL/AL.« L2 with a binary fraction of 0.57 (72)..," K-dwarfs have masses in the range 0.47 $\leq~M/{\rm M}_\odot$ $<$ 0.84 and binary fraction of 0.45 \citep{Mayor92} and G-dwarfs have masses from 0.84 $\leq~M/{\rm +M}_\odot~<$ 1.2 with a binary fraction of 0.57 \citep{Duquennoy91}." + All stars more massive than MM. are grouped together and assigned a binary fraction of unity. as massive stars have a much larger binary [raction than low-mass stars (e.g.?77.andreferencestherein)..," All stars more massive than $_\odot$ are grouped together and assigned a binary fraction of unity, as massive stars have a much larger binary fraction than low-mass stars \citep[e.g.][and references +therein]{Abt90,Mason98,Kouwenhoven05,Kouwenhoven07,Pfalzner07}." + Clusters with an initial binary fraction of unity foraff stars are also created in order to test the hypothesis that all stars form in binary svstems and that single stars are solely the result of the dynamical processing of binarics (2???)," Clusters with an initial binary fraction of unity for stars are also created in order to test the hypothesis that all stars form in binary systems and that single stars are solely the result of the dynamical processing of binaries \citep{Kroupa95a,Kroupa95b,Goodwin05}." +" Secondary masses are drawn from a [Lat mass ratio distribution with the constraint that if the companion mass is 0.004., This happens approximately for $t>0.004$. + We also confirm from this analysis that the time accuracy parameter η needs to be chosen small enough in order to get the best convergence with the feedback methods., We also confirm from this analysis that the time accuracy parameter $\eta$ needs to be chosen small enough in order to get the best convergence with the feedback methods. +" Finally, regarding the spatial energy distribution, it is clear that concentrating the injection over a smaller number of particles gives a higher energy jump (meaning a larger time-level drop), and hence produces a slightly worse energy conservation."," Finally, regarding the spatial energy distribution, it is clear that concentrating the injection over a smaller number of particles gives a higher energy jump (meaning a larger time-level drop), and hence produces a slightly worse energy conservation." +" We conclude that, when applying the proposed integration scheme, there are no dramatic differences either in concordance, or in energy conservation accuracy, or in performances for the set of parameters we explored."," We conclude that, when applying the proposed integration scheme, there are no dramatic differences either in concordance, or in energy conservation accuracy, or in performances for the set of parameters we explored." + In this section we simulate an explosion event in a self-gravitating gas halo., In this section we simulate an explosion event in a self-gravitating gas halo. + The initial conditions are similar to the ones in 9Μ09., The initial conditions are similar to the ones in SM09. +" However, the injected energy is placed off-centre to follow the blast evolution in the presence of pressure and density gradients."," However, the injected energy is placed off-centre to follow the blast evolution in the presence of pressure and density gradients." +" In cosmological simulations of structure formation, the sources of mechanical and thermal feedback (SNe and BHs) are generally situated in a similar environment."," In cosmological simulations of structure formation, the sources of mechanical and thermal feedback (SNe and BHs) are generally situated in a similar environment." +" Though idealised, the setup gives a qualitative and quantitative view of the above scenario."," Though idealised, the setup gives a qualitative and quantitative view of the above scenario." +" We create a spherical particle distribution of density profile pxr? by spatially remapping a uniform, spherical distribution of particles through the radial transformation where R=1 in the same system of units used for Sedov’s blast wave problem."," We create a spherical particle distribution of density profile $\rho\propto r^{-2}$ by spatially remapping a uniform, spherical distribution of particles through the radial transformation where $R=1$ in the same system of units used for Sedov's blast wave problem." + The sphere is cut out from a uniform distribution of N=128° particles in a cubic volume of side L=2., The sphere is cut out from a uniform distribution of $N=128^3$ particles in a cubic volume of side $L=2$. + The total mass of the gas sphere is unity., The total mass of the gas sphere is unity. + We assign an internal energy of 0.05., We assign an internal energy of 0.05. + The system is evolved including self-gravity up to time t=3 when relaxation has already taken place (Evrard 1988).., The system is evolved including self-gravity up to time $t=3$ when relaxation has already taken place \citep{Evrard1988}. . + We chose, We chose +"into account the cases in which corotation is inside the zone being investigated; a minimum of star formation is expected at 2=Q,.",into account the cases in which corotation is inside the zone being investigated; a minimum of star formation is expected at $\Omega=\Omega_p$. + An interesting case is the Milky Way., An interesting case is the Milky Way. + A simple model of chemical enrichment was proposed by Mishurov et al. (, A simple model of chemical enrichment was proposed by Mishurov et al. ( +"2002) for our Galaxy, in which the star formation rate is proportional to €)—Q,.","2002) for our Galaxy, in which the star formation rate is proportional to $\Omega-\Omega_p$." +" These authors argue that the minimum (or the plateau) in the gradient of metallicity of our Galaxy, observed using different tracers (eg."," These authors argue that the minimum (or the plateau) in the gradient of metallicity of our Galaxy, observed using different tracers (eg." +" Maciel Quireza 1999, using planetary nebulae and Andrievsky et al."," Maciel Quireza 1999, using planetary nebulae and Andrievsky et al." + 2004 using Cepheids) is coincident with the corotation radius., 2004 using Cepheids) is coincident with the corotation radius. +" The above interpretation for the existence of minima or plateaus in the metallicity gradients is not easy to verify in other galaxies, however, a correlation between radii of minima and/or inflexions in the metallicity distribution and the corotation radius was found by (?) using published data."," The above interpretation for the existence of minima or plateaus in the metallicity gradients is not easy to verify in other galaxies, however, a correlation between radii of minima and/or inflexions in the metallicity distribution and the corotation radius was found by \citep{Sca2010} using published data." + One of the difficulties to identify the corotation is that this resonance is not necessarily situated in the optical disk., One of the difficulties to identify the corotation is that this resonance is not necessarily situated in the optical disk. +" Nevertheless, ?) proposed a test to identify galaxies for which the corotation is favorably placed in the optical disk."," Nevertheless, \cite{Canzian98} proposed a test to identify galaxies for which the corotation is favorably placed in the optical disk." + This test only requires moderately deep imaging and no spectroscopic observations are needed., This test only requires moderately deep imaging and no spectroscopic observations are needed. +" In this paper we present the study of the radial gradients of metallicity in three of the best candidates identified by the Cazian’s test (IC0167, NGC1042 and NGC6907) to verify if the connection between metallicity breaks and corotation holds for these galaxies."," In this paper we present the study of the radial gradients of metallicity in three of the best candidates identified by the Cazian's test (IC0167, NGC1042 and NGC6907) to verify if the connection between metallicity breaks and corotation holds for these galaxies." +" The observations were performed using the Gemini Multi-Object Spectrograph (GMOS), pointed towards 232 regions distributed in these galaxies."," The observations were performed using the Gemini Multi-Object Spectrograph (GMOS), pointed towards 232 regions distributed in these galaxies." + Different statistical methods were employed to getO abundances from the observed emission lines., Different statistical methods were employed to get abundances from the observed emission lines. + The sample of galaxies and regions are presented in the section 2 of this paper., The sample of galaxies and regions are presented in the section 2 of this paper. + Observations and data reduction are described in section 3., Observations and data reduction are described in section 3. + The photometric and spectroscopic results are presented in section 4., The photometric and spectroscopic results are presented in section 4. +" Finally the results are discussed in section 5, where the corotation radii of these galaxies are estimated."," Finally the results are discussed in section 5, where the corotation radii of these galaxies are estimated." + In order to perform our study we searched in the literature for galaxies for which the corotation is expected to be favorably placed in the optical disk., In order to perform our study we searched in the literature for galaxies for which the corotation is expected to be favorably placed in the optical disk. +" This was done by selecting three of thebest candidates tested by 7) (Table 1)) according to the following criteria: The fact that the selected galaxies do not have strong bars may simplify the interpretation of the data, since only the secular effect of the spiral arms may be predominant on these galaxies."," This was done by selecting three of thebest candidates tested by \cite{Canzian98} (Table \ref{tbl-1}) ) according to the following criteria: The fact that the selected galaxies do not have strong bars may simplify the interpretation of the data, since only the secular effect of the spiral arms may be predominant on these galaxies." + To perform the spectroscopy we adopted the following procedures to select the regions of each galaxy :, To perform the spectroscopy we adopted the following procedures to select the regions of each galaxy : +In the local universe. most galaxies [all onto the IIubble Sequence (7)— which runs from older. red. quiescent galaxies wilh a rl! surface-brightness profiles (ο star-lormine. eas-rich disks with exponential luminosity distributions.,"In the local universe, most galaxies fall onto the Hubble Sequence \citep{HubbleSeq} which runs from older, red, quiescent galaxies with a $r^{1/4}$ surface-brightness profiles to star-forming, gas-rich disks with exponential luminosity distributions." +" These light profiles are generally described by the ? parameter. defined through Z(r)xrt"". where n typically ranges from 1 (an exponential disk) to ~4 (an v1- aw spheroid)."," These light profiles are generally described by the \citet{Sersic} parameter, defined through $I(r) \propto r^{1/n}$, where $n$ typically ranges from $\sim 1$ (an exponential disk) to $\sim 4$ (an $^{1/4}$ -law spheroid)." + Out to intermediate (2~1.5) redshifts. galaxies can generally be placed onto the local IDubble Sequence quite reliably (7?)..," Out to intermediate $z \sim 1.5$ ) redshifts, galaxies can generally be placed onto the local Hubble Sequence quite reliably \citep{Cons04}." + llowever. at larger clistances. this sequence breaks down. as most sources appear clumpy ancl inegular (e.g..22277) ancl are therefore diffieult to classilv.," However, at larger distances, this sequence breaks down, as most sources appear clumpy and irregular \citep[e.g.,][]{Steidel96,Papovich05,Conselice05,Venemans05,Pirzkal07} + and are therefore difficult to classify." +. Consequently. although the morphological parameters of distant galaxies can be quantified via the use of codes such as (?) ancl (?).. these parameters do not necessarily directly translate into the familiar IIubble sequence seen in (he nearby. universe.," Consequently, although the morphological parameters of distant galaxies can be quantified via the use of codes such as \citep{GALFIT} and \citep{GIM2D}, these parameters do not necessarily directly translate into the familiar Hubble sequence seen in the nearby universe." + Moreover. (he robustness of the derived parameters is hiehly dependent on the signal-to-noise (S/N) of the measurement. wilh simulations suggesting that a S/N of al least 15 is required (7)— to reliably. fit a igh-redshift galaxy.," Moreover, the robustness of the derived parameters is highly dependent on the signal-to-noise $S/N$ ) of the measurement, with simulations suggesting that a $S/N$ of at least 15 is required \citep{Ravindranath06} to reliably fit a high-redshift galaxy." + To address some of these difficulties. a number of non-parametrie measures of galaxy norphologv have been developed. including the concentration. asymmetry. ancl clumpiness indices (CAS:?).. and the Gini coefficient. which measures a prolile's departure from uniformity (?)..," To address some of these difficulties, a number of non-parametric measures of galaxy morphology have been developed, including the concentration, asymmetry, and clumpiness indices \citep[CAS;][]{CAS}, and the Gini coefficient, which measures a profile's departure from uniformity \citep{Lotz04}." + These svstems have been used extensively on samples of high-redshift galaxies. since they require no a priori knowledge about the functional form of the luminosity distribution.," These systems have been used extensively on samples of high-redshift galaxies, since they require no a priori knowledge about the functional form of the luminosity distribution." + In addition. unlike other fitting techniques which use smooth (svo-dimensional profiles. these non-parametric techniques ean also quantify (he non-uniformity of a galaxy. (1.e.. test for the presence of stu-Iorming regions). and define its asymmetry.," In addition, unlike other fitting techniques which use smooth two-dimensional profiles, these non-parametric techniques can also quantify the non-uniformity of a galaxy (i.e., test for the presence of star-forming regions), and define its asymmetry." + Their one drawback. of course. is (hat the values one obtains may depend on the image depth. and that this sensitivitv has not been well-quantified for hieh-redshilt galaxies.," Their one drawback, of course, is that the values one obtains may depend on the image depth, and that this sensitivity has not been well-quantified for high-redshift galaxies." + The majority of galaxies known at high ἐς> 2.5) redshifts have been identified via the Lyiman-break (technique. wherein galaxies wilh Lyiman-limit discontinuities are identified by," The majority of galaxies known at high $z \geq 2.5$ ) redshifts have been identified via the Lyman-break technique, wherein galaxies with Lyman-limit discontinuities are identified by" +spectrun. and weak ivou K line (Siebert et al.,"spectrum, and weak iron K line (Siebert et al." + 1999. Carpe et al.," 1999, Grupe et al." + 2000)., 2000). +" The mass of ROB JOOLL|193 can be an order of maguitude larger if the DER. size scales with the huninosity of ionizing οσοΜπι instead of the Iuninositv at απ if its extremely steep continuum in the optical spectrum (o,&δι Siebert et al."," The mass of RGB J0044+193 can be an order of magnitude larger if the BLR size scales with the luminosity of ionizing continuum instead of the luminosity at and if its extremely steep continuum in the optical spectrum $\alpha_{opt} \simeq -3.1$, Siebert et al." + L999) exteuds iuto far UV., 1999) extends into far UV. + ITowever. we notice that the equivalent width of ID) is normal iu this object. sugeesting such kiud of correction is uot adequate.," However, we notice that the equivalent width of $\beta$ is normal in this object, suggesting such kind of correction is not adequate." + Tf above mass estimation is correct. the existence of radio-oud NLS1s sugeests that neither large mass of the DII nor a low accretion rate is necessary for the formation of a powerful radio jet.," If above mass estimation is correct, the existence of radio-loud NLS1s suggests that neither large mass of the BH nor a low accretion rate is necessary for the formation of a powerful radio jet." + So what else factor is relevant. spin of a BIT or the euviromnoeut of the galactic nuclei?," So what else factor is relevant, spin of a BH or the environment of the galactic nuclei?" + If a jet is powered by the spin energy of the DII through Dlaudford Zuajek (1977) moechanigin. both rapid spin of the BIT aud a strong magnetic Seld are required for the formation of powerful radio jets.," If a jet is powered by the spin energy of the BH through Blandford Znajek (1977) mechanism, both rapid spin of the BH and a strong magnetic field are required for the formation of powerful radio jets." + Formation of a rapidly spiuuiug BIT in NUSIs can be fouud in various schemes: a massive hole is formed through collapsing of a rotating gas clouds. through accreting material by a seeded stall hole and by πιοοπι of small holes.," Formation of a rapidly spinning BH in NLS1s can be found in various schemes: a massive hole is formed through collapsing of a rotating gas clouds, through accreting material by a seeded small hole and by merging of small holes." + In particular. the hole spins up very fast in NLS1s as they are thought to accrete at close to or even supper-Eddington rate.," In particular, the hole spins up very fast in NLS1s as they are thought to accrete at close to or even supper-Eddington rate." + It can easily reach the equilibium between the spin-up by accretion aud the spin-down by the Blaudford-Zuajek mechanism (Moderski. Sikora Lasota 1998) uuless the NLSIs phase is extremely short (less than a few 10* years).," It can easily reach the equilibrium between the spin-up by accretion and the spin-down by the Blandford-Znajek mechanism (Moderski, Sikora Lasota 1998) unless the NLS1s phase is extremely short (less than a few $10^7$ years)." + Strong maguctic field can be either created by the dvuiauo in the accretion disk or amplified by compressing the convected magnetic field yozen inthe acercted material., Strong magnetic field can be either created by the dynamo in the accretion disk or amplified by compressing the convected magnetic field frozen in the accreted material. + It remains unexpected that radio loud NLSIs are so rare., It remains unexpected that radio loud NLS1s are so rare. + Alternatively. it was sugeested that the observed radio jets are related not oulv with the center cugine but also with the environment of the nuclei that provide the confinement of the RLjets.," Alternatively, it was suggested that the observed radio jets are related not only with the center engine but also with the environment of the nuclei that provide the confinement of the jets." + If this is indeed the case. the ost galaxies of the NLESIs should be also a massive elliptical galaxies.," If this is indeed the case, the host galaxies of the RL NLS1s should be also a massive elliptical galaxies." + We speculate that they deviate from the relation between mass of DIT aud that of bulge because he DIT is still in the rapid growth phase. We lave no data ον the bulge masses of these three NLSIs.," We speculate that they deviate from the relation between mass of BH and that of bulge because the BH is still in the rapid growth phase, We have no data on the bulge masses of these three NLS1s." + Nelsou Whittle (1996) suggestoo that |OIII] A5007 width is a eood indicator of stellar velocity dispersion in elliptical galaxies and spiral bulges., Nelson Whittle (1996) suggest that [OIII] $\lambda 5007$ width is a good indicator of stellar velocity dispersion in elliptical galaxies and spiral bulges. + The |OIII| widths are 670 aud 750 lan + for RN J01312-1258 and RGB JO011]193 (Siebert et al 1999: Cape et al., The [OIII] widths are 670 and 750 km $^{-1}$ for RX J0134.2-4258 and RGB J0044+193 (Siebert et al 1999; Grupe et al. + 20003. respectively. which correspoud to stellar velocity dispersions of 285 aud 319 lan +. indicating of massive spheroidal conponent iu both galaxies.," 2000), respectively, which correspond to stellar velocity dispersions of 285 and 319 km $^{-1}$, indicating of massive spheroidal component in both galaxies." + This would eive BID masses of about 1-G 108 AL. in these two objects if they were followed BIT mass aud stellar velocity dispersion relation (Fig., This would give BH masses of about 4-6 $10^8$ $_\odot$ in these two objects if they were followed BH mass and stellar velocity dispersion relation (Fig. + 1 of Nelson 2000)., 1 of Nelson 2000). + These masses are oue order of magnitude larger than the DII masses estimated frou the BLR-kincematics method. consistent with our guess.," These masses are one order of magnitude larger than the BH masses estimated from the BLR-kinematics method, consistent with our guess." + The [OTH] is extremely weak in PINS 0558-501 and its has not been given by Corbin (1997). but secius. also relative broad.," The [OIII] is extremely weak in PKS 0558-504 and its has not been given by Corbin (1997), but seems also relative broad." + However. a direct measurement of the stellay velocity dispersion in those objects is needed before auy firm conclusion can be drawn.," However, a direct measurement of the stellar velocity dispersion in those objects is needed before any firm conclusion can be drawn." + To sununarize. we find that the rapid flare observed iu PISS 0558-501un requires an effective radiative efficiency of close to one.," To summarize, we find that the rapid flare observed in PKS 0558-504 requires an effective radiative efficiency of close to one." + This can be explained either by associating the dare with the relativistic radio Jets or magnetic heated corona above an accretion disk., This can be explained either by associating the flare with the relativistic radio jets or magnetic heated corona above an accretion disk. + Future smnultaucous mouitor of this object iu radio aud X-ray. bands would be crucial in discrimination the two possibility., Future simultaneous monitor of this object in radio and X-ray bands would be crucial in discrimination the two possibility. + We showed that a maguetic field of strougth of at least a few 10! Gauss is required in the latter case., We showed that a magnetic field of strength of at least a few $10^4$ Gauss is required in the latter case. + Future observation with a large photon collecting areas detector. such as ALANI program. will allow wriuterrupt monitoring the detail spectral evolution of the fare. vielding striuseut constraints on the models.," Future observation with a large photon collecting areas detector, such as MAXI program, will allow un-interrupt monitoring the detail spectral evolution of the flare, yielding stringent constraints on the models." + We found that the masses im three RL NLSIs are niuch lower than that for radio loud quasars. which may sueeestOO that the black holes in uarrow liue NLSI are still iu the phase of rapid growth.," We found that the masses in three RL NLS1s are much lower than that for radio loud quasars, which may suggest that the black holes in narrow line NLS1 are still in the phase of rapid growth." +In this section. we discuss the dependence of meridional flow ancl dilferential rotation on [ree parameters.,"In this section, we discuss the dependence of meridional flow and differential rotation on free parameters." + The parameter set is shown in Table 1 (eases 12-17)., The parameter set is shown in Table \ref{param} (cases 12-17). + À first we investigate the influence of the variation of the A effect., At first we investigate the influence of the variation of the $\Lambda$ effect. + The A effect has (wo free parameters. ie. amplitude Ay and inclination angle A (see §??)).," The $\Lambda$ effect has two free parameters, i.e., amplitude $\Lambda_0$ and inclination angle $\lambda$ (see \ref{s:lambda}) )." +" Amplitude is thought to become smaller with a larger stellar angular velocity. due to the saturation of the correlations such as (0.0) and (0505). where eL. 05 and οὐ, are the radial. latitudinal and longitudinal component turbulent velocities. respectively."," Amplitude is thought to become smaller with a larger stellar angular velocity, due to the saturation of the correlations such as $\langle v'_rv'_\phi \rangle$ and $\langle v'_\theta v'_\phi \rangle$, where $v_r'$, $v_\theta'$ and $v_\phi'$ are the radial, latitudinal and longitudinal component turbulent velocities, respectively." + Fig., Fig. + 11 shows that meridional flow becomes slower with a smaller Ag.keeping the Qy value constant (Case 10).," \ref{vari_some} shows that meridional flow becomes slower with a smaller $\Lambda_0$,keeping the $\Omega_0$ value constant (Case 10)." + It is clear with the result of 77 (hat meridional flow becomes slow with a larger angular velocity when the variation of Ag is included., It is clear with the result of \ref{taylor} that meridional flow becomes slow with a larger angular velocity when the variation of $\Lambda_0$ is included. + Brownetal.(2008) reported this effect with their three-cdimensional hyvdrodynamie calculation., \cite{2008ApJ...689.1354B} reported this effect with their three-dimensional hydrodynamic calculation. + When meridional [low is slow. the entropy. gradient generated by the subaciabatic laver is small. ancl differential rotation approaches the Tavlor-Proudman The inclination angle is thought to be small with large stellar angular velocity values. since the motion across (he rotational axis is restricted. (INiehatinov&Riiciger1993)..," When meridional flow is slow, the entropy gradient generated by the subadiabatic layer is small, and differential rotation approaches the Taylor-Proudman The inclination angle is thought to be small with large stellar angular velocity values, since the motion across the rotational axis is restricted \citep{1993A&A...276...96K}." + In case 12. differential rotation with a small inclination angle (A= 2.5°) is ealeulated.," In case 12, differential rotation with a small inclination angle $\lambda=2.5^\circ$ ) is calculated." + Other parameters are (he same as case 1., Other parameters are the same as case 1. + The racial distribution of meridional flow is shown in Fig. H1.., The radial distribution of meridional flow is shown in Fig. \ref{vari_some}. + Meridional flow becomes faster with a smaller inclination angle., Meridional flow becomes faster with a smaller inclination angle. + Because of the efficient angular momentum transport in the z direction when the inclination angle is small. the second term on the right hand side of Eq. (45))," Because of the efficient angular momentum transport in the $z$ direction when the inclination angle is small, the second term on the right hand side of Eq. \ref{therm01}) )" + is large., is large. +" This generates a large w,,. Le. [ast meridional flow.", This generates a large $\omega_\phi$ i.e. fast meridional flow. +of the cavity preferentially carves away the part of the envelope responsible for the 70 fflux.,of the cavity preferentially carves away the part of the envelope responsible for the 70 flux. +" By contrast, there is almost no variation as a function of iin the SPIRE filters."," By contrast, there is almost no variation as a function of in the SPIRE filters." + The optical and near-IR emission from protostellar systems is dominated by the source itself and the scattered light from the circumstellar envelope., The optical and near-IR emission from protostellar systems is dominated by the source itself and the scattered light from the circumstellar envelope. +" Thus, face-on models are typically brighter and bluer compared to those in which the central star is either wholly or partially obscured by the disk."," Thus, face-on models are typically brighter and bluer compared to those in which the central star is either wholly or partially obscured by the disk." +" At optical and near-IR wavelengths, these objects are quite often extremely faint or undetected even in unbiased photometry surveys due to high obscurataion."," At optical and near-IR wavelengths, these objects are quite often extremely faint or undetected even in unbiased photometry surveys due to high obscurataion." + Figures 3 shows that in the PACS filters this effect becomes largely unimportant as the main emission is from the envelope., Figures \ref{FigPACSless} shows that in the PACS filters this effect becomes largely unimportant as the main emission is from the envelope. + We find similar results for the other combinations of flux and flux density diagnostics (not shown)., We find similar results for the other combinations of flux and flux density diagnostics (not shown). +" We have concentrated on a single central star; however, the models are applicable to all low mass stars."," We have concentrated on a single central star; however, the models are applicable to all low mass stars." + The observed fluxes and SEDs simply scale with the mass of the central object as determined by the envelope density profile and the accretion luminosity equations., The observed fluxes and SEDs simply scale with the mass of the central object as determined by the envelope density profile and the accretion luminosity equations. +" When the mass of the central star is changed, the envelope density remains the same but the infall rate changes."," When the mass of the central star is changed, the envelope density remains the same but the infall rate changes." +" And, the mass accretion rate for a given luminosity scales inversely with the central object mass."," And, the mass accretion rate for a given luminosity scales inversely with the central object mass." +" Thus, considerable overlap does exist in the observed fluxes for different mass protostars."," Thus, considerable overlap does exist in the observed fluxes for different mass protostars." + This result further demonstrates that PACS and SPIRE are best suited for constraining the envelope and disk properties and provide limited constraints on the central object itself., This result further demonstrates that PACS and SPIRE are best suited for constraining the envelope and disk properties and provide limited constraints on the central object itself. + The HOPS program (Fischeretal. 2010)) imaged 4 protostars in Orion L 1641 region for which PACS 70 and 160 pphotometry is available for 3 sources., The HOPS program \cite{hops}) ) imaged 4 protostars in Orion L 1641 region for which PACS 70 and 160 photometry is available for 3 sources. + These stars are shown with the diamond symbol in Fig. 2.., These stars are shown with the diamond symbol in Fig. \ref{FigPACS}. +" Based on this diagnostic alone, we can conclude that all 3 HOPS sources are much more luminous than our typical protostar of 1Lo."," Based on this diagnostic alone, we can conclude that all 3 HOPS sources are much more luminous than our typical protostar of 1." +". Only 3 sources with two-band photometry are in the HOPS field; nonetheless, the sources are not clustered but spread over a broad range of color and flux density values in Fig. 2,,"," Only 3 sources with two-band photometry are in the HOPS field; nonetheless, the sources are not clustered but spread over a broad range of color and flux density values in Fig. \ref{FigPACS}," + implying that a broad range of values must also exist for the other parameters., implying that a broad range of values must also exist for the other parameters. + These conclusions are indeed confirmed by detailed model SED fits over the 1-870 rrange for the HOPS sources (Fischeretal. 2010))., These conclusions are indeed confirmed by detailed model SED fits over the 1-870 range for the HOPS sources \cite{hops}) ). +" The model grid presented here provides the expected flux densities and flux density ratios for 20,160 low-mass protostellar SEDs, useful for determining the phase space occupied by protostar in the ffilters."," The model grid presented here provides the expected flux densities and flux density ratios for 20,160 low-mass protostellar SEDs, useful for determining the phase space occupied by protostar in the filters." + Disentangling the contributions of the various, Disentangling the contributions of the various +comparing the years 1978-1986 to the years 1992-1999. possibly due to distinet activity cycles.,"comparing the years 1978–1986 to the years 1992–1999, possibly due to distinct activity cycles." + Here we derive the period using the full data set. using a variety of techniques summarized in Table 2..," Here we derive the period using the full data set, using a variety of techniques summarized in Table \ref{tab:periods}." + From these results we adopt a photometric period of 308.8+2.5 d (see inset of Fig. 1))., From these results we adopt a photometric period of $308.8\pm2.5$ d (see inset of Fig. \ref{fig:tsEph}) ). + Given the errors on the individual results and the obvious spot evolution. we cannot comfortably give the period with higher precision.," Given the errors on the individual results and the obvious spot evolution, we cannot comfortably give the period with higher precision." + The corresponding ephemeris is given in Table | and is marked by dashed vertical lines in Fig. ].., The corresponding ephemeris is given in Table \ref{tab:results} and is marked by dashed vertical lines in Fig. \ref{fig:tsEph}. + As can be seen. the ephemeris can not always reproduce the data. indicating that the spots are changing size and configuration.," As can be seen, the ephemeris can not always reproduce the data, indicating that the spots are changing size and configuration." + From Fig., From Fig. + it is clear that when the star is fainter. V—7 is higher (1.e.. the star is redder) which points to cool spots as the cause of the variation.," \ref{fig:tsEph} it is clear that when the star is fainter, $V-I$ is higher (i.e., the star is redder) which points to cool spots as the cause of the variation." + Since the period is likely much longer than typical spot lifetimes we cannot hope to extract any quantitative information on the amount of differential rotation., Since the period is likely much longer than typical spot lifetimes we cannot hope to extract any quantitative information on the amount of differential rotation. + We will now describe the methods used to derive the periods in Table 2.., We will now describe the methods used to derive the periods in Table \ref{tab:periods}. + Both the Discrete Fourier. Transform (DFT:e.g..?) and Period04 (?) were used. where we prewhitened with two long periods corresponding to long-term drifts.," Both the Discrete Fourier Transform \citep[DFT; e.g.,][]{reegen2007} and Period04 \citep{period04} were used, where we prewhitened with two long periods corresponding to long-term drifts." + PeriodO4 is developed for asteroseismic applications where the light curve can be assumed to be made up of sinusoidal components., Period04 is developed for asteroseismic applications where the light curve can be assumed to be made up of sinusoidal components. + This makes it inappropriate for our analysis of the long term variations which are changing in amplitude and possibly also in period., This makes it inappropriate for our analysis of the long term variations which are changing in amplitude and possibly also in period. + The usual formulafor the period precision based on a mix of white and 1/f noise therefore has no physical meaning., The usual formulafor the period precision based on a mix of white and $1/f$ noise therefore has no physical meaning. + The CLEAN algorithm (alsoknownasiterativesine-wavefitting:e.g..?) revealed only one main peak in the resulting amplitude spectrum after pre-whitening with the long-term drifts.," The CLEAN algorithm \citep[also known as iterative sine-wave fitting; e.g.,][]{frandsen+1995} + revealed only one main peak in the resulting amplitude spectrum after pre-whitening with the long-term drifts." + The Lomb-Scargle periodogram gives results similar to the DFT. but with slightly lower error.," The Lomb-Scargle periodogram gives results similar to the DFT, but with slightly lower error." + The Lafler-Kinman analysis (2). gives a similar result. but the periodogram is not as convincing — a trait shared by the Minimum String Length (MSL) method.," The Lafler-Kinman analysis \citep{lafler+kinman1965} gives a similar result, but the periodogram is not as convincing — a trait shared by the Minimum String Length (MSL) method." + The Phase Dispersion Minimization (PDM) tend to generate higher period aliases. but even so the peak was clearly identified. although not very well determined.," The Phase Dispersion Minimization (PDM) tend to generate higher period aliases, but even so the peak was clearly identified, although not very well determined." + From its position in the HR diagram. EK Ert is expected to show p-mode oscillations that are stochastically excited. and damped by near surface convection similar to what is observed in the Sun and other solar-like stars (2)..," From its position in the HR diagram, EK Eri is expected to show p-mode oscillations that are stochastically excited and damped by near surface convection similar to what is observed in the Sun and other solar-like stars \citep{bedding+kjeldsen2003}." + We therefore carried out high-cadence (Af=8min) spectroscopic. monitoring during three consecutive nights using HARPS as outlined in Sect. 2.2..," We therefore carried out high-cadence $\Delta t \approx 8\,$ min) spectroscopic monitoring during three consecutive nights using HARPS as outlined in Sect. \ref{obs_spec}." + In addition. five nights of high-cadence photometric monitoring was conducted as described in Sect.," In addition, five nights of high-cadence photometric monitoring was conducted as described in Sect." + 2.1 The time series is shown in Fig.," \ref{obs_phot} + The time series is shown in Fig." + 2 and shows significant variability of a few metres per second (peak-to-peak) with periods of roughly | hour., \ref{fig:seis} and shows significant variability of a few metres per second (peak-to-peak) with periods of roughly 1 hour. + The slight night-to-night offsets are likely due to slow variations in the overall activity level., The slight night-to-night offsets are likely due to slow variations in the overall activity level. + In Fig., In Fig. + 3 we show the Fourier power spectrum of the time series. which shows the variability as an excess power in the frequency range μΗΖ.," \ref{fig:fourier} we show the Fourier power spectrum of the time series, which shows the variability as an excess power in the frequency range $~\mu$ Hz." + This excess agrees with the expected frequency of maximum power estimated from scaling the solar value (2).. which gives roughly 340 Hz.," This excess agrees with the expected frequency of maximum power estimated from scaling the solar value \citep{kjeldsen+bedding1995}, which gives roughly 340 $\mu$ Hz." + The power at very low frequency (=50 μΗΖ) is predominantly caused by the slow linear trend seen on the third night and is probably not due to oscillations.," The power at very low frequency $\approx 50\, \mu$ Hz) is predominantly caused by the slow linear trend seen on the third night and is probably not due to oscillations." + The frequency spectra of the Sun and other solar-like stars show an almost regular series of peaks., The frequency spectra of the Sun and other solar-like stars show an almost regular series of peaks. + From this. one can extract the spacing between modes of successive radial order called the large separation. Av. which provides a very precise measure of the mean density of the star.," From this, one can extract the spacing between modes of successive radial order called the large separation, $\Delta\nu$, which provides a very precise measure of the mean density of the star." + By scaling the solar value we find that the expected large separation of EK Eri (usingthescalingformulafrom?) is around 20 μΗ7Ζ.," By scaling the solar value we find that the expected large separation of EK Eri \citep[using the scaling formula from][]{kjeldsen+bedding1995} + is around $20$ $\mu$ Hz." + Due to the short and sparse coverage the present data set does not allow detection of the individual frequencies or the large separation., Due to the short and sparse coverage the present data set does not allow detection of the individual frequencies or the large separation. + However. we are able to estimate the amplitude per mode from the excess power in the Fourier spectrum using the approach by ?..," However, we are able to estimate the amplitude per mode from the excess power in the Fourier spectrum using the approach by \citet{Kjeldsen05}." + First. the Fourier spectrum is converted into power density by dividing by the area under the spectral window.," First, the Fourier spectrum is converted into power density by dividing by the area under the spectral window." + Then we convolve the spectrum with a Gaussian with a width of 4Av. to create just a single smooth hump of excess power and finally we multiply by Av/4.09 (?) and take the square root to get the amplitude per radial mode.," Then we convolve the spectrum with a Gaussian with a width of $4\Delta\nu$ , to create just a single smooth hump of excess power and finally we multiply by $\Delta\nu/4.09$ \citep{kjeldsen+2008} and take the square root to get the amplitude per radial mode." +"and the integration goes over ó and ó, which are azimuthal angles in the frame of the respective rings.",and the integration goes over $\phi$ and $\phi_1$ which are azimuthal angles in the frame of the respective rings. +" Hle found. the maximun. precession frequency tobe when AH,=3/3 and the maximum torque to be where AM,=2aRAR, is the mass of an inclined annulus on which we consider the torque and X,=X(I).", He found the maximum precession frequency tobe when $R/R_1=\sqrt{3/7}$ and the maximum torque to be where $M_1=2\pi \Sigma_1 R_1 \delta R_1$ is the mass of an inclined annulus on which we consider the torque and $\Sigma_1=\Sigma (R_1)$. + 1n this formula AZ is the mass of the annulus at 7? which provides the greatest torque., In this formula $M$ is the mass of the annulus at $R$ which provides the greatest torque. + We replace ÀJ by the mass of the disc. M4 to obtain an upper limit on the total torque on the annulus at Z2.," We replace $M$ by the mass of the disc, $M_{\rm + d}$ to obtain an upper limit on the total torque on the annulus at $R_1$." + The magnitude of the viscous torque is (equation (23)) because We multiply by the area of the ring to find the viscous torque acting on a ring of width of?) at radius £2) to be We now compare the magnitude of the maximum eravitational torque to the viscous torque and subsituting we find With 7—2 and cos= la R=Ky and Ly=Yrs we lind that £4=3>10TAR/AL.) and at f=Raw and R=y3/1. then fous=LOLOCALSAL.).," The magnitude of the viscous torque is (equation \ref{main}) ) because We multiply by the area of the ring to find the viscous torque acting on a ring of width $\delta R_1$ at radius $R_1$ to be We now compare the magnitude of the maximum gravitational torque to the viscous torque and subsituting we find With $\beta=2$ and $\cos \gamma \approx 1$ at $R=R_{\rm in}$ and $R_1=\sqrt{7/3}R_{\rm in}$ we find that $\xi_{\rm grav}= 3 \times +10^{-4}(M_{\rm d}/{\rm M_\odot})$ and at $R_1=R_{\rm out}$ and $R=\sqrt{3/7}R_1$ then $\xi_{\rm grav}=10^{-4}(M_{\rm d}/{\rm + M_\odot})$." + Using the disc mass derived. in Section 3.3. of M4=3.10°M. we findat R=fy. Sony—09 and at RpΞRaw. Sere=O83.," Using the disc mass derived in Section \ref{sec:mass} of $M_{\rm d}=3 \times 10^3 \,\rm M_\odot$ we find at $R=R_{\rm in}$, $\xi_{\rm grav}= 0.9$ and at $R_1=R_{\rm out}$, $\xi_{\rm grav}=0.3$." + This dise mass is the critical one at which the gravity torques become as important as the viscous torques., This disc mass is the critical one at which the gravity torques become as important as the viscous torques. + For smaller disc masses self gravity torques would be unimportant., For smaller disc masses self gravity torques would be unimportant. + In any case the gravitational torque Is not as large as the viscous torque even at its maximum so we are justified in neglecting it., In any case the gravitational torque is not as large as the viscous torque even at its maximum so we are justified in neglecting it. + However. it ought to be included in any numerical models especially for larger dise masses.," However, it ought to be included in any numerical models especially for larger disc masses." + In this section we compare the maser data to our analytical disc models and find parameters which give the best fits., In this section we compare the maser data to our analytical disc models and find parameters which give the best fits. + We use the maser distribution data tabulated in the online version of Argonetal.(2007)., We use the maser distribution data tabulated in the online version of \cite{A07}. +".. This lists positions of each maser in the plane of the sky. cy, and way."," This lists positions of each maser in the plane of the sky, $z_{\rm m}$ and $x_{\rm m}$." + For the first set of data. DMOS6C. we correct the north-south position of the masers (Alice Argon. private Communication).," For the first set of data, BM056C, we correct the north-south position of the masers (Alice Argon, private communication)." + ‘They correlated the first three epochs at a less accurate position than later epochs and the data in the online table for BALOS6C reflect this., They correlated the first three epochs at a less accurate position than later epochs and the data in the online table for BM056C reflect this. +" From the relativistic velocity. (4. in column 3 of Table 5 in the online table of Argon (2007).. we find the frequency where e=2.998.10!""emis"," From the relativistic velocity, $v_{\rm rel}$, in column 3 of Table 5 in the online table of \cite{A07}, we find the frequency where $c = 2.998 \times 10^{10}\,\rm cm\,s^{-1}$." +" Then we apply the Correction and ary, remains the same.", Then we apply the correction and $x_{\rm m}$ remains the same. + 1n order to get an estimate of the measurement error we bin the maser data points., In order to get an estimate of the measurement error we bin the maser data points. + We put the data into 11 bins and find the average c; and 2; in each where 7=1.2...11.," We put the data into 11 bins and find the average $\bar{x_i}$ and $\bar{z_i}$ in each where $i=1,2...11$." + We then find the standard deviations of each average point. σι and m;;.," We then find the standard deviations of each average point, $\sigma_{ix}$ and $\sigma_{iz}$." + We list these in Table 1.., We list these in Table \ref{table2}. + In Figure 2. we plot all of the maser data in the top plot and below we plot the inned data points with error bars., In Figure \ref{dataplot} we plot all of the maser data in the top plot and below we plot the binned data points with error bars. +" The svmmetrv of the velocity distribution of the masers ells us that the black hole is on the line wy,=0 and we ind the position of the black hole. sac. from the svmmetry of the shape of the maser distribution."," The symmetry of the velocity distribution of the masers tells us that the black hole is on the line $x_{\rm m}=0$ and we find the position of the black hole, $z_{\rm add}$, from the symmetry of the shape of the maser distribution." +" We use the inner hree points on the right in the binned data and. fined an interpolated corresponding ty, value on the left hand side at he positive iy.", We use the inner three points on the right in the binned data and find an interpolated corresponding $z_{\rm m}$ value on the left hand side at the positive $x_{\rm m}$ . +" We can then find the midpoint of these two zy, values from the left and right hand. sides.", We can then find the midpoint of these two $z_{\rm m}$ values from the left and right hand sides. + We average over the three points calculated and find that σα=0.52 in he frame of the masers., We average over the three points calculated and find that $z_{\rm add}=0.52$ in the frame of the masers. + We have the shape of the disc section as given in the, We have the shape of the disc section as given in the +observed range of the aabundance ratio.,observed range of the abundance ratio. + W3IRS4. and possibly W3IRS5 present interesting exceptions of relative deficiency predicted in most nucleosynthesis models SNe.," W3IRS4, and possibly W3IRS5 present interesting exceptions of relative deficiency predicted in most nucleosynthesis models SNe." + This likely confines the progenitors of the SNe to be stars of relatively high mass (225M.. ) and high metallicity (Z7-0.02)., This likely confines the progenitors of the SNe to be stars of relatively high mass $\ga$ $_\sun$ ) and high metallicity $\sim$ 0.02). + Kawabataetal...(2010) and Peretsetal...