source,target
 Finally. Figure 5 also plots the line of sight velocity vectors of cach galaxy. after subtracting out a mean Vireo velocity of L061 kin/s (Bingech 1999). aud. the estimated r200 (1.55 Mpc) for Vireo. determined by MeLaughllin (1999).," Finally, Figure \ref{virgogeom} also plots the line of sight velocity vectors of each galaxy, after subtracting out a mean Virgo velocity of 1064 km/s (Binggeli 1999), and the estimated r200 (1.55 Mpc) for Virgo, determined by McLaughlin (1999)."
 Without transverse velocities for these galaxies. a full dynamical interpretation is nmupossible: nonetheless. we can οἶσα useful information from this plot.," Without transverse velocities for these galaxies, a full dynamical interpretation is impossible; nonetheless, we can glean useful information from this plot."
 As Virgo'« ceutral galaxy. it is no surprise that AIST has a low line of sight motion (64=213 km/s) with respect to the cluster as a whole.," As Virgo's central galaxy, it is no surprise that M87 has a low line of sight motion $v_{\rm rel} = 243$ km/s) with respect to the cluster as a whole."
 Sitting  1 Alpe behind the cluster core. ATSUs low velocity (Lt kim/s) suggests it is either near apocenter ona low angular momentum orbit — likely having passed near the cluster ceuter a few Cor ago or moving on a more tanecutial orbit which keeps it out of the cluster center.," Sitting $\sim$ 1 Mpc behind the cluster core, M84's low velocity $-4$ km/s) suggests it is either near apocenter on a low angular momentum orbit – likely having passed near the cluster center a few Gyr ago -- or moving on a more tangential orbit which keeps it out of the cluster center."
 As MIO is not projected onto the cluster core. its low velocity 67 km/s) places little constraint on its orbit.," As M49 is not projected onto the cluster core, its low velocity $-67$ km/s) places little constraint on its orbit."
 ILoxcever. the presence of am X-rav bowshock to the north of N9 argues that the ealaxy is falling into Vireo’s hot iutracluster medium from the south (win Sarazin 1996).," However, the presence of an X-ray bowshock to the north of M49 argues that the galaxy is falling into Virgo's hot intracluster medium from the south (Irwin Sarazin 1996)."
 Ouly M86 aud M89 have sieuificaut line of sight motion with respect to the cluster center 1308 kimn/s aud =721 κής. respectively).," Only M86 and M89 have significant line of sight motion with respect to the cluster center $-1308$ km/s and $-724$ km/s, respectively)."
 M86 is either moving at high speed through the core. or just about to enter it. depending on the adopted. distance. while M89 either passed through the core ~ 1-2 Car ago (if it lacks significant transverse velocity) or Is on a niore tanecutial orbit that keeps it further from the core.," M86 is either moving at high speed through the core, or just about to enter it, depending on the adopted distance, while M89 either passed through the core $\sim$ 1-2 Gyr ago (if it lacks significant transverse velocity) or is on a more tangential orbit that keeps it further from the core."
 We first examine the enviromental question by, We first examine the environmental question by
where we have taken the timescale {ς [rom Equation 23. to be my7.27.05M.fMgion Gyr for fiducial temperature parameters ancl for joy«1.,"where we have taken the timescale $t_{\infty}$ from Equation \ref{growtime} to be $7.2 n_{ism,5}^{-3/2}f_v^4M_{BH,0,10}$ Gyr for fiducial temperature parameters and for $n_{ism,5} < 1$."
 For ο2 Gvr. the ensemble of about 10° black holes will produce ~107 erg |. as much luminosity as a modest Sevlert galaxy or a single black hole of about 10211. aaccreting near the Edcdington limit.," For $t \sim 2$ Gyr, the ensemble of about $10^6$ black holes will produce $\sim 10^{43}$ erg $^{-1}$, as much luminosity as a modest Seyfert galaxy or a single black hole of about $10^5$ accreting near the Eddington limit."
 For comparison. supernovae provide an input of about Loy~10” erg | in a galaxy like the Milky Wavy for which the star formation rate is about 1 to κο astar formation rate of 10 tinight give Lo~3x107 eres +.," For comparison, supernovae provide an input of about $L_{SN} \sim 10^{49}$ erg $^{-1}$ in a galaxy like the Milky Way for which the star formation rate is about 1 $^{-1}$, so a star formation rate of 10 $^{-1}$ might give $L_{SN} \sim
3\times10^{42}$ erg $^{-1}$."
 The black hole input at about 2Gy is comparable to. and might even sliehtly exceed (he input. power from supernovae.," The black hole input at about 2Gy is comparable to, and might even slightly exceed the input power from supernovae."
 Figure 4 gives the luminosity versus time for various values of the interstellar density and Figure 5 illustrates the sensitivity of the luminosity to the velocity parameter.fJ...," Figure 4 gives the luminosity versus time for various values of the interstellar density and Figure 5 illustrates the sensitivity of the luminosity to the velocity parameter,$f_v$."
 The total energy liberated by the number of black holes. Nay. accreting from 14+lau to fis We will again adopt (he approximation of a constant value of μμ to write Invoking we can wrlle. which becomes For lyμι<<1 ly. this reduces to," The total energy liberated by the number of black holes, $N_{BH}$, accreting from $t_o + t_{delay}$ to $t$ is We will again adopt the approximation of a constant value of $R_{BH}$ to write Invoking we can write, which becomes For $t_0 + t_{delay} << t << t_{\infty}$ this reduces to"
sliding window smoothing over 5 PI channels.,sliding window smoothing over 5 PI channels.
 The spectra so derived are still somewhat noisy. but not at a level which alters (he results presented here.," The spectra so derived are still somewhat noisy, but not at a level which alters the results presented here."
 A grid of models is generated across a range of temperatures aud redshifts using XSPEC. with a MEIXAL plasma. 1/3rd Solar abundances. <nf> is set to a high Galactic Intitude maximum of 1xI0?!em?. and (he results are robust to reasonable variations im these quantities.," A grid of models is generated across a range of temperatures and redshifts using XSPEC, with a MEKAL plasma, 1/3rd Solar abundances, $<nH>$ is set to a high Galactic latitude maximum of $1\times 10^{21}$ $^2$, and the results are robust to reasonable variations in these quantities."
 Az is set to 0.1 and 1 is actually set over à range from 0.1 to 12.9 keV in steps of 0.1 keV. although only temperatures of 0.2. 0.5. 1.0. 2.0. 4.0. and 6.0 keV are presented here.," $\Delta z$ is set to $0.1$ and $kT$ is actually set over a range from 0.1 to 12.9 keV in steps of $0.1$ keV, although only temperatures of 0.2, 0.5, 1.0, 2.0, 4.0, and 6.0 keV are presented here."
 The spectra are then lorward-lolded through the on-axis RAIF’s and ARFE's for the respective instruments., The spectra are then forward-folded through the on-axis RMF's and ARF's for the respective instruments.
 In the case of the Chandra. [ront-illuminated. CCD device CACIS-D. off-axis responses are also used in an effort to evaluate the effect. of radiation damage induced charge-transler inefficiencies (CTI) (see 82.2 &33).," In the case of the Chandra front-illuminated CCD device (ACIS-I), off-axis responses are also used in an effort to evaluate the effect of radiation damage induced charge-transfer inefficiencies (CTI) (see 2.2 3)."
 All Chandra responses used here assume Chat basic CTI corrections have beeen applied (o the data (e.g. (2000)))., All Chandra responses used here assume that basic CTI corrections have beeen applied to the data (e.g. \citet{tow00}) ).
 The corrections reduce (he position dependence (on the chips) of the gain and evade distributions (which distort the inferred photon energies). but an energy ancl position dependent degradation of spectral resolution remains.," The corrections reduce the position dependence (on the chips) of the gain and grade distributions (which distort the inferred photon energies), but an energy and position dependent degradation of spectral resolution remains."
 An unrestricted search is then made for the maximal signal-to-noise bv varving the lower GE) aid upper (£5) energy bands independently. as a function of z.," An unrestricted search is then made for the maximal signal-to-noise by varying the lower $E_1$ ) and upper $E_2$ ) energy bands independently, as a function of $z$."
 Figures 1.2.3. and 4 present (he optimal band search results for. respectively. the Chandra ACIS-I. ACIS-S. the XNMM-Newton MOS. and PN instruments.," Figures 1,2,3, and 4 present the optimal band search results for, respectively, the Chandra ACIS-I, ACIS-S, the XMM-Newton MOS, and PN instruments."
 some of the energv band limits show clear features as a function of redshift. however these all correspond. (o. small variations in actual signal-to-noise. as is reflected. by the smoothness of the 0.5-2 keV (o optimal ratio curves.," Some of the energy band limits show clear features as a function of redshift, however these all correspond to small variations in actual signal-to-noise, as is reflected by the smoothness of the 0.5-2 keV to optimal ratio curves."
 The features are due to the combination ol the shape of the instrumental response and features in the background and source spectra., The features are due to the combination of the shape of the instrumental response and features in the background and source spectra.
 For example. in Figure 2. the upper limit band pass curve for 1=6 keV (heaviest line) exhibits a sharp drop as the spectrum redshifts Irom z=0.6 to 0.7.," For example, in Figure 2, the upper limit band pass curve for $kT=6$ keV (heaviest line) exhibits a sharp drop as the spectrum redshifts from $z=0.6$ to 0.7."
 This is entirely due to the location of a flourescent Si Ix-o. line (at ~1.7 keV) in the background. from reflection in the Chandra mirror assembly.," This is entirely due to the location of a flourescent Si $\alpha$ line (at $\sim 1.7$ keV) in the background, from reflection in the Chandra mirror assembly."
 As the redshift of the source increases a critical point is reached where the optimal band edge crosses this backeround line. and (he optimum jumps to a lower enerey.," As the redshift of the source increases a critical point is reached where the optimal band edge crosses this background line, and the optimum jumps to a lower energy."
 The Κον results may be summarized as follows., The key results may be summarized as follows.
 For all instruments. plasmas with AT<2 keV have optimal bands which differ significantly [rom the 0.5-2 keV bandpass.," For all instruments, plasmas with $kT<2$ keV have optimal bands which differ significantly from the 0.5-2 keV bandpass."
" For the coolest plasma considered here (0.2 keV. 2.3x10"" IN) at z=0.1 the 0.5-2 keV band sulfers a"," For the coolest plasma considered here $0.2$ keV, $2.3\times 10^6$ K) at $z=0.1$ the 0.5-2 keV band suffers a"
" For the coolest plasma considered here (0.2 keV. 2.3x10"" IN) at z=0.1 the 0.5-2 keV band sulfers a."," For the coolest plasma considered here $0.2$ keV, $2.3\times 10^6$ K) at $z=0.1$ the 0.5-2 keV band suffers a"
blown away.,blown away.
 The normalization changes slightly. by losing a factor of f /z.if rj is redetined as the Bondi accretion radius (as in WEN) for gas at the galaxy virial temperature.," The normalization changes slightly, by losing a factor of $f/\pi,$ if $r_1$ is redefined as the Bondi accretion radius (as in WFN) for gas at the galaxy virial temperature."
 It compares well with the results of Ferrarese Merritt (2000) and Gebhardt et al (2000) for reasonable values of f... £j and fo: The above result demonstrates that a wind is not essential for expelling the gas surrounding a growing black hole.," It compares well with the results of Ferrarese Merritt (2000) and Gebhardt et al (2000) for reasonable values of $f,$ $f_1$ and $f_2$: The above result demonstrates that a wind is not essential for expelling the gas surrounding a growing black hole."
 In the present model it appears more as if the galaxy potential determines the black hole mass. rather than the other way round.," In the present model it appears more as if the galaxy potential determines the black hole mass, rather than the other way round."
 Note however that the gravitational binding energy of a galactic bulge. where the velocity dispersion of the bulge is 300e300kms.ft. is Lug22010PegMyadsec.," Note however that the gravitational binding energy of a galactic bulge, where the velocity dispersion of the bulge is $300 v_{300}\kmps,$ is $E_{\rm bulge}\approx 2\times 10^{-6}v_{300}^2 M_{\rm bulge} c^2$."
 The energy from the central black hole Lyon&510ο“.," The energy from the central black hole $E_{\rm AGN}\approx 5\times
10^{-4}M_{\rm bulge} c^2$."
 So only one per cent of that energy can have a major effect on the formation of that bulge and that effect may have occurred when both the black hole and galaxy were young., So only one per cent of that energy can have a major effect on the formation of that bulge and that effect may have occurred when both the black hole and galaxy were young.
 For the above model with the free parameters set to the values given in section 3 of ΕΝ. we present in Figs.," For the above model with the free parameters set to the values given in section 3 of WFN, we present in Figs."
 1-4 results on the yield of Compton-thick quasars in deep exposures with Chandra and XMM., 1–4 results on the yield of Compton-thick quasars in deep exposures with Chandra and XMM.
 Firstly. Fig.," Firstly, Fig."
 | shows as a function of redshift the total areal density of Compton-thick AGN in the model with intrinsic luminosities in excess of L0t+., 1 shows as a function of redshift the total areal density of Compton-thick AGN in the model with intrinsic luminosities in excess of $10^{44}$.
 As discussed by WEN. however. such sources are obscured by Ny~12 when the obscured phase begins (where Mvp=1.5107! 7. the column density above which a source becomes Compton-thick). and by Ny3p at its end.," As discussed by WFN, however, such sources are obscured by $N_{\rm H} \sim 15 N_{\rm{T}}$ when the obscured phase begins (where $N_{\rm T}=1.5 \times 10^{24}$ , the column density above which a source becomes Compton-thick), and by $N_{\rm H} \sim 3 N_{\rm{T}}$ at its end."
 Since there is no scattered flux included in the model spectra and the direct emission is almost completely suppressed for NycLOA tespecially below keV). the vast majority of the sources contributing to Fig.," Since there is no scattered flux included in the model spectra and the direct emission is almost completely suppressed for $N_{\rm H} > 10N_{\rm T}$ (especially below ), the vast majority of the sources contributing to Fig."
 | will not be visible to Chandra or XMM., 1 will not be visible to Chandra or XMM.
 This is borne out by Figs., This is borne out by Figs.
" 2. 3 and 4. described below. which were produced by convolving the object spectra in the observed frame with ""response functions? giving the effective area of the telescope and detector combination under consideration."," 2, 3 and 4, described below, which were produced by convolving the object spectra in the observed frame with `response functions' giving the effective area of the telescope and detector combination under consideration."
 In Fig., In Fig.
 2 we show the areal density as a function of redshift of both the Compton-thick and Compton-thin AGN (the latter also includes the unobscured quasars). which would produce more than 30 counts in the band in a exposure with XMM on the EPIC pn chip.," 2 we show the areal density as a function of redshift of both the Compton-thick and Compton-thin AGN (the latter also includes the unobscured quasars), which would produce more than 30 counts in the band in a exposure with XMM on the EPIC pn chip."
 This is repeated in Fig., This is repeated in Fig.
 3 for a 100 ks exposure., 3 for a 100 ks exposure.
 Fig., Fig.
 4 shows the analogous plot for the band with the Chandra ACIS $3 chip. with the count hreshold reduced to 10 counts owing to the smaller PSF (and hus lower internal background) compared to XMM.," 4 shows the analogous plot for the band with the Chandra ACIS S3 chip, with the count threshold reduced to 10 counts owing to the smaller PSF (and thus lower internal background) compared to XMM."
 The majority of the detected objects contributing to the yields are quite close o the count thresholds., The majority of the detected objects contributing to the yields are quite close to the count thresholds.
 For example. if the XMM threshold is increased to 40 counts. the yield of Compton-thick (Compton-hin plus unobscured) AGN falls over all redshift by a factor 2—3 (1.5—2).," For example, if the XMM threshold is increased to 40 counts, the yield of Compton-thick (Compton-thin plus unobscured) AGN falls over all redshift by a factor 2–3 (1.5–2)."
 Similarly. increasing the Chandra detection threshold to 15 counts. results in a fall by a factor of 2.5 in the yield of Compton- objects. whilst the number of Compton-thin and unobscured objects are relatively unchanged.," Similarly, increasing the Chandra detection threshold to 15 counts, results in a fall by a factor of 2.5 in the yield of Compton-thick objects, whilst the number of Compton-thin and unobscured objects are relatively unchanged."
 Most of the predicted Compton-thick sources should become detectable in exposures of IMs (Fig., Most of the predicted Compton-thick sources should become detectable in exposures of 1Ms (Fig.
 5). such as are now being done with Chandra (e.g. Alexander et al 2001: Rosati et al 2001).," 5), such as are now being done with Chandra (e.g. Alexander et al 2001; Rosati et al 2001)."
 In an S4.S.L aremin? region and | Ms exposure we predict [82 sources (Compton thick and thin) in the 2-8 keV band whereas Alexander et al (2001) find 102., In an $8.4\times 8.4$ $^2$ region and 1 Ms exposure we predict 182 sources (Compton thick and thin) in the 2–8 keV band whereas Alexander et al (2001) find 102.
 We do not consider that this discrepancy in numbers is serious. since most of the sources would be close to the detection threshold.," We do not consider that this discrepancy in numbers is serious, since most of the sources would be close to the detection threshold."
 That many of the sources are seen in both soft and hard energy bands (Alexander et al 2001) is also not a major problem since a few per cent of the primary soft radiation may be scattered into our line of sight., That many of the sources are seen in both soft and hard energy bands (Alexander et al 2001) is also not a major problem since a few per cent of the primary soft radiation may be scattered into our line of sight.
 The important issue of the redshift distribution of the sources is considered in the next Section., The important issue of the redshift distribution of the sources is considered in the next Section.
 where we also discuss the implications of these resultsfor the interpretation of deep Chandra and XMM surveys., where we also discuss the implications of these resultsfor the interpretation of deep Chandra and XMM surveys.
? introduced the concept of completeness to study the selection ellects introduced by observatory architectures on clirect searches for sub-stellar Companions.,\citet{brown2004a} introduced the concept of completeness to study the selection effects introduced by observatory architectures on direct searches for sub-stellar companions.
 Assuming distributions for semi-major axis aud eccentricity of planetary orbits. Brown calculated the probability that a companion would fall outside the telescope's central obscuration during au observation of a star.," Assuming distributions for semi-major axis and eccentricity of planetary orbits, Brown calculated the probability that a companion would fall outside the telescope's central obscuration during an observation of a star."
 2? subsequently expauded this concept to include the selection ellects due to the photometric restrictions ou observability introduced. by telescope optics. and ? demonstrated how completeness could be evaluated for indirect Companion detection methods such as astrometry.," \citet{brown2005} subsequently expanded this concept to include the selection effects due to the photometric restrictions on observability introduced by telescope optics, and \citet{brown2009} demonstrated how completeness could be evaluated for indirect companion detection methods such as astrometry."
 Completeness has also, Completeness has also
is expected to start ~3 4 Myr alter the birth of a star cluster (Leitherer et al.,is expected to start $\sim$ 3 – 4 Myr after the birth of a star cluster (Leitherer et al.
 1999). the ages we have determined for the SSC £6 Myr) are consistent wilh such a supposition.," 1999), the ages we have determined for the SSC $\lsim 6$ Myr) are consistent with such a supposition."
 Given their measured radial velocities and estimated ages. the clusters must have formed within a few kpe of their current locations. unless their tangential velocities are considerably larger (han their radial velocities.," Given their measured radial velocities and estimated ages, the clusters must have formed within a few kpc of their current locations, unless their tangential velocities are considerably larger than their radial velocities."
 This latter feature rules out the idea (hat the clusters ormed at much larger radii in (he outer halo of the merging svstem. then fell into the nuclear regions:clusters.," This latter feature rules out the idea that the clusters formed at much larger radii in the outer halo of the merging system, then fell into the nuclear regions;."
 The alternative explanation. (hat we have caught the σος in the ejection phase. and that (he line splitting is caused by the ejection of gas by SSC [formed in the quiescent. diffuse gas (??7) is dillicult to reconcile with the observations.," The alternative explanation, that we have caught the SSC in the ejection phase, and that the line splitting is caused by the ejection of gas by SSC formed in the quiescent, diffuse gas \citep{Goodwin97a,Goodwin97b,Bastian06} is difficult to reconcile with the observations."
 Bi particular. in such a case it is not clear why (he component apparently at rest relative to the ambient gas has relatively broad lines and a [NII]6548/1Lo. ratio consistent with shocks or AGN photoionization. whereas the component shifted relative to the rest. [rane (presumably. the ejected component in (his scenario) has narrow lines and an HII region-like Πα. ratio characteristic of stellar photoionization: one would expect (he reverse {ο be (he case.," In particular, in such a case it is not clear why the component apparently at rest relative to the ambient gas has relatively broad lines and a $\alpha$ ratio consistent with shocks or AGN photoionization, whereas the component shifted relative to the rest frame (presumably the ejected component in this scenario) has narrow lines and an HII region-like $\alpha$ ratio characteristic of stellar photoionization; one would expect the reverse to be the case."
" Finally we note (hat. despite the apparently ""Iree-floating status indicated by (heir enussion line kinematics. (he SSC'/IILI regions are linked with a more extensive interstellar medium (ISAT) in (he host galaxies."," Finally we note that, despite the apparently “free-floating” status indicated by their emission line kinematics, the SSC/HII regions are linked with a more extensive interstellar medium (ISM) in the host galaxies."
 First. there is clear morphological evidence from our hieh resolution ACS images that the vong star clusters are associated with dust lanes in the host galaxy (see Figure 1).," First, there is clear morphological evidence from our high resolution ACS images that the young star clusters are associated with dust lanes in the host galaxy (see Figure 1)."
 Second. at the location of C1/€2. the grevscale representation of the long-slit spectrum (see Figure 11) shows a clear enhancement in (he fIux of the broad and narrow components. suggesting a link between (he HII regions and the more diffuse gas.," Second, at the location of C1/C2, the greyscale representation of the long-slit spectrum (see Figure 11) shows a clear enhancement in the flux of the broad and narrow components, suggesting a link between the HII regions and the more diffuse gas."
 It is interesting to compare our results for PNS1345—12 with previous studies of YSP in ULIRGs., It is interesting to compare our results for PKS1345+12 with previous studies of YSP in ULIRGs.
" ? carried out an IST imaging study concentrating on bright star forming, knots for a sample of nine ""warm ULIBGs. including PINS13454+12. using hieh resolution D- and I-band images taken with the Wide Field Planetary Camera on the IST."," \cite{Surace98} carried out an HST imaging study concentrating on bright star forming knots for a sample of nine “warm” ULIRGs, including PKS1345+12, using high resolution B- and I-band images taken with the Wide Field Planetary Camera on the HST."
 The stellar svnthesis models of ? were used (ο estimate the ages ancl masses of the bright knots in, The stellar synthesis models of \cite{Bruzual93} were used to estimate the ages and masses of the bright knots in
position of the high energv 5 rav peak.,position of the high energy $\gamma$ –ray peak.
 However. from. the decontamination we performed. the spectrum appears consistently to extend. to the higher detected: intrinsic energies. Le. 280 keV in the blazar rest. frame.," However, from the decontamination we performed, the spectrum appears consistently to extend to the higher detected intrinsic energies, i.e. 280 keV in the blazar rest frame."
 At the lowest energies. «1 keV. the BeppoSAX observations robustly confirmed the presence of a fattening in the spectrum found in the ROSAT PSPC spectrum (Boller et al.," At the lowest energies, $< 1$ keV, the $Beppo$ SAX observations robustly confirmed the presence of a flattening in the spectrum found in the ROSAT PSPC spectrum (Boller et al."
 2000)., 2000).
 Secondly. below 0.4 keV emission a factor  20 in excess of the [attened spectrum has been found (see Fig.," Secondly, below 0.4 keV emission a factor $\sim$ 20 in excess of the flattened spectrum has been found (see Fig."
 1)., 1).
 The origin of the Πα{οπής has been discussed in some detail by several authors (CapX οἱ al 1997. Fiore et al 1998. Elvis et al 1998. Boller οἱ al 2000. Yuan ct al 2000. Fabian et al 2000. Reeves Turner 2000). but no «elinite conclusion could. be crawn.," The origin of the flattening has been discussed in some detail by several authors (Cappi et al 1997, Fiore et al 1998, Elvis et al 1998, Boller et al 2000, Yuan et al 2000, Fabian et al 2000, Reeves Turner 2000), but no definite conclusion could be drawn."
 Certainly. the detection of such feature by dilleren instruments (ROSAT. ASCA. DeppoS AN) argues. agains any svstematic mis-calibration ellect.," Certainly, the detection of such feature by different instruments (ROSAT, ASCA, $Beppo$ SAX) argues against any systematic mis-calibration effect."
 The first interesting point which has been mace is tha the [lattening scems to be associated only with radiolou objects. therefore suggesting its origin to be intrinsic.," The first interesting point which has been made is that the flattening seems to be associated only with radio–loud objects, therefore suggesting its origin to be intrinsic."
 The number of good quality X-ray spectra of radio.quiet quasars ab zoc1.5 ds unfortunately limitec., The number of good quality X-ray spectra of radio–quiet quasars at $z> 1.5$ is unfortunately limited.
" However. the recen results by Vignali et al (2000). combined with the findings w Reeves ""Turner (2000). imply that in only 2 out of 15 radioquiet quasars (in the range 2=LS2.5) a positive detection of Dlattening corresponding to Ny1077 em ws been established. despite the biased selection of XNrav oud sources."," However, the recent results by Vignali et al (2000), combined with the findings by Reeves Turner (2000), imply that in only 2 out of 15 radio–quiet quasars (in the range $z=1.8-2.5$ ) a positive detection of flattening corresponding to $N_H \sim 10^{22}$ $^{-2}$ has been established, despite the biased selection of X–ray loud sources."
 For comparison. 5 out of 6 radioloud objects in the same redshift range have equivalent Nyz1077E em2 (sce Fig.," For comparison, 5 out of 6 radio–loud objects in the same redshift range have equivalent $N_H \ge 10^{22}$ $^{-2}$ (see Fig."
 6)., 6).
 We therefore favour the possibility that the lattening is due το an intrinsic property of the source. »ossiblv associated with the radioloudness. phenomenon.," We therefore favour the possibility that the flattening is due to an intrinsic property of the source, possibly associated with the radio–loudness phenomenon."
 evertheless we note that radio-Ioud objects tend to be more Xrav luminous and so vield the best spectra at a given redshift ancl therefore in the following we also discuss the »xossible role of absorption of intergalactic origin., Nevertheless we note that radio-loud objects tend to be more X–ray luminous and so yield the best spectra at a given redshift and therefore in the following we also discuss the possible role of absorption of intergalactic origin.
 We consider it unlikely that large (galactic) scale gas is responsible for the Nray absorption. given the large masses of gas implied by such hypothesis as well as the lack of any clear connection with the radioloud phenomenon.," We consider it unlikely that large (galactic) scale gas is responsible for the X–ray absorption, given the large masses of gas implied by such hypothesis as well as the lack of any clear connection with the radio–loud phenomenon."
 Vherefore in the followingὃν we concentrate on the nuclear and/or Cosmological properties which could account for such eature., Therefore in the following we concentrate on the nuclear and/or cosmological properties which could account for such feature.
 A further Κον piece of information is the presence of a systematic trend. of the Hattening in the spectra of radiooucl quasars to increase with redshift. (Cappi et al 1997. Fiore et al.," A further key piece of information is the presence of a systematic trend of the flattening in the spectra of radio--loud quasars to increase with redshift (Cappi et al 1997, Fiore et al."
 1998. Reeves Turner 2000).," 1998, Reeves Turner 2000)."
 The inclusion. of the recent. results on UNJI028.6-0844. (Yuan et al 2000). PAINO525-3343 (Fabian et al 2000) and €DI428|4217 itself strengthens and extends his behavior up to zc4.7. as shown in Fig.," The inclusion of the recent results on RXJ1028.6-0844 (Yuan et al 2000), PMN0525-3343 (Fabian et al 2000) and GB1428+4217 itself strengthens and extends this behavior up to $z\ge 4.7$, as shown in Fig."
 6., 6.
 Although no correlation. between the flattening and other spectral woperty has been previously found. we stress the possible oesence of a significant trend of increasing Ny with increasing hard X.rav (intrinsic 210 keV band) luminosity. as can be argued [rom Fig.," Although no correlation between the flattening and other spectral property has been previously found, we stress the possible presence of a significant trend of increasing $N_{\rm H}$ with increasing hard X–ray (intrinsic 2–10 keV band) luminosity, as can be argued from Fig."
 7., 7.
 Unfortunately small statistics do not allow us to cisentangle the redshift and. luminosity. dependences., Unfortunately small statistics do not allow us to disentangle the redshift and luminosity dependences.
 1n Fig., In Fig.
 6 we also show the line-of-sight value of Ny due to the intergalactic medium (IGM). assumine solar abundances., 6 we also show the line-of-sight value of $N_{\rm H}$ due to the intergalactic medium (IGM) assuming solar abundances.
 I£ the IGM was enriched by redshifts of abou 4 to the same metallicity as clusters of galaxies then the correlation with redshift could be explained., If the IGM was enriched by redshifts of about 4 to the same metallicity as clusters of galaxies then the correlation with redshift could be explained.
 As cliscussec in the ROSAT PSPC work on GB 1428|4217 Boller et a 2000) this conclusion does not agree with observations of the metallicity of the Lyman à forest., As discussed in the ROSAT PSPC work on GB 1428+4217 (Boller et al 2000) this conclusion does not agree with observations of the metallicity of the Lyman $\alpha$ forest.
 Only if there was a strong correlation between enrichment and temperature of the IGM phase might some agreement occur. but even then the enrichment requirements would be huge.," Only if there was a strong correlation between enrichment and temperature of the IGM phase might some agreement occur, but even then the enrichment requirements would be huge."
 A more. plausible interpretation of the apparen correlation shown in Fig., A more plausible interpretation of the apparent correlation shown in Fig.
 6 would then be that it arises from, 6 would then be that it arises from
of the core mass.,of the core mass.
" Note that equations (la-b) of being written as proportionalities. they are valid when fig9«fuos. and not just when toro,fas."," Note that equations (1a-b) of being written as proportionalities, they are valid when $\tau_{GExp} \propto \tau_{cross}$, and not just when $\tau_{GExp} \simeq \tau_{cross}$."
 The energy-driven feedback model. however. shows that gas can be expelled on time-scales shorter or longer than a erossing-time (see Fig. 7).," The energy-driven feedback model, however, shows that gas can be expelled on time-scales shorter or longer than a crossing-time (see Fig. \ref{fig:fb0p03}) )."
" One may be puzzled by a gas expulsion time-scale Tog longer than a core erossing-time 7,4, since it implies a gas velocity slower than the core escape velocity VW.", One may be puzzled by a gas expulsion time-scale $\tau_{GExp}$ longer than a core crossing-time $\tau_{cross}$ since it implies a gas velocity slower than the core escape velocity $V_e$.
 Yet. this is not necessarily surprising.," Yet, this is not necessarily surprising."
 The escape velocity is defined for objects subjected solely to gravity. while the shell of gas. in addition to being subjected to its own self-gravity. keeps being powered and pushed outwards by continuing stellar winds. ionized region over-pressure. etc.," The escape velocity is defined for objects subjected solely to gravity, while the shell of gas, in addition to being subjected to its own self-gravity, keeps being powered and pushed outwards by continuing stellar winds, ionized region over-pressure, etc."
 In other words. a shell velocity slower than the core escape velocity may not necessarily preclude the gas from being unbound from its parent core.," In other words, a shell velocity slower than the core escape velocity may not necessarily preclude the gas from being unbound from its parent core."
 Within the paradigm that most stars form in gas-embedded clusters. cluster infant weight-loss and infant mortality appear as significant drivers of galaxy field star populations2008).," Within the paradigm that most stars form in gas-embedded clusters, cluster infant weight-loss and infant mortality appear as significant drivers of galaxy field star populations."
". Consequently. reconstructing the star formation history of galaxies from their cluster age distribution requires a firm grasp on the time-evolution of the integrated bound Taction μι. that is. the bound fraction 75,4 of stars integrated over the core mass function at a given age2009)."," Consequently, reconstructing the star formation history of galaxies from their cluster age distribution requires a firm grasp on the time-evolution of the integrated bound fraction $\overline{F_{bound}}$, that is, the bound fraction $F_{bound}$ of stars integrated over the core mass function at a given age."
. As we now illustrate. this also requires a fair knowledge of he core mass-radius relation.," As we now illustrate, this also requires a fair knowledge of the core mass-radius relation."
 Building on the compact models of Fig., Building on the compact models of Fig.
" 3 (e. Doge=Skpe and Dog= 4&pey. Table 2 illustrates how75,,,5,/! varies with he slope 9 of the core mass-radius relation. and with the upper imit 7n, and slope PB of a power-law core mass function dNxmPum,"," \ref{fig:fb} (i.e. $D_{gal}=8\,kpc$ and $D_{gal}=4\,kpc$ ), Table \ref{tbl:gal} illustrates how$\overline{F_{bound}}$ varies with the slope $\delta$ of the core mass-radius relation, and with the upper limit $m_{up}$ and slope $-\beta$ of a power-law core mass function $dN \propto m^{-\beta} dm$."
" We consider two upper limits to the core mass range to illustrate the sensitivity of 5,,,/ to this parameter.", We consider two upper limits to the core mass range to illustrate the sensitivity of $\overline{F_{bound}}$ to this parameter.
" In he left part of Table 2.. 14)=3x107AL, is the upper limit to he mass range of the data shown in Fig. |.."," In the left part of Table \ref{tbl:gal}, $m_{up}=3 \times 10^4\,M_{\sun}$ is the upper limit to the mass range of the data shown in Fig. \ref{fig:obs},"
 and from which we obtain the normalizations of our core mass-radius relations., and from which we obtain the normalizations of our core mass-radius relations.
" In the right part. we adopt 7,5=107M..."," In the right part, we adopt $m_{up}=10^7\,M_{\sun}$."
 While most reported young cluster mass functions have B.~2 (see references in Section 4.1). he mass function of molecular cores is shallower with B1.71998)..," While most reported young cluster mass functions have $\beta \simeq 2$ (see references in Section \ref{subsec:mf}) ), the mass function of molecular cores is shallower with $\beta \simeq 1.7$."
 Given that uncertainty. Table 2 considers both cases p," Given that uncertainty, Table \ref{tbl:gal} considers both cases ."
rep).. When D<2. ligher-mass cores contribute a greater fraction of the total gas mass than their low-mass counterparts.," When $\beta < 2$, higher-mass cores contribute a greater fraction of the total gas mass than their low-mass counterparts."
" For instance. B=1.7 leads Oo cores more massive than 109A... to contribute ~50 For Peore models. F5, 1s independent of the core mass ‘unction parameters B and nn, since clusters experience mass-independent infant weigth-loss."," For instance, $\beta =1.7$ leads to cores more massive than $10^6\,M_{\sun}$ to contribute $\simeq 50$ For $\rho_{core}$ models, $\overline{F_{bound}}$ is independent of the core mass function parameters $\beta$ and $m_{up}$ since clusters experience mass-independent infant weigth-loss."
" As quoted earlier. the compact roore and βίος models do not lead to significantly different FrewUMeore) relations. which arealso similar for both D,=8kpe and (Fig. 39."," As quoted earlier, the compact $r_{core}$ and $\rho_{core}$ models do not lead to significantly different $F_{bound}(m_{core})$ relations, which arealso similar for both $D_{gal}=8kpc$ and $D_{gal}=4kpc$ (Fig. \ref{fig:fb}) )."
" This is a direct consequence of having rjr,0.05 (no or weak tidal field impact) over the whole core mass range 102- 107 M... for the rare and Peore models when D,z:A&pe (Fig. 4).", This is a direct consequence of having $r_h/r_t \lesssim 0.05$ (no or weak tidal field impact) over the whole core mass range $10^2$ $10^7$ $M_{\sun}$ for the $r_{core}$ and $\rho_{core}$ models when $D_{gal} \geq 4kpc$ (Fig. \ref{fig:crr}) ).
 As u result. the integrated bound fraction is ο0.3 for rio and po; models at Dog= 4-8 kkpe. irrespective of 6 and mu.," As a result, the integrated bound fraction is $\overline{F_{bound}} \simeq 0.3$ for $r_{core}$ and $\rho_{core}$ models at $D_{gal}=4$ $8$ kpc, irrespective of $\delta$ and $m_{up}$."
" In contrast. to raise 7/7, from LOTSM... to 10M... reduces Fround tor Leore models since in that case higher-mass embedded clusters are more efficiently destroyed than. their low-mass counterparts."," In contrast, to raise $m_{up}$ from $10^{4.5}\,M_{\sun}$ to $10^7\,M_{\sun}$ reduces $\overline{F_{bound}}$ for $\Sigma _{core}$ models since in that case higher-mass embedded clusters are more efficiently destroyed than their low-mass counterparts."
" Besides. this sensitivity of the integrated bound fraction 75,4 to the core mass upper limit is strengthened for shallow power-law core mass functions (B=1.7) and/or in case of stronger tidal field (e.g. D,=J&pe instead of Dy;=δκρο)."," Besides, this sensitivity of the integrated bound fraction $\overline{F_{bound}}$ to the core mass upper limit is strengthened for shallow power-law core mass functions $\beta=1.7$ ) and/or in case of stronger tidal field (e.g. $D_{gal} = 4kpc$ instead of $D_{gal} = 8kpc$ )."
 Independently of the tidal field impact. we note that the cluster-forming core mass-radius relation is also relevant to the two topics discussed in the next sections.," Independently of the tidal field impact, we note that the cluster-forming core mass-radius relation is also relevant to the two topics discussed in the next sections."
 The mass-radius relation of cluster-forming cores also determines their mean density and crossing-time Type. thus how fast clusters experience infant weight-loss following gas-expulsion: the shorter the core crossing-time. the faster cluster evolution through violent relaxation.," The mass-radius relation of cluster-forming cores also determines their mean density and crossing-time $\tau_{cross}$, thus how fast clusters experience infant weight-loss following gas-expulsion: the shorter the core crossing-time, the faster cluster evolution through violent relaxation."
 If cluster-forming cores have a constant surface density. more massive clusters evolve more slowly than their low-mass counterparts owing to their lower volume density. hence longer crossing-time.," If cluster-forming cores have a constant surface density, more massive clusters evolve more slowly than their low-mass counterparts owing to their lower volume density, hence longer crossing-time."
 In contrast. if cluster-forming cores have a constant radius. more massive clusters have a higher density. thus shorter crossing-time and the duration of their violent relaxation (in units of Myr) is shorter (see fig.," In contrast, if cluster-forming cores have a constant radius, more massive clusters have a higher density, thus shorter crossing-time and the duration of their violent relaxation (in units of Myr) is shorter (see fig."
 | in for an application to the time-evolution of the cluster mass function)., 1 in for an application to the time-evolution of the cluster mass function).
 Constant volume density cores are all characterised by the same crossing-time and. thus. evolve at the same rate through violent relaxation regardless of their mass.," Constant volume density cores are all characterised by the same crossing-time and, thus, evolve at the same rate through violent relaxation regardless of their mass."
" If the mean number density of cluster-forming cores is nj,77IQemI. unsO.35Mvr and all cluster stars due to become unbound owing to gas expulsion have erossed the tidal radius boundary by a cluster age of at most LOOTposs or MMyr."," If the mean number density of cluster-forming cores is $n_{H_2}\simeq10^4\,cm^{-3}$, $\tau_{cross}\simeq 0.45Myr$ and all cluster stars due to become unbound owing to gas expulsion have crossed the tidal radius boundary by a cluster age of at most $100 \tau_{cross}$ or Myr."
" If the core mean number density is 10 times higher. 7j,IQem.ὃς then Toss7O15Mvr. implying that violent relaxation is over by an age of ~I5 MMyr."," If the core mean number density is 10 times higher, $n_{H_2}\simeq10^5\,cm^{-3}$, then $\tau_{cross}\simeq 0.15Myr$, implying that violent relaxation is over by an age of $\simeq 15$ Myr."
" The core mass-radius relation is also relevant to self-enrichment models of old globular clusters. in which the cluster-forming core is often referred to as a ""protoglobular cloud’."," The core mass-radius relation is also relevant to self-enrichment models of old globular clusters, in which the cluster-forming core is often referred to as a `protoglobular cloud'."
 Blue populations of globular clusters in elliptical galaxies show a blue-tilt. i.e. brighter clusters are redder than their fainter counterparts.," Blue populations of globular clusters in elliptical galaxies show a `blue-tilt', i.e. brighter clusters are redder than their fainter counterparts."
 This colour-magnitude relation is often interpreted as the imprint of the higher efficiency of more massive clusters to retain type II supernova ejecta and to achieve greater metallicity., This colour-magnitude relation is often interpreted as the imprint of the higher efficiency of more massive clusters to retain type II supernova ejecta and to achieve greater metallicity.
 It must be borne in mind. however. that such a conclusion sensitively depends on the slope of the core mass-radius relation.," It must be borne in mind, however, that such a conclusion sensitively depends on the slope of the core mass-radius relation."
 While infer a positive slope for their predicted mass-metallicity relation. predict that massive clusters are more metal-rich.," While infer a positive slope for their predicted mass-metallicity relation, predict that massive clusters are more metal-rich."
 This discrepancy arises because of different assumed core mass-radius relations., This discrepancy arises because of different assumed core mass-radius relations.
 build on either constant protoglobular eloud radii or constant protoglobular cloud volume densities., build on either constant protoglobular cloud radii or constant protoglobular cloud volume densities.
" On the other hand. the model of (20013... applied to the Galactic Old Halo globular cluster system and developed before the ""blue-tilt in ellipticals was discovered. builds on pressure-bounded isothermal spheres for which ateare99 Feare."," On the other hand, the model of , applied to the Galactic Old Halo globular cluster system and developed before the `blue-tilt' in ellipticals was discovered, builds on pressure-bounded isothermal spheres for which $m_{core}\propto r_{core}$ ."
 Their conclusion that less massive clusters are more metal-rich arises because type IT supernova ejecta mix with a lower amount of primordial gas., Their conclusion that less massive clusters are more metal-rich arises because type II supernova ejecta mix with a lower amount of primordial gas.
 Contrasting the models of and therefore illustrates that the slope of the globular cluster mass-metallicity, Contrasting the models of and therefore illustrates that the slope of the globular cluster mass-metallicity
interacting particles are non-degenerate (1.e.. dilute) and non-relativistic (1e.. their rest mass energy is large compared to KT).,"interacting particles are non-degenerate (i.e., dilute) and non-relativistic (i.e., their rest mass energy is large compared to $kT$ )."
 Hence. one can use a Maxwell-Boltzmann velocity distribution with Newtonian kinetic energy because where the exponential factor involving the rest mass energy drops out with a proper normalization of the distribution function.," Hence, one can use a Maxwell-Boltzmann velocity distribution with Newtonian kinetic energy because where the exponential factor involving the rest mass energy drops out with a proper normalization of the distribution function."
 Also note that when both particles 1 and 2 obey Maxwell-Boltzmann statistics. so does their relative velocity (Clayton1968).," Also note that when both particles $1$ and $2$ obey Maxwell-Boltzmann statistics, so does their relative velocity \citep{cla68}."
. Hence. the thermally averaged capture rate per particle pair is given by where µ denotes the reduced mass for the particles 1 and 2.," Hence, the thermally averaged capture rate per particle pair is given by where $\mu$ denotes the reduced mass for the particles $1$ and $2$."
 In the photodisintegration reaction rate. however. the relative velocity of the photon with respect to the target nucleus is always the speed of light c.," In the photodisintegration reaction rate, however, the relative velocity of the photon with respect to the target nucleus is always the speed of light $c$."
 This eliminates any dependence of the reaction rate on the velocity distribution of the target nucler (Thielemannetal.1998)., This eliminates any dependence of the reaction rate on the velocity distribution of the target nuclei \citep{thi98}.
. Therefore. the photonuclear reaction rate (0cj-3 becomes an integral of the reaction eross section over a Planck energy distribution for the photons: Using the fact that for a Planck distribution we can equivalently write Eq. (7))," Therefore, the photonuclear reaction rate $\langle\sigma c\rangle_{\gamma3}$ becomes an integral of the reaction cross section over a Planck energy distribution for the photons: Using the fact that for a Planck distribution we can equivalently write Eq. \ref{eq:Inverse Reaction Rate}) )"
 in more familiar form where ¢(3)=1.20206 isthe Riemann zeta function and E. denotes the photon energy., in more familiar form where $\zeta(3) = 1.20206$ isthe Riemann zeta function and $E_{\gamma}$ denotes the photon energy.
 The integration threshold is the Q- value of the capture reaction (seeFigure 1)) or zero in the case of negative Q., The integration threshold is the $Q$ -value of the capture reaction (seeFigure \ref{fig:Energy Figure}) ) or zero in the case of negative $Q$.
 It is difficult to determine the cross section 7-3 directly from experiment., It is difficult to determine the cross section $\sigma_{\gamma3}$ directly from experiment.
 However. the interaction between photons and matter is very weak (e/hc<1) so that the reaction can be treated with first order perturbation theory.," However, the interaction between photons and matter is very weak $(e^{2}/\hbar c\ll1)$ so that the reaction can be treated with first order perturbation theory."
 In this case. the transition probabilities become proportional to the matrix elements of the perturbing Hamiltonian and the hermiticity of the perturbing Hamiltonian gives rise to a simple relation between the capture and disintegration cross sections.," In this case, the transition probabilities become proportional to the matrix elements of the perturbing Hamiltonian and the hermiticity of the perturbing Hamiltonian gives rise to a simple relation between the capture and disintegration cross sections."
 This is known as the (Blatt&Weisskopf 199])., This is known as the \citep{bla91}.
. Fora reaction involving a ground-state to ground-state transition for two nuclei with energy £. leading to a gamma ray with energy E.=EQ this is given by where sg;=2j;1 are the spin degeneracy factors for the ground state of the nuclei and the Kronecker delta function accounts for the special case of indistinguishable interacting nuclei.," For a reaction involving a ground-state to ground-state transition for two nuclei with energy $E$, leading to a gamma ray with energy $E_{\gamma}=E+Q$ this is given by where $g_{i} = 2 j_i + 1 $ are the spin degeneracy factors for the ground state of the nuclei and the Kronecker delta function accounts for the special case of indistinguishable interacting nuclei."
 Using this detailed balance equation.the photodisintegration rate for a single-state transition can be related to the forward capture rate.," Using this detailed balance equation,the photodisintegration rate for a single-state transition can be related to the forward capture rate."
 Substituting Eq. (10)), Substituting Eq. \ref{eq:Detailed Balance}) )
 into Eq. (7)), into Eq. \ref{eq:Inverse Reaction Rate}) )
 and also changing the variable from E. to E=E.—Q in the integration. one can average over the velocity distribution of the ground-state interacting nuclei (σον as follows: At this point. one usually introduces the approximation: Here. we point out that by inserting this approximation and then correcting for it. Eq. (11))," and also changing the variable from $E_{\gamma}$ to $E=E_{\gamma}-Q$ in the integration, one can average over the velocity distribution of the ground-state interacting nuclei $\langle\sigma c\rangle_{\gamma3}$ as follows: At this point, one usually introduces the approximation: Here, we point out that by inserting this approximation and then correcting for it, Eq. \ref{eq:Inverse Reaction Rate 2}) )"
 can be rewritten in the following exact form: where R is a small and dimensionless number which ts formally given by The generalization. of Eq. (13)), can be rewritten in the following exact form: where $R$ is a small and dimensionless number which is formally given by The generalization of Eq. \ref{eq:Ratio of Reaction Rates 3}) )
 to the average over thermally populated states among the initial and final nuclei is straightforward (Clayton1968:Iliadis.2007).," to the average over thermally populated states among the initial and final nuclei is straightforward \citep{cla68, Iliadis07}."