(2010) recently reported the discovery of a new category of subluminous supernovae., \citet{kawabata2010} and \citet{perets2010} recently reported the discovery of a new category of subluminous supernovae. + Although the origin for such faint supernovae is still controversial. (hese authors reported the unusual composition in the supernovae ejecta with rich helium and calcium.," Although the origin for such faint supernovae is still controversial, these authors reported the unusual composition in the supernovae ejecta with rich helium and calcium." + It would be interesting to examine (he nucleosvnthesis vields in this class of supernovae in regard of the aabundance ratios., It would be interesting to examine the nucleosynthesis yields in this class of supernovae in regard of the abundance ratios. + We conducted a comprehensive survey of HIC]. J=1—0 line in the Galaxy., We conducted a comprehensive survey of HCl $J=1-0$ line in the Galaxy. + Of the 27 sources/positions observed. fourteen show emission. nne show absorption. (wo showed marginal detection in emission. and (wo are non-detections.," Of the 27 sources/positions observed, fourteen show emission, nine show absorption, two showed marginal detection in emission, and two are non-detections." + Fourteen of the sources/positions were also observed in the J=1-Olransilion., Fourteen of the sources/positions were also observed in the $J=1-0$ transition. +" RADEN simulations show that LCI] emission is mostly associated with warm dense eas. of order 10"" 7."," RADEX simulations show that HCl emission is mostly associated with warm dense gas, of order $10^6$ $^{-3}$ ." + LIC] abundance is fairly uniform. in the range 10.! to a fewx10. 7. in general agreement wilh previous studies of OAIC-1 by5chilke.Phillips.&Wang(1995) and Salez.Frerking.&Langer (1996)..," HCl abundance is fairly uniform, in the range $10^{-10}$ to a few$\times10^{-9}$ in general agreement with previous studies of OMC-1 by\citet{spw1995} and \citet{sfl1996}. ." + However.," However," +The solar wind is a plasma that is observed to be turbulent with fluctuations at à broad range of scales (Tu&MarschCarbone2005:Petrosyanetal. 2010).,"The solar wind is a plasma that is observed to be turbulent with fluctuations at a broad range of scales \citep{tu95,goldstein95,horbury05,bruno05a,petrosyan10}." +. It is usually modeled as à cascade of energy from large scales (e.g..Wicks 2010). where the energy is injected. to small scales (e.g..Chenetal. 2010a).. where kinetic processes dissipate the energy (e.g..Schekochihinetal.2009).," It is usually modeled as a cascade of energy from large scales \citep[e.g.,][]{wicks10a}, where the energy is injected, to small scales \citep[e.g.,][]{chen10b}, where kinetic processes dissipate the energy \citep[e.g.,][]{schekochihin09}." +. The inertial range fluctuations are thought to be primarily un nature. with Alfvén--wave-like polarizations Davis1971) and phase speeds close to the sspeed (Baleetal.2005).," The inertial range fluctuations are thought to be primarily in nature, with -wave-like polarizations \citep{belcher71} and phase speeds close to the speed \citep{bale05}." + There are various theories of tturbulence. based on interacting packets of wwaves.," There are various theories of turbulence, based on interacting packets of waves." +" The theory of Goldreich&Sridhar(1995).. based on critical balance. predicts that the ffluctuations have a perpendicular one-dimensional energy spectrum. E(k)~. where K, is the wavevector perpendicular to the magneticky field."," The theory of \citet{goldreich95}, based on critical balance, predicts that the fluctuations have a perpendicular one-dimensional energy spectrum $E(k_\perp)\sim k_\perp^{-5/3}$, where $k_\perp$ is the wavevector perpendicular to the magnetic field." + The theory of Boldyrev (2006).. which 1n addition assumes scale-dependent alignment. predicts that their spectrum is ΕΚ}~ky.," The theory of \citet{boldyrev06}, which in addition assumes scale-dependent alignment, predicts that their spectrum is $E(k_\perp)\sim k_\perp^{-3/2}$." + Similar predictions also exist for the multitude of imbalanced theories (e.g..Lithwicketal.2007;Bhattacharjee2010:Podesta201 1)..," Similar predictions also exist for the multitude of imbalanced theories \citep[e.g.,][]{lithwick07,beresnyak08,chandran08,perez09,podesta10c,podesta11b}." + In the solar wind at | AU. it has been shown that the spectral index of the magnetic field is close to —5/3 on average but that the spectral index of the velocity is closer to —3/2 (e.g.. 2011)..," In the solar wind at 1 AU, it has been shown that the spectral index of the magnetic field is close to $-5/3$ on average but that the spectral index of the velocity is closer to $-3/2$ \citep[e.g.,][]{mangeney01,podesta07,salem09,tessein09,podesta10d,wicks11}." + This difference between the two fields is not consistent with any of the current theories of tturbulence and is one of the currently unsolved problems of solar wind turbulence., This difference between the two fields is not consistent with any of the current theories of turbulence and is one of the currently unsolved problems of solar wind turbulence. + Past measurements of the electric field spectrum in the frame of the spacecraft found it to closely match the magnetic field (Baleetal.2005:Sahraout2009).," Past measurements of the electric field spectrum in the frame of the spacecraft found it to closely match the magnetic field \citep{bale05,sahraoui09}." +. These measurements used single intervals of data but it has been shown (e.g..Tesseinetal.2009) that the velocity and magnetic field have a large spread of spectral indices. and many intervals are needed to determine the average behavior.," These measurements used single intervals of data but it has been shown \citep[e.g.,][]{tessein09} that the velocity and magnetic field have a large spread of spectral indices and many intervals are needed to determine the average behavior." + In this Letter. we present a survey of electric field measurements in the solar wind using many intervals of data.," In this Letter, we present a survey of electric field measurements in the solar wind using many intervals of data." + We explain why the electric field in the spacecraft frame follows the magnetic field and make new measurements of the electric field in the mean solar wind frame., We explain why the electric field in the spacecraft frame follows the magnetic field and make new measurements of the electric field in the mean solar wind frame. + In Section 2.. we describe the data set. in Section 3. we discuss our results and in Section 4. we present our conclusions.," In Section \ref{sec:data}, , we describe the data set, in Section \ref{sec:results} we discuss our results and in Section \ref{sec:conclusions} we present our conclusions." + We used data from the mission (Angelopoulos 20100... which is an extension of the mission (Angelopoulos2008).," We used data from the mission \citep{angelopoulos10}, which is an extension of the mission \citep{angelopoulos08}." +. During late 2010. the two spacecraft and P2)) moved from equatorial Earth orbits to Lunar Lagrange orbits (~ 60 Ry from the Earth).," During late 2010, the two spacecraft and ) moved from equatorial Earth orbits to Lunar Lagrange orbits $\sim$ 60 $R_{\text{E}}$ from the Earth)." + Periods of solar wind data were selected in which each spacecraft was upstream of the Moon. out of Earth’s ton foreshock and the required instruments were operational.," Periods of solar wind data were selected in which each spacecraft was upstream of the Moon, out of Earth's ion foreshock and the required instruments were operational." + The selected days are: days 245-257. 308-310. 316-318. 337-343 of 2010 and days 1-3. 40-42 of 2011 forPI: days 217-230. 275-284. 304—307. 361—364 of 2010 and days 25-28 of 2011 forP2.," The selected days are: days 245–257, 308–310, 316–318, 337–343 of 2010 and days 1–3, 40–42 of 2011 for; days 217–230, 275–284, 304--307, 361–364 of 2010 and days 25–28 of 2011 for." +. The same day in both spacecraft was avoided so that the intervals are independent., The same day in both spacecraft was avoided so that the intervals are independent. + All of the data from these days were split into 6 hr sections resulting in 272 intervals. of which were in slow solar wind (6:500 km s! ).," All of the data from these days were split into 6 hr sections resulting in 272 intervals, of which were in slow solar wind $<$ 500 km $^{-1}$ )." + Spin resolution (—3 s) electric field data. E... from the electric field instrument (EFI:Bonnelletal.2008) was used. along with spin resolution magnetic field data. B. from the fluxgate magnetometer (FGM:Austeretal.2008) and varying resolution ion velocity. v. and ion number density. 7. onboard moments from the electrostatic analyzer (ESA:Mc-Faddenetal. 2008).," Spin resolution $\sim$ 3 s) electric field data, , from the electric field instrument \citep[EFI;][]{bonnell08} was used, along with spin resolution magnetic field data, $\mathbf{B}$, from the fluxgate magnetometer \citep[FGM;][]{auster08} and varying resolution ion velocity, $\mathbf{v}$, and ion number density, $n$, onboard moments from the electrostatic analyzer \citep[ESA;][]{mcfadden08}." +. A despun spacecraft coordinate system (DSL) was used. in which z ts the spacecraft spin axis.," A despun spacecraft coordinate system (DSL) was used, in which $z$ is the spacecraft spin axis." + The DSL system for ts approximately the same as the geocentric solar ecliptic (GSE) system with the sign of the y- and ς- axes reversed., The DSL system for is approximately the same as the geocentric solar ecliptic (GSE) system with the sign of the $y$ - and $z$ - axes reversed. + The wire boom electric field antennas are in the x—v plane and extend a few Debye lengths from the spacecraft., The wire boom electric field antennas are in the $x$ $y$ plane and extend a few Debye lengths from the spacecraft. + Data with the currently. most recent calibrations (vOI) were used for all instruments., Data with the currently most recent calibrations (v01) were used for all instruments. + For iit was found that some extra calibration was needed., For it was found that some extra calibration was needed. + A fit. varyingthe," A least-squares fit, varyingthe" +are removed from regions closer to the planet and scattered onto orbits which almost intersect the planet’s (shown by the dashed black line).,are removed from regions closer to the planet and scattered onto orbits which almost intersect the planet's (shown by the dashed black line). + The vertical solid blue line shows the chaotic zone width according to ?., The vertical solid blue line shows the chaotic zone width according to . +". More eccentric particles are destabilised at greater semi-major axes than less eccentric ones, as was seen in the results from the encounter map."," More eccentric particles are destabilised at greater semi-major axes than less eccentric ones, as was seen in the results from the encounter map." +" Hence, the encounter map appears to be giving an accurate picture of the dynamics."," Hence, the encounter map appears to be giving an accurate picture of the dynamics." +" Additionally, the region above the dashed black line is almost totally devoid of particles, due to scattering by the planet (these particles have either collided with the planet or are in the unstable population just below the black line which is in the process of being scattered)."," Additionally, the region above the dashed black line is almost totally devoid of particles, due to scattering by the planet (these particles have either collided with the planet or are in the unstable population just below the black line which is in the process of being scattered)." + This justifies our labelling of planet-crossing orbits as “chaotic” in Figure 1.., This justifies our labelling of planet-crossing orbits as “chaotic” in Figure \ref{fig:chaoticzone}. + The standard derivation of the chaotic zone width takes the widths of the mean motion resonances to be independent of eccentricity., The standard derivation of the chaotic zone width takes the widths of the mean motion resonances to be independent of eccentricity. +" Working from the resonance Hamiltonian where Jος€? is the canonical momentum, ϐ is the resonant argument, and ( is a parameter measuring distance to the nominal resonance location??),, one can show that the width of a resonance at low eccentricity is approximately"," Working from the resonance Hamiltonian where $J\propto e^2$ is the canonical momentum, $\theta$ is the resonant argument, and $\beta$ is a parameter measuring distance to the nominal resonance location, one can show that the width of a first-order resonance at low eccentricity is approximately" +"close to the T,-method with an absolute difference of about 0.04 dex.",close to the $T_{\rm e}$ -method with an absolute difference of about 0.04 dex. + The lowest dispersion is found with the use of the m]/Hf vs. π] diagram., The lowest dispersion is found with the use of the $\beta$ vs. ] diagram. +" For the majority of the diagrams, the difference and the dispersion are larger in the regime of low metallicity (12+log(O/H)< 8.0)."," For the majority of the diagrams, the difference and the dispersion are larger in the regime of low metallicity $< 8.0$ )." + For the other diagrams this difference is about 0.25 dex., For the other diagrams this difference is about 0.25 dex. +" The O/H abundances via detailed models are in consonance with the ones via T,-method for the objects analyzed and the dispersion derived is lower than the one obtained using diagnostic diagrams.", The O/H abundances via detailed models are in consonance with the ones via $T_{\rm e}$ -method for the objects analyzed and the dispersion derived is lower than the one obtained using diagnostic diagrams. +" For the ionization parameter, in Fig. 6,,"," For the ionization parameter, in Fig. \ref{f5}," + we plotted U against the oxygen abundance obtained from diagnostic diagrams presented in Section 4 as well as those obtained from detailed models.," we plotted $U$ against the oxygen abundance obtained from diagnostic diagrams presented in Section \ref{diag} + as well as those obtained from detailed models." +" The results for galaxies andHi regions are indicated by different symbols (red and black dots, respectively)."," The results for galaxies and regions are indicated by different symbols (red and black dots, respectively)." + The πι/Ηβ vs. u] and n] vs. n] estimates larger U values than the ones via other methods., The $\beta$ vs. ] and ] vs. ] estimates larger $U$ values than the ones via other methods. + There is not a clear trend of, There is not a clear trend of +"the density ⋠⋅field is. real rather than complex. C757els=obs677,. resulting in &|1 independent measurements of C7: There is no need for us to use the mocified weighting formula of Pechles (1973 equation 53).","the density field is real rather than complex, $C_{\ell +m}^{\rm obs} = C_{\ell,-m}^{\rm obs}$, resulting in $\ell+1$ independent measurements of $C_\ell$: There is no need for us to use the modified weighting formula of Peebles (1973 equation 53)." +" In our case. J;,, does not vary significantly with m."," In our case, $J_{\ell m}$ does not vary significantly with $m$." + We verified that the mocified weighting formula produced indistinguishable results., We verified that the modified weighting formula produced indistinguishable results. +" One consequence of the partial sky is to ""mix, the harmonic coefficients such that the measured angular power spectrum at £ depends on a range of C5; around (—f: The angled brackets refer to an imagined averaging over many realizations of cdensitv fields. generated hy C. in accordance with equation. 2.."," One consequence of the partial sky is to “mix” the harmonic coefficients such that the measured angular power spectrum at $\ell$ depends on a range of $C_{\ell'}$ around $\ell' = \ell$: The angled brackets refer to an imagined averaging over many realizations of density fields generated by $C_\ell$ , in accordance with equation \ref{eqcldef}." +" Peebles showed. that SooRae=d: he. mixing does not spuriously enhance the measured power (this is accomplished by the factor Ji, in equation 5))."," Peebles showed that $\sum_{\ell'} +R_{\ell\ell'} = 1$; i.e. mixing does not spuriously enhance the measured power (this is accomplished by the factor $J_{\ell m}$ in equation \ref{eqclpeeb}) )." +" Fora complete sky. Rij=9,7. where 8,=1 (m =n) or O (mmz n)."," For a complete sky, $R_{\ell\ell'} = \delta_{\ell\ell'}$, where $\delta_{mn} = 1$ $m = n$ ) or 0 $m \ne n$ )." + For a partial sky. the matrix fy. can be computed from the geometry of the surveyed region (Llauser Peebles 1973).," For a partial sky, the matrix $R_{\ell\ell'}$ can be computed from the geometry of the surveyed region (Hauser Peebles 1973)." + Figure 2 illustrates the result for the NVSS for £—10 (computed using Hauser Peebles 1973 equation 12).," Figure \ref{figrll} + illustrates the result for the NVSS for $\ell = 10$ (computed using Hauser Peebles 1973 equation 12)." + The NVSS covers a sullicientlv. [large fraction. of the skv (75 per cent) that mixing only occurs at the ~15 per cent level and can be neglected. because the underlying C spectrum. is smooth: We checked the NWSS {ή matrix for other multipoles { and Found very similar results., The NVSS covers a sufficiently large fraction of the sky (75 per cent) that mixing only occurs at the $\sim 15$ per cent level and can be neglected because the underlying $C_\ell$ spectrum is smooth: We checked the NVSS $R_{\ell\ell'}$ matrix for other multipoles $\ell$ and found very similar results. + This argument ensures that the measured multipoles are statistically independent το a σου approximation., This argument ensures that the measured multipoles are statistically independent to a good approximation. + The statistical error on the estimator of equation 5. ds (Peebles 1973 equation SI)., The statistical error on the estimator of equation \ref{eqclpeeb} is (Peebles 1973 equation 81). + There are two components of the error: The error for the m=0 case in equation 10. is ereater cause zl is purely real. rather than complex.," There are two components of the error: The error for the $m = 0$ case in equation \ref{eqclsig} is greater because $A_{\ell 0}$ is purely real, rather than complex." +" In the latter case. we are averaging over the real and imaginary parts of Ain, two independent estimates of C. which reduces he overall statistical error by a factor v2."," In the latter case, we are averaging over the real and imaginary parts of $A_{\ell m}$, two independent estimates of $C_\ell$, which reduces the overall statistical error by a factor $\sqrt{2}$." + For a partial sky equation 10. is an approximation. because the variance of multipoles of given £ depends on the underlying power spectrum at (4¢.," For a partial sky equation \ref{eqclsig} is an approximation, because the variance of multipoles of given $\ell$ depends on the underlying power spectrum at $\ell' \ne \ell$." + As discussed. above. this ellect is negligible for the NWSS.," As discussed above, this effect is negligible for the NVSS." + The averagingὃνe over m (equation 8)) decreases the error in the observation., The averaging over $m$ (equation \ref{eqclobs}) ) decreases the error in the observation. + Combining the errors of equation 10.. assuming estimates at cdillerent mm are statistically independent.: the resulting. error in. C7obs7 is+ We used. Monte. Carlo simulations to verifv that equation 11. produced results within 5 per cent of the true error for all relevant. multipoles.," Combining the errors of equation \ref{eqclsig}, assuming estimates at different $m$ are statistically independent, the resulting error in $C_\ell^{\rm obs}$ is We used Monte Carlo simulations to verify that equation \ref{eqclerr} + produced results within 5 per cent of the true error for all relevant multipoles." +" Our only addition to the formalism. of Peebles (1973) was to increase the total variance on the estimate of 6), bv a factor Lffas. where fire=AQ/tr is the fraction of sky covered (i.c. niultiph equation 11. by 1JVfas)."," Our only addition to the formalism of Peebles (1973) was to increase the total variance on the estimate of $C_\ell$ by a factor $1/f_{\rm +sky}$, where $f_{\rm sky} = \Delta \Omega/4\pi$ is the fraction of sky covered (i.e. multiply equation \ref{eqclerr} by $1/\sqrt{f_{\rm +sky}}$ )." + ‘This correction factor was motivated by Scott. Srednicki and White (1994) as a fundamental property of sample variance fora partial sky. and is part of the standard CALB fornialism (e.g. Boned. Efstathiou Tegmark. 1997).," This correction factor was motivated by Scott, Srednicki and White (1994) as a fundamental property of sample variance for a partial sky, and is part of the standard CMB formalism (e.g. Bond, Efstathiou Tegmark 1997)." + For the NVSS geometry. fa=0.75. thus this correction corresponds to a LO per cent increase in the error.," For the NVSS geometry, $f_{\rm sky} = +0.75$, thus this correction corresponds to a $\sim 10$ per cent increase in the error." + ltadio sources have complex. morphologies and large linear sizes (up to and exceeding | Mpc)., Radio sources have complex morphologies and large linear sizes (up to and exceeding 1 Mpc). +" A radio-source catalogue such as the NWSS will contain entries which are cillerent components of the same galaxy (For example. the two racio lobes of a ""classical double” radio galaxv)."," A radio-source catalogue such as the NVSS will contain entries which are different components of the same galaxy (for example, the two radio lobes of a “classical double” radio galaxy)." + The broad angular resolution of the NVSS beam. leaves over 90. per cent of radio sources unresolved: however. the remaining multiple-component sources have a small but. measurable ellect on the angular power spectrum.," The broad angular resolution of the NVSS beam leaves over 90 per cent of radio sources unresolved; however, the remaining multiple-component sources have a small but measurable effect on the angular power spectrum." + lt ds relatively simple to model the effect of multiple-component sources on the estimator for C'; described. in Section 3.2.., It is relatively simple to model the effect of multiple-component sources on the estimator for $C_\ell$ described in Section \ref{secestharm}. + Phe relevant angular scales (£« 100) are much bigger than any component separation. and equation 4. can be replaced. by where Nica is the total number of galaxies and ce;is the number of components of the ‘th galaxy.," The relevant angular scales $\ell < 100$ ) are much bigger than any component separation, and equation \ref{eqalm} can be replaced by where $N_{\rm gal}$ is the total number of galaxies and $c_i$is the number of components of the $i$ th galaxy." + Phus the quantity is unchanged by the presence of multiple components (6 denotes the average number of components per galaxy. and N=GoNa ds the total number of catalogue entries. as in equation: 4)).," Thus the quantity is unchanged by the presence of multiple components $\overline{c}$ denotes the average number of components per galaxy, and $N = +\overline{c} \times N_{\rm gal}$ is the total number of catalogue entries, as in equation \ref{eqalm}) )." + But C77 TEMin equation: 5. depends on, But $C_{\ell m}^{\rm obs}$ in equation \ref{eqclpeeb} depends on +Using the barvochemical potential jo as a measure for the barvon density of the svstem (i.e. for the total number of barvons minus that of antibaryons. per unit volume). we (hen expect the phase diagram of QCD to have the general schematic form shown in relphase..,"Using the baryochemical potential $\mu$ as a measure for the baryon density of the system (i.e., for the total number of baryons minus that of antibaryons, per unit volume), we then expect the phase diagram of QCD to have the general schematic form shown in \\ref{phase}." + Given QCD as the fundamental theory of strong interactions. we can use the QCD Lagrangian as dvnamies input to derive the resulting (hermocdvnanucs of strongly interacting matter.," Given QCD as the fundamental theory of strong interactions, we can use the QCD Lagrangian as dynamics input to derive the resulting thermodynamics of strongly interacting matter." + For vanishing barvochemical potential. j£—0. this can be evaluated with the help of the lattice regularisation. leading to finite temperature lattice QCD.," For vanishing baryochemical potential, $\mu=0$, this can be evaluated with the help of the lattice regularisation, leading to finite temperature lattice QCD." + Belore turning to the study of strongly interacting matter in QCD. we illustrate (he transition from hadronnie matter to quark-gluon. plasma by a very simple model.," Before turning to the study of strongly interacting matter in QCD, we illustrate the transition from nic matter to quark-gluon plasma by a very simple model." + For an ideal gas of nmassless pions. (he pressure as Iunction of the temperature is given bv (the Stefan-Doltzmann form where the [actor 3 accounts for (he three charge states of the pion.," For an ideal gas of massless pions, the pressure as function of the temperature is given by the Stefan-Boltzmann form = 3 T^4 where the factor 3 accounts for the three charge states of the pion." + The corresponding form for an ideal quark-eluon plasma with (vo flavors and three colors is, The corresponding form for an ideal quark-gluon plasma with two flavors and three colors is = 2 8 + (3 2 2 2) T^4 - B = 37 T^4 - B. +BAO result.,BAO result. + We also show in Fig., We also show in Fig. + 3. the best-fit ratios of Dy when the SDSS-LESN data are simultaneously fit with he BAO data., \ref{fig_bao} the best-fit ratios of $\DV$ when the SDSS-II SN data are simultaneously fit with the BAO data. + Phe SN constraints dominate these results »ecause of their smaller uncertainty., The SN constraints dominate these results because of their smaller uncertainty. + In the following we use the famous reciprocity relation (Etherington1933:Ellis1971). or distance cluality to compare the SN and BAO «distance scales.," In the following we use the famous reciprocity relation \citep{1933PMag...15..761E, 1971grc..conf..104E}, or distance duality to compare the SN and BAO distance scales." + In. detail. the angular diameter distance and luminosity clistance are related by (for à discussion. see e.g. Bassett&Ixunz 2004)).," In detail, the angular diameter distance and luminosity distance are related by (for a discussion, see e.g, \citealt{2004PhRvD..69j1305B}) )." + This relation relies on photon conservation. but. holds for any geometry and any metric theory of gravity where photons follow null ecodesies.," This relation relies on photon conservation, but holds for any geometry and any metric theory of gravity where photons follow null geodesics." + Therefore. it is a general test of our uncerlsing assumptions about the nature of our Universe.," Therefore, it is a general test of our underlying assumptions about the nature of our Universe." + One might have expected that the distance duality relation has already been tightly constrained by observations of the blackbody. €MD spectrum. from the CODIS FILAS experiment (Alatheretal.|1994).., One might have expected that the distance duality relation has already been tightly constrained by observations of the blackbody CMB spectrum from the COBE FIRAS experiment \citep{1994ApJ...420..439M}. + However. this observation does not constrain ceviations from distance dualitv as 16 photon number may. not be conserved. (either through xoduction or loss of photons) or more radically. photons =nav not follow null geodesics.," However, this observation does not constrain deviations from distance duality as the photon number may not be conserved (either through production or loss of photons) or more radically, photons may not follow null geodesics." + Also. a grev dust component wt absorbed photons independent of frequency would not cause spectral distortions away from a blackbody in re CAIB since all frequencies would be alfected: equally.," Also, a grey dust component that absorbed photons independent of frequency would not cause spectral distortions away from a blackbody in the CMB since all frequencies would be affected equally." + However. this grey. dust would cause strong deviations from istance duality since it would make the luminosity distance o any objects larger while leaving the angular diameter istance unchanged.," However, this grey dust would cause strong deviations from distance duality since it would make the luminosity distance to any objects larger while leaving the angular diameter distance unchanged." + Another way to hice the distance duality effects from CAB observations would be to allect photon number only at much higher or lower frequencies iui the microwave., Another way to hide the distance duality effects from CMB observations would be to affect photon number only at much higher or lower frequencies than the microwave. + This is. for example. what was needed o make the axion-photon mixing proposal for the dimming of the SNeIa consistent with CAIB constraints. (C'saki.Ixaloper.&Terning 2002)..," This is, for example, what was needed to make the axion-photon mixing proposal for the dimming of the SNeIa consistent with CMB constraints \citep{2002PhRvL..88p1302C}." + ovond the CMD. several other analyses. using similar data to that discussed. herein. have reported. evidence for violations of distance duality at the ~2e. level (Bassett&WKunz2004:Lazkoz.NesserisPerivolaropoulos 2008)..," Beyond the CMB, several other analyses, using similar data to that discussed herein, have reported evidence for violations of distance duality at the $\sim 2\sigma$ level \citep{2004PhRvD..69j1305B, 2008JCAP...07..012L}." +. We revisit this issue here using a methodology. similar to that. outlined by More.Bovy.&Loge(2009)— and Avgoustidis.Verde.&Jimenez(2009) that does not rely on the absolute calibration of the distances to compute the ratio dg(z)/(daCz(1|237)., We revisit this issue here using a methodology similar to that outlined by \citet{2009ApJ...696.1727M} and \citet{2009JCAP...06..012A} that does not rely on the absolute calibration of the distances to compute the ratio $d_L(z)/(d_A(z)(1+z)^2)$. + Instead. we check the relative behaviour of this ratio as a function of redshift by testing the consistency of the ratio at two redshifts. z=0.2 and >=0.35 where we now have updated BAO measurements from Percivaletal.(2009).," Instead, we check the relative behaviour of this ratio as a function of redshift by testing the consistency of the ratio at two redshifts, $z=0.2$ and $z=0.35$ where we now have updated BAO measurements from \citet{2009arXiv0907.1660P}." +. In the following we parameterize the distance duality relation in what we call the a-mocdel as where a=00 represents the expected: distance. duality relation. and therefore à=0 indicates a possible violation.," In the following we parameterize the distance duality relation in what we call the $\alpha$ -model as where $\alpha=0$ represents the expected distance duality relation, and therefore $\alpha \ne 0$ indicates a possible violation." +" ‘To quantify the cliserepancy between the two measures. we replace Da, in Eq. (9))"," To quantify the discrepancy between the two measures, we replace $D_M$ in Eq. \ref{equation_dv}) )" + with d; from σα. (12)).," with $d_L$ from Eq. \ref{equation_duality}) )," + and derive the relation On the right-hand side. δν)Do(zo) is given by the BAO measurements. while ei(22)d(21) and ες(Lf(zs) have to be inferred from the SDSS-IE SN data.," and derive the relation On the right-hand side, $D_V(z_1)/D_V(z_2)$ is given by the BAO measurements, while $d_L^2(z_2)/d_L^2(z_1)$ and $H(z_1)/H(z_2)$ have to be inferred from the SDSS-II SN data." + We caleulate d; and H(z) using the two methocls introduced above., We calculate $d_L$ and $H(z)$ using the two methods introduced above. +" First. we use the results from the qu fitting. and subsequently we calculate d,(2.5) and {τι(ο) at redshifts of 0.2 and 0.35."," First, we use the results from the $q_0$ fitting, and subsequently we calculate $d_L(z, q_0)$ and $H(z, q_0)$ at redshifts of $0.2$ and $0.35$." + The parameter o. and its error. are then caleulated by Iq. (13)).," The parameter $\alpha$, and its error, are then calculated by Eq. \ref{equation_duality_test}) )." + We note that Eq., We note that Eq. + 13. probes the consistency. of the ralio at one redshift given the ratio at the other recdshift and is therefore not sensitive to any scaling proportional to (1.12)? but would be sensitive to any other loss function., \ref{equation_duality_test} probes the consistency of the ratio at one redshift given the ratio at the other redshift and is therefore not sensitive to any scaling proportional to $(1+z)^2$ but would be sensitive to any other loss function. + For the second. method. we use the sliding window echnique to derive Diay=casu]° (see Ίσα. (10)))," For the second method, we use the sliding window technique to derive $\vec{D}_{V,\;{\rm SN}} \equiv [zA^2_0 A_1] ^{1/3}$ (see Eq. \ref{eq_sliding_window}) ))" + and he corresponding covariance matrix at the two redshifts (20.2 and z= 0.35) where we have BAO measurements., and the corresponding covariance matrix at the two redshifts $z=0.2$ and $z=0.35$ ) where we have BAO measurements. + The best fit and error of à is calculated by applying Bayes heorem., The best fit and error of $\alpha$ is calculated by applying Bayes theorem. + In detail we mocel Dpao2Jbqpzy5DOSI at the two redshifts based on Iq.," In detail we model $\vec{D}_{V,\;{\rm BAO}}=\beta (1+z)^{2\alpha/3}\vec{D}_{V,\;{\rm SN}}$ at the two redshifts based on Eq." + 13. where <7 is a free scale xvwameter absorbing {ο and the scale of the sound horizon reat recombination.," \ref{equation_duality_test} + where $\beta$ is a free scale parameter absorbing $H_0$ and the scale of the sound horizon $r_s$ at recombination." + We then calculate the likelihood of the BAO £A measurements for a and. 2. by integrating over," We then calculate the likelihood of the BAO $\vec{D}_{V}$ measurements for $\alpha$ and $\beta$ , by integrating over" +by the stream flow. lending plausibility to the suggested origin (Meaburnetal.2005).,"by the stream flow, lending plausibility to the suggested origin \citep{Meaburn:2005}." + Paper [ argued that long thin tails are produced only when subsonic streams interact with subsonic mass injection (all Mach numbers are defined in the reference frame of the clump)., Paper I argued that long thin tails are produced only when subsonic streams interact with subsonic mass injection (all Mach numbers are defined in the reference frame of the clump). + Paper II dealt with the interactions of hypersonic and transonte streams with injected matter., Paper II dealt with the interactions of hypersonic and transonic streams with injected matter. + Pittardetal.(2005.henceforthPaperHl) investigated the interaction of hypersonic flows with multiple clumps and the interaction of transonic flows with two adjacent clumps., \citet[][henceforth Paper~III]{Pittard:2005} investigated the interaction of hypersonic flows with multiple clumps and the interaction of transonic flows with two adjacent clumps. + We will consider only single clump interactions although both photographs of tails and the recent estimate of 23000 cometary knots (Meixneretal.2005) suggest multiple clump interactions might occur in the Helix., We will consider only single clump interactions although both photographs of tails and the recent estimate of 23000 cometary knots \citep{Meixner:2005} suggest multiple clump interactions might occur in the Helix. + In Papers I to HII it was assumed that there was a large temperature contrast between a hot global flow and injected gas with the stream gas behaving adiabatically and the injected gas behaving tsothermally., In Papers I to III it was assumed that there was a large temperature contrast between a hot global flow and injected gas with the stream gas behaving adiabatically and the injected gas behaving isothermally. + Tail dynamics and morphology are determined by the thermal behaviour and temperature contrast of the stream and source gas as well as by the Mach number of the incident stream., Tail dynamics and morphology are determined by the thermal behaviour and temperature contrast of the stream and source gas as well as by the Mach number of the incident stream. + Paper IV investigates a broader range of incident Mach numbers and temperature contrasts using spherical clump geometry (Paper HII shows that the differences between spherical and cylindrical geometry are small)., Paper IV investigates a broader range of incident Mach numbers and temperature contrasts using spherical clump geometry (Paper III shows that the differences between spherical and cylindrical geometry are small). + Results are also given for the case where both stream and source gases behave isothermally., Results are also given for the case where both stream and source gases behave isothermally. + This is appropriate 1f the stream gas as well as the source gas is photoronized and we utilise these results here., This is appropriate if the stream gas as well as the source gas is photoionized and we utilise these results here. + Computational details are given in Papers III and IV., Computational details are given in Papers III and IV. + An important result from these new calculations is that identifiable long thin tails persist to appreciably higher Mach number interactions than suggested in Papers I and IL., An important result from these new calculations is that identifiable long thin tails persist to appreciably higher Mach number interactions than suggested in Papers I and II. + This is quantified in Paper IV., This is quantified in Paper IV. + Mass loss from the clumps in the Helix is due to photoionization., Mass loss from the clumps in the Helix is due to photoionization. + Clump images show the mass injection is strongest in the direction towards the central star., Clump images show the mass injection is strongest in the direction towards the central star. + In Paper III it was shown that anisotropic mass injection made very little difference to the flow morphology in the case of a hypersonic wind interacting with source material., In Paper III it was shown that anisotropic mass injection made very little difference to the flow morphology in the case of a hypersonic wind interacting with source material. + Comparison of. tail structures for subsonic and transonic stream interactions where there Is anisotropic injection is given in Paper IV., Comparison of tail structures for subsonic and transonic stream interactions where there is anisotropic injection is given in Paper IV. + Results for a mass injection rate contrast of 20:1 (front to rear) show small differences in the tail morphologies and tail velocity structures between the isotropic and anisotropic cases once the flow has gone a few injection radii., Results for a mass injection rate contrast of 20:1 (front to rear) show small differences in the tail morphologies and tail velocity structures between the isotropic and anisotropic cases once the flow has gone a few injection radii. + We use results for isotropic mass injection here., We use results for isotropic mass injection here. + Although the models of Paper IV are far more extensive than previously given. they have still à major simplification.," Although the models of Paper IV are far more extensive than previously given, they have still a major simplification." + They contain only two gas phases (stream and injected gas) which may mix., They contain only two gas phases (stream and injected gas) which may mix. + The Helix tails possibly represent a three phase system that includes ionised stream gas and both neutral and ionised injected gas (e.g..O'Dell&Handron1996;O'Dell 2000).," The Helix tails possibly represent a three phase system that includes ionised stream gas and both neutral and ionised injected gas \citep[e.g.,][]{ODell:1996,ODell:2000}." +. To treat this properly requires the inclusion of radiation transfer. Meaburnetal.," To treat this properly requires the inclusion of radiation transfer. \citet{Meaburn:1998}," +(1998)... ΟΡε(2000) and Meaburnetal.(2005) have shown that it is likely that clumps are overrun by photoionized gas that may be tonized AGB wind possibly contaminated with evaporated knot gas., \citet{ODell:2000} and \citet{Meaburn:2005} have shown that it is likely that clumps are overrun by photoionized gas that may be ionized AGB wind possibly contaminated with evaporated knot gas. + We consider tail formation in an interaction where photoionized gas overruns clumps that lose material by photoionization., We consider tail formation in an interaction where photoionized gas overruns clumps that lose material by photoionization. + An tsothermal-isothermal assumption for the thermal behaviour of the stream and source gas Is appropriate., An isothermal-isothermal assumption for the thermal behaviour of the stream and source gas is appropriate. + It is unlikely in general that the clumps are being overrun by the very hot He gas since the clumps have an average outward velocity of 14kms7! (Meaburnetal.1998) and the hot gas is dynamically inert with an expansion velocity of less than 11.kms7! (Meaburnetal.2005)., It is unlikely in general that the clumps are being overrun by the very hot $^{++}$ gas since the clumps have an average outward velocity of $14\;\kmps$ \citep{Meaburn:1998} and the hot gas is dynamically inert with an expansion velocity of less than $11\;\kmps$ \citep{Meaburn:2005}. +. On the other hand. there might be clumps that are overrun by this hot gas since the velocity dispersion of the knots is around 6—8kms! (Μεαρetal.1998).," On the other hand, there might be clumps that are overrun by this hot gas since the velocity dispersion of the knots is around $6-8\;\kmps$ \citep{Meaburn:1998}." +. The temperature contrast between the stream gas and injected gas may be high., The temperature contrast between the stream gas and injected gas may be high. + O'Dell(1998) suggests that the temperature of the He gas is in excess of 2x107K (because of the lack of O77 cooling)., \citet{ODell:1998} suggests that the temperature of the $^{++}$ gas is in excess of $2 \times 10^{4}\;{\rm K}$ (because of the lack of $^{++}$ cooling). + Henryetal.(1999) have modelled the ionization structure of the nebula and shown that the gas temperature drops from about 4x10K near the star to 107K at a distance where helium is about in the form of , \citet{Henry:1999} have modelled the ionization structure of the nebula and shown that the gas temperature drops from about $4 \times 10^{4}\;{\rm K}$ near the star to $10^{4}\;{\rm K}$ at a distance where helium is about in the form of $^{++}$. +He Meaburnetal.(1998) and Meaburnetal.(2005). favour the overrunning of clumps by expanding photoionized gas in the region where [OIL] is emitted., \citet{Meaburn:1998} and \citet{Meaburn:2005} favour the overrunning of clumps by expanding photoionized gas in the region where [OIII] is emitted. + This gas has a temperature of about 10K (Henryetal.1999).. and is overrunning the clumps with a velocity of about 17kms! relative to the clump global expansion velocity of 14.kms-l," This gas has a temperature of about $10^{4}\;{\rm K}$ \citep{Henry:1999}, and is overrunning the clumps with a velocity of about $17\;\kmps$ relative to the clump global expansion velocity of $14\;\kmps$." + The temperature of gas injected from the source is uncertain., The temperature of gas injected from the source is uncertain. + O'Delletal.(2005) note that the temperature of photoionized gas flowing from à clump towards the star decreases outwards from the density peak just behind. the ionisation front on the clump surface., \citet{ODell:2005} note that the temperature of photoionized gas flowing from a clump towards the star decreases outwards from the density peak just behind the ionisation front on the clump surface. + Some injection will occur from the sides of clumps where the diffuse radiation field softens the average photon energy leading to gas temperatures that could be a factor of around 2 lower than the temperature of gas excited by the direct radiation field (VanBlerkom&Army1972:Cantoetal. 