. One must first replace the ground state (g.s.), One must first replace the ground state (g.s.)
 to g.s., to g.s.
 forward reaction cross section 74» with a weighted average over the thermal population of states µ in the target nucleus |. and also sum over all final states 1n product nucleus 3. (," forward reaction cross section $\sigma_{1 2}$ with a weighted average over the thermal population of states $\mu$ in the target nucleus 1, and also sum over all final states in product nucleus $3$ . ("
Note that we only consider light particle (p.5). G15). or (0.5). reactions for which we can ignore their excitation.),"Note that we only consider light particle $(p,\gamma)$, $(n,\gamma)$, or $(\alpha,\gamma)$, reactions for which we can ignore their excitation.)"
 Thus. the effective stellar thermal forward rate becomes which can also be written as where the stellar enhancement factor Αι is defined by Usually. tabulated thermonuclear reaction rates are given as the ground state rate and the stellar enhancement factor must be determined from a statistical model calculation as in Holmesetal. (1976)... Woosleyet.al. (1978).. Rauscher and Rauscher&Thielemann (2004). ," Thus, the effective stellar thermal forward rate becomes which can also be written as where the stellar enhancement factor $R_{t t}$ is defined by Usually, tabulated thermonuclear reaction rates are given as the ground state rate and the stellar enhancement factor must be determined from a statistical model calculation as in \cite{Holmes76}, , \cite{Woosley78}, , \cite{Rauscher00} and \cite{Rauscher04}. ."
The thermally averaged photonuclear rate for a distribution of excitedstates in initial and final heavy nuclei then becomes The generalization of the detailed balance condition of Eq. (13)), The thermally averaged photonuclear rate for a distribution of excitedstates in initial and final heavy nuclei then becomes The generalization of the detailed balance condition of Eq. \ref{eq:Ratio of Reaction Rates 3}) )
 Is, is
Absorption from ionized matter in. the. X-ray spectrum of AGN (the so-called warm absorber) was discovered many years ago (Halpern 1984).,Absorption from ionized matter in the X-ray spectrum of AGN (the so-called warm absorber) was discovered many years ago (Halpern 1984).
 Since then. many advances in its understanding have been made. and we know now that it is present in about half of Seyfert galaxies (e.g. Reynolds 1997) and that the matter is photoronized.," Since then, many advances in its understanding have been made, and we know now that it is present in about half of Seyfert galaxies (e.g. Reynolds 1997) and that the matter is photoionized."
 Warm absorbers are also known to vary. and indeed the first discovered absorber was variable (Halpern 1984).," Warm absorbers are also known to vary, and indeed the first discovered absorber was variable (Halpern 1984)."
 The location of the warm absorber (or. indeed. of the absorbers. as more than one tonizing zone is often found) is. however. largely uncertain.," The location of the warm absorber (or, indeed, of the absorbers, as more than one ionizing zone is often found) is, however, largely uncertain."
 There is some evidence for its origin as a wind from the dusty torus envisaged in unification models for Seyfert galaxies (Blustin et al., There is some evidence for its origin as a wind from the dusty torus envisaged in unification models for Seyfert galaxies (Blustin et al.
 2005). but cases in which an origin from the disk seems to be preferred do also exist (Krongold et al.," 2005), but cases in which an origin from the disk seems to be preferred do also exist (Krongold et al."
 2007)., 2007).
 Mrk 704 ts a local (220.029234) Seyfert 1.2 galaxy (Veron-Cetty Veron 2010). bright enough in X-rays to be detected by Swift/BAT (Ajello et al.," Mrk 704 is a local $z$ =0.029234) Seyfert 1.2 galaxy (Veron-Cetty Veron 2010), bright enough in X-rays to be detected by $Swift$ /BAT (Ajello et al."
 2008)., 2008).
 In this paper we report on extreme warm absorber variability. on yearly time scales. revealed by two XMM-Newton observations. and possible variability on monthly time scales from short Swift/XRT observations.," In this paper we report on extreme warm absorber variability, on yearly time scales, revealed by two $Newton$ observations, and possible variability on monthly time scales from short Swift/XRT observations."
 The paper is organized as follows: in Section 2 we report on the XMM-Newton observations and data reduction. while the relative data analysis are discussed in Section 3.," The paper is organized as follows: in Section 2 we report on the $Newton$ observations and data reduction, while the relative data analysis are discussed in Section 3."
 Section 4 presents the analysis of the Suvfr and ASCA observations. while the results are summarized and discussed in Section 5.," Section 4 presents the analysis of the $Swift$ and $ASCA$ observations, while the results are summarized and discussed in Section 5."
 XMM-Newton observed Mrk 704 twice. on 2005-10- (OBSID:: 0300240101) and on 2008-11-02(OBSID: 0502091601).," $Newton$ observed Mrk 704 twice, on 2005-10-21 : 0300240101) and on 2008-11-02: 0502091601)."
 In both cases. EPIC pn and MOS were in Small Window mode (apart from MOS? in the first observation. which was in Full Frame mode). which ensures that no significant pile-up is present. as verified with the tool. in the pn detectors (the only one used for the analysis).," In both cases, EPIC pn and MOS were in Small Window mode (apart from MOS2 in the first observation, which was in Full Frame mode), which ensures that no significant pile-up is present, as verified with the tool, in the pn detectors (the only one used for the analysis)."
 Mrk 704 is by far the brightest source in the field of view., Mrk 704 is by far the brightest source in the field of view.
 Data were reduced with 10.0.0. using calibration files generated on 2010-6-11.," Data were reduced with 10.0.0, using calibration files generated on 2010-6-11."
 Screening for intervals of flaring particle background was done consistently with the choice of extraction radi. in an iterative process based on the procedure to maximize the signal-to-noise ratio described by Piconcellt et al. (," Screening for intervals of flaring particle background was done consistently with the choice of extraction radii, in an iterative process based on the procedure to maximize the signal-to-noise ratio described by Piconcelli et al. ("
2005).,2005).
 After this process. the net exposure time was of about 15 and 68 ks for the 2005 and the 2008 observation. respectively. adopting extraction radit of 36 and 40 aresec. and patterns O to 4.," After this process, the net exposure time was of about 15 and 68 ks for the 2005 and the 2008 observation, respectively, adopting extraction radii of 36 and 40 arcsec, and patterns 0 to 4."
 The background spectra were extracted from source-free circular regions with a radius of 50 aresec., The background spectra were extracted from source-free circular regions with a radius of 50 arcsec.
 The same regions were used for the timing analysis., The same regions were used for the timing analysis.
 Spectra were binned in order to oversample the instrumental resolution by at least a factor of 3 and to have no less than 30 counts in each background-subtracted spectral channel., Spectra were binned in order to oversample the instrumental resolution by at least a factor of 3 and to have no less than 30 counts in each background-subtracted spectral channel.
 The latter requirement allows us to use the y statistics as a goodness-of-fit-test., The latter requirement allows us to use the $\chi^2$ statistics as a goodness-of-fit-test.
 RGS source and background spectra were extracted with standard procedures. adopting the data reduction pipelineRGSPROC.. and choosing the NED optical nucleus of Mrk 704 as the reference point for the attitude solution.," RGS source and background spectra were extracted with standard procedures, adopting the data reduction pipeline, and choosing the NED optical nucleus of Mrk 704 as the reference point for the attitude solution."
 We will use in this paper only data from the EPIC pn and the RGS camera. because after the latest release of the EPIC pn redistribution and the RGS contamination model (May 2010) their cross-calibration is as good as (A. Pollock. private communication).," We will use in this paper only data from the EPIC pn and the RGS camera, because after the latest release of the EPIC pn redistribution and the RGS contamination model (May 2010) their cross-calibration is as good as (A. Pollock, private communication)."
 In Fig., In Fig.
 1. the 2-10 keV (upper panel). 0.3-2 keV. (middle panel) and the (2-10 keV)/(0.3-2 keV) hardness ratio (HR) light curves are shown for the first (left) and the second (right)," \ref{lc_obs} the 2-10 keV (upper panel), 0.3-2 keV, (middle panel) and the (2-10 keV)/(0.3-2 keV) hardness ratio (HR) light curves are shown for the first (left) and the second (right)"
The author would like to thank Alariangcla Bernardi. Nacho ‘Trujillo and Michele Cappellari for useful communications and Ancrey= Ixravtsov. Robert οἱµια. Joshua Frieman. Nick Cinecdin and Steve Went for helpful discussions ane conversations.,"The author would like to thank Mariangela Bernardi, Nacho Trujillo and Michele Cappellari for useful communications and Andrey Kravtsov, Robert Feldmann, Joshua Frieman, Nick Gnedin and Steve Kent for helpful discussions and conversations."
 The author also eratefullv acknowledges the referee. comments that were helpful. in clarifying and improving the manuscript significantly., The author also gratefully acknowledges the referee comments that were helpful in clarifying and improving the manuscript significantly.
 10° , $10^{6}$ 
2008).,.
". The origin of this non-trivial result lies in two facts: First, at late times, the emission is dominated by photons emitted off-axis (from angles 0>>T'—!, see figure 1))."," The origin of this non-trivial result lies in two facts: First, at late times, the emission is dominated by photons emitted off-axis (from angles $\theta \gg \Gamma^{-1}$, see figure \ref{fig1}) )."
" Due to the strong dependence of the Doppler shift on the angle to the line of sight, these photons are seen at much lower energies than photons emitted on-axis."," Due to the strong dependence of the Doppler shift on the angle to the line of sight, these photons are seen at much lower energies than photons emitted on-axis."
" Second, at any given instance, an observer sees simultaneously photons that are emitted from a range of radii and angles eq. "," Second, at any given instance, an observer sees simultaneously photons that are emitted from a range of radii and angles (see eq. \ref{eq:t_N}) )."
"As each photon has a finite probability of (seebeing emitted5)). from a given radius, and is seen at a particular Doppler shift, the observed spectrum and flux can only be described in terms of probability density functions (see refsec:prob))."," As each photon has a finite probability of being emitted from a given radius, and is seen at a particular Doppler shift, the observed spectrum and flux can only be described in terms of probability density functions (see \\ref{sec:prob}) )."
 These functions provide a mathematical tool to describe the probability of photons to be emitted from radius r and into angle 0., These functions provide a mathematical tool to describe the probability of photons to be emitted from radius $r$ and into angle $\theta$.
" Using these functions, we calculated an analytical approximation to the observed spectrum (eq. 3.1)),"," Using these functions, we calculated an analytical approximation to the observed spectrum (eq. \ref{eq:f_nu}) ),"
 which is the main result of this work., which is the main result of this work.
 'The analytical approximation was tested with a Monte-Carlo simulation that tracks the evolution of thermal photons in relativistically expanding plasma refsec:numerics))., The analytical approximation was tested with a Monte-Carlo simulation that tracks the evolution of thermal photons in relativistically expanding plasma \\ref{sec:numerics}) ).
 The simplified analytical calculations(8 are found to be in very good agreement with the accurate numerical results figure , The simplified analytical calculations are found to be in very good agreement with the accurate numerical results (see figure \ref{fig2}) ).
"In spite of the success(see in reproducing2)). the low energy spectral slopes at late times, the theory is still not completed."," In spite of the success in reproducing the low energy spectral slopes at late times, the theory is still not completed."
" For parameters characterizing GRBs, the thermal peak naturally falls at the sub-MeV range (see (T$25.)refsec:numerical, esults)), all hencetheobservedpeakcannaturwWledhpl inadi"," For parameters characterizing GRBs, the thermal peak ( $T_{\max}^{ob}$ ) naturally falls at the sub-MeV range (see \\ref{sec:numerical_results}) ), hence the observed peak can naturally be explained as having a thermal origin."
"eerim clostgino.Hoe aspltéceabl edrawbac s. Since above ty the flux decays rapidly, F(t)«t? eq. 3.1)),"," However, a noticeable drawback of the theory as stated in this manuscript, is that the same parameters lead to very short characteristic time scale, $t_N \approx 10^{-5}$ s. Since above $t_N$ the flux decays rapidly, $F_{\nu}(t) \propto t^{-2}$ (see eq. \ref{eq:f_nu}) ),"
" one expects relatively weak thermal signal (seeat t>>ty, which can stilla be very short time."," one expects a relatively weak thermal signal at $t \gg t_N$, which can still be very short time."
" We note though, that the calculation of ty in equation 5 is based on the assumption of constant outflow velocity."," We note though, that the calculation of $t_N$ in equation \ref{eq:t_N} is based on the assumption of constant outflow velocity."
" This assumption is too simplified: in order to reach high Lorentz factor, the plasma needs to undergo an acceleration phase, and so the average Lorentz factor below the photosphere is less than the terminal Lorentz factor."," This assumption is too simplified: in order to reach high Lorentz factor, the plasma needs to undergo an acceleration phase, and so the average Lorentz factor below the photosphere is less than the terminal Lorentz factor."
" As a result, we expect that in practice the characteristic time scale relevant for thermal emission in GRBs is longer than the one considered in equation 5.."," As a result, we expect that in practice the characteristic time scale relevant for thermal emission in GRBs is longer than the one considered in equation \ref{eq:t_N}."
 The exact delay time depends on several uncertain conditions., The exact delay time depends on several uncertain conditions.
" One is the content of the fireball: for example, Poynting-flux dominated fireball is expected to have slower acceleration than matter dominated fireball 2002;Drenkhahn&SpruitGian-nios(Drenkhahn&Spruit2005,2006)."," One is the content of the fireball: for example, Poynting-flux dominated fireball is expected to have slower acceleration than matter dominated fireball \citep{Drenk02,DS02, GS05, GS06}."
". Another is the baryon load (Joka2010),, and in particular the baryon distribution along the jet (Morsonyetal.2007;Lazzati2009;Mizutaetal.2010): although in this manuscript we considered a steady outflow, clearly the outflow in GRBs is characterized by regions of higher and lower densities, and is thus not steady (edge effects due to the finite opening angle may also play a role at late times)."," Another is the baryon load \citep{Ioka10}, and in particular the baryon distribution along the jet \citep{MLB07, LMB09, MNA10}: although in this manuscript we considered a steady outflow, clearly the outflow in GRBs is characterized by regions of higher and lower densities, and is thus not steady (edge effects due to the finite opening angle may also play a role at late times)."
" An additional source of discrepancy between the theoretical predictions developed in this paper and the observed spectrum, lies in the fact that the theory here does not consider any additional, non-thermal radiative processes."," An additional source of discrepancy between the theoretical predictions developed in this paper and the observed spectrum, lies in the fact that the theory here does not consider any additional, non-thermal radiative processes."
" As shown here, photospheric emission is capable of reproducing the peak energy and the low energy spectral slope (o in the “Band” function) seen in GRBs (at late times)."," As shown here, photospheric emission is capable of reproducing the peak energy and the low energy spectral slope $\alpha$ in the “Band” function) seen in GRBs (at late times)."
" However, photospheric emission is not capable of of producing high energy photons (above T9.< MeV), as are seen in some GRBs by the LAT detector on board theFermi satellite."," However, photospheric emission is not capable of of producing high energy photons (above $T_{\max}^{ob} \lesssim \MeV$ ), as are seen in some GRBs by the LAT detector on board the satellite."
" The inclusion of high energy, non-thermal photons, necessitates additional radiative mechanisms, that must take place following dissipation processes that occur above the photosphere (e.g.,inGRBO080916Canalysisoutflow;seeZhang&Pe’er 2009)."," The inclusion of high energy, non-thermal photons, necessitates additional radiative mechanisms, that must take place following dissipation processes that occur above the photosphere \citep[e.g., in GRB080916C
analysis of the high energy emission imply Poynting dominated outflow;
see][]{ZP09}."
". Additional radiative mechanisms, such as synchrotron emission or Compton scattering, naturaly produce a broad band energy spectrum, and thus may contribute not only to the high energy spectrum but to the low energy part (below the thermal peak) as well."," Additional radiative mechanisms, such as synchrotron emission or Compton scattering, naturally produce a broad band energy spectrum, and thus may contribute not only to the high energy spectrum but to the low energy part (below the thermal peak) as well."
" The overall observed spectra below the thermal peak is thus generally expected to be hybrid- i.e., composed of both thermal and non-thermal parts."," The overall observed spectra below the thermal peak is thus generally expected to be hybrid- i.e., composed of both thermal and non-thermal parts."
" The exact contribution of the non-thermal part may vary from burst to burst, depending on the values of the free model parameters, such as the radius of the photosphere, the dissipation radius, the strength of the magnetic field, etc."," The exact contribution of the non-thermal part may vary from burst to burst, depending on the values of the free model parameters, such as the radius of the photosphere, the dissipation radius, the strength of the magnetic field, etc."
" In principle, the inclusion of thermal photons contributes to the high energy, non thermal part of the spectrum as well, as these photons serve as seed photons for Compton scattering by the non-thermal electrons and hot pairs (Rees&Mészáros2005;Pe'eret 2010)."," In principle, the inclusion of thermal photons contributes to the high energy, non thermal part of the spectrum as well, as these photons serve as seed photons for Compton scattering by the non-thermal electrons and hot pairs \citep{RM05, PMR05, PMR06, LazBeg10,
 Bel10}."
. The exact contribution of the thermal photons depend on the optical depth at the dissipation radius., The exact contribution of the thermal photons depend on the optical depth at the dissipation radius.
" alot the resulting adissibethawspectrum has a complex shape, that is very different than either a thermal spectrum or the optically thin synchrotron - synchrotron self Compton (SSC) model predictions (Pe'eretal.2005,2006).."," If the dissipation radius is close to the photosphere, the resulting spectrum has a complex shape, that is very different than either a thermal spectrum or the optically thin synchrotron - synchrotron self Compton (SSC) model predictions \citep{PMR05, PMR06}."
" On the other hand, if the dissipation occurs at large radii, the two components, thermal and non-thermal, can be decoupled, a fact that can lead to a clear identification of the thermal component, as is in the case of GRB090902B"," On the other hand, if the dissipation occurs at large radii, the two components, thermal and non-thermal, can be decoupled, a fact that can lead to a clear identification of the thermal component, as is in the case of GRB090902B"
"VI The above constraints can be shown to lead to four parameter sub-regimes where viable solutions exist in the Hall regime, and to three in the Ohm regime (I refer the reader to KSW10 for more details)."," The above constraints can be shown to lead to four parameter sub-regimes where viable solutions exist in the Hall regime, and to three in the Ohm regime (I refer the reader to KSW10 for more details)."
 The constraints for the Hall regime are summarised in Table 1.., The constraints for the Hall regime are summarised in Table \ref{table:constraints}.
 These are differentiated by the values of the combinations Beofio and 2Λο (=2To|Gio| in this limit) in comparison with unity.," These are differentiated by the values of the combinations $\beta_{\rm e 0} \beta_{\rm i 0}$ and $2\Lambda_{\rm 0}$ $=
2\Upsilon_{\rm 0} |\beta_{\rm i 0}|$ in this limit) in comparison with unity."
 Our numerical solutions (SKW11) confirm these predictions: We find that no physically-relevant solutions are found outside the boundaries specified by these constraints., Our numerical solutions (SKW11) confirm these predictions: We find that no physically-relevant solutions are found outside the boundaries specified by these constraints.
 We also explored the dependence of the solutions on the model parameters., We also explored the dependence of the solutions on the model parameters.
" We found that increasing the relative contribution of the Hall diffusivity results in a smaller magnetically-reduced density scale-height, and in a higher location above the disc midplane of both the base of the wind and the sonic surface."," We found that increasing the relative contribution of the Hall diffusivity results in a smaller magnetically-reduced density scale-height, and in a higher location above the disc midplane of both the base of the wind and the sonic surface."
" As a result, the density at the sonic point, and the associated mass outflow rate, are reduced."," As a result, the density at the sonic point, and the associated mass outflow rate, are reduced."
" Our calculations also show that, in all diffusivity regimes, viable solutions satisfy the requirement that the neutral — ion momentum exchange time be shorter than the disc orbital time (Y 1)."," Our calculations also show that, in all diffusivity regimes, viable solutions satisfy the requirement that the neutral – ion momentum exchange time be shorter than the disc orbital time $\Upsilon \gtrsim 1$ )."
" This is, therefore, a fundamental constraint on the wind solutions considered here."," This is, therefore, a fundamental constraint on the wind solutions considered here."
" Finally, we found that the magnetic field polarity modifies both the properties of the solutions and the parameter ranges where these exist when the Hall regime is dynamically important."," Finally, we found that the magnetic field polarity modifies both the properties of the solutions and the parameter ranges where these exist when the Hall regime is dynamically important."
" This reflects the dependence of the Hall diffusivity on the sign of B,.", This reflects the dependence of the Hall diffusivity on the sign of $B_z$.
" Specifically, our analysis shows that for two of the Hall sub-regimes (Cases { and iii in Table 1)), positive and"," Specifically, our analysis shows that for two of the Hall sub-regimes (Cases $i$ and $iii$ in Table \ref{table:constraints}) ), positive and"
The final step then is to correct the biasing parameter. b. for the luminosity of our sample.,"The final step then is to correct the biasing parameter, $b$, for the luminosity of our sample."
 Norberg (2001) found from the analysis of the galaxy correlation functions on scales <105. Mpe that. Assuming that this relation also holds in our quasi-linear regime of S20h.+ Mpe. then allows us to determine «3 at redshift 7=0 and luminosity L=L..7 Table 3. shows the results for .7 derived in the analysis presented here. both before and after converting to redshift +=0 and luminosity £= L..," Norberg (2001) found from the analysis of the galaxy correlation functions on scales $<10\;h^{-1}$ Mpc that, Assuming that this relation also holds in our quasi-linear regime of $8-20\;h^{-1}$ Mpc, then allows us to determine $\beta$ at redshift $z=0$ and luminosity $L=L_*$ Table \ref{tab:xires} shows the results for $\beta$ derived in the analysis presented here, both before and after converting to redshift $z=0$ and luminosity $L=L_*$."
 Also shown are other results derived from the 2dFGRS by previous authors., Also shown are other results derived from the 2dFGRS by previous authors.
 It can be seen that there is a remarkably good agreement between all the results presented., It can be seen that there is a remarkably good agreement between all the results presented.
 We note that these results have been derived by applyinglinear corrections to a selection ofquasi-linear regimes. which may introduce systematic errors into our results.," We note that these results have been derived by applying corrections to a selection of regimes, which may introduce systematic errors into our results."
 This is a particular concern for the results of Verde (2002). which correspond to the smallest separation ranges used.," This is a particular concern for the results of Verde (2002), which correspond to the smallest separation ranges used."
 We have derived a variety of different parameterisations for the 2dFGRS correlation function. €(o.7). for different spectral types.," We have derived a variety of different parameterisations for the 2dFGRS correlation function, $\xi(\sigma,\pi)$, for different spectral types."
 The two types we have used can roughly be interpreted as dividing our galaxy sample on the basis of their relative amount of current, The two types we have used can roughly be interpreted as dividing our galaxy sample on the basis of their relative amount of current
ng22.887505107? em. yielding ke2520075135 keV em.,"$n_R=
2.88^{+0.19}_{-0.19}\times 10^{-5}$ $^{-3}$ , yielding $k_R =
5200^{+2140}_{-2140}$ keV $^{2}$ ."
" Correspondingly. we find k,=363) keV em’."," Correspondingly, we find $k_c=36^{+20}_{-20}$ keV $^{2}$."
 Finally. from Eq. (," Finally, from Eq. ("
8) we derive the total mass M=1.222«10M...,"8) we derive the total mass $M= 1.2^{+0.7}_{-0.7}\times
10^{15}\,M_{\odot}$."
 Note that if one insisted on applying the SM also to temperature and brightness profiles from the centroid on the basis of Eqs. (, Note that if one insisted on applying the SM also to temperature and brightness profiles from the centroid on the basis of Eqs. (
"6) and (7). one would obtain r;=104*1 kpe and a related lower bound &,z12410 keV env.","6) and (7), one would obtain $r_f=104^{+4}_{-4}$ kpc and a related lower bound $k_c\approx 124^{+120}$ keV $^2$."
 The large variance in the above parameters entering the entropy floors signals complex substructures. that may be interpreted as a high density. low entropy clump (‘cold drop’) around the ray peak.," The large variance in the above parameters entering the entropy floors signals complex substructures, that may be interpreted as a high density, low entropy clump (`cold drop') around the X-ray peak."
 Our results agrees with the analysis by Buote et al. (, Our results agrees with the analysis by Buote et al. (
2005). who in terms of two differently centered ./-models (Cavaliere Fusco-Femiano 1976) find two core sizes similar to our extensions /y.,"2005), who in terms of two differently centered $\beta$ -models (Cavaliere Fusco-Femiano 1976) find two core sizes similar to our extensions $r_f$."
 In view of the lack of radio emission and X-ray cavities. this complexity may be understood in terms of à merger having just remolded an inner region of the ICP (see Henning et al.," In view of the lack of radio emission and X-ray cavities, this complexity may be understood in terms of a merger having just remolded an inner region of the ICP (see Henning et al."
 2009)., 2009).
 We stress that such ICP substructures constitute a common. but progressively more pronounced trait. of Α1656. A2256 and A644.," We stress that such ICP substructures constitute a common, but progressively more pronounced trait, of A1656, A2256 and A644."
 In this paper we have analyzed with the Supermodel (SM) the profiles of X-ray temperature and surface brightness of the IntraCluster Plasma (ICP) in à set of six clusters (adding to the three ones preliminarily reported in CLFFO9) with existing detailed data., In this paper we have analyzed with the Supermodel (SM) the profiles of X-ray temperature and surface brightness of the IntraCluster Plasma (ICP) in a set of six clusters (adding to the three ones preliminarily reported in CLFF09) with existing detailed data.
 We have shown how effective is our SM to represent and understand the main Cool Core /Non Cool Core in terms of two physical parameters marking the full ICP entropy profile: the central value κ... and the outer slope a (see Figs.," We have shown how effective is our SM to represent and understand the main Cool Core /Non Cool Core in terms of two physical parameters marking the full ICP entropy profile: the central value $k_c$, and the outer slope $a$ (see Figs."
 1-7)., 1-7).
 Moreover. the SM makes sense of more profiles (see Figs.," Moreover, the SM makes sense of more profiles (see Figs."
" 8-11) in terms of the additional. physical parameter +, marking the extension of the entropy floor."," 8-11) in terms of the additional, physical parameter $r_f$ marking the extension of the entropy floor."
 The working of the SM may be reducedto thebones as follows., The working of the SM may be reducedto thebones as follows.
 The spatial scale for the temperature peak in the, The spatial scale for the temperature peak in the
Let us consider the thermodynamical properties of texture matter as such and in comparison with those for radiation fIuid (equasi-counterpart of texture) aud bubble matter 2+p=0.,Let us consider the thermodynamical properties of texture matter as such and in comparison with those for radiation fluid (quasi-counterpart of texture) and bubble matter $\varepsilon + p = 0$.
 First oL all. we trv (o answer the question. what is (hermodvnamical information we can obtain from an equation of state.," First of all, we try to answer the question, what is thermodynamical information we can obtain from an equation of state."
 The first thermodsynamical law savs: dE-Tds5-pdV.(l) On the other hand. following the clelinition of the entropy as a function of volume and lemperature. one can write US = Ede Comparing (hese equations. we obtain ," The first thermodynamical law says: E = T S - p V. On the other hand, following the definition of the entropy as a function of volume and temperature, one can write S = T + V. Comparing these equations, we obtain = = ( p + )."
Then the equality of mixecl derivatives vields the expression | y+ War which gives opportunities to obtain internal energy. as a function of volume and temperature from an equation of state., Then the equality of mixed derivatives yields the expression p + = T which gives opportunities to obtain internal energy as a function of volume and temperature from an equation of state.
 Let us introduce (he densities of energy and entropy such that E-ST. S= s(T)V and consider barotropic matter will linear equation of state (LEOS) p=g," Let us introduce the densities of energy and entropy such that (T) V, S=s(T) V, and consider barotropic matter with linear equation of state (LEOS) p =."
e) Then (5)) reads ure = (y+lesus) and we obtain the energy density TO τα," Then \ref{eq5}) ) reads T = +1), and we obtain the energy density = _0"
Alibertetal.(1999) are plotted using filled circles. while others are plotted using open circles.,"\citet{al99} are plotted using filled circles, while others are plotted using open circles."
 Plus sigus indicate results caleulated for stars evolving through the hot and cool edges of the instability strip. with the rate of period chanec in general being larger on the hot edge of the instability strip. ie.. for more massive stars.," Plus signs indicate results calculated for stars evolving through the hot and cool edges of the instability strip, with the rate of period change in general being larger on the hot edge of the instability strip, i.e., for more massive stars."
 Large svinbols denote stars of solar metallicity. Z= 102. iutermediate-sized sviibols denote stars witli uetallicities of Z=0.01 and Z=0.008. aud «πα sviubols denote stars of very low metallicity. Z—0.001 and Z=0.001.," Large symbols denote stars of solar metallicity, $Z = 0.02$ , intermediate-sized symbols denote stars with metallicities of $Z = 0.01$ and $Z = 0.008$, and small symbols denote stars of very low metallicity, $Z = 0.001$ and $Z = 0.004$."
 Lines have been drawn o enclose those regions within which the results or different crossing modes appear to cluster., Lines have been drawn to enclose those regions within which the results for different crossing modes appear to cluster.
 Sequences Of points indicate models tor which the ime resolution was fiue enough to calculate rate of period change over the cntire crossing of the instability strip., Sequences of points indicate models for which the time resolution was fine enough to calculate rate of period change over the entire crossing of the instability strip.
 The distribution of data points in Fie., The distribution of data points in Fig.
 we suggests a of varictydifferent couclusious regarding the models., 2 suggests a variety of different conclusions regarding the models.
 First. the different models for the vapid first crossing of the instability. strip are in very good aerecment. and display τον little variation with metallicity.," First, the different models for the rapid first crossing of the instability strip are in very good agreement, and display very little variation with metallicity."
 The first crossing of the strip is a rapid transition for all stars. regardless of individual differences in rotation rate. cte.," The first crossing of the strip is a rapid transition for all stars, regardless of individual differences in rotation rate, etc.,"
 and that is evident frou the models., and that is evident from the models.
 Evidenutly he computational codes used for calculating the ghases of shell hydrogeu. buruing in stars. while orhaps differing in detail from one source to another. generate nearly identical results. the small variation in rate of period change at specific oulsatiou period arising from the finite width of he instability strip aud the fact that more massive stars cross the strip at a greater luninosity aud at a faster rate than less iiassive stars.," Evidently the computational codes used for calculating the phases of shell hydrogen burning in stars, while perhaps differing in detail from one source to another, generate nearly identical results, the small variation in rate of period change at specific pulsation period arising from the finite width of the instability strip and the fact that more massive stars cross the strip at a greater luminosity and at a faster rate than less massive stars."
 For stars iu he first crossing of the strip. high rate of period increase at specific pulsation period corresponds ο stars on the hot edge of the strip. low rate of oriod increase to stars on the cool edge of the strip.," For stars in the first crossing of the strip, high rate of period increase at specific pulsation period corresponds to stars on the hot edge of the strip, low rate of period increase to stars on the cool edge of the strip."
 Negative period changes arise duriug the second crossing of the instability strip. which occurs diving the blue loop phase of stella evolution following the ouset of core helium burning.," Negative period changes arise during the second crossing of the instability strip, which occurs during the blue loop phase of stellar evolution following the onset of core helium burning."
 The extent of the blue loop cau depend upon a variety of factors (sec.forexample.Decker1985:Nu&Li 2001)... such as inetallieity. the treatincut of core overshooting. aud the distribution of CNO clemeuts thronghont the star.," The extent of the blue loop can depend upon a variety of factors \citep[see, for example,][]{be85,xl04}, such as metallicity, the treatment of core overshooting, and the distribution of CNO elements throughout the star."
 All factors affect how far a star enters the instability strip durug core helium burning. aud presumably affects how rapidly it evolves within the strip.," All factors affect how far a star enters the instability strip during core helium burning, and presumably affects how rapidly it evolves within the strip."
 Given the potentially huge differences in initial conditions for such stars as naim-sequenuce objects. for example. large variations iu initial rotation rate. one nuelt expect real stars to display large variations in how far they penctrate the Cepheid instability strip as core elim burning objects.," Given the potentially large differences in initial conditions for such stars as main-sequence objects, for example, large variations in initial rotation rate, one might expect real stars to display large variations in how far they penetrate the Cepheid instability stripm as core helium burning objects."
 Somewhat unexpectedly. there are also very large variatious among the models stars as well.," Somewhat unexpectedly, there are also very large variations among the models stars as well."
 Evidently. metallicity plavs ouly a minor role iu governing the at which stars traverse the instability strip.," Evidently, metallicity plays only a minor role in governing the at which stars traverse the instability strip."
 There is as much depeudeuce on the specifics of the stellar evolutionary code used., There is as much dependence on the specifics of the stellar evolutionary code used.
 The models of Alibertetal.(1999)... for example. eenerate faster rates of period decrease than do other models. despite the use of common opacity tables.," The models of \citet{al99}, for example, generate faster rates of period decrease than do other models, despite the use of common opacity tables."
 Models from individual sources are at least internally consistent in their predictions for stars of different masses and for stars du all portions of the second strip crossing., Models from individual sources are at least internally consistent in their predictions for stars of different masses and for stars in all portions of the second strip crossing.
 The rates of period decrease during mdividual strip crossings are also very simular to the variations predicted on the basis of mass differences. 1.0. predicted. variations iu rate of period decrease at a specific pulsation period are eenerallv small. except for long period Cepheids.," The rates of period decrease during individual strip crossings are also very similar to the variations predicted on the basis of mass differences, i.e, predicted variations in rate of period decrease at a specific pulsation period are generally small, except for long period Cepheids."
 The third crossing of the instability strip occurs diving the late stages of core lelimm buruiug. and gives rise to period increases. for which the predicted rates are depicted in the top portion of Fie.," The third crossing of the instability strip occurs during the late stages of core helium burning, and gives rise to period increases, for which the predicted rates are depicted in the top portion of Fig."
 2 along with those for the first crossing., 2 along with those for the first crossing.
 Mos of the comments regarding the second crossing of the strip apply equally to the third crossing., Most of the comments regarding the second crossing of the strip apply equally to the third crossing.
 Again. metallicity senis to play a less important role iu the predicted rates of period increase than differences in the evolutionary code.," Again, metallicity seems to play a less important role in the predicted rates of period increase than differences in the evolutionary code."
 The models of Alibertetal.(01999)— predict faster rates of period chauge (period increases 1n this case) tha do other models. although with less consistency for stars of ciffercut mass.," The models of \citet{al99} predict faster rates of period change (period increases in this case) than do other models, although with less consistency for stars of different mass."
 The rates of period increase durug individual strip crossings are also simular to the variatious predicted on the basis of mass differences. aud predicted variations in the rate of period increase at a specific pulsation period are eoncrally πια].," The rates of period increase during individual strip crossings are also similar to the variations predicted on the basis of mass differences, and predicted variations in the rate of period increase at a specific pulsation period are generally small."
 A wellknown problem arises for low-1ass stars in the second aud third crossings of the instability strip. siuce the blue loop phases of," A well-known problem arises for low-mass stars in the second and third crossings of the instability strip, since the blue loop phases of"
"For soft quark matter Gy=0 we obtain quark matter only in the 2SC phase, which extends up to about 1/3 of the star radius.","For soft quark matter $G_V=0$ we obtain quark matter only in the 2SC phase, which extends up to about 1/3 of the star radius."
" Increasing Gy has the effect of shifting the 2SC phase to larger radii, whereas the CFL phase develops at the center."," Increasing $G_V$ has the effect of shifting the 2SC phase to larger radii, whereas the CFL phase develops at the center."
" For the strongest coupling studied, all phases are present in the maximum mass star, with the combined 2SC and CFL paired quark matter confined within a radius that is about the half of the star."," For the strongest coupling studied, all phases are present in the maximum mass star, with the combined 2SC and CFL paired quark matter confined within a radius that is about the half of the star."
" Note that a similar internal structure is obtained for crystalline color-superconducting stars, where quark matter is confined within a radius of ~7 km for maximum mass stars with a radius ~12 km (Knippel&Sedrakian2009).."," Note that a similar internal structure is obtained for crystalline color-superconducting stars, where quark matter is confined within a radius of $\sim 7$ km for maximum mass stars with a radius $\sim 12$ km \citep{2009PhRvD..79h3007K}."
" Massive neutron stars are likely to develop cores composed of deconfined quark matter, which should be in one of the color"," Massive neutron stars are likely to develop cores composed of deconfined quark matter, which should be in one of the color"
Blantonetal.(2003) in their study of SDSS galaxies.,\citet{bl03} in their study of SDSS galaxies.
 [If in fact. galaxies are well described bv Sérrsic profiles. (hen is a useful surrogate for (he Sérrsic index ».," If, in fact, galaxies are well described by Sérrsic profiles, then is a useful surrogate for the Sérrsic index $n$."
" Consider. for instance. a galaxv whose surface brightness is perfectly described by a Sérrsic prolileof index »=2 and effective radius AH,=X."," Consider, for instance, a galaxy whose surface brightness is perfectly described by a Sérrsic profileof index $n = 2$ and effective radius $R_e = X$."
 The best-fitling exponential model for this ealaxv (fitting in the radial region OLN<RxLON) has f=LION: the best-fitting de Vaucoulerrs model has A.=0.80.N., The best-fitting exponential model for this galaxy (fitting in the radial region $0.1 X \leq R \leq 10 X$ ) has $R_e = 1.10 X$; the best-fitting de Vaucouleurs model has $R_e = 0.80 X$ .
 Combining the models gives fracDeV=0.51 [or this n=2 Sénsie galaxv., Combining the models gives $\texttt{fracDeV} = 0.51$ for this $n = 2$ Sérrsic galaxy.
 A similar fil to an ip=3 Sérrsic galaxy vields fracDeV=0.83., A similar fit to an $n = 3$ Sérrsic galaxy yields $\texttt{fracDeV} = 0.83$.
 In eeneral. if galaxies have Sérrsic profiles with 1<nx4. thenfracDeV.. as computed by the SDSS DR3 pipeline. is a monotonically increasing function of the Sérrsic index ». and thus can be used as a surrogate for n.," In general, if galaxies have Sérrsic profiles with $1 \leq n \leq 4$, then, as computed by the SDSS DR3 pipeline, is a monotonically increasing function of the Sérrsic index $n$, and thus can be used as a surrogate for $n$."
 A plot of the mean axis ratio (q) as a function of the parameter is shown in Figure 1.., A plot of the mean axis ratio $\langle q \rangle$ as a function of the parameter is shown in Figure \ref{fig:fdev}.
 The mean adaptive moments axis ratio (qu). indicated by the filled circles. shows an increasing trend. with fracDeV.. from (qu)=0.59 for galaxies with purely exponential profiles (fracDeV= 0) to (qm)=0.74 lor galaxies with pure de Vaucouleurs profiles (fracDeV= 1).," The mean adaptive moments axis ratio $\langle q_{\rm am} \rangle$, indicated by the filled circles, shows an increasing trend with , from $\langle q_{\rm am} \rangle = 0.59$ for galaxies with purely exponential profiles $\texttt{fracDeV} = 0$ ) to $\langle q_{\rm am} \rangle = 0.74$ for galaxies with pure de Vaucouleurs profiles $\texttt{fracDeV} = 1$ )."
 However. the trend in (q) is not a linear one: for galaxies with fracDeV<0.5. the value of (q) is nearly constant at (ϱ2 0.6: it is only at fracDeV=0.5 that (q) shows an increasing trend withfracDeV.," However, the trend in $\langle q \rangle$ is not a linear one; for galaxies with $\texttt{fracDeV} \la 0.5$, the value of $\langle q \rangle$ is nearly constant at $\langle q \rangle \approx 0.6$ ; it is only at $\texttt{fracDeV} \ga 0.5$ that $\langle q \rangle$ shows an increasing trend with."
. The mean isophotal axis ratio (qo3). indicated by the open circles in Figure 1.. shows less of a trend with£racDeV.," The mean isophotal axis ratio $\langle q_{25} \rangle$, indicated by the open circles in Figure \ref{fig:fdev}, shows less of a trend with."
. Except in (tlie case of nearly pure cle Vaucouleurs profiles (£racDeV= 0.9). the axis ratio of a galaxy in its outer regions doesnt seen (o depend on its surface brightness prolile.," Except in the case of nearly pure de Vaucouleurs profiles $\texttt{fracDeV} \ga 0.9$ ), the axis ratio of a galaxy in its outer regions doesn't seem to depend on its surface brightness profile."
 For convenience m analvsis.we have divided our galaxy sample into four classes. based on the value offracDeV.," For convenience in analysis,we have divided our galaxy sample into four classes, based on the value of."
". Galaxies with fracDeV< 0.1. corresponding to a Sérrsic index η<1.2. are called ex’ galaxies: (here are A.=44.289 ""ex. galaxies in our sample."," Galaxies with $\texttt{fracDeV} \leq 0.1$ , corresponding to a Sérrsic index $n \la 1.2$, are called `ex' galaxies; there are $N_{\rm ex} =
44{,}289$ `ex' galaxies in our sample."
 Galaxies wilh 0.1<fracDeV0.5. corresponding to 1.2Xn<2.0. are labeled ‘ex/de’ galaxies (CN 36.645).," Galaxies with $0.1 <
\texttt{fracDeV} \leq 0.5$, corresponding to $1.2 \la n \la 2.0$, are labeled `ex/de' galaxies $N_{\rm ex/de} = 36{,}645$ )."
 Galaxies with 0.5<fracDeV0.9. corresponding to 2.0SnS3.3. are labeled ‘defex’ galaxies (Naor= 13.780).," Galaxies with $0.5 < \texttt{fracDeV} \leq 0.9$, corresponding to $2.0 \la n \la 3.3$, are labeled `de/ex' galaxies $N_{\rm de/ex} = 13{,}780$ )."
 Finally. galaxies wilh fracDeV>0.9. corresponding to nZ3.3. are called ‘ce’ galaxies.," Finally, galaxies with $\texttt{fracDeV}
> 0.9$, corresponding to $n \ga 3.3$, are called `de' galaxies."
" The small fraction of ‘de’ galaxies in our sample (V4,= 2237) is partly due to the fact that the centrally concentrated de Vaucouleurs galaxies are less likely Lo satislv our resolution criterion. and partly due to the fact that galaxies with high Sérrsic indices are intrinsically rare: Blantonοἱal.(2003) estimated that only ~5% of the SDSS ealaxies in their sample had Sérrsic index η>3."," The small fraction of `de' galaxies in our sample $N_{\rm de} =
2237$ ) is partly due to the fact that the centrally concentrated de Vaucouleurs galaxies are less likely to satisfy our resolution criterion, and partly due to the fact that galaxies with high Sérrsic indices are intrinsically rare; \citet{bl03}
 estimated that only $\sim 5\%$ of the SDSS galaxies in their sample had Sérrsic index $n > 3$."
 The ‘de’ galaxies are rounder in their central regions than in their outer regions: 0.083.," The `de' galaxies are rounder in their central regions than in their outer regions: $\langle q_{\rm am} - q_{25} \rangle =
0.083$ ."
 This is consistent with the ‘cle’galaxies being relatively bright elliptical galaxies. for which the isophotal axisratios tend to decrease wilh increasing semimajor axis length (Iden.Forbes.&Terlevieh 2001)..," This is consistent with the `de'galaxies being relatively bright elliptical galaxies, for which the isophotal axisratios tend to decrease with increasing semimajor axis length \citep{rf01}. ."
 By contrast. (he‘ex’ galaxies are actually slightly flatter in (heir central regionsthan in their outer regions: (quà—q25)= —0.017.," By contrast, the`ex' galaxies are actually slightly flatter in their central regionsthan in their outer regions: $\langle q_{\rm am} -
q_{25} \rangle = -0.017$ ."
of the star. and the transition to non-axisymmetrie equilibrium is a matter simply of stretching this flux tube into a more complex arrangement.,"of the star, and the transition to non-axisymmetric equilibrium is a matter simply of stretching this flux tube into a more complex arrangement."
 In the process of stretching the tube. the toroidal component (i.e. the component parallel to the axis of the tube. the neutral line) is amplified (since the tube becomes narrower). and the poloidal component becomes weaker. eventually bringing the two components to roughly equal strengths. because the energy minimum for a given helicity. i.e. for a given product of toroidal and poloidal tield strengths. will have the two components roughly equal to each other.," In the process of stretching the tube, the toroidal component (i.e. the component parallel to the axis of the tube, the neutral line) is amplified (since the tube becomes narrower), and the poloidal component becomes weaker, eventually bringing the two components to roughly equal strengths, because the energy minimum for a given helicity, i.e. for a given product of toroidal and poloidal field strengths, will have the two components roughly equal to each other."
" At higher£,/£ ratios therefore. more stretching is required to make the two components equal."," At higher$E_{\rm p}/E$ ratios therefore, more stretching is required to make the two components equal."
 This can be clearly seen in fig. 16.., This can be clearly seen in fig. \ref{fig:map-higher}.
" Now. in the case where £,/E=1 the field has zero magnetic helicity and no amount of flux-tube stretching can result in an equilibrium."," Now, in the case where $E_{\rm p}/E=1$ the field has zero magnetic helicity and no amount of flux-tube stretching can result in an equilibrium."
 However. there are diffusive processes at work which can either create helicity or split the one original flux tube into two or more tubes which can have helicity of different signs and which add up to zero. although it is likely that a lot of time will pass before any equilibrium is reached and the energy of the equilibrium will be very much lower than the original energy.," However, there are diffusive processes at work which can either create helicity or split the one original flux tube into two or more tubes which can have helicity of different signs and which add up to zero, although it is likely that a lot of time will pass before any equilibrium is reached and the energy of the equilibrium will be very much lower than the original energy."
 In this paper. I have looked at the lower and upper limits on the fractions of energ' in the poloidal and toroidal components of an axisymmetric magnetic field.," In this paper, I have looked at the lower and upper limits on the fractions of energy in the poloidal and toroidal components of an axisymmetric magnetic field."
" To tind these limits. I took the output from a simulation where a ""turbulent! initial magnetic field evolves into an axisymmetrie equilibrium. ehanged the relative strengths of the poloidal and toroidal components by hand. and used that as the initial conditions for new simulations."," To find these limits, I took the output from a simulation where a `turbulent' initial magnetic field evolves into an axisymmetric equilibrium, changed the relative strengths of the poloidal and toroidal components by hand, and used that as the initial conditions for new simulations."
 This was supplemented with more analytic methods including the necessary and sufficient stability conditions found by Tayler(1973) (it is incidentally found that four of his six conditions are always met at every point in the star)., This was supplemented with more analytic methods including the necessary and sufficient stability conditions found by \citet{Tayler:1973} (it is incidentally found that four of his six conditions are always met at every point in the star).
 The two methods are in broad agreement., The two methods are in broad agreement.
" The result of this investigation is that while the upper limit on he poloidal energy fraction £),/£7 is around SOM. the lower limit depends on factors such as the radius of the neutral line mand can be between 1% and roughly 5% for a star constructed from a xolytrope of index »=3 (which approximates to an upper-main-sequence star) and where the ratio of magnetic to thermal energies LU=L/400."," The result of this investigation is that while the upper limit on the poloidal energy fraction $E_{\rm p}/E$ is around $80\%$, the lower limit depends on factors such as the radius of the neutral line $r_{\rm n}$ and can be between $1\%$ and roughly $5\%$ for a star constructed from a polytrope of index $n=3$ (which approximates to an upper-main-sequence star) and where the ratio of magnetic to thermal energies $E/U=1/400$."
" This lower limit is expected to be proportional to he ratio {εἰς so that (£5,/Lai~LOLYt."," This lower limit is expected to be proportional to the ratio $E/U$, so that $(E_{\rm p}/E)_{\rm crit} \sim 10 E/U$."
" These limits will also depend on other factors not explicitly explored here. such as he equation of state and density profile of the star. but these should not affect the results in more than a modest quantitative manner: ywwever in a NS we might expect a lower limit of (£5,/E)~ /U."," These limits will also depend on other factors not explicitly explored here, such as the equation of state and density profile of the star, but these should not affect the results in more than a modest quantitative manner; however in a NS we might expect a lower limit of $(E_{\rm p}/E)_{\rm crit} \sim 10^3 E/U$ ."
 The upper limit found here broadly confirms what was expectedE from the analysis in Paper II and from the analyses of Wright(1973) and Markey&Tayler (19743... who found that the toroidal field must be at least about a quarter of the strength of the," The upper limit found here broadly confirms what was expected from the analysis in Paper II and from the analyses of \citet{Wright:1973} and \citet{MarandTay:1974}, , who found that the toroidal field must be at least about a quarter of the strength of the"
of the sien of the ICAL temperature eradieut.,of the sign of the ICM temperature gradient.
 In our approach. we self-cousisteutlv included the amplification of the iuagnetie feld due to the shearing motions. eas conrpresson enhanced by radiative cooling. aud the kinematic dynanio associated with the anisotropic nature of conduction.," In our approach, we self-consistently included the amplification of the magnetic field due to the shearing motions, gas compression enhanced by radiative cooling, and the kinematic dynamo associated with the anisotropic nature of conduction."
 Our key fiudiugs The software used in this work was in part developed bv the DOE-supported ASC/Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago., Our key findings The software used in this work was in part developed by the DOE-supported ASC/Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago.
 AIR thauks the staff NASA Ames Research ceuter for technical help with performing the rus at the supercomputer where most of the mus were performed., MR thanks the staff NASA Ames Research center for technical help with performing the runs at the supercomputer where most of the runs were performed.
 We are indebted το Cliris Daley for his assistance with the particle aud eravity modules iu theFLASH code., We are indebted to Chris Daley for his assistance with the particle and gravity modules in the code.
 We thauk Eliot Quatacrt. Alaxin Markeviteh. Chistoph Pfronuner. Paul Nulsen. Chnristino Jones. Larry David. Dil Forman. Milos Alilosavljevic. John Zullone. Mikhail Medvedev. Steve Balbus. and Fabian Ueitsch for Tn order to check the tuplementation of the cosinological terius in the MIID equations we evolved spatially coustant imnatter density aud magnetic field while ueelecting any velocity perturbations.," We thank Eliot Quataert, Maxim Markevitch, Christoph Pfrommer, Paul Nulsen, Christine Jones, Larry David, Bill Forman, Milos Milosavljevic, John ZuHone, Mikhail Medvedev, Steve Balbus, and Fabian Heitsch for In order to check the implementation of the cosmological terms in the MHD equations we evolved spatially constant matter density and magnetic field while neglecting any velocity perturbations."
 The result of this test is shown in Figure 9., The result of this test is shown in Figure 9.
 In the left paucl we show the scaling of the temperature (i arbitrary units) with the cosmological expansion factor e., In the left panel we show the scaling of the temperature (in arbitrary units) with the cosmological expansion factor $a$.
 Shown are ie code result for the physical temperature aud the nower law fit (solid ancl dashed Lunes are practically incdistineuishable)., Shown are the code result for the physical temperature and the power law fit (solid and dashed lines are practically indistinguishable).
 The slope of Ti)να7 agrees with je standard theoretical expectation., The slope of $T(a)\propto a^{-2}$ agrees with the standard theoretical expectation.
 The right paucl shows the plivsical maguetic field in arbitrary units as a wmiction of the scaling parameter a aid a powerlaw fit to us relation. both as a function of thie scaling paraiueter a.," The right panel shows the physical magnetic field in arbitrary units as a function of the scaling parameter $a$ and a powerlaw fit to this relation, both as a function of the scaling parameter $a$."
 Hore again the fit is perfect. the soid aud dashed lines overlap. aud the slope of. the fielda is. (B(o)X@P 7) eusures re conservation of the magnetic flux.," Here again the fit is perfect, the solid and dashed lines overlap, and the slope of the field is $B(a)\propto a^{-2}$ ) ensures the conservation of the magnetic flux."
 Iu order to test the implementation of the anisotropic thermal conduction module we compared uear theory ALTI ervowth rates with the code results, In order to test the implementation of the anisotropic thermal conduction module we compared linear theory MTI growth rates with the code results.
 This test is very simular to the one discussed ia Parrish Stone (2008)., This test is very similar to the one discussed in Parrish Stone (2008).
" That is we set up a two dimensional stratified lydrostatic atinosphere with very shallow density aud temperature profiles such that where TZ and p, are coustauts"," That is, we set up a two dimensional stratified hydrostatic atmosphere with very shallow density and temperature profiles such that where $T_{o}$ and $\rho_{o}$ are constants."
" The characteristic Ienethscale 4,4, was set to of the horizontal height", The characteristic lengthscale $y_{o}$ was set to of the horizontal height
‘Thus. when we calculate the work function for the original mocel integrating between logg<=2.24 and the surface. we obtain similar growth rate values as those of the pertllell moclel(Eig.Bg. 9)).,"Thus, when we calculate the work function for the original model integrating between $\log q \leq -2.24$ and the surface, we obtain similar growth rate values as those of the pertHeH model(Fig. \ref{fig:cmpgrou}) )."
 In the case of low racial order g-mocdes (Pig. 6...," In the case of low radial order -modes (Fig. \ref{fig:zoommiecin-deltap},"
 solid lines) some subtle mode trapping seems still to be present., solid lines) some subtle mode trapping seems still to be present.
 This may be due to remnant mode trapping elTeets caused by the C-O/Lle transition. in the same wav as cescribed below for low radial order p-moces.," This may be due to remnant mode trapping effects caused by the C-O/He transition, in the same way as described below for low radial order -modes."
 When we cancel out the sharp peak of the C-O/Lle chemical transition. keeping the Le/ll peak. we still obtain the original pattern of trapped mocles. with total kinetic energy. erowth rate ancl period dilferences similar to those of the original model (Fig. 2..," When we cancel out the sharp peak of the C-O/He chemical transition, keeping the He/H peak, we still obtain the original pattern of trapped modes, with total kinetic energy, growth rate and period differences similar to those of the original model (Fig. \ref{fig:allgkin},"
 Fig., Fig.
 3. crosses ancl dashed. lines)., \ref{fig:allgdeltap} crosses and dashed lines).
 Thus. this chemical transition plavs no role in high racial order g-mode trapping.," Thus, this chemical transition plays no role in high radial order -mode trapping."
 However. for lower order modes (Fig. 6..," However, for lower order modes (Fig. \ref{fig:zoommiecin-deltap},"
 left panel. crosses ancl dashed lines). it may have some inlluence. which is revealed in certain alterations to the total kinetic energy of each mode.," left panel, crosses and dashed lines), it may have some influence, which is revealed in certain alterations to the total kinetic energy of each mode."
 The logarithm of the total kinetic energy. and corresponcing erowth rates. for the pmode spectrum are shown in Fig. 10..," The logarithm of the total kinetic energy, and corresponding growth rates, for the -mode spectrum are shown in Fig. \ref{fig:allpkin}."
 The depicted racial orders correspond to frequencies ranging from about 6 to 25 mllz., The depicted radial orders correspond to frequencies ranging from about 6 to 25 mHz.
 There are certain modes which show values higher than the mean kinetic energv in the original and perturbed models., There are certain modes which show values higher than the mean kinetic energy in the original and perturbed models.
 We investigate if this could also be an elfect of mode trapping., We investigate if this could also be an effect of mode trapping.
 Following again the asymptotic theory of nonracdial oscillations Classoul 1050 Smoeversctal.1995: Smevers& 2007)) pemocles of the same degree £ and consecutive racial order A. will have constant frequeney separation. Av. given by: Thus. the mode trapping signature for p-mocdoes would show up in the deviations in the large frequency spacing for the original and the perturbecl Lefll model (Fig. 11)).," Following again the asymptotic theory of nonradial oscillations \citealp{tassoul80}; ; \citealp{smeyers95}; \citealp{smeyers07}) ) -modes of the same degree $\ell$ and consecutive radial order $k$, will have constant frequency separation, $\Delta \nu$, given by: Thus, the mode trapping signature for -modes would show up in the deviations in the large frequency spacing for the original and the perturbed He/H model (Fig. \ref{fig:allpdeltanuk}) )."
 We have plotted the radial and horizontal cisplacement eigenfunctions [for the original model p-modes with niaximum (p9). intermediate (ps) and minimum (p?) total kinetic energv (Fig. 12)).," We have plotted the radial and horizontal displacement eigenfunctions for the original model -modes with maximum 9), intermediate 8) and minimum 7) total kinetic energy (Fig. \ref{fig:p9p8p7y1y2}) )."
 We found that all modes. show higher amplitude in the envelope. as expected for p-modes.," We found that all modes show higher amplitude in the envelope, as expected for -modes."
 We found that the pO mode shows the highest. amplitude in the outer envelope for the 3 modes under comparison., We found that the 9 mode shows the highest amplitude in the outer envelope for the 3 modes under comparison.
 Llowever. ultimately what accounts for the higher total kinetic energy is the higher amplitude of the eigenfunctions in the innermost lavers of the star. where the moce is trapped due to the pinching elfect of the C-O/Lle interface on the cigenfunetions.," However, ultimately what accounts for the higher total kinetic energy is the higher amplitude of the eigenfunctions in the innermost layers of the star, where the mode is trapped due to the pinching effect of the C-O/He interface on the eigenfunctions."
 This can be seen in Fig., This can be seen in Fig.
 13. (elt) that shows the local contribution to the kinetic energy of the trapped. normal anc confined. modes. pO. ps. pr. respectively. normalised to the maximum ofp," \ref{fig:indecinet-trabajop9p8p7} (left) that shows the local contribution to the kinetic energy of the trapped, normal and confined modes, 9, 8, 7, respectively, normalised to the maximum of."
7 Although not shown for the sake of clarity. the maximum. kinetic energy value for the pO trapped mode reaches one order of maenitude higher.," Although not shown for the sake of clarity, the maximum kinetic energy value for the 9 trapped mode reaches one order of magnitude higher."
 The plot of the differential work for a trapped. normal and confined moce (Fig. 13..," The plot of the differential work for a trapped, normal and confined mode (Fig. \ref{fig:indecinet-trabajop9p8p7},"
 right) shows that significant energv interchange is only produced. at the Z-bump: and here. driving is higher for the trapped mode.," right) shows that significant energy interchange is only produced at the Z-bump; and there, driving is higher for the trapped mode."
 As it is the case for low-radial order g-modes. à maximum in kinetic energy does not translate into a minimum growth rate value or the mode.," As it is the case for low-radial order -modes, a maximum in kinetic energy does not translate into a minimum growth rate value for the mode."
 This is explained. by the maximum kinetic energy being due to a higher amplitude of the eigenfunctions in the region logq0.8. which for p-modes does not ive significant influence on driving.," This is explained by the maximum kinetic energy being due to a higher amplitude of the eigenfunctions in the region $\log q \gtrsim -0.8$, which for -modes does not have significant influence on driving."
 Neither do the higher amplitudes of the cigenfunetions of the trapped. mode at he driving region lead to a maximum growth rate value. as consecutive higher racial order modes have even higher amplitudes.," Neither do the higher amplitudes of the eigenfunctions of the trapped mode at the driving region lead to a maximum growth rate value, as consecutive higher radial order modes have even higher amplitudes."
 We conclude that the influence of the work function prevails over the influence of the Kinetic energy in he computation of the growth rate., We conclude that the influence of the work function prevails over the influence of the kinetic energy in the computation of the growth rate.
 Pressure modes with higher racial orders. not shown in Fig. 10..," Pressure modes with higher radial orders, not shown in Fig. \ref{fig:allpkin},"
 display kinetic energy monotonically increasing. an elfect. of the nodes accumulating in the surface limit imposed by the boundary conditions. as it is well described in Charpinetetal.(2000).," display kinetic energy monotonically increasing, an effect of the nodes accumulating in the surface limit imposed by the boundary conditions, as it is well described in \citet{charpinet00}."
.. Phe trapping effect. caused. by the C-O/LIe transition is no longer produced. as is expected [or high-radial order pure p-mocdes propagating only in the external lavers of the star.," The trapping effect caused by the C-O/He transition is no longer produced, as is expected for high-radial order pure -modes propagating only in the external layers of the star."
 When we cancel the Le/ll. or the sharp peak of the C- chemical transitions in the Brunt-Vaiisalla frequency. ancl also the corresponding bumps in the sound. speed at these locations. we still find a Kinetic energy. pattern. and an oscillating profile of the growth rate. both similar to those of the original model (Fig. 10..," When we cancel the He/H, or the sharp peak of the C-O/He chemical transitions in the Brunt-Väiisällä frequency, and also the corresponding bumps in the sound speed at these locations, we still find a kinetic energy pattern, and an oscillating profile of the growth rate, both similar to those of the original model (Fig. \ref{fig:allpkin},"
 solid and dashed lines. respectively).," solid and dashed lines, respectively)."
 Therefore. neither the Πο. nor the C-O/Le chemical transition. nor the sound speed at these locations. seem to have any significant influence on the kinetic energy or on the tendeney to driving ofthe pamocdoes.," Therefore, neither the He/H, nor the C-O/He chemical transition, nor the sound speed at these locations, seem to have any significant influence on the kinetic energy or on the tendency to driving of the -modes."
 This result was the expected. for the growth rate. for reasons given above. but not for the kinetic energy. as we presumed the modification of the C-O/lle transition would show in the kinetic energv. profile. due to changes in the amplitude of the eigenfunctions.," This result was the expected for the growth rate, for reasons given above, but not for the kinetic energy, as we presumed the modification of the C-O/He transition would show in the kinetic energy profile, due to changes in the amplitude of the eigenfunctions."
 However. eigenfunction profiles similar to those of Fig.," However, eigenfunction profiles similar to those of Fig."
 12. are retained for trapped. normal and confined modes of the perturbed. models.," \ref{fig:p9p8p7y1y2}
 are retained for trapped, normal and confined modes of the perturbed models."
 The reason may be due to that. in fact. the €C-O/Ile transition still exists(see Fig. 7.. ," The reason may be due to that, in fact, the C-O/He transition still exists(see Fig. \ref{fig:n2pert}, ,"
left) as we only cancelled out its steep peak. eiving a softer profile.," left) as we only cancelled out its steep peak, giving a softer profile."
 We conclude for the g-mode spectrum that:, We conclude for the -mode spectrum that:
suddenly steepening in the following intervaln.,suddenly steepening in the following interval.
" Unfortunately. errors are such that again we are unable to make any statements regarding changes to Zi, or Pigου."," Unfortunately, errors are such that again we are unable to make any statements regarding changes to $F_{\rm K\alpha}$ or $\Gamma_{10-20}$."
 However. we note that fic. is generally high for these time intervals associated with this hard flare event.," However, we note that $F_{\rm K\alpha}$ is generally high for these time intervals associated with this hard flare event."
 Table 6. details these results., Table \ref{tab4-rxteflare} details these results.
 As with the flare. Fig.," As with the flare, Fig."
" 12. for the flare hints at changes in P, on short time intervals (e.g. and m) It is clear from the spectral analysis thus far that conditions can alter suddenly and erratically.", \ref{fig13-xteflareplts} for the flare hints at changes in $F_{\rm K\alpha}$ on short time intervals (e.g. and ) It is clear from the spectral analysis thus far that conditions can alter suddenly and erratically.
 In order to assess whether a more simplified picture exists. we investigate spectral features of the deep minima in contrast with flare type events. using a model that consist of simple power law and redshifted Gaussian component.," In order to assess whether a more simplified picture exists, we investigate spectral features of the deep minima in contrast with flare type events, using a model that consist of simple power law and redshifted Gaussian component."
 Table 8 confirms the findings of Section 4.2.1 such that in general. I5io tends to be flatter during the minima in contrast to the flare states.," Table \ref{tab6-intgammachange} confirms the findings of Section 4.2.1 such that in general, $\Gamma_{3-10}$ tends to be flatter during the minima in contrast to the flare states."
 A close comparison of Εςτο versus Γιο5o for the differing states suggests that we are largely seeing intrinsic changes in the power law slope rather than reflection. although it is likely that we are seeing contributions from both effects.," A close comparison of $\Gamma_{3-10}$ versus $\Gamma_{10-20}$ for the differing states suggests that we are largely seeing intrinsic changes in the power law slope rather than reflection, although it is likely that we are seeing contributions from both effects."
 Additionally. ratio plots of data against model using a power law fit show that there is a noticeable change in the line flux. profile. as well as the reflection component. similar to that seen in Fig.," Additionally, ratio plots of data against model using a power law fit show that there is a noticeable change in the line flux, profile, as well as the reflection component, similar to that seen in Fig."
 7aa. We find evidence from flux-correlated studies that Εντο steepens significantly with flux CAL40~0.06 for a doubling of the flux from tof4: Fig., \ref{fig7-ratioplts}a a. We find evidence from flux-correlated studies that $\Gamma_{3-10}$ steepens significantly with flux $\rm \Delta \Gamma_{3-10} \sim 0.06$ for a doubling of the flux from to; Fig.
 13au) while surprisingly. the iron line strength appears to remain constant (at most differing by ~1.5«10 from flux-correlated studies).," \ref{fig14-fluxgammaew}a a) while surprisingly, the iron line strength appears to remain constant (at most differing by $\sim 1.5 \times 10^{-5}$ from flux-correlated studies)."
 Changes to Dj.ου GNio20~ 0.3) and Vg CAT~200 eV) are also evident and anticorrelate with flux (Fig.," Changes to $\Gamma_{10-20}$ $\rm \Delta \Gamma_{10-20} \sim
0.3$ ) and $W_{\rm K\alpha}$ $\Delta W_{\rm K\alpha} \sim 200$ eV) are also evident and anticorrelate with flux (Fig."
 |3bb for the latter)., \ref{fig14-fluxgammaew}b b for the latter).
" A close look at events corresponding to deep minima versus flares reinforces the finding that changes to the intrinsic power law slope are evident. with a comparably steeper LF,το value during the flares."," A close look at events corresponding to deep minima versus flares reinforces the finding that changes to the intrinsic power law slope are evident, with a comparably steeper $\Gamma_{3-10}$ value during the flares."
 Figs., Figs.
" 13. illustrate that the behaviour of the intrinsic photon index and Vy, during the flares is consistent with the correlated behaviour.", \ref{fig14-fluxgammaew} illustrate that the behaviour of the intrinsic photon index and $W_{\rm K\alpha}$ during the flares is consistent with the flux-correlated behaviour.
 We find that reflection increases with flux when fitting flux-separated data with a complex model that includes the reflected spectrum., We find that reflection increases with flux when fitting flux-separated data with a complex model that includes the reflected spectrum.
 Curiously. reflection. fraction /?. anticorrelates with," Curiously, reflection fraction $R$ anticorrelates with"
Cosmic ravs (CR) seem an important source of atmospheric ionisation in the solar svslem planets.,Cosmic rays (CR) seem an important source of atmospheric ionisation in the solar system planets.
 Observation of Earth clouds. however. suggest that the actual charge production is not overly efficient. but nevertheless important for coagulation processes.," Observation of Earth clouds, however, suggest that the actual charge production is not overly efficient but nevertheless important for coagulation processes."
 Nicoll Harrison (2010) determine 17...150e per particle in cloud edees on Earth which can be directly. related (ο ionisation by cosmic ravs.," Nicoll Harrison (2010) determine $17\,\ldots\,150$ e per particle in cloud edges on Earth which can be directly related to ionisation by cosmic rays."
 The charging of the cloud particles is. however. not a direct result of the impact of the high enerey CR particle on the cloud but rather of the ion current that develops from the CH. ionisation of the gas above the cloud.," The charging of the cloud particles is, however, not a direct result of the impact of the high energy CR particle on the cloud but rather of the ion current that develops from the CR ionisation of the gas above the cloud."
 These ions attach to the cloud particles., These ions attach to the cloud particles.
 The question is whether galactie cosmic rays could be a global source of ionisation [or extrasolar low-mass objects., The question is whether galactic cosmic rays could be a global source of ionisation for extrasolar low-mass objects.
 Dust clouds are an integral part of the atnosphleres of very. low mass objects like Brown Dwarls and planets., Dust clouds are an integral part of the atmospheres of very low mass objects like Brown Dwarfs and planets.
 Clouds determine the local chemistry by element consumption and they. influence the radiative and convective energy. (ransport bv (heir large opacity in the atmospheres., Clouds determine the local chemistry by element consumption and they influence the radiative and convective energy transport by their large opacity in the atmospheres.
 The aim of this paper is to demonstrate (hat dust grains in Brown Dwarl abmospheres can be charged. and to investigate whether the presence of dust in Brown Dwarl atimosphleres can contribute to ils overall ionization level. a necessary. condition for magnetic coupling of the atmosphere.," The aim of this paper is to demonstrate that dust grains in Brown Dwarf atmospheres can be charged, and to investigate whether the presence of dust in Brown Dwarf atmospheres can contribute to its overall ionization level, a necessary condition for magnetic coupling of the atmosphere."
 For (his purpose. we focused on collisional processes of the dust phase to cause additional ionization of the atmosphere. an aspect that has not vel been considered in earlier research.," For this purpose, we focused on collisional processes of the dust phase to cause additional ionization of the atmosphere, an aspect that has not yet been considered in earlier research."
 We. however. acknowledge that a large variety of micro-physical processes can be involved into the ionisation of a mineral cloud which have nol vel been taken into account in our model.," We, however, acknowledge that a large variety of micro-physical processes can be involved into the ionisation of a mineral cloud which have not yet been taken into account in our model."
 We find that collisional energies can be hieh enough to ionize the cust phase over the whole extension of atmospheric clouds of a late tvpe Brown Dwarl CIagy—1600. log(g)= 5) and over a large part in a giant. plauet's," We find that collisional energies can be high enough to ionize the dust phase over the whole extension of atmospheric clouds of a late type Brown Dwarf $_{\rm eff}$ =1600, $\log(g)=5$ ) and over a large part in a giant planet's"
"irradiance followed the actual TSI variations, observed with Virgo, to a correlation coefficient of 0.9625.","irradiance followed the actual TSI variations, observed with Virgo, to a correlation coefficient of 0.9625."
" This corresponds to a standard deviation of relative to the variation of TSI, if the error introduced by the proxy reconstruction is uncorrelated with the true light curve."," This corresponds to a standard deviation of relative to the variation of TSI, if the error introduced by the proxy reconstruction is uncorrelated with the true light curve."
" Although it is not possible to tell how this error is distributed across the solar disk, we condend that the true astrometric jitter can not belarger than our estimates by more than this amount, which is when added in quadrature."," Although it is not possible to tell how this error is distributed across the solar disk, we condend that the true astrometric jitter can not be than our estimates by more than this amount, which is when added in quadrature."
" The error is carried by many classes of different spatial scale, but only large scale perturbations count in the integration in first moment."," The error is carried by many classes of different spatial scale, but only large scale perturbations count in the integration in first moment."
" Most of this error is probably confined to small-scale structures, which should cancel in integration."," Most of this error is probably confined to small-scale structures, which should cancel in integration."
" Known imperfections, such as the ringing features centered on the centers of activity, caused by too many plage classes, do not result in an appreciable image shift."," Known imperfections, such as the ringing features centered on the centers of activity, caused by too many plage classes, do not result in an appreciable image shift."
" Besides, some of the TSI variation not accounted for by the reconstruction is due to magnetic features appearing in the outer rim of the solar disk of the radius), which is missing in our data."," Besides, some of the TSI variation not accounted for by the reconstruction is due to magnetic features appearing in the outer rim of the solar disk of the radius), which is missing in our data."
 Planets revolving around their host stars produce sinusoidal variations in the astrometric position., Planets revolving around their host stars produce sinusoidal variations in the astrometric position.
" The main harmonic of these variations has the orbital period of the planet, and an amplitude defined by the mass of the star, the mass of the planet, and the orbital semimajor axis."," The main harmonic of these variations has the orbital period of the planet, and an amplitude defined by the mass of the star, the mass of the planet, and the orbital semimajor axis."
 Planets in eccentric orbits also produce higher-order harmonics (overtones) of smaller amplitudes., Planets in eccentric orbits also produce higher-order harmonics (overtones) of smaller amplitudes.
" The spectroscopic method of exoplanet detection, based on precision measurements of stellar radial velocity, utilizes the Lomb-Scargle periodogram analysis (e.g.,Fischeretal. 2008),, which is aimed at detecting statistically significant sinusoidal variations in irregularly sampled data with a zero mean (Scargle1982).."," The spectroscopic method of exoplanet detection, based on precision measurements of stellar radial velocity, utilizes the Lomb-Scargle periodogram analysis \citep[e.g.,][]{fis}, which is aimed at detecting statistically significant sinusoidal variations in irregularly sampled data with a zero mean \citep{sca}."
" A similar ""joint"" power spectrum periodogram was suggested for 2D astrometric detection by (2008).."," A similar “joint"" power spectrum periodogram was suggested for 2D astrometric detection by \citet{cat}."
" In order to evaluate the impact of magnetic jitter on detection of low-mass planets, we employ in this paper a generalized amplitude spectrum analysis, which, unlike the periodogram, includes the constant term in the set of fitting functions."," In order to evaluate the impact of magnetic jitter on detection of low-mass planets, we employ in this paper a generalized amplitude spectrum analysis, which, unlike the Lomb-Scargle periodogram, includes the constant term in the set of fitting functions."
" A constant offset in position is a physical astrometric parameter, which can not be simply subtracted from the raw data."," A constant offset in position is a physical astrometric parameter, which can not be simply subtracted from the raw data."
 The linear problem, The linear problem
 I-structure nuplies that the rig in 2 cannot have been produced by euission.,$I$ -structure implies that the ring in $P$ cannot have been produced by emission.
 Iu the next section. we first discuss what processes can cause the observed distiibutious of P. o aud RAL in the ving.," In the next section, we first discuss what processes can cause the observed distributions of $P$, $\phi$ and $RM$ in the ring."
 Subsequeutly. we shall describe iu Sect.," Subsequently, we shall describe in Sect."
 6 some known structures and objects in the ISAL ancl discuss whether these are related to the ring structure.," \ref{s5:conn} some known structures and objects in the ISM, and discuss whether these are related to the ring structure."
 From comparison of the 7 aud P maps in Fig. 9..," From comparison of the $I$ and $P$ maps in Fig. \ref{f5:ring},"
 it is clear that the structuic dn P cannot. even iu part. be caused by structure iu I.," it is clear that the structure in $P$ cannot, even in part, be caused by structure in $I$."
 Structure in P can also be created by unissine large-scale structure iu Q iud/or U. but iu Sect.," Structure in $P$ can also be created by missing large-scale structure in $Q$ and/or $U$, but in Sect."
 2.1 we have shown that in these observations mussing large-scale structure cannot dominate.," \ref{ss5:off}
 we have shown that in these observations missing large-scale structure cannot dominate."
 Therefore. the ring in P is most lik‘ly due toa lack of depolarization.," Therefore, the ring in $P$ is most likely due to a lack of depolarization."
 Several depolarization mechamisias can contribute to create the ring in P., Several depolarization mechanisms can contribute to create the ring in $P$.
 We shall discuss briefly the different depolarization mechanisius thought to be of importance (for details see Taverkorn et 22003a.)).," We shall discuss briefly the different depolarization mechanisms thought to be of importance (for details see Haverkorn et 2003a,b)."
 Depth depolarization is defined as all depolarization processes occurring alo1g the line of sight and can be due to different plivsica processes., Depth depolarization is defined as all depolarization processes occurring along the line of sight and can be due to different physical processes.
 First. if tle magnetic feld in a svuchrotron ¢παΤο medium has small-scale structure. then the emitted Gutrinsic) polarization augle of the svuchrotron raclation will varv along the line of sight. causing wavolereth independent depolarization.," First, if the magnetic field in a synchrotron emitting medium has small-scale structure, then the emitted (intrinsic) polarization angle of the synchrotron radiation will vary along the line of sight, causing wavelength independent depolarization."
 Secondly. if the medimm also coutains thermal electrons. the polarization angle o the radiation will be modulates by Faraday rotation as well which causes additioua depolwization (internal Faraday dispersion).," Secondly, if the medium also contains thermal electrons, the polarization angle of the radiation will be modulated by Faraday rotation as well, which causes additional depolarization (internal Faraday dispersion)."
 So siuall-scale structure in (parallel) magnetic field and/or tlerma electron density within the svuchrotron euittiue medium causes simulbscale depolarization., So small-scale structure in (parallel) magnetic field and/or thermal electron density within the synchrotron emitting medium causes small-scale depolarization.
 These processes were described analytically by Sokoloff et ((1998) for severa different geometries of the nmiedinu. aud nuuercallv in Ilaverkornu et ((20035) usine observational constraints.," These processes were described analytically by Sokoloff et (1998) for several different geometries of the medium, and numerically in Haverkorn et (2003b) using observational constraints."
" We modeled the effect of depth depolarization iu the observations of the riug-structure sine simple distributions of electron density 0», and maeunetic field DB on a rectangularC» C»erid.", We modeled the effect of depth depolarization in the observations of the ring-structure using simple distributions of electron density $n_e$ and magnetic field $B$ on a rectangular grid.
 These distributions are not self-cousisteut. but the oulv goal of this simple model is to obtain a P aud o distribution that is simular to the observations. aapproximately linear m o and vine-like in P.," These distributions are not self-consistent, but the only goal of this simple model is to obtain a $P$ and $\phi$ distribution that is similar to the observations, approximately linear in $\phi$ and ring-like in $P$ ."
" Svuchrotron radiation of cuussivity ©XDi is enütted in the regions where D, is nou-zero. aud ds Faracday-rotated while propagatingo through the iieciun. depending ou the local By aud ος distributions."," Synchrotron radiation of emissivity $\varepsilon
\propto B_{\perp}^2$ is emitted in the regions where $B_{\perp}$ is non-zero, and is Faraday-rotated while propagating through the medium, depending on the local $B_{\pl}$ and $n_e$ distributions."
" Furthermore. a polarized background contribution D, is added. which is also Faracday-rvotated."," Furthermore, a polarized background contribution $P_b$ is added, which is also Faraday-rotated."
 Both magnetic field coluponcuts. parallel and perpendicular to the liue of sieht. and the electron deusity distribution were assed to decrease as a power Luv outwards.," Both magnetic field components, parallel and perpendicular to the line of sight, and the electron density distribution were assumed to decrease as a power law outwards."
 The specific values of the power law indices were chosen so that the observed o and RA distributions were approximately reproduced (Fig. 10)).," The specific values of the power law indices were chosen so that the observed $\phi$ and $RM$ distributions were approximately reproduced (Fig. \ref{f5:sim}) ),"
 tthe maenetic field decreases as 1D (oulv at ro»ry. Where ry is a free parameter 00) and the electron cleasity decreases :we 0.," the magnetic field decreases as $r^{-5}$ (only at $r > r_0$, where $r_0$ is a free parameter too) and the electron density decreases as $r^{-0.4}$."
 This figurec» shows the model oitput P aud o at 5 frequencies; and RAL.," This figure shows the model output $P$ and $\phi$ at 5 frequencies, and $RM$."
" We have chosen By=3.5µία. Dj,=2wn eo—05 ?. and P,=1 Ik. This reproduces the sipe and magnitude of o and RAL reasonablv well. but the P distribulon is very differeut frou the observed ouc."," We have chosen $B_{\pl} = -3.5~\mu$ G, $B_{\perp} = -2~\mu$ G, $n_e = 0.2$ $^{-3}$, and $P_b = 4$ K. This reproduces the shape and magnitude of $\phi$ and $RM$ reasonably well, but the $P$ distribution is very different from the observed one."
 First. the predicted P at the center is 1üuch larger thaLis observed.," First, the predicted $P$ at the center is much larger than is observed."
 However. this «liscrepancy could be explaime| by assmniueac lotic maguetic field component at the center of the circle: (vitliotuo worrving vet what this coud mean physically).," However, this discrepancy could be explained by assuming a chaotic magnetic field component at the center of the circle (without worrying yet what this could mean physically)."
 This would result o—1 depolarization :uid a lower observed Pint 1ο center of +t10 modeled circle., This would result in depolarization and a lower observed $P$ in the center of the modeled circle.
 Ilowever. a nore severe problem ds posed bv the waveleneth ependence of the model xedietions.," However, a more severe problem is posed by the wavelength dependence of the model predictions."
" Although our uxxlels lave verv cliffereut DB aud η, distributions and cther sprerical or cvlincdrica sSviunietry. they all show a disinct wavelenetl depeudeuce of the peak in P. asin Fie. 10.."," Although our models have very different $B$ and $n_e$ distributions and either spherical or cylindrical symmetry, they all show a distinct wavelength dependence of the peak in $P$, as in Fig. \ref{f5:sim}."
 But frou the observations. he position of the peak in 7? does not clange with waveleugth. see ie.o 9..," But from the observations, the position of the peak in $P$ does not change with wavelength, see Fig. \ref{f5:ring}. ."
 The wavelenetlo «epeudeuce of P aprears to be a generic property of all models involving de]volarization due to depth depolarizatio1., The wavelength dependence of $P$ appears to be a generic property of all models involving depolarization due to depth depolarization.
 Towever. the mechauisin that can create waveleneth independent depolarization. ttangled magnetic fields. vields structure iu Il. contrary to what is observed.," However, the mechanism that can create wavelength independent depolarization, tangled magnetic fields, yields structure in $I$, contrary to what is observed."
 Therefore we conclude that depth depolarization cannot be the main process that creates the ving in P. although we do expect depth depolarization to be present. iin depolarizing the backeround.," Therefore we conclude that depth depolarization cannot be the main process that creates the ring in $P$, although we do expect depth depolarization to be present, in depolarizing the background."
 Demu depolarization. fthe averaeino out of polarization vectors within oue svuthesized bean. is senificaut iu the field.," Beam depolarization, the averaging out of polarization vectors within one synthesized beam, is significant in the field."
 As there is structure in RAL on beam scales. it is likely fhat RAL varies on scales sunaller than the beau as well.," As there is structure in $RM$ on beam scales, it is likely that $RM$ varies on scales smaller than the beam as well."
" Furtheruxxe. at the »o»tious of the depolarization canals. the iuflueuce of juni depoluization is clearly visible. see Sect, SX. ("," Furthermore, at the positions of the depolarization canals, the influence of beam depolarization is clearly visible, see Sect. \ref{ss5:can}. ("
Partial) beam depolarization can destrov the linear o(M )-xelatiou. but does not necessarilv do so.,"Partial) beam depolarization can destroy the linear $\phi(\lambda^2)$ -relation, but does not necessarily do so."
 At low xlarized iuteusities. the iuffueuce of beam de]volarization can be consideralle. and observed RAL values at low volarized intensity should be 1sed with care. as they ca- deviate from the truce RAL value.," At low polarized intensities, the influence of beam depolarization can be considerable, and observed $RM$ values at low polarized intensity should be used with care, as they can deviate from the true $RM$ value."
 Deuu depolarization. due to chaotic structure d- huization angle on scales smaller than the beam. can arise dueto taneled maeuetic fields and/or sinall- variations in thermal electron ceusity.," Beam depolarization, due to chaotic structure in polarization angle on scales smaller than the beam, can arise dueto tangled magnetic fields and/or small-scale variations in thermal electron density."
 À possible explanation for the lack of P iu the central part of the ving couldbe a chaotic magnetic field in the ceuter. while the outer parts of the rime must exhibit very cohercut," A possible explanation for the lack of $P$ in the central part of the ring couldbe a chaotic magnetic field in the center, while the outer parts of the ring must exhibit very coherent"
time for anything other than the tendeney for gap formation and the elobal cise morpholgv to be inferred.,time for anything other than the tendency for gap formation and the global disc morpholgy to be inferred.
 Consequently run G4 will not be discussed further here., Consequently run G4 will not be discussed further here.
 Run G5 has been described in paper LL. ancl showed a tendeney toward. clear gap formation with the response olt1e disc due to the presence of the planet being strongly. non linear.," Run G5 has been described in paper III, and showed a tendency toward clear gap formation with the response of the disc due to the presence of the planet being strongly non linear."
 Consequently the perturbations induced in the disc bv the protoplanet are very much larger than those tha arise because of the turbulence., Consequently the perturbations induced in the disc by the protoplanet are very much larger than those that arise because of the turbulence.
 This results in the Illuctuations in the torque experienced. by the protoplanet belig sienificantly smaller (in relative terms) than observed in the previously described. runs Cl. 62. and. €i3. and a well defined running time average of the torque. being obtained.," This results in the fluctuations in the torque experienced by the protoplanet being significantly smaller (in relative terms) than observed in the previously described runs G1, G2, and G3, and a well defined running time average of the torque being obtained."
 Figure 21. shows the running time average o “the orque per unit mass obtained from run G5. with the u»per ine corresponding to the inner disc torque. the lowest line corresponding to the outer cise torque. and the middle line he running time average of the total torque.," Figure \ref{fig22} shows the running time average of the torque per unit mass obtained from run G5, with the upper line corresponding to the inner disc torque, the lowest line corresponding to the outer disc torque, and the middle line the running time average of the total torque."
 Lt is clear rom his figure that a large torque is exerted on the protoplanet ior to gap formation. but that as the gap proceecs lo open and material is pushed. away from the planet the orque diminishes.," It is clear from this figure that a large torque is exerted on the protoplanet prior to gap formation, but that as the gap proceeds to open and material is pushed away from the planet the torque diminishes."
 The running time averaged torques due o the inner and outer disc appear to be approaching well defined asymptotic values. which are unalfected by turbiwent luctuations. but the continued decrease in the running (ime averages indicates that gap formation is still ongoing at the end of the simulation.," The running time averaged torques due to the inner and outer disc appear to be approaching well defined asymptotic values, which are unaffected by turbulent fluctuations, but the continued decrease in the running time averages indicates that gap formation is still ongoing at the end of the simulation."
 We note that the use of a closed. inner boundarv dn his simulation. combined. with the close proximity of the λαοί to the inner boundary. cause the density of inner disc to be maintained at an artificially high love after gap formation.," We note that the use of a closed inner boundary in this simulation, combined with the close proximity of the planet to the inner boundary, cause the density of the inner disc to be maintained at an artificially high level after gap formation."
 This leads o the net torque on 1ο λαοί being negative out. close to zero., This leads to the net torque on the planet being negative but close to zero.
 Under more σοιlora circumstances in which 10 inner disc can accrete onto the central star. an inner cavity is expected to form such the he torque on the protoplanet is dominated. by the outer disc (e.g. Nelson et al.," Under more general circumstances in which the inner disc can accrete onto the central star, an inner cavity is expected to form such that the torque on the protoplanet is dominated by the outer disc (e.g. Nelson et al."
 2000)., 2000).
 It we adopt the dise mode described. in section 3.1 used to normatlisecl the results oresented in figure 2.. anc estimate the migration time using equation 2 and a torque per unit mass due to the outer clise in ligure 21 of 1-210 then we obtain Taig2+10! vr. for a planet at 5.2 AU.," If we adopt the disc model described in section \ref{calibration} used to normalised the results presented in figure \ref{fig2}, and estimate the migration time using equation \ref{tmig-sim} and a torque per unit mass due to the outer disc in figure \ref{fig22} of $T=-10^{-5}$, then we obtain $\tau_{mig} \simeq 4 \times 10^4$ yr, for a planet at 5.2 AU."
 The tvpe IH migration time appropriate to gap forming protoplancts is given by the viscous evolution time Tig=(-EMo) where p=all-Q is the kinematic viscosity., The type II migration time appropriate to gap forming protoplanets is given by the viscous evolution time $\tau_{mig}= (2r_p^2)/(3 \nu)$ where $\nu=\alpha H^2 \Omega$ is the kinematic viscosity.
 Fora disc model with à27.10 and {ἐν=0.01. the estimated. type Η migration tin10 ds Τοντ—45.101 vr. in: reasonable agreement with. the reult obtained from the simulation (9.," For a disc model with $\alpha \simeq 7 \times 10^{-3}$ and $H/r=0.07$, the estimated type II migration time is $\tau_{mig}=4.5 \times 10^4$ yr, in reasonable agreement with the result obtained from the simulation G5."
 We note that the above estimates for type LE migration times correspond to disc models with full 2x azimuthal domains. and that it is unclear which precise value he running mean of the outer clise torque will approach once gap formation is complete.," We note that the above estimates for type II migration times correspond to disc models with full $2 \pi$ azimuthal domains, and that it is unclear which precise value the running mean of the outer disc torque will approach once gap formation is complete."
 Nonetheless. the reasonable agreement obtained in the estimates suggests that gap forming protoplanets in turbulent disces undergo migration at the expected type LE rate;," Nonetheless, the reasonable agreement obtained in the estimates suggests that gap forming protoplanets in turbulent discs undergo migration at the expected type II rate."
 A similar result was obtain ciun paper HE for tvpe HE migration rates in turbulent disces with full 27 azimuthal domains., A similar result was obtained in paper II for type II migration rates in turbulent discs with full $2 \pi$ azimuthal domains.
 lt is clear that a well defined trend. arises. when considering the interaction between embedded protoplanets ancl turbulent cises., It is clear that a well defined trend arises when considering the interaction between embedded protoplanets and turbulent discs.
 Lower mass objects that are unable to perturh the turbulent background. flow significantly are subject to strong torque Uuctuations that are likely to dominate. their orbital evolution., Lower mass objects that are unable to perturb the turbulent background flow significantly are subject to strong torque fluctuations that are likely to dominate their orbital evolution.
 As the protoplanet mass increases so that the amplitude of the spiral wakes that it excites become larger than the turbulent density fluctuations. the relative magnitudes of the torque Iuctuations decrease. and the migration is likely to become similar to tvpe I migration (although with a significant noise component).," As the protoplanet mass increases so that the amplitude of the spiral wakes that it excites become larger than the turbulent density fluctuations, the relative magnitudes of the torque fluctuations decrease, and the migration is likely to become similar to type I migration (although with a significant noise component)."
 For larger protoplanet masses that allow eap formation. the ellect of the turbulent Ductuations is small. with the migration being essentially the same as the standard type LE picture.," For larger protoplanet masses that allow gap formation, the effect of the turbulent fluctuations is small, with the migration being essentially the same as the standard type II picture."
 These trends are also observed in the shearing box simulations that are described below., These trends are also observed in the shearing box simulations that are described below.
 Details of the shearing box simulations Bal - Bat are given in table 2.., Details of the shearing box simulations Ba1 - Ba4 are given in table \ref{table2}.
" These were cach continued. from a siniulation with fully developed: turbulence. BaO alter inserting a protoplanet with values of the dimensionless parameter CAML,PO)=ALR?(AL,HU) measuring the mass of the protoplanet equal to 0.1.0.3.1 and. 2 respectively."," These were each continued from a simulation with fully developed turbulence Ba0 after inserting a protoplanet with values of the dimensionless parameter $GM_p /( H^3\Omega_p^2) = M_p R^3/(M_* H^3)$ measuring the mass of the protoplanet equal to $0.1, 0.3, 1$ and $2$ respectively."
" In. this section. ©, and are the angular velocity and radius of the centre of the box."," In this section, $\Omega_p$ and $R$ are the angular velocity and radius of the centre of the box."
 Thus simulations Bal ancl Ba2 are directly comparable to the global simulations G2 and G8 in terms, Thus simulations Ba1 and Ba2 are directly comparable to the global simulations G2 and G3 in terms
"The best fit position for3125... found by averaging the OT order data from three IIRC-S datasets. is (CI2000) =he2022POG. the31725'|9""6 with rums Ες of zm6 iu cach COOLinate due to aaspect uncertainties.","The best fit position for, found by averaging the $0^{\rm th}$ order data from the three HRC-S datasets, is (J2000) $\alpha=07^{\rm
h}20^{\rm m}24\fs96$, $\delta=-31\degr25\arcmin49\farcs6$, with rms uncertainty of $\approx 0\farcs6$ in each coordinate due to aspect uncertainties."
 This is cousisteut (171 away) with the optical position (ναι&vauKerkwijk1998)., This is consistent $1\farcs4$ away) with the optical position \citep{kvk98}.
". The N-rav source appears unresolved and its profile is consistent with that of a point source (half-power radius of zz 05),", The X-ray source appears unresolved and its profile is consistent with that of a point source (half-power radius of $\approx 0\farcs5$ ).
 For the IIIRI data. we extracted the events within a circle of radius 145 pixels (2275) coutered ou the source;," For the HRI data, we extracted the events within a circle of radius 45 pixels $22\farcs5$ ) centered on the source."
 We used a circle of radius 200 pixels (100) for the PSPC data., We used a circle of radius 200 pixels $100\arcsec$ ) for the PSPC data.
 These events were barveeutered using the programs aud aud corrected to Barvecutric Dynamical Time (TDB) according to Cox(2000.p.11).., These events were barycentered using the programs and and corrected to Barycentric Dynamical Time (TDB) according to \citet[][p.\ 14]{allen}.
 We extracted the LLECS eveuts within a circle with radius of 25 pixels (200) centered on the source and restricted to those with pulscanvariant (PI) amplitudes that were less than 90 (energies «0.95 keV). m order to maximize the sieual-to-noise.," We extracted the LECS events within a circle with radius of 25 pixels $200\arcsec$ ) centered on the source and restricted to those with pulse-invariant (PI) amplitudes that were less than 90 (energies $< 0.95$ keV), in order to maximize the signal-to-noise."
 Finally. we barvceeutered the events with the toolbaryconv.," Finally, we barycentered the events with the tool."
". For cach dataset, we computed Z? power spectra around the known &.39-8 period."," For each dataset, we computed $Z_{1}^{2}$ power spectra around the known 8.39-s period."
 Specifically. we explored the period range from) 8.3976 s to S.105 s iu steps of7ps (oversampling bv factors of 20S00 relative the nominal step-size of PZ/AT. where Py=8.39 s is the approximate period aud AT is the span of the dataset from Table 1)).," Specifically, we explored the period range from 8.376 s to 8.405 s in steps of $7 \mbox{ }\mu{\rm s}$ (oversampling by factors of 20–800 relative the nominal step-size of $P_{0}^{2}/\Delta
T$, where $P_{0}=8.39$ s is the approximate period and $\Delta T$ is the span of the dataset from Table \ref{tab:sum}) )."
 As can be secu from Figure 1. all but the MURC-S aud IIIRI-2 datasets vielded unambiguous period estimates., As can be seen from Figure \ref{fig:zn2} all but the HRC-S and HRI-2 datasets yielded unambiguous period estimates.
 For the IIRC-S and IIRE-2 sets the period estimates are anbieuous because the large gaps iu the observations result in strong side-lobes., For the HRC-S and HRI-2 sets the period estimates are ambiguous because the large gaps in the observations result in strong side-lobes.
 In Figure 2.. we display the best-fit periods for the munambiguous determünatious as well as possible periods for the ITRC-S aud IIBE-2 datasets.," In Figure \ref{fig:sum}, we display the best-fit periods for the unambiguous determinations as well as possible periods for the HRC-S and HRI-2 datasets."