1998).," Some injection will occur from the sides of clumps where the diffuse radiation field softens the average photon energy leading to gas temperatures that could be a factor of around 2 lower than the temperature of gas excited by the direct radiation field \citep{VanBlerkom:1972,Canto:1998}." +. As a reasonable range for the temperatures we use calculations from Paper IV. for ratios of isothermal sound speeds (cs/c;. stream gas to injected gas) of L:] (equal temperatures) and 2:1 (a temperature ratio of 4:1).," As a reasonable range for the temperatures we use calculations from Paper IV for ratios of isothermal sound speeds $c_{\rm S}/c_{\rm i}$, stream gas to injected gas) of 1:1 (equal temperatures) and 2:1 (a temperature ratio of 4:1)." + In Fig., In Fig. + | we give tail density structures for a sound speed ratio of 2:1 for incident stream Mach numbers M=1.2.4.," \ref{fig:rho1} we give tail density structures for a sound speed ratio of 2:1 for incident stream Mach numbers $M=1,2,4$." + In Fig., In Fig. + 2. we give the same information for a sound speed ratio 1:1., \ref{fig:rho2a} we give the same information for a sound speed ratio 1:1. + However a sound speed ratio of unity gives a tail density effectively the same as that of the stream and the plots of Fig., However a sound speed ratio of unity gives a tail density effectively the same as that of the stream and the plots of Fig. + 2. therefore do not show systematic tail structure., \ref{fig:rho2a} therefore do not show systematic tail structure. + The results of Paper IV demonstrate that the injected gas maintains its identity and there is very little mixing between it and stream gas., The results of Paper IV demonstrate that the injected gas maintains its identity and there is very little mixing between it and stream gas. + So to show this. we plot in Fig.," So to show this, we plot in Fig." + 3 the advected scalar that distinguishes between the stream and injected gases., \ref{fig:rho2b} the advected scalar that distinguishes between the stream and injected gases. + A recognisable tail of injected gas is embedded in stream σας., A recognisable tail of injected gas is embedded in stream gas. +whether the dillerences between emission anc absorption could be due simply (to small scale structure in the interstellar mecium (Faison and Goss 2001. Deshpande 2000).,"whether the differences between emission and absorption could be due simply to small scale structure in the interstellar medium (Faison and Goss 2001, Deshpande 2000)." + To get around (his problem requires an enission-absorption study using (hie smallest possible bean size for (he emission and using background sources which are relatively large. if possible (he same size as the beam.," To get around this problem requires an emission-absorption study using the smallest possible beam size for the emission and using background sources which are relatively large, if possible the same size as the beam." + The new mosaic survevs of the Galactic plane. combining single dish and interlerometer data. allow this for the first time.," The new mosaic surveys of the Galactic plane, combining single dish and interferometer data, allow this for the first time." + The Southern Galactic Plane Survey (8GP5. MeClure-Griffiths et al.," The Southern Galactic Plane Survey (SGPS, McClure-Griffiths et al." + 2000) and the Canadian Galactic Plane Survey (CGPS. Taylor et al.," 2000) and the Canadian Galactic Plane Survey (CGPS, Taylor et al." + 2002. Strasser et al.," 2002, Strasser et al." + 2002) provide good cqualitv emission-absorption spectrum pairs using extended. eontiniun sources at low latitudes. with a beam small enough to mitigate the effects of variations in (he emission and absorption over small angles.," 2002) provide good quality emission-absorption spectrum pairs using extended continuum sources at low latitudes, with a beam small enough to mitigate the effects of variations in the emission and absorption over small angles." + In (his paper we concentrate on a small. test region of the SGPS (MeClIure-Grifliths et al.," In this paper we concentrate on a small, test region of the SGPS (McClure-Griffiths et al." +" 2001) which has been mapped at relatively high resolution (FWIIM 90"")).", 2001) which has been mapped at relatively high resolution (FWHM ). + Over the next vear maps of the rest of the 72210 square degrees of (he GPS with similar resolution will become available. which will provide some 30 times the number of background sources as (hose considered here.," Over the next year maps of the rest of the $\sim$ 210 square degrees of the SGPS with similar resolution will become available, which will provide some 30 times the number of background sources as those considered here." + The purpose of this paper is to test methods of analvsing the emission- spectrum pairs. aud their interpretation.," The purpose of this paper is to test methods of analysing the emission-absorption spectrum pairs, and their interpretation." + The next section (2) discusses the best wav to obtain the spectra from the data., The next section (2) discusses the best way to obtain the spectra from the data. + We then consider what the absorption spectra alone tell us about (he opacity of (he ISM in the inner galaxy. (section 3)., We then consider what the absorption spectra alone tell us about the opacity of the ISM in the inner galaxy (section 3). + Then comes the tricky question of how best to combine the information from the emission and absorption spectra to estimate (he spin temperatures of (he cool clouds (section 4)., Then comes the tricky question of how best to combine the information from the emission and absorption spectra to estimate the spin temperatures of the cool clouds (section 4). + We consider several fitting techniques (hat parallel approaches used in past studies at intermediate latitudes., We consider several fitting techniques that parallel approaches used in past studies at intermediate latitudes. + Finally we discuss the implications of the spin temperature distribution for observable quantities like the peak brishtiess temperature of the emission ancl self-absorption (section 5)., Finally we discuss the implications of the spin temperature distribution for observable quantities like the peak brightness temperature of the emission and self-absorption (section 5). + The 21-cmn line is one of the only transitions in the entire electromagnetic spectrum for which emission aud absorption are both relatively easy to detect [rom the same region., The 21-cm line is one of the only transitions in the entire electromagnetic spectrum for which emission and absorption are both relatively easy to detect from the same region. + The two fundamental spectra are the brightness temperature of the emission. Z5(0). ancl the optical depth. το).," The two fundamental spectra are the brightness temperature of the emission, $T_B(v)$, and the optical depth, $\tau (v)$." +" Where there is no background continuum we observe 7, directly. ancl toward an extremely strong background source we observe 7 with negligable contribution from the emission. but toward most continuum sources we see a mixture of emission ancl absorption."," Where there is no background continuum we observe $T_B$ directly, and toward an extremely strong background source we observe $\tau$ with negligable contribution from the emission, but toward most continuum sources we see a mixture of emission and absorption." + This section deals with the optimum method for obtaining Z5 aud 7 [rom the survey cata., This section deals with the optimum method for obtaining $T_B$ and $\tau$ from the survey data. + There are alwavs more weak background sources than strong ones: to get as many absorption spectra as possible in a given area we need to find (he most effective wav to extract, There are always more weak background sources than strong ones; to get as many absorption spectra as possible in a given area we need to find the most effective way to extract +erating.,grating. + The nominal dispersion for this configuration is ~0.5 AX/fpixel. while measurements of the FWILAL of are lines indicate a spectral resolution of zL4 aat AL5O0A.," The nominal dispersion for this configuration is $\sim + 0.5$ /pixel, while measurements of the FWHM of arc lines indicate a spectral resolution of $\approx 1.4$ at $\sim \lambda4500$." +. Phe blue spectra are shown in Figures 6 and 7., The blue spectra are shown in Figures 6 and 7. + For RA J0544.1.7100 the LL? line has an equivalent width of EW = -0.20+0., For RX J0544.1–7100 the $\beta$ line has an equivalent width of EW = $\pm$. +02.4.. The spectrum of the optical counterpart to RA JO544.1-7100 in the classification region is displaved in Figure 6. together with that of the BOY standard v Ori.," The spectrum of the optical counterpart to RX J0544.1-7100 in the classification region is displayed in Figure 6, together with that of the B0V standard $\nu$ Ori." + The spectrum of a Be star of similar spectral class is included for comparison., The spectrum of a Be star of similar spectral class is included for comparison. + This is LID 161103. &iven as DO.51LHI-Ve by Steele et al. (," This is HD 161103, given as B0.5III-Ve by Steele et al. (" +1999).,1999). + Though the spectrum. of RA 700. has a low signal-to-noise ratio. photospheric lines are relatively clear and strong shortwards of 4200A.," Though the spectrum of RX $-$ 700 has a low signal-to-noise ratio, photospheric lines are relatively clear and strong shortwards of $\sim 4200$." +. Weak ALOSOA aand A4686;V iindicate that the spectral type of RX J0544.1-7100. as in most counterparts to De/X-ray binaries. is close to DO.," Weak $\lambda4089$ and $\lambda4686$ indicate that the spectral type of RX J0544.1-7100, as in most counterparts to Be/X-ray binaries, is close to B0." + Since this lines are weak and A4200 LIs not present. the star cannot be earlier.," Since this lines are weak and $\lambda4200$ is not present, the star cannot be earlier." + Phe weakness of 10 triplet and. shows that it is not an evolved star., The weakness of the triplet and shows that it is not an evolved star. + Since the presence of lines indicates a spectral tvpe earlier than 130.5. we classify the optical counterpart to RN J0544.1-7100 as DOV. with an uncertainty of half a Es»ectral subtype (due to the low SNR).," Since the presence of lines indicates a spectral type earlier than B0.5, we classify the optical counterpart to RX J0544.1-7100 as B0V, with an uncertainty of half a spectral subtype (due to the low SNR)." + If we assume this spectral class of DOV then we can letermine the line of sight extinction to our source [ron 16 photometry in Table 1., If we assume this spectral class of B0V then we can determine the line of sight extinction to our source from the photometry in Table 1. + A star of this spectral type has absolute magnitudes of B=4.3. V=4.0 and R=3.87.," A star of this spectral type has absolute magnitudes of B=–4.3, V=–4.0 and R=–3.87." + The distance modulus to the LMC is [8.50.2 magnituces (Westerlind 1997)., The distance modulus to the LMC is $\pm$ 0.2 magnitudes (Westerlund 1997). + In order to get agreement between a reddened version of these photometric magnitudes ancl our observations it is necessary to assume L(B-V)=0.26£0.06., In order to get agreement between a reddened version of these photometric magnitudes and our observations it is necessary to assume $\pm$ 0.06. + If we also consider the uncertainty of a half sub-class in the spectral type. then this uncertainty could be as large as 0.08.," If we also consider the uncertainty of a half sub-class in the spectral type, then this uncertainty could be as large as 0.08." + Schwering Israel (1991) quote a foreground reddening to the LMC in the range 0.07 to 0.17 and from their Figure Th it can be seen that RN JO544.1-7100 lies in the region of highest reddenine where E(B-V)~0.15., Schwering Israel (1991) quote a foreground reddening to the LMC in the range 0.07 to 0.17 and from their Figure 7b it can be seen that RX J0544.1-7100 lies in the region of highest reddening where $\sim$ 0.15. + Our result. is consistent within errors with their value., Our result is consistent within errors with their value. + I£ the redeeninge to this svsten proves to be higher than expected then some of this may be accounted for [rom local cireumstellar extinction around the Be star., If the reddening to this system proves to be higher than expected then some of this may be accounted for from local circumstellar extinction around the Be star. + Using the Lla EW = and Equation 5 from Fabregat Torrejon (1998). we can estimate that £°°(B- V)=0.03.," Using the $\alpha$ EW = and Equation 5 from Fabregat Torrejon (1998), we can estimate that $E^{cs}$ (B-V)=0.03." + Interestingly. the Ht photometry presented. here [rom the PALASS survey indicate more than just a hieh level of interstellar redcdening.," Interestingly, the IR photometry presented here from the 2MASS survey indicate more than just a high level of interstellar reddening." + Phe intrinsic (JIx) for a DOV star is -0.23. where as we have an observed. value of -0.01.," The intrinsic (J–K) for a B0V star is -0.23, where as we have an observed value of -0.01." +. Using our value of E(BV)20.26 gives E(J.Ix)20.14. and hence a predieted observed value of (J)Ix)—-0.09.," Using our value of E(B–V)=0.26 gives E(J–K)=0.14, and hence a predicted observed value of (J–K)=-0.09." + Though the errors on the 2ALASS values. especially Ix. are rather Large. there is à suggestion of further reddening in the Lt band arising from the presence of a circumstellar disk.," Though the errors on the 2MASS values, especially K, are rather large, there is a suggestion of further reddening in the IR band arising from the presence of a circumstellar disk." + On the question of LMC membership there can be little doubt that this system lies in the LMC., On the question of LMC membership there can be little doubt that this system lies in the LMC. + Ehe position of the Ilo emission line corresponds to a red shift of 2284-45 kms. and the redshift of the absorption lines in the blue spectrum to an average value of 22080 km/s. Both of these data sets are consistent with LMC membership (for example. Fischer. Weleh Mateo (1993) quote a mean velocity for a cluster in the LMC of 25142 kmj/s)," The position of the $\alpha$ emission line corresponds to a red shift of $\pm$ 45 km/s, and the redshift of the absorption lines in the blue spectrum to an average value of $\pm$ 80 km/s. Both of these data sets are consistent with LMC membership (for example, Fischer, Welch Mateo (1993) quote a mean velocity for a cluster in the LMC of $\pm$ 2 km/s)." + ]t is almost certain that the largest peak in the OGLE power spectrum (at 286d) reflects the global changes taking place in the luminosity., It is almost certain that the largest peak in the OGLE power spectrum (at 286d) reflects the global changes taking place in the luminosity. + The total data run is only approximately 900cL. so it is not really long cnough to claim that a ~300el period. could. be a coherent modulation in any convincing manner.," The total data run is only approximately 900d, so it is not really long enough to claim that a $\sim$ 300d period could be a coherent modulation in any convincing manner." + It is much more likely that the Ποιαος seen are similar to those seen in other Be stars., It is much more likely that the fluctuations seen are similar to those seen in other Be stars. + Certainly the two relatively deep minima at PJD ~1290 and. 71600 will be providing a lot of the power seen around. 7300d., Certainly the two relatively deep minima at TJD $\sim$ 1290 and $\sim$ 1600 will be providing a lot of the power seen around $\sim$ 300d. + The only detection of this source in X-ray has been reported bv Schmidtke et al (1994)., The only detection of this source in X-ray has been reported by Schmidtke et al (1994). + Their ROSATLT observations were carried out on 11 Feb 1991 which. interestingly. correspond toa binary phase of 0.90 (phase 0.0 has been defined here as the peak optical Hus).," Their ROSAT observations were carried out on 11 Feb 1991 which, interestingly, correspond to a binary phase of 0.90 (phase 0.0 has been defined here as the peak optical flux)." + In addition. Schmidtke et al (1999) report a non-detection by ROSAT at binary phase 0.58 (22 July 1995).," In addition, Schmidtke et al (1999) report a non-detection by ROSAT at binary phase 0.58 (22 July 1995)." + Consequently it is possible that the N-ray. flux is modulated in the same manner as the optical. though the evidence so far is rather sparse.," Consequently it is possible that the X-ray flux is modulated in the same manner as the optical, though the evidence so far is rather sparse." + In the case of RA J0520.5-6932 the optical modulation, In the case of RX J0520.5-6932 the optical modulation +and non-Gaussian simulations which will be performed. in next section we will compute the first. cumulants of the coellicients. of. the two spherical wavelets considered. in this paper for the HIIEALI'ix. scheme.,and non-Gaussian simulations which will be performed in next section we will compute the first cumulants of the coefficients of the two spherical wavelets considered in this paper for the HEALPix scheme. + For the SLAW the coellicients correspond. to three dillerent. details: diagonal. vertical and horizontal.," For the SHW the coefficients correspond to three different details: diagonal, vertical and horizontal." + Since those details are. directly obtained from linear operations of the four neighbour pixels (as we saw in the previous section) and pixels are not equally separated. all over the sphere. correlations present in the emperature fuctuations make the wavelet. coefficients. to oe biased.," Since those details are directly obtained from linear operations of the four neighbour pixels (as we saw in the previous section) and pixels are not equally separated all over the sphere, correlations present in the temperature fluctuations make the wavelet coefficients to be biased." +" ""This bias produces a peaked distribution with respect to a Gaussian and therefore a positive kurtosis in the hree details of the SII. coellicients even for temperature realizations derived from normal distributions (as can be seen from table 1. the mean value of the kurtosis for the inest resolution of the Gaussian model is displaced. about 10σ from zero)."," This bias produces a peaked distribution with respect to a Gaussian and therefore a positive kurtosis in the three details of the SHW coefficients even for temperature realizations derived from normal distributions (as can be seen from table 1, the mean value of the kurtosis for the finest resolution of the Gaussian model is displaced about $10\sigma$ from zero)." + In the case of the SAILIW we only have à type of coefficients. for cach scale., In the case of the SMHW we only have a type of coefficients for each scale. + Since this is a continuous. rotationally invariant wavelet -and thus not adapted to the pixelisation- no bias is produced in this case.," Since this is a continuous, rotationally invariant wavelet -and thus not adapted to the pixelisation- no bias is produced in this case." + The discriminating power of the spherical wavelets will be tested using Gaussian. and non-Gaussian simulations with different amounts of either skewness or kurtosis introduced using the Edgeworth expansion. and normalized to a power Esjxectrum C consistent with observations (as cliscussecl bove).," The discriminating power of the spherical wavelets will be tested using Gaussian and non-Gaussian simulations with different amounts of either skewness or kurtosis introduced using the Edgeworth expansion, and normalized to a power spectrum $C_l$ consistent with observations (as discussed above)." + Since the skewness and kurtosis are introclucecl at 10 highest resolution through the Ecleeworth expansion (as described. above). we expect to detect them with the gakewness and kurtosis of the spherical wavelet: coefficients uso at the highest resolutions.," Since the skewness and kurtosis are introduced at the highest resolution through the Edgeworth expansion (as described above), we expect to detect them with the skewness and kurtosis of the spherical wavelet coefficients also at the highest resolutions." + Thus we will consider for 1ο analysis the first five resolution scales starting [from the inest one., Thus we will consider for the analysis the first five resolution scales starting from the finest one. + The scales go as powers of 2 for the SIIW. and or comparison we choose the same values for the ΟΛΗΙΑΝ) xwameter A: 1.2.4.8 and 16 pixels.," The scales go as powers of 2 for the SHW and for comparison we choose the same values for the SMHW parameter $R$: 1, 2, 4, 8 and 16 pixels." + We can relate the scales of the two wavelets by looking to the scaling functions., We can relate the scales of the two wavelets by looking to the scaling functions. + The relation between the side. s. of the step function (scaling ‘unction for the Haar wavelet) and the dispersion /? of the Gaussian is: 5= v2zHR.," The relation between the side, $s$, of the step function (scaling function for the Haar wavelet) and the dispersion $R$ of the Gaussian is: $s=\sqrt{2\pi} R$ ." + Then. for the finest scale s=2 jxels. which corresponds to an 2z0.5 pixels which is approximately 1 pixel.," Then, for the finest scale $s=2$ pixels, which corresponds to an $R\approx 0.8$ pixels which is approximately 1 pixel." + Results obtained in Fourier space are equivalent to hose obtained in real space if the functions. considered are bandwidth limited GQvith the bandwidth included. in he one covered by the. pixelisation)., Results obtained in Fourier space are equivalent to those obtained in real space if the functions considered are bandwidth limited (with the bandwidth included in the one covered by the pixelisation). + We have checked his for the finest resolution of the SMIIW., We have checked this for the finest resolution of the SMHW. + The average difference between the SALLI coellicients. computed by direct. convolution in real space and going to Fourier space is <1K., The average difference between the SMHW coefficients computed by direct convolution in real space and going to Fourier space is $< 1\%$. + Given the 5 values of skewness or kurtosis corresponding to the 5 resolution scales for the SMIEIN and the 15 values for the SLIW (5 scales for. each of the 3. details). we would like to construct a test statistic which. combining all this information. can best distinguish. between the two hypotheses: a) fy: the data are drawn from a Ciaussian model. b) £44: the data are drawn from a non-Caussian model with either skewness or kurtosis.," Given the 5 values of skewness or kurtosis corresponding to the 5 resolution scales for the SMHW and the 15 values for the SHW (5 scales for each of the 3 details), we would like to construct a test statistic which, combining all this information, can best distinguish between the two hypotheses: a) $H_0$ : the data are drawn from a Gaussian model, b) $H_1$: the data are drawn from a non-Gaussian model with either skewness or kurtosis." + The best test statistic in the sense of maximum power for à given significance level is given by the likelihood ratio: where fGr|H4) and Ην). are the pdf of the data given hypotheses {4ο and £1. respectively.," The best test statistic in the sense of maximum power for a given significance level is given by the likelihood ratio: where $f(\vec{x}|H_0)$ and $f(\vec{x}|H_1)$ are the pdf of the data given hypotheses $H_0$ and $H_1$, respectively." + Since we do not know those multivariate pdLÁs and would be tremendously costly in cpu time to determine them by Monte: Carlo simulations. we use as test statistic the simpler Fisher linear discriminant function (Fisher 1936: see also Cowan 1998).," Since we do not know those multivariate pdf´s and would be tremendously costly in cpu time to determine them by Monte Carlo simulations, we use as test statistic the simpler Fisher linear discriminant function (Fisher 1936; see also Cowan 1998)." + This discriminant has been recently used. by Barreiro. and Ilobson (2001) to study the cliscriminanting power of planar wavelets to detect non-Gaussianity in the CAIB in small patches of the sky., This discriminant has been recently used by Barreiro and Hobson (2001) to study the discriminanting power of planar wavelets to detect non-Gaussianity in the CMB in small patches of the sky. + The Fisher cliscriminant is a linear function of the data that maximizes the distance between the two pdfs. g(fHo) Εμ such a distance defined asthe ratio (76.τινιEaD;|a}.," The Fisher discriminant is a linear function of the data that maximizes the distance between the two pdf's, $g(t|H_0)$ and $g(t|H_1)$, such a distance defined as the ratio $(\tau_0-\tau_1)^2/(\Sigma_0^2+\Sigma_1^2)$." + PS LokE =0.1. are the mean and the variance of ο). respectively.," $\tau_k$ and $\Sigma_k^2$, $k=0,1$, are the mean and the variance of $g(t|H_k)$, respectively." + The Fisher discriminant is given by: with WM—vay|Vi and Vy the covariance matrix and £i the mean values of ΗΕ)., The Fisher discriminant is given by: with $W=V_0+V_1$ and $V_k$ the covariance matrix and $\vec\mu_k$ the mean values of $f(\vec{x}|H_k)$. +" In the particular case that ""Filo) and 111} are both multidimensional Gaussians with the same covariance matrix. the Fisher discriminant is equivalent to the likelihood ratio."," In the particular case that $f(\vec{x}|H_0)$ and $f(\vec{x}|H_1)$ are both multidimensional Gaussians with the same covariance matrix, the Fisher discriminant is equivalent to the likelihood ratio." + The mean values and covariance matrices of the skewness and kurtosis at each resolution level for the Gaussian and non-Gaussian models are. obtained from a large number of simulations., The mean values and covariance matrices of the skewness and kurtosis at each resolution level for the Gaussian and non-Gaussian models are obtained from a large number of simulations. + In the next section we use those simulations to compare the power of the test p—1.3 to discriminate against the alternative hypothesis ff) at à given significance level à for the two spherical wavelets.," In the next section we use those simulations to compare the power of the test $p\equiv +1-\beta$ to discriminate against the alternative hypothesis $H_1$ at a given significance level $\alpha$ for the two spherical wavelets." + à and 3 account for the probability of rejecting the null hvpothesis lio when it is actually true (error of the first kind) and the probability of accepting Ly when the true hypothesis is Lf and not ffy (error of the second. kind). respectively.," $\alpha$ and $\beta$ account for the probability of rejecting the null hypothesis $H_0$ when it is actually true (error of the first kind) and the probability of accepting $H_0$ when the true hypothesis is $H_1$ and not $H_0$ (error of the second kind), respectively." +" The decision to accept or reject {4ο is done by defining a critical region for the statistic /: if the value off is greater than a cut value fo, the hypothesis Ly is rejected.", The decision to accept or reject $H_0$ is done by defining a critical region for the statistic $t$; if the value of $t$ is greater than a cut value $t_{cut}$ the hypothesis $H_0$ is rejected. + Thus. a and 3are given by: ‘Thiskind of analysis is very much along the lines of the one performed by Barreiro and. Hobson. (2001) for planar wavelets.," Thus, $\alpha$ and $\beta$are given by: Thiskind of analysis is very much along the lines of the one performed by Barreiro and Hobson (2001) for planar wavelets." + From now on a value for the sensitivity of a=1% will be adopted., From now on a value for the sensitivity of $\alpha=1\%$ will be adopted. +"in the dense. helimnianich. atinosphiere results in a sienificant decrease in the clissociation fraction of molecular hivdrogeu. with a corresponding chauge inthe IL,Πο Collision-Diduced Absorption (CTA) opacity, Which is linoar function of my.","in the dense, helium-rich atmosphere results in a significant decrease in the dissociation fraction of molecular hydrogen, with a corresponding change in the $\rm H_{2}-He$ Collision-Induced Absorption (CIA) opacity, which is linear function of $n_{\rm H_{2}}$." +" Tn section 3. we illustrate the impact of the interactions on the To/TMi ratio on a sequence of white dwarf atmosphere models with τμ= (0001. a eravitv of logy=8 (ces). aud a homogeucous composition of Πο/Π=107.104.and100, where He/II is the uunmnber abundance ratio."," In section 3, we illustrate the impact of the interactions on the $\rm H_{2}/H \,\textrm{\scriptsize{I}}$ ratio on a sequence of white dwarf atmosphere models with $T_{\rm eff}\rm=4000 \, K$ , a gravity of $\rm log \ \it g \rm = 8$ (cgs), and a homogeneous composition of ${\rm He/H} =10^{2},10^{4}, \ \rm and \ 10^{6}$, where He/H is the number abundance ratio." + The condition for chemical equilibrium (at a eiven density aud temperature) for the dissociation reaction: is given by (Cox&Ciuli1968) where µε is a chemical poteutial ofthe species íi expressed as Iu the above equation. Ay is the Doltzuiuun constant. / the Planck coustaut. Z the temperature.5 Ly; the ground state euerev. s; the number density. Z; the unperturbed internal partition function. and 50; is the mass.," The condition for chemical equilibrium (at a given density and temperature) for the dissociation reaction: is given by \citep{CG} + where $\mu_{i}$ is a chemical potential ofthe species $i$ expressed as In the above equation, $k_{B}$ is the Boltzmann constant, $h$ the Planck constant, $T$ the temperature, $E_{0,i}$ the ground state energy, $n_{i}$ the number density, $Z_i$ the unperturbed internal partition function, and $m_{i}$ is the mass." + The first two terms on the r.l.s., The first two terms on the r.h.s. + of equation (3)) represeut the ideal conutributious of ranslational aud imternal degrees of freedom auk nonidd is the non-ideal contribution to the chemical potential arising from the interparticle interactions im the fluid., of equation \ref{91}) ) represent the ideal contributions of translational and internal degrees of freedom and $\mu_{i}^{non-id}$ is the non-ideal contribution to the chemical potential arising from the interparticle interactions in the fluid. +" Setting:Dos pr;Q,""UOndd= (we recover the standard Sala equation for dissociation of molecular hydrogen: where Dy=2Eyqg,LuinLltscV is the dissociation cncrev of the isolated hydrogen molecule."," Setting $\mu_{i}^{non-id}\rm =0$ we recover the standard Saha equation for dissociation of molecular hydrogen: where $D_{0}=2E_{0,\rm H\,\textrm{\tiny{I}}}-E_{0,\rm H_{2}}=\rm 4.478 \, eV$ is the dissociation energy of the isolated hydrogen molecule." + Even for trace species. Like Ili or IL. in deuse helimu. the 45nondd which arise from interactions with the atoms are not neglieible aud in principle should be comparable iu macuitucde to annondd," Even for trace species, like $\rm H\,\textrm{\scriptsize{I}}$ or $\rm H_{2}$ in dense helium, the $\mu_{i}^{non-id}$ which arise from interactions with the atoms are not negligible and in principle should be comparable in magnitude to $\mu_{He}^{non-id}$." + If we define the quantity AZ as the non-ideal equilibrium equation can be written in the followiug form Comparing CE) with (6)). we see that the nou-ideal effects ou the dissociation equilibria caube interpreted as à change in the dissociation ΟΠΟΙΟΥ wea value of AI.," If we define the quantity $\Delta I$ as the non-ideal equilibrium equation can be written in the following form Comparing \ref{3}) ) with \ref{6}) ), we see that the non-ideal effects on the dissociation equilibrium can be interpreted as a change in the dissociation energy by a value of $\Delta I$." + For simplicity. we will follow his interpretation hereafter.," For simplicity, we will follow this interpretation hereafter." + We curphasize that lis description of the nou-ideal contribution to he chemical equilibrium (Eq., We emphasize that this description of the non-ideal contribution to the chemical equilibrium (Eq. +" 6) isidentical tothe occupation probabilitv formalism, of Hunuucr&Alibalas(1988). if there is only one bouud state in he partition function (e.g. low temperature Ii) or if the gnonhjdd is the same for all bound states J: of: the Sryspecies ([ (Qu?nondd=ΗΕτνfn;| rendus constant in Eq.(2.17) of Ihunununer&Ἁπμαίας (1988)))."," 6) is tothe occupation probability formalism of \citet{HM} if there is only one bound state in the partition function (e.g. low temperature $\rm H \, \textrm{\scriptsize{I}}$ ) or if the $\mu_{i,j}^{non-id}$ is the same for all bound states $j$ of the species $i$ $\mu_{i,j}^{non-id}=\partial f(V,T,{n_{i,j}})/\partial n_{i,j}$ remains constant in Eq.(2.17) of \citet{HM}) )." +" In. both cases. he occupation probability cau be factored out of the partition function aud written as ¢AtkoT (Ba,"," In both cases, the occupation probability can be factored out of the partition function and written as $e^{-\Delta I/k_BT}$ (Eq." +" 6),", 6). + Tu the atinosphere of cool white dwarts. hydrogen exist nmostlv asΠο aud ΤΠ and the Τι1. ratio is governed by reaction (1)) only.," In the atmosphere of cool white dwarfs, hydrogen exist mostly as$\rm H_2$ and $\rm H\,\textrm{\scriptsize{I}}$ , and the $\rm H\,\textrm{\scriptsize{I}}/H_2$ ratio is governed by reaction \ref{1}) ) only." + For a eiven temperature. deusitv p. aud the atinosphere composition gy= Πο. the nuuber densities of II» aud IIr are: where refers to the hydrogen species ouly.," For a given temperature, density $\rho$ , and the atmosphere composition $y=\rm He/H$ , the number densities of $\rm H_2$ and $\rm H\,\textrm{\scriptsize{I}}$ are: where refers to the hydrogen species only." +wwhich is ~107 times fainter than the peak flix of tle March 1997 outburst.,which is $\sim10^3$ times fainter than the peak flux of the March 1997 outburst. + Given the NFI position. we have searched for signatures of Π archival ASAI data.," Given the NFI position, we have searched for signatures of in archival ASM data." + The ASM is fully operational since March 1996 aud monitors cach position on the sky in 2 to 12 keV during 90 sec snapshots with a frequency. of 5 to LO times a dav at a seusitivitv of ~10 miCTab per dav of observervatious on uncrowded fields (Levine et al., The ASM is fully operational since March 1996 and monitors each position on the sky in 2 to 12 keV during 90 sec snapshots with a frequency of 5 to 10 times a day at a sensitivity of $\sim10$ mCrab per day of observervations on uncrowded fields (Levine et al. + 1996)., 1996). + The lightcurve for aat [-dav resolution is prescuted in Fie., The lightcurve for at 4-day resolution is presented in Fig. + Gaa. There is he suggestion for a detection during 5 instances. a regular interval times of about 262 d. We tested this seriodicity bv first filtering out the data within 10 d of closest aproaches to the Sun aud all data after NJD 51150 vecamse there does not appear to be an outburst there. and then calculating the variance statistic ϐ as definec w Stelhugwerf (1978) for a range of test periods. sec Fie.," \ref{figasm}a a. There is the suggestion for a detection during 5 instances, at regular interval times of about 262 d. We tested this periodicity by first filtering out the data within 10 d of closest aproaches to the Sun and all data after MJD 51450 because there does not appear to be an outburst there, and then calculating the variance statistic $\theta$ as defined by Stellingwerf (1978) for a range of test periods, see Fig." + 6bb. The resulting period is 262£5 d. The epoch or peak flux is MALJD 50786., \ref{figasm}b b. The resulting period is $262\pm5$ d. The epoch for peak flux is MJD 50786. + The predicted times ο: outbursts are mdicated in again Fig., The predicted times of outbursts are indicated in again Fig. + 6:6 Onlv the las xedieted outburst does not appear to have materialized., \ref{figasm}a a. Only the last predicted outburst does not appear to have materialized. + The two WFC detections svuchronize with the 2ud ane Sth outburst., The two WFC detections synchronize with the 2nd and 5th outburst. + A folded light curve (Fie., A folded light curve (Fig. + Gee} shows au average outburst profile which lasts ~15 davs., \ref{figasm}c c) shows an average outburst profile which lasts $\sim$ 15 days. + The average peak flux is {παςrab., The average peak flux is 4 mCrab. + Due to the harduess of the spectrum measured with the WEC a search of the DATSE data was made to see if wwas detectable. in the hard X-rays., Due to the hardness of the spectrum measured with the WFC a search of the BATSE data was made to see if was detectable in the hard x-rays. + The BATSE experiment onboard the Conipton (ατα[αν Observatory (Fisliman et al., The BATSE experiment onboard the Compton Gamma-Ray Observatory (Fishman et al. + 1989) using the Large Area Detectors (LADs) can mouitor the whole «kv aliuost continuously in the cuerev rauge of 20 keV to 2 MeV with a typical daily 30 scusitivity of etter than 100 ταςτα), 1989) using the Large Area Detectors (LADs) can monitor the whole sky almost continuously in the energy range of 20 keV to 2 MeV with a typical daily $\sigma$ sensitivity of better than 100 mCrab. +", Detector counting rates with 16 οποιον chaunel energy resolution aud ao tinüng resolution of 2.018 secouds (CONT data) are used for our data analysis.", Detector counting rates with 16 energy channel energy resolution and a timing resolution of 2.048 seconds (CONT data) are used for our data analysis. + To produce the ]lisht curve. single step occultation data were taken using a standard Earth occultation analysis technique used for mouitoring hard X-rawv sources (ILbunmon ct al.," To produce the light curve, single step occultation data were taken using a standard Earth occultation analysis technique used for monitoring hard X-ray sources (Harmon et al." + 1992)., 1992). + Tutertercuce from known bright sources was removed., Interference from known bright sources was removed. + The suele occultation step data were then fit with a power, The single occultation step data were then fit with a power +2.1The Secular le labelratio Ly) F(k)det(z 144),"From the identity =, which is nothing but Gauss' Law in 2d electrostatics (for a unit point charge located at position $k=q$ ), we thus find = ( k - ^0) - }(k - ^p)." +" ntsH hep) det lesyelnce)CLT)= = |—— Note (GP), G,,09,4,."," Averaging this equation with its complex-conjugate, we finally obtain that (k,k^*) = |^2 = ( k - ^0) - }(k - ^p)." + Ilence. I --ye’ GPis lower diagonal matrix. and that computationofthe= last determinant in (??)) isimmediate. a label Ef Thus. inorder havesnot given realizationof Lf. F(A)is holomorphic funcüon," Since the poles live entirely on the real axis, going off it and into the fourth quadrant in the complex $k$ -plane, we obtain our desired DOR.Continuing the analogy with 2d electrostatics \cite{electrostatics}, observe that \ref{DOR}) ) is nothing but the Poisson equation, relating the charge distribution on the LHS, to the electrostatic potential W(k,k^*) = |^2 = on the RHS." +ofA.aud has al the eigenvalues of Πρεςand poles (on therealaxis) eigenvalues," Moreover, note that the real quantity $\Big|\det(z-H_{eff})\Big|^2$ in \ref{electrostaticpot}) ) is proportional to the determinant of the $2N\times 2N$ operator = ." +»xow.,below. + Most studies to date have been limited because heir analysis has been performed. on a small number. of individual haloes., Most studies to date have been limited because their analysis has been performed on a small number of individual haloes. + Since halo-to-halo variations are large. his may prevent the derivation of statistically significant results.," Since halo-to-halo variations are large, this may prevent the derivation of statistically significant results." + In addition. all studies are still alfected: at. some evel by numerical resolution.," In addition, all studies are still affected at some level by numerical resolution." + The available tests show that he subhaloes seen in a particular object. are reproduced moderately well in mass. but not in position or velocity. when the same object is resimulated multiple times with varving resolution (Chigna et al.," The available tests show that the subhaloes seen in a particular object are reproduced moderately well in mass, but not in position or velocity, when the same object is resimulated multiple times with varying resolution (Ghigna et al." + 2000: Springel et al., 2000; Springel et al. + 2001: Stoehr et al 2002. 2003).," 2001; Stoehr et al 2002, 2003)." + This is a result. of the well known divergenceὃν of neighboringoὃν trajectories in. nonlinear dynamical svstenms., This is a result of the well known divergence of neighboring trajectories in nonlinear dynamical systems. + In this paper. we carry out a systematic study of the properties of subhaloes in the halo population of a single. large-scaleὃν cosmologicale simulation. and we complement this by analysing a multi-resolution set of resimulations of a single “Alilky Wav halo. together with a set of high-resolution resimulations of eight cillerent rich clusters.," In this paper, we carry out a systematic study of the properties of subhaloes in the halo population of a single, large-scale cosmological simulation, and we complement this by analysing a multi-resolution set of resimulations of a single `Milky Way' halo, together with a set of high-resolution resimulations of eight different rich clusters." + ‘These resimulations allow us to investigate how numerical resolution and halo-to-halo variation allect the conclusions from our cosmological simulation., These resimulations allow us to investigate how numerical resolution and halo-to-halo variation affect the conclusions from our cosmological simulation. + We do not. however. carry out a full study of the numerical. requirements for fully converged numerical results for the properties of subhaloes.," We do not, however, carry out a full study of the numerical requirements for fully converged numerical results for the properties of subhaloes." +" Previous studies of subhaloes within haloes of different scale have emphasised similarities to a large extent. the internal structure of a ""Milkv Was’ halo looks like a scaled version of that of a rich. cluster halo (Moore οἱ al.", Previous studies of subhaloes within haloes of different scale have emphasised similarities – to a large extent the internal structure of a `Milky Way' halo looks like a scaled version of that of a rich cluster halo (Moore et al. + 1999: Helm White 2001: Stochr ct al., 1999; Helmi White 2001; Stoehr et al. + 2003: De Lucia et al., 2003; De Lucia et al. + 2004: Desai et al., 2004; Desai et al. + 2004)., 2004). + We show below that this scaling is not exact. and that a better model assumes the mass clistribution of. low-mass subhaloes to be the same as in the Universe as a whole. once the dillering definitions of an object/s boundary. are accounted for.," We show below that this scaling is not exact, and that a better model assumes the mass distribution of low-mass subhaloes to be the same as in the Universe as a whole, once the differing definitions of an object's boundary are accounted for." + We show that galaxy haloes have fewer high-mass subhaloes than rich clusters because of their earlier formation times., We show that galaxy haloes have fewer high-mass subhaloes than rich clusters because of their earlier formation times. + Indeed. even among haloes of given mass. the number of massive subhaloes correlates well with formation time. as rellected in the halo's central concentration.," Indeed, even among haloes of given mass, the number of massive subhaloes correlates well with formation time, as reflected in the halo's central concentration." +" The emphasis of earlier high resolution work on solving the ""overmereing problem’ has given rise to the impression that the subhaloes are typically objects which formed at very early times.", The emphasis of earlier high resolution work on solving the `overmerging problem' has given rise to the impression that the subhaloes are typically objects which formed at very early times. + We demonstrate below that this is not the case., We demonstrate below that this is not the case. + Even at low subhalo masses. most subhaloes were accreted onto the main halo at low redshift. in most cases well below >=1.," Even at low subhalo masses, most subhaloes were accreted onto the main halo at low redshift, in most cases well below $z=1$." + This is important when considering the formation paths of present-day cluster galaxies., This is important when considering the formation paths of present-day cluster galaxies. + Our paper is organized. as follows., Our paper is organized as follows. + We introduce our various simulation sets in Section 2., We introduce our various simulation sets in Section 2. + In Section 3. we compare the halo mass abundance function measured from our cosmological simulation with theoretical predictions and with earlier. numerical data.," In Section 3, we compare the halo mass abundance function measured from our cosmological simulation with theoretical predictions and with earlier numerical data." + ln Section 4. we investigate the subhalo population as a function of halo mass ancl of redshift.," In Section 4, we investigate the subhalo population as a function of halo mass and of redshift." + Phe spatial distribution of subhaloes within haloes is also discussed in Section 4., The spatial distribution of subhaloes within haloes is also discussed in Section 4. + In Section 5 we investigate the infall ancl mass-LIoss histories of present-day. subhaloes. as well as the fate of objects that are accreted onto bigger clusters at carly times.," In Section 5 we investigate the infall and mass-loss histories of present-day subhaloes, as well as the fate of objects that are accreted onto bigger clusters at early times." + We discuss our results ancl set out our conclusions in Section 6., We discuss our results and set out our conclusions in Section 6. + We have carried out a cosmological simulation of a AC DAI universe in a periodic cube of side 110 5. Mpe., We have carried out a cosmological simulation of a $\Lambda$ CDM universe in a periodic cube of side 110 $h^{-1}$ Mpc. + The total number of particles is 4007. and the individual particle mass is 1.73107bAALS Τίς," The total number of particles is $400^3$, and the individual particle mass is $1.73\times10^9h^{-1}{\rm M\odot}$." + is a factor of 8 better than he mass resolution of the CLIE. simulations published by Παπια et al. (, This is a factor of 8 better than the mass resolution of the GIF simulations published by Kauffmann et al. ( +1999) but otherwise the parameters ancl output strategy of the simulations are rather similar.,1999) but otherwise the parameters and output strategy of the simulations are rather similar. + We herefore call our new simulation CIE2., We therefore call our new simulation GIF2. +" The cosmological xwanmeters adopted. are: Q=0.8. A=0.7. ax=0.9. and f=0.7: We choose initial lluetuation power spectrum index n— 1. with the transfer function. produced by CMDBEAST (Seljak Zaledarriaga 1996) for Q,4°=0.0196."," The cosmological parameters adopted are: $\Omega=0.3$, $\lambda=0.7$, $\sigma_{8}=0.9$ , and $h=0.7$; We choose initial fluctuation power spectrum index $n=1$ , with the transfer function produced by CMBFAST (Seljak Zaldarriaga 1996) for $\Omega_bh^2=0.0196$." + Initial conclitions were produced. by imposing perturbations on an initially uniform state. representecl ww a glass. distribution of particles., Initial conditions were produced by imposing perturbations on an initially uniform state represented by a `glass' distribution of particles. + This we generatel with the method developed by White (1993) which involves evolution [rom a Poisson distribution. with the sien of ewlon's Constant changed. when caleulating peculiar gravitational forces., This we generated with the method developed by White (1993) which involves evolution from a Poisson distribution with the sign of Newton's constant changed when calculating peculiar gravitational forces. + Fluctuations are imposed. using the algorithm described in Efstathiou ct al. (, Fluctuations are imposed using the algorithm described in Efstathiou et al. ( +1985).,1985). + Based on he Zeldovich (1970) approximation. a Caussian random 101 is set up by perturbing the positions of the particles and by assigning them velocities according to the growing mode solution of linear theory.," Based on the Zeldovich (1970) approximation, a Gaussian random field is set up by perturbing the positions of the particles and by assigning them velocities according to the growing mode solution of linear theory." + In order to save computational time. we performed the simulation in two steps.," In order to save computational time, we performed the simulation in two steps." + First. we ran the simulation from high redshift until += 1 the parallel version of (Couchman. Thomas Pearce 1995: Maclarlane et al.," First, we ran the simulation from high redshift until $z=2.2$ with the parallel version of (Couchman, Thomas Pearce 1995; Macfarland et al." + 1998)., 1998). + At these times the particle distributions are lightlv. clustered. ancl thus the based. gravity solver is quite efficient., At these times the particle distributions are lightly clustered and thus the based gravity solver is quite efficient. + We then completed. the simulation. with a tree-based parallel code. (Springel. Yoshida White 2001). which has better performance in the heavily clustered regime.," We then completed the simulation with a tree-based parallel code, (Springel, Yoshida White 2001), which has better performance in the heavily clustered regime." + Since the two codes adopt. dillerent force-softening schemes. it is necessary to match the force shape at. the time we switch [rom one code to the other.," Since the two codes adopt different force-softening schemes, it is necessary to match the force shape at the time we switch from one code to the other." + The softened force becomes Newtonian at a distance of about. 2.3¢ forHYDRA. while this occurs at a cistance of 2.8c forCCADGIZT.," The softened force becomes Newtonian at a distance of about $2.3\epsilon$ for, while this occurs at a distance of $2.8\epsilon$ for." + Experimentation showed that a [factor of 1.06. namely Obvia=106€cuasa- produces an excellent match of the two force laws.," Experimentation showed that a factor of 1.06, namely $\epsilon_{\rm Hydra}= 1.06\epsilon_{\rm Gadget}$, produces an excellent match of the two force laws." + ln. practice. we started the simulation. at 2—49 with c—7h. !kpe in comoving units withinILYDRA. and changed the softening to ο=6.6044 !kpe for the continuation with after redshift 2.2.," In practice, we started the simulation at $z=49$ with $\epsilon=7h^{-1}$ kpc in comoving units within, and changed the softening to $\epsilon = 6.604 h^{-1}$ kpc for the continuation with after redshift 2.2." + The simulation was carried. out on 5120 processors of the Cray δις at the Rechenzentrum Garching. the supercomputer centre of the Max-Planck Society.," The simulation was carried out on 512 processors of the Cray T3E at the Rechenzentrum Garching, the supercomputer centre of the Max-Planck Society." + We stored the cata at 50 output times logarithmicallyspacedbetween 1|z2202and 1|z= I.This enables us to construct halo, We stored the data at 50 output times logarithmicallyspacedbetween $1+z=20$ and $1+z=1$ .This enables us to construct halo +centroid of the Local Group) >2000his+. for which radial velocities should provide a reasonable proxy lor distances.,"centroid of the Local Group) $>2000~km s^{-1}$, for which radial velocities should provide a reasonable proxy for distances." + The results for these galaxies for which the luminosities are most secure are listed in Table 3., The results for these galaxies for which the luminosities are most secure are listed in Table 3. + These data confirm the previous conclusion (hat barred and unbarred galaxies of IIubble stages à - ab - b - be have similar luminosities. and hence presumably comparable masses.," These data confirm the previous conclusion that barred and unbarred galaxies of Hubble stages a - ab - b - bc have similar luminosities, and hence presumably comparable masses." + As was the case in Table 2. galaxies of (ype SBe are again (on average) found to be less Iuminous than those of type Sc.," As was the case in Table 2, galaxies of type SBc are again (on average) found to be less luminous than those of type Sc." + Finally a comparison between the Iuminosity distributions of various kinds of earlv-tvpe ealaxies is shown in Table 4 and is plotted in Figure 2., Finally a comparison between the luminosity distributions of various kinds of early-type galaxies is shown in Table 4 and is plotted in Figure 2. + The most striking feature of these data dis that the S0 + SDO galaxies are. on average. about a magnitude [ainter than are E and Sa + SBa galaxies.," The most striking feature of these data is that the S0 + SB0 galaxies are, on average, about a magnitude fainter than are E and Sa + SBa galaxies." + A I&-8 test shows that there is less than a chance that the SO + SBO sample was drawn [rom the same parent population as that of the E and Sa +5Ba galaxies., A K-S test shows that there is less than a chance that the S0 + SB0 sample was drawn from the same parent population as that of the E and Sa +SBa galaxies. + This result strongly suggests that SO + SBO galaxies lie on evolutionary tracks that. on average. differ significantly from those of galaxies that [all along the E - Sa - Sab - Sb - She and E - 5Da - SBab - SBb - SBhbe sequences.," This result strongly suggests that S0 + SB0 galaxies lie on evolutionary tracks that, on average, differ significantly from those of galaxies that fall along the E - Sa - Sab - Sb - Sbc and E - SBa - SBab - SBb - SBbc sequences." + The data presented above show. as has previously been emphasized by van den Dergh (1998. p.61). thal 90 galaxies are nol truly. intermediate between galaxies of tvpes E and Sa.," The data presented above show, as has previously been emphasized by van den Bergh (1998, p.61), that S0 galaxies are not truly intermediate between galaxies of types E and Sa." + This view conflicts with that - ]Iubble (1936. pp.44-45) who introduced SQ ealaxies as a “more or less hypothetical” ‘lass to bridee the chasim between elliptical and spiral galaxies.," This view conflicts with that of Hubble (1936, pp.44-45) who introduced S0 galaxies as a “more or less hypothetical” class to bridge the chasm between elliptical and spiral galaxies." + The data listed in Table 3 so show that the svstematical luminosity difference between SO galaxies on the one hand. xl E and Sa galaxies on the other. is also present in (he sub-sample of galaxies with the best-determined. Iuminosities.," The data listed in Table 3 also show that the systematical luminosity difference between S0 galaxies on the one hand, and E and Sa galaxies on the other, is also present in the sub-sample of galaxies with the best-determined luminosities." + Following in the footsteps of de Vaucouleurs (1959). Sandage," Following in the footsteps of de Vaucouleurs (1959), Sandage" +erid in this paper also uses this version in atmosphere and envelope calculations.,grid in this paper also uses this version in atmosphere and envelope calculations. + To our knowledge there is no comparable published study of DB white dwarfs., To our knowledge there is no comparable published study of DB white dwarfs. + However. there is in Beauchampetal.