 As can be seen from Figure 2. the ambieuity of the IIRC-S aud IIRI-2 datasets can be resolved provided we assiune (reasonably) that the period evolves smoothly with time.," As can be seen from Figure \ref{fig:sum}, the ambiguity of the HRC-S and HRI-2 datasets can be resolved provided we assume (reasonably) that the period evolves smoothly with time."
 Our choice of period (for IIRC-S aud HRE2) and the best Gt periods (for the other datasets) are shown in Table 1.., Our choice of period (for HRC-S and HRI-2) and the best fit periods (for the other datasets) are shown in Table \ref{tab:sum}.
 The errors ou the periods were determined using the analytical expression from Ransom(2001)., The errors on the periods were determined using the analytical expression from \citet{ransom01}.
. While that expression was derived for FFT power spectra. Zi power spectra have the same statistics (both are exponcutially distributed) so the same relations should apply (we lave verified this with numerical simulations).," While that expression was derived for FFT power spectra, $Z_{1}^{2}$ power spectra have the same statistics (both are exponentially distributed) so the same relations should apply (we have verified this with numerical simulations)."
 We also show iuTable 1. times-of-arrival (TOAs) for cach of the datasets.," We also show inTable \ref{tab:sum}
 times-of-arrival (TOAs) for each of the datasets."
 The data in Table are consistent with there being no nieasurable P: fitting for a linear spin-down gives Po—SS91115(8) s at NJD 51633 aud, The data in Table \ref{tab:sum} are consistent with there being no measurable $\dot{P}$ : fitting for a linear spin-down gives $P=8.391115(8)$ s at MJD 51633 and
significance level.,significance level.
 Assuming that the jet emission is opticallv thin. this result if true [or I1IBLs. implies that the IIDLs show predominantly longitudinal jet. 2 fields. while the LBLs possess predominantly (ransverse jel D fields.," Assuming that the jet emission is optically thin, this result if true for HBLs, implies that the HBLs show predominantly longitudinal jet $B$ fields, while the LBLs possess predominantly transverse jet $B$ fields."
 Clearly (his bimodality in D field structure needs to be tested with a larger sample of IIBLs., Clearly this bimodality in $B$ field structure needs to be tested with a larger sample of HBLs.
 We note that the jet EVPAs of those IIBLs which have allernatively been classified as IBLs by ?.. occupy the middle of the EVPA range (between 20 - 70°).," We note that the jet EVPAs of those HBLs which have alternatively been classified as IBLs by \citet{Nieppola06}, occupy the middle of the EVPA range (between 20 - $\degr$ )."
 This behaviour also warrants further investigation., This behaviour also warrants further investigation.
 some of the IIDLs show evidence for a ‘spine-sheath’ 2 field structure. with the inner region of the jet having transverse 2 fields and the edges having longitudinal / fields.," Some of the HBLs show evidence for a `spine-sheath' $B$ field structure, with the inner region of the jet having transverse $B$ fields and the edges having longitudinal $B$ fields."
 This tvpe of 2 field structure has been observed in other blazars (727). and it could result from interaction of the jet with the surrounding medium. or due to jet acceleration being a function of the angular distance from the jel axis. producing a velocity. structure (?)..," This type of $B$ field structure has been observed in other blazars \citep{Attridge99,Giroletti04b} and it could result from interaction of the jet with the surrounding medium, or due to jet acceleration being a function of the angular distance from the jet axis, producing a velocity structure \citep{Ghisellini05}."
 Alternativelv. as ? and ? have pointed out. this could be associated with the presence of a helical 2 field associated with the jets of these objects.," Alternatively, as \citet{GabuzdaMurrayCronin04} and \citet{Lyutikov05} have pointed out, this could be associated with the presence of a helical $B$ field associated with the jets of these objects."
" Such fields could come about in a natural wav due to (he ""winding up” of a seed field via the combination of outflow. aud rotation of the central black-holeaccretion-disk system.", Such fields could come about in a natural way due to the “winding up” of a seed field via the combination of outflow and rotation of the central black-hole–accretion-disk system.
 Particularlygood examples of a 'spine-sheath! D [field structure are 1227+255 (Fig. 10)), Particularlygood examples of a `spine-sheath' $B$ field structure are 1227+255 (Fig. \ref{fig:1227}) )
 and 11214502 (Fie. 12))., and 1727+502 (Fig. \ref{fig:1727}) ).
 We were able to derive tentative (wo-epoch apparent speeds for a number of the objects in our sample from the mocdel-fitiing results in Table 5.. either on their own or combined," We were able to derive tentative two-epoch apparent speeds for a number of the objects in our sample from the model-fitting results in Table \ref{modelBLL}, , either on their own or combined"
electronic. form.,electronic form.
onlv.. They are also available [rom the authors., They are also available from the authors.
 For 10 of our 12 sample galaxies. NICMOS imaging with theZ5 is available from theS57 archive.," For 10 of our 12 sample galaxies, NICMOS imaging with the is available from the archive."
 We retrieved the re-reduced FIGOW (comparable to 4-band) images from the archive., We retrieved the re-reduced F160W (comparable to $H$ -band) images from the archive.
 However. we improved the quality of some of these images by doing additional data reduction to remove artifacts.," However, we improved the quality of some of these images by doing additional data reduction to remove artifacts."
 We relied on header. information to place the images on an astrometrically correct. erid., We relied on header information to place the images on an astrometrically correct grid.
 The images are all taken with the NIC2 camera. with a pixel size of 07075.," The images are all taken with the NIC2 camera, with a pixel size of 0.075."
 1n most cases. the image retrieved. from the archive is a combination of several individual exposures.," In most cases, the image retrieved from the archive is a combination of several individual exposures."
 For NGC 3516 and NGC 3982. however. one single exposure was available. and these images in fact improved most due to our additional data reduction.," For NGC 3516 and NGC 3982, however, one single exposure was available, and these images in fact improved most due to our additional data reduction."
 Regan Mulchaey. (1999). published: two of these images (NGC 3516 and NGC 3982)., Regan Mulchaey (1999) published two of these images (NGC 3516 and NGC 3982).
 We show the central areas of all images in bie., We show the central areas of all images in Fig.
 1. with the same scale and orientation.," 1, with the same scale and orientation."
 In most of the objects. a wealth of detail can be seen in the CNR.," In most of the objects, a wealth of detail can be seen in the CNR."
 The emission usually coincides with the location of the SE ring. and most of the individual bright knots are due to regions of current SE.," The emission usually coincides with the location of the SF ring, and most of the individual bright knots are due to regions of current SF."
 Dust lanes and/or SE regions often outline spiral-like patterns. which will be discussed in more detail below. and in Paper LL.," Dust lanes and/or SF regions often outline spiral-like patterns, which will be discussed in more detail below, and in Paper III."
 In this section. we describe some of the results of the NIIt imaging of our sample galaxies. as shown in detail in Fig.," In this section, we describe some of the results of the NIR imaging of our sample galaxies, as shown in detail in Fig."
 1(HST NIR images) and Fig., 1 NIR images) and Fig.
 2 (ground based. multi-band images and. profile fits)., 2 (ground based multi-band images and profile fits).
 A more systematic study of parameters derived. from these data in combination with optical imaging of the complete galaxy dises is forthcoming (Papers LE ane LL)., A more systematic study of parameters derived from these data in combination with optical imaging of the complete galaxy discs is forthcoming (Papers II and III).
 Our broad-band NI images are remarkably smooth. ane do not show any structure in the CN (Fig.," Our broad-band NIR images are remarkably smooth, and do not show any structure in the CNR (Fig."
 2a), 2a).
 The colour index images. however. show a red ring-like structure. possibly outlining a single spiral arm that departs from the," The colour index images, however, show a red ring-like structure, possibly outlining a single spiral arm that departs from the"
Iu real SZ observations. instrumental ioise and primary CMB cause additional errors iu the SZ statistics such as the power spectrum and peak παοι counts.,"In real SZ observations, instrumental noise and primary CMB cause additional errors in the SZ statistics such as the power spectrum and peak number counts."
 We ueed to estimate these ellects to derive optimal observing strategies to ueasure these statistics in the preseuce of noise., We need to estimate these effects to derive optimal observing strategies to measure these statistics in the presence of noise.
 With these observational errors. our methods 2)) to extract 3D eas information is liitec aud we must check their feasibility.," With these observational errors, our methods \ref{sec:application}) ) to extract 3D gas information is limited and we must check their feasibility."
 In this section. we take AMIBA as our target to address tlese Isstles.," In this section, we take AMIBA as our target to address these issues."
 AMIBA is a 19 element interferometer with 1.2 meter dishes., AMIBA is a 19 element interferometer with $1.2$ meter dishes.
 All dishes are closely packed in three concentric rings., All dishes are closely packed in three concentric rings.
 It operates at Ager=90 Ghz with Av=16 Ghz. system noise Z4=100 Is and system ellicieney 10.7.," It operates at $\nu_{\rm center}=90$ Ghz with $\Delta \nu=16$ Ghz, system noise $T_{\rm sys}=100$ K and system efficiency $\eta\sim0.7$."
 At this Lrequeney. O2—1L.6y with Sp(90Chz)0.5.," At this frequency, $\Theta\simeq -1.6y$ with $S_T(90 {\rm Ghz})\simeq0.8$."
 The goal of this experiment is to image maps of the CMB sky with are minute resolution., The goal of this experiment is to image maps of the CMB sky with arc minute resolution.
 We consider observations with fixed integration time aud aim at fiudiug the optimal sky area Q axl sky fractional coverage Fas=OfI5 for a given statistics., We consider observations with fixed integration time and aim at finding the optimal sky area $\Omega$ and sky fractional coverage $f_{\rm sky}=\Omega/4\pi$ for a given statistics.
 For closely packed interferometers observing such weak signals. te erouud fringe can be a major source of noise.," For closely packed interferometers observing such weak signals, the ground fringe can be a major source of noise."
 To eliminate the [n]0‘ound fringe. AMIBA plans to drift scan: the telescope is parked while the sky critts by.," To eliminate the ground fringe, AMIBA plans to drift scan: the telescope is parked while the sky drifts by."
 Thus assures that the grouxd frige renalus constant with time., This assures that the ground fringe remains constant with time.
 The mean value of each fringe is then subtracted [rom the SCall. Cleauly elimiuatlug the erouud.," The mean value of each fringe is then subtracted from the scan, cleanly eliminating the ground."
 A [ield is mosaicked by a series of adjacent scans. and the nost uilorn coverage Is achieved by incrementally offsetting the pointing ceuter ou each sceau to vield a finely samplec 2-D map.," A field is mosaicked by a series of adjacent scans, and the most uniform coverage is achieved by incrementally offsetting the pointing center on each scan to yield a finely sampled 2-D map."
 The raw output of the experiment are correlations. two for eacl baseine. polarizaiol and frequency chanuel correspouding to the real aud. imaginary correlat«Y outjus.," The raw output of the experiment are correlations, two for each baseline, polarization and frequency channel, corresponding to the real and imaginary correlator outputs."
 We ca1 Iüuk of each of these outputs to correspoud to an image of the sky filterec throeh some auisol‘opic beam., We can think of each of these outputs to correspond to an image of the sky filtered through some anisotropic beam.
 As a first step. we cau combine degenerate baselines ancl »olarizatiois. recluciug the 171 baselines to 30 non-degenerate baselines.," As a first step, we can combine degenerate baselines and polarizations, reducing the 171 baselines to 30 non-degenerate baselines."
 Since tle CAMB is expeced to not )e significantly inpolarized. we Call COIDDine the two polarization channels. leadiug to 60 raw inays per [requecy channel.," Since the CMB is expected to not be significantly unpolarized, we can combine the two polarization channels, leading to 60 raw maps per frequency channel."
 These Naps can be mereed optimally 1ito one globa map by couvolviug: each map wit its own beam. txd scalingl each nap to the same noise level. aud coadcding these uaps. resultiny ed ina “Clean map.," These maps can be merged optimally into one global map by convolving each map with its own beam, and scaling each map to the same noise level, and coadding these maps, resulting in a 'clean' map."
 Each of he coustiueut naps lac explicily white noise. so tlie 1olse statistics of te stunmect lap t‘e easily compuable.," Each of the constituent maps had explicitly white noise, so the noise statistics of the summed map are easily computable."
 The ‘clea1 nap can be deconvolved by the uatural beam. resulting in a --atural map.," The 'clean' map can be deconvolved by the natural beam, resulting in a 'natural' map."
 ΤΙis natural ma dIs an image of the sky. couvoved with the natt‘al beam of the telescope plus whie noise., This 'natural' map is an image of the sky convolved with the natural beam of the telescope plus white noise.
 The arele aveaged natural beam is si0wn in fig. 9.., The angle averaged natural beam is shown in fig. \ref{fig:beam}.
" The CMB intensity fluctuation df, uaeasttrec by AMIBA has three components: the primary CMB. te SZ effect aud the instrumental olse."," The CMB intensity fluctuation $\delta I_{\nu}$ measured by AMIBA has three components: the primary CMB, the SZ effect and the instrumental noise."
 I is related to the temperature [Iuctuatjou by, It is related to the temperature fluctuation by
a chain of hvdrostatie stages.,a chain of hydrostatic stages.
 “Phe assumption that TEE correlates with line formation depths can be tested as well., The assumption that TEE correlates with line formation depths can be tested as well.
 We applied our plane.parallel models to compute formation depths of the line cores of the ancl lines., We applied our plane–parallel models to compute formation depths of the line cores of the and lines.
 |t appeared that the core of the strong 4686 line forms much closer to the surface (at. column mass  0.01 ecem 7) than any of the lines., It appeared that the core of the strong 4686 line forms much closer to the surface (at column mass $\sim$ 0.01 $^{-2}$ ) than any of the lines.
 However. this was not the case with the two other lines (5411 and 4541 AY) we used in our study.," However, this was not the case with the two other lines (5411 and 4541 ) we used in our study."
 Similar tests have been carried out for other eroups of lines but assuming an LYE line formation., Similar tests have been carried out for other groups of lines but assuming an LTE line formation.
 These exercises suggest that. before. combining lines in different. groups and computing their average RVs. one has to be sure (of course under the assumption that our planeparallel models are applicable) that their depths of formation are similar.," These exercises suggest that before combining lines in different groups and computing their average RVs, one has to be sure (of course under the assumption that our plane–parallel models are applicable) that their depths of formation are similar."
 The velocity.excitation relationship found for many hot supergiants (Llutchings 1976) exists also in HD. 188209., The velocity–excitation relationship found for many hot supergiants (Hutchings 1976) exists also in HD 188209.
 In Figs., In Figs.
 5 and 6 we present plots of mean RY versus TEE and standard: deviations of the mean RY versus “TEL for the different groups of lines computed. for all dates. (the last two lines in Table 2)., 5 and 6 we present plots of mean RV versus TEE and standard deviations of the mean RV versus TEE for the different groups of lines computed for all dates (the last two lines in Table 2).
 These plots exclude a pure Ixeplerian. motion as the only cause of the ΗΝ variations., These plots exclude a pure Keplerian motion as the only cause of the RV variations.
 Pulsations and stochastic motions (intrinsic wind variations caused by some hyedrodynamical instabilities) in the wind can bring to the RV. variations as well., Pulsations and stochastic motions (intrinsic wind variations caused by some hydrodynamical instabilities) in the wind can bring to the RV variations as well.
 I£ we suppose that stochastic variations are not important. then the existence of a standard deviation-EEI. relationship would suggest that deeper lavers in the atmosphere pulsate with smaller amplitudes.," If we suppose that stochastic variations are not important, then the existence of a standard deviation-TEE relationship would suggest that deeper layers in the atmosphere pulsate with smaller amplitudes."
 “Phe aniplituce of pulsations increases when approaching to the surface., The amplitude of pulsations increases when approaching to the surface.
 The period search was carried out with help of the package (Dhillon Privett 1997) of the software., The period search was carried out with help of the package (Dhillon Privett 1997) of the software.
 The following strategy was applied when looking for a periodic signal in the RY curves of dillerent groups of lines., The following strategy was applied when looking for a periodic signal in the RV curves of different groups of lines.
 Due to the large gaps (especially between runs 5 and. 6) in our observations. we first. decided to study each of the runs 5. 6 and 7 separately.," Due to the large gaps (especially between runs 5 and 6) in our observations, we first decided to study each of the runs 5, 6 and 7 separately."
 The algorithm (Roberts et al., The algorithm (Roberts et al.
 LOST) was emploved. to cover a space of loop gains rom 0.2 to 0.6 and the number of iterations from LO to ew hundreds., 1987) was employed to cover a space of loop gains from 0.2 to 0.6 and the number of iterations from 10 to few hundreds.
 The convergence. of the periodograms was achieved for the majority of eroups of lines in all three runs., The convergence of the periodograms was achieved for the majority of groups of lines in all three runs.
 The mean frequeney suggested by most of the groups in all hree runs is O4440.05 + (2.24 days)., The mean frequency suggested by most of the groups in all three runs is $\pm$ 0.05 $^{-1}$ (2.24 days).
 However. this »eriod is very close to the Nvquist frequency Smallest Data Interval)) of the data and might be misleading.," However, this period is very close to the Nyquist frequency $\times$ Smallest Data Interval)) of the data and might be misleading."
 We have also looked for periodic signals in the combined data of all groups obtained in all runs (Table. 2)., We have also looked for periodic signals in the combined data of all groups obtained in all runs (Table 2).
" The maximum and minimum. frequencies were set to LOO and QO. respectively,"," The maximum and minimum frequencies were set to 100 and 0, respectively."
 A analysis of the time series of the majority of groups revealed a frequency of O.5140.1 days (1.95 days)., A analysis of the time series of the majority of groups revealed a frequency of $\pm$ 0.1 $^{-1}$ (1.95 days).
 The gain factor was 0.1 at the first iteration. hen was decreased. by 15-20 iteration until stabilization.," The gain factor was 0.1 at the first iteration, then was decreased by 15-20 iteration until stabilization."
 The average RY for each date obtained by averaging the Ws of allthe groups revealed a frequency. of 0470.12 lon (2.1 davs)., The average RV for each date obtained by averaging the RVs of allthe groups revealed a frequency of $\pm$ 0.12 $^{-1}$ (2.1 days).
 Again.: both frequencies⋅: are very. close o the Nyquist frequeney ane we should discard them.," Again, both frequencies are very close to the Nyquist frequency and we should discard them."
 We must point out that our periodograms did not show any »aks at frequencies smaller than 0.4., We must point out that our periodograms did not show any peaks at frequencies smaller than 0.4 $^{-1}$.
 The next strongest peak which appeared. in our periodograms was near 0.1564:0.15. + (6.4 days), The next strongest peak which appeared in our periodograms was near $\pm$ 0.15 $^{-1}$ (6.4 days).
 Clearly this period. is not alfected by sampling., Clearly this period is not affected by sampling.
 We have also analysed the RY data using the Lomb-Scargle method (Lomb 1976. Scargle 1982) which allows to compute statistical probability. of peaks in periocdograms.," We have also analysed the RV data using the Lomb-Scargle method (Lomb 1976, Scargle 1982) which allows to compute statistical probability of peaks in periodograms."
 To ensure reliable significance values. the minimum. number of permutations was set. LOO.," To ensure reliable significance values, the minimum number of permutations was set 100."
" The probability that the period is not equal to 6.4 days. was alwavs less than 30 ο,A.", The probability that the period is not equal to 6.4 days was always less than 30 $\%$.
 The peak at 6.4 days appears in all periodograms but given its significance value. we cannot definitely rule out its non-physical nature.," The peak at 6.4 days appears in all periodograms but given its significance value, we cannot definitely rule out its non-physical nature."
 In Figs., In Figs.
 7 and S we show the and the periodogranis and the fitting of a sin curve to folded data. respectively.," 7 and 8 we show the and the periodograms and the fitting of a sin curve to folded data, respectively."
 All hot supergiants have variable profiles in their spectra (Rosendahl 1973)., All hot supergiants have variable profiles in their spectra (Rosendahl 1973).
 The shape of the may vary from P (νο to inverse P €vg. double-peaked.. pure absorption and/or emission (Ebbets 1982) with typical time-scales of the order of davs.," The shape of the may vary from P Cyg to inverse P Cyg, double-peaked, pure absorption and/or emission (Ebbets 1982) with typical time-scales of the order of days."
 The nature of this variability is not vet understood., The nature of this variability is not yet understood.
 The existence of variable asymmetric outllows/infalls of matter ancl some corotating structures related. to. surface. inhomogenitics ancl possible magnetic fields have been proposed. for BA-type (Ixaufer et al., The existence of variable asymmetric outflows/infalls of matter and some corotating structures related to surface inhomogenities and possible magnetic fields have been proposed for BA-type (Kaufer et al.
 1996) and. O-tvpe (Fullerton. et. al., 1996) and O-type (Fullerton et al.
.. 1996: Ixaper. ct al., 1996; Kaper et al.
 1997) supergiants., 1997) supergiants.
 In addition. there have been. detailed: stucdes of the rotating giant loop in 7 Orionis (Ixraelian. Chentsov Musaev 1997) and the corotating spiral structures in LED. 64760 and LID 93521 (Llowarth et al.," In addition, there have been detailed studies of the rotating giant loop in $\beta$ Orionis (Israelian, Chentsov Musaev 1997) and the corotating spiral structures in HD 64760 and HD 93521 (Howarth et al."
 1998: Fullerton et al., 1998; Fullerton et al.
 1997)., 1997).
 Lt is of course very σοι to distinguish. binary svstenms from single stars without understanding the nature of variability., It is of course very difficult to distinguish binary systems from single stars without understanding the nature of variability.
 As Thaller (1907) suggests. the can suller some peculiar variability due to the colliding winds in a binary system.," As Thaller (1997) suggests, the can suffer some peculiar variability due to the colliding winds in a binary system."
 The time evolution of profiles in three cilferent runs is shown in Figure 9., The time evolution of profiles in three different runs is shown in Figure 9.
 The average profile consists of three components. a central emission. accompanied. by blue and red. absorptions.," The average profile consists of three components, a central emission accompanied by blue and red absorptions."
 We have not observed. a single profile without a central reversal., We have not observed a single profile without a central reversal.
 Ehe emission. is not always centered. exactly on the rest wavelength but is varving., The emission is not always centered exactly on the rest wavelength but is varying.
 It may approach the continuum level. go above it ancl clecrease rapidly in strength.," It may approach the continuum level, go above it and decrease rapidly in strength."
 Apparently the time-scale of the variability is at least one day., Apparently the time-scale of the variability is at least one day.
" The 5""! run has been divided into two parts (runs 5a 5b) with four successive nights in each.", The $^{\rm th}$ run has been divided into two parts (runs 5a 5b) with four successive nights in each.
 Ehe variability is observed over a wide range from about 400 to 200 kims, The variability is observed over a wide range from about $-$ 400 to 200 ${\rm km}~{\rm s}^{-1}$ .
 We have already seen in Section 4.2 that our spherical, We have already seen in Section 4.2 that our spherical
As a check on our procedure. we stack the best fits to the individual SEDs for both models.,"As a check on our procedure, we stack the best fits to the individual SEDs for both models."
 The stacks are siuilar to the purple aud orange curves in Figure 3.., The stacks are similar to the purple and orange curves in Figure \ref{fig:sed}.
 Along the same lines. we assess the qualities of the individual fits.," Along the same lines, we assess the qualities of the individual fits."
 All galaxies favor the Druzual&Chazr-lot(2003). models. with median values for (zeus aud of 0.91 and L3. respectively.," All galaxies favor the \cite{bc03} models, with median values for $\chi^2_{\rm BC03}$ and $\chi^2_{\rm M05}$ of 0.91 and 4.3, respectively."
 VaysWhereas both the Brugual&Charlot(2003) and Maraston(2005) SPS models can reproduce the aan ccolors in the selection box. the exact colors at fixed age and star formation timescale are slightlv different.," Whereas both the \cite{bc03} and \cite{ma05} SPS models can reproduce the and colors in the selection box, the exact colors at fixed age and star formation timescale are slightly different."
 Iu order to test whether these πια] differences cause ai bias that favors a particular SPS aodel. we split the post-starburst galaxy sample at το. andrepeatedth canalysis forboth samples.," In order to test whether these small differences cause a bias that favors a particular SPS model, we split the post-starburst galaxy sample at $=0.55$, and repeated the analysis for both sub-samples."
 BothSE Dsaresignificantlybetter fithythe sub BrusulC ο Tite Fulleom po dex.," Both SEDs are significantly better fit by the \cite{bc03} models (with similar fit qualities as for the full composite spectrum), where the redder sample is older by $\sim$ 0.1 dex."
" Additionally, we repeat the analysis for a redder yomndary ViniO.6. gieliingasamplcof-110 ealaxies."," Additionally, we repeat the analysis for a redder boundary $<0.6$, yielding a sample of $\sim$ 110 galaxies."
 The composite spectrum is better fit bv a slightly older stellar population. but stil strongly avors the Brugual&Charlot(2003) models above he Maraston(2005).," The composite spectrum is better fit by a slightly older stellar population, but still strongly favors the \cite{bc03} models above the \cite{ma05}."
.. Altogether. this confirms our biased selection.," Altogether, this confirms our unbiased selection."
 MacArthuretal.(2010) compare the near-infrared Huxes of two spiral galaxies to predictions frou loue-slit spectra. reporting better consistency with the Alaraston(2005) models than with Druzual&Char-ot (2003).," \cite{mac10} compare the near-infrared fluxes of two spiral galaxies to predictions from long-slit spectra, reporting better consistency with the \cite{ma05} models than with \cite{bc03}."
. However. the interpretation of their results is coniplicated by the preseuce of a siguificautlv. older stellar population. which coutributes to the total light. aud the presence of dust. which nav inimuc the effects of a TP-AGB star population.," However, the interpretation of their results is complicated by the presence of a significantly older stellar population, which contributes to the total light, and the presence of dust, which may mimic the effects of a TP-AGB star population."
 Nonetheless. if is possible that the Maraston(2005) uodel indeed provides a better description for the SED shape during the evolution phase of these spiral galaxies.," Nonetheless, it is possible that the \cite{ma05} model indeed provides a better description for the SED shape during the evolution phase of these spiral galaxies."
 Aavastonetal.(2006.2007) use the broadbaud jotonietryv of seven spectroscopically confirmed galaxies ) assess the fit quality of different SPS inodels aud find no overall preference for a particular SPS model.," \cite{ma06,ma07} use the broadband photometry of seven spectroscopically confirmed galaxies to assess the fit quality of different SPS models and find no overall preference for a particular SPS model."
 Ouly one galaxy (ID 3650) of this sample would have entered our selection (see Figure 2))., Only one galaxy (ID 3650) of this sample would have entered our selection (see Figure \ref{fig:sel}) ).
 We have re-fitted this galaxy usine the same method as for the colposite spectruni acl broadly consistent with Marastonetal.(2006) we neither find a strong xeference for a particular SPS model (see Table 1)).," We have re-fitted this galaxy using the same method as for the composite spectrum, and – broadly consistent with \cite{ma06} – we neither find a strong preference for a particular SPS model (see Table \ref{tab:mod}) )."
 Thus. the differences in fitting techniques do not account or the laree discrepancy in X? value for the composite spectrmm.," Thus, the differences in fitting techniques do not account for the large discrepancy in $\chi^2$ value for the composite spectrum."
 Moreover. as several galaxies i our sample. in particular at ligher redshift. are alinost equally well fit bv the Marastou(2005) inodels. our study is uot in disagreement with Marastonetal.(2006).," Moreover, as several galaxies in our sample, in particular at higher redshift, are almost equally well fit by the \cite{ma05} models, our study is not in disagreement with \cite{ma06}."
. This redshift dependence may be caused by the fact hat the metallicity aud dust coutent at fixed stellar nass evolve with redshift (c.e..Exbetal.2006:Nbüolinoetal. 2008).. and thus it may be possible that the contribution from TP-ACGD stars also chanees with time.," This redshift dependence may be caused by the fact that the metallicity and dust content at fixed stellar mass evolve with redshift \cite[e.g.,][]{er06,mai08}, and thus it may be possible that the contribution from TP-AGB stars also changes with time."
 We test this bv splitting our sample at 2=1.56 aud repeating the analyses for both sub-s:uuples., We test this by splitting our sample at $z=1.56$ and repeating the analyses for both sub-samples.
 Although. for both samples the Druzual&Charlot(2003) inodels provide siguificauthy better fits. the relative fit quality of the Maraston(2005) aodels versus Druzual&Char-lot(2003) increases with redshift.," Although, for both samples the \cite{bc03}
 models provide significantly better fits, the relative fit quality of the \cite{ma05} models versus \cite{bc03} increases with redshift."
 Future work might be able to separate these trends and coustrain TP-AGB models as a function of stellar mass aud metallicity., Future work might be able to separate these trends and constrain TP-AGB models as a function of stellar mass and metallicity.
 The difference in fit quality between the Druzual&Charlot(2003). and Marastou(2005) models for the conrposite post-starburst ealaxy spectrum reflects the differcut treatments of the TP-AGD phase.," The difference in fit quality between the \cite{bc03} and \cite{ma05}
 models for the composite post-starburst galaxy spectrum reflects the different treatments of the TP-AGB phase."
 Our results suggest that the treatineut by Druzual&Charlot(2003) Is tore appropriate for our post-starburst galaxy sample than that of the Maraston(2005) models., Our results suggest that the treatment by \cite{bc03} is more appropriate for our post-starburst galaxy sample than that of the \cite{ma05} models.
 We use the flexible (FSPS) models by Conroyetal.(2009.2010) to obtain a more quantitative constraint on the TP-AGB phase. as FSPS allows the modification of the bolometric huuimositv aud effective temperature of the TP-AGB stars.," We use the flexible (FSPS) models by \cite{co09,co10} to obtain a more quantitative constraint on the TP-AGB phase, as FSPS allows the modification of the bolometric luminosity and effective temperature of the TP-AGB stars."
 Werten ho lie ας) conrposite post-starburst galaxy spoectrun. restricting the wavelength region to A«6000 aand assunndug the latest default Padova TP-ACB models (Cdrardietal.2000:AMarigo&Carardi2007:ALarigoetal. 2008).," We start with the best-fit FSPS model to the composite post-starburst galaxy spectrum, restricting the wavelength region to $\lambda<6000$ and assuming the latest default Padova TP-AGB models \citep{gi00,mg07,mar08}."
. Similar to the other models. this is a stellar population with ((f/vr)29.01. ((r/yr)—85.1. aud au oof 0.£ mag (for solar metallicitv).," Similar to the other models, this is a stellar population with $t$ /yr)=9.04, $\tau$ /yr)=8.1, and an of 0.4 mag (for solar metallicity)."
 Next. we fix the age. star formation timescale and dust coutent of the stellar population aud vary both the effective temperature aud bolometric luminosity of the TP-ACB stars. quantified as shifts with respect to the Padova evolutionary tracks. aandL.. respectively.," Next, we fix the age, star formation timescale and dust content of the stellar population and vary both the effective temperature and bolometric luminosity of the TP-AGB stars, quantified as shifts with respect to the Padova evolutionary tracks, and, respectively."
 Thus. we ignore any potential degeneracies betweenT..L.. aud other stellar yopulation properties (Conroyetal.2009).," Thus, we ignore any potential degeneracies between, and other stellar population properties \citep{co09}."
. Figure L illustrates the influence of both parameters on the SED and shows their 47 contours, Figure \ref{fig:fsps} illustrates the influence of both parameters on the SED and shows their $\chi^2$ contours.
 The best fit has a reduced 47 value of 0.75. thus similar to Diruzual&Charlot(2003).," The best fit has a reduced $\chi^2$ value of 0.75, thus similar to \cite{bc03}."
. The composite post-starburst ealaxv spectrun sugeests that the predicted effective eniperatures of TP-AGD stars iu the Padova models are consistent with our observations. but the overall uninositv is ~0.5 dex lower.," The composite post-starburst galaxy spectrum suggests that the predicted effective temperatures of TP-AGB stars in the Padova models are consistent with our observations, but the overall luminosity is $\sim$ 0.5 dex lower."
 Tn this Letter. we define a photometrically selected saluple of 62 post-starburst ealaxics from the NAIBS and use their composite SED to obtain new constraints ou the SED shape during the time that the TP-ACD stars are thought to be most dominaut.," In this Letter, we define a photometrically selected sample of 62 post-starburst galaxies from the NMBS and use their composite SED to obtain new constraints on the SED shape during the time that the TP-AGB stars are thought to be most dominant."
 The SED is well fit by the Druzual&Charlot(2003) SPS models. while the Alaraston(2005) models do not reproduce the rest-frame optical and near-infrared parts of the SED simultancously. implying that these models eive too much weight to TP-AGB stars.," The SED is well fit by the \cite{bc03} SPS models, while the \cite{ma05} models do not reproduce the rest-frame optical and near-infrared parts of the SED simultaneously, implying that these models give too much weight to TP-AGB stars."
" This has previously been found by Conroy&Cuuu(2010) usimg post-starburst ealaxies in the SDSS,", This has previously been found by \cite{cg10} using post-starburst galaxies in the SDSS.
 The high-resolution photometric sampling of the NMDS allows us to derive quantitative constraiuts on the huninositv in the TP-ACGD phase., The high-resolution photometric sampling of the NMBS allows us to derive quantitative constraints on the luminosity in the TP-AGB phase.
 Using the FSPS, Using the FSPS
 (c.e.. (oe.Staneketal.2003:ILorth2003).," \citep[e.g.,][]{tota97, wije98} \citep[e.g.,][]{stan03, hjor03}, \citep[the current record is $z = 8.2$ for GRB~090423;][]{tanv09, salv09}."
. ~O.1 AL. + ," \citep[e.g.,][]{fynb03, lefl03, fruc06} $\sim$ $M_{\odot}$ $^{-1}$ \citep[e.g.,][]{sava09, leve10, sven10}."
than SERs derived from UV. optical. NIR waveleneths (c.g..Dergeretal.2003:LeFloch2006)... (," than SFRs derived from UV, optical, NIR wavelengths \citep[e.g.,][]{berg03, lefl06}. ("
2) Laree hydrogen column deusities (Αα21072 2) are observed along the line of sight to GRBs (e.g.Jakobssouetal.2006:Schady2007:Zhengct 2009)... (,"2) Large hydrogen column densities $N_{\rm H} \gsim 10^{22}$ $^{-2}$ ) are observed along the line of sight to GRBs \citep[e.g.,][]{jako06, scha07, zhen09}. ("
3) About of CRBs are vdark GRBs” (e...FyuboCereineretal. 2011).,"3) About of GRBs are “dark GRBs” \citep[e.g.,][]{fynb01, djor01, fynb09, grei11}."
. The nature of davk GRBs. which are characterized by the faintuess of their optical afterglow compared to their X-ray afterglow (Jakobssonetal.200I:vanderHorstetal. 2009).. is not vet well uuderstood and one possible explanation is due to the large dust extinction along the line of sight to GRBs (e...Perleyetal. 2009).," The nature of dark GRBs, which are characterized by the faintness of their optical afterglow compared to their X-ray afterglow \citep{jako04, vand09}, is not yet well understood and one possible explanation is due to the large dust extinction along the line of sight to GRBs \citep[e.g.,][]{perl09}."
". So far. only a small fraction of CRB hosts have been studied for which ligh obscured star formation is indicated (οιοι,Tauviretal.2001:Priddey20060)."," So far, only a small fraction of GRB hosts have been studied for which high obscured star formation is indicated \citep[e.g.,][]{tanv04, prid06}."
 Whether GRB hosts have obscured star formation is still nucertain because it is difficult to identity them when heir optical afterelows are extincted by dust., Whether GRB hosts have obscured star formation is still uncertain because it is difficult to identify them when their optical afterglows are extincted by dust.
 An alternative approach for understanding star-Oration activity iu CRB hosts is to measure the amount of molecular eas. which is the iugredieut for star orimation.," An alternative approach for understanding star-formation activity in GRB hosts is to measure the amount of molecular gas, which is the ingredient for star formation."
 The CO emission. line observatious provide he information of molecular gas mass. dynamical mass. and star-formation cficiency in CRB hosts without being affected by dust extinction.," The CO emission line observations provide the information of molecular gas mass, dynamical mass, and star-formation efficiency in GRB hosts without being affected by dust extinction."
 Thus far. oulv a few efforts ave been mace to search for 1iolecular eas in GRB hosts (Table 13): CO (10) observations of the CRB 030329 vost (IKolinoetal.2005:Endo2007).. CO (32) observations of the GRB 9850125 host (IIatsukadeetal. 2007).. and CO (32) observatious of the CRB 090123 vost (Staunwayctal.2011).," Thus far, only a few efforts have been made to search for molecular gas in GRB hosts (Table \ref{tab:summary}) ): CO (1–0) observations of the GRB 030329 host \citep{kohn05, endo07}, CO (3–2) observations of the GRB 980425 host \citep{hats07}, and CO (3–2) observations of the GRB 090423 host \citep{stan11}."
.. No CO emission has been detected froin GRB hosts and whether CRBhosts have sufficient molecular gas to παλιταπα their star formation relains unknown., No CO emission has been detected from GRB hosts and whether GRBhosts have sufficient molecular gas to maintain their star formation remains unknown.
 Iu this paper. we report a search for CO line cussion," In this paper, we report a search for CO line emission"
is for halos with mass LO?M.. and the bottom panel for 101ΔΕ. halos.,"is for halos with mass $10^{6} \Msun$, and the bottom panel for $10^{7} \Msun$ halos."
 We separated the halos out by nmiass to delineate the effect. of spin from. that of mass., We separated the halos out by mass to delineate the effect of spin from that of mass.
 We. first computed. the overall correlation function for all halos in the eiven mass range. and then used two sub-samples based on their spin parameter.," We first computed the overall correlation function for all halos in the given mass range, and then used two sub-samples based on their spin parameter."
 The cuts in spin parameter. were chosen so that one third of the halos were in the high and low spin bins respectively., The cuts in spin parameter were chosen so that one third of the halos were in the high and low spin bins respectively.
 The error bars show Poisson errors in DD). When counting halo pairs for the spin cut samples. we employed two methods.," The error bars show Poisson errors in $DD(r)$, When counting halo pairs for the spin cut samples, we employed two methods."
 First. we counted only pairs where roth halos were in the given bin. and these results are shown in Figure 3..," First, we counted only pairs where both halos were in the given bin, and these results are shown in Figure \ref{corr}."
 We also counted the pairs where only one halo was in the high or low spin bin., We also counted the pairs where only one halo was in the high or low spin bin.
 This method of counting oroduced similar results as the first method., This method of counting produced similar results as the first method.
" We find that there is a cistinction in the correlation ""unction when the data are separated by the spin parameter.", We find that there is a distinction in the correlation function when the data are separated by the spin parameter.
 Ligh spin halos are more strongly clustered than low spin 1alos. similar to the result found by Bettetal.(2007) in the Millennium Simulation.," High spin halos are more strongly clustered than low spin halos, similar to the result found by \citet{bett07} in the Millennium Simulation."
 We also find that the dillerence in clustering is preserved over a range of redshifts., We also find that the difference in clustering is preserved over a range of redshifts.
 The excess clustering is due to the fact that in a denser environment. halos feel stronger tidal torques. and thus have larger angular momentum and spin parameters.," The excess clustering is due to the fact that in a denser environment, halos feel stronger tidal torques, and thus have larger angular momentum and spin parameters."
 The correlation function can be Gt to a power-law. €(r)=GB). where BR is the correlation length.," The correlation function can be fit to a power-law, $\xi(r) = (r/R)^\gamma$, where $R$ is the correlation length."
 We find the high spin halos have a correlation length on average 25% larger than the low spin halos over the various mass ancl redshift. slices used. here., We find the high spin halos have a correlation length on average $25\%$ larger than the low spin halos over the various mass and redshift slices used here.
 The slope. 5. did not show any correlation with spin. mass. or redshift.," The slope, $\gamma$, did not show any correlation with spin, mass, or redshift."
 In this paper. we have examined. the angular momentum distribution of simulated high redshift dark matter halos and their correlation functions.," In this paper, we have examined the angular momentum distribution of simulated high redshift dark matter halos and their correlation functions."
 While the angular momentunm. distributions for this population are well fit by log-normal distributions as is the case for lower redshift and more massive halos. we find that the clustering properties of the ugh redshift population depend on the value of spin.," While the angular momentum distributions for this population are well fit by log-normal distributions as is the case for lower redshift and more massive halos, we find that the clustering properties of the high redshift population depend on the value of spin."
 For a given mass bin selecting by spin. we find that the correlation unction is higher for high spin halos.," For a given mass bin selecting by spin, we find that the correlation function is higher for high spin halos."
 This is an important rend and appears to be robust., This is an important trend and appears to be robust.
 Although in this study we aave restricted ourselves to the analysis of dark matter only simulations. the different correlation lengths of high and ow spin halos are likely to have an important impact in eedback from these carly galaxies.," Although in this study we have restricted ourselves to the analysis of dark matter only simulations, the different correlation lengths of high and low spin halos are likely to have an important impact in feedback from these early galaxies."
 Pop LLL stars appear to jwe a large impact on their environment due to radiative (Johnson.Criet.&Bromm2007:Whalenetal.2008). and supernova (Ciriefetal.2007:Whalen2008). feedback.," Pop III stars appear to have a large impact on their environment due to radiative \citep{johnson07,whalen08b} and supernova \citep{grief07,whalen08} feedback."
 We note here that in a recent paper OShea&Norman(2007) tracked the spin parameters of halos that formed the irst stars in 12 cosmological random realizations ancl cid not ind a correlation between halo spin and collapse time., We note here that in a recent paper \citet{oshea07} tracked the spin parameters of halos that formed the first stars in 12 cosmological random realizations and did not find a correlation between halo spin and collapse time.
 The, The
order of he Eddington one. the disc hickuess stavs moderate and a verticalv integrated approximalon iav be retained discs) 21.,"order of the Eddington one, the disc thickness stays moderate and a vertically integrated approximation may be retained ) \cite{abr88}."
" Iu the limit ri21. though. the beliaviou of the disc iux the possible relevance of strong outflows still remain open isstes,"," In the limit $\dot m \gg 1$, though, the behaviour of the disc and the possible relevance of strong outflows still remain open issues."
 Once again. the problem is iulcreutly 2D. aud t1C sinultauneous roles of convection. advection and outflows have to be assessed in order o model pro]xlv the expeced SED.," Once again, the problem is inherently 2D, and the simultaneous roles of convection, advection and outflows have to be assessed in order to model properly the expected SED."
" Uulike for the the optically thin ADAF/C‘DAF cases. he observable catures of these optically thick solutio have heen investigate in onlv a hateful of cases so far σον, thus reducing t general appreciation of their importance for interpreting observations."," Unlike for the the optically thin ADAF/CDAF cases, the observable features of these optically thick solutions have been investigated in only a handful of cases so far \cite{szu96,mine00}, thus reducing the general appreciation of their importance for interpreting observations."
" The ADAF solution has received a ereat deal of interest in the last decade vecause of its potential capabilitv to explain the observajonal data from our Galactic Ceuter 2771,"," The ADAF solution has received a great deal of interest in the last decade because of its potential capability to explain the observational data from our Galactic Center \cite{mf01,n02}."
 On the other laud. ecometrically hick adiabatic flows are ical models to test elobal immerical simulations of pdTWD turbuleut accretion fkws against. without having ο deal with the complicous of radiative ranster needed to simulate thin. radiative cfiicicut disces.," On the other hand, geometrically thick adiabatic flows are ideal models to test global numerical simulations of MHD turbulent accretion flows against, without having to deal with the complications of radiative transfer needed to simulate thin, radiative efficient discs."
" Indec. already when rw 1D apoxoxination of sclfsinulay ADAF theory is abandoned. aud the ""ul 2D liaure of the problem is anavsed. both from the theoretical poiut of VICW: 2277 and from inunuercal smiulatious 26.25 it is clear that radiativelv inefficient flows are prone to strong convective ΠαςταΜος aid/or powerful Olflows."," Indeed, already when the 1D approximation of self-similar ADAF theory is abandoned, and the full 2D nature of the problem is analysed, both from the theoretical point of view \cite{nia00} and from numerical simulations \cite{ia00,hb02}, it is clear that radiatively inefficient flows are prone to strong convective instabilities and/or powerful outflows."
" I1 general σος, convective flows are more likely at low walues of the viscosiv parameter. while stroug outflows are generated or hieh values of ay."," In general \cite{bb99,ia00}, convective flows are more likely at low values of the viscosity parameter, while strong outflows are generated for high values of $\alpha_{\rm v}$."
 Iu he former case (purely coivective flows). accretion is cffocively tow.-ifled. witi Little or no mass inflow or outflow: the euergv extracted 1 the Inner part is couvectively transported outward.," In the former case (purely convective flows), accretion is effectively stifled, with little or no mass inflow or outflow: the energy extracted in the inner part is convectively transported outward."
 Such a redistribution ¢ Xelorgv αλλος fiuid elements in he accreting gas alters the purely advective nature of the flow and modifies the radial profiles of plivsical quantities. as the deusity. with profound implication for the iuterpretation of the observed radiation.," Such a redistribution of energy among fluid elements in the accreting gas alters the purely advective nature of the flow and modifies the radial profiles of physical quantities, as the density, with profound implication for the interpretation of the observed radiation."
" Iu the latter case. svsteniaic outflows remove lass and energy from he flow. with little aceretion outo tle black hole σοι,"," In the latter case, systematic outflows remove mass and energy from the flow, with little accretion onto the black hole \cite{hbs01,hb02}."
" Despite the ie efforts made by several eroups. bot «n the theory aud ou the simulation side. the relative inportance of convectioi ad outflow for acliabatic flows 1s still matter of a vigorous debate 25,56. the controversy being essentially over he capability of any bydrodvuamical model supplemented with a-like viscosity prescriptions to capture the basic plivsical properties of an inherently magueto-lydrodvuamical system."," Despite the big efforts made by several groups, both on the theory and on the simulation side, the relative importance of convection and outflow for adiabatic flows is still matter of a vigorous debate \cite{bh02,nq02}, the controversy being essentially over the capability of any hydrodynamical model supplemented with $\alpha$ -like viscosity prescriptions to capture the basic physical properties of an inherently magneto-hydrodynamical system."
 As usual. it appears likely that such controversy wil oulv be settled with the collection of more constraiius observational data.," As usual, it appears likely that such controversy will only be settled with the collection of more constraining observational data."
 , 
We also note. however. that their simulated galaxy has a virial temperature below 1x10! Ix hence does not possess (he eflicient atomic cooling.,"We also note, however, that their simulated galaxy has a virial temperature below $1\times 10^4~$ K hence does not possess the efficient atomic cooling."
 It is possible that. for galaxies with efficient atomic cooling. star formation ellicieney may be much higher (than what Abel (2002) simulation indicates.," It is possible that, for galaxies with efficient atomic cooling, star formation efficiency may be much higher than what Abel (2002) simulation indicates."
 Detailed simulations will be invaluable., Detailed simulations will be invaluable.
" Finally. we note that. if star lormation in cooling shells produced by exploding massive Pop U1 stus. the ""Pop 11.5"" stars proposed bv Mackey (2003). is efficient. Chev may make a non-neeligible contribution to the pool of ionizing photons."," Finally, we note that, if star formation in cooling shells produced by exploding massive Pop III stars, the “Pop II.5"" stars proposed by Mackey (2003), is efficient, they may make a non-negligible contribution to the pool of ionizing photons."
 These stars might form at oll-center locations aud (hus might possess a relatively larger ionizing photon escape Iraction., These stars might form at off-center locations and thus might possess a relatively larger ionizing photon escape fraction.
 The counteracting factor is that these stars might be substantially less massive than the first eeneralion meltal-Iree stars. since the metallicity of the eas in the cooling shells may be «uite hieh. hence are less efficient ionizing photon emitters.," The counteracting factor is that these stars might be substantially less massive than the first generation metal-free stars, since the metallicity of the gas in the cooling shells may be quite high, hence are less efficient ionizing photon emitters."
" Adopting the best fit standard cold dark matter model with a fixed power-law index by WAIAP observations with O1;= 0.27. Q,= 0.047. A=0.73. Hj,=T2km/s/Mpe. n,=0.99 and o,=0.90 (Spergel 2003) ancl based on the observed Thomson optical depthli due to intergalaetic medium by WMADP (Ixogut 2003).B we are able to craw several relatively secure conclusions will regard to Pop LI star formation processes al very. high redshilt. ("," Adopting the best fit standard cold dark matter model with a fixed power-law index by WMAP observations with $\Omega_M=0.27$ , $\Omega_b=0.047$ , $\Lambda=0.73$, $H_0=72$ km/s/Mpc, $n_s=0.99$ and $\sigma_8=0.90$ (Spergel 2003) and based on the observed Thomson optical depth due to intergalactic medium by WMAP (Kogut 2003), we are able to draw several relatively secure conclusions with regard to Pop III star formation processes at very high redshift. ("
1) The combination of the normal Salpeter IME for Pop III metal-Iree stars and the absence of a dramatic upturn in the star formation efficiency. and/or ionizing photon escape fraction at high redshift ἐς2 6) would produce a Thomson optical depth due to IGA at reionization of z.< 0.09. inconsistent with the observed 7.=0.17£0.04 (6894) (IXogut. 2003) al >26 level. (,1) The combination of the normal Salpeter IMF for Pop III metal-free stars and the absence of a dramatic upturn in the star formation efficiency and/or ionizing photon escape fraction at high redshift $z>6$ ) would produce a Thomson optical depth due to IGM at reionization of $\tau_e \le 0.09$ inconsistent with the observed $\tau_e=0.17\pm 0.04$ $68\%$ ) (Kogut 2003) at $\ge 2\sigma$ level. (
2) A top-heavy IMIF for the Pop III metal-Iree stars and. plausible star formation efficiency and ionizing photon escape. as gauged by the corresponding values for Pop I ealaxies recuired in order (o achieve the second reionization finale al 2~6 vield 7.<0.12: (3) In the event that the metal enrichment elliciency of the intergalactie mediun by Pop HI stars is very low thus Pop II era is prolonged. one may be able to obtain 7.=0.15. (,"2) A top-heavy IMF for the Pop III metal-free stars and plausible star formation efficiency and ionizing photon escape, as gauged by the corresponding values for Pop II galaxies required in order to achieve the second reionization finale at $z\sim 6$ yield $\tau_e \le 0.12$; (3) In the event that the metal enrichment efficiency of the intergalactic medium by Pop III stars is very low thus Pop III era is prolonged, one may be able to obtain $\tau_e = 0.15$. ("
4) It seems quite improbable to reach τ>0.17 even with verv massive Pop III stus. unless (1) Che cosmological model power index » is positively tilted to n>1.03 and/or Gi) Pop HI star formation in minihalos with molecular hwdrogen cooling has an efficiency eH.fff)>0.01 (süll requiring ionizing photon escapefraction greater(han 0.3) or (Gii) alternatively.there may be unknown. non-stellar ionizing sources at very. high,"4) It seems quite improbable to reach $\tau_e \ge 0.17$ even with very massive Pop III metal-free stars, unless (i) the cosmological model power index $n$ is positively tilted to $n\ge 1.03$ and/or (ii) Pop III star formation in minihalos with molecular hydrogen cooling has an efficiency $c_*(H_2,III)>0.01$ (still requiring ionizing photon escapefraction greaterthan $0.3$ ) or (iii) alternatively,there may be unknown, non-stellar ionizing sources at very high"
"of the TLUSTY OSTAR2002 and BSTAR2006 SEDs (Lanz&Hubeny2003,2007) we can interpolate on effective temperature, surface gravity, and metallicity, as we cannot vary abundances individually.","of the TLUSTY OSTAR2002 and BSTAR2006 SEDs \citep{lanz, lanz07} we can interpolate on effective temperature, surface gravity, and metallicity, as we cannot vary abundances individually."
 We used TLUSTY to be consistent with the physical calibration of the spectral classes presented by Heapetal.(2006)., We used TLUSTY to be consistent with the physical calibration of the spectral classes presented by \citet{srh06}.
. The interpolation methods have been generalized and many other grids of stellar SEDs are available., The interpolation methods have been generalized and many other grids of stellar SEDs are available.
 We have developed a domain decomposition method to compute these grids on MPI-aware parallel machines., We have developed a domain decomposition method to compute these grids on MPI-aware parallel machines.
 Each grid point is an independent model calculation and so can be done on separate computer nodes., Each grid point is an independent model calculation and so can be done on separate computer nodes.
 'This results in a speedup that is of the order of the number of available processors., This results in a speedup that is of the order of the number of available processors.
 The capability to compute grids of photoionization models where certain key parameters are incremented in equidistant linear or logarithmic steps was introduced several years ago and has been discussed in Porteretal.(2006).., The capability to compute grids of photoionization models where certain key parameters are incremented in equidistant linear or logarithmic steps was introduced several years ago and has been discussed in \citet{porter}.
 We recently enhanced this capability by parallelizing the algorithm using the Message Passing Interface (MPI) specification., We recently enhanced this capability by parallelizing the algorithm using the Message Passing Interface (MPI) specification.
 This allows much larger grids to be computed in parallel on distributed clusters of computers., This allows much larger grids to be computed in parallel on distributed clusters of computers.
 The calculations are set up in such a way that each core calculates a separate model (domain decomposition) and all the results are gathered when the grid has finished., The calculations are set up in such a way that each core calculates a separate model (domain decomposition) and all the results are gathered when the grid has finished.
 The communication overhead is negligible since the MPI threads only need to communicate when the grid calculation starts and finishes., The communication overhead is negligible since the MPI threads only need to communicate when the grid calculation starts and finishes.
 Hence this algorithm is highly efficient and scales well to high numbers of cores for sufficiently large grids., Hence this algorithm is highly efficient and scales well to high numbers of cores for sufficiently large grids.
SERD since we have not attempted to correct for the contributions of faint sources below our flux. limits.,SFRD since we have not attempted to correct for the contributions of faint sources below our flux limits.
 The SFRD from our submillimeter sources can be estimated under the assumption that star formation domunates ACN coutributions., The SFRD from our submillimeter sources can be estimated under the assumption that star formation dominates AGN contributions.
" We can calenulate the contribution of the c6 nuuJv subinillineter sources at +=1.3 toSu, the SERD using Eq. 135:", We can calculate the contribution of the $S_{850\mu{\rm m}}>6$ mJy submillimeter sources at $z=1-3$ to the SFRD using Eq. \ref{mdot3};
 we find Uulike the nuuber distribution versus redshift. the SFRD needs large corrections for coimpleteuess due to re fact that we are detecting only relatively bright sources here (at about six times the DIunuinositv at which je subiuillimeter background is primarily resolved). aud ie distribution dN/dS mereases rapidly as 5$ decreases.," we find Unlike the number distribution versus redshift, the SFRD needs large corrections for completeness due to the fact that we are detecting only relatively bright sources here (at about six times the luminosity at which the submillimeter background is primarily resolved), and the distribution $dN/dS$ increases rapidly as $S$ decreases."
 To estimate the completeness correction. we assunie rat the ο.” of Noon S and : factorize. NfdSd.=gOSτν," To estimate the completeness correction, we assume that the dependences of $N$ on $S$ and $z$ factorize, $d^2N/dSdz=g(S)h(z)$."
 This is a plausible assuuption iu jo ubnüillimeter where the fluxes are nearly independent of redshift: nonetheless. in view of the Simail et ((1999)) y.udy. this assuniption remains to be confined.," This is a plausible assumption in the submillimeter where the fluxes are nearly independent of redshift; nonetheless, in view of the Smail et (1999b) study, this assumption remains to be confirmed."
 We can determine the completeness correction for the SFRD using the empirical uuuber distribution at juu vorsus 5$ that describes the measured submillimeter counts above nuntyv (Bareer. Cowie. Sanders 1999).," We can determine the completeness correction for the SFRD using the empirical number distribution at $\mu$ m versus $S$ that describes the measured submillimeter counts above mJy (Barger, Cowie, Sanders 1999)."
 We are iaklàiug the assumption that the flux to Ley conversion. based on Arp 220 applies in the low submillimeter flux region: the populationjustification is that even the dominant ~1 nuuJv are near-ULIG sources., We are making the assumption that the flux to $L_{FIR}$ conversion based on Arp 220 applies in the low submillimeter flux region; the justification is that even the dominant $\sim 1$ mJy population are near-ULIG sources.
 The completeness correction over all subuullumeter fluxes is therefore the measured 850 jun extragalactic background light (EBL) divided by the 850 jan light above nuudJy., The completeness correction over all submillimeter fluxes is therefore the measured $850\ \mu$ m extragalactic background light (EBL) divided by the $850\ \mu$ m light above mJy.
 The 850 jan EBL weasurement of 3.1«10+ ddeg7? from Puget et (01996) and L4s10! 3 frou Fixsen et (4905) inplyv. correction factors in the submillimeter of 1l aud 15. respectively.," The $850\ \mu$ m EBL measurement of $3.1\times 10^4$ $^{-2}$ from Puget et (1996) and $4.4\times 10^4$ $^{-2}$ from Fixsen et (1998) imply correction factors in the submillimeter of 11 and 15, respectively."
 Thus. the estimated total submillimeter contribution to the SFRD iu units of hgM.vr+Mpc?n is where we have used the factor of 11 completcucss correction.," Thus, the estimated total submillimeter contribution to the SFRD in units of $h_{65}\ \rm{M_\odot}\ \rm{yr}^{-1}\ {\rm Mpc}^{-3}$ is where we have used the factor of 11 completeness correction."
" More speculatively, we can determine the SFRD from lugher vedshift sources using our two 26 ΙΙ submillimeter sources without radio counterparts."," More speculatively, we can determine the SFRD from higher redshift sources using our two $>6$ mJy submillimeter sources without radio counterparts."
 In this case we use the volune from 2=36 and the actual area surveved in the submillimeter., In this case we use the volume from $z=3-6$ and the actual area surveyed in the submillimeter.
" We fud After including the factor of 11 completeness correction. this becomes II958 used photometric redshift estimates to infor that four of their five 5s,72 nuuJyv sources were imn the redshift range +=2.L."," We find After including the factor of 11 completeness correction, this becomes H98 used photometric redshift estimates to infer that four of their five $S_{850\mu{\rm m}}>2$ mJy sources were in the redshift range $z=2-4$."
 While these source identifications were problematic. it appears likely from the preseut work that the redshifts do lic in this rough redshift ranuec.," While these source identifications were problematic, it appears likely from the present work that the redshifts do lie in this rough redshift range."
 Using our paraincters and a scaled Απρ 220 SED. we Bud that the SERD for their sources with O4=0 is 0.10005Do;M.yr.1Mpe7.," Using our parameters and a scaled Arp 220 SED, we find that the SFRD for their sources with $\Omega_\Lambda=0$ is $0.10^{+0.08}_{-0.05}\ h_{65}\ {\rm M_\odot}\ {\rm yr}^{-1}\ {\rm Mpc}^{-3}$."
 If we make a completeness correction to include the contribution below nuuJy. we obtain SFRD-0.28!απhosM.xr|Mpe iu good agreement with our result in Eq. 21a..," If we make a completeness correction to include the contribution below mJy, we obtain $0.28^{+0.22}_{-0.14}\ h_{65}\ {\rm M_\odot}\ {\rm yr}^{-1}\ {\rm Mpc}^{-3}$, in good agreement with our result in Eq. \ref{eqtruesfrdsmma}."
 The presence of a substantial fraction of ACN-dominated ULIG sources would reduce the above SFRDs., The presence of a substantial fraction of AGN-dominated ULIG sources would reduce the above SFRDs.
 Iu a recent near-infrared spectroscopic study of 61 local ULICs. VVeilleux. Sanders. Jim (1999) found ACN characteristics in 20025 per cent of the sample. which increased to 3550 per ceut for the sample with Lyy>oP Πρ ," In a recent near-infrared spectroscopic study of 64 local ULIGs, \markcite{veilleux99}V Veilleux, Sanders, Kim (1999) found AGN characteristics in $20-25$ per cent of the sample, which increased to $35-50$ per cent for the sample with $L_{IR}>10^{12.3}\ {\rm L}_\odot$ ."
Thus. our 76 uunJy coutributions to the SFRD lav need to be reduced by a factor ~1.52.," Thus, our $>6$ mJy contributions to the SFRD may need to be reduced by a factor $\sim 1.5-2$."
 However. the lower ACN fraction in fainter ULICs seen locally suggests that AGN coutiunination may be less of an issue for the extrapolated SERD of the whole submillimeter population.," However, the lower AGN fraction in fainter ULIGs seen locally suggests that AGN contamination may be less of an issue for the extrapolated SFRD of the whole submillimeter population."
 The determination of the SFRD fron) optical observations has been a subject of inteuse investigation., The determination of the SFRD from optical observations has been a subject of intense investigation.
 Observations first indicated a rather rapid rise in the SFRD from:=01 followed by a sharp decline at higher redshifts with the peak SFRD being :1.5 (Madau ct 11996)., Observations first indicated a rather rapid rise in the SFRD from $z=0-1$ followed by a sharp decline at higher redshifts with the peak SFRD being $z\sim 1.5$ (Madau et 1996).
 A recent modification in the inferred optical SERD at low redshifts was made by CCowie. Songaila. Darger (1999). whose data indicated a more gradual rise in the SFRD than had previously beeu found by LLilly et ((1996).," A recent modification in the inferred optical SFRD at low redshifts was made by \markcite{cowie99}C Cowie, Songaila, Barger (1999), whose data indicated a more gradual rise in the SFRD than had previously been found by \markcite{lilly96}L Lilly et (1996)."
 Tt was realized that dust obscuration effects could result in factors of 3 to 5 (PPettini et 11997: MMoeurer. Heckman. Calzetti 1999) iucreases in the SERD at lugh redshift.," It was realized that dust obscuration effects could result in factors of 3 to 5 \markcite{pettini97}P Pettini et 1997; \markcite{meurer99}M Meurer, Heckman, Calzetti 1999) increases in the SFRD at high redshift."
 With these rather uncertain dust corrections taken iuto account. it has been argued that the SFRD flattous at a coustaut SPRDz0.2ligsM.xr1Mpe jin the O4=0 cosinologv for >=1...5 (Steidel et 11999).," With these rather uncertain dust corrections taken into account, it has been argued that the SFRD flattens at a constant $\rm{SFRD}\approx 0.2\ h_{65}\ \rm{M}_\odot\ \rm{yr}^{-1}\ \rm{Mpc}^{-3}$ in the $\Omega_\Lambda=0$ cosmology for $z=1-5$ (Steidel et 1999)."
 Iu Fig., In Fig.
 Hl we compare the star formation history in the optical (without extinction corrections) with that which we obtain in the submillimeter both before (Eqs., \ref{figsfrdvsz} we compare the star formation history in the optical (without extinction corrections) with that which we obtain in the submillimeter both before (Eqs.
 θα and 22a: solid triangles) aud after (Eqs., \ref{eqsfrdsmma} and \ref{eqhisfrdsmma}; solid triangles) and after (Eqs.
 2la and 23a:: solid circles) correcting for iuconipleteness., \ref{eqtruesfrdsmma} and \ref{eqhitruesfrdsmma}; solid circles) correcting for incompleteness.
 We also iuchide our newly deteriiued radio SFRD lanits (Eqs., We also include our newly determined radio SFRD limits (Eqs.
 17a. aud 18a)) on the figure as solid squares., \ref{eqlowradioa} and \ref{eqhiradioa}) ) on the figure as solid squares.
 The submillimeter contribution to the SERD interred from our 26 nuuJw observations is comparable to the ultravioletfoptical contribution to the SFRD., The submillimeter contribution to the SFRD inferred from our $>6$ mJy observations is comparable to the ultraviolet/optical contribution to the SFRD.
 The two wavelength regimes are Likely sample cdiffercut stages iu ealaxy formation., The two wavelength regimes are likely sampling different stages in galaxy formation.
 The subuullunecter detects the formation, The submillimeter detects the formation
 of the isothermal ,edge of the isothermal plateau.
"Once the planet edgedecouples, it is released inside plateau.the itself a of inward since the plateau,temperature regiongradient vanishes."," Once the planet decouples, it is released inside the plateau, itself a region of inward migration since the temperature gradient vanishes."
" As disk migrationevolution continues, the soon finds itself at the outer of the decoupledisothermal planet and starts migrating outwards."," As disk evolution continues, the decoupled planet soon finds itself at the outer edge of the isothermal plateau, and starts migrating outwards."
"edge For planets ofΜα, plateau,decoupling occurs at rp=1 AAU at MMyr 3bb)."," For planets of, decoupling occurs at $r_p$ AU at Myr b)."
 The planet then rapidly descends the temperature gradient until it reaches the outer equilibrium radius., The planet then rapidly descends the temperature gradient until it reaches the outer equilibrium radius.
" However, this radius too moves inward faster than the planet can migrate, so the planet enters the isothermal outer disk (where T~T;), another region of slow inward migration."," However, this radius too moves inward faster than the planet can migrate, so the planet enters the isothermal outer disk (where $T\simeq{T_b}$ ), another region of slow inward migration."
" At this stage, a planet of still has time to migrate from ry—2.0 AU to ry—1.5 AU before the density drops too low to drive further migration 3dd)."," At this stage, a planet of still has time to migrate from $r_p=2.0$ AU to $r_p=1.5$ AU before the density drops too low to drive further migration d)."
 The of is planetstrongly coupled and would follow the outer equilibrium radius until it hit the inner boundary of our model at AAU., The planet of is strongly coupled and would follow the outer equilibrium radius until it hit the inner boundary of our model at AU.
 The halt at AAU seen in 3ee represents an artificial termination of the simulation., The halt at AU seen in e represents an artificial termination of the simulation.
"Figure At that point, two criteria had been fulfilled."," At that point, two criteria had been fulfilled."
" First, the scale height had become smaller than the Hill radius of the so gap formation should have occurred."," First, the scale height had become smaller than the Hill radius of the planet, so gap formation should have occurred."
" This is not planet,sufficient to terminate the simulation, because the inward motion of the equilibrium radius itself occurs at the timescale of Type II "," This is not sufficient to terminate the simulation, because the inward motion of the equilibrium radius itself occurs at the timescale of Type II migration."
"However, the second criterion was that the mass migration.parameter determining Type II migration, 7? (Mordasinietal. 2009)), had become smaller than the planet's mass."," However, the second criterion was that the mass parameter determining Type II migration, $\varSigma{r^2}$ \citealp{Mordasini}) ), had become smaller than the planet's mass."
" At this Type II becomes planet dominated and we stage,consider that it migrationcomes to a halt."," At this stage, Type II migration becomes planet dominated and we consider that it comes to a halt."
 The smaller planets never carve 5aps., The smaller planets never carve gaps.
"We investigate migration in disks with different values of My and Mo, yet constrained by lifetime of without differences."," We investigate migration in disks with different values of $\dot{M}_{\rm w}$ and $\dot{M_0}$, yet constrained by a lifetime of Myr, without finding qualitative differences."
"a A in MMyr, findingbehavior is qualitativeseen for hotter disks.", A change in migration behavior is only seen for hotter disks.
" changeFor agg=0.1, migrationthe disks show onlyOz:1 throughout."," For $\alpha_{\rm SS}$ =0.1, the disks show $\varTheta \approx 1$ throughout."
 where the [ist term in each of these is (he uncorrelatecl piece that matches what we lind using results [rom our svnthetic survevs.,", where the first term in each of these is the uncorrelated piece that matches what we find using results from our synthetic surveys."
 This also matches what we expect [rom the Fisher matrix for this fit., This also matches what we expect from the Fisher matrix for this fit.
 Furthermore. lor τας=0.1725. we find that Ér220.025.," Furthermore, for $z_{\rm max}=0.1725$, we find that $r\approx 0.025$."
 We find that this value of r is consistent with the statistics of the galaxy velocities in the simulation box. where we estimated using 5.000 random galaxies. One further issue is whether or not it is advantageous to throw away low redshift data points.," We find that this value of $r$ is consistent with the statistics of the galaxy velocities in the simulation box, where we estimated using $5,000$ random galaxies, One further issue is whether or not it is advantageous to throw away low redshift data points."
 To explore this. we add a random intrinsic scatter of 0.1 mag to the SN magnitudes. in addition to the peculiar velocity error.," To explore this, we add a random intrinsic scatter of $0.1$ mag to the SN magnitudes, in addition to the peculiar velocity error."
" We (hen throw away all data points that have a final(observed) redshift below a cutoff 2y4,.", We then throw away all data points that have a final(observed) redshift below a cutoff $z_{\rm min}$.
 The resulting errors are shown in Table 4.. lor AN=500 and τς=0.1725.," The resulting errors are shown in Table \ref{zmin}, for $N=500$ and $z_{\rm max}=0.1725$."
" We thus find that the optimal minimum redshift is z44,20.02. for which we lind a 7% reduction in total error."," We thus find that the optimal minimum redshift is $z_{\rm min}\approx 0.02$, for which we find a $7\%$ reduction in total error."
 We also find. for these survey parameters. that the error due to peculiar velocities is (he same order of magnitude as (he error due to the intrinsic scatter alone.," We also find, for these survey parameters, that the error due to peculiar velocities is the same order of magnitude as the error due to the intrinsic scatter alone."
" We give some of the results of fit Gi). for zi,=0. in Table 5.. where oy is the error in O4."," We give some of the results of fit (ii), for $z_{\rm min}=0$, in Table \ref{3param}, where $\sigma_{\Lambda}$ is the error in $\Omega_{\Lambda}$."
 These errors scale asoctka and(," These errors scale as,, and."
13) This time we find i»=0.036 when τας=0.1725. which isstill consistent with our prior rough estimate [rom galaxy statistics.," This time we find $r=0.036$ when $z_{\rm max}=0.1725$, which isstill consistent with our prior rough estimate from galaxy statistics."
" By adding an intrinsic magnitude scatter of0.1 mag lo a survey with NV=500 and za,=0.1725. we now find the optimal minimum redshift to be tii,= 0.01. this time vielding a total error reduction of 9%."," By adding an intrinsic magnitude scatter of $0.1$ mag to a survey with $N=500$ and $z_{\rm max}=0.1725$, we now find the optimal minimum redshift to be $z_{\rm min}=0.01$ , this time yielding a total error reduction of $9\%$ ."
 We find once again that the, We find once again that the
"Note that as a consequence of the isospin svmmetry of the nucleon-nucleon interactions. we have and A7"" (therefore A1) does not depend on the matter composition but only on the barvon density nmn—om,|ons","Note that as a consequence of the isospin symmetry of the nucleon-nucleon interactions, we have ${\cal K}^{nn}\{n_n,n_p\}={\cal K}^{pp}\{n_p,n_n\}$ and ${\cal K}^{np}$ (therefore $\lambda_1$ ) does not depend on the matter composition but only on the baryon density $n_{\rm b}=n_n+n_p$."
" This means that entrainment effects are not allectecl by the various chemical reactions that may occur inside the core. as discussed in Section Ἐν, "," This means that entrainment effects are not affected by the various chemical reactions that may occur inside the core, as discussed in Section \ref{sect.composition}. ."
"In the high density limit ην3Land anyX1. all the elements of the mobility matrix become equal. AK""mm, "," In the high density limit $\beta_3 n_n \gg 1$ and $\beta_3 n_p \gg 1$, all the elements of the mobility matrix become equal ${\cal K}^{q q^\prime} \rightarrow m/n_{\rm b}$."
As a consequence. the non-relativistic elfective masses tend to m7/m—»nj/nmy.," As a consequence, the non-relativistic effective masses tend to $m^q_\star/m \rightarrow n_q/n_{\rm b}$."
 This asvmptotic limit which corresponds to the strongest entrainment cllects (see the discussion of Section 3)) is never reached in neutron star core for the nucleon-nucleon interactions considered in this work. since m2; is tvpicallvy of the order of I0po (see Table 3)).," This asymptotic limit which corresponds to the strongest entrainment effects (see the discussion of Section \ref{sect.non-rel.hydro}) ) is never reached in neutron star core for the nucleon-nucleon interactions considered in this work, since $m/\beta_3$ is typically of the order of $\sim 10 \rho_0$ (see Table \ref{table.forces.properties}) )."
 We have selected. elective forces according to the following criteria., We have selected effective forces according to the following criteria.
" First of all. the chosen forces have to vield. reasonable values of the ""semi-empirical saturation properties of infinite uniform symmetric nuclear matter. namely the equilibrium or saturation density vy (or the mass density po= nom). the binding energy per nucleon the symmetry energy. coefficient with =tn, nj)/m.. and the incompressibility modulus Global fits to essentially all the available experimental nuclear mass data vield ngo0.16[m. 7.0, o10 MeV. a,c2835 AleV and A220.240 MeV (2).."," First of all, the chosen forces have to yield reasonable values of the “semi-empirical” saturation properties of infinite uniform symmetric nuclear matter, namely the equilibrium or saturation density $n_0$ (or the mass density $\rho_0=n_0 m$ ), the binding energy per nucleon the symmetry energy coefficient with $I= (n_n-n_p)/n_{\rm b}$ , and the incompressibility modulus Global fits to essentially all the available experimental nuclear mass data yield $n_0 \simeq 0.16$ $^{-3}$, $a_v\simeq -16$ MeV, $a_s \simeq 28-35$ MeV and $K_\infty \simeq 220-240$ MeV \citep{lunney-03}."
 Due to the strong interactions. the mass of the individual nucleons in nuclear matter is different from the bare mass and can be written as in which m and m; are the so-called isoscalar ancl isovector effective masses respectively (see for instance 2)).," Due to the strong interactions, the mass of the individual nucleons in nuclear matter is different from the bare mass and can be written as in which $m^*_s$ and $m^*_v$ are the so-called isoscalar and isovector effective masses respectively (see for instance \citealt{farine-01}) )."
 The isovector effective mass is à crucial microscopic input since it controls directly the strength of entrainment cllects in mixtures., The isovector effective mass is a crucial microscopic input since it controls directly the strength of entrainment effects in neutron-proton mixtures.
 Indeed the parameter :2; which determines the mobility matrix. Eqs. (107)).(108))," Indeed the parameter $\beta_3$ which determines the mobility matrix, Eqs. \ref{eq.kappann}) \ref{eq.kappapp}) )"
 and. (109)). is given by In principle. this isovector cllective mass can be determined from measurements of the giant isovector clectric dipole resonance in finite nuclei (consisting of relative motions between neutrons and protons).," and \ref{eq.kappanp}) ), is given by In principle, this isovector effective mass can be determined from measurements of the giant isovector electric dipole resonance in finite nuclei (consisting of relative motions between neutrons and protons)."
 Nevertheless estimates are model dependent providing values mz/m0.7. Lat saturation density (see in particular the ciscussion of 2? in Sect., Nevertheless estimates are model dependent providing values $m^{*}_v/m\sim 0.7-1$ at saturation density (see in particular the discussion of \citealt{lunney-03} in Sect.
 HHI-D-5-0)., III-B-5-e).
 Microscopic many-body calculations in infinite uniform nuclear matter starting from the bare nucleon-nucleon interaction lead to an isovector elfective mass around m/m~0.7 (see for instance 2))., Microscopic many-body calculations in infinite uniform nuclear matter starting from the bare nucleon-nucleon interaction lead to an isovector effective mass around $m^{*}_v/m\sim 0.7$ (see for instance \citealt{zuo-06}) ).
 Besides we consider only those effective forces that have been constrained to fit the uniform infinite neutron matter equation of state., Besides we consider only those effective forces that have been constrained to fit the uniform infinite neutron matter equation of state.
 Otherwise these elective forces could not be reliably extrapolated to the neutron rich matter inside neutron star core., Otherwise these effective forces could not be reliably extrapolated to the neutron rich matter inside neutron star core.
 The main deficiencies of elective forces is the existence of instabilities that are not found by microscopic caleulations (???)..," The main deficiencies of effective forces is the existence of instabilities that are not found by microscopic calculations \citep{margueron-02, agrawal-04,lesinski-06}."
 Especially many Skyrme forces predict a spurious ferromagnetic transition in neutron matter above some critical densities., Especially many Skyrme forces predict a spurious ferromagnetic transition in neutron matter above some critical densities.
 We thus require that no such instabilities occur in the density range of interest p«3po by imposing that the dimensionless Landau parameter. usually noted Cy. be greater than 1 in neutron matter (following the analvsis of 2)).," We thus require that no such instabilities occur in the density range of interest $\rho < 3 \rho_0$ by imposing that the dimensionless Landau parameter, usually noted $G_0$, be greater than $-1$ in neutron matter (following the analysis of \citealt{margueron-02}) )."
 Ht turns out that this criterion is very restrictive., It turns out that this criterion is very restrictive.
 Several forces that reproduce reasonably well both the saturation properties of svmmetrie nuclear matter and the neutron matter equation ofstate do not pass this test., Several forces that reproduce reasonably well both the saturation properties of symmetric nuclear matter and the neutron matter equation of state do not pass this test.
 For instance. the parametrization IUVEP (?).. which was the first attempt to construct an effective force for astrophysical applications. predicts that neutron matter becomes spin polarized slightly above saturation density 20.175 [m7 (the density [or the onset. of instability is obtained by solving Gy= 1).," For instance, the parametrization RATP \citep{ratp-82}, which was the first attempt to construct an effective force for astrophysical applications, predicts that neutron matter becomes spin polarized slightly above saturation density $\simeq 0.175$ $^{-3}$ (the density for the onset of instability is obtained by solving $G_0=-1$ )."
 Likewise the forces SEM. and Skyrme 1. which have been applied to study dense matter in neutron stars and. supernova cores (7277)... vield a ferromagnetic transition density in neutron matter c0.212 (m.? and c0.256 £m.7 respectively.," Likewise the forces SkM and Skyrme $1^{\prime}$, which have been applied to study dense matter in neutron stars and supernova cores \citep{bonche-82,lattimer-85,lassaut-87, lorenz-93}, yield a ferromagnetic transition density in neutron matter $\simeq 0.212$ $^{-3}$ and $\simeq 0.256$ $^{-3}$ respectively."
 We have found that only the forces of the Saclayv-Lyon group (277).and the recent parametrization LNS (?) satisfy all the aboveconditions.," We have found that only the forces of the Saclay-Lyon group \citep{chabanat-97,chabanat-98,chabanat-err-98} and the recent parametrization LNS \citep{cao-06} satisfy all the aboveconditions."
 They. prediet a ferromagnetic instability in neutron matter like the other forces. but at significantly higher densities ~34ρυ which we do not consider in this work.," They predict a ferromagnetic instability in neutron matter like the other forces, but at significantly higher densities $\sim 3-4 \rho_0$ which we do not consider in this work."
 The force LNS seems the most appropriate to describe neutron star core since, The force LNS seems the most appropriate to describe neutron star core since
per solar mass of stars formed. was found to vary between ~10. Laud ~5«10.7 for a side rauge of possible metal-free IMEs.,"per solar mass of stars formed, was found to vary between $\sim 10^{-4}$ and $\sim 5 \times 10^{-3}$ for a wide range of possible metal-free IMFs."
 Note that while our two simple PPSN rate deusities are chosen such that thev can be casily rescaled by the reader. they are nevertheless consistent with the ranec of ;>L values predicted i more sophisticated models. as discussed iu $85.," Note that while our two simple PPSN rate densities are chosen such that they can be easily rescaled by the reader, they are nevertheless consistent with the range of $z \gtrsim 1$ values predicted in more sophisticated models, as discussed in 5."
 Furthermore. the total amount of iietals produced in our simple models is consistent with the element abundances observed in extremely metal-poor Calactic halo stars.," Furthermore, the total amount of metals produced in our simple models is consistent with the element abundances observed in extremely metal-poor Galactic halo stars."
 Asstuuing a typical value of 200 NL. of metals ejected per PPSNaud integrating down to τ=2.5. one obtains values ~6G«10?AD. ? for both of our PPSN rate deusitv models.," Assuming a typical value of 200 $\msun$ of metals ejected per PPSNand integrating down to $z=2.5$, one obtains values $\sim 6 \times 10^5 \msun$ $^{-3}$ for both of our PPSN rate density models."
 This corresponds to a mass fraction of barvous that have been processed by VMS of ~G10ον which is consistent with the 37«10. limits inferred by Oh (2001) to explain the relative abundances in extremely metal-poor Galactic stars.," This corresponds to a mass fraction of baryons that have been processed by VMS of $\sim 6 \times 10^{-5}$, which is consistent with the $3-7 \times 10^{-5}$ limits inferred by Oh (2001) to explain the relative abundances in extremely metal-poor Galactic stars."
 The resulting observed counts for these models are given in Figure { for two liiting magnitudes., The resulting observed counts for these models are given in Figure \ref{fig:Iband} for two limiting magnitudes.
 Iu the upper paucls. we take a fay=26 maguitude lnüt. appropriate for the Iustitute for Astronomy (fA) Deep Survey (Barris 2001). a erouncd-based survey that covered a total of 2.5 deg? frou September 2001 to April 2002.," In the upper panels, we take a $I_{\rm AB} = 26$ magnitude limit, appropriate for the Institute for Astronomy (IfA) Deep Survey (Barris 2004), a ground-based survey that covered a total of 2.5 $^2$ from September 2001 to April 2002."
 As we are interested in rare objects this tvpe of survey is more constraimiues that a more detailed. smaller-area searches such as theZ[ubble Wigher : Supernova Search (Riess 2001: Strolger 2001).," As we are interested in rare objects, this type of survey is more constraining that a more detailed, smaller-area searches such as the Higher $z$ Supernova Search (Riess 2004; Strolger 2004)."
 From this figure we see that existing data sects. if properly analvzed. are casily able to place usefuü constraints on VAIS formation at low redshifts.," From this figure we see that existing data sets, if properly analyzed, are easily able to place useful constraints on VMS formation at low redshifts."
 Given a typical PPSN aiodel like 200-I for example. the already realized TEA survew can be used to place a constraint of <1% of the total star formation rate density out to a redshitt ~1.," Given a typical PPSN model like 200-I for example, the already realized IfA survey can be used to place a constraint of $\lesssim 1 \%$ of the total star formation rate density out to a redshift $\sim 1$."
 Similarly. extreme models such as 250-8 can be probed out to redshifts ~2. all within the coutex of a recent SN search driven dy completely differcu science Goals.," Similarly, extreme models such as 250-S can be probed out to redshifts $\sim 2$, all within the context of a recent SN search driven by completely different science goals."
 Note however that these lits are stronglv dependent ou siguificant mixiug in the SN progenitor or he production of Ni. and thus models such as 150-2. remain largely uuconstrained by the TEA survey.," Note however that these limits are strongly dependent on significant mixing in the SN progenitor or the production of $^{56}$ Ni, and thus models such as 150-W remain largely unconstrained by the IfA survey."
 Iu the bottom panels of Figure Lowe consider a liniting naenitude of νο=27. appropriate for the COSMOSsurvev'. un ongoing project that will cover 2 dee? using he on IST.," In the bottom panels of Figure \ref{fig:Iband} we consider a limiting magnitude of $I_{\rm AB} = 27$, appropriate for the COSMOS, an ongoing project that will cover 2 $^2$ using the on HST."
 Raising the iutiug magnitude from Jap=26 to fap=27 has thexunary effect of extending the sensitivity out to slightly uigher redshifts., Raising the limiting magnitude from $I_{\rm AB} = 26$ to $I_{\rm AB} = 27$ has theprimary effect of extending the sensitivity out to slightly higher redshifts.
 This pushes the probed rauge fro11 2<1 ο τς1.5 in the 200-I case aud frou :xz2 to:<3 in the 250-S case., This pushes the probed range from $z \lesssim 1$ to $z \lesssim 1.5$ in the 200-I case and from $z \lesssim 2$ to $z \lesssim 3$ in the 250-S case.
 Again this is all in the coutext of an ongoing survey., Again this is all in the context of an ongoing survey.
 Even with this fainter limiting magnitude. rowever. low-luuinosity like 150-W are extremely difficult to find. aud remain arecly uucoustrainecd.," Even with this fainter limiting magnitude, however, low-luminosity like 150-W are extremely difficult to find, and remain largely unconstrained."
 This shortcoming ds easily overcome by moving to NIB wavelengths., This shortcoming is easily overcome by moving to NIR wavelengths.
 In Figure 5.. we calculate the PPSN coustraints that would be obtained from three possible realizations of the planned space-based (IDEAL).," In Figure \ref{fig:Hband}, , we calculate the PPSN constraints that would be obtained from three possible realizations of the planned space-based ."
 Iu the upper aud ceutral paucls, In the upper and central panels
closest to the observer.,closest to the observer.
 This curve demonstrates the fact that in addition to the largest erains. (he grains closest to (he source also add much power to the core of the scattering halo.," This curve demonstrates the fact that in addition to the largest grains, the grains closest to the source also add much power to the core of the scattering halo."
 By moving these grains closer to the observer the central scattering peak loses power accordinelv., By moving these grains closer to the observer the central scattering peak loses power accordingly.
 This fit is qualitatively about as good as the fit of the NAIRN curve with a uniform dust distribution., This fit is qualitatively about as good as the fit of the XMRN curve with a uniform dust distribution.
 It could be improved by extending the size distribution to still larger sizes while keeping the dust-lo-gas ratio constant al the original value of 0.0066., It could be improved by extending the size distribution to still larger sizes while keeping the dust-to-gas ratio constant at the original value of 0.0066.
 As demonstrated with the examples of the three uniform line-of-sight. distributions (solid. dotted. and dashed lines). the addition of still larger grains would steepen the dot-dashed profile in the central core and lower the intensity in the outer halo. as required by the observations.," As demonstrated with the examples of the three uniform line-of-sight distributions (solid, dotted, and dashed lines), the addition of still larger grains would steepen the dot-dashed profile in the central core and lower the intensity in the outer halo, as required by the observations."
 The results of our caleulations show that extending the \IRN grain size distribution to larger grain sizes. as characterized bv the NMBRN model. results in a better fit to the X-aay halo of Nova Cyvgni 1992.," The results of our calculations show that extending the MRN grain size distribution to larger grain sizes, as characterized by the XMRN model, results in a better fit to the X-ray halo of Nova Cygni 1992."
 This suggests that particles with sizes larger than 0.25 jou constitute a significant mass fraction of the interstellar dust population along one line of sight through the general ISAT., This suggests that particles with sizes larger than 0.25 $\mu$ m constitute a significant mass fraction of the interstellar dust population along one line of sight through the general ISM.
 Our results are therefore the first extension of the conclusions of Frisch et al. (, Our results are therefore the first extension of the conclusions of Frisch et al. (
1999) bevond the local Galactic neighborhood of the solar svstem.,1999) beyond the local Galactic neighborhood of the solar system.
 ILowever. in contrast to the locally-basecl result of Frisch et al. (," However, in contrast to the locally-based result of Frisch et al. ("
1999). we do not find any evidence that the dust-to-@as mass ratio along the Nova Cvgni 1992 line-ol-sight must be larger (han the canonical interstellar value.,"1999), we do not find any evidence that the dust-to-gas mass ratio along the Nova Cygni 1992 line-of-sight must be larger than the canonical interstellar value."
 We need to examine {ο what extent our conclusions depend on the specilic cust model used in the calewlations., We need to examine to what extent our conclusions depend on the specific dust model used in the calculations.
 It is possible that other functional forms of the grain size distribution. different. dust compositions. or different dust morphology may provide an improved fit to the Nova Cvgni 1992 halo.," It is possible that other functional forms of the grain size distribution, different dust compositions, or different dust morphology may provide an improved fit to the Nova Cygni 1992 halo."
CC 2 1-42 DEC DD - dy.where. rj is the inner boundary of the dise.,C = 1- 4a )^2 D = where $r_{ms}$ is the inner boundary of the disc.
" The equation of conservation of mass remains valid. while hydrostatic equilibrium in the vertical direction leads to a corrected expression for the half thickness of the disc (Riffert Herold 1995). (2)Ver where c,=(p/p) 7. p and p are the total pressure and density of the disk. respectively."," The equation of conservation of mass remains valid, while hydrostatic equilibrium in the vertical direction leads to a corrected expression for the half thickness of the disc (Riffert Herold 1995), H, where $c_{\rm
s}=(p/\rho)^{1/2}$ , $p$ and $\rho$ are the total pressure and density of the disk, respectively."
" The viscous shear 7, 1s also corrected as = OIαρ. and the angular momentum equation can be simplified as (Riffert Herold 1995. Lei et al."," The viscous shear $T_{r \phi}$ is also corrected as = - p, and the angular momentum equation can be simplified as (Riffert Herold 1995, Lei et al."
" 2009) =pepe The equation of state is PP = + habt Petpy. where Peay. Pag. Po. and p, are the gas pressure from nucleons. radiation pressure of photons. degeneracy pressure of electrons. and radiation pressure of neutrinos. respectively (see. e.g. Di Matteo et al."," 2009) = The equation of state is p = + + +, where $p_{\rm gas}$, $p_{\rm rad}$, $p_{\rm e}$, and $p_\nu$ are the gas pressure from nucleons, radiation pressure of photons, degeneracy pressure of electrons, and radiation pressure of neutrinos, respectively (see, e.g. Di Matteo et al."
 2002: Liu et al., 2002; Liu et al.
 2007)., 2007).
" The energy equation is written as = + tQ. where Qu. Quan. Όρμος and Q, are the viscous heating rate. the advective cooling rate. the cooling rate due to photodisintegration of a-particles and the cooling due to the neutrino radiation. respectively (see. e.g. Di Matteo et al."," The energy equation is written as = + +, where $Q_{\rm vis}$, $Q_{\rm adv}$, $Q_{\rm photo}$ and $Q_\nu$ are the viscous heating rate, the advective cooling rate, the cooling rate due to photodisintegration of $\alpha$ -particles and the cooling due to the neutrino radiation, respectively (see, e.g. Di Matteo et al."
 2002: Liu et al., 2002; Liu et al.
 2007)., 2007).
" The heating rate Qi, is expressed as The equation system consisting of Eqs. (", The heating rate $Q_{\rm vis}$ is expressed as = The equation system consisting of Eqs. (
1). (2). (4)-(13) is closed for an unknown precession period P. It can be numerically solved for a given parameter set of M. M. a. and a.,"1), (2), (4)-(13) is closed for an unknown precession period $P$ It can be numerically solved for a given parameter set of $M$ $\dot{M}$ , $a$ , and $\alpha$."
 We show P as a function of M for the parameter sets («à=0.9. M=Μα a= 0.01). (a= 0.9. M=3M. e= 0.1). (a=0.Ι. M2 3M.«= 0.1) and (a=0.1. M=3M. av= 0.01) in Fig.," We show $P$ as a function of $\dot{M}$ for the parameter sets $a=0.9$, $M = 3 M_\odot$, $\alpha=0.01$ ), $a=0.9$ , $M = 3 M_\odot$, $\alpha=0.1$ ), $a=0.1$, $M = 3 M_\odot$, $\alpha=0.1$ ) and $a=0.1$, $M = 3 M_\odot$, $\alpha=0.01$ ) in Fig."
 2., 2.
 It is found that P varies from tens of milliseconds to 10 ks. if M=001~10 Mis. a=0.01~0.1. anda=0.1~0.9.," It is found that $P$ varies from tens of milliseconds to 10 ks, if $\dot{M}=0.01\sim 10$ $M_\odot$ /s, $\alpha=0.01\sim 0.1$, and $a=0.1\sim 0.9$."
 It can approach the timescale of lighteurve or be longer than the accretion timescale whose provide a couple of possibilitiesof lightcurve., It can approach the timescale of lightcurve or be longer than the accretion timescale whose provide a couple of possibilitiesof lightcurve.
 Incollapsar scenario. the centralblack holewould be rapidly rotates. 1.e.. ¢ 0.9.For the compact object mergers.the spinof theblack hole is not strictly as high asthat in the," Incollapsar scenario, the centralblack holewould be rapidly rotates, i.e., $a\gtrsim 0.9$ .For the compact object mergers,the spinof theblack hole is not strictly as high asthat in the"
with a possibly different coustaut C that depend ou 7.,with a possibly different constant $C$ that depend on $T$.
 Iudeed. the terii 7 enters in estimating oyphUU since (3.16)) is now replaced (see again Figure 3)) by This shows the claim.," Indeed, the term $T$ enters in estimating $\<\Psi\tilde{f}\>^{(\g/2)}_{t,\R^{2}}$ since \ref{fin_add}) ) is now replaced (see again Figure \ref{fig3}) ) by This shows the claim."
 oO , $\hfill{\Box}$ 
" Atz~ 5,? reported the UV LF from a combination of HDF and Subaru images, totalling a survey area about 1/9 of ours.","At $z\sim5$ , \citet{iwata07} reported the UV LF from a combination of HDF and Subaru images, totalling a survey area about 1/9 of ours."
? based their study on approximately 100 LBGs from very deep ACS and NICMOS imaging., \citet{oesch07} based their study on approximately 100 LBGs from very deep ACS and NICMOS imaging.
" ? also defined a z~5 sample from their observations, combining Vi'z and Ri’z’ selected objects, as did ?.."," \citet{yoshida06} also defined a $z\sim 5$ sample from their observations, combining $Vi'z'$ and $Ri'z'$ selected objects, as did \citet{ouchi04a}. ."
 ? selected 275 Veo6i775Zg50 LBGs to estimate az~5 UV LE, \citet{giavalisco04} selected 275 $V_{606}i_{775}z_{850}$ LBGs to estimate a $z\sim 5$ UV LF.
" ? also measured a sample of 1416 V-dropouts from their deep HST ACS sample, which resulted in an estimation of the UV LF down to Mj600,48=—17.16."," \citet{bouwens07} also measured a sample of 1416 V-dropouts from their deep HST ACS sample, which resulted in an estimation of the UV LF down to $M_{1600,AB}=-17.16$."
" Similar to the Schechter parameters found for z~4, there is. a large discrepancy. in. the literature. for the Schechter parameters at z~5."," Similar to the Schechter parameters found for $z \sim 4$, there is a large discrepancy in the literature for the Schechter parameters at $z \sim 5$."
 The statistical uncertainties in the Schechter parameters is very small for our r-dropout sample., The statistical uncertainties in the Schechter parameters is very small for our $r$ -dropout sample.
" Note however that several systematic uncertainties are not included in these error ellipses, see Sect. 4.3.."," Note however that several systematic uncertainties are not included in these error ellipses, see Sect. \ref{sec:robust}."
" Our results agree reasonably well, within the 1—o level, with many previous determinations at z~5."," Our results agree reasonably well, within the $1-\sigma$ level, with many previous determinations at $z\sim 5$."
 In Fig., In Fig.
" 14. we compare the SFR density values given in Table 3 to values reported by ?,, who made use of z GALEX data, ? at intermediate z, and ? at high z."," \ref{fig:sfrd} we compare the SFR density values given in Table \ref{tab:sfrd} to values reported by \citet{schiminovich05}, who made use of $z$ GALEX data, \citet{reddy09} at intermediate $z$, and \citet{bouwens09} at high $z$."