(1999) a reference to spectroscopic fits of optical and UV data. which favors the version ML2/1.25.," However, there is in \citet{Beauchamp.Wesemael.ea99} a reference to spectroscopic fits of optical and UV data, which favors the version ML2/1.25." + We note that these conclusions for DAs and DBs are based on observed spectra and thus deseribe the atmospheric layers. which produce the emerging light. i.e.. above rg=I.," We note that these conclusions for DAs and DBs are based on observed spectra and thus describe the atmospheric layers, which produce the emerging light, i.e., above $ \tau_\mathrm{R} \approx 1$." + It is well established that the deeper layers of the atmosphere and envelope are not necessarily correctly described by the same version of the mixing-length approximation., It is well established that the deeper layers of the atmosphere and envelope are not necessarily correctly described by the same version of the mixing-length approximation. + The atmospheric parameters of 229-38 are Toy == 117700 K. logg == 8.10. when analyzed with ML2/0.6 models.," The atmospheric parameters of 29-38 are $T_\mathrm{eff}$ = 700 K, $\log g$ = 8.10, when analyzed with ML2/0.6 models." + The convection zone in such a model is extremely thin. and has a lower boundary at around optical depth 10.," The convection zone in such a model is extremely thin, and has a lower boundary at around optical depth 10." + Such a thin ονΖ has a thermal timescale. defined as of less than 1s.," Such a thin cvz has a thermal timescale, defined as of less than 1s." + However. 229-38 is a variable ZZ Ceti star. with a shortest period a little larger than 200s.," However, 29-38 is a variable ZZ Ceti star, with a shortest period a little larger than 200s." + Wingetetal.(1983) and Tassouletal.(1990) argued that the thermal timescale of the evz should be similar to the period. that is the evz should be much deeper than indicated by the atmospheric ML parameters.," \cite{Winget.van-Horn.ea83} + and \citet{Tassoul.Fontaine.ea90} argued that the thermal timescale of the cvz should be similar to the period, that is the cvz should be much deeper than indicated by the atmospheric ML parameters." + The same conclusion ts reached by fitting the non-linear light-curve; the thermal timescale at 7700 K is predicted to be = 100s (Montgomery.2005)., The same conclusion is reached by fitting the non-linear light-curve; the thermal timescale at 700 K is predicted to be $\approx 100$ s \citep{Montgomery05}. + From a completely different point of view. a similar conclusion was reached by Ludwigetal.(1994).," From a completely different point of view, a similar conclusion was reached by \cite{Ludwig.Jordan.ea94}." +.. By comparing the mean temperature structure in two-dimensional hydrodynamic simulations of the outer layers of a DA white dwarf with model atmospheres using MLT. they found that no single MLT version can describe the entire structure of the cvz.," By comparing the mean temperature structure in two-dimensional hydrodynamic simulations of the outer layers of a DA white dwarf with model atmospheres using MLT, they found that no single MLT version can describe the entire structure of the cvz." + The efficiency. or in the MLT parameterization the length. must increase with depth.," The efficiency, or in the MLT parameterization the mixing-length, must increase with depth." + We therefore calculated a second set of DA envelopes. where the ΜΙΤ version was switched to ML2/2.0 in the envelope calculation.," We therefore calculated a second set of DA envelopes, where the MLT version was switched to ML2/2.0 in the envelope calculation." +" The result depends strongly on the exact structure of the atmosphere model and the location of the ""matching point”. the starting point in the envelope integration."," The result depends strongly on the exact structure of the atmosphere model and the location of the “matching point”, the starting point in the envelope integration." + If this layer is below the atmospheric cvz. e.g.. deeper than Tgx10 m the case of the G29-38 model. or at such large depth that the convection is nearly adiabatic. the envelope integration will not produce any deepening of the evz. regardless of the efficiency of the MLT version.," If this layer is below the atmospheric cvz, e.g., deeper than $\tau_\mathrm{R} \approx 10$ in the case of the G29-38 model, or at such large depth that the convection is nearly adiabatic, the envelope integration will not produce any deepening of the cvz, regardless of the efficiency of the MLT version." + The matching must occur within the super-adiabatic part of the atmospheric convection zone for the change in efficiency to influence the model structure., The matching must occur within the super-adiabatic part of the atmospheric convection zone for the change in efficiency to influence the model structure. + We considered the optical depth of this layer as a free parameter and calibrated it by demanding a thermal timescale of = [00s for the G29-38 model., We considered the optical depth of this layer as a free parameter and calibrated it by demanding a thermal timescale of $\approx 100$ s for the G29-38 model. + This is of course unsatisfactory. and in the future we hope to find a more consistent description with a smooth change of efficiency from shallow to deeper layers.," This is of course unsatisfactory, and in the future we hope to find a more consistent description with a smooth change of efficiency from shallow to deeper layers." + Nevertheless. our choice is supported by the pulsation properties of the DAs and should provide more realistic estimates of diffusion timescales.," Nevertheless, our choice is supported by the pulsation properties of the DAs and should provide more realistic estimates of diffusion timescales." + The situation is more favorable for the DB stars than for the DAs., The situation is more favorable for the DB stars than for the DAs. + Benvenuto&Althaus(1997) compared results for thermal timescales and evz depths in DBs between the more sophisticated convection theory of Canuto&Mazzitelli(1991.1992) and Canutoetal.(1996).. with different simple ΜΙΤ versions.," \cite{Benvenuto.Althaus97} compared results for thermal timescales and cvz depths in DBs between the more sophisticated convection theory of \citet{Canuto.Mazzitelli91,Canuto.Mazzitelli92} and \citet{Canuto.Goldman.ea96}, with different simple MLT versions." + They concluded that a convective efficiency between ML2/1.0 and ML2/2.0 reproduces the results and predicts the correct location of the blue edge of the DB instability strip., They concluded that a convective efficiency between ML2/1.0 and ML2/2.0 reproduces the results and predicts the correct location of the blue edge of the DB instability strip. + This was confirmed by Córsicoetal.(2008)... who concluded that only ML2/1.25 predicts the correct location.," This was confirmed by \cite{Corsico.Althaus.ea08}, who concluded that only ML2/1.25 predicts the correct location." + À similar result was also obtained from the light-curve fitting of the prototype variable DB star 3358 (Montgomery.2007)., A similar result was also obtained from the light-curve fitting of the prototype variable DB star 358 \citep{Montgomery07}. + We thus chose this version for both the atmosphere and the envelope calculations., We thus chose this version for both the atmosphere and the envelope calculations. + More fundamentally. it ts well known that the MLT approximation provides a poor deseription of the various aspects of a real convection zone.," More fundamentally, it is well known that the MLT approximation provides a poor description of the various aspects of a real convection zone." + For the case of DA white dwarfs. this was studied with an extensive comparison of two-dimensional radiation-hydrodynamie simulations with 1D structures by Freytagetal.(1996).," For the case of DA white dwarfs, this was studied with an extensive comparison of two-dimensional radiation-hydrodynamic simulations with 1D structures by \cite{Freytag.Ludwig.ea96}." +". Even the definition of the lower boundary is ambiguous: depending on whether one uses the classical stability criterion. the layers with significant convective flux. or the layers with non-zero velocities. the resulting mass in the ""convection zone” can differ by orders of magnitude."," Even the definition of the lower boundary is ambiguous: depending on whether one uses the classical stability criterion, the layers with significant convective flux, or the layers with non-zero velocities, the resulting mass in the “convection zone” can differ by orders of magnitude." + While the temperature structure (related to convective flux) is probably the most important quantity for the pulsational properties. for diffusion timescales. the mixed region with non-zero velocity is relevant.," While the temperature structure (related to convective flux) is probably the most important quantity for the pulsational properties, for diffusion timescales, the mixed region with non-zero velocity is relevant." + In the example studied by Freytagetal.(1996).. the mass 1n the latter is 300 times higher than in the former.," In the example studied by \citet{Freytag.Ludwig.ea96}, the mass in the latter is 300 times higher than in the former." + The general result that the velocity field extends far below the lower limit of the unstable region and even the flux overshoot was also confirmed by Montgomery&Kupka(2004) with their non-local model of convection in DAs., The general result that the velocity field extends far below the lower limit of the unstable region and even the flux overshoot was also confirmed by \citet{Montgomery.Kupka04} with their non-local model of convection in DAs. + This implies that the diffusion timescales in stars with convection zones may beorders of magnitude larger than estimated with our current MLT approximations., This implies that the diffusion timescales in stars with convection zones may beorders of magnitude larger than estimated with our current MLT approximations. + For the calculation of diffusion timescales we follow closely the fundamental works of Paquetteetal.(1986a) and Paquetteetal. (1986b)., For the calculation of diffusion timescales we follow closely the fundamental works of \citet{Paquette.Pelletier.ea86} and \citet{Paquette.Pelletier.ea86*b}. +. From the tables in the first paper. we take the fit coefficients for the calculation of Coulomb collision integrals and the diffusion coefficients as well as thermal diffusion coefficients.," From the tables in the first paper, we take the fit coefficients for the calculation of Coulomb collision integrals and the diffusion coefficients as well as thermal diffusion coefficients." + The equations to calculate diffusion velocities are taken from the second paper with two minor modifications., The equations to calculate diffusion velocities are taken from the second paper with two minor modifications. +" First. we use what the authors call the ""second method"" for the thermal diffusion coefficient."," First, we use what the authors call the “second method” for the thermal diffusion coefficient." + This is based on the approach by Chapman&Cowling(1970).. and the necessary data can be found in the first paper cited above.," This is based on the approach by \citet{Chapman.Cowling70}, and the necessary data can be found in the first paper cited above." + The second change is purely cosmetic., The second change is purely cosmetic. + To determine the effective charge of the trace element 2. we calculate an effective tonization potential yor as described in their Eqs.," To determine the effective charge of the trace element 2, we calculate an effective ionization potential $\chi_\mathrm{eff}$ as described in their Eqs." + 19-21. and compare this with the true ionization potentials y(Z) of the ions of element 2 with charge Z.," 19-21, and compare this with the true ionization potentials $\chi(Z)$ of the ions of element 2 with charge $Z$ ." + Rather than taking the effective charge as Z. if," Rather than taking the effective charge as $Z$ , if" +Probing stellar. interiors through measurements of the characteristics of their eigen-oscillations has been limited to few stars.,Probing stellar interiors through measurements of the characteristics of their eigen-oscillations has been limited to few stars. + With ground-based. spectroscopic observations and the launch of space experiments of high photometric precision such as MOST. CoRoT andKepler. stellar seismology promises rich harvests.," With ground-based, spectroscopic observations and the launch of space experiments of high photometric precision such as MOST, CoRoT and, stellar seismology promises rich harvests." + This 15 true for different types of stars: individual eigen-modes of some main-sequence stars have been observed photometrically (e.g.?).. but in the case of red giants. oscillations have been detected in several hundred stars thanks to CoRoT observations (??).. whereas previously this kind of oscillations had been detected in only about a dozen red giants (see.amongothers.2222)..," This is true for different types of stars: individual eigen-modes of some main-sequence stars have been observed photometrically \citep[e.g.][]{Michel08}, but in the case of red giants, oscillations have been detected in several hundred stars thanks to CoRoT observations \citep{deRidder09,Hekker09}, whereas previously this kind of oscillations had been detected in only about a dozen red giants \citep[see, among others,][]{Frandsen02,Barban07,Tarrant07,Zechmeister08}." + More recently. the launch of the mission provided a larger number of oscillating red giants than CoRoT and allowed some analyses of their global seismic characteristics (222)... while the analysis of red giants detected by CoRoT continue (???)..," More recently, the launch of the mission provided a larger number of oscillating red giants than CoRoT and allowed some analyses of their global seismic characteristics \citep{Bedding10,Huber10,Kallinger10b}, while the analysis of red giants detected by CoRoT continue \citep{Mosser10,Kallinger10a,Hekker10}." + Because of their size. red giants present oscillations with relatively low frequencies (roughly from 10 to µΗΖ).," Because of their size, red giants present oscillations with relatively low frequencies (roughly from 10 to $\mu$ Hz)." + The length and the continuity of observations allowed by space-borne experiments is thus very important for the detection of these oscillations., The length and the continuity of observations allowed by space-borne experiments is thus very important for the detection of these oscillations. + The continuity and stability of the time series yield Fourier spectra unperturbed at low frequency. where the acoustic oscillations of red-giant stars are expected.," The continuity and stability of the time series yield Fourier spectra unperturbed at low frequency, where the acoustic oscillations of red-giant stars are expected." + Our knowledge of stellar oscillations can now be tested for evolved stars., Our knowledge of stellar oscillations can now be tested for evolved stars. + Oscillating red-giant stars can of course be individually analyzed (e.g.?).. but the first consequence of their large number is the need for an analysis method sufficiently automated to allow the exploitation of these samples.," Oscillating red-giant stars can of course be individually analyzed \citep[e.g.][]{Carrier10}, but the first consequence of their large number is the need for an analysis method sufficiently automated to allow the exploitation of these samples." + As another consequence. the large samples provide a global view of the analyzed objects. for example. using scaling relations between mode parameters and global stellar parameters that provide a general view across the whole H-R diagram.," As another consequence, the large samples provide a global view of the analyzed objects, for example, using scaling relations between mode parameters and global stellar parameters that provide a general view across the whole H-R diagram." + Some scaling laws have been derived (e.g.22???) using ground-based data and more recently space missions.," Some scaling laws have been derived \citep[e.g.][]{Kjeldsen95,Chaplin08,Chaplin09,Hekker09,Stello09} using ground-based data and more recently space missions." + A recent and convincing example was the use of the large frequency separation distribution and the frequency of the maximum in the power spectrum. with which the population of CoRoT red giants was identified to be mainly stars of the red clump (He-burningstars.see?.for details).," A recent and convincing example was the use of the large frequency separation distribution and the frequency of the maximum in the power spectrum, with which the population of CoRoT red giants was identified to be mainly stars of the red clump \citep[He-core burning stars, see][for details]{Miglio09}." + These scaling relations provide in particular new insights into the stochastic excitation and damping of the modes., These scaling relations provide in particular new insights into the stochastic excitation and damping of the modes. + The latter is still poorly understood even for solar p-modes., The latter is still poorly understood even for solar $p$ -modes. + ? have shown that both radiative losses and turbulent viscosity play a major role in mode damping., \citet{Goldreich91} have shown that both radiative losses and turbulent viscosity play a major role in mode damping. + In contrast. ? and ? found that the damping is dominated by the modulation of turbulent pressure. whereas the results of ? suggest that the perturbation of the convective heat flux is dominant.," In contrast, \citet{Gough80} and \citet{Balmforth92} found that the damping is dominated by the modulation of turbulent pressure, whereas the results of \citet{MAD06} suggest that the perturbation of the convective heat flux is dominant." + One can then expect that each contribution exhibits a different relation with. fundamental parameters. hence one can seek scaling relations to help identify the dominant physical. mechanism involved in mode damping.," One can then expect that each contribution exhibits a different relation with fundamental parameters, hence one can seek scaling relations to help identify the dominant physical mechanism involved in mode damping." + A first scaling law between the width and the effective temperature Το of the star has been proposed by ?.., A first scaling law between the width and the effective temperature $T_{\rm eff}$ of the star has been proposed by \citet{Chaplin09}. . +reheating mechanism.,reheating mechanism. + Faleke ct al. (, Falcke et al. ( +1998) also. observed garong Ilo emission associated with radio galaxies in Cbs. uxd speculated that it is due to radio-jet interactions with the ICM. or to the injection of material from. infalling spiral galaxies.,"1998) also observed strong $_{2}$ emission associated with radio galaxies in CFs, and speculated that it is due to radio-jet interactions with the ICM or to the injection of material from infalling spiral galaxies." + Ixrabbe ct al. (, Krabbe et al. ( +2000) presented LE ancl Ix-band spectral imaging of NGC 1275. the cD galaxy. at 1 centre. of the Perseus cluster. a CF.,"2000) presented H and K-band spectral imaging of NGC 1275, the cD galaxy at the centre of the Perseus cluster, a CF." + They cited. the central concentration of the II» emission. --s relatively low ancl uniform temperature (1500-3000I)) vic AGN-relatecl excitation mechanism as evidence against 16 CF hypothesis.," They cited the central concentration of the $_{2}$ emission, its relatively low and uniform temperature ) and AGN-related excitation mechanism as evidence against the CF hypothesis." + But such properties are in fact entirely consistent with the expectation that much of the gas is too cold (<<100 I)) to emit significant LH» emission. and is only observed when excited in some wav. in this case bv the ACN itself.," But such properties are in fact entirely consistent with the expectation that much of the gas is too cold $<100$ ) to emit significant $_{2}$ emission, and is only observed when excited in some way, in this case by the AGN itself." + We have recently begun a near-infrared. study. of the 1l» emission in a sample of 28 CTI CCGs. chosen to be the =nost optically Line luminous in the complete spectral stuck. Xx 217 ROSAT-selected clusters of Crawford et al. (," We have recently begun a near-infrared study of the $_{2}$ emission in a sample of 28 CF CCGs, chosen to be the most optically line luminous in the complete spectral study of 217 ROSAT-selected clusters of Crawford et al. (" +1999).,1999). + La this paper we present J. HE and Ix band spectra of Cygnus A. which was observed early in the programme.," In this paper we present J, H and K band spectra of Cygnus A, which was observed early in the programme." + At redshift =0.056. it is bv some considerable margin. the most powerful radio source in the local universe and. like the raclio galaxy 3€205. similar in power to the zc1 ΙΙΙ radio sources.," At redshift $z=0.056$, it is by some considerable margin the most powerful radio source in the local universe and, like the radio galaxy 3C295, similar in power to the $z \geq 1$ FRII radio sources." + Lt resides in a moderately rich. cooling Low cluster with a mass deposition rate of ~250 (Revnolels Fabian 1996): X-ray observations also reveal an absorbed power-law component from the quasar nucleus (Ueno οἱ al.," It resides in a moderately rich, cooling flow cluster with a mass deposition rate of $\sim 250$ (Reynolds Fabian 1996); X-ray observations also reveal an absorbed power-law component from the quasar nucleus (Ueno et al." + 1994). which further manifests itsel through scattered broad emission lines (Antonucel. Hurt Kinney L994: Ogle et al.," 1994), which further manifests itself through scattered broad emission lines (Antonucci, Hurt Kinney 1994; Ogle et al." + 1997)., 1997). + This paper is structured. as follows: the observations and data reduction are described in section 2. followed in section 3 bv a discussion of the extended emission in the linesof molecular hydrogen. the hydrogen recombination lines of Paa. Pas. Br? and Bré. and EFell]AAI1.258.1.644: in section 4. we make deductions about the gas content and molecular excitation mechanisms within the central lew ofCvenus A.inthe context of the current understanding of the Cl and the obscured quasar.," This paper is structured as follows: the observations and data reduction are described in section 2, followed in section 3 by a discussion of the extended emission in the linesof molecular hydrogen, the hydrogen recombination lines of $\alpha$, $\gamma$, $\gamma$ and $\delta$, and $\lambda\lambda1.258,1.644$; in section 4, we make deductions about the gas content and molecular excitation mechanisms within the central few of Cygnus A, in the context of the current understanding of the CF and the obscured quasar." + The cosmological parameters. {4ο=50kms and qu=0.5 are adopted: throughout. vielding a spatial scale of tat the redshift of Cyenus A. The observations were taken with the CGS4 spectrograph on the United Ixingdom Infrarecl ‘Velescope (UINERT) in September and. October 1999. as shown in the observation log in Table 1.," The cosmological parameters $H_{0}=50$ and $q_{0}=0.5$ are adopted throughout, yielding a spatial scale of $^{-1}$ at the redshift of Cygnus A. The observations were taken with the CGS4 spectrograph on the United Kingdom Infrared Telescope (UKIRT) in September and October 1999, as shown in the observation log in Table 1." + Phe 256 InSb array. 40 L/mm erating and 300 mim focal length. camera were in place. vielding a spatial scale of 0.61 avesce per pixel and spectral resolutions of 610. SSO and EWIIM (in the J. LL and [x bands. respectively) with a 2-pixel wide slit aligned north-south.," The $256\times256$ InSb array, 40 l/mm grating and 300 mm focal length camera were in place, yielding a spatial scale of 0.61 arcsec per pixel and spectral resolutions of 610, 880 and FWHM (in the J, H and K bands, respectively) with a 2-pixel wide slit aligned north-south." + The NDSTAHIS mode was usec alone with the conventional object-skv-sky-object. nodcing pattern. thus obviating the need for separate bias and dark current frames and permitting the computation of an external error for each pixel: it also reduces the required accuracy. of the fat-field frame.," The NDSTARE mode was used along with the conventional object-sky-sky-object nodding pattern, thus obviating the need for separate bias and dark current frames and permitting the computation of an external error for each pixel; it also reduces the required accuracy of the flat-field frame." + Atmospheric absorption features were removed. by ratioing with some of the main sequence E. stars tabulated at the telescope which were calibrated against photometric stancareds (except. for the J-bancl exposure acquired: under non-photometric conditions. and for which an approximate lux calibration. was obtained by matching the continuum evel with that in the LH-band).," Atmospheric absorption features were removed by ratioing with some of the main sequence F stars tabulated at the telescope which were calibrated against photometric standards (except for the J-band exposure acquired under non-photometric conditions, and for which an approximate flux calibration was obtained by matching the continuum level with that in the H-band)." + On- and off-line data reduction. was performed. using version. V1.3-0. of the Portable €6GS4 Data Iteduction package available through Starlink., On- and off-line data reduction was performed using version V1.3-0 of the Portable CGS4 Data Reduction package available through Starlink. + Row-by-row spectra were extracted from the fullv-reduced. spectral images and converted. to ASCIL format or use with the emission-line fitting package ΟΡΟΙ (Tennant 1991)., Row-by-row spectra were extracted from the fully-reduced spectral images and converted to ASCII format for use with the emission-line fitting package QDP/PLT (Tennant 1991). + Emission lines were fitted. with gaussian components atop a linear continuum., Emission lines were fitted with gaussian components atop a linear continuum. + Spectra from the nuclear row of Cyvenus A are. shown in Fig. Ll.., Spectra from the nuclear row of Cygnus A are shown in Fig. \ref{fig:cygAspec}. + Many. of the Lines were previously identified » Ward et al. (, Many of the lines were previously identified by Ward et al. ( +1991) ancl Thornton. ct al. (,1991) and Thornton et al. ( +1999). in earlier UINIICE spectra.,1999) in earlier UKIRT spectra. + Phe blue shoulder on Paa is Xausiblv due to HeLELAT.8639. (using case D theory and he LeLHLA4686 flux in Osterbrock Aliller 1975. its wedieted Hux is 3.10 Lj) and also perhaps ο HeLAAT.8691.1.8702. (although we cannot predict their luxes): Thornton et al. (," The blue shoulder on $\alpha$ is plausibly due to $\lambda1.8639$ (using case B theory and the $\lambda4686$ flux in Osterbrock Miller 1975, its predicted flux is $3\times10^{-16}$ ) and also perhaps to $\lambda\lambda1.8691,1.8702$ (although we cannot predict their fluxes); Thornton et al. (" +1999). however. ascribed it entirely o very high excitation Ls O-serics lines.,"1999), however, ascribed it entirely to very high excitation $_{2}$ O-series lines." + Using the list of coronal lines in Ferguson et al. (, Using the list of coronal lines in Ferguson et al. ( +1907). we identify several new such lines. viz. ,"1997), we identify several new such lines, viz. [" +Ca VIH[A2.32. Si NJALA3. and S IX]A1.252. in addition to those previously known between 2.0 and 2.15. As an alternative to S LXJAL.252. the blue component of the doublet near 1.32554. could. instead. be 1101A1.2531 and/or HH» v=2-0 QGO. but if it were the latter. the absence of the Q(1). Q(38) and. Q(5) lines of this series (which should be much stronger uncer thermal excitation) would be hard to explain.,"Ca $\lambda 2.32$ , [Si $\lambda 1.43$ and [S $\lambda 1.252$, in addition to those previously known between 2.0 and $\mu$ m. As an alternative to [S $\lambda 1.252$, the blue component of the doublet near $\mu$ m could instead be $\lambda1.2531$ and/or $_{2}$ v=2-0 Q(4), but if it were the latter, the absence of the Q(1), Q(3) and Q(5) lines of this series (which should be much stronger under thermal excitation) would be hard to explain." + In the present data. many of the identified. emission. lines extend. significantly bevond the instrumental point spread. function (PSE). as described below.," In the present data, many of the identified emission lines extend significantly beyond the instrumental point spread function (PSF), as described below." + Fig., Fig. + 2 shows the emission line [uxes as functions of position along the slit., \ref{fig:extlines} shows the emission line fluxes as functions of position along the slit. + The nuclear light of the L-band exposure [alls on two rows of the chip. so the Fell]AL.644 points in Figs.," The nuclear light of the H-band exposure falls on two rows of the chip, so the $\lambda 1.644$ points in Figs." + 2 and 3. have been shifted. by [0.5 pixel., \ref{fig:extlines} and \ref{fig:kinem} have been shifted by $+0.5$ pixel. + ALL the lines are spatially extended. especially to the north. and by up to in the case of v—1-0 S(1).," All the lines are spatially extended, especially to the north, and by up to in the case of v=1-0 S(1)." + Phere are notable variations in the line ratios. e.g. in SCI)/8(3). and in ratios involving Fell] AA1.258. 1.644. Drs and v—1-0 S(L). which we discuss in section 4.," There are notable variations in the line ratios, e.g. in S(1)/S(3), and in ratios involving [FeII] $\lambda\lambda1.258,1.644$ , $\gamma$ and v=1-0 S(1), which we discuss in section 4." + We caution. however. that there are systematic uncertaintiesin the 8(3) lux in rows 9698 owing to the blending of this line with Si VIJAT.962.," We caution, however, that there are systematic uncertaintiesin the S(3) flux in rows 96–98 owing to the blending of this line with [Si $\lambda$ 1.962." +and found that the CO. band appeared to be much stronger in the spectra based on the old models than ou the esent models.,and found that the $_2$ band appeared to be much stronger in the spectra based on the old models than on the present models. + At the first elauce. this is rather surprising because C ο abundances iu the old models are only about dex larger than those in the present models.," At the first glance, this is rather surprising because C O abundances in the old models are only about dex larger than those in the present models." +" Towever. we realized immediately that the CO» abundance is extremely sensitive to both C ο abundances because the COs abuudauce depends ou the cube of C O abundances Cleo,κAe AZ)."," However, we realized immediately that the $_2$ abundance is extremely sensitive to both C O abundances because the $_2$ abundance depends on the cube of C O abundances $A_{\rm CO_2} \propto A_{\rm C}A_{\rm O}^{2}$ )." + We recall that the stroug dependence of he COs abunudauce ci inctallicity. [FeΠΙ2... was oxeviouxlv kuown by a detailed thermochemical analysis of the C. N. and O bearing gaseous uolecules (Lodders&Feeley002).," We recall that the strong dependence of the $_2$ abundance on metallicity, [Fe/H], was previously known by a detailed thermochemical analysis of the C, N, and O bearing gaseous molecules \citep{Lodders02}." +. The above result demoustrates that at least two differeut series of model photospheres are needed or the analysis of the CO» baud observed withAWARE., The above result demonstrates that at least two different series of model photospheres are needed for the analysis of the $_2$ band observed with. + For this purpose. we reconsider our old version of UCM: based on he classical C ο abundances to represent a case of rather high C O abundances.," For this purpose, we reconsider our old version of UCMs based on the classical C O abundances to represent a case of rather high C O abundances." + Our current version of UCM based on the new ο O abundances will serve as representing a case of the reduced ο ο abundances compared to the old version of the UCAIs., Our current version of UCMs based on the new C O abundances will serve as representing a case of the reduced C O abundances compared to the old version of the UCMs. +", An important implication of this result is that the metallicity (C O abundances) in brown cbwarts should have a variety of values.", An important implication of this result is that the metallicity (C O abundances) in brown dwarfs should have a variety of values. + The interpretation and analysis of the spectra of cool cawarts already have a rather long history (e.g.Narkpatrick2005:Bureasseretal.20062:etal.2009:Yamamura 2010).. and the effecof metallicity has been discussed by some authors.," The interpretation and analysis of the spectra of cool dwarfs already have a rather long history \citep[e.g.][]{Kirkpatrick05, Burgasser06a, +Leggett07a, Cushing08, Stephens09, Yamamura10}, and the effectof metallicity has been discussed by some authors." + For xanrple. Durgasserotal.(20065) have measured the streugths of the major Ποῦ and bauds in the ju region iu a large sample of T dwarts. aud found that the resultaut spectra indices plotted against spectral type revealec considerable scatter.," For example, \citet{Burgasser06b} have measured the strengths of the major $_2$ O and $_4$ bands in the $\mu$ m region in a large sample of T dwarfs, and found that the resultant spectral indices plotted against spectral type revealed considerable scatter." + Several reasons for this result including the effects of dust. gravity. arc metallicity have been considered. but it appearce difficult to separate the effect of metallicity from the remaining parenieters.," Several reasons for this result including the effects of dust, gravity, and metallicity have been considered, but it appeared difficult to separate the effect of metallicity from the remaining paremeters." + Leeecttetal.(2009) have shown that the effect of metallicity ou the SEDs of T chwarts should be significant. but noted that other parameters such as gravity can affect the SEDs similarly.," \citet{Leggett09} have shown that the effect of metallicity on the SEDs of T dwarfs should be significant, but noted that other parameters such as gravity can affect the SEDs similarly." + This result again showed he difficulty in determining metallicity uiiquely roni SEDs., This result again showed the difficulty in determining metallicity uniquely from SEDs. + Also. the so-called “blue” L dwarfs classified as L subdwarfs have been interpreted to jave low metallicity with [Fe/U] from στο 1.0 (c.g.Durgasseretal.2009).. mt those L dwarfs with unusually. blue near-infrared colors can also ο explained by a patchy cloud model (Folkesetal.2007:Aarleyet2010).," Also, the so-called “blue” L dwarfs classified as L subdwarfs have been interpreted to have low metallicity with [Fe/H] from $-1.5$ to $-1.0$ \citep[e.g.][]{Burgasser09}, , but those L dwarfs with unusually blue near-infrared colors can also be explained by a patchy cloud model \citep{Folkes07, Marley10}." +. The brief survey outlined above reveals that he problem of metallicity in brown chwarts is still uuresolved., The brief survey outlined above reveals that the problem of metallicity in brown dwarfs is still unresolved. + In this paper. we will show clear evidence of mctallicity variations m brown dwarfs or the first time.," In this paper, we will show clear evidence of metallicity variations in brown dwarfs for the first time." + Iu fact. the most important significance of the discovery of COs with is that it demonstrated the variations of the C O abundances bv at least in brown dwarfs aud that it provided a means by which to estimate the C O abundances in very cool cdwarfs.," In fact, the most important significance of the discovery of $_2$ with is that it demonstrated the variations of the C O abundances by at least in brown dwarfs and that it provided a means by which to estimate the C O abundances in very cool dwarfs." + Iu Paper 1. we have analyzed the spectra aud discussed the basic physical parameters of our objects in detail.," In Paper I, we have analyzed the spectra and discussed the basic physical parameters of our objects in detail." + There we have applied the conventional method based on a direct Comparison of the observed aud predicted spectra., There we have applied the conventional method based on a direct comparison of the observed and predicted spectra. + Iu this per. we exanuue the results of Paper I bv a nore detailed numerical method iu Section ??.. and we confirm that the physical parameters deteriuued in Paper I mostly agree with those sedo on the reduced-chi-square nimnuuization nethod within the estimated errors.," In this paper, we examine the results of Paper I by a more detailed numerical method in Section \ref{sec:fitcmp}, and we confirm that the physical parameters determined in Paper I mostly agree with those based on the reduced-chi-square minimization method within the estimated errors." + A problem. rowever. is that an adequate application of such a rigorous nuierical mcthod requires the input data of sufficient accuracy.," A problem, however, is that an adequate application of such a rigorous numerical method requires the input data of sufficient accuracy." +" Unfortunately. hne iuput data — our present models of brown dwarts απο uot precise enough for this purpose. as discussed in Section 1.5 of Paper I. Therefore the uuucerical method does not necessuilv provide the best answer and the traditional fitting method ""by eve"" can still be useful for some cases."," Unfortunately, the input data — our present models of brown dwarfs — are not precise enough for this purpose, as discussed in Section 4.5 of Paper I. Therefore the numerical method does not necessarily provide the best answer and the traditional fitting method “by eye” can still be useful for some cases." + For these reasons. we use the physical pariuneters determined iu Paper I aud adopt the same approach as Paper I. eve-fitting. throughout this paper.," For these reasons, we use the physical parameters determined in Paper I and adopt the same approach as Paper I, eye-fitting, throughout this paper." + Our two series of UCAS are referred to as UCALa and ολο aud they ouly differ in € O abuudauces as sunnunarzed iu Table 1. ," Our two series of UCMs are referred to as UCM-a and UCM-c, and they only differ in C O abundances as summarized in Table \ref{tbl:tbl1}. ." +The UCALa series is based ou the classicalC, The UCM-a series is based on the classicalC +uncertainties. are reported in Table L..,"uncertainties, are reported in Table \ref{magfield}." + Evpical uncertainties are 100-150 €i. The longitudinal magnetic field is observed to change from. about 2 kG to |:5 kG. Such a strong loneitucinal field suggests an organized magnetic field with a likely surface dipole component stronger than SN Κέα. The rotation period of LIER 7355 remains unclear following the analysis of original HIPPARCOS data by Ixoen. Ever (2002)., Typical uncertainties are 100-150 G. The longitudinal magnetic field is observed to change from about $-$ 2 kG to +2.5 kG. Such a strong longitudinal field suggests an organized magnetic field with a likely surface dipole component stronger than 8 kG. The rotation period of HR 7355 remains unclear following the analysis of original HIPPARCOS data by Koen Eyer (2002). + The proposed “single minimum” period of approximately 0.26 d would seem. from the rotational velocity. to imply that the star is rotating more rapidly than the critical (break-up) rotation rate.," The proposed “single minimum” period of approximately 0.26 d would seem, from the rotational velocity, to imply that the star is rotating more rapidly than the critical (break-up) rotation rate." + Unfortunately. our new photometry from the 011 telescope at. C'TIO does not resolve this ambiguity. as both the shorter period and the longer period (~ 0.52 d) produce reasonable lieht curves.," Unfortunately, our new photometry from the 0.9m telescope at CTIO does not resolve this ambiguity, as both the shorter period and the longer period $\sim$ 0.52 d) produce reasonable light curves." + However. when the longitudinal magnetic Ποιά measurements. are. plotted with both periods. the longitudinal magnetic field cannot be phased. with the 0.26 day period in à reasonable fashion.," However, when the longitudinal magnetic field measurements are plotted with both periods, the longitudinal magnetic field cannot be phased with the 0.26 day period in a reasonable fashion." + However. when phased with the 0.52 clay period the longitudinal fielcl measurements describe a smooth. approximately sinusoidal variation from 2 kG to 12.5 kG (Fig. 2)).," However, when phased with the 0.52 day period the longitudinal field measurements describe a smooth, approximately sinusoidal variation from $-$ 2 kG to +2.5 kG (Fig. \ref{fullper}) )." + A periodogram of the combined. HIPPATRCOS ancl οΓιο. photometry. in the region near the LLPPARCOS solution. gives two closely spaced. periods. 0.5214184 d and 0.5214404 d. Phe longer period is consistent with the periods derived by both. Mikuláuseek et al. (," A periodogram of the combined HIPPARCOS and CTIO photometry, in the region near the HIPPARCOS solution, gives two closely spaced periods, 0.5214184 d and 0.5214404 d. The longer period is consistent with the periods derived by both Mikul\'{a}\\u{s}eek et al. (" +2010) ancl Rivinius ct al. (,2010) and Rivinius et al. ( +2010).,2010). + Pherefore. we tentatively select the longer period of and a photometric light curve consisting ofminima.," Therefore, we tentatively select the longer period of and a photometric light curve consisting of." +. We define a new cphemeris for 11. 7355: The Ου is determined from one of the minima in the photometric light curve obtained from the new CPLO data., We define a new ephemeris for HR 7355: The $_{0}$ is determined from one of the minima in the photometric light curve obtained from the new CTIO data. + 3oth sets of photometry are plotted. and phased in Fig. 3..," Both sets of photometry are plotted and phased in Fig. \ref{photLC}," + according to this new ephemeris., according to this new ephemeris. + We computed the periodogram of the eight magnetic field measurements and obtained a best fit period of 0.523 c 0.006 d. consistent with the period found by photometry.," We computed the periodogram of the eight magnetic field measurements and obtained a best fit period of 0.523 $\pm$ 0.006 d, consistent with the period found by photometry." + When the D; measurement are phased according to Eq. (, When the $B_\ell$ measurement are phased according to Eq. ( +3). the magnetic extrema occur at phases 70.3 ancl «0.5.,"3), the magnetic extrema occur at phases $\sim$ 0.3 and $\sim$ 0.8." + The sinusoidal variation of the longitudinal magnetic field indicates an important dipole component to the stellar magnetic field., The sinusoidal variation of the longitudinal magnetic field indicates an important dipole component to the stellar magnetic field. + Using the characteristics of the sinusoidal fit to the magnetic data and the stellar parameters with their error bars (derived in 833). we can estimate the geometry and strength of the dipole: the inclination of the rotational axis with respect to the line of sight to the observer. ὃν the obliquity of the dipole axis relative to the rotational axis. 7. and. the polar strength of the surface dipole field. By. as described by e.g. Wade et al. (," Using the characteristics of the sinusoidal fit to the magnetic data and the stellar parameters with their error bars (derived in 3), we can estimate the geometry and strength of the dipole: the inclination of the rotational axis with respect to the line of sight to the observer, $i$, the obliquity of the dipole axis relative to the rotational axis, $\beta$, and the polar strength of the surface dipole field, $B_{d}$, as described by e.g. Wade et al. (" +1997).,1997). +" We have determined the allowed range of inclinations 38<70.3. 1054 Cf,/100)0N, (Ppxs~3 Ir. 1). po Vpxs Vouxs are the volumes corresponding to the horizon of CAV interferometers for DNSs aud BII-NS ierecrs respectively: the ratio between these volumes ds Vouns/Vpxs10.", The large offset of some SHBs from their host galaxy is consistent with that of $z < 0.3$ $z > 0.3$ $10$ $(f_b^{-1}/100)(\Delta_1/100)^{\alpha} \sim 0.1$ $\rho_{DNS}\sim 3 $ $^{-3}$ $^{-1}$ $g_{\rm B}$ $V_{\rm DNS}$ $V_{\rm BHNS}$ are the volumes corresponding to the horizon of GW interferometers for DNSs and BH-NS mergers respectively; the ratio between these volumes is $V_{\rm BHNS}/V_{\rm DNS} \sim 10$. + Here 4=1 for Advanced LIGO/Vireo and i=3\10! for LIGO/Vireo take iuto account the different volunes sampled by the two imstruneut classes (see e.g. Cutler Thorue 2002)., Here $\eta=1$ for Advanced LIGO/Virgo and $\eta=3\times 10^{-4}$ for LIGO/Virgo take into account the different volumes sampled by the two instrument classes (see e.g. Cutler Thorne 2002). + While it is estimated that ouly gp0.01 of primordial NS-NS/BIT svsteis are DII-NS binaries (Belezvuski et al., While it is estimated that only $g_{\rm B}\sim 0.01 $ of primordial NS-NS/BH systems are BH-NS binaries (Belczynski et al. + 2007). the Taction of such systems in GCs. though prescuthy uuknown. might well be lugher. their main formation chaunel beiug the exchanec interaction of a binary containing a NS and a cluster star with an isolated BIL (Devecchi ct al 2007).," 2007), the fraction of such systems in GCs, though presently unknown, might well be higher, their main formation channel being the exchange interaction of a binary containing a NS and a cluster star with an isolated BH (Devecchi et al 2007)." + Dynamical star cluster simulations point to a fairly large population of ΟΙΤΗ binaries in GC. but wave not vet provided estimates of gp (O'Leary ct al.," Dynamical star cluster simulations point to a fairly large population of BH-BH binaries in GCs, but have not yet provided estimates of $g_{\rm B}$ (O'Leary et al." + 2006)., 2006). + For instance for tle elobular cluster parameters adopted by Sadowski et al. (, For instance for the globular cluster parameters adopted by Sadowski et al. ( +2008) NS-NS/DII binaries are expected to form at a very slow pace. and it is nof surprising hat 10 such svstenis were produced in those simulations.,"2008) NS-NS/BH binaries are expected to form at a very slow pace, and it is not surprising that no such systems were produced in those simulations." + We note that ax long as gp20.15 the rate of detectable CAV events from DIT-NS binaries will be higher than that ποιι DNSs (see Eq., We note that as long as $g_{\rm B}\gsim 0.15 $ the rate of detectable GW events from BH-NS binaries will be higher than that from DNSs (see Eq. + 5)., 5). + We assume gp=0.5 (and the other fiducial values in Eq.(5)) iu the estimates of Neay even below. and report also in parentheses the values correspouding to gp Oand L. respectively.," We assume $g_{\rm B} = 0.5 $ (and the other fiducial values in Eq.(5)) in the estimates of $N_{GW}$ given below, and report also in parentheses the values corresponding to $g_{\rm B}\sim 0$ and $1$ , respectively." + For Advanced LIGO/Virgo we find that events roni primordial aud dynamically formed NS-NS/BIT binaries are expected at a rate of ~ PE bound ~218 iq 5. 150). respectively.," For Advanced LIGO/Virgo we find that events from primordial and dynamically formed NS-NS/BH binaries are expected at a rate of $\sim$ 14 $^{-1}$ and $\sim 248$ $^{-1}$ (45, 450), respectively." + For gy=0.5 the latter event rate is dominated by mereiug DILNS binaries formed in GCs (~226 1) and is close to the upper end of the ranee estimated by Ialogera et al. (, For $g_{\rm B}= 0.5 $ the latter event rate is dominated by merging BH-NS binaries formed in GCs $\sim 226$ $^{-1}$ ) and is close to the upper end of the range estimated by Kalogera et al. ( +2006) for primordial DNSs.,2006) for primordial DNSs. + For present seeucration interferometers Eq., For present generation interferometers Eq. + 5 eives 1 eveut in 238 vears aud 1 eveut in 13 vears (7lL. 7 vears) from primordial and dvuauiically formed systems. respectively.," 5 gives 1 event in 238 years and 1 event in 13 years (74, 7 years) from primordial and dynamically formed systems, respectively." + There are preseutlv substantial uucertaiuties iu the values of the parameters iu Eq.