 The uncorrected SFRDs are in good agreement with each other and show a smooth redshift evolution., The uncorrected SFRDs are in good agreement with each other and show a smooth redshift evolution.
" However, it is clear that the dust correction is the major uncertainty because of the age-dust degeneracy."," However, it is clear that the dust correction is the major uncertainty because of the age-dust degeneracy."
 We use the same dust correction as ? and also include systematic uncertainties in the error bars., We use the same dust correction as \citet{bouwens09} and also include systematic uncertainties in the error bars.
" In this paper we use the CFHT Legacy Survey Deep fields to estimate the UV Luminosity Functions of the largest u, g-, and r-dropouts samples to date."," In this paper we use the CFHT Legacy Survey Deep fields to estimate the UV Luminosity Functions of the largest $u$, $g$ -, and $r$ -dropouts samples to date."
 As our samples are all extracted from the same dataset this study is ideally suitedto study a timeevolution of the luminosity function in the redshift, As our samples are all extracted from the same dataset this study is ideally suitedto study a timeevolution of the luminosity function in the redshift
respectively the poloidal aud toroidal field components. evaluated at the surface of the filament: The dots. squares. aud x's represent models of types 1. 2 and 3 respectively.,"respectively the poloidal and toroidal field components, evaluated at the surface of the filament: The dots, squares, and x's represent models of types 1, 2, and 3 respectively."
" Note that D.ςD,s is sinall or nanv of our models because the toroidal maeuetic field dominates iu he outer cuvelope. Lear the radius of pressure truncation."," Note that $\ratio$ is small for many of our models because the toroidal magnetic field dominates in the outer envelope, near the radius of pressure truncation."
 The ratio of: D.FB. is substanwally higher iu he interior regions of the filameut., The ratio of $\Bz/\Bphi$ is substantially higher in the interior regions of the filament.
 Au interesting feature of Figure 2 is that the polarization outterus are of he first type for a large portion of our models., An interesting feature of Figure \ref{fig:space} is that the polarization patterns are of the first type for a large portion of our models.
 Thus. may of our 110dels are qualitativedv simular to the Alatthews aud Wilson (2000) map of the Orion filament. discussed ii1 Section [.2..," Thus, many of our models are qualitatively similar to the Matthews and Wilson (2000) map of the Orion filament, discussed in Section \ref{sec:patterns}."
 We Bud this type opattern for most models with B.ςλες~0.1., We find this type of pattern for most models with $\ratio\appleq 0.1$.
 Generally. polarization patterus of the second type occur when Bes/Bos~0.33. and the third type occurs for interiuediate values between abou 0.1 αnd 0.33.," Generally, polarization patterns of the second type occur when $\ratio\appgeq 0.33$, and the third type occurs for intermediate values between about 0.1 and 0.33."
 This may be uuderstood as follows., This may be understood as follows.
" When D.s/D,,s is sua1. the models are dominated by the toroidal field component so that he xoloidal field is ineffective at canceling the polarization due to the toroidal field. as discussed iu Section [.2.."," When $\ratio$ is small, the models are dominated by the toroidal field component so that the poloidal field is ineffective at canceling the polarization due to the toroidal field, as discussed in Section \ref{sec:patterns}."
 Thus. the polarization pattern is of tvpe L.," Thus, the polarization pattern is of type 1."
" However. ax B.s is mereased relative to D,,s. he competition becomes stronger 1util D.« becomes dominant along some line of sight. which first occurs whe1 D.s/D,,«szOL."," However, as $\Bzs$ is increased relative to $\Bphis$, the competition becomes stronger until $\Bzs$ becomes dominant along some line of sight, which first occurs when $\ratio \approx 0.1$."
 This results iu a 907 Hip in the polarization vectors at this position. which we categorizet( as the first Type 5n model.," This results in a $90^\circ$ flip in the polarization vectors at this position, which we categorize as the first Type 3 model."
 The exact opposite occurs when Bogδις is increased past about k:?)ὃν, The exact opposite occurs when $\ratio$ is increased past about $0.33$.
 Past this poiut. the toroidal feld. component becomes too weak compared to the poloidal field to POCuce a flip in the polarization vectors resulΠιο in Type 2 patterns.," Past this point, the toroidal field component becomes too weak compared to the poloidal field to produce a flip in the polarization vectors resulting in Type 2 patterns."
 Figure 3.Mi shows the deeree to which the Cluission is depolarized for all three types of polarizatio- ottern., Figure \ref{fig:depolarized} shows the degree to which the emission is depolarized for all three types of polarization pattern.
" We define the polarization hole dept las (PincaDuiVPna Where Pig, is the masiuuuu volarization percentage iu the map and D, is the local mimi polarization percentage at the localon of the volarization hole with the lowest polarization."," We define the polarization hole depth as $(P_{max}-P_{min})/P_{max}$, where $P_{max}$ is the maximum polarization percentage in the map and $P_{min}$ is the local minimum polarization percentage at the location of the polarization hole with the lowest polarization."
" We find that the polarization hole depth ecucrally Increases. With scatter. as a function of D.DB,« for Type 1 ποσο] from 0 when DB,s/D,s-0 O 1004 when B,s/D,,s=0.1."," We find that the polarization hole depth generally increases, with scatter, as a function of $\ratio$ for Type 1 models from $0\%$ when $\ratio=0$ to $100\%$ when $\ratio=0.1$."
 This is easily iuclerstood by essentially the same argument eiven in thie previous paragraph., This is easily understood by essentially the same argument given in the previous paragraph.
" There is no 5ienificaut poarization hole when D.D,s is πμ because coutributious to the volarization arising frou t16 poloidal field do not effectively cancel the larger coutrilnitions from the toroida| field along anv line of sight.", There is no significant polarization hole when $\ratio$ is small because contributions to the polarization arising from the poloidal field do not effectively cancel the larger contributions from the toroidal field along any line of sight.
" The deph of the polarization hole increases until D..yBosaw0.1. where he first Type 3 pattern οneregcs,"," The depth of the polarization hole increases until $\ratio \approx 0.1$, where the first Type 3 pattern emerges."
" Note that the poarization hole depth is alwavs 1X4 for Type EMi models. since D,;,=0 at the locations where the orieutiou of the polarization vectors flips by 90."," Note that the polarization hole depth is always $100\%$ for Type 3 models, since $P_{min}=0$ at the locations where the oriention of the polarization vectors flips by $90^\circ$."
" Tucreasing B.s/D,s decreases t1e depth of t16 polarization hole for Type 2 models. since the contribution to the polarization froin the toroidal Seld becnues progressively less effective at canceling he polarization due to the dominant pooidal fie"," Increasing $\ratio$ decreases the depth of the polarization hole for Type 2 models, since the contribution to the polarization from the toroidal field becomes progressively less effective at canceling the polarization due to the dominant poloidal field."
 We define the width of the epolarized region as the distance beween the polarization maxima ou either side of the polarization hole., We define the width of the depolarized region as the distance between the polarization maxima on either side of the polarization hole.
 Panel 3b » shows the ratio of this sviIth divided by the filament diameter., Panel \ref{fig:depolarized}b b shows the ratio of this width divided by the filament diameter.
" Generally. this ratio increases with D.ςδι,s for Type 1 models. frou nearly 0 to about 0.1. which occurs at the point where the uodels clauge to Eype 3."," Generally, this ratio increases with $\ratio$ for Type 1 models, from nearly $0$ to about $0.4$, which occurs at the point where the models change to Type 3."
" This fractional widhn continues to increase past this point until B.s/D,,szm0.25. whereiC the poarization width jumps discontinuously to the full width of the fibuneut."," This fractional width continues to increase past this point until $\ratio \approx 0.23$, where the polarization width jumps discontinuously to the full width of the filament."
 This happens OCATISC of a chanec in the qualitative behaviour of the polarization vectors near the οσο of the flament., This happens because of a change in the qualitative behaviour of the polarization vectors near the edge of the filament.
 Note fiat the pol:wization percentage shown in Figure 1 js a πάπα at the outer οσο of the filameit for Type Ll modes. but a αλαπα for Type 2 models.," Note that the polarization percentage shown in Figure \ref{fig:types} is a minimum at the outer edge of the filament for Type 1 models, but a maximum for Type 2 models."
 As we move through a, As we move through a
marked as Gl. G2. G8. G4 and G5 in Fig.,"marked as G1, G2, G3, G4 and G5 in Fig."
 9 fall within the slit., 9 fall within the slit.
 The spectra reveal that they are all emission line galaxies at different z than the quasar., The spectra reveal that they are all emission line galaxies at different $z$ than the quasar.
 The spatial profile of the emission. lines along DPA 115 (Fig., The spatial profile of the emission lines along PA 115 (Fig.
" 13) is dominated by a barely resolved. central component of ISGEO.04"" (vs. 1.600.049.", 13) is dominated by a barely resolved central component of $\pm$ $\arcsec$ (vs. $\pm$ $\arcsec$ ).
 Phe seeing F'WLILM. was very similar at the beginning and. the end. of this object. exposures. so seeing variations during the spectroscopic observations are not Likely to plav a role and the line emission is actually spatially extended.," The seeing FWHM was very similar at the beginning and the end of this object exposures, so seeing variations during the spectroscopic observations are not likely to play a role and the line emission is actually spatially extended."
" The implied. intrinsic size is —1"" or ~5.5 kpc.", The implied intrinsic size is $\sim$ $\arcsec$ or $\sim$ 5.5 kpc.
 Given the strong contamination by the nuclear emission. it is not possible to isolate the emission from this ELL to analyse the kinematic and ionization properties.," Given the strong contamination by the nuclear emission, it is not possible to isolate the emission from this EELR to analyse the kinematic and ionization properties."
In addition. very [aint emission is detected. at 37. level towards the West (indicated with ΠΟΙΟ in Fig.,"In addition, very faint emission is detected at $\sim$ $\sigma$ level towards the West (indicated with “EELR” in Fig."
 13) up to a radial extent of or −∕∕⋅38.5 kpe from⋅ the continuum. centroicd., 13) up to a radial extent of $\arcsec$ or 38.5 kpc from the continuum centroid.
. ThisTl quasarju (F'ig.àld)(Γιά) appears to |be interacting[ting withwill a companion galaxy (Cil in the figure). although a chance projection cannot be discarded from the image alone.," This quasar (Fig.â14) appears to be interacting with a companion galaxy (G1 in the figure), although a chance projection cannot be discarded from the image alone."
 The FORS?2 slit was located at PA 65. crossing both nuclei.," The FORS2 slit was located at PA 65, crossing both nuclei."
 The nuclear spectrum shows strong5 continuum compared with the other quasars in the sample— and a very broad. underlying H2 component (Fig.al5)., The nuclear spectrum shows strong continuum compared with the other quasars in the sample and a very broad underlying $\beta$ component (Fig.â15).
 Phe flux of this component has not been included in the 111 lux used. to calculate the nuclear line ratios (Table 2)., The flux of this component has not been included in the $\beta$ flux used to calculate the nuclear line ratios (Table 2).
 Broad underlying Hell might also be present., Broad underlying HeII might also be present.
 Several FeV] emission lines are detected. CFeVIIA3586.. LABT59. FeVIH]JA5159).," Several [FeVII] emission lines are detected $\lambda$ 3586, $\lambda$ 3759, $\lambda$ 5159)."
 Forbidden high ionization lines (FILL) have been detected in the spectra of many active galaxies (c.g. Penston ct al. 1984.. ," Forbidden high ionization lines (FHIL) have been detected in the spectra of many active galaxies (e.g. Penston et al. \citeyear{pen84}, ,"
Mullanev et al. 2009))., Mullaney et al. \citeyear{mul09}) ).
 Their ionization potential is, Their ionization potential is
and in Table 3 we present the final abuudances.,and in Table \ref{table:abundances} we present the final abundances.
 Iun the discussion to follow we express our abundances relative to the solar values of(2006)., In the discussion to follow we express our abundances relative to the solar values of.
. The abundance dependences ou the stellar parameters are given in Table 1.., The abundance dependences on the stellar parameters are given in Table \ref{table:abundanceUncertainties}.
 Iu Figure L we present our |Fe/TI| determinations for the two sample regions iu the upper panel of Figure L., In Figure \ref{fig:FeH} we present our [Fe/H] determinations for the two sample regions in the upper panel of Figure \ref{fig:FeH}.
 Iu the lower panel of Figure | we graphically represent the median |Fe/TII] aud its interquartile rauge as a function of angular distance (A. as defined in (2005))) from the main body of Ser., In the lower panel of Figure \ref{fig:FeH} we graphically represent the median [Fe/H] and its interquartile range as a function of angular distance $\Lambda_{\odot}$ as defined in ) from the main body of Sgr.
 Ao two-sided Ix-S test is used to determine the probability that the stream samples were drawn from the core sample2005)., A two-sided K-S test is used to determine the probability that the stream samples were drawn from the core sample.
. The percentages above ch sample in the lower panel of Figure { show the probability that this is the case., The percentages above each sample in the lower panel of Figure \ref{fig:FeH} show the probability that this is the case.
 Low values of this probability indicate that the assumption that the stream samples are sinülu to that of +i6 core is a poor one., Low values of this probability indicate that the assumption that the stream samples are similar to that of the core is a poor one.
 More distant material is seen fo be progressively less like the core sunple., More distant material is seen to be progressively less like the core sample.
" A eradieut of (2.140,3)&10.7 dex/degree is determined from) a least-squares fit to the core. A. =66"" and A.=132"" samples."," A gradient of $-(2.4\pm0.3)\times10^{-3}$ dex/degree is determined from a least-squares fit to the core, $\Lambda_{\odot}$ $^{\circ}$ and $\Lambda_{\odot}$ $^{\circ}$ samples."
 At a mean distance of 22 kpc this projects to (9.121.1)ς10! dex / kpe., At a mean distance of 22 kpc this projects to $-(9.4\pm1.1)\times10^{-4}$ dex / kpc.
 The target stars have been taken from the study of aud are selected therein on the basis of their 2\LASS colours as ejut stars., The target stars have been taken from the study of and are selected therein on the basis of their 2MASS colours as M-giant stars.
 The judicious selection of isolates the upper red giaut brauch (ROB) of Ser with low contamination from the Milky Wav (MW) field., The judicious selection of isolates the upper red giant branch (RGB) of Sgr with low contamination from the Milky Way (MW) field.
 However. it also imposes a bias towards metalrich stars as detailed in(2003).," However, it also imposes a bias towards metal-rich stars as detailed in."
. Metallicitfies of [Fe/TI}<1 dex are essentially excluded due to this colour selection., Metallicities of $ < -1$ dex are essentially excluded due to this colour selection.
 To minimise the effects of this inposed metallicity bias on our fiudiues. the above figures compare our results with literature data that impose identical colour selection of the M-giauts.," To minimise the effects of this imposed metallicity bias on our findings, the above figures compare our results with literature data that impose identical colour selection of the M-giants."
 Utilisation of ΑΙ. also muposes an age ranee to the sample of stars we study., Utilisation of M-giants also imposes an age range to the sample of stars we study.
 An M-giant of [Fe/T] NI dex (typical of the Ser core: 20051) possesses an age of 22.5 Cr., An M-giant of [Fe/H] = $-0.4$ dex (typical of the Sgr core; ) possesses an age of 2–2.5 Gyr.
 At lower metallicities an older age is required to reach the same JJv color (for example a 1M... [Fe/T]| 0.1 star is 0.1 dex younger than a [Fe/II| = -0.7 star at. IW=1.0: 2008))., At lower metallicities an older age is required to reach the same $J$$-$$K$ color (for example a $_{\odot}$ [Fe/H] = -0.4 star is 0.1 dex younger than a [Fe/H] = -0.7 star at $J$$-$$K$ =1.0; ).
 Qur results mav be compared to the metallicity eracieut observed in the more extcusively studied leading arm material., Our results may be compared to the metallicity gradient observed in the more extensively studied leading arm material.
 As noted above. the leading ari is more extensively phased mixed.," As noted above, the leading arm is more extensively phased mixed."
 That is to sav the material lost in successive orbits is not as spatially differentiated as in the trailing arm., That is to say the material lost in successive orbits is not as spatially differentiated as in the trailing arm.
 This effect would be expected to reduce the apparent imnoetalliitv. &eradicnt aloug the leading arn compared to the trailne ari., This effect would be expected to reduce the apparent metallicity gradient along the leading arm compared to the trailing arm.
 In their study of the leading aria M. eiauts.(2007).. report the metallicity distribution fiction ((AIDF) in two regions: one centred at A.~230° of around 1007 in extent. and another region at A.30° (proposed to be old leading ari debris displaced ~390° from the main body).," In their study of the leading arm M giants, report the metallicity distribution function (MDF) in two regions; one centred at $\Lambda_{\odot} \sim 230^{\circ}$ of around $^{\circ}$ in extent, and another region at $\Lambda_{\odot} \sim 30^{\circ}$ (proposed to be old leading arm debris displaced $\sim 390^{\circ}$ from the main body)."
" The mean inetallicities ave found to be 0.7 dex aud l.l dex respectively,", The mean metallicities are found to be $-0.7$ dex and $-1.1$ dex respectively.
" Taken together with the mean imetalliitv of the core. this equates to a metallicity eradient of 2.2«10"" dex/deeree."," Taken together with the mean metallicity of the core, this equates to a metallicity gradient of $-2.2\times10^{-3}$ dex/degree."
 This is compatible with the present results for the trailing aru., This is compatible with the present results for the trailing arm.
 The |Fe/II| eeradient we derive her oes also compatible with the mean metallicity determined. again frou M-giauts. iu the sample of (amarkecd MOT in Figure 1).," The [Fe/H] gradient we derive here is also compatible with the mean metallicity determined, again from M-giants, in the sample of (marked M07 in Figure \ref{fig:FeH}) )."
" Further. it is noteworthy that our observed |Fe/II| gradient continues to the ""North Galactic Cap positive velocity’ eroup which is ascribed by to au old wrap of the trailing aru."," Further, it is noteworthy that our observed [Fe/H] gradient continues to the 'North Galactic Cap positive velocity' group which is ascribed by to an old wrap of the trailing arm."
 The North Calactic Cap saluple is not used in our determination of the motallicity eradieut of the trailing arin since there is possible coufusion with other kinematically distinct substructures in the direction of the North Galactic Cap sample., The North Galactic Cap sample is not used in our determination of the metallicity gradient of the trailing arm since there is possible confusion with other kinematically distinct substructures in the direction of the North Galactic Cap sample.
 The North Galactic Cap suuple occupies au area of the sky oeji which there is both leading aud trailing ari material as well as material from the Vireo Stellar Stream 2009)., The North Galactic Cap sample occupies an area of the sky in which there is both leading and trailing arm material as well as material from the Virgo Stellar Stream .
. The dynamical models of predict that while the lealues ar uaterial atthe position. of the North Galactic Cap sample will possess uceative velocities. the railing material will possess velocities of 100Vesp<200 |.," The dynamical models of predict that while the leading arm material atthe position of the North Galactic Cap sample will possess negative velocities, the trailing material will possess velocities of $100<V_{GSR}<200$ $^{-1}$."
 The Vireo Stellar Stream naterial possesses a colder velocity profile ceutred at Ve;sg100 1., The Virgo Stellar Stream material possesses a colder velocity profile centred at $V_{GSR}\sim 100$ $^{-1}$.
 shows hat considerable overlap iu radial velocity exists vetween the two svstenis and cousequeutlv it is, shows that considerable overlap in radial velocity exists between the two systems and consequently it is
which do permmte the connected couponcuts of A.,which do permute the connected components of $\tilde{A}$.
 A connected component Ay of A will be a cover of A with covering eroup Dy: thus Py is isomorphic to the quotient eroup zi)(Ay). aud in partieular it is abelian.," A connected component $\tilde{A}_0$ of $\tilde{A}$ will be a cover of $A$ with covering group $\Gamma_0$; thus $\Gamma_0$ is isomorphic to the quotient group $\pi_1(A)/\pi_1(\tilde{A}_0)$, and in particular it is abelian."
" We now take the Stein factorization of σιX.»F2, which gives where the ecnerie fibre of o is an abclian surface; such as Ay."," We now take the Stein factorization of $\tilde{\pi}:\tilde{X}\rightarrow\P^2$ , which gives where the generic fibre of $\phi$ is an abelian surface, such as $\tilde{A}_0$."
 Moreover. τιZ Eds a Calois cover with Galois group T/Ty: the points of τ1(f) correspond to the different connected components of cL and T/Ty acts frecly and transitively on these components.," Moreover, $\tau:Z\rightarrow\P^2$ is a Galois cover with Galois group $\Gamma/\Gamma_0$; the points of $\tau^{-1}(t)$ correspond to the different connected components of $\tilde{A}$, and $\Gamma/\Gamma_0$ acts freely and transitively on these components."
 In particular. Z>E? is a d/-to-L cover. where d divides d. (," In particular, $Z\rightarrow\P^2$ is a $d^{\prime}$ -to-1 cover, where $d^{\prime}$ divides $d$. ("
This illustrates the utility of the restrictions that d is one in classes 5 and 6. and one or two in class 3.),"This illustrates the utility of the restrictions that $d$ is one in classes 5 and 6, and one or two in class 3.)"
 The problem of coustructing examples cau be formulated as follows., The problem of constructing examples can be formulated as follows.
 Cave X from one of the six classes. we look for a fibration of X by abelian surfaces over a unface Z.," Given $\tilde{X}$ from one of the six classes, we look for a fibration of $\tilde{X}$ by abelian surfaces over a surface $Z$."
" Wo try to express Z as a Galois cover r:Z>μὲ, with Galois group ΕΤο."," We try to express $Z$ as a Galois cover $\tau:Z\rightarrow\P^2$, with Galois group $\Gamma/\Gamma_0$."
 Of course τ inst be ramified since I? is simply counected., Of course $\tau$ must be ramified since $\P^2$ is simply connected.
 There will be a quoticut N/Ty which is also fibved by abelian surfaces overZ., There will be a quotient $\tilde{X}/\Gamma_0$ which is also fibred by abelian surfaces over$Z$.
 The problem is to extend the action of [/Ty ou Z. which has fixed-points. to a fixed-point free action on N/Ty: for then the quotient is the required four-fold VY. ντος by abelian surfaces over F7.," The problem is to extend the action of $\Gamma/\Gamma_0$ on $Z$, which has fixed-points, to a fixed-point free action on $\tilde{X}/\Gamma_0$; for then the quotient is the required four-fold $X$ , fibred by abelian surfaces over $\P^2$."
 The following diagram sunumnuauizes this construction., The following diagram summarizes this construction.
 Tf some clement of [/Ty fixes s€Z. then that element iust act in a free manner on the abelian surface fibre above s.," If some element of $\Gamma/\Gamma_0$ fixes $s\in Z$, then that element must act in a fixed-point free manner on the abelian surface fibre above $s$."
 Usually the quotieut of this action will again be an abelian surface. aud thus the element should act by a translation.," Usually the quotient of this action will again be an abelian surface, and thus the element should act by a translation."
 This suggests that P/Ty should be abelian. aud we will keep this as a οπήςπιο principle when coustructing examples.," This suggests that $\Gamma/\Gamma_0$ should be abelian, and we will keep this as a guiding principle when constructing examples."
 However. there may not be a point sCZ fixed bx the entire eroup 1Τι. so we wont find necessarily find that the entire eroup acts as translations on a single abclian surface.," However, there may not be a point $s\in Z$ fixed by the entire group $\Gamma/\Gamma_0$, so we won't find necessarily find that the entire group acts as translations on a single abelian surface."
 Moreover. s could lic iu the discriminantlocus of the abelian surface fibration. iiplviug that the fibre above s is a degeneration rather than a simooth abelian surface.," Moreover, $s$ could lie in the discriminantlocus of the abelian surface fibration, implying that the fibre above $s$ is a degeneration rather than a smooth abelian surface."
 Retumineg tow:NV> TP. we have the followingresults coucerning direct Mages of the structure sheaf.," Returning to $\pi:X\rightarrow\P^2$ , we have the followingresults concerning direct images of the structure sheaf."
Accurale ages for nearby stellar clusters are the basic observational templates that constrain the formation history of our Galaxy and the Universe.,Accurate ages for nearby stellar clusters are the basic observational templates that constrain the formation history of our Galaxy and the Universe.
 Unfortunately. theoretical isochrones fit to the upper main sequence provide absolute ages for the most thoroughly studied voung open clusters that are still uncertain by a factor of two (Staulferetal.2000).," Unfortunately, theoretical isochrones fit to the upper main sequence provide absolute ages for the most thoroughly studied young open clusters that are still uncertain by a factor of two \citep{sta00}."
. The uncertainty niainly results from (he dependence of (he lifetime of massive stars on (hie size ol their convective cores., The uncertainty mainly results from the dependence of the lifetime of massive stars on the size of their convective cores.
 Convective core overshoot brings fresh hvdiogen-rich material to the core. extending the stellar lifetime on the main sequence.," Convective core overshoot brings fresh hydrogen-rich material to the core, extending the stellar lifetime on the main sequence."
 As a result. cluster age estimates are «quite sensitive to (he degree of convective core overshoot in (he theoretical calculations.," As a result, cluster age estimates are quite sensitive to the degree of convective core overshoot in the theoretical calculations."
 There is evidence that the inclusion of convective core overshoot results in an improved agreement between theoretical evolution rates ancl umber counts in the Hertzsprune gap. and also an improved fit to (he width of the main sequence turnolL in open clusters (Andersen.Nordstrom.1990:Demarque.Sarajedini.&Guo 1994).," There is evidence that the inclusion of convective core overshoot results in an improved agreement between theoretical evolution rates and number counts in the Hertzsprung gap, and also an improved fit to the width of the main sequence turnoff in open clusters \citep{and90,dem94}."
. Thus. theoretical caleulations (hat include convective core overshoot result in an older absolute age scale relative to theoretical calculations (hat do not.," Thus, theoretical calculations that include convective core overshoot result in an older absolute age scale relative to theoretical calculations that do not."
 Calibrating the older convective core overshoot age scale recquires an independent technique for determining stellar cluster ages., Calibrating the older convective core overshoot age scale requires an independent technique for determining stellar cluster ages.
 Lithium depletion age dating is one possibility. and in (his paper we discuss the reliability of Chis technique.," Lithium depletion age dating is one possibility, and in this paper we discuss the reliability of this technique."
 The lithium depletion boundary (LDB) technique is an independent method to determine the age of open clusters with ages (hat range from 20 to 200 Mvr., The lithium depletion boundary (LDB) technique is an independent method to determine the age of open clusters with ages that range from 20 to 200 Myr.
 Proton reactions destrov Li* near a destruction temperature. Tj~2.5xLO? Ix. easily obtained under stellar conditions.," Proton reactions destroy $^{7}$ near a destruction temperature, $_{D}\sim 2.5\times 10^{6}$ K, easily obtained under stellar conditions."
 In general. (he presence or absence of photospheric lithium determines whether sullicient lime has passed [for a majoritv of the stellar material to reach depths in the star where T-—Tp.," In general, the presence or absence of photospheric lithium determines whether sufficient time has passed for a majority of the stellar material to reach depths in the star where $_{D}$."
 For stars that are fully convective during pre-main-sequence contraction (Mz0.4 AL. ). the convective overturn timescale is much less than the evolutionary timescale. and the entire lithium content is rapidly destroved when the stellar core temperature. Το reaches Tp.," For stars that are fully convective during pre-main-sequence contraction $\la 0.4$ $_{\odot}$ ), the convective overturn timescale is much less than the evolutionary timescale, and the entire lithium content is rapidly destroyed when the stellar core temperature, $_{C}$, reaches $_{D}$."
 Since the rate at which the core temperature increases to the destruction temperature is a strong function of stellar mass. spectral observations of Li* in fully convective stars during pre-anain-sequence contraction is an accurate age diagnostic.," Since the rate at which the core temperature increases to the destruction temperature is a strong function of stellar mass, spectral observations of $^{7}$ in fully convective stars during pre-main-sequence contraction is an accurate age diagnostic."
 Higher mass stars reach the condition Te =Ty at an earlier age and higher luminosity than lower mass stars. and the lithium abundance decreases by a [ictor of 100 over a very narrow luminosity.," Higher mass stars reach the condition $_{C}=$ $_{D}$ at an earlier age and higher luminosity than lower mass stars, and the lithium abundance decreases by a factor of 100 over a very narrow luminosity."
 LDB ages have been obtained [or several voung open clusters: the Pleiades. Alpha Per. IC 2391. NGC 2547 (Stauffer.Schultz.&Wirkpatrick1998:Staufferοἱal.1999:Bar-radovNavascués.Statler.&Patten1999:Oliveiraοἱal... 2003).," LDB ages have been obtained for several young open clusters: the Pleiades, Alpha Per, IC 2391, NGC 2547 \citep{sta98,sta99,bar99,oli03}."
. In an independent analvsis. Jeffries&Navlor(2000) verifiecl (he conclusions of the previous open cluster studies that the LDD ages are ~1.6 times older (han upper mainu-sequence-lilling ages without. convective core overshoot.," In an independent analysis, \citet{jef00} verified the conclusions of the previous open cluster studies that the LDB ages are $\sim$ 1.6 times older than upper main-sequence-fitting ages without convective core overshoot."
 Jeffries&Navlor(2000). [ind that the observational, \citet{jef00} find that the observational
rocky planet. (he latter acts as a test particle (to leading order).,"rocky planet, the latter acts as a test particle (to leading order)."
 If the rocky planet migrates sufficiently slowly. it generally becomes locked. into mean motion resonance with the Hot Jupiter.," If the rocky planet migrates sufficiently slowly, it generally becomes locked into mean motion resonance with the Hot Jupiter."
 Continued migration of the second body then pushes both planets inward. although {his motion ceases if the second body reaches the inner edge of the disk (and Chis motion becomes ineffective if (he second planet is too small).," Continued migration of the second body then pushes both planets inward, although this motion ceases if the second body reaches the inner edge of the disk (and this motion becomes ineffective if the second planet is too small)."
 Η migration ceases. (he resulting pair of planets could survive in or near resonance.," If migration ceases, the resulting pair of planets could survive in or near resonance."
 If the Hot Jupiter can be observed in (ransil. the second body can produce transit timing variations (ASSC).," If the Hot Jupiter can be observed in transit, the second body can produce transit timing variations (ASSC)."
 If migration occurs too quickly. the second planet passes through mean motion resonance (Quillen 2006. Netchum et al.," If migration occurs too quickly, the second planet passes through mean motion resonance (Quillen 2006, Ketchum et al."
 2011) and will often experience a close encounter with the Hot Jupiter., 2011) and will often experience a close encounter with the Hot Jupiter.
 The interaction event can result in either a collision between the planets (and assimilation of the rocky body) or the accretion of one planet (generally the smaller one) by the star., The interaction event can result in either a collision between the planets (and assimilation of the rocky body) or the accretion of one planet (generally the smaller one) by the star.
 Planets are rarely scattered out of (he solar svstem because the exavitational potential of the star (for a 4-day orbit) is deeper (han that of the Jovian planet (escape thus requires 3-body effects)., Planets are rarely scattered out of the solar system because the gravitational potential of the star (for a $\sim4$ -day orbit) is deeper than that of the Jovian planet (escape thus requires 3-body effects).
 One goal of this work is (ο determine (he branching ratios for the various outcomes survival. acceretion. scaltering into (he star as a function of (Jovian) planetary. mass aud orbital eccentricity.," One goal of this work is to determine the branching ratios for the various outcomes — survival, accretion, scattering into the star — as a function of (Jovian) planetary mass and orbital eccentricity."
 We approach this problem by performing direct. numerical integrations of migrating planetary svstems. Le. we integrate the full set of 18 phase space variables for the 3-bodx problem consisting of the star. Hot Jupiter. aud a second migrating planet.," We approach this problem by performing direct numerical integrations of migrating planetary systems, i.e., we integrate the full set of 18 phase space variables for the 3-body problem consisting of the star, Hot Jupiter, and a second migrating planet."
 These integrations are carried out. using a D-5 integration scheme., These integrations are carried out using a B-S integration scheme.
 In addition to gravitv. we include forcing terms that represent inward migration ancl eccentricitv damping: these additional effects arise due to the forces exerted on the planet(s) by the circumstellar disk.," In addition to gravity, we include forcing terms that represent inward migration and eccentricity damping; these additional effects arise due to the forces exerted on the planet(s) by the circumstellar disk."
 However. we cdo not model the disk directly. but rather include forcing terms to model its behavior.," However, we do not model the disk directly, but rather include forcing terms to model its behavior."
" We consider simple disk models where the surface density. aud temperature distribution are power-laws in radius. ye where X, and 71 are normalization constants."," We consider simple disk models where the surface density and temperature distribution are power-laws in radius, )^p where $\Sigma_1$ and $T_1$ are normalization constants."
" Here we taker,=1AU. so the coellicients M4 and 7, correspond to values at 1 AU."," Here we take $r_1=1$AU, so the coefficients $\Sigma_1$ and $T_1$ correspond to values at 1 AU."
 The index p=1—2. where the intermediate value p—3/2 arises for the Minimum Mass Solar Nebula (Weidenschiling 1977) and where recent observations suggest p—0.940.2 (Andrews et al.," The index $p=1-2$, where the intermediate value $p=3/2$ arises for the Minimum Mass Solar Nebula (Weidenschilling 1977) and where recent observations suggest $p=0.9\pm0.2$ (Andrews et al."
 2010)., 2010).
 The normalization for the surface density has a range of values. with X4221500—4500 e/cni? (Ixuchner 2004).," The normalization for the surface density has a range of values, with $\Sigma_1\approx1500-4500$ $^2$ (Kuchner 2004)."
 The power-law index of the temperature profile qzz3/4 for a viscous accretion disk (Pringle 1981) and a flat reprocessing disk (Adams Shu 1936). whereas q221/2 lor a flared reprocessing disk (Chiang Goldreich 1997).," The power-law index of the temperature profile $q\approx3/4$ for a viscous accretion disk (Pringle 1981) and a flat reprocessing disk (Adams Shu 1986), whereas $q\approx1/2$ for a flared reprocessing disk (Chiang Goldreich 1997)."
 The latter value is often used to describe the early solar nebula (Weidenschilling 1977)., The latter value is often used to describe the early solar nebula (Weidenschilling 1977).
 The disk scale height //— a5/€. where ay is the sound speed. which is determined by," The disk scale height $H=a_S/\Omega$ , where $a_S$ is the sound speed, which is determined by"
 e. ο2z G ¢&=wir) p=pr) 0£=0 , $v_c$ $v_c\approx$ $G$ $\psi=\psi(r)$ $\rho=\rho(r)$ $\delta {\mathcal L}=0$ 
to predict the X-ray emission from the WIIIM.,to predict the X-ray emission from the WHIM.
 Compared to our previous work (2006).. we exploited the good spatial resolution (on the order of the adopted gravitational softening of 7.5 h.| kpe. compared to the ~195 ! kpe resolution element used by Cen Ostriker 1999) of a Lagrangian simulation to create hieh resolution maps of 1e barvon distribution.," Compared to our previous work \cite{Ursino06}, we exploited the good spatial resolution (on the order of the adopted gravitational softening of $7.5$ $^{-1}$ kpc, compared to the $\sim195$ $^{-1}$ kpc resolution element used by Cen Ostriker 1999) of a Lagrangian simulation to create high resolution maps of the baryon distribution."
 We locused our attention on the effect of the metallicity model used on the X-ray Mnission., We focused our attention on the effect of the metallicity model used on the X-ray emission.
 A\letallicity in the filaments is one of (he greatest uncertainties in this tvpe of V.imulations., Metallicity in the filaments is one of the greatest uncertainties in this type of simulations.
 Observations of the interealactic medium put some limits on metals in the InterGalactic Medium (IGM)., Observations of the intergalactic medium put some limits on metals in the InterGalactic Medium (IGM).
" At z<0.5 groups and clusters have metallicity Ze0.3 Z.. while Ly-a clouds have Z~0.1 Z. wilh a large scatter (0.01<Z/Z.,«1)."," At $z\lesssim0.5$ groups and clusters have metallicity $\textrm{Z}\sim 0.3$ $_\odot$, while $\alpha$ clouds have $\textrm{Z}\sim0.1$ $_\odot$ with a large scatter $0.01<\textrm{Z/Z}_\odot<1$ )."
 Going at higher redshifts metallicity becomes lower. possibly by a factor 10 already al 2223 Finoguenov.elProchaskaetal.(2004):Simcoe (2006).," Going at higher redshifts metallicity becomes lower, possibly by a factor 10 already at $z\approx3$ \cite{Finoguenov03, Prochaska04, Simcoe06}."
. From the analvsis of the low redshift absorbers. colder WIIM structures have Z~0.15 Z. Danforth&Shull(2008).," From the analysis of the low redshift absorbers, colder WHIM structures have $\textrm{Z}\sim0.15$ $_\odot$ \cite{Danforth08}."
. Although there is à possible correlation between higher metallicities and higher densities. a simple modeling of IGM metallicity is difficult.," Although there is a possible correlation between higher metallicities and higher densities, a simple modeling of IGM metallicity is difficult."
 At present time it is even uncertain if ihere was an early metal enrichment (22 4). if metals in the IGM are due to the newborn (z« 2) galaxies. or if metal enrichment history is described by a mixture of the two models Aguirre&Schave.(2005).," At present time it is even uncertain if there was an early metal enrichment $z\approx4$ ), if metals in the IGM are due to the newborn $z<2$ ) galaxies, or if metal enrichment history is described by a mixture of the two models \cite{Aguirre05}."
. Cosmologieal simulations with an acetate physical description (galactic winds. star formation. black hole feedback. and so forth) ean come to an avail in reproducing the proper metallicity Cen&Ostriker(1999b):Borganietal.(2004):Ostriker(2006):Tornatoreetal.(2009):Wiersma (2009b).," Cosmological simulations with an accurate physical description (galactic winds, star formation, black hole feedback, and so forth) can come to an avail in reproducing the proper metallicity \cite{CenOst99b, 
Borgani04, CenOst06, Tornatore09, Wiersma09b}."
. These models predict that the average WIIIM metallicity is of the order of 0.1 Z. but the behavior as a function of density changes widely from simulation to simulation., These models predict that the average WHIM metallicity is of the order of $0.1$ $_\odot$ but the behavior as a function of density changes widely from simulation to simulation.
 Due to the lack of üght constraints on metallicity [rom both observations and simulations. we allowed our code to work with a set ol metallicity models. in addition to the one coming directly [rom the Borgani simulation.," Due to the lack of tight constraints on metallicity from both observations and simulations, we allowed our code to work with a set of metallicity models, in addition to the one coming directly from the Borgani simulation."
 Thanks to this degree of freeclom we were able to investigate the dependence of the soft X-ray emission on the different metallicity models., Thanks to this degree of freedom we were able to investigate the dependence of the soft X-ray emission on the different metallicity models.
 The paper is structured as follows., The paper is structured as follows.
 In 2. we introduce the hydrodvnamic cosmological simulation.in 3 we describe the code we used to simulate the X-ray emission in a selected lied of view. in 4 we show the simulated images and spectra. in 5 we discuss how the emitted spectra depend on (he metallicity models.," In \ref{Model} we introduce the hydrodynamic cosmological simulation, in \ref{Simulation} we describe the code we used to simulate the X-ray emission in a selected field of view, in \ref{Results} we show the simulated images and spectra, in \ref{Metallicity-emission} we discuss how the emitted spectra depend on the metallicity models."
 The general properties of the cosmological model are described in details in Dorgani et al. (, The general properties of the cosmological model are described in details in Borgani et al. (
2004) and references therein.,2004) and references therein.
 The simulation uses a flat A cold dark matter CACDM), The simulation uses a flat $\Lambda$ cold dark matter $\Lambda$ CDM)
simplifying assumption of isotropic rellection ancl write the reflected intensity in the form: In order to calculate the time-varving iron line profiles and the corresponding continuum light curves we used the Following 1) We use a rav-tracing technique to follow the trajectories of photons [from positions (r.y) on the observers image plane to the disc. keeping track of all Jover-Lindequist Coordinates LiGr. y). rGr.gn). Cr.gy). (Cr.y). until the photons either intersect the accretion disc plane or disappear below the event horizon (Phe observer is located. at F=10003. 6= Poand ó=OUS where ? is the inclination).,"simplifying assumption of isotropic reflection and write the reflected intensity in the form: In order to calculate the time-varying iron line profiles and the corresponding continuum light curves we used the following 1) We use a ray-tracing technique to follow the trajectories of photons from positions $(x,y)$ on the observer's image plane to the disc, keeping track of all Boyer-Lindquist coordinates $\tilde{t}_{do}(x,y)$ , $r(x,y)$, $\theta(x,y)$, $\phi(x,y)$, until the photons either intersect the accretion disc plane or disappear below the event horizon (The observer is located at $r=1000m$, $\theta=i$ and $\phi=0^{o}$, where $i$ is the inclination)."
 We then calculate the redshift factor corresponding to the particular final position of a photon and its arrival time from the disc., We then calculate the redshift factor corresponding to the particular final position of a photon and its arrival time from the disc.
 We generate an image of approximately 1600| pixels covering roughly an area of 160m«160m. 2) Using the time dependent ionization and illumination pattern described above and albedo eg;(Le.£). we specify the emoergent [ux from the disc as a function of time and energy in the fixed. spectral band. ic. we integrate. all. photons coming [rom regions of equal arrival time regions on the accretion disc at à particular energy.," We generate an image of approximately $1600\times 1600$ pixels covering roughly an area of $160m\times 160m$ 2) Using the time dependent ionization and illumination pattern described above and albedo $a_{R}(E,\xi)$, we specify the emergent flux from the disc as a function of time and energy in the fixed spectral band, i.e. we integrate all photons coming from regions of equal arrival time regions on the accretion disc at a particular energy."
 In doing so we also take into account the fact that the source changes its position and rotate the illumination and ionization patterns accordingly., In doing so we also take into account the fact that the source changes its position and rotate the illumination and ionization patterns accordingly.
 This allowed: us to compute the reflected. spectrum as a function of time and thus the reflected component of the light curve., This allowed us to compute the reflected spectrum as a function of time and thus the reflected component of the light curve.
 We use the following formulae (see appendix € [or additional explanations): where by(1) is the contribution to the flux from the Hare at the n-th position given hy: where gv. is the redshift factor for the clise-to-ohserver case. αμ is the pixel surface area on the observer's image plane. ro is the distance from the black hole svstem and Pato|hte.," We use the following formulae (see appendix C for additional explanations): where $F^{(n)}_{R}(t)$ is the contribution to the flux from the flare at the n-th position given by: where $g_{do}$ is the redshift factor for the disc-to-observer case, $dxdy$ is the pixel surface area on the observer's image plane, $r_{0}$ is the distance from the black hole system and $\tilde{t}=
\tilde{t}_{sd}+\tilde{t}_{do}$."
 3) We compute the direct Dux component by propagating photons from the source to the observer., 3) We compute the direct flux component by propagating photons from the source to the observer.
 We use a formula analogous to that above to calculate this 4) Llaving specified the illumination pattern aud ionization state for a given position of the flare above the accretion disc. we determine the contribution of each. eric clement on the disc surface to the iron line profile from the formula: where fy(9.0) is the integrated. over a fixed. energy banc X-ray flux at the given. position on the clisc.," We use a formula analogous to that above to calculate this 4) Having specified the illumination pattern and ionization state for a given position of the flare above the accretion disc, we determine the contribution of each grid element on the disc surface to the iron line profile from the formula: where $F_{X}(r,\phi)$ is the integrated over a fixed energy band X-ray flux at the given position on the disc."
 The above function is the Creen’s function. (transfer. function) corresponding to the n-th position of the 5) In the last step we use the transfer functions for single isolated ]ares in order to calculate the observed iron line Hux variations., The above function is the Green's function (transfer function) corresponding to the n-th position of the 5) In the last step we use the transfer functions for single isolated flares in order to calculate the observed iron line flux variations.
 We use the following expression: where we also take into account the delays due to the revolution of the flare around the black hole., We use the following expression: where we also take into account the delays due to the revolution of the flare around the black hole.
 As in the case of he reflected Dux. we interpolate the contributions to the Dux rom the isolated [ares and then add the interpolated Luxes.," As in the case of the reflected flux, we interpolate the contributions to the flux from the isolated flares and then add the interpolated fluxes."
 ote that the binning of the transfer functions in time would introduce a small adcditional (artificial) flux variability. oeause we physically rotate the illumination pattern.," Note that the binning of the transfer functions in time would introduce a small additional (artificial) flux variability, because we physically rotate the illumination pattern."
 This is because the dillerences between the arrival times [rom he neighbouring disc elements on the approaching side of he dise would be shorter compared to the corresponding dillerences on the opposite sido., This is because the differences between the arrival times from the neighbouring disc elements on the approaching side of the disc would be shorter compared to the corresponding differences on the opposite side.
 We present iron line [lux variations and the corresponding ight curves lor one full. revolution of the [lare around he black hole with a step-like luminosity variation in the ocal [rame of reference of the Iare., We present iron line flux variations and the corresponding light curves for one full revolution of the flare around the black hole with a step-like luminosity variation in the local frame of reference of the flare.
 This is for illustrative purposes and we stress that while it is trivial. for example. to eeneralize the code to include arbitrary intrinsic Luminosity variations in the rest frame of the flare. we do not. wish o complicate the interpretation of the results.," This is for illustrative purposes and we stress that while it is trivial, for example, to generalize the code to include arbitrary intrinsic luminosity variations in the rest frame of the flare, we do not wish to complicate the interpretation of the results."
 Future observations may guide us as to how to introduce additional jpdilications in the computations., Future observations may guide us as to how to introduce additional modifications in the computations.
 Phe results in the present form can in principle be applied to the case of Isolated Dares or at least strong outbursts accompanied by minor ones., The results in the present form can in principle be applied to the case of isolated flares or at least strong outbursts accompanied by minor ones.
 In he computations we assume that the source omits a power aw spectrum with energy index a=1., In the computations we assume that the source emits a power law spectrum with energy index $\alpha=1$.
 Fie and Fig.2 present the light. curves., Fig.1 and Fig.2 present the light curves.
 The light curves are a superposition of the direct. flux. from the lave and the reflected lux from the disc., The light curves are a superposition of the direct flux from the flare and the reflected flux from the disc.
 The small olfset oween these (wo. components (note the shift. between initial and final times of the reflected ane direct Dux) is due o the additional time photonsneed to propagate towards he disc and back., The small offset between these two components (note the shift between initial and final times of the reflected and direct flux) is due to the additional time photonsneed to propagate towards the disc and back.
 Phe small albedo of the cise material, The small albedo of the disc material
of the source/sky itself.,of the source/sky itself.
" The zoomed image shows the first 20 DCEs, where DEC=0 corresponds to the sky measurement, DCE-1 the stim, DCE- 2 to 7 to observations in the ""internal dark reference” and DCE=8 is the sky measurement followed by another six DCEs and the next calibration stim (DCE=15)."," The zoomed image shows the first 20 DCEs, where DEC=0 corresponds to the sky measurement, DCE=1 the stim, DCE= 2 to 7 to observations in the ""internal dark reference"" and DCE=8 is the sky measurement followed by another six DCEs and the next calibration stim (DCE=15)."
" We note that the level of the DCE=7 is essentially zero, because in the data reduction pipeline this is the ""reference"" measurement that is subtracted from each BCD."," We note that the level of the DCE=7 is essentially zero, because in the data reduction pipeline this is the 'reference' measurement that is subtracted from each BCD."