(5) and therefore a precise estimate of the expected ummber of detectable CAV event cannot be made vet., There are presently substantial uncertainties in the values of the parameters in Eq.(5) and therefore a precise estimate of the expected number of detectable GW event cannot be made yet. + Towever it should be possible iu the near future to coustrain more tieltly the uncertain parameters m Eq (5)., However it should be possible in the near future to constrain more tightly the uncertain parameters in Eq (5). +" Concerning the beaminο factor. a few additional detailed studies of the optical afterglow of SUBs with currently available iustruuentation will allow adore precise deteruination of f,."," Concerning the beaming factor, a few additional detailed studies of the optical afterglow of SHBs with currently available instrumentation will allow a more precise determination of $f_{b}^{-1}$." + Taken at face value. preseut estimates range over a factor of ~2.6.," Taken at face value, present estimates range over a factor of $\sim 2.6$." + The local SUB event rate Ry. while constrained by the large sample of SITBs revealed by DATSE. can vary up to a factor of ~L8 depending ou the redshift distribution ancl incidence of dvuiuically formed SIBs (see Sect.," The local SHB event rate $R_0$, while constrained by the large sample of SHBs revealed by BATSE, can vary up to a factor of $\sim 1.8$ depending on the redshift distribution and incidence of dynamically formed SHBs (see Sect." + 2.1 and 2.2)., 2.1 and 2.2). + The latter is preseutlv deteriuined through 11 SUBs. but the sample of SUBs with secure redshift is steadily inercasingand should triple bv the endoftheSwift mission.," The latter is presently determined through 11 SHBs, but the sample of SHBs with secure redshift is steadily increasingand should triple by the endoftheSwift mission." + A more accurate determination of the lower eud of theSUB huuinositv functiou. will likely require more sensitive CRB detectors than currently available:, A more accurate determination of the lower end of theSHB luminosity function will likely require more sensitive GRB detectors than currently available; +discussed in section ?7?..,discussed in section \ref{adialgo}. + The ADI technique attenuates the PSF noise in two steps: (i) by subtraction of a relerence image {ο remove correlated speckles and (1) bv the combination of all residual images after FOV alignment to average the residual noise., The ADI technique attenuates the PSF noise in two steps: (i) by subtraction of a reference image to remove correlated speckles and (ii) by the combination of all residual images after FOV alignment to average the residual noise. + The noise attenuation V/AN is defined as the ratio of the local noise NV in an image over the noise AN of the residual image., The noise attenuation $N/\Delta N$ is defined as the ratio of the local noise $N$ in an image over the noise $\Delta N$ of the residual image. + The noise attenuation obtained by the subtraction of the reference PSF. LN/.NAN6(6.7.ορ). is a [function of the angular separation. 9. the lime interval 7 between the image and its relerence and the individual image exposure time {ως (including overheads).," The noise attenuation obtained by the subtraction of the reference PSF, $\left[ N/\Delta N \right]_{\rm{S}}(\theta, \tau, t_{\rm{exp}})$, is a function of the angular separation, $\theta$, the time interval $\tau$ between the image and its reference and the individual image exposure time $t_{\rm{exp}}$ (including overheads)." + Strong quasi- speckle correlation between. successive images leads {ο strong attenuation and (hus better detection limits for a given total integration time., Strong quasi-static speckle correlation between successive images leads to strong attenuation and thus better detection limits for a given total integration time. + A good and stable seeing is thus expected to deliver better ADI quasi-static speckle attenuation., A good and stable seeing is thus expected to deliver better ADI quasi-static speckle attenuation. + For a perfect case when all static and quasi-static speckles have been removed by ADI. detection limits are ultimately limited by short-livecl alinospheric speckles (hat have a correlation timescale of a few tens of ms. shorter than the time interval required to obtain sullicient FOV rotation to build the ADI reference PSF.," For a perfect case when all static and quasi-static speckles have been removed by ADI, detection limits are ultimately limited by short-lived atmospheric speckles that have a correlation timescale of a few tens of ms, shorter than the time interval required to obtain sufficient FOV rotation to build the ADI reference PSF." + The additional noise attenuation resulting [rom the combination of n de-rotated residual images is friction of the correlation of those images., The additional noise attenuation resulting from the combination of $n$ de-rotated residual images is function of the correlation of those images. + This attenuation is given by nir. where neg ds the effective number of uncorrelated residual images: if all residuals are uncorrelatect. then nay=n.," This attenuation is given by $\sqrt{n_{\rm{eff}}}$, where $n_{\rm{eff}}$ is the effective number of uncorrelated residual images; if all residuals are uncorrelated, then $n_{\rm{eff}}=n$." + Equivalently. for an image sequence of total time /=foc). one has to wail for a time before (wo de-rotated residual images are decorrelated.," Equivalently, for an image sequence of total time $t = t_{\rm{exp}}n$, one has to wait for a time before two de-rotated residual images are decorrelated." + Thus the total noise attenuation N/AN will be For simplicitv. let us consider a dominant speckle noise having a correlation timescale Tapeck," Thus the total noise attenuation $N/\Delta N$ will be For simplicity, let us consider a dominant speckle noise having a correlation timescale $\tau_{\rm{speck}}$." + Lhe ADI noise attenuation resulting from the combination of all difference images is [unction of zie., The ADI noise attenuation resulting from the combination of all difference images is function of $\tau_{\rm{speck}}$. +" Is behavior can be defined Lor (wo limiting regimes: a) when either 7,54 is much longer than 7 or shorter than /,44, and b) Tyee 15 longer than /;44 but shorter than T", Its behavior can be defined for two limiting regimes: a) when either $\tau_{\rm{speck}}$ is much longer than $\tau$ or shorter than $t_{\rm{exp}}$ and b) $\tau_{\rm{speck}}$ is longer than $t_{\rm{exp}}$ but shorter than $\tau$. + In the first regime.e the residuals of consecutive imagee differences are decorrelated. either because the correlated structure of the PSF which lasts for long (mes (7:544=> 7) has been," In the first regime, the residuals of consecutive image differences are decorrelated, either because the correlated structure of the PSF which lasts for long times $\tau_{\rm{speck}} \gg \tau$ ) has been" +by Whittetetal.(1992).,by \citet{Whittet92}. +". The difference between the average P.A. obtained for these four measurements and that obtained by Whittetetal.(1992) is ~6°, which is very close to the statistical deviation of our measurements thus discarding any further correction for the zero angle calibration."," The difference between the average P.A. obtained for these four measurements and that obtained by \citet{Whittet92} is $\sim 6\degr$, which is very close to the statistical deviation of our measurements thus discarding any further correction for the zero angle calibration." + Table 5 contains a summary of our near-IR and optical polarization data for stars with a signal-to-noise in the polarization intensity higher than unity., Table \ref{tab:IRdata} contains a summary of our near-IR and optical polarization data for stars with a signal-to-noise in the polarization intensity higher than unity. + Column 1 gives the star's identification number in our catalogue., Column 1 gives the star's identification number in our catalogue. + Columns 2 and 3 show the equatorial coordinates., Columns 2 and 3 show the equatorial coordinates. + Column 4 gives the J-band magnitude., Column 4 gives the $J$ -band magnitude. + Columns 5 to 12 show the polarization degree and the polarization P.A. (with their uncertainties) for the R and J bands., Columns 5 to 12 show the polarization degree and the polarization P.A. (with their uncertainties) for the $R$ and $J$ bands. +" The last two columns indicate the rotator position used to acquire the near-IR data, and the object type, respectively."," The last two columns indicate the rotator position used to acquire the near-IR data, and the object type, respectively." +" Figure 4 shows that, excluding star 13, the polarization P.A. distribution measured in the J-band is quite narrow with a meanposition angle of aand a standard deviation of only 12?."," Figure \ref{histPA} shows that, excluding star 13, the polarization P.A. distribution measured in the $J$ -band is quite narrow with a meanposition angle of and a standard deviation of only $\degr$." + We note that the J-band polarization uncertainties may be overestimated., We note that the $J$ -band polarization uncertainties may be overestimated. +" First, the aforementioned standard deviation is about half the mean 1-c- uncertainty of the polarization P.A., and second, there is a very good agreement between the near-IR and optical data (see next section)."," First, the aforementioned standard deviation is about half the mean $\sigma$ uncertainty of the polarization P.A., and second, there is a very good agreement between the near-IR and optical data (see next section)." + shows the spatial distribution of the near-IR polarization vectors overlaid on the 2MASS J-band image., \\ref{IRpolmap} shows the spatial distribution of the near-IR polarization vectors overlaid on the 2MASS $J$ -band image. + The polarized stars with a declination below 31°10’ have larger polarization degrees than those above this value.," The polarized stars with a declination below $31\arcdeg +10'$ have larger polarization degrees than those above this value." + This subsample comprises most of stars with mean P.A. ~ 160°., This subsample comprises most of stars with mean P.A. $\simeq$ $\degr$ . + Star number 13 is the only object in our catalogue presenting intrinsic, Star number 13 is the only object in our catalogue presenting intrinsic +size.,size. + Nevertheless. there is still the possibility Chat we may ail to fine the true minimum. especially if the shape of he function is complex.," Nevertheless, there is still the possibility that we may fail to find the true minimum, especially if the shape of the function is complex." + Indeed. evidence is found that we fail to obtain the elobal minimum in some of our results (see later).," Indeed, evidence is found that we fail to obtain the global minimum in some of our results (see later)." + Llowever. we our not undulv worried by his since a local minimum will result in smaller value of 2(Cassl£.A)Cuax($.1)). than that calculated [rom the rue minimum.," However, we our not unduly worried by this since a local minimum will result in smaller value of $2\!\left({\cal +L_{\mathrm{max}}}(\hat{\xi},\hat{\lambda})-{\cal +L_{\mathrm{max}}}(\hat{\xi},1)\right)$ than that calculated from the true minimum." + Thus. we will fail to detect non.normality rather than falsely claim: nonnormality.," Thus, we will fail to detect non–normality rather than falsely claim non–normality." + The bivariate skewness and kurtosis are simple to calculate., The bivariate skewness and kurtosis are simple to calculate. + However. the bivariate power transformation method. has the same challenges as in the univariate case.," However, the bivariate power transformation method has the same challenges as in the univariate case." + Again. we are trving to minimize a 2-dimensional function and so we turn to the simplex minimizer.," Again, we are trying to minimize a 2-dimensional function and so we turn to the simplex minimizer." + Obviously. by using Chis minimizer we inherit the same problems as for the univariate transformation.," Obviously, by using this minimizer we inherit the same problems as for the univariate transformation." + Finally. we look at the lincarity of the temperature pairs and (it. 3) pair.," Finally, we look at the linearity of the temperature pairs and $\Re$, $\Im$ ) pair." + We add separately three nonlinear terms to our model of the data: where. as before. ο; are elements from the variate x;.," We add separately three non–linear terms to our model of the data: where, as before, $x_{ij}$ are elements from the variate $\mathv{x}_i$." + Our task is now simply to assessthe significance of the coefficient zd» for the three nonlinear terms using Equation (32))., Our task is now simply to assessthe significance of the coefficient $A_2$ for the three non–linear terms using Equation \ref{eqn:ttest}) ). + In this section. we present the results of our analysis on the WALAPderived data.," In this section, we present the results of our analysis on the WMAP–derived data." + Throughout the section. the expectation value of a statistic £(Q). if. non.zero. is marked in the figures as a straight line.," Throughout the section, the expectation value of a statistic $E(Q)$, if non–zero, is marked in the figures as a straight line." + Phe clark grey areas in the plots represent the confidence regions., The dark grey areas in the plots represent the confidence regions. + For example. if the distribution of £(Q) is (or approximates for large n) a normal distribution. then the dark grey region signifies E(QD) 1.959960.," For example, if the distribution of $E(Q)$ is (or approximates for large $n$ ) a normal distribution, then the dark grey region signifies $E(Q)\pm 1.95996\sigma$ ." + Phe light erey region is the confidence region., The light grey region is the confidence region. + Ln section 6.1.. we cisplay ane diseuss the results of applying our statistics to temperature pairs from the assembley maps. the frequency maps. the CALBonly. maps and a sample Gaussian Monte Carlo (MO) map.," In section \ref{sec:realspace}, we display and discuss the results of applying our statistics to temperature pairs from the assembley maps, the frequency maps, the CMB–only maps and a sample Gaussian Monte Carlo (MC) map." + The latter map is used as a reference guide and to reassure us that he computation of a statistic is accurate., The latter map is used as a reference guide and to reassure us that the computation of a statistic is accurate. + For cach map. he statistics were applied to LOO binned distributions and herefore. we expect one value (for each statistic) to be outside the confidence region.," For each map, the statistics were applied to 100 binned distributions and therefore we expect one value (for each statistic) to be outside the confidence region." + In section 6.2.. we discuss he same analvsis on the spherical harmonic coefficients obtained from the CAIBonly maps and the same sample Gaussian MC map.," In section \ref{sec:harmonicspace}, we discuss the same analysis on the spherical harmonic coefficients obtained from the CMB–only maps and the same sample Gaussian MC map." + For cach map. the statistics are applied o 501 distributions (/=100 600) and as such we expect 5 points bevond the confidence region.," For each map, the statistics are applied to 501 distributions $\ell=100-600$ ) and as such we expect 5 points beyond the confidence region." + The results of the application of the univariate methocls on the temperature pairs are clisplaved in Figures 1--s.., The results of the application of the univariate methods on the temperature pairs are displayed in Figures \ref{fig:skew1}- \ref{fig:uni_trans2}. + We cdisplav the results for AY) to increase clarity. although unsurprising. the corresponding plots for Z5 resemble those or jM.," We display the results for $\Delta T_1$ to increase clarity, although unsurprising, the corresponding plots for $\Delta T_2$ resemble those for $\Delta T_1$." + The skewness results are shown in Figures | ancl 2.., The skewness results are shown in Figures \ref{fig:skew1} and \ref{fig:skew2}. + The assembly data shows no signs of being skewed., The assembly data shows no signs of being skewed. + Llowever. he two noncosmological frequencies (A and Ava) are very skewed.," However, the two non–cosmological frequencies $K$ and $Ka$ ) are very skewed." + Clearly. the maps are heavily contaminated: with Galactic foregrounds even outside the kp2 cut.," Clearly, the maps are heavily contaminated with Galactic foregrounds even outside the kp2 cut." + Moreover. he construction of the kp2 mask means that the shape of he distribution of A. has an artificial cut.olf at high AY.," Moreover, the construction of the kp2 mask means that the shape of the distribution of $K$ has an artificial cut–off at high $\Delta T$." + The skewness coefficients appear uniform across all angular separations., The skewness coefficients appear uniform across all angular separations. + Looking at the results [rom the cosmological requencies. the € band frequency appears slightly positively skeweel but the two higher frequeney display no sign of nonnormality.," Looking at the results from the cosmological frequencies, the $Q$ band frequency appears slightly positively skewed but the two higher frequency display no sign of non–normality." + Interestinglv. when we look at the CAIBonly maps. the POLL map appears negatively skewed- there are roughly 15 points outside the confidence region.," Interestingly, when we look at the CMB--only maps, the TOH map appears negatively skewed- there are roughly 15 points outside the confidence region." + ‘This is the opposite sign to the two noncosmological bancs which may suggest that the foreground:removal process has resulted. in an over-subtraction., This is the opposite sign to the two non–cosmological bands which may suggest that the foreground–removal process has resulted in an over-subtraction. + Lhe ILC map also appears to be slightly negatively skewed., The ILC map also appears to be slightly negatively skewed. + The analyses of the kurtosis coellicicnt are. shown in Figures 3. and 4.., The analyses of the kurtosis coefficient are shown in Figures \ref{fig:kurt1} and \ref{fig:kurt2}. + Phe kurtosis is higher than expected in all S assembly maps ancl across all angular separations., The kurtosis is higher than expected in all 8 assembly maps and across all angular separations. + The kurtosis is even greater in the noncosmological frequency maps suggesting that not all the foreground information has n removed. from the assembly maps., The kurtosis is even greater in the non–cosmological frequency maps suggesting that not all the foreground information has been removed from the assembly maps. + “Phe two CALBonly maps also hint at this but with less certainty., The two CMB–only maps also hint at this but with less certainty. + Both maps jwe a slightly higher than expected kurtosis especially when he two are compared to results from the Gaussian MC map., Both maps have a slightly higher than expected kurtosis especially when the two are compared to results from the Gaussian MC map. + That is to sav. their distributions are too peaked. and as with he skewness results suggests errors in foreground modelling.," That is to say, their distributions are too peaked, and as with the skewness results suggests errors in foreground modelling." + DAgostino’s test statistic is shown in Figures 5. and 6.., D'Agostino's test statistic is shown in Figures \ref{fig:D1} and \ref{fig:D2}. + The statistic is an omnibus statistic so it should. be unsurprising that it also pick up evidence of nonnormality in all the WALADPderived. maps., The statistic is an omnibus statistic so it should be unsurprising that it also pick up evidence of non–normality in all the WMAP–derived maps. + Again. the results from. the assembly maps have values mainly outside the confidence region.," Again, the results from the assembly maps have values mainly outside the confidence region." + This shift away from the expected. value is even greater for the A and. Aa bands., This shift away from the expected value is even greater for the $K$ and $Ka$ bands. + The three cosmological frequency. maps. produce results that appear nonnormal but with much less significance than the Galactic bands., The three cosmological frequency maps produce results that appear non–normal but with much less significance than the Galactic bands. + Phe two CALBonly maps also appear nonnormal., The two CMB–only maps also appear non--normal. + At this point. we note that both the kurtosis aud D'Agostino's statistic have a greater shift away [rom their expected: values for the Galactic [frequencies for the very large and. very small angles.," At this point, we note that both the kurtosis and D'Agostino's statistic have a greater shift away from their expected values for the Galactic frequencies for the very large and very small angles." + Ελπίς feature is seen later on in the other statistics we employ., This feature is seen later on in the other statistics we employ. + The results of the shifted.power transformation of the data sets are shown in Figures 7 and S.., The results of the shifted–power transformation of the data sets are shown in Figures \ref{fig:uni_trans1} and \ref{fig:uni_trans2}. . + This part of our analvsis was the most computationally challenging aspect. therefore. we are pleased to seethat the result. from. the Gaussian MC map is as expected.," This part of our analysis was the most computationally challenging aspect, therefore, we are pleased to seethat the result from the Gaussian MC map is as expected." + Due to the challenge, Due to the challenge +The twin Solar Terrestrial Relations Observatory (STEREO: Ixaiser et al.,The twin Solar Terrestrial Relations Observatory (STEREO; Kaiser et al. + 2003: Howard et al., 2008; Howard et al. + 2008) spacecraft provide simultaneous observations from two clilferent points of view.," 2008) spacecraft provide simultaneous observations from two different points of view," + -11:50:26.,= -11:50:26. + 123151 was observed with a single field with the pointing center at RA (J2000) = 23:17:21.0 and Dec (J2000) = 59:23:49.00., I23151 was observed with a single field with the pointing center at RA (J2000) = 23:17:21.0 and Dec (J2000) = 59:28:49.00. + We used MWC349 as the primary [αν calibrator. | 3213/30345 as the Pandas ME," We used MWC349 as the primary flux calibrator, and 3C273/3C345 as the bandpass calibrators." + The time dependence gain was monitored by observing 1741-038. 1830-210. andGILDAS ¢22004-420.," The time dependence gain was monitored by observing 1741-038, 1830-210, and 2200+420." + The visibility data were calibrated and imaged using (he standard procedure in package., The visibility data were calibrated and imaged using the standard procedure in GILDAS package. + The svsteniic velocities are 43.6 [or 118264 and -54.4 for 123151., The systemic velocities are 43.6 $^{-1}$ for I18264 and -54.4 $^{-1}$ for I23151. + The nominal spectral resolution was about 0.4 ! and averaged to about 1: | for SiO (2-1)., The nominal spectral resolution was about 0.4 $^{-1}$ and averaged to about 1 $^{-1}$ for SiO (2-1). + The continuum rms in the 2nim band was ~0.7 mJy for 18264 and ~0.2 mJy for I23151., The continuum rms in the 3mm band was $\sim$ 0.7 mJy for I18264 and $\sim$ 0.2 mJy for I23151. + The observations of the NII; (1.1) and (2.2) lines were carried out on 1997 December 13 for 123151 in the D configuration. and on 2001 July 23 lor I18264 in the C configuration of the VLAτι.," The observations of the $_3$ (1,1) and (2,2) lines were carried out on 1997 December 13 for I23151 in the D configuration, and on 2001 July 23 for I18264 in the C configuration of the VLA." + In both observations. we used the correlator mode 4 which provided 3.13 MIIz bandwidth for both the left and risht polarizations of the (1.1) and (2.2) lines. respectively.," In both observations, we used the correlator mode 4 which provided 3.13 MHz bandwidth for both the left and right polarizations of the (1,1) and (2,2) lines, respectively." + The spectral resolutions of the observations was 48 KHz. or 0.6 | at the NIL; line frequencies.," The spectral resolutions of the observations was 48 KHz, or 0.6 $^{-1}$ at the $_3$ line frequencies." + The pointing center of the observations was RA(J2000) = 18:29:14.31. Dec(J2(n = -11:50:25.6 for I18264 and RA(J2000) = 23:17:21.10. Dee(J2000) = 59:28:48.6 for 1231.," The pointing center of the observations was RA(J2000) = 18:29:14.31, Dec(J2000) = -11:50:25.6 for I18264 and RA(J2000) = 23:17:21.10, Dec(J2000) = 59:28:48.6 for I23151." + The on-source integration per source was about 1 hour., The on-source integration per source was about 1 hour. + The visibility data were calibrat and imaged in the AIPS package., The visibility data were calibrated and imaged in the AIPS package. + The left and right polarizations were averaged during imaging to reduce the noise level in the data., The left and right polarizations were averaged during imaging to reduce the noise level in the data. + The svnthesizecl beam size was about 4 [or the 123151 images. and 278x20 for I18264 images.," The synthesized beam size was about $''$ for the I23151 images, and $2''\!.8 \times 2''\!.0$ for I18264 images." + The rms noise level is 7 mJv per 0.6 ! channel., The rms noise level is 7 mJy per 0.6 $^{-1}$ channel. + For both sources. we detected strong emission in SiO (J—2-1) and HPCO — (J—1-0).," For both sources, we detected strong emission in SiO (J=2-1) and $^{13}$ $^+$ (J=1-0)." + 113264 has detectable anunonia emission al an rms of 7 mJv per 0.6 kms.! channel. and 123151 was not detected in NIL; at an rms of 8 mJy. per 0.6 ! channel.," I18264 has detectable ammonia emission at an rms of 7 mJy per 0.6 $^{-1}$ channel, and I23151 was not detected in $_3$ at an rms of 8 mJy per 0.6 $^{-1}$ channel." + Fie., Fig. + Dl. presents the 3.4 mim and 1.3 mam conünuum emission of the (wo sources., \ref{cont} presents the 3.4 mm and 1.3 mm continuum emission of the two sources. + For 118264. the 1.3 mmn amd 3.4 mum conünuunm emission resolve (wo peaks with the stronger one in the west.," For I18264, the 1.3 mm and 3.4 mm continuum emission resolve two peaks with the stronger one in the west." + While lor I23151. the continuum emission remains singlv peaked even al," While for I23151, the continuum emission remains singly peaked even at" +source is not clear.,source is not clear. + Phe ICM at the cores of some clusters is composed. of interacting cold. ancl hot. eas (Canizares. Alarket Donahue 1988: Fukazawa et al.," The ICM at the cores of some clusters is composed of interacting cold and hot gas (Canizares, Market Donahue 1988; Fukazawa et al." + 1994)., 1994). + Detailed studies show that thermal evaporation as predicted. by classical theory (Spitzer 1962) should be very. cllicient in the LOCAL ( Cowie Binney 1977: Binney Cowie 1951: Fabian Nulsen 1977: Loewenstein Fabian 1990: Fabian 1994)., Detailed studies show that thermal evaporation as predicted by classical theory (Spitzer 1962) should be very efficient in the ICM ( Cowie Binney 1977; Binney Cowie 1981; Fabian Nulsen 1977; Loewenstein Fabian 1990; Fabian 1994). + These works interpret the ICM. observations as a reduction of the magnitude of the thermal conductivity below that precictecl by classical theory., These works interpret the ICM observations as a reduction of the magnitude of the thermal conductivity below that predicted by classical theory. + The evidence for heat [lux inhibition at the ISAL LOCAL ACGNs. ane a osystems ds indirect.," The evidence for heat flux inhibition at the ISM, ICM, AGNs, and $\alpha$ systems is indirect." + Direct conformation of heat [lux inhibition exists in the solar corona and wind for three decades (Montgomery. Dame Iundhausen LOGS).," Direct conformation of heat flux inhibition exists in the solar corona and wind for three decades (Montgomery, Bame Hundhausen 1968)." + Recent measurements performed. with Ulysses (Seime et al., Recent measurements performed with Ulysses (Scime et al. + 1994) confirm that between 1.2 and 5.4 AU. heat flux is inhibited compared to its Spitzer value.," 1994) confirm that between 1.2 and 5.4 AU, heat flux is inhibited compared to its Spitzer value." +" This work concentrates on the ICM observations. with a strong emphasis on the ""cooling flow model (CEM: ef."," This work concentrates on the ICM observations, with a strong emphasis on the ""cooling flow model"" (CFM; cf." + Fabian et al., Fabian et al. + 1984. 1991 Fabian 1994 for a review).," 1984, 1991 Fabian 1994 for a review)." + The CEM reproduces the observed. properties of the LOCAL in the central part of galaxy clusters very. well. but only with the assumption of strong heat [Lux inhibition. ic. heat [Lux is ignored.," The CFM reproduces the observed properties of the ICM in the central part of galaxy clusters very well, but only with the assumption of strong heat flux inhibition, i.e. heat flux is ignored." + “Phe justification of this hypothesis has been heuristic. ancl has presumed that heat fux inhibition is obtained by a tangled magnetic field (in a manner which is not vet clear”).," The justification of this hypothesis has been heuristic, and has presumed that heat flux inhibition is obtained by a tangled magnetic field (""in a manner which is not yet clear"")." + This paper considers heat lux inhibition in the frame work of a rigorous discussion. ancl attempts to quantify the level of heat Dux inhibition.," This paper considers heat flux inhibition in the frame work of a rigorous discussion, and attempts to quantify the level of heat flux inhibition." + In doing so we partially rely on works that consider heat [ux inhibition in the solar wind ( Gary Feldman 1977: Gary et al., In doing so we partially rely on works that consider heat flux inhibition in the solar wind ( Gary Feldman 1977; Gary et al. + 1994 and Scime et al., 1994 and Scime et al. + 1994). due to whistlers.," 1994), due to whistlers." + The LOCAL observations require heat conductivity suppression (heat flux inhibition) compared to the Spitzer value by at least two orders of magnitude. ancl sometimes up to four orders of magnitude (Pistinner Shaviv 1996: Pistinner. Levinson Eichler 1996).," The ICM observations require heat conductivity suppression (heat flux inhibition) compared to the Spitzer value by at least two orders of magnitude, and sometimes up to four orders of magnitude (Pistinner Shaviv 1996; Pistinner, Levinson Eichler 1996)." + lteducing the electron mean free path would lead to heat Hux inhibition., Reducing the electron mean free path would lead to heat flux inhibition. + Mechanisms that would accomplish this can be divided into two main theoretical classes: The first mechanism is realized when a tangled magnetic 101 pervades the plasma (for details ef., Mechanisms that would accomplish this can be divided into two main theoretical classes: The first mechanism is realized when a tangled magnetic field pervades the plasma (for details cf. + Cowie Binney 1981. Rosner Tucker 1989: Tao 1995: Pistinner Shaviv 1996).," Cowie Binney 1981, Rosner Tucker 1989; Tao 1995; Pistinner Shaviv 1996)." + The second comes about when self excited. electron plasma “waves exist (Gary Feldman 1977: Jafelice 1992: Levinson LEichler 1992: Pistinner et al.," The second comes about when self excited electron plasma ""waves exist"" (Gary Feldman 1977; Jafelice 1992; Levinson Eichler 1992; Pistinner et al." + 1996)., 1996). + These asma waves are expected to scatter the heat carrving electrons. thereby reducing their mean free path.," These plasma waves are expected to scatter the heat carrying electrons, thereby reducing their mean free path." + The classification mace above ds quantitative (Goldstein. IXlimas Sandri 1975). and it follows from the different physical processes involved.," The classification made above is quantitative (Goldstein, Klimas Sandri 1975), and it follows from the different physical processes involved." + More specifically. let fp and rj be the coherence length of the magnetic field and the electron gyroradius respectively. then: Large scale tangling. (1). is now seriously constrained and in any case “questionable” (Tao 1995: Pistinner Shaviv 1996).," More specifically, let $l_{B}$ and $r_{l}$ be the coherence length of the magnetic field and the electron gyroradius respectively, then: Large scale tangling, (i), is now seriously constrained and in any case ""questionable"" (Tao 1995; Pistinner Shaviv 1996)." + It seems. that only a very particular family of magnetic field correlation. functions can inhibit heat conduction., It seems that only a very particular family of magnetic field correlation functions can inhibit heat conduction. + These correlation functions have Lorentzian rather than Gaussian properties. and the physical basis for their origin is not νο clear.," These correlation functions have Lorentzian rather than Gaussian properties, and the physical basis for their origin is not yet clear." + In. contrast. electromagnetic electron. plasma waves. (ii). obtained [from a. collisionless plasma model (Levinson Lichler. 1992). provide. large inhibition factors when applied to the CEM (Pistinner. ct al.," In contrast electromagnetic electron plasma waves (ii), obtained from a collisionless plasma model (Levinson Eichler 1992), provide large inhibition factors when applied to the CFM (Pistinner, et al." + 1996)., 1996). + The model of Levinson Eichler (1992) follows Cary Feldman (1977) and invokes whistler-clectron interaction to suppress the heat transfer., The model of Levinson Eichler (1992) follows Gary Feldman (1977) and invokes whistler-electron interaction to suppress the heat transfer. + In light of our. findings (Pistinner et al., In light of our findings (Pistinner et al. + 1996) and the observational information aud interpretation accumulated. during the past three decades. heat conduction. theory in cdilluse astrophysical plasmas should. be reexamined.," 1996) and the observational information and interpretation accumulated during the past three decades, heat conduction theory in diffuse astrophysical plasmas should be reexamined." + Scattering by plasma turbulence should be considered along with Coulomb collisions., Scattering by plasma turbulence should be considered along with Coulomb collisions. + Plasma turbulence results from collective phenomena. and may [ead το electron-waves resonant. pitch-angle scattering.," Plasma turbulence results from collective phenomena, and may lead to electron-waves resonant pitch-angle scattering." + Non-magnetized plasmas are studied in detail. and under some conditions ion acoustic turbulence. leacis to heat-ux inhibition (Galeey Natanzon 1984).," Non-magnetized plasmas are studied in detail, and under some conditions ion acoustic turbulence leads to heat-flux inhibition (Galeev Natanzon 1984)." + Jallliche (1992) considers this possibility in the context of the CEM., Jaffliche (1992) considers this possibility in the context of the CFM. + Alrough he ignores strict requirements for ion-acoustic waves excitation. he finds insullicient heat inhibition.," Although he ignores strict requirements for ion-acoustic waves excitation, he finds insufficient heat inhibition." + Levinson Eichler (1992) follow Gary Feldman (1977) and consider heat [ux inhibition by whistlers., Levinson Eichler (1992) follow Gary Feldman (1977) and consider heat flux inhibition by whistlers. + Gary Feldman (1977) fined that the inhibition obtained by whistler-electron scattering in the (significantly magnetized) solar wind is not large., Gary Feldman (1977) find that the inhibition obtained by whistler-electron scattering in the (significantly magnetized) solar wind is not large. + Levinson Lichler (1992) show that. collision dominated: plasmas are. subject. to Weibel type instabilities that generate the whistler electromagnetic mode clleetively. and find strong heat Ες inhibition inweakly maenetizecl plasmas.," Levinson Eichler (1992) show that collision dominated plasmas are subject to Weibel type instabilities that generate the whistler electromagnetic mode effectively, and find strong heat flux inhibition in magnetized plasmas." + “Lhe differences between the conclusions of Gary Feldman ancl Levinson Eichler (1992) result. from cdillerent magnitudes of the assumed magnetic contribution to total pressures: Whereas Gary Feldman assume comparable magnetic and gas pressures as is appropriate for the solar wind. Levinson Eichler (1992) consider a weakly magnetized plasma.," The differences between the conclusions of Gary Feldman and Levinson Eichler (1992) result from different magnitudes of the assumed magnetic contribution to total pressures: Whereas Gary Feldman assume comparable magnetic and gas pressures as is appropriate for the solar wind, Levinson Eichler (1992) consider a weakly magnetized plasma." + Levinson Eiehler (1992) conclude that if the magnetic oessure is small compared. to the gas. pressure. heat-Iux inhibition along field. lines is ellective.," Levinson Eichler (1992) conclude that if the magnetic pressure is small compared to the gas pressure, heat-flux inhibition along field lines is effective." + In. any case. both reatments neglect geometric details of the plasma processes involved.," In any case, both treatments neglect geometric details of the plasma processes involved." +" In particular. the assumption of a BCA scattering operator used by Levinson Eichler 1992. (followed: by ""ustinner et al."," In particular, the assumption of a BGK scattering operator used by Levinson Eichler 1992 (followed by Pistinner et al." + 1996) to calculate the particle distribution unction. which neglects the piteh angle dependence: of," 1996) to calculate the particle distribution function, which neglects the pitch angle dependence of" +iw) 5Γ sources have optical spectra typical of LINERS of starburst galaxies (al have stroug [OTI] eiiission).,iv) 5 sources have optical spectra typical of LINERS of starburst galaxies (all have strong [OII] emission). + eTje umber of chance coincidences in 45 error boxesis ONνο for broac lue quasar ak I for narrow line AGN (including in this category strong |OTI CLUISSI1Oi line galaxies like LINERS aud starburst galaxies)., $\bullet$ The number of chance coincidences in 45 error boxesis $<0.8-1.5$ for broad line quasar and $<4$ for narrow line AGN (including in this category strong [OII] emission line galaxies like LINERS and starburst galaxies). + ο A least 5) of the narrow enudssion line ACN lie in small groups and/or i interactme coues., $\bullet$ At least 5 of the narrow emission line AGN lie in small groups and/or in interacting couples. + eo Ayout Lf:H) of the error-boxes. studied in detail coualms no ‘reasonable’ (iu foris of Νταν to optical ratio o known classes of sources) counterpart to the source (ow1i to R=20.5 eOXtical spectroscopy indicaes a wide varietv of specra. with a huge fractio of “intermediate” objects (type 121.9 ACN. red? quasars).," $\bullet$ About 1/3 of the error-boxes studied in detail contains no `reasonable' (in terms of X-ray to optical ratio of known classes of sources) counterpart to the X-ray source down to R=20.5 $\bullet$ Optical spectroscopy indicates a wide variety of spectra, with a large fraction of “intermediate” objects (type 1.8-1.9 AGN, `red' quasars)." + Figure 2a) plots the Iuninositv of the ideutified TELLAS sources as a functio1 of their redshlift., Figure 2a) plots the luminosity of the identified HELLAS sources as a function of their redshift. + We have iceutifications of broad line qtasars up to z=2.76 and huninosity of ~10/9 ore sl alAC of narrow line AGN up to z=0.E and huuinositv of ~Lot! cre l ," We have identifications of broad line quasars up to z=2.76 and luminosity of $\sim10^{46}$ erg $^{-1}$, and of narrow line AGN up to z=0.4 and luminosity of $\sim10^{44}$ erg $^{-1}$ ." +Figure 2b) plots the (S-ID/(S|ID) of he identified. sources as, Figure 2b) plots the (S-H)/(S+H) of the identified sources as +as characterized by (defined below).,as characterized by (defined below). + A recent. aud possibly related result is that Seyfert Is with broad chussion lines tend to have hard (fiat) Nav spectral slopes (e.g. Brandt. Mathur. Elvis 1997).," A recent, and possibly related result is that Seyfert 1s with broad emission lines tend to have hard (flat) X-ray spectral slopes (e.g., Brandt, Mathur, Elvis 1997)." + Iu a hard-N-ray-sclected sample of (mostly Sevfert) ACN. narrow fux correlates well with N-rav flux. while broad Balmer lues do not (Cwossan 1992).," In a hard-X-ray-selected sample of (mostly Seyfert) AGN, narrow flux correlates well with X-ray flux, while broad Balmer lines do not (Grossan 1992)." + The physical origin of these diverse and imterrelated correlations has vet to be deteruiued., The physical origin of these diverse and interrelated correlations has yet to be determined. + We are launching a large-scale effort to probe these effects in large samples. using both data and analysis as homogeneous as possible.," We are launching a large-scale effort to probe these effects in large samples, using both data and analysis as homogeneous as possible." + Alay plysically iuformative trends intrinsic to QSOs may be masked by dispersion iu the data due to either low signal-to-noise or variability., Many physically informative trends intrinsic to QSOs may be masked by dispersion in the data due to either low signal-to-noise or variability. + An oenportant tool for studying elobal properties of QSOs is the co-addition of data for samples of QSOs., An important tool for studying global properties of QSOs is the co-addition of data for samples of QSOs. + Th this paper. we concentrate on an analysis of composite optical/UV spectra of subsamples of QSOs erouped by the relative y.reneth of their soft N-rav cussion.," In this paper, we concentrate on an analysis of composite optical/UV spectra of subsamples of QSOs grouped by the relative strength of their soft X-ray emission." + Although the signal-to-noise ratio (S/N) for the individual spectra i both samples we study here tends to be about 10 or less per resolution clement. the co-addition (averaging) of spectra with simular continui properties allow us to increase the S/N aud constraiu the properties of the average QSO.," Although the signal-to-noise ratio (S/N) for the individual spectra in both samples we study here tends to be about 10 or less per resolution element, the co-addition (averaging) of spectra with similar continuum properties allow us to increase the S/N and constrain the properties of the average QSO." + Through averaging. a ereater nuniber of enussion lines. with a wider rauge of ionization energies. and fuer details iu enuüssion line profiles become measurable.," Through averaging, a greater number of emission lines, with a wider range of ionization energies, and finer details in emission line profiles become measurable." + This techuique has been applied in several recent studies (0.8... Cristiani Vio 1990. Francis et al.," This technique has been applied in several recent studies (e.g., Cristiani Vio 1990, Francis et al." + 1991. Osmer. Porter. Green 1991. Zheug ct al.," 1991, Osmer, Porter, Green 1994, Zheng et al." + 1996)., 1996). + What is lost is a roliable measure of the intrinsic dispersion iu the observed correlations., What is lost is a reliable measure of the intrinsic dispersion in the observed correlations. + Uowever. it is nuaportaut to first discover the correlations intrinsic to the average QSO.," However, it is important to first discover the correlations intrinsic to the average QSO." + The sources of dispersion iu the relationship cau later be studied if data of adequate S/N are available for a large enough sample., The sources of dispersion in the relationship can later be studied if data of adequate S/N are available for a large enough sample. + Table 1l sunuuarizes nean continua properties for the N-rav bright and X-ray fant sibsamples we culled from. the LBQS and QSO samples described below., Table 1 summarizes mean continuum properties for the X-ray bright and X-ray faint subsamples we culled from the LBQS and QSO samples described below. + Optical auc X-raw huuinositics are taken from Green ct al. (, Optical and X-ray luminosities are taken from Green et al. ( +1995) aud Cxecn (1996). aud assuine My=50 kn and qj=0.5.,"1995) and Green (1996), and assume $H_0=50$ km and $q_0=0.5$." +" The slope of a hypothetical powerlaw connecting aud 2 keV is defined asa,=0.381lostbus.). so that is larger for objects with stronger optical cussion relative to N-raw."," The slope of a hypothetical powerlaw connecting and 2 keV is defined as $\aox\, = 0.384~{\rm +log} (\frac{ \lopt}{\lx })$, so that is larger for objects with stronger optical emission relative to X-ray." + The Large Bright Quasar Survey (LBQS: Hewett. Foltz Chattee 1995) is a sample of more than a thousaud QSOs. wniformb-sclected over a wide rauge of redshitts.," The Large Bright Quasar Survey (LBQS; Hewett, Foltz Chaffee 1995) is a sample of more than a thousand QSOs, uniformly-selected over a wide range of redshifts." + LBOS QSO candidates were selected using the Automatic Plate Aleasuring Machine (πο Trimble 1981) to scan Ul. Schuuidt direct photographic aud objective prisa plates., LBQS QSO candidates were selected using the Automatic Plate Measuring Machine (Irwin Trimble 1984) to scan UK Schmidt direct photographic and objective prism plates. +" A combination of quantifiable selection tecliniques were used. including color-selection. selection of objects with stroug cussion lines. selection of objects having τουματος, absorption features or contiuuun breaks."," A combination of quantifiable selection techniques were used, including color-selection, selection of objects with strong emission lines, selection of objects having redshifted absorption features or continuum breaks." + The technique appears to be highly efficient at finding QSOs with 0.2<2«3.3. a significantly broader range than past work.," The technique appears to be highly efficient at finding QSOs with $0.21.175."," The X-ray faint sample (XF hereafter, 54 QSOs) includes both detections and lower limits with $\aox \ge 1.475$." + QSOs with lower limits below that value could rightly belong cither to the NB or NF sample. and so are excluded from cousideration.," QSOs with lower limits below that value could rightly belong either to the XB or XF sample, and so are excluded from consideration." + Note also that the value of 1.175 does not imply that is measured to such accuracy., Note also that the value of 1.475 does not imply that is measured to such accuracy. + Rather. if provides a convenieut dividing liue near the median of the small rauge of values (~1.2 to 1.6) typically measured in QSOs.," Rather, it provides a convenient dividing line near the median of the small range of values $\sim 1.2$ to $1.6$ ) typically measured in QSOs." +" Continuum properties of the final NF aud NB (6,selected) saamples are listed in Table 1.", Continuum properties of the final XF and XB -selected) samples are listed in Table 1. + Iu survival analysis. if the lowest (highest) point iu the data set is an upper (lower) lait. the mean is not well defined. since the distribution is nof norimalizable. and so the outlviug censored point is redefined as a detection.," In survival analysis, if the lowest (highest) point in the data set is an upper (lower) limit, the mean is not well defined, since the distribution is not normalizable, and so the outlying censored point is redefined as a detection." + For the NF sample. we list here the value of that redefined uat. where the distribution is truncated.," For the XF sample, we list here the value of that redefined limit, where the distribution is truncated." + The resulting mean value is biased. so that the true mean values of aid for the LBOS ΝΕ sample are probably even more Navy faint than those listed.," The resulting mean value is biased, so that the true mean values of and for the LBQS XF sample are probably even more X-ray faint than those listed." +" We find no significant differences in the distributious of redshift.NG, Or between our NB Pgaud NF subsiuuples of the LBQS."," We find no significant differences in the distributions of redshift, or between our XB and XF subsamples of the LBQS." + Iu any case. the cussion line properties of the LBQS as a whole show no strong dependence on either Iunimositv or redshift (Francis et al.," In any case, the emission line properties of the LBQS as a whole show no strong dependence on either luminosity or redshift (Francis et al." + 1993)., 1993). + To explore changes in QSO UV spectra as a function ofayy... we include a previously compiled sample of QSOs observed bw both theLerplorer {ΙΟ} audEinstein.," To explore changes in QSO UV spectra as a function of, we include a previously compiled sample of QSOs observed by both the ) and." + This sample was sclected as cescribed in Green (1996). by requiring that the QSOs iu the uuuple have. soft N-rav data available in Wilkes et al. (," This sample was selected as described in Green (1996), by requiring that the QSOs in the sample have soft X-ray data available in Wilkes et al. (" +199D). we defiue,"1994), we define" +"where we assume that xii, gives photorates as in the VAL ‘ratefile CMillaretal.1997... and. discussed. further below).","where we assume that $\chi_{\rm ism}$ gives photorates as in the UMIST ratefile \citealt{millar.et.al97}, and discussed further below)." + Phere is some uncertainty in this. since the radiation fick may be harder than that of the interstellar medium.," There is some uncertainty in this, since the radiation field may be harder than that of the interstellar medium." + We use the canonical cosmic rav ionisation rate of ὅτι1310 ls! ," We use the canonical cosmic ray ionisation rate of $\chi_{\rm ism}=1.3 \times +10^{-17}~{\rm s^{-1}}$ ." +The evolution of the interelump medium can be followed ina very similar way to that of a clump., The evolution of the interclump medium can be followed in a very similar way to that of a clump. + In this single-point calculation. the initial composition in the AGB atmosphere is the same as for a clump but the parcel of gas is assumed to have an initial density lower by a factor of 10 compared with the clump.," In this single-point calculation, the initial composition in the AGB atmosphere is the same as for a clump but the parcel of gas is assumed to have an initial density lower by a factor of 10 compared with the clump." + The density falls off with the square of the distance from the star. as appropriate for a steady spherically symmetric How.," The density falls off with the square of the distance from the star, as appropriate for a steady spherically symmetric flow." + n(t) (ientin, n(t)=10^6 (. +iTeures A parcel of 5gas will then experience an extinction that Varies as F(G, A parcel of gas will then experience an extinction that varies as (. +e-c Since the clump and interebump mecdim will initally have 10 the same temperature. itis assumed for simplicity that 1e interclump medium temperature is the same as that of 10 clump. and therefore varies as given by Equation 5.," Since the clump and interclump medim will initally have the the same temperature, it is assumed for simplicity that the interclump medium temperature is the same as that of the clump, and therefore varies as given by Equation 5." + This is unlikely to be true in the later stages of the PN νοτος when the interclump medium will be hotter than 1e clumps but this will only accelerate the destruction of rose molecules that survived the drop in extinction., This is unlikely to be true in the later stages of the PN evolution when the interclump medium will be hotter than the clumps but this will only accelerate the destruction of those molecules that survived the drop in extinction. + In the »eriod. of interest. the range of temperatures involved. does not influence the chemistry very strongly.," In the period of interest, the range of temperatures involved does not influence the chemistry very strongly." + The chemical model used is similar to the one employed in Viti&Williams(1999)., The chemical model used is similar to the one employed in \citet{viti&williams99}. +. llowever. we have mace considerable changes to the chemistry.," However, we have made considerable changes to the chemistry." + To all the basic species (O. C. CO ete)," To all the basic species (O, C, CO etc.)" + we have added all the species (mainly hivelrocarbons) that are thought to be abundant at the initial stage of the PPN: this chemistry also includes species that have an unpaired electron located on an internal or terminal carbon atom., we have added all the species (mainly hydrocarbons) that are thought to be abundant at the initial stage of the PPN; this chemistry also includes species that have an unpaired electron located on an internal or terminal carbon atom. + For most of these additions. the UMIST rate file for gas phase reactions. involving several hundred species (Millaretal.1997)... ancl which is normally: used routinely in our models. did not have a sullicient. network of reactions.," For most of these additions, the UMIST rate file for gas phase reactions, involving several hundred species \citep{millar.et.al97}, and which is normally used routinely in our models, did not have a sufficient network of reactions." + Pherclore the formation and destruction routes were taken from Frenklach&Feigelson(1989)., Therefore the formation and destruction routes were taken from \citet{frenklach&feigelson89}. +.. Phe reaction rates were fitted. by using dilferent formulae from. the UALS ones., The reaction rates were fitted by using different formulae from the UMIST ones. + To account. for that. we have mocified our code to include new rate cocllicicnts calculations taken from Cau(2001).," To account for that, we have modified our code to include new rate coefficients calculations taken from \citet{cau01}." +. For some of those reactions. no rate coellicients are available and Frenklach&Feigelson(1989) determine them from the rate coefficients of their inverse reactions: we have emploved the same method here.," For some of those reactions, no rate coefficients are available and \citet{frenklach&feigelson89} determine them from the rate coefficients of their inverse reactions: we have employed the same method here." + We have not included three-body reactions., We have not included three-body reactions. +" We have also excluded reactions which use an ""unspecified! species as a collisional body causing de-excitation or dissociation.", We have also excluded reactions which use an `unspecified' species as a collisional body causing de-excitation or dissociation. + Phese may be of some relevance ancl should. be included. in further studies., These may be of some relevance and should be included in further studies. + Note that Frenklach&Feigelson(1989). also extrapolated their rate coellicients to temperatures very. cilferent. from. those at which they were measured., Note that \citet{frenklach&feigelson89} also extrapolated their rate coefficients to temperatures very different from those at which they were measured. + we 1-4 results of the calculations of he evolution of molecular fractional abundances in. clump and interclump gas. for several illustrative species.," We present in Figures 1-4 results of the calculations of the evolution of molecular fractional abundances in clump and interclump gas, for several illustrative species." + In ‘Table Lowe give the computed. fractional abundances of potentially observable species in the clump. ancl also the clump:interclump ratio of abundances. for several epochs xtween about 2 and 10 thousand: vears. ic. the period of ransition from PPN to PN phases.," In Table 1 we give the computed fractional abundances of potentially observable species in the clump, and also the clump:interclump ratio of abundances, for several epochs between about 2 and 10 thousand years, i.e. the period of transition from PPN to PN phases." + The figures show generally the same qualitative ohaviour., The figures show generally the same qualitative behaviour. + X comparison of clump and interclump abundances shows that molecules are photocdissociated earlier in the interclump than in the clump gas. as expected.," A comparison of clump and interclump abundances shows that molecules are photodissociated earlier in the interclump than in the clump gas, as expected." + Thus molecules survive longer in the clumps. and so the ratio of clump to interclump abundances varies stronglv.," Thus molecules survive longer in the clumps, and so the ratio of clump to interclump abundances varies strongly." + For example. the CN abundance ratio varies from 0.26 at 2550 vr to 270 at. 10050 vr. à factor of 1000.," For example, the CN abundance ratio varies from 0.26 at 2550 yr to 270 at 10050 yr, a factor of 1000." + Figure 1 shows the clump ancl interelump evolution of CO and CN fractional abuncances., Figure 1 shows the clump and interclump evolution of CO and CN fractional abundances. + “Phese represent molecules that have high. and low initial abuncances. respectively. Le. in the stellar. atmosphere of the AGB star.," These represent molecules that have high and low initial abundances, respectively, i.e. in the stellar atmosphere of the AGB star." + The abundance of CO remains high in both clump and interclump eas until photoclissociation begins to play a role as the gas density and extinction. decline during the expansion. with CO in the higher density clump gas surviving until later times.," The abundance of CO remains high in both clump and interclump gas until photodissociation begins to play a role as the gas density and extinction decline during the expansion, with CO in the higher density clump gas surviving until later times." +" On the other hand. CN is a molecule formed. as a product. of photodissociation. of larger species. here called aiproduct. Since photoclissociation is [faster in the interclump gas. the production of CN is also faster there initially, so CN rises faster in the interclump 5σας than in the clump.1 but also declines earlier."," On the other hand, CN is a molecule formed as a product of photodissociation of larger species, here called a. Since photodissociation is faster in the interclump gas, the production of CN is also faster there initially, so CN rises faster in the interclump gas than in the clump, but also declines earlier." + Similar effects. are observed. for. other. species., Similar effects are observed for other species. + The simple carbon chains Cyll and CLL are both degradation products of larger species. and the time evolution illustrated in Figure 2 shows that their abundances peak in the interclump eas earlier (by. several thousand vears) than in the clump gas.," The simple carbon chains ${\rm C_4H}$ and ${\rm C_5H}$ are both degradation products of larger species, and the time evolution illustrated in Figure 2 shows that their abundances peak in the interclump gas earlier (by several thousand years) than in the clump gas." + Figure 3 shows the time evolution of ο11» (whieh is abundant in the stellar atmosphere) anc Cylls. a degradation product of larger species.," Figure 3 shows the time evolution of ${\rm C_2H_2}$ (which is abundant in the stellar atmosphere) and ${\rm C_4H_2}$ , a degradation product of larger species." + Their behaviours are, Their behaviours are +of the internal structure of the clouds and the initial mass function (IMF) of stars can provide insights on the processes responsible for the formation of stars.,of the internal structure of the clouds and the initial mass function (IMF) of stars can provide insights on the processes responsible for the formation of stars. +" The mass distribution of molecular clouds, and cores within them have been extensively studied in the past twenty years."," The mass distribution of molecular clouds, and cores within them have been extensively studied in the past twenty years." +" Until recently, it was believed that the mass distribution of CO clumps was described by ANco/AlogM=M-? with a=0.740.2 for the Milky Way (Kramer et al."," Until recently, it was believed that the mass distribution of CO clumps was described by $\Delta N_{\rm {CO}}/\Delta +\log M=M^{-\alpha}$ with $\alpha=0.7\pm 0.2$ for the Milky Way (Kramer et al." +" 1998, Rosolowski 2004)."," 1998, Rosolowski 2004)." +" The mass distribution of prestellar cores, the direct progenitors of stars and stellar systems, as observed in dust continuum is much steeper, resembling the Salpeter IMF with a power law index of a=1.35 (Motte et al."," The mass distribution of prestellar cores, the direct progenitors of stars and stellar systems, as observed in dust continuum is much steeper, resembling the Salpeter IMF with a power law index of $\alpha=1.35$ (Motte et al." + 1998; Enoch et al., 1998; Enoch et al. + 2008)., 2008). +" However, recent papers questioned the impact of the source extraction scheme used to segment the data on the final mass distribution shape (Pineda et al."," However, recent papers questioned the impact of the source extraction scheme used to segment the data on the final mass distribution shape (Pineda et al." + 2009)., 2009). + Buckle et al. (, Buckle et al. ( +2010) found a steeper mass distribution for small scale CO clumps.,2010) found a steeper mass distribution for small scale CO clumps. +" Also, in most cases, different tracers are required to trace different structures such as dense cores and molecular clumps, raising the question of detection biases."," Also, in most cases, different tracers are required to trace different structures such as dense cores and molecular clumps, raising the question of detection biases." +" Statistics is often a problem too, binning small number of objects introduce artifacts (Reid Wilson 2006)."," Statistics is often a problem too, binning small number of objects introduce artifacts (Reid Wilson 2006)." + Therefore some confusion exists on what is the real mass structure of molecular clouds., Therefore some confusion exists on what is the real mass structure of molecular clouds. + Another important physical aspect of molecular cloud structure is the probability density function (PDF) of the gas volume density., Another important physical aspect of molecular cloud structure is the probability density function (PDF) of the gas volume density. + This quantity has received only little attention (e.g. Dring et al., This quantity has received only little attention (e.g. Dring et al. + 1996 for HI; Smith Scalo 2009 for CO) but potentially contains crucial information on the processes at the origin of the density fluctuations., 1996 for HI; Smith Scalo 2009 for CO) but potentially contains crucial information on the processes at the origin of the density fluctuations. +" For instance, turbulence-driven fragmentation"," For instance, turbulence-driven fragmentation" +17.5 for 6 dof thus excluding all but the most contrived of local iuiodels.,17.5 for 6 dof $-$ thus excluding all but the most contrived of local models. + The data are also mareiually iuconsisteut with that of the total galactic column density aloug the line of sight of each burst (47 = 9.6 for 6 dof}., The data are also marginally inconsistent with that of the total galactic column density along the line of sight of each burst $\chi^2$ = 9.6 for 6 dof). + Assmuing. that bursts are cosmological ia origin. we next tested whether the data could support an additional average absorption above ((i.c.. mtriusie to the source and/or host object).," Assuming, that bursts are cosmological in origin, we next tested whether the data could support an additional average absorption above (i.e., intrinsic to the source and/or host object)." + However. at cosinologica distances the effective iis increased by (Morrison MeCanunon 1983) since the spectra turnover ds reduce by (11:) due to the redeshüft.," However, at cosmological distances the effective is increased by $z$ $^{2.6}$ (Morrison McCammon 1983) since the spectral turnover is reduced by $z$ ) due to the red-shift." + Therefore. we simultaneously inchided both he galactic absorption and an additional red-shiftcc absorption to represcut intrinsic absorption within the cuviroumen local to the afterglow.," Therefore, we simultaneously included both the galactic absorption and an additional red-shifted absorption to represent intrinsic absorption within the environment local to the afterglow." + In the model convention within NSPEC. this i9 designated wabs*zwabs*zpower.," In the model convention within XSPEC, this is designated wabs*zwabs*zpower." + The values of i were fixed at the values eiven iu Table 1., The values of $z$ were fixed at the values given in Table 1. + Tn cases where : has not determined directly. the best estimated value is used. aud ifthat docs not exist (6.8... iu the cases of GRD980329 aud GRDB950519) 2 is allowed to be a free parameter.," In cases where $z$ has not been determined directly, the best estimated value is used, and if that does not exist (e.g., in the cases of GRB980329 and GRB980519) $z$ is allowed to be a free parameter." + If oll the additiona red-shifted absorptious are coustrained to have the same value. the vesultine best-fit has a 47 of 91.3 for 98 dof for an average additional red-shifted oof (LOLAZS) & 1022 atom 2.," If all the additional red-shifted absorptions are constrained to have the same value, the resulting best-fit has a $\chi^2$ of 94.3 for 98 dof for an average additional red-shifted of $\pm ^{0.28}_{0.51}$ ) $\times$ $^{22}$ atom $^{-2}$." + Fixing the red-shifted colum deusity to zero and re-fitting. results in a 4? of 101.1 for 99 dof.," Fixing the red-shifted column density to zero and re-fitting, results in a $\chi^2$ of 101.1 for 99 dof." + Thus. the addition of this colhunu is sienificau under an F tes at the >92% level.," Thus, the addition of this column is significant under an F test at the $>$ level." + Since the predic5 spectrui iu blas wave models varies little from event to event (e.g... Wijers et al.," Since the predicted spectrum in blast wave models varies little from event to event (e.g., Wijers et al." + 1997). we next tied thespectral slopes.," 1997), we next tied thespectral slopes." + Re-fitting resulted iu à 4? of 100.1 for 101 dof for an average red-shifted oof (ur & 1023 atom P and best-fitÜ a of. 00.10.11202E, Re-fitting resulted in a $\chi^2$ of 100.4 for 104 dof for an average red-shifted of ${\pm ^{3.4}_{4.8}}$ ) $\times$ $^{21}$ atom $^{-2}$ and best-fit $\alpha$ of $\pm ^{0.10}_{0.12}$. +p We note that for strong sources such as the Crab. the uucertaintv in the fitted vvalues is- a few. μὴ atoll D. due largely to uncertainties in low energy calibration.," We note that for strong sources such as the Crab, the uncertainty in the fitted values is a few $^{20}$ atom $^{-2}$, due largely to uncertainties in low energy calibration." +" Towever. for weak sources, such as afterelows. the unucertaiuty is dominated bv the uncertainty in background subtraction."," However, for weak sources, such as afterglows, the uncertainty is dominated by the uncertainty in background subtraction." + From studies of weals sources we estimate this to be ors2% of the statistical error., From studies of weak sources we estimate this to be $\approxlt$ of the statistical error. + The ecneral properties of afterglows are in remarkable agreement with the predictions of even the simplest fireball models (Meszaros Rees 1997) iu which a relativistic blast wave raciates its energy as it decelerates * plowing through the surrounding medimm., The general properties of afterglows are in remarkable agreement with the predictions of even the simplest fireball models (Meszaros Rees 1997) in which a relativistic blast wave radiates its energy as it decelerates by plowing through the surrounding medium. + As the fireball slows down. the peak of the enmütted radiation shifts iu time to lower cucreies producing the observed oower-huwv decays in the X-ray. optical aud radio (e.e.. Wasiman 1997: Wijers Calama 1998 and references herein}.," As the fireball slows down, the peak of the emitted radiation shifts in time to lower energies producing the observed power-law decays in the X-ray, optical and radio (e.g., Waxman 1997; Wijers Galama 1998 and references therein)." + The diversity in afterglow behavior is most casily explained by beaming and/or the differences im radiative losses at carly times (Meszaros et al., The diversity in afterglow behavior is most easily explained by beaming and/or the differences in radiative losses at early times (Meszaros et al. + 1998: Wijers Galama 1998)., 1998; Wijers Galama 1998). + ILowever. afterglows are onlv detected optically about half of the time. leading to the sugecstiou that there mast be significant extinction at the source.," However, afterglows are only detected optically about half of the time, leading to the suggestion that there must be significant extinction at the source." + The extinction is generally. believed. to be in the form of dust whose existence has been inferred by the observed reddening iu the optical spectra of CRBOTL211 aud more receutlv. CRB9S0329.," The extinction is generally believed to be in the form of dust whose existence has been inferred by the observed reddening in the optical spectra of GRB971214 and more recently, GRB980329." + In addition. the detection of the [ο 11] eenissionu line aud also an [Meg 1| absorption line (Metzger et al.," In addition, the detection of the [O ] emission line and also an [Mg ] absorption line (Metzger et al." + 1997a) in GRD970508 indicates the presence of a relatively deuse mediunu (Alctzeer et al., 1997a) in GRB970508 indicates the presence of a relatively dense medium (Metzger et al. + 1900)., 1997b). + Caven that the estimated redshifts for afterelows lic in the rauge 1l3.5. when star formation was at its peak (e.g.. Macdau et al.," Given that the estimated redshifts for afterglows lie in the range 1–3.5, when star formation was at its peak (e.g., Madau et al." + 1998) aud that the progenitors of CRBOTO50s. GRD971211. CRB9S0329 and CRDB9850702 appear to be well located inside their respective host galaxies. it secnus jumselv that GRB are associated with star forming reeions.," 1998) and that the progenitors of GRB970508, GRB971214, GRB980329 and GRB980702 appear to be well located inside their respective host galaxies, it seems likely that GRB are associated with star forming regions." + This is supported by the high effective. temperature implied by the relative strengths of the [O 11] and [Ne 11 ines observed in the optical spectra of GRD970508 aud sugeests the presence of a substantial population of hassive stars and thus active star formation (Bloom et ., This is supported by the high effective temperature implied by the relative strengths of the [O ] and [Ne ] lines observed in the optical spectra of GRB970508 and suggests the presence of a substantial population of massive stars and thus active star formation (Bloom et al. + 19958)., 1998). + The apparent longevity of the observed afterglows aud he observation of N-rayv precursors by. (Murakaiui ct al., The apparent longevity of the observed afterglows and the observation of X-ray precursors by (Murakami et al. +" 1991) support α ""αμ fireball inodel (Rees Moesziros 1998).", 1991) support a “dirty” fireball model (Rees Meszaros 1998). +" Although both hvperuova and neutron star merger models can satisfy energeties requirements DU"" eres 1 we would expect a fraction of neutron star mergers to take place well outside their host ealaxies - purely due to the high proper imotiou acquired iu two consecutive supernova explosions."," Although both hypernova and neutron star merger models can satisfy energetics requirements $>$ $^{53}$ ergs $^{-1}$, we would expect a fraction of neutron star mergers to take place well outside their host galaxies - purely due to the high proper motion acquired in two consecutive supernova explosions." + The act that the observed optical trausieuts of (and possibly 5) bursts are well located within simall host galaxies. is suggestive aud would teud to favor hvperuova models.," The fact that the observed optical transients of 4 (and possibly 5) bursts are well located within small host galaxies, is suggestive and would tend to favor hypernova models." +" Iu these models (Woosley 1993: Paczvuski 1998). a very massive (51034 ,.) star collapses. producing a ""dirty fireball ~300) tines more hunuinous than a supernova (~L0°! ere)."," In these models (Woosley 1993; Paczynski 1998), a very massive $\sim$ $\msun$ ) star collapses, producing a “dirty” fireball $\sim$ 300 times more luminous than a supernova $\sim$ $^{54}$ erg)." + This large amount of energy is obtained from the rotational energy of a err black-hole. formed in the core collapse., This large amount of energy is obtained from the rotational energy of a Kerr black-hole formed in the core collapse. + Since such massive stars die voung (~10° ves) and therefore close to where they were born. a natural consequence is that GRD trace the star formation rate aud should be associated with high deusity. dusty regious.," Since such massive stars die young $\sim$ $^6$ yrs) and therefore close to where they were born, a natural consequence is that GRB trace the star formation rate and should be associated with high density, dusty regions." + The available data support this., The available data support this. + For example. bv comparing the color cAvectra of GRD971211 and GRDB970508. IIalperu ct al. (," For example, by comparing the color spectra of GRB971214 and GRB970508, Halpern et al. (" +1998) caleulate that an additional oot « --107. atom 2 2.is required: at the distance. of GRD97121 to explain the extreme reddening of the spectrin.,1998) calculate that an additional of $\times$ $^{21}$ atom $^{-2}$ is required at the distance of GRB971214 to explain the extreme reddening of the spectrum. + Reichart (1998) has shown that in order to reconcile the optical decay and spectral profiles. there iust be a red-shifted source of extinction at the burst site of 1.9 « 1031 atom 7.," Reichart (1998) has shown that in order to reconcile the optical decay and spectral profiles, there must be a red-shifted source of extinction at the burst site of 1.9 $\times$ $^{21}$ atom $^{-2}$ ." + Πο further areues that this absorber is probably the host galaxy of GRB9OT121 Lat a of 1.89., He further argues that this absorber is probably the host galaxy of GRB971214 at a $z$ of 1.89. + Tavlor et al. (, Taylor et al. ( +1998) arene Youn radio observations,1998) argue from radio observations +trend in overestimating outer source counts (especially at low values). since it 15 favorable to detect them on top of a positive background fluctuation (an effect known as Eddington bias. see Hasinger et al. 1993::,"trend in overestimating outer source counts (especially at low values), since it is favorable to detect them on top of a positive background fluctuation (an effect known as Eddington bias, see Hasinger et al. \cite{hasinger1993};" + Moretti et al. 2002))., Moretti et al. \cite{moretti2002}) ). + This again adds on the enhancement of outer sources., This again adds on the enhancement of outer sources. + The first bias leads to the loss of BFS. but it does not affect our selected sources.," The first bias leads to the loss of BFS, but it does not affect our selected sources." + The effect of the second bias on the estimated flux can be evaluated a posteriori from the duration of the pointings and the number of counts., The effect of the second bias on the estimated flux can be evaluated a posteriori from the duration of the pointings and the number of counts. + Very conservative assumptions give a factor of ~2 as the maximum overestimate., Very conservative assumptions give a factor of $\sim 2$ as the maximum overestimate. + This source 1s the brightest of our sample and the one with the highest number of detected photons., This source is the brightest of our sample and the one with the highest number of detected photons. + The good statistics involves à small detection. algorithm. error. radius. so the position determination is quite accurate (see Fig. 2)).," The good statistics involves a small detection algorithm error radius, so the position determination is quite accurate (see Fig. \ref{finding1}) )." + The boresight correction was performed with the known position of the quasar HE 0419-5657 and the nucleus of NGC 1547 as well as with other eleven sources matched to optical catalogs., The boresight correction was performed with the known position of the quasar HE 0419-5657 and the nucleus of NGC 1547 as well as with other eleven sources matched to optical catalogs. + The source is close (~15” but actually more than 5 c) to a bright star (BJ213.31. F=11.61 in the GSC2.2); this makes less reliable the lower limit on the fy/fop. in particular in the red band.," The source is close $\sim 15''$ but actually more than 5 $\sigma$ ) to a bright star (BJ=13.31, F=11.61 in the GSC2.2); this makes less reliable the lower limit on the $\rm f_{X}/f_{opt}$, in particular in the red band." + There are two fake USNO B1.0 sources along the saturation spikes of the bright star (see Fig. 2))., There are two fake USNO B1.0 sources along the saturation spikes of the bright star (see Fig. \ref{finding1}) ). + The source was observed with Einstein (1E. 0420.7-5723) and with the ROSAT PSPC (IWGAJ0421.7-5716) and was also detected as a RASS Bright Source (IRXS JO42144.0-571601)., The source was observed with Einstein (1E 0420.7-5723) and with the ROSAT PSPC (1WGAJ0421.7-5716) and was also detected as a RASS Bright Source (1RXS J042144.0-571601). + The WGA computed flux is 8.8x107 erg emo? s7!. consistent with the RASS count rate.," The WGA computed flux is $8.8\times 10^{-13}$ erg $^{-2}$ $^{-1}$, consistent with the RASS count rate." + Taking into account the caveats on the count rate to flux conversion. this could mean that there is no evidence for long term flux variations.," Taking into account the caveats on the count rate to flux conversion, this could mean that there is no evidence for long term flux variations." + We re-extracted the archival PSPC observation of this source (sequence rp700034n00)., We re-extracted the archival PSPC observation of this source (sequence rp700034n00). + The source was very close to the PSPC rib: despite this. we attempted a rough spectral analysis.," The source was very close to the PSPC rib; despite this, we attempted a rough spectral analysis." +" We extracted source photons from a circle of radius 200"" centered on source position.", We extracted source photons from a circle of radius $200''$ centered on source position. +" We used as background region a circle of radius 240"". centered in an empty region south of the source."," We used as background region a circle of radius $240''$, centered in an empty region south of the source." + The collected counts were 321., The collected counts were 321. + We rebinned channels by a variable factor in order to have at least 20 photons in each bin., We rebinned channels by a variable factor in order to have at least 20 photons in each bin. + Channels 1-11 and 136-256 were ignored., Channels 1-11 and 136-256 were ignored. + Figure 3 shows the resulting spectrum. which we then fitted with XSPEC (v.11.2).," Figure 3 shows the resulting spectrum, which we then fitted with XSPEC (v.11.2)." + Due to the poor statistics. we," Due to the poor statistics, we" +el al.,et al. + 2002; Iwasawa et al., 2002; Iwasawa et al. + 2005)., 2005). + CT AGN may represent a significant fraction of the accretion power in the Universe and indeed a correction for the CT. contribution to the estimates of the SMDILI local mass density has (ο be included in the ealeulations (Marconi et al., CT AGN may represent a significant fraction of the accretion power in the Universe and indeed a correction for the CT contribution to the estimates of the SMBH local mass density has to be included in the calculations (Marconi et al. + 2004)., 2004). + An unbiased census of extremely obscured AGN would require to survey the hard X.ταν skv above 10 keV with good sensitivity., An unbiased census of extremely obscured AGN would require to survey the hard X–ray sky above 10 keV with good sensitivity. + Such an argument is one of the Κον scientific drivers ol the (Ilarrison et al., Such an argument is one of the key scientific drivers of the (Harrison et al. + 2010) and (Takahashi et al., 2010) and (Takahashi et al. + 2010) missions. which will be launched in the next lew vears. and of the mission study (Pareschi οἱ al.," 2010) missions, which will be launched in the next few years, and of the mission study (Pareschi et al." + 2010)., 2010). + For the time being. one has to rely on the observations obtained bv the highenergy detectors on boardBEPPOSAN.INTEGRAL. ancl. more recently.Suzaku.," For the time being, one has to rely on the observations obtained by the high–energy detectors on board, and, more recently,." + Allsky surveys were performed using both the IBIS coded-mask telescope onboard and the BAT detector on boardswiet., All–sky surveys were performed using both the IBIS coded-mask telescope onboard and the BAT detector on board. + Though limited to bright and thus lowredshift sources. thev have proven to be quite successful.," Though limited to bright and thus low–redshift sources, they have proven to be quite successful." + More than one hundred AGN are reported in both (Beckmann et al., More than one hundred AGN are reported in both (Beckmann et al. + 2009) and catalogues (TIueller et al., 2009) and catalogues (Tueller et al. + 2010: Cusumano et al 2010)., 2010; Cusumano et al 2010). + llard X.rav selection is less biased against absorption and (hus provides a useful benchmark to study the column density distribution of observed AGN and the fraction of C'T sources in (he local Universe., Hard X–ray selection is less biased against absorption and thus provides a useful benchmark to study the column density distribution of obscured AGN and the fraction of CT sources in the local Universe. + The large majority of ancl sources were observed by AMAL andChandra aud their broad band X.rav spectra discussed by Winter οἱ al. (, The large majority of and sources were observed by XMM and and their broad band X–ray spectra discussed by Winter et al. ( +2008).,2008). +" While the already known. nearby CT AGN were recovered by and surveys. the fraction of ""newly discovered CT AGN is surprisingly low and apparently inconsistent. by about a factor of 2. with that predicted by Gilli et al. ("," While the already known, nearby CT AGN were recovered by and surveys, the fraction of “newly"" discovered CT AGN is surprisingly low and apparently inconsistent, by about a factor of 2, with that predicted by Gilli et al. (" +2007) in the local Universe.,2007) in the local Universe. + On the basis of these findings. it has been proposed (Treister οἱ al.," On the basis of these findings, it has been proposed (Treister et al." + 2009) that the contribution of CT AGN to the hard X.rav background may be significantly lower (bv a factor of 2 to 3) than previously thought. with important implications for the evolution of the accretion power.," 2009) that the contribution of CT AGN to the hard X–ray background may be significantly lower (by a factor of 2 to 3) than previously thought, with important implications for the evolution of the accretion power." + since absorption column densities are often mnieasured on relatively poor quality spectra (taken [rom non-simultaneous observations. above and below about LO keV. and combining different instruments. the CT traction ancl. more in general. the absorption distribution in (he local Universe may still be subject to several uncertainties.," Since absorption column densities are often measured on relatively poor quality X--ray spectra taken from non-simultaneous observations, above and below about 10 keV, and combining different instruments, the CT fraction and, more in general, the absorption distribution in the local Universe may still be subject to several uncertainties." + Good quality simultaneous spectra extending over the 0.5100 keV energy range are needed for a robust measurenent of absorption column densities. especially in the Compton thick regime.," Good quality simultaneous spectra extending over the 0.5–100 keV energy range are needed for a robust measurement of absorption column densities, especially in the Compton thick regime." + Moreover. nearby obseured AGN always show excess emission above the extrapolation of the obscured nuclear specirum (e.g. Turner οἱ al.," Moreover, nearby obscured AGN always show excess emission above the extrapolation of the obscured nuclear spectrum (e.g. Turner et al." + 1997)., 1997). + Soft. Xταν spectroscopy is a powerful tool to study (he origin of this component which is plausibly related {ο warm gas photoionized bv the nuclear continuum (Guainazzi Bianchi 2007)., Soft X–ray spectroscopy is a powerful tool to study the origin of this component which is plausibly related to warm gas photoionized by the nuclear continuum (Guainazzi Bianchi 2007). + The Xray detectors onboard. the Japanese satellite are well suited to this purpose. αἱ least as far as “local” AGN are concerned.," The X–ray detectors onboard the Japanese satellite are well suited to this purpose, at least as far as “local"" AGN are concerned." + We have conceived a program wilh lo observe nearby. relatively X.ray," We have conceived a program with to observe nearby, relatively X–ray" +inthe regionsof py «2GeV/c.,unpolarized $pA$ and $\Sigma A$ collisions. + We analyze hyperon andanti-hvperon polarizations in, We find that the $\frac{1}{2}$ baryon contains an intrinsic +We thank Dr Chiranjib Ixonar who performed the GAIRT observations of and the staff ofthe GAIRT instrument. operated by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research.,"We thank Dr Chiranjib Konar who performed the GMRT observations of and the staff of the GMRT instrument, operated by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research." + This project was supported in part bv the ALNISW funds for scientific research in vears 20092012 under the contract No., This project was supported in part by the MNiSW funds for scientific research in years 2009–2012 under the contract No. + 3812/D/1103/2009/306., 3812/B/H03/2009/36. + The presented work facilitated the MAPS Catalog of POSS-I provided bv the University of Minnesota (http://aps.umn.edu/)., The presented work facilitated the MAPS Catalog of POSS-I provided by the University of Minnesota ). +L.. S. acknowledges the support from the Polish \INISW through the grant. N-N203-380336., S. acknowledges the support from the Polish MNiSW through the grant N-N203-380336. +By analogy with the 1-Iaver svstem. in the 2-laver case we should expect resonance to be found near where the (4X4) determinant of the coellicients in equations (17)-(20) vanishes.,"By analogy with the 1-layer system, in the 2-layer case we should expect resonance to be found near where the (4X4) determinant of the coefficients in equations (17)-(20) vanishes." + In the homogeneous case (lp= 0) this determinant is a quartic equation lor the complex eigenfrequency w of the dvnamos of the 2-laver svstem., In the homogeneous case $A_F=0$ ) this determinant is a quartic equation for the complex eigenfrequency $\omega$ of the dynamos of the 2-layer system. + Being a til order svstem. we can nol in general find closed or simple algebraic forms for either the amplitudes of the response to the top forcing. or the phase speed ancl growth rate of the unforced dynamo.," Being a 4th order system, we can not in general find closed or simple algebraic forms for either the amplitudes of the response to the top forcing, or the phase speed and growth rate of the unforced dynamo." + Bul only small programs are necessary {ο get results., But only small programs are necessary to get results. +" For the case with [ονας, we find the amplitudes and phases of Ai.Ap.Dp.D; in terms of the amplitude and phase of Ay by application of Cramers rule (refs)."," For the case with forcing, we find the amplitudes and phases of $A_U,A_L,B_U,B_L$ in terms of the amplitude and phase of $A_F$ by application of Cramers rule (refs)." + We apply Cramers rule to equations (21)-(24) defined in symbolic form as, We apply Cramers rule to equations (21)-(24) defined in symbolic form as +in 1996 Mas.,in 1996 May. + The full amplitude of the sinusoidal fit to the light. curve is S.O+1.2 counts/sec. which translates to μὴ. of the mean count rate.," The full amplitude of the sinusoidal fit to the light curve is $\pm$ 1.2 counts/sec, which translates to $\pm$ of the mean count rate." + This is smaller than the mean amplitude ofthe 3028-s period = 28+4% and the mean depth of the 3001-s dips 3545%.., This is smaller than the mean amplitude of the 3028-s period – $\pm$ and the mean depth of the 3001-s dips – $\pm$. + The superposition of these three signals can explain the deepest. observed. dips that sometimes reach almost (6. total obscuration), The superposition of these three signals can explain the deepest observed dips that sometimes reach almost (i.e. total obscuration). + To check whether the third peak in the power spectrum could be an artifact of the window function. a noiseless simulation of the 1996 Alay set was created.," To check whether the third peak in the power spectrum could be an artifact of the window function, a noiseless simulation of the 1996 May set was created." + A svnthetic light Curve was built using two sinusoids at the 3001 anc 3028-s periods., A synthetic light curve was built using two sinusoids at the 3001 and 3028-s periods. + These sinusoids were given the same amplitudes they have in the data and sampled according to the window function., These sinusoids were given the same amplitudes they have in the data and sampled according to the window function. + There was no evidence for significant power at the proposed. period., There was no evidence for significant power at the proposed period. + In an attempt to check whether uncorrelated noise could »* responsible for the presence of the new peak in the power spectrum. the two previously known periods. (3001 ane 3028 s) were subtracted from the cata.," In an attempt to check whether uncorrelated noise could be responsible for the presence of the new peak in the power spectrum, the two previously known periods (3001 and 3028 s) were subtracted from the data." + The remaining »oiunts. assumed to be white noise. were shulllecd ranclomly tween the timings.," The remaining points, assumed to be white noise, were shuffled randomly between the timings." + A power spectrum was calculated for each random configuration., A power spectrum was calculated for each random configuration. + Phe highest peak at the range =0-40 ! in 1000 simulations did not reach the height of , The highest peak at the range f=20-40 $^{-1}$ in 1000 simulations did not reach the height of $_{3}$. +In a cdillerent test. that checks the significance of a hird peak in the presence of two others. we took the svnthetie light curves (see previous section) and now acdcdec noise. defined as the root mean square of the origina data minus the periods. mocdelled.," In a different test, that checks the significance of a third peak in the presence of two others, we took the synthetic light curves (see previous section) and now added noise, defined as the root mean square of the original data minus the periods modelled." + We then searched: for the highest peak in a small interval (28.9-29.1 eveles/dav) around the candidate period (£;)., We then searched for the highest peak in a small interval (28.9-29.1 cycles/day) around the candidate period $_{3}$ ). +" The lower value is cietatec by the nearby. presence of the 3001-s period (£,).", The lower value is dictated by the nearby presence of the 3001-s period $_{1}$ ). + In. 1000 simulations. no peak reached the height of the candidate periodicity.," In 1000 simulations, no peak reached the height of the candidate periodicity." + Figs., Figs. + le & 2e show an individual example of this simulation., 1c $\&$ 2c show an individual example of this simulation. + Another test we tried. was to assess the probability. that correlated: noise. could. be responsible for the candidate periodicity., Another test we tried was to assess the probability that correlated noise could be responsible for the candidate periodicity. + In. the absence of a model for the correlated noise. the best test is to use the repeatability between cillerent datasets.," In the absence of a model for the correlated noise, the best test is to use the repeatability between different datasets." + Thus the 1996 Alay cata were divided into two subsets the first and last five runs., Thus the 1996 May data were divided into two subsets – the first and last five runs. + Power spectra of, Power spectra of +g;=D;|ery. where r; is a random munber drawn roni a Caussian distribution with a mean of 0 aud standard deviation of 1.,"$y_i=B_i+\epsilon_ir_i$, where $r_i$ is a random number drawn from a Gaussian distribution with a mean of 0 and standard deviation of 1." + To recover from y;. we first make a guess of the solution Py and then use equation (2)) to recover the true parameters.," To recover from $y_i$, we first make a guess of the solution $_0$ and then use equation \ref{eqn:dscuti_er}) ) to recover the true parameters." + We do us for four different scenarios for both the single star and the binary system. without including photometric information (OS&4;pp and OSsyrp| ASL): (1) using 1ο ποας Lucasuremenuts a mode (black diamonds in Figure 10.. OS4;pp) (2) using the nou- measurements a correctly identified iode (red crosses in Figures 10. and H.. OSs;gp |ASL). (3) using the non-seinuüc neasurenments and ancorrectly identified iode the wrong deeree 6 (blue crosses). and (1) usine the non-scismuc measurements and aumcorrectly ideutified node the wrong radial order 1 (ereon crosses).," We do this for four different scenarios for both the single star and the binary system, without including photometric information $_{S/EB}$ and $_{S/EB}$ ): (1) using the non-seismic measurements a mode (black diamonds in Figure \ref{fig:inversions}, $_{S/EB}$ ), (2) using the non-seismic measurements a correctly identified mode (red crosses in Figures \ref{fig:inversions} and \ref{fig:fitage}, $_{S/EB}$ +AS1), (3) using the non-seismic measurements and an identified mode — the wrong degree $\ell$ (blue crosses), and (4) using the non-seismic measurements and an identified mode — the wrong radial order $n$ (green crosses)." + The recovered paraneters for 10.000 realizations are shown in Figures 10 and 11..," The recovered parameters for 10,000 realizations are shown in Figures \ref{fig:inversions} and \ref{fig:fitage}." + We show only the four parameters of the pulsating/ star discussed im Section ?7.., We show only the four parameters of the pulsating star discussed in Section \ref{sec:4.1}. + The left/right panels show the results for tle single star (OS5$." + Authors thank Ix.Subramanian and J-Chenelur for useful discussions., Authors thank K.Subramanian and J.Chenglur for useful discussions. + JSB thanks CSUR India for financial support., JSB thanks CSIR India for financial support. +As incutioned above. our main goal is the determination of the gas density profile. py(r} once a specific dark matter distribution. ον.) is given.,"As mentioned above, our main goal is the determination of the gas density profile ${\rho}_g(r)$ once a specific dark matter distribution $M_{\mathrm{DM}}(r)$ is given." + Supposing as before that Aor)=AMpywtr). it is evideut that ο) follows froin Eq. (1))," Supposing as before that $M_{\mathrm{tot}}(r) \simeq M_{\mathrm{DM}}(r)$ , it is evident that ${\rho}_g(r)$ follows from Eq. \ref{a1}) )" +" provided that 7,(7) is specified.", provided that ${T}_g(r)$ is specified. + Previous studies (ATakinoctal.1997:Sutoet1998) accomplished this task by assuniug which was suggested to formalize the coudition hat the gas temperature is close to the virial eniperature of the DAL.," Previous studies \citep{masasu, +susama} accomplished this task by assuming which was suggested to formalize the condition that the gas temperature is close to the virial temperature of the DM." + Iowever. the virial heorem is a global relation that characterizes a cluster as a whole — if just arises by intcerating he Jeaus equation over the system aud so As a matter of fact. this stumbling block cau ο side-stepped in a remarkably simple fashion.," However, the virial theorem is a global relation that characterizes a cluster as a whole – it just arises by integrating the Jeans equation over the system – and so As a matter of fact, this stumbling block can be side-stepped in a remarkably simple fashion." +" Because of the equivalence principle. the velocity of a test particle in an external eravitational ποια, is independent of the particle mass."," Because of the equivalence principle, the velocity of a test particle in an external gravitational field is independent of the particle mass." + This circumstance leads to the guess This relation was tested against ununerical s«inulatious (Tostetal.2009).. which demonstrated its validity with &=L1 toa very good approximation.," This circumstance leads to the guess This relation was tested against numerical simulations \citep{host2009}, which demonstrated its validity with $\kappa =1$ to a very good approximation." + These uunmerical simulations (savetal.2007:Spriugel2005:Valdarnini2006) are reliable oulv on scales ereater than 0.1resyy. while the best N-rav observations are sensitive to a radius which is almost a factor ΠΕ," These numerical simulations \citep{kay,springel,valdarnini} are reliable only on scales greater than $\sim 0.1 \,r_{2500}$, while the best X-ray observations are sensitive to a radius which is almost a factor 3 smaller." + is therefore possible that heating or cooling maw shift & away from. unity in the verv centre., It is therefore possible that heating or cooling may shift $\kappa$ away from unity in the very centre. +" Ποσο, outside that region W= Lis expected."," Hence, outside that region $\kappa=1$ is expected." + Actually. a look. back at Eq. (13))," Actually, a look back at Eq. \ref{a12}) )" +" confirms the remarkable fact that Ho=1 holds regardless of the actual shape of the DM velocity anisotropy profile 0),", confirms the remarkable fact that $\kappa=1$ holds regardless of the actual shape of the DM velocity anisotropy profile $\beta (r)$. +" As we shall sec. starting froma specific underlying DM density profile ppatCé). one can evaluate ον) aud the- get the gas temperature profile T,(r) uniquely."," As we shall see, starting from a specific underlying DM density profile $\rho_{\mathrm{DM}}(r)$, one can evaluate $T_{\mathrm{DM}}(r)$ and then get the gas temperature profile $T_g(r)$ uniquely." + Before closing this section. a remark is in order.," Before closing this section, a remark is in order." + Observations show that some clusters lack a ceutral cocine flow., Observations show that some clusters lack a central cooling flow. + In such a situation. lvdrostatic equilixiun is expected to hold all the wav down to he centre.," In such a situation, hydrostatic equilibrium is expected to hold all the way down to the centre." +" Actually. for typical ceutral values of the electron uuuber deusitv Εν.