" We also note that the sky itself (DCE=8) is at ~3 MJy/sr, which is the final TPM measurement."," We also note that the sky itself (DCE=8) is at $\sim3$ MJy/sr, which is the final TPM measurement."
 The comparison of the TPM with the photometric observation shows that the light contribution of the telescope at 160 um is ~1.3 MJy/sr., The comparison of the TPM with the photometric observation shows that the light contribution of the telescope at 160 $\mu$ m is $\sim 1.3$ MJy/sr.
" The level of spurious emission due to the telescope background emission at 160 um is 1.0+0.2 The absolute calibration of 160 44m TPM relies on the standard 160 um calibration, which is based on asteroids, that is tied itself to the 24 and 70 um MIPS absolute calibration to be internally consistent (?).."," The level of spurious emission due to the telescope background emission at 160 $\mu$ m is $\pm$ 0.2 The absolute calibration of 160 $\mu$ m TPM relies on the standard 160 $\mu$ m calibration, which is based on asteroids, that is tied itself to the 24 and 70 $\mu$ m MIPS absolute calibration to be internally consistent \citep{2007PASP..119.1038S}."
" Finally, we stress that a single DCE at 160 uum does not cover the 160 jum beam (40"")), hence the TPM mode was designed to move the scan mirror to cover the beam in one cycle."," Finally, we stress that a single DCE at 160 $\mu$ m does not cover the 160 $\mu$ m beam ), hence the TPM mode was designed to move the scan mirror to cover the beam in one cycle."
 A standard TPM 160 um observation contains four cycles., A standard TPM 160 $\mu$ m observation contains four cycles.
" The final product for a single 160 um TPM observation is a 5x5' small mosaic, and for our measurements we calculated the mean over such an image."," The final product for a single 160 $\mu$ m TPM observation is a $\times$ small mosaic, and for our measurements we calculated the mean over such an image."
" The two ELAIS N1 TPM observations at 160 um took 2386 s with 88 s on source each, while the two photometric observations using the enhanced mode took 671 secs with 54 secs on each source."," The two ELAIS N1 TPM observations at 160 $\mu$ m took 2386 s with 88 s on source each, while the two photometric observations using the enhanced mode took 671 secs with 54 secs on each source."
" These numbers illustrate the efficiency of the two modes; for every second on source at TPM, about seven seconds woth of data are used for calibration and latency decay."," These numbers illustrate the efficiency of the two modes; for every second on source at TPM, about seven seconds woth of data are used for calibration and latency decay."
" We used the 25 deg? data cube (x, y, velocities) centered on ELAIS N1."," We used the 25 $^2$ data cube (x, y, velocities) centered on ELAIS N1."
 These data were obtained in 2006 and 2010 withthe 100-meter Green Bank Telescope (GBT)., These data were obtained in 2006 and 2010 withthe 100-meter Green Bank Telescope (GBT).
" Spectra were measured over a 5?x5° area centered on (f,b) = (85.5°,+44.3°) every 3.5’ in both coordinates.", Spectra were measured over a $5^o \times 5^o$ area centered on $\ell$ $b$ ) = $^o$ $^o$ ) every $\arcmin$ in both coordinates.
 Data were taken by in-band frequency switching yielding spectra with a velocity coverage —450<Visa€+355 km s anda velocity resolution of 0.80 km.s~!., Data were taken by in-band frequency switching yielding spectra with a velocity coverage $-450 \leq V_{LSR} \leq +355$ km $^{-1}$ and a velocity resolution of 0.80 $^{-1}$.
" Spectra were calibrated, corrected for stray radiation, and placed on a brightness temperature (Τη) scale as described in ?) and ?).."," Spectra were calibrated, corrected for stray radiation, and placed on a brightness temperature $T_b$ ) scale as described in \citet{2010ASPC..438..156B} and \citet{2011A&A...536A..81B}."
 A third-order polynomial was fit to the emission-free regions of the spectra to remove any residual instrumental baseline., A third-order polynomial was fit to the emission-free regions of the spectra to remove any residual instrumental baseline.
" The final data cube has a root mean square (rms) noise in a single channel of 0.12 K of Ty, and an effective angular resolution of 9.4’x9.1’ in € and b, We distinguish three velocity components in the gas data: the local, intermediate (IVC), and high velocity cloud (HVC)."," The final data cube has a root mean square (rms) noise in a single channel of 0.12 K of $T_b$, and an effective angular resolution of $9.4 \arcmin \times 9.1 \arcmin$ in $\ell$ and $b$, We distinguish three velocity components in the gas data: the local, intermediate (IVC), and high velocity cloud (HVC)."
 These are shown in Fig. 8.., These are shown in Fig. \ref{fig:GBT}.
" The HVC is centered around -115 km/s and the IVC around -23 km/s, as illustrated in Fig. 9.."," The HVC is centered around -115 km/s and the IVC around -23 km/s, as illustrated in Fig. \ref{fig:comp_spectra}."
" This figure shows velocity spectra along three lines of sight, each of which is dominated by one component."," This figure shows velocity spectra along three lines of sight, each of which is dominated by one component."
 The IVC and the HVC are clearly seen in the middle and bottom panels., The IVC and the HVC are clearly seen in the middle and bottom panels.
" We used IRIS (re-processed IRAS data) maps at 60 and 100 uum to measure the emissivities of the dust correlated to the components and derive the CIB power spectrum at 100 um. This new generation of IRAS images was processed using a more reliable zodiacal light subtraction, from a calibration and zero level compatible with DIRBE and a more reliable destriping (?).. "," We used IRIS (re-processed IRAS data) maps at 60 and 100 $\mu$ m to measure the emissivities of the dust correlated to the components and derive the CIB power spectrum at 100 $\mu$ m. This new generation of IRAS images was processed using a more reliable zodiacal light subtraction, from a calibration and zero level compatible with DIRBE and a more reliable destriping \citep{2005ApJS..157..302M}. ."
"At 100 uum, the IRIS product also represents a significant improvement on the ?) maps."," At 100 $\mu$ m, the IRIS product also represents a significant improvement on the \citet{1998ApJ...500..525S} maps."
 IRIS keeps the full, IRIS keeps the full
"where Aj,z P4. As#Pa. and Ayz0.","where $A_1\ne P_{g\theta}$ , $A_2\ne P_{\theta\theta}$ , and $A_3\ne0$."
 The importance of the extra higher order terms was emphasised most recently by Scoccimarro(2004)., The importance of the extra higher order terms was emphasised most recently by \citet{Sco04}.
. In addition to these redshift-space effects. the linear theory relation between 6 and 8. given in Eq. (69).," In addition to these redshift-space effects, the linear theory relation between $\delta$ and $\theta$, given in Eq. \ref{eq:lin_f}) ),"
 will break down in the quasi-linear regime. so we should expect the shapes of PL. Pu and Pu to be different.," will break down in the quasi-linear regime, so we should expect the shapes of $P_{gg}$, $P_{g\theta}$ and $P_{\theta\theta}$ to be different."
 The relationship between Eqns., The relationship between Eqns.
 (8 I5p can be written where Gtk.po) has the property lim;ροκ40)=I.," \ref{eq:pgs_lin} \ref{eq:pgs_qlin}) ) can be written where $G(k,\mu^2)$ has the property $\lim_{k\to0}G(k,\mu^2)=1$."
 The standard model for redshift-space distortions includes a component caused by an uncorrelated velocity dispersion that grows on small scales., The standard model for redshift-space distortions includes a component caused by an uncorrelated velocity dispersion that grows on small scales.
" Such a model is motivated by the idea of ""thermal motion"" of particles in collapsed structures. which causes the Fingers-Of-God (FOG) observed in redshift surveys (Jackson 1972)."," Such a model is motivated by the idea of “thermal motion” of particles in collapsed structures, which causes the Fingers-Of-God (FOG) observed in redshift surveys \citep{Jac72}."
". An additional component comprising uncorrelated particle motions will dilute both the galaxy overdensity 6,. and the “extra” overdensity term caused by the linear distortions. €."," An additional component comprising uncorrelated particle motions will dilute both the galaxy overdensity $\delta_g$, and the “extra” overdensity term caused by the linear distortions, $\theta$."
 Motivated by numerical simulations (Sheth&Diaferio2001:Huffetal.2007) and the halo model (White2001:Seljak20013.. we ean assume that the centre of mass of a halo. around which galaxies orbit. still moves according to (quasi-Minear motion.," Motivated by numerical simulations \citep{SheDia01,HSWSW07} and the halo model \citep{Whi01,Sel01}, we can assume that the centre of mass of a halo, around which galaxies orbit, still moves according to (quasi-)linear motion."
 Such a model leads to the much-used ‘streaming’ models (e.g.Hamilton1998) where with Εμ.) a function that depends on the distribution of random pair velocities in collapsed objects. which is often written as a function of v=Kc. where c is the rms velocity dispersion.," Such a model leads to the much-used `streaming' models \citep[e.g.][]{HamiltonReview} where with $F(k,\mu^2)$ a function that depends on the distribution of random pair velocities in collapsed objects, which is often written as a function of $y=k\sigma$, where $\sigma$ is the rms velocity dispersion."
 In order to mateh behaviour on large scales. we require lim;»F(k.47)=|.," In order to match behaviour on large scales, we require $\lim_{k\to0}F(k,\mu^2)=1$."
 We have written the equation in this form to highlight the similarity with Eq. (16)., We have written the equation in this form to highlight the similarity with Eq. \ref{eq:G}) ).
 Note that this model is constructed by a rather ad-hoc splicing of linear. quasi-linear and non-linear behaviour which ignores the scale-dependence of the mapping between real and redshift space separations (Fisher1995:Scoccimarro2004.andreferences therein)... while Eq. (169) ," Note that this model is constructed by a rather ad-hoc splicing of linear, quasi-linear and non-linear behaviour which ignores the scale-dependence of the mapping between real and redshift space separations \citep[][and references therein]{Fis95,Sco04}, while Eq. \ref{eq:G}) )"
was based on the analysis of the redshift-space distortions in the linear limit., was based on the analysis of the redshift-space distortions in the quasi-linear limit.
 In general FOG are difficult to model well. and their amplitude is strongly dependent on the mean halo mass and satellite fraction of the population under consideration (White2001:Seljak2," In general FOG are difficult to model well, and their amplitude is strongly dependent on the mean halo mass and satellite fraction of the population under consideration \citep{Whi01,Sel01}."
00 Previous work has concentrated on models with Gaussian or Exponential distributions (e.g.Coleetal.1995:Peacock&Dodds1996) for the pairwise velocity dispersion in configuration space.," Previous work has concentrated on models with Gaussian or Exponential distributions \citep[e.g.][]{cole95,PeaDod96} for the pairwise velocity dispersion in configuration space."
 For an Exponential model for the pairwise velocity dispersion in configuration space. weexpeet a Lorentz damping factor for the power spectrum. while the Gaussian dispersion translates to a Gaussian damping of the power spectrum These terms have the same behaviour to first order.," For an Exponential model for the pairwise velocity dispersion in configuration space, weexpect a Lorentz damping factor for the power spectrum, while the Gaussian dispersion translates to a Gaussian damping of the power spectrum These terms have the same behaviour to first order."
 The exact form of Fk.48). and the value of c is strongly dependent on the galaxy population Jing&Borner2004:Lietal. 2007).," The exact form of $F(k,\mu^2)$, and the value of $\sigma$ is strongly dependent on the galaxy population \citep{Jing04,Li07}. ."
". An alternative approach would be to try to ""eliminate"" the FOG by applying a halo finding algorithm to the sample and manually moving galaxies either to halo centres. or to a spherically symmetric distribution around these centres (e.g. Tegmark 2004))."," An alternative approach would be to try to “eliminate” the FOG by applying a halo finding algorithm to the sample and manually moving galaxies either to halo centres, or to a spherically symmetric distribution around these centres (e.g. \citealt{tegmark04}) )."
 Such approaches tend to mask the fact that the radial “compression” is still model dependent. and requires a similar free parameter to 7 in Eq. (20)).," Such approaches tend to mask the fact that the radial “compression” is still model dependent, and requires a similar free parameter to $\sigma$ in Eq. \ref{eq:pgs_combined}) )."
" This ""parameter"" controls the probability density function for the distortion of any galaxy in redshift space (Reid&Spergel2008).", This “parameter” controls the probability density function for the distortion of any galaxy in redshift space \citep{reid08}.
. However. FOG compression does have the advantage of including extra information in the analvsis from the phases. which are used to locate the halos.," However, FOG compression does have the advantage of including extra information in the analysis from the phases, which are used to locate the halos."
" Dealing directly with the FOG is not the same as extending the linear model. and P... P, Pee into the non-linear regime. as discussed in the previous section."," Dealing directly with the FOG is not the same as extending the linear model, and $P_{gg}$, $P_{g\theta}$ $P_{\theta\theta}$ into the non-linear regime, as discussed in the previous section."
" The real-space effect of random thermal motion of galaxies on small scales would lead P,, to decrease in amplitude. because of the decoherence of density and velocity divergence. while P,, increases."," The real-space effect of random thermal motion of galaxies on small scales would lead $P_{g\theta}$ to decrease in amplitude, because of the decoherence of density and velocity divergence, while $P_{\theta\theta}$ increases."
 We showed in Eq. (16)), We showed in Eq. \ref{eq:G}) )
 that a similar function to F(A.47) would be required to include quasi-linear behaviour in the redshift-space power spectrum.," that a similar function to $F(k,\mu^2)$ would be required to include quasi-linear behaviour in the redshift-space power spectrum."
 In this case We would not expect that these simple damping models can simultaneously match both the quasi-linear and fully non-linear behaviour (Fisher1995:Scoceimarro2004..," In this case we would not expect that these simple damping models can simultaneously match both the quasi-linear and fully non-linear behaviour \citep{Fis95,Sco04}."
. Clearly. if Εμ.) has two roles. we must reconsider any implied or assumed physical meaning in the function.," Clearly, if $F(k,\mu^2)$ has two roles, we must reconsider any implied or assumed physical meaning in the function."
 So. for example. the physical arguments that the Exponential form should be a better match to the average velocity dispersion in halos (Sheth1996:Peacock&DoddsWhite2001) are not applicable.," So, for example, the physical arguments that the Exponential form should be a better match to the average velocity dispersion in halos \citep{She96,PeaDod96,Whi01} are not applicable."
 For consistency with the standard ‘streaming model’. we continue to refer to the function Ft&.po)as a small-scale velocity dispersion (SSVD) model.," For consistency with the standard `streaming model', we continue to refer to the function $F(k,\mu^2)$as a small-scale velocity dispersion (SSVD) model."
 Following our review of the theory behind redshift-space distortions presented in Sections 2.1-—2.5.. we are left with a model of the redshift-space galaxy power spectrum To first order in &. both the Gaussian and Exponential forms for Fk.gc) considered in Section 2.5 act as an extra f° component with amplitude determined by c.," Following our review of the theory behind redshift-space distortions presented in Sections \ref{sec:lin}- \ref{sec:nlin}, we are left with a model of the redshift-space galaxy power spectrum To first order in $k$, both the Gaussian and Exponential forms for $F(k,\mu^2)$ considered in Section \ref{sec:nlin} act as an extra $\mu^6$ component with amplitude determined by $\sigma$."
 This fitting function ean act as an approximate correction for both quasi-linear and non-linear terms in the mapping between linear real-space and observed redshift-, This fitting function can act as an approximate correction for both quasi-linear and non-linear terms in the mapping between linear real-space and observed redshift-space.
" P, is independent of galaxy density bias. and is directly related to the matter velocity power spectrum. provided there is no velocity bias. caused by a mis-mateh between the distribution of galaxy velocities and the distribution of velocities in all matter."," $P_{\theta\theta}$ is independent of galaxy density bias, and is directly related to the matter velocity power spectrum, provided there is no velocity bias, caused by a mis-match between the distribution of galaxy velocities and the distribution of velocities in all matter."
 Eq. (205) , Eq. \ref{eq:pgs_combined}) )
could be fitted to data directly using a Likelihood approach (Hamilton2000:Tegmarketal.2004.2006).. resulting in observational constraints on. Pi. Pu. and Pu.," could be fitted to data directly using a Likelihood approach \citep{hamilton00,tegmark04,tegmark06}, resulting in observational constraints on $P_{gg}$, $P_{g\theta}$, and $P_{\theta\theta}$."
 Linking P... Pa. and [με to the matter power spectrum requires further assumptions.," Linking $P_{gg}$, $P_{g\theta}$ , and $P_{\theta\theta}$ to the matter power spectrum requires further assumptions."
 Following the deterministic. linear local galaxy bias model presented in Eq. €10)).," Following the deterministic, linear local galaxy bias model presented in Eq. \ref{eq:lin_bias}) ),"
 and the assumption of no velocity bias. the three power spectra are related to the matter power spectrum according to Eqns. 11..," and the assumption of no velocity bias, the three power spectra are related to the matter power spectrum according to Eqns. \ref{eq:Pmass_relations},"
 which leads toamodel This allows observations to constrain the matter. power spectrum multiplied by /7., which leads toamodel This allows observations to constrain the matter power spectrum multiplied by $f^2$ .
 We show that this model matches simulation results on large-scales in Section 6.., We show that this model matches simulation results on large-scales in Section \ref{sec:sim_results}. .
 If Eq. (21)), If Eq. \ref{eq:pgs_comb_lin}) )
 holds. Likelihood fits could be used to measure /otmass) and box¢(mass) from the measured power spectra.," holds, Likelihood fits could be used to measure $f\sigma_8({\rm mass})$ and $b\sigma_8({\rm mass})$ from the measured power spectra."
 Alternatively. we show in thenext Section that estimators of the matter power spectrum multiplied by /* can be constructed. based on a Legendre polynomial decomposition of theredshift-space power spectrum.," Alternatively, we show in thenext Section that estimators of the matter power spectrum multiplied by $f^2$ can be constructed, based on a Legendre polynomial decomposition of theredshift-space power spectrum."
Detailed studies of the structure of radio. pulsar pulse profiles are essential for understanding the pulsar emission mechanism and the forms of the pulsar emission beam.,Detailed studies of the structure of radio pulsar pulse profiles are essential for understanding the pulsar emission mechanism and the forms of the pulsar emission beam.
 Pulse profiles are remarkably stable over timescales ranging from. a [ew pulses to many vears. indicating that these profiles ave determined by permanent. physical characteristics of the neutron star and its environment.," Pulse profiles are remarkably stable over timescales ranging from a few pulses to many years, indicating that these profiles are determined by permanent physical characteristics of the neutron star and its environment."
 Many. profile properties can be explained. very well by the hollow-cone mocel of pulsar emission. developed: by Raclhakrishnan Cooke 969) anc IWomesaroll (1970). shortly after the discovery ‘the first pulsar.," Many profile properties can be explained very well by the “hollow-cone” model of pulsar emission developed by Radhakrishnan Cooke (1969) and Komesaroff (1970), shortly after the discovery of the first pulsar."
 This magnetic-pole model. further developed by Sturrock (1971) and Rucerman Sutherland 975). involves charges streaming from the polar cap along he open field lines. radiating in the direction of their motion and forming an emission cone aligned with the magnetic axis of the star.," This “magnetic-pole” model, further developed by Sturrock (1971) and Ruderman Sutherland (1975), involves charges streaming from the polar cap along the open field lines, radiating in the direction of their motion and forming an emission cone aligned with the magnetic axis of the star."
 As more pulsars were discovered. many were ound to have two. three or even more pulse components. »ompting various ellorts to. classify and. interpret. the various forms(e.," As more pulsars were discovered, many were found to have two, three or even more pulse components, prompting various efforts to classify and interpret the various forms."
g... Backer 1973: Rankin 1983. 1993: Lyne Manchester 1988).," Backer 1973; Rankin 1983, 1993; Lyne Manchester 1988)."
 In this paper we draw attention to the strange snotches” in the profiles of DO950|08 and. two. other pulsars. J0437.i4715 and. 1929|10.," In this paper we draw attention to the strange “notches” in the profiles of B0950+08 and two other pulsars, J0437–4715 and B1929+10."
 ALL three stars exhibit very similar double “notch” features which appear to have virtually nothing to do with the component structures of their very illerent. profiles.," All three stars exhibit very similar double “notch"" features which appear to have virtually nothing to do with the component structures of their very different profiles."
 D0950|OS ancl D1929|10 have rotational periods of 253 and 227 ms. whereas J0437.4715 isa binary millisecond pulsar with a period of only 5.75 ms.," B0950+08 and B1929+10 have rotational periods of 253 and 227 ms, whereas J0437–4715 is a binary millisecond pulsar with a period of only 5.75 ms."
 Significantly. these stars are some of the very closest among the pulsar populationall with dispersion measures (DMs) of about 3. pe * and parallax-cdeterminec distances of some 262-5.Ia 331410 and. 1703 pe (Brisken 22000. 2002)and. in spite of the fact that they all have rather ordinary spindown values. all have been detected in the optical and/or soft x-rav region (Alienani 2002: De Luca 22003: Wang 11997: Zavlin 22002).," Significantly, these stars are some of the very closest among the pulsar population—all with dispersion measures (DMs) of about 3 pc $^{-3}$ and parallax-determined distances of some $\pm$ 5, $\pm$ 10 and $\pm$ 3 pc (Brisken 2000, 2002)—and, in spite of the fact that they all have rather ordinary spindown values, all have been detected in the optical and/or soft x-ray region (Mignani 2002; De Luca 2003; Wang 1997; Zavlin 2002)."
 1309050|0S and. 131929|10 ave among the brightest pulsars in the radio skvClavlorefa£1993).. and JO437.4715 is well known as the brightest millisecond pulsar.," B0950+08 and B1929+10 are among the brightest pulsars in the radio \cite{ppcat}, and J0437–4715 is well known as the brightest millisecond pulsar."
 In relsecrobsres Νο discuss our observations of D0950|OS. present its average pulse profiles and describe the unusual features.," In \\ref{sec:obsres} we discuss our observations of B0950+08, present its average pulse profiles and describe the unusual features."
 In relsce:ciscuss we compare these features with similar ones seen in the profiles of 4715 and DB1929]|]10 and discuss possible physical interpretations., In \\ref{sec:discuss} we compare these features with similar ones seen in the profiles of $-$ 4715 and B1929+10 and discuss possible physical interpretations.
 Observations presented in this section were made using the 305-m1 Arecibo Telescope in Puerto Rico., Observations presented in this section were made using the 305-m Arecibo Telescope in Puerto Rico.
 Observations at 430 Mllz were obtained using the Arecibo Observatory Fourier Transform Machine TM) with 1024 channels across a 10-Mllz bandpass ancl with 409.6-yrs sampling., Observations at 430 MHz were obtained using the Arecibo Observatory Fourier Transform Machine ) with 1024 channels across a 10-MHz bandpass and with $\mu$ s sampling.
 D0950|08. was observed at 430 MlIz on ALJDs 51182. 51188 and 51180 (4th. 101 and llth of January. 1999) for durations of 3000. 3700 and. 2500 seconds. respectively.," B0950+08 was observed at 430 MHz on MJDs 51182, 51188 and 51189 (4th, 10th and 11th of January, 1999) for durations of 3000, 3700 and 2500 seconds, respectively."
 The 1475-MllIz. data’ presented were acquired with the Wiclebancl Arecibo Pulsar Processor (WAPDP')) with 128 channels across a 100-MlIz bancpass ancl 256-//5 sampling., The 1475-MHz data presented were acquired with the Wideband Arecibo Pulsar Processor ) with 128 channels across a 100-MHz bandpass and $\mu$ s sampling.
 Observations of BOO50|OS at this frequency. were taken on ALJDs 52187 and 52189 (Sth and 7th of October. 2001) for durations of 1100 and. 7200 seconds. respectively.," Observations of B0950+08 at this frequency were taken on MJDs 52187 and 52189 (5th and 7th of October, 2001) for durations of 1100 and 7200 seconds, respectively."
 For cach BOO50|08 observation. pulse phases were," For each B0950+08 observation, pulse phases were"
(36%)) and 189 belong to the S/Irr population (64).,) and 189 belong to the S/Irr population ).
 The velocity histogram of the combined. set. (the hashed listogram in the lower panel of Fig. 7)), The velocity histogram of the combined set (the hashed histogram in the lower panel of Fig. \ref{vhist}) )
 shows some evidence or kurtosis. based on the average of 6 kurtosis tests (Pinkney et al.," shows some evidence for kurtosis, based on the average of 6 kurtosis tests (Pinkney et al."
 1996). and a clear excess of galaxies at lower velocities.," 1996), and a clear excess of galaxies at lower velocities."
 The dillerence in the velocity centroid of the two morphologically-clistinet samples is reduced to 167 km s (164 km in the cluster rest frame) at a significance of Sy=1.5., The difference in the velocity centroid of the two morphologically-distinct samples is reduced to 167 km $^{-1}$ (164 km $^{-1}$ in the cluster rest frame) at a significance of $S_{\rm V} = 1.5$.
 The spatial distribution of both the I2/80 galaxies and the S/lrr galaxies is strongly elongated with position angles of 102 and 107. respectively. in the equatorial coordinate frame.," The spatial distribution of both the E/S0 galaxies and the S/Irr galaxies is strongly elongated with position angles of $^{\circ}$ and $^{\circ}$, respectively, in the equatorial coordinate frame."
 This corresponds to 146° and 151 in the Galactic coordinate reference frame: these angles are indicated by the arrows in the top-rieht corner of the right panels in Fig. &.., This corresponds to $^{\circ}$ and $^{\circ}$ in the Galactic coordinate reference frame; these angles are indicated by the arrows in the top-right corner of the right panels in Fig. \ref{dsall}.
 The uncertainty in the position angle is 3., The uncertainty in the position angle is $\sim$ $^{\circ}$.
 As before. the I2/80 population appears relaxed.," As before, the E/S0 population appears relaxed."
 Their velocity. centroid remains constant throughout the cluster (4979 2 S5 kms+ for all the E/SO galaxies within the Abell radius) and no substructure is detected by the Dressler-Sheetman d-test., Their velocity centroid remains constant throughout the cluster (4979 $\pm$ 85 km $^{-1}$ for all the E/S0 galaxies within the Abell radius) and no substructure is detected by the Dressler-Shectman $\delta$ -test.
 Phe velocity scale (551). o£ the LE/SO sample shows a distinct decrease as a function of radius (see ‘Table 3)). again a signature of a relaxed rich cluster (tines et al.," The velocity scale $S_{\rm BI}$ ) of the E/S0 sample shows a distinct decrease as a function of radius (see Table \ref{norsubstr}) ), again a signature of a relaxed rich cluster (Rines et al."
 2003)., 2003).
 The spiral galaxy population. on the other hand. appears far from. relaxed.," The spiral galaxy population, on the other hand, appears far from relaxed."
 “Phe velocity. centroid increases with increasing radius (shifting by ~200 km + across the Abell racius) and the velocity scale stavs roughly constant at ~960 km +., The velocity centroid increases with increasing radius (shifting by $\sim$ 200 km $^{-1}$ across the Abell radius) and the velocity scale stays roughly constant at $\sim$ 960 km $^{-1}$.
 Phe Monte Carlo simulations of the Dressler-Sheetman d-test of the ο galaxies indicate that only of the simulations show a larger degree of substructure compared to the observed amount of. substructure., The Monte Carlo simulations of the Dressler-Shectman $\delta$ -test of the S/Irr galaxies indicate that only of the simulations show a larger degree of substructure compared to the observed amount of substructure.
 The results of the o-test of the combined sample (CN.= 296) is shown in the right panels of Fig. S.., The results of the $\delta$ -test of the combined sample $N = 296$ ) is shown in the right panels of Fig. \ref{dsall}.
 We have identified: two spiral-vich subgroups based on the Dressler-Sheetman d-test of the ο population alone., We have identified two spiral-rich subgroups based on the Dressler-Shectman $\delta$ -test of the S/Irr population alone.
 When displaying those S/lrr galaxies for which 0;7225. two distinct groups appear.," When displaying those S/Irr galaxies for which $\delta_i > 2.25$, two distinct groups appear."
 In Fig., In Fig.
 9. the distribution in Galactic coordinates of the 296 cluster members are shown. where spiral galaxies with 6;z2.25 are shown as encircled dots.," \ref{subgroup} the distribution in Galactic coordinates of the 296 cluster members are shown, where spiral galaxies with $\delta_i > 2.25$ are shown as encircled dots."
 This 9; limit was chosen based on the outcome of the, This $\delta_i$ limit was chosen based on the outcome of the
"Note that, according to our scenario, each subsequent stellar generation in w Cen neednot differ substantially in age.","Note that, according to our scenario, each subsequent stellar generation in $\omega$ Cen need differ substantially in age."
 This is in contrast with early claims that c Cen harbors stellar populations with an internal age spread that can reach several Gyr???)., This is in contrast with early claims that $\omega$ Cen harbors stellar populations with an internal age spread that can reach several Gyr.
". It should be noted, however, that these earlier results were obtained without taking into account the possibility of different levels of He enrichment in the different populations, which can lead to biases in the age estimates."," It should be noted, however, that these earlier results were obtained without taking into account the possibility of different levels of He enrichment in the different populations, which can lead to biases in the age estimates."
" In addition, it has also been recently suggested that the ages of the different populations in w Cen are indeed very similar, perhaps to within 2 Gyr(???)."," In addition, it has also been recently suggested that the ages of the different populations in $\omega$ Cen are indeed very similar, perhaps to within 2 Gyr."
". That a uniform-age solution is consistent with the cluster's CMD is clearly shown in Figure 8 of?,, where fit to high-quality ACS@HST photometry is shown in the aconstant-age/multiple-Y scenario."," That a uniform-age solution is consistent with the cluster's CMD is clearly shown in Figure 8 of, where a fit to high-quality ACSHST photometry is shown in the constant-age/multiple-Y scenario."
" As for the previous PS classes, in panel h of Figure 5 we show schematically the expected shape of the diagnostic [Na/Fe] vs. [O/Fe] diagram."," As for the previous PS classes, in panel h of Figure \ref{FIGMassiveGC} we show schematically the expected shape of the diagnostic [Na/Fe] vs. [O/Fe] diagram."
 The corresponding HR diagrams for this class of PS are shown in Figure 6.., The corresponding HR diagrams for this class of PS are shown in Figure \ref{FIGIsoMassiveGC}.
" In regard to the age issue and w Cen's CMD, one can observe from Figure 6 two important points: As a final comment regarding the origin of the putative TG (i.e., the more metal-rich) component in w Cen, we note that it clearly corresponds to a component in this cluster."," In regard to the age issue and $\omega$ Cen's CMD, one can observe from Figure \ref{FIGIsoMassiveGC} two important points: As a final comment regarding the origin of the putative TG (i.e., the more metal-rich) component in $\omega$ Cen, we note that it clearly corresponds to a component in this cluster."
" However, it is not clear to us how several Gyr can go by after the SN II explosions until such a metal-rich component is formed?)."," However, it is not clear to us how several Gyr can go by after the SN II explosions until such a metal-rich component is formed."
". SN Ia do not appear to constitute a feasible solution, since the most metal-rich stars in w Cen are also highly enriched in O and Na with respect to SG stars(??2)."," SN Ia do not appear to constitute a feasible solution, since the most metal-rich stars in $\omega$ Cen are also highly enriched in O and Na with respect to SG stars."
". In fact, yields of SN II do show an increase in Na, but not in O — which means that, according to our scenario, TG stars will have [O/Fe] similar to SG stars, but higher [Na/Fe] and [Fe/H]."," In fact, yields of SN II do show an increase in Na, but not in O – which means that, according to our scenario, TG stars will have [O/Fe] similar to SG stars, but higher [Na/Fe] and [Fe/H]."
 This is precisely the behavior that is observed in Figure 19 of?.., This is precisely the behavior that is observed in Figure 19 of.
" In summary, according to our scenario, in the case of a very massive progenitor, we expect that SG stars are He-"," In summary, according to our scenario, in the case of a very massive progenitor, we expect that SG stars are He-"
lo hierarchical cosmologies such as the now-standard ACDAL model. objects like the dark halo of our Alilky Way. grow through the merging of previously collapsed svstems with a wide range of masses.,"In hierarchical cosmologies such as the now-standard $\Lambda$ CDM model, objects like the dark halo of our Milky Way grow through the merging of previously collapsed systems with a wide range of masses."
" Even the earliest. detailed: moclels for the erowth of a “Alilky Way"" showed. that. simple assumptions for star formation elliciency imply. many more visible satellites than are actually observed (Ixaulfmann. White Guiderdoni 1993)."," Even the earliest detailed models for the growth of a “Milky Way” showed that simple assumptions for star formation efficiency imply many more visible satellites than are actually observed (Kauffmann, White Guiderdoni 1993)."
 These authors argued that gas conlensation and thus star. formation. must be strongly suppressed in systems with low escape velocity. perhaps ον photoionisation heating.," These authors argued that gas condensation and thus star formation must be strongly suppressed in systems with low escape velocity, perhaps by photoionisation heating."
 This echoed Efstathiou’s (1992) arguments on the related question of why the faint-end slope ofthe observed galaxy luminosity Function is much shallower han predicted by the simple hierarchical galaxy formation heory of White Rees (1978) and its later reworkings in he CDM context (e.g. White Frenk 1991)., This echoed Efstathiou's (1992) arguments on the related question of why the faint-end slope of the observed galaxy luminosity function is much shallower than predicted by the simple hierarchical galaxy formation theory of White Rees (1978) and its later reworkings in the CDM context (e.g. White Frenk 1991).
 This issue crew relatively little. attention until N-)ody techniques became capable of simulating halos with runclreds of thousands of particles., This issue drew relatively little attention until N-body techniques became capable of simulating halos with hundreds of thousands of particles.
 Moore (1999) ane Ixlvpin (1999) showed that galaxy. halos in a CDA cosmogony are not smooth svstems., Moore (1999) and Klypin (1999) showed that galaxy halos in a CDM cosmogony are not smooth systems.
 Roughly of the mass within their virialised regions is contributed by a hos of dense ποbound substructures., Roughly of the mass within their virialised regions is contributed by a host of dense self-bound substructures.
 These are the surviving cores of objects which merged. together to make the final system. and so correspond. directly. to the overabundan satellites of the earlier models.," These are the surviving cores of objects which merged together to make the final system, and so correspond directly to the overabundant satellites of the earlier models."
 Phe apparent overabundance may again be reconciled with the small number of visible satellites by invoking the inhibiting elfects of photo-heating Bullock. Ixravtsov Weinberg 2000. Benson 2002).," The apparent overabundance may again be reconciled with the small number of visible satellites by invoking the inhibiting effects of photo-heating (Bullock, Kravtsov Weinberg 2000, Benson 2002)."
 Both Moore (1999) and Whypin (1999) emphasised a dilLIerent xoblem. however.," Both Moore (1999) and Klypin (1999) emphasised a different problem, however."
" Phe maximum circular velocities of the LO or 20 most massive substructures within a Milky Way halo are predicted to be in the range 20 to 60 km/s. whereas he observed velocity. dispersions of 7 of the Milkv Way's 11 satellites are below 10 km/s. Halo mocels typically have well over a hundred substructures with maximum circular velocity above 10 km/s. This discrepancy has been considered: a 7erisis"" Lor the conventional ACDAL cosmogony. prompting proposals to modify the microscopic properties of the dark matter (c.g. Spergel Steinhardt 2000: Moore 2000: Yoshida 2000: 3ode. Ostriker Turok 2001)."," The maximum circular velocities of the 10 or 20 most massive substructures within a Milky Way halo are predicted to be in the range 20 to 60 km/s, whereas the observed velocity dispersions of 7 of the Milky Way's 11 satellites are below 10 km/s. Halo models typically have well over a hundred substructures with maximum circular velocity above 10 km/s. This discrepancy has been considered a “crisis” for the conventional $\Lambda$ CDM cosmogony, prompting proposals to modify the microscopic properties of the dark matter (e.g. Spergel Steinhardt 2000; Moore 2000; Yoshida 2000; Bode, Ostriker Turok 2001)."
 We here examine the discrepancy. more critically. using .XCDM simulations with similar resolution to the best simulations of Moore (1999) or Power (2002).," We here examine the discrepancy more critically, using $\Lambda$ CDM simulations with similar resolution to the best simulations of Moore (1999) or Power (2002)."
 We analyse the potential well structure of the most massive “satellites” in our final svstem. calculating the velocity dispersion profiles predicted if stellar systems identical in structure to the observed satellites are placed in each.," We analyse the potential well structure of the most massive “satellites” in our final system, calculating the velocity dispersion profiles predicted if stellar systems identical in structure to the observed satellites are placed in each."
 Remarkably. we find excellent agreement with the observed. velocity dispersions. even for svstenis," Remarkably, we find excellent agreement with the observed velocity dispersions, even for systems"
 , 
We must also consider the possibility that the sub-mm excess detected in NGC 1705 is not as a result of an extra dust component.,We must also consider the possibility that the sub-mm excess detected in NGC 1705 is not as a result of an extra dust component.
 One hypothesis arguing against such a conclusion is that the sub-mm excess could originate instead from hot (~100 K) dust with a dust emissivity index =I! and the temperature fluctuations of very small grains (Lisenfeld et al., One hypothesis arguing against such a conclusion is that the sub-mm excess could originate instead from hot $\sim$ 100 K) dust with a dust emissivity index =1 and the temperature fluctuations of very small grains (Lisenfeld et al.
 2002)., 2002).
 The excess could also be explained through a change in the emissivity of the cold dust grains., The excess could also be explained through a change in the emissivity of the cold dust grains.
 For an example of how the emissivity may change as we move into differing temperature regimes. Dupac et al. (," For an example of how the emissivity may change as we move into differing temperature regimes, Dupac et al. ("
2003) suggest that 8 decreases with increasing temperatures. from ~2 in cold (T ~ 11-20 K) regions to 0.8 to 1.6 in warmer regions (T ~ 35 - 80 K).,"2003) suggest that $\beta$ decreases with increasing temperatures, from $\sim$ 2 in cold (T $\sim$ 11-20 K) regions to 0.8 to 1.6 in warmer regions (T $\sim$ 35 - 80 K)."
 In contrast. Paradis et al. (," In contrast, Paradis et al. ("
2009) showed that the spectral shape of emissivity are always steeper in the FIR ( -600 jum) and flatten in the submm and mm regions.,2009) showed that the spectral shape of emissivity are always steeper in the FIR ( $\rm\lambda < 600~{\rm\mu m} $ ) and flatten in the submm and mm regions.
 In regions where dust is significantly colder in the molecular phase than in the atomic phase. an increase in the emissivity by a factor of 23 was detected only in the FIR. whilst the emissivity for the dust in the atomic and molecular phases become comparable again in the submm and mm wavelength range.," In regions where dust is significantly colder in the molecular phase than in the atomic phase, an increase in the emissivity by a factor of $\rm\simeq $ 3 was detected only in the FIR, whilst the emissivity for the dust in the atomic and molecular phases become comparable again in the submm and mm wavelength range."
 The observed break in the emissivity spectrum is in qualitative agreement with the dust emission model of Ménny et al. (, The observed break in the emissivity spectrum is in qualitative agreement with the dust emission model of Ménny et al. (
2007). which invokes quantum effects in amorphous solids to explain the flatness of the observed submm emission spectrum and also produces a break in the emissivity slope around 600. jm.,"2007), which invokes quantum effects in amorphous solids to explain the flatness of the observed submm emission spectrum and also produces a break in the emissivity slope around 600 $~{\rm\mu m} $."
 However. one must exercise caution in adopting such an interpretation.," However, one must exercise caution in adopting such an interpretation."
 Flux uncertainties. especially in the Rayleigh-Jeans regime. can affect the results for the SED fits as far as temperature and emissivity are concerned. as fitting fluxes near the SED peak produces inaccurate temperature and dust spectral index estimates.," Flux uncertainties, especially in the Rayleigh-Jeans regime, can affect the results for the SED fits as far as temperature and emissivity are concerned, as fitting fluxes near the SED peak produces inaccurate temperature and dust spectral index estimates."
 In addition. line-of-sight temperature (and density) variations can also affect the SED fitting (Shetty et al. (," In addition, line-of-sight temperature (and density) variations can also affect the SED fitting (Shetty et al. ("
2009a.b)).,"2009a,b))."
 Longer wavelength fluxes in the Jeans part of the spectrum (= 600 jm) may hore accurately recover the spectral index. but both methods are very sensitive to noise (Shetty et al. (," Longer wavelength fluxes in the Rayleigh-Jeans part of the spectrum $\geq$ 600 $\mu$ m) may more accurately recover the spectral index, but both methods are very sensitive to noise (Shetty et al. ("
2009a.b)).,"2009a,b))."
 An additional alternative. to a cold dust component is spinning dust where the rotational dynamics of very small interstellar grains can explain the 10 - 100. GHz component of the diffuse Galactic background via electric dipole rotational emission under normal interstellar conditions (Draine Lazarian 1998a.b).," An additional alternative to a cold dust component is spinning dust where the rotational dynamics of very small interstellar grains can explain the 10 - 100 GHz component of the diffuse Galactic background via electric dipole rotational emission under normal interstellar conditions (Draine Lazarian 1998a,b)."
 However. Jones (2009) notes that observations by Dickinson et al. (," However, Jones (2009) notes that observations by Dickinson et al. ("
2006). which searched for a microwave emission excess in an H [I region. puts an upper limit on the dust emission at 31 GHz and appears to be inconsistent with the spinning dust model.,"2006), which searched for a microwave emission excess in an H II region, puts an upper limit on the dust emission at 31 GHz and appears to be inconsistent with the spinning dust model."
 Given the unsatisfactory evidence arguing against the use of amorphous carbon to explain the sub-mm excess. we conclude that the most likely scenario to explain the observed excess is that of an additional cold dust component.," Given the unsatisfactory evidence arguing against the use of amorphous carbon to explain the sub-mm excess, we conclude that the most likely scenario to explain the observed excess is that of an additional cold dust component."
and the gauge-independent variables by = 1060!tery δαν ο =,and the gauge-independent variables by = +a^2 Q - ] = .
 The two basic dependent observables are distance and growth rate., The two basic dependent observables are distance and growth rate.
 Distance measures are based on standard candles. rulers. or number densities as a function of redshift: growth rate measures are based on density in linear theory.," Distance measures are based on standard candles, rulers, or number densities as a function of redshift; growth rate measures are based on density in linear theory."
" All distance measures are ultimately based on the comoving distance to redshift z ""mach the SNe Type I a observations measure the magnitude of distant SNe. given by nmga(z)=Slog,[Cl+ro]M."," All distance measures are ultimately based on the comoving distance to redshift $z$ r = _0^z = _a^1, the SNe Type I a observations measure the magnitude of distant SNe, given by $m_B(z) = 5 {\rm log}_{10} [(1+z) r(z)] + {\cal M}$."
 The effect of for distance measures is through the background expansion of the universe.1.6... from the Hubble parameter H(z)2H(a)/a.," The effect of for distance measures is through the background expansion of the universe, from the Hubble parameter $H(z) =
\HH(a)/a$."
 For CMB data. this comes in through the angular diameter distance and the sound horizon ," For CMB data, this comes in through the angular diameter distance and the sound horizon D_A(a) = a _1^a = a _1^a s(a) = _0^a = _0^a."
The density are affected by the presence of firstly through the Hubble parameter. and secondly through the linear ofenergy.. as in eqs (??.. 9)). or eqs (22.. ??.. ??)).," The density are affected by the presence of firstly through the Hubble parameter, and secondly through the linear of, as in eqs \ref{eq:pert}, , \ref{eq:pert2}) ), or eqs \ref{eq:2q}, \ref{eq:2psi}, \ref{eq:2dm}) )."
 For the CMB power spectrum. the effect of these is feltmost strongly in the ISW effect at low /. as well as in a shift of the peak positions.," For the CMB power spectrum, the effect of these is feltmost strongly in the ISW effect at low $l$, as well as in a shift of the peak positions."
 The low / observations ean be understood as follows., The low $l$ observations can be understood as follows.
" The behaviour of the temperature anisotropy power spectrum in the CMB is given by the covariance of the temperature fluctuation expanded in spherical harmonies C, = An AG ""]iF where P, is the initial power spectrum. jo 1s the conformal time today. and AQ.jo) is the transfer function at each /."," The behaviour of the temperature anisotropy power spectrum in the CMB is given by the covariance of the temperature fluctuation expanded in spherical harmonics C_l = 4 _x _l(k, _0)|^2, where ${\cal P}_x$ is the initial power spectrum, $\eta_0$ is the conformal time today, and $\Delta_l(k, \eta_0)$ is the transfer function at each $l$ ."
 On large scales the transfer functions are of the form Aq οor Apsstu(30) where APS) are the contributions from the last scattering surface from the ordinary Sachs-Wolfe effect and temperature anisotropy. and ADS(k) is the contribution due to the change in the potential o along the line of sight and is called the integrated Sachs-Wolfe (ISW) effect.," On large scales the transfer functions are of the form _l(k, _0) = +, where $\Delta_l^{\rm LSS}(k)$ are the contributions from the last scattering surface from the ordinary Sachs-Wolfe effect and temperature anisotropy, and $\Delta_l^{\rm ISW}(k)$ is the contribution due to the change in the potential $\phi$ along the line of sight and is called the integrated Sachs-Wolfe (ISW) effect."
" The ISW contribution can be written as ""ouka where Τί) is the optical depth due to scattering of the photons along the line of sight. and /j(x) are the spherical Bessel functions."," The ISW contribution can be written as = _0)], where $\tau(\eta)$ is the optical depth due to scattering of the photons along the line of sight, and $j_l(x)$ are the spherical Bessel functions."
" The frame-invariant potential o. defined in terms of the Weyl tensor. is equivalent to the Bardeen potential in the absence of anisotropic stress and given by the Poisson equation Κωξ ""πο δρ while its derivative in a matter plus universe. which is the source term for the ISW contribution. is given by kKeowrs ~40G |(33)"," The frame-invariant potential $\phi$, defined in terms of the Weyl tensor, is equivalent to the Bardeen potential in the absence of anisotropic stress and given by the Poisson equation k^2 = -4 G a^2, while its derivative in a matter plus universe, which is the source term for the ISW contribution, is given by k^2 = -4 G + ) ]."
 From the above equations. it is clear that the magnitude of the ISW contribution is dependent on the late time evolution of the total densityperturbations.. therefore on theperturbations.," From the above equations, it is clear that the magnitude of the ISW contribution is dependent on the late time evolution of the total density, therefore on the."
. It should be noted however. that these are not independent of other cosmological parameters. and the effect of could be masked due to the degeneracy of the parameters with other parameters such as Ho and the curvature of the universe.," It should be noted however, that these are not independent of other cosmological parameters, and the effect of could be masked due to the degeneracy of the parameters with other parameters such as $H_0$ and the curvature of the universe."
" To study ΕΡΕ models under this formalism. we consider a w- parameterization which may represent a large class of varying models (Corasanitiefal.2003) wparmw(a) = where Wo is the equation of state of dark energy today. wy, 18 the equation of state in the matter dominated era. e, is the scale factor at which the transition between wo and ww, takes place. and A, is the width of the transition."," To study EDE models under this formalism, we consider a $w$ -parameterization which may represent a large class of varying models \cite{coras} w(a) =, where $\w$ is the equation of state of dark energy today, $\wm$ is the equation of state in the matter dominated era, $\at$ is the scale factor at which the transition between $\w$ and $\wm$ takes place, and $\dt$ is the width of the transition."
" If 1, is allowed to be a free parameter this parameterization can encompass a large class of models. including ACDM and w= constant models."," If $\wm$ is allowed to be a free parameter this parameterization can encompass a large class of models, including $\ld$ CDM and $w =$ constant models."