&lau? and temperature Tc10K~s.5keV (Sarazin1986).. the scattering time turus out to be tear~M07. which is much smaller than the corresponding gas cooling time fí,,;~LOTye. so that local lyvdvostatic equilibrium is iudecd fulfilled outside a ceutral spherical region of radius lpc."," Actually, for typical central values of the electron number density $n_e \simeq1 {\mathrm{cm}}^{-3}$ and temperature $T\simeq10^8 \, {\mathrm{K}} \simeq 8.5 \, {\mathrm{keV}}$ \citep{1986RvMP...58....1S}, the scattering time turns out to be $t_{\mathrm{scat}} \sim 10^2 \mathrm{yr}$, which is much smaller than the corresponding gas cooling time $t_{\mathrm{cool}} \sim 10^{7} \mathrm{yr}$, so that local hydrostatic equilibrium is indeed fulfilled outside a central spherical region of radius $\sim 1 \, {\rm pc}$." + Assuming further that tli eas teniperature is roughly constant in the immer cluster region. the eas deusitv profile caunot be cuspy as long as Mpy(r)xrca with e>1 for re»0.," Assuming further that the gas temperature is roughly constant in the inner cluster region, the gas density profile cannot be cuspy as long as $M_{\mathrm{DM}}(r) \propto r^a$ with $a > 1$ for $r \to 0$." + This is at odds with bliud extrapolations of fitting formalac for the temperature and density stich as those used in Vikhlininetal., This is at odds with blind extrapolations of fitting formulae for the temperature and density such as those used in \cite{vikhlinin}. +(2006).. We now proceed to the actual derivation of the eas density profile py(r) frou the properties of the dominating DM distribution., We now proceed to the actual derivation of the gas density profile ${\rho_g} (r)$ from the properties of the dominating DM distribution. + As a preliminary step. we notice that Eqs. (1))," As a preliminary step, we notice that Eqs. \ref{a1}) )" + and (6)) can be trivially combined to yield Owing to Eqs. (5)), and \ref{a5}) ) can be trivially combined to yield Owing to Eqs. \ref{a4}) ) +" and (15)) with &=1, straightforward manipulations pernüt to recast Eq. (16))"," and \ref{a13}) ) with $\kappa = 1$, straightforward manipulations permit to recast Eq. \ref{a15}) )" + iuto the form where we have defined the deusity slopes spare) of the DAT aud τρ) of the gas as with OX standing for cither DM or g., into the form where we have defined the density slopes $\gamma_{\mathrm{DM}}(r)$ of the DM and $\gamma_g(r)$ of the gas as with $X$ standing for either $\mathrm{DM}$ or $g$. + We stress that Eq. (17)), We stress that Eq. \ref{a16}) ) + captures a crucial poiut of the present investigation: oulv the gas density slope appears on its left-hand. side. whereas ouly quantities pertaining to the DAL appear on its right-hand side.," captures a crucial point of the present investigation: only the gas density slope appears on its left-hand side, whereas only quantities pertaining to the DM appear on its right-hand side." + It should be appreciated that this result merely relies upon the equality of eas and, It should be appreciated that this result merely relies upon the equality of gas and +We determine the two-point spatial correlation function of clusters at cdillerent redshifts as a function of cluster mass (hresholcd.,We determine the two-point spatial correlation function of clusters at different redshifts as a function of cluster mass threshold. + The comoving mass thresholds range from (Qwithin 1.5 4! comoving Mpc) to 5x10fhAL..., The comoving mass thresholds range from $_{1.5} \geq 2\times10^{13} \ h^{-1}$ (within 1.5 $h^{-1}$ comoving Mpc) to $5\times10^{14} \ h^{-1}$. + The redshifts investigated range [rom z = 0 (o 3., The redshifts investigated range from $z$ = 0 to 3. +" The correlation Function is determined for each sample by comparing (he observed distribution of cluster pairs as a function of pair separation wilh the distribution in random catalogs within the same volume: €,.0°)=Fpp(r)/Εμ)71. where Fpp(r) and Freie) are the frequencies of cluster-cluster pairs as a function of pair separation + in the data and in random catalogs. respectively,"," The correlation function is determined for each sample by comparing the observed distribution of cluster pairs as a function of pair separation with the distribution in random catalogs within the same volume: $\xi_{cc}(r) = F_{DD}(r)/F_{RR}(r) - 1$, where $F_{DD}$ $r$ ) and $F_{RR}$ $r$ ) are the frequencies of cluster-cluster pairs as a function of pair separation $r$ in the data and in random catalogs, respectively." + The number of clusters decreases with increasing mass and redshift. [rom 2x10? to ~10* clusters: the most massive (rarest) clusters are therefore studied only at the lower part of the redshift range.," The number of clusters decreases with increasing mass and redshift, from $2\times10^5$ to $\sim10^3$ clusters; the most massive (rarest) clusters are therefore studied only at the lower part of the redshift range." + Since the cluster abundance ina LSCDAML model decreases more rapicly with redshift (han in LCDAM. this model is onlv studied up to z=1.," Since the cluster abundance in a TSCDM model decreases more rapidly with redshift than in LCDM, this model is only studied up to $z = 1$." + Poisson statistical error-bars are used in (he correlation function analvsis., Poisson statistical error-bars are used in the correlation function analysis. +" Comoving scales and a Hubble constant of Hj=1005hins+ |!1 are used throughout,", Comoving scales and a Hubble constant of $_0 = 100 \ h \ km \ s^{-1}$ $^{-1}$ are used throughout. + The evolution of the cluster correlation funetion as a function of redshift is illustrated in Figure 1 for LCDM for two mass threshold samples (2xLOM and Lx10At ))., The evolution of the cluster correlation function as a function of redshift is illustrated in Figure 1 for LCDM for two mass threshold samples $2\times10^{13}$ and $1\times10^{14} \ h^{-1}$ ). +" The best-fit power-law correlation function. £(r) = (5-)Ry""n . is also presented for each sample."," The best-fit power-law correlation function, $\xi$ $r$ ) = $\frac{r}{R_{0}}$ $^{-\gamma}$, is also presented for each sample." + The bestfits are derived lor scales r<505h.+ \Ipe., The bestfits are derived for scales $r \leq 50 \ h^{-1}$ Mpc. + The power-law slope was treated both as a [ree parameter ancl as a fixed value of >=2: the latter is (he (vpical slope found in the simulations., The power-law slope was treated both as a free parameter and as a fixed value of $\gamma = 2$; the latter is the typical slope found in the simulations. + The best-fits shown in Figure 1 are for a fixed slope 5=2., The best-fits shown in Figure 1 are for a fixed slope $\gamma = 2$. + The results are similar for a [ree slope fit. as discussed below.," The results are similar for a free slope fit, as discussed below." + The evolution of the cluster correlation [function is apparent in Fieure l1: clusters are more stronglv correlated at. higher reclshilt., The evolution of the cluster correlation function is apparent in Figure 1: clusters are more strongly correlated at higher redshift. + This is of course opposite to the evolution of the mass correlation function. which decreases with redshift.," This is of course opposite to the evolution of the mass correlation function, which decreases with redshift." + The enhancement of the cluster correlation strength with redshift is due to the imereased bias of the clusters relative to the underlving mass distribution: i.e.. the same comoving mass clusters represent higher density peaks of (he mass distribution as the reclshilt increases (hus amplifvine their correlation strength (see. for example. Cole&Mo&White1996.2002:Sheth.Mo.Tormen2001:\losearclinietal. 2001)) Figure 2 presents (he best-fit correlation function slope 5 as a function of cluster redshilt and cluster mass.," The enhancement of the cluster correlation strength with redshift is due to the increased bias of the clusters relative to the underlying mass distribution: i.e., the same comoving mass clusters represent higher density peaks of the mass distribution as the redshift increases thus amplifying their correlation strength (see, for example, \citealt{col89, moh96, moh02, she01, mos01}) ) Figure 2 presents the best-fit correlation function slope $\gamma$ as a function of cluster redshift and cluster mass." + The best slope for LCDM is 5~2 for z<0.5 clusters., The best slope for LCDM is $\gamma \sim 2$ for $z \la 0.5$ clusters. + The slope steepens bv ~20%. t0 5~2.3—2.5. as the redshift increases to z~2—3.," The slope steepens by $\sim 20\%$, to $\gamma \sim 2.3 - 2.5$, as the redshift increases to $z \sim 2 - 3$." + This steepening can also be seen in (he correlation function of the high-redshift samples in Figure 1., This steepening can also be seen in the correlation function of the high-redshift samples in Figure 1. + The TSCDM model (Figure 2b) vields a slightly steeper average slope: ~ 2.3 al 2E0.5. increasing only slightly to ~2.5 αἱ ze 1.," The TSCDM model (Figure 2b) yields a slightly steeper average slope: $\sim$ 2.3 at $z \la 0.5$, increasing only slightly to $\sim 2.5$ at $z \sim 1$ ." + The evolution of the cluster correlation function is presented in Figure 3 [ον clusters with, The evolution of the cluster correlation function is presented in Figure 3 for clusters with +In the first paper of this series. we argued that. charged erains can act like small capacitors and initiate electron. avalanche processes (hat produce large numbers of [ree electrons.,"In the first paper of this series, we argued that charged grains can act like small capacitors and initiate electron avalanche processes that produce large numbers of free electrons." + If many of these events superimpose and enough electrons leak out of the streamers. the degree of gas ionisation could be increased to such an extent that the eloud might couple to a large scale magnetic field.," If many of these events superimpose and enough electrons leak out of the streamers, the degree of gas ionisation could be increased to such an extent that the cloud might couple to a large scale magnetic field." + In (his paper. we have demonstrated. (hat the cloud particles can be charged in substellar and planetary. atiiosphlieres on (he basis of turbulence induced inter-grai collisions alone.," In this paper, we have demonstrated that the cloud particles can be charged in substellar and planetary atmospheres on the basis of turbulence induced inter-grain collisions alone." + The next step is to quantify the number of electrons that potentially can be produced by these collisions in the whole cloud., The next step is to quantify the number of electrons that potentially can be produced by these collisions in the whole cloud. + This would also allows to investigate if inter-grain collisions have the potential to produce enough charges to allow a coupling with a large scale magnetic field in the case that these charges are released into (he gas phase where thev have a greater mobility., This would also allows to investigate if inter-grain collisions have the potential to produce enough charges to allow a coupling with a large scale magnetic field in the case that these charges are released into the gas phase where they have a greater mobility. + The energies produced by dust-dust collisions are larger (han the ionisation energy by several orders of magnitude in most of the brown dwarf cloud volume or a fraction of it in gas planets if the cloud is turbulent., The energies produced by dust-dust collisions are larger than the ionisation energy by several orders of magnitude in most of the brown dwarf cloud volume or a fraction of it in gas planets if the cloud is turbulent. + Such high energies which also exceed the thermal electron energy. (black dotted line. Fig. 12)).," Such high energies which also exceed the thermal electron energy (black dotted line, Fig. \ref{fig:col_energy}) )," + suggest that electrons could escape from the grain surfaces into the gas., suggest that electrons could escape from the grain surfaces into the gas. + Whether the electrons affected by dust-cust collisions remain within the dust phase or whether they indeed escape [rom the grain surface depends on their kinetic enerev gained during (he collisions and on the electronegativity of the surrounding gas phase constituents., Whether the electrons affected by dust-dust collisions remain within the dust phase or whether they indeed escape from the grain surface depends on their kinetic energy gained during the collisions and on the electronegativity of the surrounding gas phase constituents. + In (the case of destructive erain processes. (he potentially charge-carrving dust surface increases and charges could escape more easily inlo (he gas as evaporation processes are faster.," In the case of destructive grain processes, the potentially charge-carrying dust surface increases and charges could escape more easily into the gas as evaporation processes are faster." + Many more mechanisms can influence this process (see introduction to Sect. ??)), Many more mechanisms can influence this process (see introduction to Sect. \ref{s:colion}) ) + in addition to profound uncertainties in the microphvsies of dust charging., in addition to profound uncertainties in the microphysics of dust charging. +bottom curves assume that Reg is twice the best fit value.,"bottom curves assume that $R_{\rm + eff}$ is twice the best fit value." +" We haveassumed Metetlar=10°—10 for globular clusters, Mgtellar=10°—10°Mo for dwarfMc spheroidals and nuclear star clusters, and Maja;=109—10HM for early type galaxies, limiting our investigation to the mass ranges probed by Shenetal.(2003);Walker"," We haveassumed $M_{\rm stellar}= +10^5-10^7 M_\odot$ for globular clusters, $M_{\rm stellar}= 10^5-10^8 +M_\odot$ for dwarf spheroidals and nuclear star clusters, and $M_{\rm + stellar}= 10^8-10^{11} M_\odot$ for early type galaxies, limiting our investigation to the mass ranges probed by \cite{Shen2003,Walker2009,Seth2008}." +" In this plot the vina>>o limit of Equation 6 becomes (2008)..evident: at low stellar masses, for every type of stellar distribution but for the early type galaxies, R,-- does not depend on Reg, and it is determined only by the BH mass and the assumed vyina."," In this plot the $v_{\rm + wind} \gg \sigma$ limit of Equation 6 becomes evident: at low stellar masses, for every type of stellar distribution but for the early type galaxies, $R_{\rm acc}$ does not depend on $R_{\rm eff}$, and it is determined only by the BH mass and the assumed $v_{\rm wind}$." +" 'Theearly type galaxies generate deeper potential wells, never reaching the Uwing>>o limit."," Theearly type galaxies generate deeper potential wells, never reaching the $v_{\rm + wind} \gg \sigma$ limit." + The bolometric luminosity of the massive black hole can be written as:DD where e represents the fraction of the accreted mass that is radiated away.," The bolometric luminosity of the massive black hole can be written as:, where $\epsilon$ represents the fraction of the accreted mass that is radiated away." +" The nature of the accretion process, and the consequent value of e, is rather uncertain."," The nature of the accretion process, and the consequent value of $\epsilon$ , is rather uncertain." + AGNs accrete through accretion discs with a high efficiency (€~ 0.1)., AGNs accrete through accretion discs with a high efficiency $\epsilon\sim 0.1$ ). +" Supermassive BHs at thecenters of quiescent galaxies, including the Milky Way, can have luminosities as low as ~10-?—10-8 of their Eddington values Loewensteinetal. and well below the luminosity(e.g. one would estimate (2001))),assuming e~0.1."," Supermassive BHs at thecenters of quiescent galaxies, including the Milky Way, can have luminosities as low as $\sim 10^{-9}-10^{-8}$ of their Eddington values (e.g. \cite{Loewenstein2001}) ), and well below the luminosity one would estimate assuming $\epsilon\sim 0.1$." +" Following Merloni&Heinz(2008) we define A= Lgaqa, where Lpo1 is the bolometric luminosity and Lya/Lgaa=ΑπαΜΡΗπΙρΕ/στc1.3x10(Mpn/Mco) erg s! is the Eddington luminosity."," Following \cite{Merloni2008} we define $\lambda \equiv L_{\rm bol}/L_{\rm Edd}$ , where $L_{\rm bol}$ is the bolometric luminosity and $L_{\rm Edd}=4 \pi G M_{\rm BH} m_{\rm p} c / \sigma_{\rm T} \simeq 1.3 \times 10^{38} (M_{\rm BH}/M_{\odot})$ erg $^{-1}$ is the Eddington luminosity." +" We write the radiative efficiency, e, as a combination of the accretion efficiency, η, that depends only on the location of the innermost stable circular orbit*,, here assumed to be 7=0.1, and of a term, ‘acc, that depends on the properties of the accretion flow itself: €=7Macc."," We write the radiative efficiency, $\epsilon$, as a combination of the accretion efficiency, $\eta$, that depends only on the location of the innermost stable circular , here assumed to be $\eta=0.1$, and of a term, $\eta_{\rm acc}$, that depends on the properties of the accretion flow itself: $\epsilon=\eta\,\eta_{\rm acc}$." + We also define m=nMC?/Lgaa., We also define $\dot m=\eta \dot M c^2/L_{\rm Edd}$. +" For ‘radiatively efficient’ accretion, Nace=1."," For `radiatively efficient' accretion, $\eta_{\rm acc}=1$." +" To estimate the X-ray luminosity, we apply a simple bolometric correction, and assume that the X-ray luminosity is a fraction 7x of the bolometric luminosity."," To estimate the X–ray luminosity, we apply a simple bolometric correction, and assume that the X-ray luminosity is a fraction $\eta_{\rm X}$ of the bolometric luminosity." + Ho et al. (, Ho et al. ( +"1999) suggest that for low-luminosity AGN, with Eddington rates between 10-9 and 107° the luminosity on the [0.5-10] keV band represents a fraction 0.06-0.33 of the bolometric luminosity.","1999) suggest that for low-luminosity AGN, with Eddington rates between $10^{-6}$ and $10^{-3}$ the luminosity on the [0.5-10] keV band represents a fraction 0.06-0.33 of the bolometric luminosity." +" We assume here nx=0.1, so that Lx=nxeMc’, where e=η0.1."," We assume here $\eta_{\rm X}=0.1$, so that $L_{\rm X}=\eta_{\rm X}\, \epsilon\, \dot M c^2$, where $\epsilon=\eta=0.1$." + We refer to this model as ‘radiatively efficient’., We refer to this model as `radiatively efficient'. +" Since the accretion rates we find are very sub-Eddington, we assume, in a second model, that the accretion flow is optically thin and geometrically thick."," Since the accretion rates we find are very sub-Eddington, we assume, in a second model, that the accretion flow is optically thin and geometrically thick." +" In this state the radiative power is strongly suppressed (e.g.,Narayan&Yi1994;Abramowiczetal."," In this state the radiative power is strongly suppressed \citep[e.g.,][]{Narayan1994,Abramowicz1988}." +" 1988).. Merloni&Heinz(2008) suggest that this transition occurs at m«ma=3x1077, and that Ίος=(m/ma), sothat e= n(m/mer)."," \cite{Merloni2008} suggest that this transition occurs at $\dot m<\dot m_{\rm cr}=3\times 10^{-2}$, and that $\eta_{\rm acc}=(\dot m/\dot m_{\rm cr})$, sothat $\epsilon=\eta(\dot m/\dot m_{\rm cr})$ ." +" The X-ray luminosity is therefore: Lx= nxeMc?, where again nx=0.1."," The X-ray luminosity is therefore: $L_{\rm X}=\eta_{\rm X}\, \epsilon\, \dot M c^2$ , where again $\eta_{\rm X}=0.1$." +" We refer to this model as “radiatively inefficient""."," We refer to this model as “radiatively inefficient""." +" In Figure4 we show the accretion rate, in Eddington units, when we assume 7= 0.1."," In Figure\ref{fedd} we show the accretion rate, in Eddington units, when we assume $\eta=0.1$ ." + Hereafter we vary the mass of the massive black hole from 100Me to 10*M , Hereafter we vary the mass of the massive black hole from $100\msun$ to $10^4\msun$ +a reddened photosphere).,a reddened photosphere). + The intrinsic colours for stars on a 2 Myr isochrone are indicated by the solid line. whereas the dotted line yields the locus of dereddened colours of classical T Tauri stars according to Meyeretal.(1997).," The intrinsic colours for stars on a 2 Myr isochrone are indicated by the solid line, whereas the dotted line yields the locus of dereddened colours of classical T Tauri stars according to \cite{mch97}." +. The dashed lines define the region of normal reddening using the reddening law from Rieke&Lebofsky(1985) (the normal reddening region of main sequence stars would be very similar to the one of the stars on the 2 Myr isochrone)., The dashed lines define the region of normal reddening using the reddening law from \cite{rl85} (the normal reddening region of main sequence stars would be very similar to the one of the stars on the 2 Myr isochrone). + The seatter of the X-ray sources outside this region is significant and it 1s probably an effect of the unreliability of the 2MASS photometric data in this crowded area., The scatter of the X-ray sources outside this region is significant and it is probably an effect of the unreliability of the 2MASS photometric data in this crowded area. + Nevertheless in the diagram we have identified 10 sources which appear to have significant IR excess (1.8. He to the right of the normal reddening region) and therefore could be embedded young objects., Nevertheless in the diagram we have identified 10 sources which appear to have significant IR excess (i.e. lie to the right of the normal reddening region) and therefore could be embedded young objects. + The presence of an IR excess for, The presence of an IR excess for +robust estimate of the orbital period.,robust estimate of the orbital period. + This is particularly obvious in the plot of the transit mid-point uucertainies which shows that periods less than ~10 days lave ar superior constraints ou the calculated epheimericdes., This is particularly obvious in the plot of the transit mid-point uncertainies which shows that periods less than $\sim 10$ days have far superior constraints on the calculated ephemerides. + Iu contrast. the longer period cxoplaucts often ouly je one orbit completely monitored and it is possible. hough uuconunuon. for the resulting transit window to ecole comparable to the orbital period of the planet.," In contrast, the longer period exoplanets often only have one orbit completely monitored and it is possible, though uncommon, for the resulting transit window to become comparable to the orbital period of the planet." + The ideal targets to monitor iu an observing canmpaignu end to occupy the lower-vight corucr of the plot of ransit window as à fiction of trausit probabilitv., The ideal targets to monitor in an observing campaign tend to occupy the lower-right corner of the plot of transit window as a function of transit probability. + These dlanets have the highest likelihood of vieldiug successtul detections. though this population is dominated by short- plauets.," These planets have the highest likelihood of yielding successful detections, though this population is dominated by short-period planets." + Figue 23 shows the uet increase in the size of he transit windows for this sample of exopluiets bv conmgxuiues the first transit windows after discovery with he first transit window occuring after a JD of 2151979.5 (CE 2009 May 28 00:00 UT)., Figure \ref{increase} shows the net increase in the size of the transit windows for this sample of exoplanets by comparing the first transit windows after discovery with the first transit window occurring after a JD of 2454979.5 (CE 2009 May 28 00:00 UT). + The open circles shown in the bottom right of the figure are those long-period dauets for which au additional trausit window bevoud ἐν as not vet occurred aud so the size of the transit window relmaius wnchanecd., The open circles shown in the bottom right of the figure are those long-period planets for which an additional transit window beyond $t_p$ has not yet occurred and so the size of the transit window remains unchanged. + Note that the distribution of points in this plot now resembles the distribution shown im the ransit mid-point wucertainty plot of Figure 2.. since the ransit duration estinate is unaffected by the passage of tine.," Note that the distribution of points in this plot now resembles the distribution shown in the transit mid-point uncertainty plot of Figure \ref{tranwinplots}, since the transit duration estimate is unaffected by the passage of time." + Therefore. the transit window size merease for he short-period planets is much slower over time than or the loug-period planets.," Therefore, the transit window size increase for the short-period planets is much slower over time than for the long-period planets." + This indicates that. even hough many more orbits of the short-period planets rave occurred. the transit mud-poiut uucertaimtv reniains dominated by the macertaimty iu the period.," This indicates that, even though many more orbits of the short-period planets have occurred, the transit mid-point uncertainty remains dominated by the uncertainty in the period." + The size of he transit window for the loue-period plaucts can be ought into a managable regime for photometric follow-up with relatively small usage of large telescope time., The size of the transit window for the long-period planets can be brought into a managable regime for photometric follow-up with relatively small usage of large telescope time. + Without such au effort. it clear frou these plots that it will be iuipossible to ascertain whether or not many of the long-period planets transit their host stars.," Without such an effort, it clear from these plots that it will be impossible to ascertain whether or not many of the long-period planets transit their host stars." + As described in Section. 2.2.. a considerable ummber of lugh transit probability targets are not feasible (depending upon telescope access) to observe because the uncertainty in the predicted transit mid-point are too ligh to justify the observing time required.," As described in Section \ref{pardepend}, a considerable number of high transit probability targets are not feasible (depending upon telescope access) to observe because the uncertainty in the predicted transit mid-point are too high to justify the observing time required." + This can load to transit windows of mouths and even vears du duration., This can lead to transit windows of months and even years in duration. + The acquisition of just a handful of new radial velocity measurements at carefully optimised times can reduce the size of a transit window by au order of magnitude., The acquisition of just a handful of new radial velocity measurements at carefully optimised times can reduce the size of a transit window by an order of magnitude. + Here we describe. by way of two examples. how obtaimime further radial velocity measurements for known exoplauets cau aprove the transit ephemoerides.," Here we describe, by way of two examples, how obtaining further radial velocity measurements for known exoplanets can improve the transit ephemerides." + These exiunples were chosen based upon their very different periods. relatively high transit probabilities. availability of radial velocity data. aud differeut transit windows aud discovery dates.," These examples were chosen based upon their very different periods, relatively high transit probabilities, availability of radial velocity data, and different transit windows and discovery dates." + In each of the examples. we have sinulated four additional micasurcments by using the best-fit orbital parauncters to determine the racial velocity at later epochs and adopting the mean of the discovery data precision for the simulated measurement nucertaimtics.," In each of the examples, we have simulated four additional measurements by using the best-fit orbital parameters to determine the radial velocity at later epochs and adopting the mean of the discovery data precision for the simulated measurement uncertainties." + The simulated measurements were then passed through a eaussian filter. which produced scatter consistent with the uncertainties. then appended to the discovery data.," The simulated measurements were then passed through a gaussian filter, which produced scatter consistent with the uncertainties, then appended to the discovery data." + The plauet orbiting the star WD 190228 was discovered by Perrieretal.(2003) as part of a group of new planets announced bv the ELODIE team.," The planet orbiting the star HD 190228 was discovered by \citet{per03} + as part of a group of new planets announced by the ELODIE team." + The planet is in a L116 dav orbit around a Co sub-eiaut star with an eccentricity of ~0.5., The planet is in a $\sim 1146$ day orbit around a G sub-giant star with an eccentricity of $\sim 0.5$. + The eccentric nature of the orbi resulted im no radial velocity data beiug acquired by the discovery tezüu when the planet was close to periapsis. since the plauet speuds a very stall portion of its orbi near that location.," The eccentric nature of the orbit resulted in no radial velocity data being acquired by the discovery team when the planet was close to periapsis, since the planet spends a very small portion of its orbit near that location." + Calculations for the first predicted transit to occur after JD 2151979.5 (see Figure 3)) vicka a transit mid-point macertainty of 88.9 davs aud a trausi window of 178.9 davs., Calculations for the first predicted transit to occur after JD 2454979.5 (see Figure \ref{increase}) ) yield a transit mid-point uncertainty of 88.9 days and a transit window of 178.9 days. + The geometric transit probability of this planet is 1% which is relatively high for a plane of this orbital period., The geometric transit probability of this planet is $\sim 1$ which is relatively high for a planet of this orbital period. + However. the larec transit window makes this an uufeasible target to observe. particularly frou the eround where a substautial fraction of the total transit window will remain uncovered (assiunius only oue erounud-based telescope at a particular lougitude is being used).," However, the large transit window makes this an unfeasible target to observe, particularly from the ground where a substantial fraction of the total transit window will remain uncovered (assuming only one ground-based telescope at a particular longitude is being used)." + Iun Fieure Lo we show the discovery data of Perrieretal.(2003) alous with four additional sunulated uecasureieuts., In Figure \ref{HD190228plot} we show the discovery data of \citet{per03} along with four additional simulated measurements. + The simulated data are cach separated Toni each other bv 50 davs., The simulated data are each separated from each other by 50 days. + Note that the simulated ueasurenieuts have been acquired while the planet is speediug past periapsis., Note that the simulated measurements have been acquired while the planet is speeding past periapsis. + The periastron passage of au orbit. particularly for a highlv ecceutric orbit. is where he planet is moving the fastest and so occupies a relatively stall fraction of the total phase space.," The periastron passage of an orbit, particularly for a highly eccentric orbit, is where the planet is moving the fastest and so occupies a relatively small fraction of the total phase space." + Thus. he ereatest constraints durus the shortest period of iue can be made by sampling this part of the orbit.," Thus, the greatest constraints during the shortest period of time can be made by sampling this part of the orbit." + These effects have been discussed at leneth iun the contest of the effects of eccentric orbits on period analysis (Cunning2001). cadence optiuizatiou for radial velocity surveys (vaneetal.2008).. aud adaptive scheduling algorithms (Ford2008).," These effects have been discussed at length in the context of the effects of eccentric orbits on period analysis \citep{cum04}, cadence optimization for radial velocity surveys \citep{kan08b}, and adaptive scheduling algorithms \citep{for08}." +. The orbital paramcters of ΠΟ 190228 were re- from the combination of discovery aud simulated data using the method described by I&aueetal. and Itaneetal. (2009)..., The orbital parameters of HD 190228 were re-computed from the combination of discovery and simulated data using the method described by \citet{kan07b} and \citet{kan09b}. . + The original and revised, The original and revised +The sspectrum of has revealed a sharp drop. by a factor 2 in the spectrum at an energy just above 7 keV. This is to our knowledge the first detection of such a feature in an AGN.,"The spectrum of has revealed a sharp drop, by a factor $\gs +2$ in the spectrum at an energy just above 7 keV. This is to our knowledge the first detection of such a feature in an AGN." + The limited statistics and complex continuum mean that the identification of this feature remains ambiguous., The limited statistics and complex continuum mean that the identification of this feature remains ambiguous. + We have considered models involving either partial covering of the X-ray source by cold material. or emission from an ionised accretion disc. but both these explanations have drawbacks.," We have considered models involving either partial covering of the X-ray source by cold material, or emission from an ionised accretion disc, but both these explanations have drawbacks." + The energy of the feature is strongly suggestive of absorption by neutral iron., The energy of the feature is strongly suggestive of absorption by neutral iron. + However. a complex partial covering model is required in order that the soft X-ray spectrum be relatively unaffected by he absorber.," However, a complex partial covering model is required in order that the soft X-ray spectrum be relatively unaffected by the absorber." + A further implication of the partial covering model is that the underlying power-law is unusually steep (Dz 3.5)., A further implication of the partial covering model is that the underlying power-law is unusually steep $\Gamma \approx 3.5$ ). + A similar feature. namely a sharp drop near 7.1 keV with relatively ittle fluorescence emission. was observed in the peculiar X-ray binary Cir X-I (Brandt 1996).," A similar feature, namely a sharp drop near 7.1 keV with relatively little fluorescence emission, was observed in the peculiar X-ray binary Cir X-1 (Brandt 1996)." + In this case the spectral feature is almost certainly due to partial covering., In this case the spectral feature is almost certainly due to partial covering. + An important consequence of the partial covering model is hat the unabsorbed X-ray luminosity of is an order of magnitude higher than the observed (absorbed) luminosity., An important consequence of the partial covering model is that the unabsorbed X-ray luminosity of is an order of magnitude higher than the observed (absorbed) luminosity. + We iive calculated the a... values for the absorbed and unabsorbed fluxes at 2 keV ¢the flux density at 2500 iis taken from Leighly 2000).," We have calculated the $\rm +\alpha_{ox}$ values for the absorbed and unabsorbed fluxes at 2 keV (the flux density at 2500 is taken from Leighly 2000)." +" The values are an,=2.0 (absorbed X-ray flux) and ays,=1.6 Cunabsorbed)."," The values are $\rm \alpha_{ox}\ =\ -2.0$ (absorbed X-ray flux) and $\rm +\alpha_{ox}\ =\ -1.6$ (unabsorbed)." +" This is suggestive of absorption (see Brandt. Laor Wills 2000: Brandt 2001. Figure 3) as almost all the objects with e,2000$ in excess of the predicted primary CMB anisotropy." +" This ""excess power has been interpreted as the SZ effect produced bv intervoeniug ealaxv clusters (???).."," This “excess power"" has been interpreted as the SZ effect produced by intervening galaxy clusters \citep{mason03,readhead04,bond02}." + Ou the other hand. a variety of uodels inchiding non-staudard primordial effects lave also been proposed as possible explanations (77)..," On the other hand, a variety of models including non-standard primordial effects have also been proposed as possible explanations \citep{voids,Bfields}." + The uique photon euission spectra of the thermal SZ effec distinguishes it from these alternative explanations for the observed anisotropy., The unique photon emission spectrum of the thermal SZ effect distinguishes it from these alternative explanations for the observed anisotropy. + The ACDARbaud powers comespondins to the simalles aneular scales die sliehtlvhiehostabove the best ft WALAPS ACDM πως., The ACBAR band powers corresponding to the smallest angular scales lie slightly above the best fit WMAP3 $\Lambda$ CDM model. + The four ( bius joiutlv. produce an excess of 51d Lyk? after the model primary power spectrum is subtracted., The four highest $\ell$ bins jointly produce an excess of $51\pm 42 \mu$ $^2$ after the model primary power spectrum is subtracted. + The combination of this result with measurements at lower frequeucies can be used to, The combination of this result with measurements at lower frequencies can be used to +Schmidt 1969: Morton Morton 1972: Dechtold et al.,Schmidt 1969; Morton Morton 1972; Bechtold et al. + 1984 that have lower spectral resolution., 1984) that have lower spectral resolution. + We also compare our lindings with these works., We also compare our findings with these works. + In comparison with previously available lists. we can say that the z—1.93727 system has been totally confirmed. as well as its structure.," In comparison with previously available lists, we can say that the z=1.93727 system has been totally confirmed, as well as its structure." + We can also pe the detection of a Lyman a line at z—1.98)95 + 0.00003. that matches the CIV. doublet reported by Sargent et al. (," We can also report the detection of a Lyman $\alpha$ line at z=1.98095 $\pm$ 0.00003, that matches the CIV doublet reported by Sargent et al. (" +1988) at z—1.9805 also noticed as Lyman Limit ο »w Bechtold ct al. (,1988) at z=1.9805 –also noticed as Lyman Limit system by Bechtold et al. ( +1984).,1984). + The first three listed absorption svstems of this QSO correspond. to systems A. D and € by Robertson Shaver (1983).," The first three listed absorption systems of this QSO correspond to systems A, B and C by Robertson Shaver (1983)." + Thus. we can confirm the presence of B and €. which Robertson Shaver (1983) left as ‘probable’.," Thus, we can confirm the presence of B and C, which Robertson Shaver (1983) left as `probable'." + A very strong line in the spectrum of Robertson Shaver (1983) at 4010 Ais likely to correspond to the Ilinc associated with the svstem (iv) at z=2.29915., A very strong line in the spectrum of Robertson Shaver (1983) at 4010.4 is likely to correspond to the line associated with the system (iv) at $z=2.29915$. + All the absorption lines not belonging to any of the above heavy-clement systems and falling in the QSO ITorest are identified as aabsorption lines., All the absorption lines not belonging to any of the above heavy-element systems and falling in the QSO forest are identified as absorption lines. + Fron the process presented in the previous sectlon we can conclude that the contamination, From the process presented in the previous section we can conclude that the contamination +"cover oof the whole phase, they cause a higher background noise than the MAGIC phase ranges, which cover only%.","cover of the whole phase, they cause a higher background noise than the MAGIC phase ranges, which cover only." +. although the points of the latter are systematically somewhat below the former., although the points of the latter are systematically somewhat below the former. +" This is self-consistent, because enclose and shows that the selection is probably very small."," This is self-consistent, because enclose and shows that the selection is probably very small." +" To determine the spectral parametersvalues, we applied a forward unfolding (?), which is the most robust method to parameterize the data."," To determine the spectral parameters, we applied a forward unfolding , which is the most robust method to parameterize the data." + The could be described power laws as shown in Table 1.., The could be described power laws as shown in Table \ref{table:1}. +" The ratio of the normalization constants between P1 and P2 at 100GeV is 0.4+0.2, which is consistent with the values directly derived from the light curves."," The ratio of the normalization constants between P1 and P2 at $100\gev$ is $0.4\pm0.2$, which is consistent with the values directly derived from the light curves." +" We cross-checked the (P1+P2)m spectrum by comparing the 2009/10 data to 2010/11 data, on- to wobble-mode data, two zenith angle ranges, two quality cut levels and four unfolding algorithms, and found that the spectrum was stable within the errors."," We cross-checked the $_\mr{M}$ spectrum by comparing the 2009/10 data to 2010/11 data, on- to wobble-mode data, two zenith angle ranges, two quality cut levels and four unfolding algorithms, and found that the spectrum was stable within the errors." +While a full application of our group finder to the SDSS MSTO sample is beyond the scope of the current work. analysis of our SS data sets suggest we might expect to find 0-4 groups. corresponding to relatively high-Iuminosity. intermediate-age accretion events on mildly eccentric orbits.,"While a full application of our group finder to the SDSS MSTO sample is beyond the scope of the current work, analysis of our S5 data sets suggest we might expect to find 0-4 groups, corresponding to relatively high-luminosity, intermediate-age accretion events on mildly eccentric orbits." + The S2 and S5 panels of imply that the majority (though not all) of these events would also be recovered from the 2MASS M-giant sample., The S2 and S5 panels of imply that the majority (though not all) of these events would also be recovered from the 2MASS M-giant sample. + Indeed. 4 groups that are plausibly associated with the ancestral siblings of the classical dwarf spheroidal satellites are apparent through visual inspection of SDSS MSTO sample (thetailsfromdis-overdensity.andtheOrphanStream.seee.g. ?).. and two of these are also seen in the M-giants.," Indeed, 4 groups that are plausibly associated with the ancestral siblings of the classical dwarf spheroidal satellites are apparent through visual inspection of SDSS MSTO sample \citep[the tails from disruption of Sagittarius, the +Monocerous ring and the Virgo overdensity, and the Orphan Stream, see +e.g.][]{2006ApJ...642L.137B}, and two of these are also seen in the M-giants." + This again indicates broad consistency between structures seen in the real stellar halo and those in our models., This again indicates broad consistency between structures seen in the real stellar halo and those in our models. + (Whilemanymorestreamsfromglobu-onlythenumberofhigher-Iuminositystreams) From it can be seen that. for data set S5. the mean fraction of material in groups is which increases to when bound groups are also included.," \citep[While +many more streams from globular clusters and lower-luminosity dwarfs +have been found in SDSS using matched-filtering techniques, e.g.,][ +these objects are missing from the stellar halo models, so we compare +only the number of higher-luminosity streams]{grillmair09} + From it can be seen that, for data set S5, the mean fraction of material in groups is which increases to when bound groups are also included." + These results are consistent with what we see for S3 survey. If we take into account the shallow depth of the S5 survey due to which the outer halo. which is also more structured (see 7)). is missed.," These results are consistent with what we see for S3 survey, if we take into account the shallow depth of the S5 survey due to which the outer halo, which is also more structured (see ), is missed." + Similarly. most bound structures are in the outer parts of the halos (see 7)). hence unlike other surveys. including them does not increase the fraction by much for S5 survey.," Similarly, most bound structures are in the outer parts of the halos (see ), hence unlike other surveys, including them does not increase the fraction by much for S5 survey." + However. when compared to the results of ?.. where they find the fractional rms deviation from a smooth analytic model. 7/total. to be around for SDSS MSTO stars. our mass fractions are apparently low.," However, when compared to the results of \citet{2008ApJ...680..295B}, where they find the fractional rms deviation from a smooth analytic model, $\sigma/{\rm total}$, to be around for SDSS MSTO stars, our mass fractions are apparently low." + It should be noted that ? had also analyzed the same set of halos as used by us and reported good agreement with the SDSS data., It should be noted that \citet{2008ApJ...680..295B} had also analyzed the same set of halos as used by us and reported good agreement with the SDSS data. + Hence the cause of the mismatch is due to the methodologies being different. which we explore below.," Hence the cause of the mismatch is due to the methodologies being different, which we explore below." + Firstly. we think that c/total cannot be directly interpreted as amount of mass in structure. e.g.. considering equally populated bins. 1f of the bins differ in mass by order of the mass in the bins one gets a/total=0.33.," Firstly, we think that $\sigma/{\rm total}$ cannot be directly interpreted as amount of mass in structure, e.g., considering equally populated bins, if of the bins differ in mass by order of the mass in the bins one gets $\sigma/{\rm total}=0.33$." + Secondly. an analytical model as adopted by them might not necessarily be a good description of the smooth component of the halo.," Secondly, an analytical model as adopted by them might not necessarily be a good description of the smooth component of the halo." + This misfit will contribute to a/total but will not give rise to any structure in our scheme.," This misfit will contribute to $\sigma/{\rm + total}$ but will not give rise to any structure in our scheme." + It is also important to note that in our clustering scheme only those structures are detected which give rise to peak in the density distribution., It is also important to note that in our clustering scheme only those structures are detected which give rise to peak in the density distribution. + Thirdly. the group finder truncates a structure when its isodensity contour hits that of another structure.," Thirdly, the group finder truncates a structure when its isodensity contour hits that of another structure." + Hence the envelope region around a structure can contribute to o/total but is ignored by us., Hence the envelope region around a structure can contribute to $\sigma/{\rm total}$ but is ignored by us. + Note. by following points in the envelope regions along density gradients one can associate them with the groups but such a classification is not free from ambiguity and in general decreases the purity of the groups.," Note, by following points in the envelope regions along density gradients one can associate them with the groups but such a classification is not free from ambiguity and in general decreases the purity of the groups." + Finally. in our analysis we only consider significant groups which stand out above the Poisson noise.," Finally, in our analysis we only consider significant groups which stand out above the Poisson noise." + However. there might be low significance fluctuations which we have deliberately ignored and these will invariably contribute to a/total.," However, there might be low significance fluctuations which we have deliberately ignored and these will invariably contribute to $\sigma/{\rm total}$." + However. low significance fluctuations unless they are massive. which is rare. wont dominate the mass fraction in structures.," However, low significance fluctuations unless they are massive, which is rare, wont dominate the mass fraction in structures." + To conclude we think that the methodologies being very different it is very difficult to interpret the results of one scheme in terms of the other., To conclude we think that the methodologies being very different it is very difficult to interpret the results of one scheme in terms of the other. + In this paper. we have explored the power of a group finding algorithm to recover structures from photometric surveys of the stellar halo and interpret their properties in terms of Galactic accretion history.," In this paper, we have explored the power of a group finding algorithm to recover structures from photometric surveys of the stellar halo and interpret their properties in terms of Galactic accretion history." + We first applied our group finder to idealized synthetic stellar surveys. which were generated from our ACDM models without accounting for observational errors.," We first applied our group finder to idealized synthetic stellar surveys, which were generated from our $\Lambda$ CDM models without accounting for observational errors." +" We find a simple dependence for the probability of detecting debris as a group on the parameters of its progenitor accretion event: the probability is highest for recent (small f,4,,) and high luminosity (large. £) events accreted along circular orbits (large e).", We find a simple dependence for the probability of detecting debris as a group on the parameters of its progenitor accretion event: the probability is highest for recent (small $t_{\rm acc}$ ) and high luminosity (large $L$ ) events accreted along circular orbits (large $\epsilon$ ). +" The strongest dependence is on t,...", The strongest dependence is on $t_{\rm acc}$. + The properties of recovered groups — the number of and fraction of material in groups. along with distribution of the stellar mass and radial distance of the groups — can in principle place constraints on the accretion history of a halo.," The properties of recovered groups — the number of and fraction of material in groups, along with distribution of the stellar mass and radial distance of the groups — can in principle place constraints on the accretion history of a halo." + Ancient accretion events (>10Civr ago) are not recovered as groups even in the absence of observational limitations because they are too phase-mixed to appear as distinct structures., Ancient accretion events $> 10\Gyr$ ago) are not recovered as groups even in the absence of observational limitations because they are too phase-mixed to appear as distinct structures. + We then applied our group finder to synthetic surveys that contained more realistic observational errors., We then applied our group finder to synthetic surveys that contained more realistic observational errors. + Our results emphasize that the capability of a photometric survey to discover structures depends upon its sample size. the distance uncertainty. the depth and the relative sampling probability of different stellar populations.," Our results emphasize that the capability of a photometric survey to discover structures depends upon its sample size, the distance uncertainty, the depth and the relative sampling probability of different stellar populations." + The broadest constraints on accretion history will come by combining the results of current and future surveys., The broadest constraints on accretion history will come by combining the results of current and future surveys. + For example. M-giants selected from 2MASS are intermediate age. high metallicity stars and hence are good tracers of relatively recent. high-luminosity accretion events with little contamination from older events.," For example, M-giants selected from 2MASS are intermediate age, high metallicity stars and hence are good tracers of relatively recent, high-luminosity accretion events with little contamination from older events." + An LSST MSTO survey would contain a range of stellar populations whose properties depend on the severity of the color cut made to select the sample., An LSST MSTO survey would contain a range of stellar populations whose properties depend on the severity of the color cut made to select the sample. + Limiting the sample to the very bluest MSTO stars increases the dominance of low-metallicity stars in the sample. and hence the sensitivity to low-luminosity accretion events.," Limiting the sample to the very bluest MSTO stars increases the dominance of low-metallicity stars in the sample, and hence the sensitivity to low-luminosity accretion events." + RR Lyraes selected from LSST are bright enough to probe beyond 100 kpe where the apocenters of the more eccentric orbits lie. and hence will find a more fair sampling of the orbital properties of accretion events.," RR Lyraes selected from LSST are bright enough to probe beyond 100 kpc where the apocenters of the more eccentric orbits lie, and hence will find a more fair sampling of the orbital properties of accretion events." + Finally. à quantitative comparison of the results of applying the group-finder to the real 2MASS M-giant sample with those from the mock (synthetic) 2MASS M-giant surveys shows the number and properties of substructures in 2MASS M-giant survey to be roughly in agreement with simulated ACDM stellar halos.," Finally, a quantitative comparison of the results of applying the group-finder to the real 2MASS M-giant sample with those from the mock (synthetic) 2MASS M-giant surveys shows the number and properties of substructures in 2MASS M-giant survey to be roughly in agreement with simulated $\Lambda$ CDM stellar halos." + These groups most likely correspond to satellites accreted more recently than LOCiz. with luminosity higher than 5«109L.. and preferably on orbits of low eccentricity.," These groups most likely correspond to satellites accreted more recently than $10 \Gyr$, with luminosity higher than $5 \times 10^6 \Lsun$ and preferably on orbits of low eccentricity." + Overall we conclude that current. and near-future photometric surveys are poised to provide a complete census of our Galaxy’s recent accretion history., Overall we conclude that current and near-future photometric surveys are poised to provide a complete census of our Galaxy's recent accretion history. + The current results from 2MASS alone map the highest-luminosity recent events. future deep MSTO surveys will fill in. the lower end of the luminosity function and RR Lyrae surveys will find debris structures that may be currently missing because the progenitor satellites were on highly radial orbits.," The current results from 2MASS alone map the highest-luminosity recent events, future deep MSTO surveys will fill in the lower end of the luminosity function and RR Lyrae surveys will find debris structures that may be currently missing because the progenitor satellites were on highly radial orbits." + Reconstructing more ancient accretion will require additional dimensions of data. such as velocity (proper motions and radial velocities of stars) and chemical abundance information.," Reconstructing more ancient accretion will require additional dimensions of data, such as velocity (proper motions and radial velocities of stars) and chemical abundance information." +was in the range 1 to 5 aresec. except at the beginning of the run for evele 29982 and throughout evele 29983. when it was 2 aresec. which Led to some spillage of light from the 6ὁ array.,"was in the range 1 to 1.5 arcsec, except at the beginning of the run for cycle 29982 and throughout cycle 29983, when it was 2 arcsec, which led to some spillage of light from the $6 \times 6$ array." + We have therefore not used those data., We have therefore not used those data. + Observations of the spectrophotometric [ux standard DD|2s8 4211 were taken to calibrate the data., Observations of the spectrophotometric flux standard BD+28 4211 were taken to calibrate the data. + Vhev were mace through a neutral density filter with attenuation factor 100 and also sullered from poor secing., They were made through a neutral density filter with attenuation factor 100 and also suffered from poor seeing. + The data reduction process emplovs specific pipeline processing of the S-Cam2 data (de Bruijne 22001). based. on the suite of software (Blackburn 1995) and a full clescription is given by Perryman ((2001) for their observations of UZ For.," The data reduction process employs specific pipeline processing of the S-Cam2 data (de Bruijne 2001), based on the suite of software (Blackburn 1995) and a full description is given by Perryman (2001) for their observations of UZ For." + Once reduced. the data can be split into dillerent. encrey bands (wavelength. ranges).," Once reduced, the data can be split into different energy bands (wavelength ranges)." +" The intrinsic SPJ resolution is such that AfAA—9. but here we use only three bands to represent ‘red’. ‘wellow’ and ""blue light."," The intrinsic STJ resolution is such that $\lambda$ $\Delta\lambda\sim 9$, but here we use only three bands to represent `red', `yellow' and `blue' light." + The enerev bands are selected: so that roughly equal numbers of events occur in each., The energy bands are selected so that roughly equal numbers of events occur in each. + The wavelength range is [limited bv the atmosphere at. short wavelengths. ancl the use of opties to suppress infrared photons at long wavelengths. ancl corresponds to approximately 680 nm.," The wavelength range is limited by the atmosphere at short wavelengths and the use of optics to suppress infrared photons at long wavelengths, and corresponds to approximately $\--$ 680 nm." + The wavelength ranges for the blue. vellow ancl red. bands here. are 470 nm. 55 Yom and 680 nm.," The wavelength ranges for the blue, yellow and red bands here are $\--$ 470 nm, $\--$ 550 nm and $\--$ 680 nm." + As part of he pipeline processing. the cata were Ila-HeleL correctoc using a single map derived. [rom sky observations.," As part of the pipeline processing, the data were flat-field corrected using a single map derived from sky observations." + The data were then corrected for atmospheric extinction using the standard La Palma tables of extinction values as a function of wavelength. and air mass. anc inally skv-hackeround subtracted.," The data were then corrected for atmospheric extinction using the standard La Palma tables of extinction values as a function of wavelength and air mass, and finally sky-background subtracted." + The pipeline processing is applied to a light curve in arbitrary time bins of 1s. The extraction of the backeround-subtractecd light. curves usec he entire 6ὁ array for the object and the two corner pixels (1.1) and (6.6) for the background.," The pipeline processing is applied to a light curve in arbitrary time bins of 1 s. The extraction of the background-subtracted light curves used the entire $6\times 6$ array for the object and the two corner pixels (1,1) and (6,6) for the background." + The backerounc ight level is then taken as the mean level curing eclipse anc his is subtracted from the source light curve., The background light level is then taken as the mean level during eclipse and this is subtracted from the source light curve. + Figure 1. shows the white light curves for eclipses 29982. 20004 and 29905 before. subtraction of the background. ogether with the backgrounds taken from the two corner jxxels (1.1) and (6.6).," Figure \ref{fig:LCback} shows the white light curves for eclipses 29982, 29994 and 29995 before subtraction of the background, together with the backgrounds taken from the two corner pixels (1,1) and (6,6)." + Once the data hac been calibrated: and. reduced. we [olded the data on the orbital period.," Once the data had been calibrated and reduced, we folded the data on the orbital period." + Phe linear ephenicris of Schwope ((2001) was used. which defines inferior conjunction of the secondary as oO=LO.," The linear ephemeris of Schwope (2001) was used, which defines inferior conjunction of the secondary as $\phi=1.0$." + Tre UPC times are transformed. to TDB (at the solar svstem barvcentre. Le. including light travel imes).," The UTC times are transformed to TDB (at the solar system barycentre, i.e. including light travel times)." + For eveles 29982 and 20993. where there is no absolute time reference. the egress is aligned to be at the same phase as in eveles 29994 and 29995.," For cycles 29982 and 29993, where there is no absolute time reference, the egress is aligned to be at the same phase as in cycles 29994 and 29995." + Figures 2. and 3 show the white. red. vellow and bue light curves. with the colour ratios vellow/red and. blue/vellow. for eveles 29993. 20994 and 29995.," Figures \ref{fig:huaqr04colours} and \ref{fig:huaqr03colours} show the white, red, yellow and blue light curves, with the colour ratios yellow/red and blue/yellow, for cycles 29993, 29994 and 29995." + The SCCOLLary star has been subtracted. from the colour ratios (but not the light curves) so that the change in the ratios is due wholly to the stream. after accretion region ingress.," The secondary star has been subtracted from the colour ratios (but not the light curves) so that the change in the ratios is due wholly to the stream, after accretion region ingress." + We extracted intervals of good secing from the standard star observation to determine the countrate in he vellow ρα. corresponding most closely to the Y band.," We extracted intervals of good seeing from the standard star observation to determine the countrate in the yellow band, corresponding most closely to the $V$ band." + This gave à zero point magnitude for 1 count/s in this band of 24.) taking into account the (assumed) lacor of 100 rom the neutral density filter.," This gave a zero point magnitude for 1 count/s in this band of 24.0, taking into account the (assumed) factor of 100 from the neutral density filter." + The corresponding maximuni rightness at oO= Llinlbigure 3 is V—14.7., The corresponding maximum brightness at $\phi=1.1$ in Figure \ref{fig:huaqr03colours} is $V=14.7$. + This indicates hat HU Aqr was in a high accretion state at 10 time of hese observations (see Schwope 22001)., This indicates that HU Aqr was in a high accretion state at the time of these observations (see Schwope 2001). + The light curves in Figures 2 and 3 show a number of features that are characteristic of an eclipsing polar svstenm.," The light curves in Figures \ref{fig:huaqr04colours} + and \ref{fig:huaqr03colours} show a number of features that are characteristic of an eclipsing polar system." + The most prominent feature is the eclipse itself. which starts with the limb of the secondary star eclipsing the accretion stream.," The most prominent feature is the eclipse itself, which starts with the limb of the secondary star eclipsing the accretion stream." + At about 020.964 the bright accretion region on the white cwarl is eclipsed in a few seconds (the white ciwarf is also eclipsed around these phases. but is much fainter).," At about $\phi$ =0.964 the bright accretion region on the white dwarf is eclipsed in a few seconds (the white dwarf is also eclipsed around these phases, but is much fainter)." + After this only the secondary star is visible. and the sequence is then approximately reversed on egress.," After this only the secondary star is visible, and the sequence is then approximately reversed on egress." + Prior to the eclipse of the white cwark we observe a pre-eclipse dip.," Prior to the eclipse of the white dwarf, we observe a pre-eclipse dip." + Figure 3.3 shows this clip centred at ó=O.S72.," Figure \ref{fig:huaqr03colours} shows this dip centred at $\phi\approx +0.872$." + The dip is caused by the eclipse of the accretion region on the white dwarl by the magnetically confined section of the accretion stream., The dip is caused by the eclipse of the accretion region on the white dwarf by the magnetically confined section of the accretion stream. + Consequently the phase of the centre of the, Consequently the phase of the centre of the + The # dependence of theAand X7 polarizations,$p_L$ = 800 GeV/c in $pCu$ collisions is shown in \ref{fgr:pBe800Sig_bar} +(his concept.,this concept. + Thus shocks heating. (hough not ruled out. is not considered as a major source of the eeniission we observe.," Thus shocks heating, though not ruled out, is not considered as a major source of the emission we observe." + AMid-IR. emission has been observed (o arise [rom star formation in the central regions of many galaxies (e.g. Telesco 1988)., Mid-IR emission has been observed to arise from star formation in the central regions of many galaxies (e.g. Telesco 1988). + The mid-IR provides an excellent trace. of HID star forming regions whose emission peaks al far-IR wavelengths (50-200 jam)., The mid-IR provides an excellent trace of HII star forming regions whose emission peaks at far-IR wavelengths (50-200 $\micron$ ). + Observations by Engargiola et al. (, Observations by Engargiola et al. ( +"1988) at 155 yan show extended emission (>48"") primarily in an east-west direction.",1988) at 155 $\micron$ show extended emission $>48\arcsec$ ) primarily in an east-west direction. + ISO oobservations by REG measure (his emission as a cold dust component (3618) consistent with dust heatecl in HI] regions (Telesco et al., ISO observations by RE96 measure this emission as a cold dust component (36K) consistent with dust heated in HII regions (Telesco et al. + 1980)., 1980). +" ILowever. observations by Pérez-Fournon Wilson (1990) in Hao show these IU] regions exist in an elliptical galactic bar at a radius ol ~50"" (~3 kpe) from the nucleus."," However, observations by rez-Fournon Wilson (1990) in $\alpha $ show these HII regions exist in an elliptical galactic bar at a radius of $\thicksim 50\arcsec$ $\thicksim 3$ kpc) from the nucleus." +" Thus these star forming regions cannot contribute to the mid-IR emission we observe within our ~11"" ffield of view.", Thus these star forming regions cannot contribute to the mid-IR emission we observe within our $\thicksim 11\arcsec$ field of view. + Star formation in the cireiumnmuclear region of NGC 4151 has been characterized. using ihe strength of polvevelic aromatic hydrocarbon eemission., Star formation in the circumnuclear region of NGC 4151 has been characterized using the strength of polycyclic aromatic hydrocarbon emission. + Galaxies with strong nuclear star formation also feature strong PAIL emission., Galaxies with strong nuclear star formation also feature strong PAH emission. + This eemission however is found to be weak or absent in AGNs with weak star formation (Roche et al., This emission however is found to be weak or absent in AGNs with weak star formation (Roche et al. + 1991: Genzel et al., 1991; Genzel et al. + 1998)., 1998). + In the case of 44151. Roche Aitken (1985) and Imanishi et al. (," In the case of 4151, Roche Aitken (1985) and Imanishi et al. (" +1998) failed to detect PAIL emission at 11.4 sam and 3.3 am respectively with their e4” apertures.,1998) failed to detect PAH emission at 11.4 $\micron$ and 3.3 $\micron$ respectively with their $\thicksim 4\arcsec$ apertures. + Further observation bv Stim et al. (, Further observation by Sturm et al. ( +1999) also failed to detect anv PAIL emission at 11.2 n. S.V qun. 7.7 jun. or 6.2 san.,"1999) also failed to detect any PAH emission at 11.2 $% +\micro n, 8.7 $\micron$, 7.7 $\micron$, or 6.2 $\micron$." +" Thus the mid-IR emission we observe on a scale of ~3.5"" is unlikely to be associated with significant star formation.", Thus the mid-IR emission we observe on a scale of $\thicksim 3.5\arcsec$ is unlikely to be associated with significant star formation. + The most likely explanation lor the “extended” mid-IR morphology in NGC 4151 is enussion from a dusiv NLR (Rieke et al., The most likely explanation for the “extended” mid-IR morphology in NGC 4151 is emission from a dusty NLR (Rieke et al. + 1981: RE96)., 1981; RE96). + Dust in (this region has a direct view ol the central engine and hence can be heated resulting in extended mid-IR. emission., Dust in this region has a direct view of the central engine and hence can be heated resulting in extended mid-IR emission. + The emission we observe follows the NLR as delineated by the [OLI] observations of INaiser et al. (, The emission we observe follows the NLR as delineated by the [OIII] observations of Kaiser et al. ( +2000). lending support to this concept.,"2000), lending support to this concept." + Mid-IR. emission coincident with ΟΠΗ NLR emission has also been observed in other galaxies such as NGC 1068 (Braatz οἱ al., Mid-IR emission coincident with [OIII] NLR emission has also been observed in other galaxies such as NGC 1068 (Braatz et al. + 1993. Cameron et al.," 1993, Cameron et al." + 1993) and Cve A (Radomski et al., 1993) and Cyg A (Radomski et al. + 2001. 2002).," 2001, 2002)." + In both galaxies dust heated by the central engine most likely contributes to (his emission., In both galaxies dust heated by the central engine most likely contributes to this emission. +are supplied by CGO0.,are supplied by CG00. + The condition of apsidal alignment requires (hat precession rates of all wires be equal to (he precession rate of a test particle at the ring midline. ancl vields PN [mear equations lor (he 2N wire masses.," The condition of apsidal alignment requires that precession rates of all wires be equal to the precession rate of a test particle at the ring midline, and yields $2N$ linear equations for the $2N$ wire masses." + The solution of this linear svstem generates a new surface density prolile. Σία).," The solution of this linear system generates a new surface density profile, $\Sigma'(a)$." + The entire calenlation is then repeated: from this new surface density. we calculate a new collisional acceleration profile [C'(a.f)]. a new set of wire precession rates due to pressure forces [(da/dD)e«]. and à new set of 2.V linear equations.," The entire calculation is then repeated: from this new surface density, we calculate a new collisional acceleration profile $\mathbf{C'}(a,f)$ ], a new set of wire precession rates due to pressure forces $\langle d\pomega/dt\rangle_{C'}$ ], and a new set of $2N$ linear equations." + In this wav. the solution for the surface densitv is iterated until convergence is achieved.," In this way, the solution for the surface density is iterated until convergence is achieved." + In practice. for model parameters appropriate to the Uranian o ancl » rines ancl the Saburnian Maxwell and Colombo ringlets (see Table 2)). we find that the solution of 6000 wire masses converges aller ~10 iterations.," In practice, for model parameters appropriate to the Uranian $\alpha$ and $\beta$ rings and the Saturnian Maxwell and Colombo ringlets (see Table \ref{param2}) ), we find that the solution of $2N = 2000$ –6000 wire masses converges after $\sim$ 10 iterations." + Because the solution is reflection- about the ring midline. only N=1000. 3000 linearly independent equations need be solved for .N. distinct wire masses.," Because the solution is reflection-symmetric about the ring midline, only $N = 1000$ –3000 linearly independent equations need be solved for $N$ distinct wire masses." + The derivative in equation (2)) is computed numerically using a Savitzkv-Golav. smoothing filter of order 2 and having a width of 20 wires (Press et al., The derivative in equation \ref{collacc}) ) is computed numerically using a Savitzky-Golay smoothing filter of order 2 and having a width of 20 wires (Press et al. + 1992)., 1992). + The svstem of 2.N. [linear equations is solved using subroutine DGESY of the LAPACHK (Linear Algebra Package) software library., The system of $2N$ linear equations is solved using subroutine DGESV of the LAPACK (Linear Algebra Package) software library. + Because many of our parameters such as c and S are only order-olnagnitude estimates. our profiles ave probably accurate {ο factors of a few. at best.," Because many of our parameters such as $c$ and $S$ are only order-of-magnitude estimates, our profiles are probably accurate to factors of a few, at best." + Nevertheless. bv accounting not only for interparticle collisions near rng boundaries but also for collisions within (he ring interior. we may explore the qualitative effects of incorporating the latter and make a first-cut. correction to the solutions obtained bv CGO00.," Nevertheless, by accounting not only for interparticle collisions near ring boundaries but also for collisions within the ring interior, we may explore the qualitative effects of incorporating the latter and make a first-cut correction to the solutions obtained by CG00." + Computed surface density profiles for the o. ». Maxwell. and Colombo ringlets. are displaved in Figures 14. respectively.," Computed surface density profiles for the $\alpha$, $\beta$, Maxwell, and Colombo ringlets are displayed in Figures 1–4, respectively." + Near the ring midline. our solutions require less mass (han those of 000. a consequence of local pressure gradients that compress the ring ancl abet rine sell-gravitv.," Near the ring midline, our solutions require less mass than those of CG00, a consequence of local pressure gradients that compress the ring and abet ring self-gravity." +" By contrast. our computed peaks in surface density near ring boundaries are larger than those of 000,"," By contrast, our computed peaks in surface density near ring boundaries are larger than those of CG00." + The reason for this is as follows., The reason for this is as follows. + As a given peak in surface density is approached from the ring midline. steep and inward-directed pressure forces nist be balanced by the outward gravitational attraction of massive endwires on the far side of the peak.," As a given peak in surface density is approached from the ring midline, steep and inward-directed pressure forces must be balanced by the outward gravitational attraction of massive endwires on the far side of the peak." +" These inward-directed forces are neglected by CGO0: accounting for them here leads to enchwire masses larger than those obtained hy 00,", These inward-directed forces are neglected by CG00; accounting for them here leads to endwire masses larger than those obtained by CG00. + These same qualitative conclusions are reached by Alosqueira Estrada. (2002). who employ various prescriptions for collisional stresses that diller from ours.," These same qualitative conclusions are reached by Mosqueira Estrada (2002), who employ various prescriptions for collisional stresses that differ from ours." + Their surface density profiles deviate [rom ours by large amounts. sometimes by more (han an order of magnitude. reflecting (he sensitivity of the shape of the prolile to choice of boundary conditions.," Their surface density profiles deviate from ours by large amounts, sometimes by more than an order of magnitude, reflecting the sensitivity of the shape of the profile to choice of boundary conditions." + Some consolation max be had in the finding of Moscequeira Estrada (2002) Chat the total ring mass. AL. is less sensitive to this choice.," Some consolation may be had in the finding of Mosqueira Estrada (2002) that the total ring mass, $M$, is less sensitive to this choice." + The chief shortcoming of all caleulations of the surface density prolile. including our own. is the prescriptive and slightly. arbitrary description of," The chief shortcoming of all calculations of the surface density profile, including our own, is the prescriptive and slightly arbitrary description of" +the technique to cosmological simulations of structure formation.,the technique to cosmological simulations of structure formation. + We summarise the results and conclude in Section 7.., We summarise the results and conclude in Section \ref{sec:concl}. + In this section we will briclhy report the gist. of the algorithm., In this section we will briefly report the gist of the algorithm. + We refer the reader to the pivotal work PALOT for a thorough treatment of the problem and for a detailed derivation of the new equation of The Lagrangian for a system of IN particles interacting only through gravity reads: where The expression for the potential d departs from its Newtonian definition due to the introduction of softening and hence of the kernel © and the related. length scale h., We refer the reader to the pivotal work PM07 for a thorough treatment of the problem and for a detailed derivation of the new equation of The Lagrangian for a system of $N$ particles interacting only through gravity reads: where The expression for the potential $\Phi$ departs from its Newtonian definition due to the introduction of softening and hence of the kernel $\phi$ and the related length scale $h$. + When this quantity has no further dependences and. is kept fixed the resulting equation of motion will resemble the Newtonian original. but for the inheritance of this additional scale: its expression is derived. by applying the Euler-Lagrange equations to (3)) and for particle 7 it will reacl: where Here 6)=Oóf0|r;rj| is the force kernel.," When this quantity has no further dependences and is kept fixed the resulting equation of motion will resemble the Newtonian original, but for the inheritance of this additional scale; its expression is derived by applying the Euler-Lagrange equations to \ref{eq:lagrange}) ) and for particle $i$ it will read: where Here $\phi^\prime = \partial \phi / \partial\left|\bmath{r}_i - \bmath{r}_j\right|$ is the force kernel." + The expressions for both the potential and the force kernel in the cubic spline case can be found in BANOO ((Appendix. A)ο, The expressions for both the potential and the force kernel in the cubic spline case can be found in BK09 (Appendix A). + The force F;;j(h) reduces to the Newtonian gravitational force for separations |r; r;|&/h and to the dependent “softened” version When fis allowed. to vary from particle to particle according to the density. of the environment a. flew complications arise., The force $\mathbf{F}_{ij}(h)$ reduces to the Newtonian gravitational force for separations $\left|\bmath{r}_i - \bmath{r}_j\right| > h$ and to the kernel-dependent “softened” version When $h$ is allowed to vary from particle to particle according to the density of the environment a few complications arise. + La order to maintain its translational invariance ancl hence ensure that the resulting dynamics would. conserve linear momentum. the Lagrangian needs to be svmmetrised.," In order to maintain its translational invariance and hence ensure that the resulting dynamics would conserve linear momentum, the Lagrangian needs to be symmetrised." + One way to do this is bv averaging over the potentials evaluated: with the softenings of the interacting pair of particles: the new Lagrangian would read: where οί)=o(|r;rj|.h).," One way to do this is by averaging over the potentials evaluated with the softenings of the interacting pair of particles; the new Lagrangian would read: where $\phi_{ij}(h_i) \equiv \phi \left(\left|\bmath{r}_i - \bmath{r}_j\right|, h\right)$." + When deriving the equation of motion from (7)). the additional dependence on the position r through # results in an extra termi besides the classical inverse square law.," When deriving the equation of motion from \ref{eq:lagrange_symm}) ), the additional dependence on the position $r$ through $h$ results in an extra term besides the classical inverse square law." + The evolution of a particle i subject only to the action of gravity and supplied with a variable softening length will in fact obey: where The additional contribution. which we will refer to as the “correction term. is attractive in nature and. will therefore act towards increasing the resulting gravitational force.," The evolution of a particle $i$ subject only to the action of gravity and supplied with a variable softening length will in fact obey: where The additional contribution, which we will refer to as the “correction term”, is attractive in nature and will therefore act towards increasing the resulting gravitational force." + If this termi. were not accounted for when using adaptive softening. the particles would be evolved according toa law incoherent with the svstem's Lagrangian. ic. energy conservation would be Lost.," If this term were not accounted for when using adaptive softening, the particles would be evolved according to a law incoherent with the system's Lagrangian, i.e. energy conservation would be lost." + We have implemented the adaptive softening formalism on the latest version of the codo. namelyGADGET-3.," We have implemented the adaptive softening formalism on the latest version of the code, namely." +. computes gravitational forces via the TreePM method. (?: 75: 2)) and. hvdrodsnamical interactions bv means of SPLE: it differs from the previous. versions of the code in that it features a more flexible domain decomposition. something that mace it suitable for simulations involving extreme levels of clustering. as the Millennium-LH (?)..," computes gravitational forces via the TreePM method \citealt{xu95}; \citealt*{bode00}; \citealt{bagla02}) ) and hydrodynamical interactions by means of SPH; it differs from the previous versions of the code in that it features a more flexible domain decomposition, something that made it suitable for simulations involving extreme levels of clustering, as the Millennium-II \citep{mII}." + Implementing adaptive softening required mocifications of the ‘Tree-algorithm ancl of the timestep criterion. along with the introduction. of the machinery to compute the softening lengths., Implementing adaptive softening required modifications of the Tree-algorithm and of the timestep criterion along with the introduction of the machinery to compute the softening lengths. + Besides the obvious change in the expression for the gravitational acceleration. the opening criterion for the nodes has been modilied in order to avoid the presence of smoothed particle-node interaction: in other words. the correction term can be non-zero only within a particle-particle interaction (more details in Sec.," Besides the obvious change in the expression for the gravitational acceleration, the opening criterion for the nodes has been modified in order to avoid the presence of smoothed particle-node interaction; in other words, the correction term can be non-zero only within a particle-particle interaction (more details in Sec." + 3.2.4 of DBIxX09)., 3.2.4 of BK09). + Phe timestep criterion emploved. by for collisionless particles reacts: where is an accuracy parameter. € is the Plummer equivalent softening (στ2.8c. where / is the support of the cubic spline kernel) ancl à the acceleration of the particle.," The timestep criterion employed by for collisionless particles reads: where $\eta$ is an accuracy parameter, $\epsilon$ is the Plummer equivalent softening $h\simeq 2.8 \epsilon$, where $h$ is the support of the cubic spline kernel) and $a$ the acceleration of the particle." + We kept the criterion. itself unchanged. ancl substituted. « with the individual value of the adaptive softening., We kept the criterion itself unchanged and substituted $\epsilon$ with the individual value of the adaptive softening. + As to the computation of the softening lengths the method. is identical to the one uses for setting the smoothing lengths in SPL calculations., As to the computation of the softening lengths the method is identical to the one uses for setting the smoothing lengths in SPH calculations. + Qualitatively. they represent the radius of the sphere centred. on the," Qualitatively, they represent the radius of the sphere centred on the" +which causes the line emission should also be visible to the observer.,which causes the line emission should also be visible to the observer. + There should be a very significant level of continuum radiation. which was not observed.," There should be a very significant level of continuum radiation, which was not observed." + In the second model. it is proposed (hat the GRB explosion is preceded. bv roughly a week or so. by a supernova explosion which ejects a dense slab of gas moving al a speed 0.le.," In the second model, it is proposed that the GRB explosion is preceded, by roughly a week or so, by a supernova explosion which ejects a dense slab of gas moving at a speed $v\sim 0.1c$." + The ejected material reaches a distance >LOY cm by the time the GRB eves olf., The ejected material reaches a distance $> 10^{15}$ cm by the time the GRB goes off. + The x-rav photons from the GRD aud early allerelow are intercepted by. the slab ancl the radiation is reprocessed into line photons (Vietvi Stella. 1993: Vietri et al.," The x-ray photons from the GRB and early afterglow are intercepted by the slab and the radiation is reprocessed into line photons (Vietri Stella, 1998; Vietri et al." + 2001)., 2001). + The eeomelry of the outflowing gas is somewhat flexible., The geometry of the outflowing gas is somewhat flexible. + It could be a quasi-spherical shell. as in the model suggested by Reeves et al. (," It could be a quasi-spherical shell, as in the model suggested by Reeves et al. (" +2002). or it could be in the form of a large funnel carved out in the previously ejected material.,"2002), or it could be in the form of a large funnel carved out in the previously ejected material." + In either case. the delav of a lew hours between the GRD and the line emission is explained as the geometrical time delay associated with the extva path length (hat photons have to travel from the GRB to the photoionized laver and then to the observer.," In either case, the delay of a few hours between the GRB and the line emission is explained as the geometrical time delay associated with the extra path length that photons have to travel from the GRB to the photoionized layer and then to the observer." + A third possibility. whieh we elaborate upon here. is (hat the supernova and the GRB go olf simultaneously. but that the radiation from the GRB and early afterglow is scattered by a nearby scattering medium and then intercepted by the expanding surface of the supernova ejecta.," A third possibility, which we elaborate upon here, is that the supernova and the GRB go off simultaneously, but that the radiation from the GRB and early afterglow is scattered by a nearby scattering medium and then intercepted by the expanding surface of the supernova ejecta." + The lines are produced from the surface lavers of the ejecta., The lines are produced from the surface layers of the ejecta. + The time delay in this case measures (he path length from the GRD to the scatterer and back to the ejecta., The time delay in this case measures the path length from the GRB to the scatterer and back to the ejecta. + The basic outline of this model was briefly described by Vietri et al. (, The basic outline of this model was briefly described by Vietri et al. ( +2001). who however considered ihe model implausible.,"2001), who however considered the model implausible." + We conclude just the opposite in this paper., We conclude just the opposite in this paper. + We argue Chat. if the lines in GRD 011211 are real. they were probably produced. by something resembling this model.," We argue that, if the lines in GRB 011211 are real, they were probably produced by something resembling this model." + Vietri et al. (, Vietri et al. ( +2001) did not specify (he nature of (he scatterer.,2001) did not specify the nature of the scatterer. + In our model. the scaltering occurs in a pair screen created bv the gamma-ray photons from the GRD.," In our model, the scattering occurs in a pair screen created by the gamma-ray photons from the GRB." + An altractive feature of the model is that the radius at which the pair screen is likely (o form is close to what is needed to explain the observed time dela., An attractive feature of the model is that the radius at which the pair screen is likely to form is close to what is needed to explain the observed time delay. + We provide some general constraints on (he various models in 822 and find serious problems with all proposals., We provide some general constraints on the various models in 2 and find serious problems with all proposals. + We show in 833 that the pair screen scattering model can account for the x-ray lines in GRD 011211 provided there is sufficient ambient clensitw in the vicinity of the GRD to scatter eamma-ravs (o produce a significant pair screen. and provided the surface lavers of the exploding star move with a significant speed ~0.3e.," We show in 3 that the pair screen scattering model can account for the x-ray lines in GRB 011211 provided there is sufficient ambient density in the vicinity of the GRB to scatter gamma-rays to produce a significant pair screen, and provided the surface layers of the exploding star move with a significant speed $\sim0.3c$." + We conclude with a summary and discussion in 844., We conclude with a summary and discussion in 4. + Some of the radiation physics relevant {ο line emission is discussed in (he Appendix A., Some of the radiation physics relevant to line emission is discussed in the Appendix A. +Some dust production in the KB occurs when ISM grains hit KBOs (Yamamoto 1998);; our source populations probably represent this mechanism well.,Some dust production in the KB occurs when ISM grains hit KBOs \citep{yama98}; our source populations probably represent this mechanism well. +" But if the KB is like the asteroid belt, then some dust production is probably associated with collisional families, perhaps like the Haumea family (Brownetal.2007)."," But if the KB is like the asteroid belt, then some dust production is probably associated with collisional families, perhaps like the Haumea family \citep{brow07}." +". Therefore, for the time being, it seems appropriate that we content ourselves with simple parametric source distributions, inspired by KBO observations, like those we used here."," Therefore, for the time being, it seems appropriate that we content ourselves with simple parametric source distributions, inspired by KBO observations, like those we used here." +" We modeled the 3-D dust distribution in the Kuiper Belt taking into account perturbations from Jupiter, Saturn, Uranus and Neptune, the destruction of dust grains via collisions, and the interaction of these phenomena, including the enhanced destruction of grains in mean motion resonances."," We modeled the 3-D dust distribution in the Kuiper Belt taking into account perturbations from Jupiter, Saturn, Uranus and Neptune, the destruction of dust grains via collisions, and the interaction of these phenomena, including the enhanced destruction of grains in mean motion resonances." + We demonstrated that the collisional grooming algorithm can approximately reproduce the Dohnanyi(1969) collisional equilibrium size though resonant trapping tends to modify the size distribution in a resonant ring., We demonstrated that the collisional grooming algorithm can approximately reproduce the \citet{dohn69} collisional equilibrium size distribution---though resonant trapping tends to modify the size distribution in a resonant ring. +" The dust level in the KB has never been directly measured; we suggested that one way to measure the dust level would be matching images of the KB dust, e.g., from a probe in the outer Solar System, to the morphology of our models."," The dust level in the KB has never been directly measured; we suggested that one way to measure the dust level would be matching images of the KB dust, e.g., from a probe in the outer Solar System, to the morphology of our models." + Searching for a ring with the gap at Neptune in this manner might be easier than measuring the D.C. dust background., Searching for a ring with the gap at Neptune in this manner might be easier than measuring the D.C. dust background. +" Here are the primary conclusions we have drawn from our models, about the Kuiper Belt dust population itself and about debris disks in general."," Here are the primary conclusions we have drawn from our models, about the Kuiper Belt dust population itself and about debris disks in general." +"in particular their figure 6(b), which show that for efficient injection and strong shocks the subshock compression is typically between 2 and 3 with a rather weak dependence on total Mach number.","in particular their figure 6(b), which show that for efficient injection and strong shocks the subshock compression is typically between 2 and 3 with a rather weak dependence on total Mach number." + The recent study (Kangetal.2008) also finds an asymptotic subshock compression of3.2(M/10)°- for M>10 where M is the shock Mach number.," The recent study \citep{KRJ} + also finds an asymptotic subshock compression of$3.2(M/10)^{0.04}$ for $M>10$ where $M$ is the shock Mach number." +" If the subshock compression automatically adjusts to a value close to 2.5 to 3, it follows that the sub-shock Mach number, and the amount of gas heating in the subshock, is essentially fixed."," If the subshock compression automatically adjusts to a value close to 2.5 to 3, it follows that the sub-shock Mach number, and the amount of gas heating in the subshock, is essentially fixed." + The inflowing gas is first heated by adiabatic compression in the shock precursor from the far upstream value To to a value Τι just in front of the subshock of where Spre is the precursor compression and then on passage through the compression 2.5 subshock by an amount (assumingστι a y=5/3 polytropic equation of state for the gas)., The inflowing gas is first heated by adiabatic compression in the shock precursor from the far upstream value $T_0$ to a value $T_1$ just in front of the subshock of where $s_{\rm pre}$ is the precursor compression and then on passage through the compression 2.5 subshock by an amount (assuming a $\gamma=5/3$ polytropic equation of state for the gas). +" This rises to for a subshock of compression ratio 3, still a relatively modest increase (if there is significant wave dissipation in the precursor it is of course possible to raise the gas temperature to higher levels (Vólketal. 1984)))."," This rises to for a subshock of compression ratio 3, still a relatively modest increase (if there is significant wave dissipation in the precursor it is of course possible to raise the gas temperature to higher levels \citep{VDM}) )." +" If the total compression, as suggested by numerous simulation studies, is of order 10, with a factor of 4 in the precursor and 2.5 in the subshock it follows that the downstream temperature is just the far upstream temperature multiplied by a factor of and is independent of the shock speed."," If the total compression, as suggested by numerous simulation studies, is of order $10$, with a factor of $4$ in the precursor and $2.5$ in the subshock it follows that the downstream temperature is just the far upstream temperature multiplied by a factor of and is independent of the shock speed." +" This is in marked contrast to the standard picture where the downstream temperature is determined purely by the shock speed (with a strong quadratic dependence) and is only very weakly dependent on the upstream temperature according to, k being Boltzmann's constant and m,the proton mass."," This is in marked contrast to the standard picture where the downstream temperature is determined purely by the shock speed (with a strong quadratic dependence) and is only very weakly dependent on the upstream temperature according to, $k$ being Boltzmann's constant and $m_p$the proton mass." +" In reality the total compression does increase with shock Mach number (Kangetal.2008 suggest roughly as the one third power, although this calculation includes Alfven wave heating effects; a naive estimate without wave heating suggests that the exponent might be as high as 3/4) and thus there is a weak dependence of the post-shock temperature on shock speed (scaling somewhere between 2/9 and1/2 power) but nothing as strong as in the unmodified case."," In reality the total compression does increase with shock Mach number \citealp{KRJ} suggest roughly as the one third power, although this calculation includes Alfven wave heating effects; a naive estimate without wave heating suggests that the exponent might be as high as 3/4) and thus there is a weak dependence of the post-shock temperature on shock speed (scaling somewhere between 2/9 and1/2 power) but nothing as strong as in the unmodified case." +" Clearly this is an extreme limit, but the rather surprising answer to the question, how cold can the postshock gas be in the limit of strong particle acceleration, is as cold as six times the upstream temperature!"," Clearly this is an extreme limit, but the rather surprising answer to the question, how cold can the postshock gas be in the limit of strong particle acceleration, is as cold as six times the upstream temperature!" + Motivated by the above discussion we now give a simple description of the gas compression and heating in a supernova remnant with strong particle acceleration., Motivated by the above discussion we now give a simple description of the gas compression and heating in a supernova remnant with strong particle acceleration. +" As an illustrative example we followa fluid element as it is swept up by the shock and compressed, initially to a density of 10 times ambient and temperature of order 6 times ambient at remnant age fg."," As an illustrative example we follow a fluid element as it is swept up by the shock and compressed, initially to a density of 10 times ambient and temperature of order 6 times ambient at remnant age $t_0$." + We assume that it then expands and cools so that the total pressure drops initially by a factor of order 4 over the time fo«t2% and then in pressure equilibrium with the interior., We assume that it then expands and cools so that the total pressure drops initially by a factor of order 4 over the time $t_0