 Models with constant or slowly varying wo—1 would be consistent with current observations. however these are not EDE models. as they have negligible amounts of at early times.," Models with constant or slowly varying $w \simeq -1$ would be consistent with current observations, however these are not EDE models, as they have negligible amounts of at early times."
 For such models. there would be very poor constraints on the transition parameters. since no significant transition takes place between early time and late timeenergy.," For such models, there would be very poor constraints on the transition parameters, since no significant transition takes place between early time and late time."
". Allowing these models in the analysis would therefore cause the constraints on d,.A to weaken."," Allowing these models in the analysis would therefore cause the constraints on $\at, \dt$ to weaken."
 Leaving the amount of early free would be interesting when comparing EDE models with ACDM and other models., Leaving the amount of early free would be interesting when comparing EDE models with $\ld$ CDM and other models.
 Such comparisons have previously shown that while it is possible to put an upper limit on the amount of earlyenergy.. it is not possible to put strong constraints on the evolution of if all the different models are considered.," Such comparisons have previously shown that while it is possible to put an upper limit on the amount of early, it is not possible to put strong constraints on the evolution of if all the different models are considered."
 Previous studies (Doran&Robbers2006;XiaViel2009) have constrained early time dark energy density to ~3% of the matter density. however. as seen in (Xia&Viel2009).. the evolution of is weakly constrained.," Previous studies \citep{ede3, ede8} have constrained early time dark energy density to $\simeq 3 \%$ of the matter density, however, as seen in \cite{ede8}, the evolution of is weakly constrained."
 In this work. we study the EDE models exclusively. to put constraints on the transition from early to late time energy.," In this work, we study the EDE models exclusively, to put constraints on the transition from early to late time ."
. If we are able to constrain the minimum redshift (or maximum seale factor) at which such a transition occurs. we would know that any signature for EDE would befound only in observations beyond that redshift.," If we are able to constrain the minimum redshift (or maximum scale factor) at which such a transition occurs, we would know that any signature for EDE would befound only in observations beyond that redshift."
"where V(ó) is the radial velocity at phase 6. > is the component of the accretion streams velocity perpendicular to the orbital plane projected along the line of sight. A is the velocity amplitude and ©, is the phase at which the observed radial velocity equals the 5, velocity when crossing from blue to red.","where $V(\phi$ ) is the radial velocity at phase $\phi$, $\gamma$ is the component of the accretion streams velocity perpendicular to the orbital plane projected along the line of sight, $K$ is the velocity amplitude and $\phi_{o}$ is the phase at which the observed radial velocity equals the $\gamma$ velocity when crossing from blue to red."
 To estimate the errors. the velocity error was adjusted to normalise the reduced xzto 1.0 since it was not possible to derive meaningful errors to the Ciaussian fits.," To estimate the errors, the velocity error was adjusted to normalise the reduced to 1.0 since it was not possible to derive meaningful errors to the Gaussian fits."
 Table 1 shows the best fit parameters and the 90 per cent confidence interval while figure 4. shows the best fits along with the data., Table \ref{rvparam} shows the best fit parameters and the 90 per cent confidence interval while figure \ref{rvew} shows the best fits along with the data.
 We now cdiseuss the implications these results have on our view of the accretion stream., We now discuss the implications these results have on our view of the accretion stream.
 We have been able to distinguish two components in the Ilydrogen line profiles: a narrow and a broad component., We have been able to distinguish two components in the Hydrogen line profiles: a narrow and a broad component.
 The broad component is most. probably: due to. emission originating from the accretion stream. close to the white chvarl because of its high maximum racial velocity., The broad component is most probably due to emission originating from the accretion stream close to the white dwarf because of its high maximum radial velocity.
 Since the stream initially has the rotational velocity of the secondary star. the broad component will be seen with maximum red shift before O=0.0 — in this case at ó 70.91.," Since the stream initially has the rotational velocity of the secondary star, the broad component will be seen with maximum red shift before $\phi$ =0.0 – in this case at $\phi\sim$ 0.91."
 The narrow component has a much lower radial velocity than the broad. component: if the narrow component originated. from the heated. face of the secondary star we would expect to see it with maximum red shift at ὁ ~0.25., The narrow component has a much lower radial velocity than the broad component: if the narrow component originated from the heated face of the secondary star we would expect to see it with maximum red shift at $\phi\sim$ 0.25.
 The fact that we see it with maximum red shift at ó ~0.98 implies that the narrow component which we can distinguish is not a good marker of the secondary star., The fact that we see it with maximum red shift at $\phi\sim$ 0.98 implies that the narrow component which we can distinguish is not a good marker of the secondary star.
 La non-eclipsing systems. where there is no extra information on the orbital phase of the secondary. it has often. been assumed that the narrow component originates [rom the irradiated. [ace of the secondary.," In non-eclipsing systems, where there is no extra information on the orbital phase of the secondary, it has often been assumed that the narrow component originates from the irradiated face of the secondary."
 In the case of MN. Ίνα we know that the maximum. red-shift. of the narrow component. occurs close to the eclipse. so cannot be emitted by the secondary.," In the case of MN Hya we know that the maximum red-shift of the narrow component occurs close to the eclipse, so cannot be emitted by the secondary."
 Instead the accretion stream close to the secondary. is the most Likely candidate and this view is supported by the fact ju the narrow component is eclipsed and with a duration longer than the white dwarf eclipse., Instead the accretion stream close to the secondary is the most likely candidate and this view is supported by the fact that the narrow component is eclipsed and with a duration longer than the white dwarf eclipse.
 We note that this may well be true for mostfall svstems. and that low-resolution Es»ectroscopy. is not a suitable method for detecting. the motion of the secondary (and thus measuring the mass ratio of the svstem).," We note that this may well be true for most/all systems, and that low-resolution spectroscopy is not a suitable method for detecting the motion of the secondary (and thus measuring the mass ratio of the system)."
 Schwope. Mantel Horne (1997). for instance. show that with higher resolution spectroscopy. it is possible to separate the narrow components emitted. by 1e stream and the secondary.," Schwope, Mantel Horne (1997), for instance, show that with higher resolution spectroscopy, it is possible to separate the narrow components emitted by the stream and the secondary."
 There are a number of svstems which show cips in soft. N-ravs which have been attributed. to the accretion stream obscuring the hot post shock region above the white chyvarl (ος Watson ct al 1989. Buckley et al 1998b).," There are a number of systems which show dips in soft X-rays which have been attributed to the accretion stream obscuring the hot post shock region above the white dwarf (eg Watson et al 1989, Buckley et al 1998b)."
 Llowever. there is only 1: other Polar in which optical lines appear in absorption during a stream cip (eb Eri: Verbunt ct al 1980. Allen. Ward Wright 1981).," However, there is only 1 other Polar in which optical lines appear in absorption during a stream dip (EF Eri: Verbunt et al 1980, Allen, Ward Wright 1981)."
 In the case of EP Eri. lines redder than 5500 appeared in absorption.," In the case of EF Eri, lines redder than 5500 appeared in absorption."
 In the case of ALN Iva we find that at ó~0.90 the Lla and L2 lines are seen in both emission and absorption. both of which are red-shiftcd.," In the case of MN Hya we find that at $\phi\sim$ 0.90 the $\alpha$ and $\beta$ lines are seen in both emission and absorption, both of which are red-shifted."
 The emission. and. absorption components of the IIa. line have radial velocities of ~270 km s and ~870 km s| respectively., The emission and absorption components of the $\alpha$ line have radial velocities of $\sim$ 270 km $^{-1}$ and $\sim$ 870 km $^{-1}$ respectively.
 Since the stream is curved and we do not know where the emission and absorption components originate we cannot determine the true velocities of these components., Since the stream is curved and we do not know where the emission and absorption components originate we cannot determine the true velocities of these components.
 It is. however. likely that the absorption component originates closer to the white dwarf than the emission component.," It is, however, likely that the absorption component originates closer to the white dwarf than the emission component."
 On the other hand. the fact there are two accreting poles (cf next section) and hence two accretion streams once the stream attaches onto the magnetic field lines of the white ναι. may complicate this interpretation.," On the other hand, the fact there are two accreting poles (cf next section) and hence two accretion streams once the stream attaches onto the magnetic field lines of the white dwarf, may complicate this interpretation."
 In 83 we presented. phase resolved optical spectra of. ALN Ίνα which show features which we interpret as cvclotron humps andestimate a magnetic field strength of the white dwarf to be D—42MCG from their spacing., In 3 we presented phase resolved optical spectra of MN Hya which show features which we interpret as cyclotron humps andestimate a magnetic field strength of the white dwarf to be $B$ =42MG from their spacing.
 This is higher than the £ ~2OAIC estimated. by Buckley. et al (19982) [rom an integrated non-Dux calibrated spectrum., This is higher than the $B\sim$ 20MG estimated by Buckley et al (1998a) from an integrated non-flux calibrated spectrum.
 Buckley οἱ al then modeled their white light optical polarimetry using B=20 MG., Buckley et al then modeled their white light optical polarimetry using $B$ =20 MG.
 ‘Lo test if their same polarimetry data can be adequately: modeled: using a field. strength. of D. =42 MG ancl determine the location of the aceretion regions on the surface of the white dwarf we measured the data points from Fie., To test if their same polarimetry data can be adequately modeled using a field strength of $B=$ 42 MG and determine the location of the accretion regions on the surface of the white dwarf we measured the data points from Fig.
 4 o£ Buckley et al (10998a) and fitted their data using the optimisation method of Potter. Hakala Cropper (1998).," 4 of Buckley et al (1998a) and fitted their data using the optimisation method of Potter, Hakala Cropper (1998)."
 Up until now most. polarimetry data. including. that. of Buckley οἱ al. have been modeled by constructing accretion regions on the surface of the white cwarl by hand and then a good fit to the data was achieved by trial ancl error.," Up until now most polarimetry data, including that of Buckley et al, have been modeled by constructing accretion regions on the surface of the white dwarf by hand and then a good fit to the data was achieved by trial and error."
 The method of Potter. Hakala Cropper finds the best fit in an objective manner.," The method of Potter, Hakala Cropper finds the best fit in an objective manner."
 In our new fit we fixed the magnetic field strength at B=42 MG and the inclination at 75 (derived from the eclipse duration. Buckley et al 19982).," In our new fit we fixed the magnetic field strength at $B$ =42 MG and the inclination at $^{\circ}$ (derived from the eclipse duration, Buckley et al 1998a)."
 The fits of Buckley ct al (19982). implied: that two accretion regions are visible (the main region being partially visible near the lower magnetic pole) ancl that they are ereathy extended. in magnetic longitude. (the secondary region is 300° in length and is near the upper pole)., The fits of Buckley et al (1998a) implied that two accretion regions are visible (the main region being partially visible near the lower magnetic pole) and that they are greatly extended in magnetic longitude (the secondary region is $^{\circ}$ in length and is near the upper pole).
 Both accretion regions were offset from their respective magnetic poles by ~ 207., Both accretion regions were offset from their respective magnetic poles by $\sim20^{\circ}$ .
 Our fits to the same polarimetric data are, Our fits to the same polarimetric data are
Eiroaetal.(2005). searched for 3.5 cm VLA sources in Serpens and. together with eighteen more evolved sources. they detected FIRSI. SMM4. SMM9/SO68N. and SMM10.,"\citet{etc+2005} searched for 3.5 cm VLA sources in Serpens and, together with eighteen more evolved sources, they detected FIRS1, SMM4, SMM9/S68N, and SMM10."
" They also searched for ISO counterparts and suggested that these four sources had an ISO counterpart: they noted that the Class 0 classification. given in the literature. for these four sources. is based on (sub-)millimetrie observations 1996:; Wolf-Chaseetal.. 1998:: Hogerheijdeet 1999)), while the Class I classification is taken from ISO mid- observations (Kaasetal... 2004))."," They also searched for ISO counterparts and suggested that these four sources had an ISO counterpart; they noted that the Class 0 classification given in the literature, for these four sources, is based on (sub-)millimetric observations \citealp{hb96}; \citealp{wbw+98}; \citealp{hds+99}) ), while the Class I classification is taken from ISO mid-IR observations \citealp{kob+04}) )."
 In the case of FIRSI. however. the cross-identification with ISO objects 258a and 258b is uncertain. since ISO objects 258a and 258b lie 2 9 aresee away from the position of the mm/submm source and. as discussed by Kaasetal. (2004).. they could be scattered light from the far-IR source FIRSI.," In the case of FIRS1, however, the cross-identification with ISO objects 258a and 258b is uncertain, since ISO objects 258a and 258b lie $\ga$ 9 arcsec away from the position of the mm/submm source and, as discussed by \citet{kob+04}, , they could be scattered light from the far-IR source FIRS1."
 Kaasetal.(2004). also exclude ISOCAM detections for SMM2 and SMM3 within the positional uncertainties., \citet{kob+04} also exclude ISOCAM detections for SMM2 and SMM3 within the positional uncertainties.
 Table 1. provides the positions for this sample of Class 0 or Q/I sources which fall in the ACIS field of view of our Serpens observation., Table \ref{tab:c0} provides the positions for this sample of Class 0 or 0/I sources which fall in the ACIS field of view of our Serpens observation.
 None of these 6 sources was detected in the recent oobservation confirming the high ratio of sub-millimiter to mid-IR luminosity for these sources. and thereby their Class 0 nature.," None of these 6 sources was detected in the recent observation confirming the high ratio of sub-millimiter to mid-IR luminosity for these sources, and thereby their Class 0 nature."
 An important result from the present study is that none of the six Class 0 sources in Table | are individually detected as X-ray sources., An important result from the present study is that none of the six Class 0 sources in Table \ref{tab:c0} are individually detected as X-ray sources.
 This non-detection can be translated in an estimate of the absorbing columr density necessary to absorb a source's emission to the level where it would become undetectable in our data (below ~ 0.1 cts/ks. as per Table 5)). assuming a spectrum and luminosity for the source.," This non-detection can be translated in an estimate of the absorbing column density necessary to absorb a source's emission to the level where it would become undetectable in our data (below $\sim$ 0.1 cts/ks, as per Table \ref{tab:src}) ), assuming a spectrum and luminosity for the source."
 We usec as proxy the X-ray spectrum of a Class I source in our field. source 60 (with 0.7 ets/ks). and increased the absorbing colum: density of its best-fit model to the value at which the model predicted source counts would be ~ 0.1 ks~!. i.e. our detectior limit.," We used as proxy the X-ray spectrum of a Class I source in our field, source 60 (with 0.7 cts/ks), and increased the absorbing column density of its best-fit model to the value at which the model predicted source counts would be $\sim$ 0.1 $^{-1}$, i.e. our detection limit."
 Source 60 would become undetectable in our data behind an absorbing column density of NCH)~40x10°? em or Ay~200.," Source 60 would become undetectable in our data behind an absorbing column density of $\nh \sim
40\times 10^{22}$ $^{-2}$ or $A_V \sim 200$."
 Source 60 has a best fit AT value of 2.4 keV anc an (intrinsic) luminosity of 10°°s7!.. which are typical for Class I sources.," Source 60 has a best fit $kT$ value of 2.4 keV and an (intrinsic) luminosity of $10^{30}$, which are typical for Class I sources."
" In the sample of five Class I sources of p Oph compiled by Ozawaetal.(2005).. the average values of AT and Lx are 3.2 keV and 2.9x10°"" erg s7!."," In the sample of five Class I sources of $\rho$ Oph compiled by \citet{ogm05}, the average values of $kT$ and $L_{\rm X}$ are 3.2 keV and $2.9\times 10^{30}$ erg $^{-1}$."
 Therefore. in the assumption that Class 0 sources have X-ray characteristics similar to Class I objects. source 60 is a good proxy.," Therefore, in the assumption that Class 0 sources have X-ray characteristics similar to Class I objects, source 60 is a good proxy."
 As already mentioned. Tsuboietal.(2001) and Hamaguchial.(2005) derive column densities of the order of (10— em™ in their X-ray observations of highly embedded YSOs.," As already mentioned, \citet{tkh+2001} and \citet{hcp+2005} derive column densities of the order of $(10-30)\times 10^{22}$ $^{-2}$ in their X-ray observations of highly embedded YSOs."
 Since these objects appear to have higher plasma temperatures than source 60 (KT.~3—4 keV) and similar luminosity. than we can exclude the possibility that X-ray sources similar to the one reported by the above authors are embedded within the mm/submm sources of Table l..," Since these objects appear to have higher plasma temperatures than source 60 $kT \sim
3-4$ keV) and similar luminosity, than we can exclude the possibility that X-ray sources similar to the one reported by the above authors are embedded within the mm/submm sources of Table \ref{tab:c0}."
 As shown in reffig:limLx.. a source with a higher plasma temperature than source 60 and the same luminosity would have to be screened by an absorbing column density higher than 40x1077 em for its count rate to be below our detection threshold.," As shown in \\ref{fig:limLx}, a source with a higher plasma temperature than source 60 and the same luminosity would have to be screened by an absorbing column density higher than $40\times 10^{22}$ $^{-2}$ for its count rate to be below our detection threshold."
 For comparison. a source with kT=4.3 keV and Ly=10? would be undetectable in our data only if screened by an absorbing column density 260«107 cm (Αν2300 mag).," For comparison, a source with $kT = 4.3$ keV and $L_X = 10^{30}$ would be undetectable in our data only if screened by an absorbing column density $\ga 60\times 10^{22}$ $^{-2}$ $A_V \ga 300$ mag)."
 A source with characteristics similar to IRAS 2139145802. reported by Getmanetal.(2006).. would have also been well visible in our observation. its properties (NCH)~101. kT= keV and Lx~2x10°! p implying in ACIS a count rate of 1.0 .," A source with characteristics similar to IRAS 21391+5802, reported by \citet{gfg+06}, would have also been well visible in our observation, its properties $\nh \sim 10^{24}$, $kT = 6.0$ keV and $L_{\rm X} \sim
2\times 10^{31}$ ) implying in ACIS a count rate of 1.0 $^{-1}$."
 If the high luminosity and plasma temperature of IRAS 2139]-5802 are. however. theresult of a flare and the more common situation is the one in which a lower luminosity.," If the high luminosity and plasma temperature of IRAS 21391+5802 are, however, theresult of a flare and the more common situation is the one in which a lower luminosity,"
luminosity ratio (B/T) and the Hubble stage(7.Simien&Vaucouleurs 1986).,"luminosity ratio (B/T) and the Hubble stage\citep[$T$,][]{SV_86}."
 Generally. the way to have a precise differentiation of the flux of the individual components is. photometric decomposition. which. in its simplest form. uses analytical functions for the radial surface brightness (SB) profiles of bulge and disk.," Generally, the way to have a precise differentiation of the flux of the individual components is photometric decomposition, which, in its simplest form, uses analytical functions for the radial surface brightness (SB) profiles of bulge and disk."
 Typically the SB distribution of disks is satisfactorily fitted by an exponential function (Freeman1970)., Typically the SB distribution of disks is satisfactorily fitted by an exponential function \citep{F_70}.
". The Sérrsic law (orn""o has supplanted the 7 law (deVaucouleurs1948) in the approximation of bulge SB distribution since the works of Andredakis&Sanders(1994) and Andredakisetal.(1995).", The Sérrsic law \citep[or $r^{1/n}$ has supplanted the $r^{1/4}$ law \citep[][]{dV_48} in the approximation of bulge SB distribution since the works of \citet{AS_94} and \citet{APB_95}.
. Bulges of early-type spirals. however. appear more exponential than. previously assumed (Baleellsetal.2003:Laurikainen2005).," Bulges of early-type spirals, however, appear more exponential than previously assumed \citep{BGD_03,LSB_05}."
. Furthermore. lower values of B/T than in earlier studies have been reported (Laurikainenetal.2005.2006.2007:Weinzirl2009).," Furthermore, lower values of B/T than in earlier studies have been reported \citep{LSB_05,LSB_06,LSB_07,WJK_09}."
 The reason for the observed lower mean values of 5 and B/T is most likely related to the multicomponent decomposition used (Laurikainenetal.2005.2007): the omission of bars (and ovals/lenses) leads to modifying bulge (mostly) and disk parameters and furthermore to B/T inflation (seealsoGadotti2008:Weinzirletal. 2009).," The reason for the observed lower mean values of $n$ and B/T is most likely related to the multicomponent decomposition used \citep{LSB_05,LSB_07}: the omission of bars (and ovals/lenses) leads to modifying bulge (mostly) and disk parameters and furthermore to B/T inflation \citep[see also][]{G_08,WJK_09}."
. Therefore. the way to have precise parameter estimates as a result of decomposition is to take all significant components in the galaxy under consideration into account. às well as to choose the right functional form for each of them.," Therefore, the way to have precise parameter estimates as a result of decomposition is to take all significant components in the galaxy under consideration into account, as well as to choose the right functional form for each of them."
 Detailed morphological characterization. 1e. disclosure of the features present. is important in the context of AGN fueling mechanisms. correlations among structural parameters. and galaxy morphological classification.," Detailed morphological characterization, i.e., disclosure of the features present, is important in the context of AGN fueling mechanisms, correlations among structural parameters, and galaxy morphological classification."
 The last one named should not be overlooked. keeping the correlation of a great deal of parameters with 7 in mind.," The last one named should not be overlooked, keeping the correlation of a great deal of parameters with $T$ in mind."
 Two basic kinds of approaches can be discerned: detailed case-by-case research on relatively small galaxy samples. which can adequately reveal and model the components present but would be an arduous task for a great number of objects. and studies of large samples in an automated manner. which would lead to results of higher statistical weight but could hardly take all structures in the individual galaxies into account (seealsoGadotti2008).," Two basic kinds of approaches can be discerned: detailed case-by-case research on relatively small galaxy samples, which can adequately reveal and model the components present but would be an arduous task for a great number of objects, and studies of large samples in an automated manner, which would lead to results of higher statistical weight but could hardly take all structures in the individual galaxies into account \citep[see also][]{G_08}."
. Our study is of the first type., Our study is of the first type.
 Its aim is to explore the morphological features related to AGN fueling mechanisms and the relations among the structural parameters. including the “SMBH mass — bulge luminosity” relation. involving detailed morphological characterization and SB decomposition of a sample of Sy galaxies.," Its aim is to explore the morphological features related to AGN fueling mechanisms and the relations among the structural parameters, including the “SMBH mass – bulge luminosity” relation, involving detailed morphological characterization and SB decomposition of a sample of Sy galaxies."
 A parallel discussion of a matched sample of inactive galaxies is presented to. study the eventual differences in the large-scale morphology and local environment of the Sy and inactive galaxies., A parallel discussion of a matched sample of inactive galaxies is presented to study the eventual differences in the large-scale morphology and local environment of the Sy and inactive galaxies.
 The morphological characterization is based on scrutinizing various types of images. maps. residuals. and profiles.," The morphological characterization is based on scrutinizing various types of images, maps, residuals, and profiles."
 The results of a multicomponent SB decomposition will be presented in a companion paper., The results of a multicomponent SB decomposition will be presented in a companion paper.
 The paper is organized as follows., The paper is organized as follows.
 Sample selection is presented in refsample.., Sample selection is presented in \\ref{sample}.
 Observations and primary data reduction. are outlined inrefobsred., Observations and primary data reduction are outlined in.
. Surface photometry steps are followed through in refsurf.., Surface photometry steps are followed through in \\ref{surf}.
 Bar characterization is described inrefbars.., Bar characterization is described in\\ref{bars}.
 refres presents the surface photometry outputs., \\ref{res} presents the surface photometry outputs.
 The local environment of the galaxies is commented on in refloc.av, The local environment of the galaxies is commented on in \\ref{loc_env}.
Adiscussion followsinS refdisc., A discussion follows in \\ref{disc}.
.AsumnmaryofourresultsisgiveninS refconcl., A summary of our results is given in \\ref{concl}.
.AsetofcontourmapsandprofilesoftheS xgalaxiesispresentedi profiles.., A set of contour maps and profiles of the Sy galaxies is presented in \\ref{profiles}. .
IndividualS vealaxiesarediscussedinAppendix findiv.., Individual Sy galaxies are discussed in \\ref{indiv}.
 Throughout the paper the linear sizes and projected linear separations in kpe have been calculated using the cosmology-corrected scale given in NASA/IPAC Extragalactic Database (NED:Ho kms!Mpce!. Ouais 0.27. Oui 0.73.2007).," Throughout the paper the linear sizes and projected linear separations in kpc have been calculated using the cosmology-corrected scale given in NASA/IPAC Extragalactic Database \citep[NED; $H_{\rm 0} $\,73\,\rm km\,\rm s^{-1}\,Mpc^{-1}$, $\Omega_{\,\rm matter}\,$ $\,0.27$, $\Omega_{\,\rm vacuum}\,$ $\,0.73$."
 We selected Sy galaxies with reverberation-based black hole masses compiled by Ho(1999) and updated by Petersonetal.(2004).. as well as relatively poorly studied Sy galaxies regarding morphological characterization and multicomponent SB profile decomposition from Véron-Cetty&Véron(1998).. on which we imposed the following constraints: The Sy sample consists of 35 galaxies.," We selected Sy galaxies with reverberation-based black hole masses compiled by \citet{H_99} and updated by \citet{PFG_04}, as well as relatively poorly studied Sy galaxies regarding morphological characterization and multicomponent SB profile decomposition from \citet{VV_98}, on which we imposed the following constraints: The Sy sample consists of 35 galaxies."
 A control sample ofinactive galaxies was selected from the Center for Astrophysics (CfA) Redshift Survey (Huchraetal.1983.1995) to compare their morphology and environment to those of the Sy sample galaxies.," A control sample ofinactive galaxies was selected from the Center for Astrophysics (CfA) Redshift Survey \citep{HDL_83,HGC_95} to compare their morphology and environment to those of the Sy sample galaxies."
 The inactive galaxies were matched on a one-to-one basis to the Sy galaxies in 7. radial heliocentric velocity Vi. absolute B-band magnitude Mi. and ellipticity e.," The inactive galaxies were matched on a one-to-one basis to the Sy galaxies in $T$, radial heliocentric velocity $V\rm _{r}$, absolute $B$ -band magnitude $M ^{B}_{\rm abs}$, and ellipticity $\epsilon$."
 For two of the Sy galaxies 22 and 11513.among the most distant ones). we could hot find any appropriate counterparts in the CfA Redshift Survey. so we selected their matched galaxies from the Sloan Digital Sky Survey (SDSS.York 2000).," For two of the Sy galaxies 2 and 1513,among the most distant ones), we could not find any appropriate counterparts in the CfA Redshift Survey, so we selected their matched galaxies from the Sloan Digital Sky Survey \citep[SDSS,][]{YAA_00}."
". Mi of an inactive galaxy was matched to M. +0""S of an Sy galaxy and the median ofthese values is given below and plottedin fAjbim..T fO"" "," $M ^{B}\rm_{abs}$ of an inactive galaxy was matched to $M^{B}\rm_{abs}\,$ $0\fm5$ of an Sy galaxy and the median ofthese values is given below and plottedin \\ref{M_AN_5ouraCfA_hbm}. ."
hevalueoSisumeanone. basedonourprelimin Mi ," The value of $0\fm5$ is a mean one, based on our preliminary decomposition results for the contribution of the AGNs to the total Sy galaxy magnitudes."
"-2088/-21""03. and € 0.19/0.20."," The median values of the matched parameters of the Sy/control sample are $T$ $=$ $0/0$ , $V\rm _{r}\,$ $\,8089$ $7934\,\rm km\,\rm s^{-1}$ , $M ^{B}\rm_{abs}\,$ $\, -20\fm88$ $-21\fm03$ and $\epsilon\,$ $\,0.19/0.20$ ."
 Their distribution is shown in À.., Their distribution is shown in \\ref{MT_AN_ourour_hbm}- \ref{E_AN_ourour_hbm}. .
"The Ik, band Iuuinosity fanction (LE) of paired galaxies is calculated using the V4 method (Schmidt 1968).",The ${\rm K_s}$ band luminosity function (LF) of paired galaxies is calculated using the ${\rm V_{max}}$ method (Schmidt 1968).
 Comparing the muuber counts of our parent sample with the 2N[ASS number counts of IxXochanek et al. (, Comparing the number counts of our parent sample with the 2MASS number counts of Kochanek et al. (
2001) in Fig.l. we estimate that the effective sky coverage of the parent sample is 650 deg?. with an error of ~5%.,"2001) in Fig.1, we estimate that the effective sky coverage of the parent sample is 650 $^2$, with an error of $\sim 5\%$."
 We will ignore this error because it is much smaller (han other errors., We will ignore this error because it is much smaller than other errors.
" Given our pair selection criteria. both components of a pair have the same μας determined by the Ix, magnitude of the primary. the redshift of the pair. and hy),=12.5."," Given our pair selection criteria, both components of a pair have the same ${\rm V_{max}}$ determined by the ${\rm K_s}$ magnitude of the primary, the redshift of the pair, and ${\rm K_{lim}=12.5}$."
" The Ix, band luminosity lancetion aud its error are caleulated using the following formulae: where (Δι1) is the luminosity function in the i-th bin of the Kk, band absolute magnitude: Nj is the number of galaxies in that bin: 0(1i)=0.5 is the bin width: Vi, 15 ihe maximum finding volume of the j-th galaxy in the bin."," The ${\rm K_s}$ band luminosity function and its error are calculated using the following formulae: where ${\rm \phi(M_{K,i})}$ is the luminosity function in the i-th bin of the ${\rm K_s}$ band absolute magnitude; ${\rm N_i}$ is the number of galaxies in that bin; ${\rm \delta(m)} = 0.5$ is the bin width; ${\rm V_{max,j}}$ is the maximum finding volume of the j-th galaxy in the bin."
 Other svmbols have the same delinilions as in Eq(2) and Eq(3)., Other symbols have the same definitions as in Eq(2) and Eq(3).
 The results are listed in Table 1 and plotted in Fig.2., The results are listed in Table 1 and plotted in Fig.2.
 The parameters of the best-lit Schechter fanction of the LF are given in Table 2., The parameters of the best-fit Schechter function of the LF are given in Table 2.
 It is well known that LF derived using Vinay method can be affected by inhomogeneous spatial distribution of galaxies., It is well known that LF derived using ${\rm V_{max}}$ method can be affected by inhomogeneous spatial distribution of galaxies.
 In the redshift distribution of the 2ALASS-2dFCRS matched catalog (Cole et al., In the redshift distribution of the 2MASS-2dFGRS matched catalog (Cole et al.
 2001). there is evidence of clustering. parlcularly a dip around z=0.04 and a sharp peak around z=0.06.," 2001), there is evidence of clustering, particularly a dip around z=0.04 and a sharp peak around z=0.06."
 Therefore. the fluctuations of the LF of paired galaxies around the smooth Schechter function (e.g. (hie excess al Mj;= —22.75) are possibly due to this effect.," Therefore, the fluctuations of the LF of paired galaxies around the smooth Schechter function (e.g. the excess at $_{\rm
K} = -22.75$ ) are possibly due to this effect."
 The stellar masses. corresponding to the absolute magnitude bins of the LE. are also listed in Table 1.," The stellar masses, corresponding to the absolute magnitude bins of the LF, are also listed in Table 1."
 Following IXochanek οἱ al. (, Following Kochanek et al. (
2001) and Cole et al. (,2001) and Cole et al. (
"2001). we first translate the isophotal IX, magnitude to the total IX, magnitude (0I,=0.2 mag). then assume","2001), we first translate the isophotal ${\rm K_s}$ magnitude to the 'total' ${\rm K_s}$ magnitude $\delta {\rm K_s} =0.2$ mag), then assume"
be established.,be established.
 During the transient. period. the test charge will be moving away from its screening charge. which only eracduallv picks up speed. ancl trails along behind.," During the transient period, the test charge will be moving away from its screening charge, which only gradually picks up speed and trails along behind."
 This is similar to the motion of the charge in our model., This is similar to the motion of the charge in our model.
 Since the transient [ields form a bridge between the initial and. fina ficlds they must have a similar form to the field of the tes charge. and extend comparably far.," Since the transient fields form a bridge between the initial and final fields they must have a similar form to the field of the test charge, and extend comparably far."
 During the period that the charge is moving (the pulse). the dipole moment will be (η)--qVi.," During the period that the charge is moving (the ), the dipole moment will be $\overline{D} (t) = qVt$."
 Before anc after the pulse the dipole moment remains at à constan value. but this is of little interest because a constant clipole moment generates no magnetic field or vector potential.," Before and after the pulse the dipole moment remains at a constant value, but this is of little interest because a constant dipole moment generates no magnetic field or vector potential."
 Lt is well known that Maxwell's equations separate in conforma time. so we will write the dipole moment in terms of η.," It is well known that Maxwell's equations separate in conformal time, so we will write the dipole moment in terms of $\eta$ ."
 Define r=7f/f) (climensionless). so that the pulseextends from. y= Tloy=r.," Define $\tau = \tau_t/R_{\mathrm{s}}(t)$ (dimensionless), so that the pulseextends from $\eta = -\tau$ to $\eta = \tau$ ."
 The subscript s on 2. indicates the source time., The subscript `s' on $R_{\mathrm{s}}$ indicates the source time.
 AO) can be treated as constant during the pulse. and the dipole moment can be expressed as a Fourier integral: We estimate the value of τι in section 10.," $R_{\mathrm{s}}(t)$ can be treated as constant during the pulse, and the dipole moment can be expressed as a Fourier integral: We estimate the value of $\tau_t$ in section \ref{sec:mass_1}."
. The z axis of the local system used in this section will be parallel to the polar axis of the polar coordinates used in the bulk of the paper., The $z$ axis of the local system used in this section will be parallel to the polar axis of the polar coordinates used in the bulk of the paper.
 We will need. only the three fields. £10. £55 ancl {οι," We will need only the three fields $F_{10}$, $F_{20}$ and $F_{12}$."
" Since Maxwell's equations separate in conformal time the elementary solutions can bewritten For dipole fields we try the following forms: with angular functions(0)=ουκ and N,(0)=(A)fdld— sin."," Since Maxwell's equations separate in conformal time the elementary solutions can bewritten For dipole fields we try the following forms: with angular functions$P_1 (\theta) = \cos \theta$ and $N_1 (\theta) \equiv {\mathrm d} P_1 (\theta)/{\mathrm d} \theta
= -\sin \theta$ ."
 Alaxwell’s equations now give (with a prime meaning dd): From (17)). (18)) and (19)) we obtain the equation for fa alone This is the analog of equation 16 of ?.. which he derived. for a space of positive curvature.," Maxwell's equations now give (with a prime meaning ${\mathrm d} /{\mathrm d} \chi$ ): From \ref{eq:dip1}) ), \ref{eq:dip2}) ) and \ref{eq:dip3}) ) we obtain the equation for $f_3$ alone This is the analog of equation 16 of \citet{mash1}, which he derived for a space of positive curvature."
 Define. fo(\)fsinhy., Define $f_4 (\chi) = f_3 (\chi) / \sinh \chi$ .
 Phen fy satisfies This is à special case. for /2 οἱ 2. of the equation forhyperbolic spherical functions. with solution (77): where IN; is a normalization factor that is. irrelevant here.," Then $f_4$ satisfies This is a special case, for $l=1$ or $l=-2$, of the equation forhyperbolic spherical functions, with solution \citep{buch1,band1}: where $N_l$ is a normalization factor that is irrelevant here."
 Choosing /212) we get the solutions of (21)) that are regular (singular) at y—0., Choosing $l=1\;(-2)$ we get the solutions of \ref{eq:f4}) ) that are regular (singular) at $\chi = 0$.
" With /|1E«0 interpreted as integration: is constructed. from that combination of fi; and fias (hat is proportional to exp(iny). because when combined with exp(fay) this represents outgoing waves: where €C,(n) is a normalizing factor to be determined."," With $l+1 < 0$ interpreted as integration: $f_3 $ is constructed from that combination of $f_{4,{\mathrm{reg}}}$ and $f_{4,{\mathrm{sing}}}$ that is proportional to $\exp (i n \chi)$, because when combined with $\exp (-i n \eta)$ this represents outgoing waves: where $C_1 (n)$ is a normalizing factor to be determined."
 Lt is convenient at this point to express fy in terms of w=tanh(x/2): From (17)) and (25)) we derive the equation for the racial electric dipole field: Similarly. from (18)) and (26)) we derive the equation for the transverse electric field: From (9)) and (10)) we can get the near-field) expression for the radial component of /Z. andby comparison with (27)) arrive at the form of the normalizing [actor C (0).," It is convenient at this point to express $f_3$ in terms of $u=\tanh (\chi/2)$: From \ref{eq:dip1}) ) and \ref{eq:f3out}) ) we derive the equation for the radial electric dipole field: Similarly, from \ref{eq:dip2}) ) and \ref{eq:f3out2}) ) we derive the equation for the transverse electric field: From \ref{eq:dipfour}) ) and \ref{eq:dipstrength}) ) we can get the near-field expression for the radial component of$E$ , andby comparison with \ref{eq:f1out}) ) arrive at the form of the normalizing factor $C_1(n)$ ."
 On the polar axis. at small distances. the radial E field at frequency nds where r— Roy.," On the polar axis, at small distances, the radial ${\mathbf E}$ field at frequency $n$ is where $r=R_{\mathrm{s}} \chi$ ."
 In the same limit (small X). (27)) gives v and so. on the axis.," In the same limit (small $\chi$ ), \ref{eq:f1out}) ) gives $f_1 (\chi) = -2{\mathrm i} C_1 (n) /(n \chi^3)$ , and so, on the axis,"
the telescope Local plane.,the telescope focal plane.
 Data were obtained on the nights of July 2 and 3 (UTC) prior to impact. on the nieht of July 4 (the impact night). when the first useful frame was exposed during the moment of impact. aid on the nights of July 5. 7 and 8. after the impact.," Data were obtained on the nights of July 2 and 3 (UTC) prior to impact, on the night of July 4 (the impact night), when the first useful frame was exposed during the moment of impact, and on the nights of July 5, 7 and 8, after the impact."
" The nights of July 6 and 9 were lost due to a combination of poor seeing (222"") and cirrus clouds.", The nights of July 6 and 9 were lost due to a combination of poor seeing $\approx$ $\arcsec$ ) and cirrus clouds.
 The integration lime used for comet spectra was 300 5 on July 2 and 3. 90 5 on July 4 and 5. and 150 s on July 7 and 3.," The integration time used for comet spectra was 300 s on July 2 and 3, 90 s on July 4 and 5, and 180 s on July 7 and 8."
 The seeing in these nights was. of course. dependent on time. wavelength and adv-mass.," The seeing in these nights was, of course, dependent on time, wavelength and air-mass."
" Typically. (he FWIIAL of standard star Games was 0.7 ""an the red channel of SNIFS and 220.85"" in the blue channel."," Typically, the FWHM of standard star frames was $\approx$ $\arcsec$ in the red channel of SNIFS and $\approx$ $\arcsec$ in the blue channel."
 The Deep Impact event was observed at a geocentric distance of 0.89 AU. resulting in a scale of 645 km |.," The Deep Impact event was observed at a geocentric distance of 0.89 AU, resulting in a scale of 645 km $^{-1}$."
 The heliocentric distance was 1.51 AU., The heliocentric distance was 1.51 AU.
 Up to the night of July 7. the telescope was tracking the non-sidereal motion of comet Tempel 1 in open loop. without euiding.," Up to the night of July 7, the telescope was tracking the non-sidereal motion of comet Tempel 1 in open loop, without guiding."
 Keeping (hie comet nucleus centered in (he field of view under (hese conditions proved rather difficult., Keeping the comet nucleus centered in the field of view under these conditions proved rather difficult.
 We selected only those Irimnes for analvsis where the full photometric aperture was within the field of view. to avoid any possible color effects from extrapolating from smaller apertures.," We selected only those frames for analysis where the full photometric aperture was within the field of view, to avoid any possible color effects from extrapolating from smaller apertures."
 However. we were using frames where the photometric skv annulus was not fully contained in the field. a situation that the IRAF apphot package is designed to handle.," However, we were using frames where the photometric sky annulus was not fully contained in the field, a situation that the IRAF apphot package is designed to handle."
 Observations of the comet were interdispersed with calibration observations. so that our coverage of the post-impact phase was not continuous.," Observations of the comet were interdispersed with calibration observations, so that our coverage of the post-impact phase was not continuous."
 Observations of a position 5 away from the comet nucleus. outside of (he comet's cona. were taken as “empty skv [ames and later used in the analvsis of some of the data.," Observations of a position $\arcmin$ away from the comet nucleus, outside of the comet's coma, were taken as “empty sky” frames and later used in the analysis of some of the data."
 Following the established procedures [or, Following the established procedures for
subtraction. then extrapolated this mass to a sphere of thickness 34 aresec: this is likely to be an overestimate. since there will be no rim on the core side of the lobe).,"subtraction, then extrapolated this mass to a sphere of thickness 34 arcsec; this is likely to be an overestimate, since there will be no rim on the core side of the lobe)."
 As shown in Table 2.. the rim has a temperature of 270.03 keV. consistent with the temperature in the outer regions of the extended gas.," As shown in Table \ref{449spec}, the rim has a temperature of $\pm$ 0.03 keV, consistent with the temperature in the outer regions of the extended gas."
 We calculate that the amount of gus swept up by the lobe front is ~~G«107 M.;., We calculate that the amount of gas swept up by the lobe front is $\sim 6 \times 10^{10}$ $_{\sun}$.
 It is therefore plausible that most of the rim gas has been evacuated from the lobe and moved to its current position by lobe expansion., It is therefore plausible that most of the rim gas has been evacuated from the lobe and moved to its current position by lobe expansion.
 The radio lobes of low-power radio galaxies are thought to be expanding subsonically on the largest scales. so that the internal oressure within the radio lobes should be similar to. but slightly ügher than that of the external environment.," The radio lobes of low-power radio galaxies are thought to be expanding subsonically on the largest scales, so that the internal pressure within the radio lobes should be similar to, but slightly higher than that of the external environment."
 However. internal radio-lobe pressures obtained by assuming an electron. filling uctor of unity. equipartition of energy in particles and magnetic fields. and that the only contribution to pressure comes from he population of synehrotron-emitting electrons. are found to be significantly than the external pressures obtained from X-ray Measurements (e.g. Morganti et al.," However, internal radio-lobe pressures obtained by assuming an electron filling factor of unity, equipartition of energy in particles and magnetic fields, and that the only contribution to pressure comes from the population of synchrotron-emitting electrons, are found to be significantly than the external pressures obtained from X-ray measurements (e.g. Morganti et al."
 1988: Worrall et al., 1988; Worrall et al.
 995: Worrall Birkinshaw 2000)., 1995; Worrall Birkinshaw 2000).
 If the lobes are expanding supersonically. these problems are exacerbated (more detailed discussion of expansion. speeds follows in Section 4.3).," If the lobes are expanding supersonically, these problems are exacerbated (more detailed discussion of expansion speeds follows in Section 4.3)."
 We determined radial pressure profiles in the X-ray environments of 3C 66B and 3C 449: these are shown in Fig. |I.., We determined radial pressure profiles in the X-ray environments of 3C 66B and 3C 449; these are shown in Fig. \ref{press}.
 Internal radio- pressures were determined using the code of Hardcastle et al. (, Internal radio-lobe pressures were determined using the code of Hardcastle et al. (
"1998). choosing an electron energy spectrum with a power-law number index of 2. minimum energy of 5»10"" eV and maximum energy of 6... LO! eV. For 3C 66B. we find the external pressure acting on the eastern lobe of 3C 66B at a radius of 75 arcsec to be a factor of ~24 higher than the equipartition internal lobe pressure. and for the southern lobe of 3C 449 we find the external pressure at a distance of 350 aresee to be ~ 16 above the internal lobe pressure.","1998), choosing an electron energy spectrum with a power-law number index of 2, minimum energy of 5 $\times 10^{6}$ eV and maximum energy of 6 $\times 10^{11}$ eV. For 3C 66B, we find the external pressure acting on the eastern lobe of 3C 66B at a radius of 75 arcsec to be a factor of $\sim$ 24 higher than the equipartition internal lobe pressure, and for the southern lobe of 3C 449 we find the external pressure at a distance of 350 arcsec to be $\sim$ 16 above the internal lobe pressure."
 The result for 3C 449 agrees with Hardcastle et al, The result for 3C 449 agrees with Hardcastle et al.
/sROSAT results. and both results are consistent withROSAT measurements for similar sources (e.g. Worrall et al.,"'s results, and both results are consistent with measurements for similar sources (e.g. Worrall et al."
 1995)., 1995).
 Therefore. as the radio lobes cannot be underpressured. we must consider which of the assumptions used to determine the internal lobe pressures are incorrect.," Therefore, as the radio lobes cannot be underpressured, we must consider which of the assumptions used to determine the internal lobe pressures are incorrect."
 In order for the population of synchrotron-emitting electrons to provide the necessary pressure without a signiticant contribution from other particles. conditions in the radio lobes ofthe two objects must deviate substantially from equipartition.," In order for the population of synchrotron-emitting electrons to provide the necessary pressure without a significant contribution from other particles, conditions in the radio lobes of the two objects must deviate substantially from equipartition."
 For 3C 66B. we tind an equipartition magnetic field strength of 0.34 nT €I nT = 105/60).," For 3C 66B, we find an equipartition magnetic field strength of 0.34 nT (1 nT = $\mu$ G)."
 To obtain pressure balance. field strengths of 30 pT or 2.0 nT are required.," To obtain pressure balance, field strengths of 30 pT or 2.0 nT are required."
 In 3C 449 we obtain similar results: the equipartition magnetic field is 0.23 nT. whereas field strengths of 20 pT or 1.2 nT are required for pressure balance.," In 3C 449 we obtain similar results: the equipartition magnetic field is 0.23 nT, whereas field strengths of 20 pT or 1.2 nT are required for pressure balance."
 However. from spectral fitting to the X-ray deficit regions coincident with these radio lobes we obtain an upper limit on the flux from inverse Compton emission of 10 nly (C 66B) and 3 nIy (3C 449). which leads to lower limits on magnetic field strength of 90 pT (3C 66B) and 80 pT (3C 449).," However, from spectral fitting to the X-ray deficit regions coincident with these radio lobes we obtain an upper limit on the flux from inverse Compton emission of 10 nJy (3C 66B) and 3 nJy (3C 449), which leads to lower limits on magnetic field strength of 90 pT (3C 66B) and 80 pT (3C 449)."
 With such fields. the lobes would still be underpressured by factors of 5 (3C 66B) and 7 (GC 449).," With such fields, the lobes would still be underpressured by factors of 5 (3C 66B) and 7 (3C 449)."
 Fig., Fig.
 10. shows that the level of inverse Compton emission expected from the lobes of 3C 449 for a field strength of 20 pT (required for pressure balance in the particle-dominated regime) is significantly higher than the upper limit of a power-law component of X-ray flux. as taken from fitting a plus power-law model to the spectrum from the lobe region.," \ref{magdom} shows that the level of inverse Compton emission expected from the lobes of 3C 449 for a field strength of 20 pT (required for pressure balance in the particle-dominated regime) is significantly higher than the upper limit of a power-law component of X-ray flux, as taken from fitting a plus power-law model to the spectrum from the lobe region."
 Therefore we conclude that in the scenario where no other particles are present. if the lobes of these two objects deviate from equipartition conditions. it must be in the direction of magnetic domination. requiring field strengths of — 1-2 nT. Such magnetic domination is not found where direct measurements of magnetic field strengths have been made from X-ray inverse Compton emission.," Therefore we conclude that in the scenario where no other particles are present, if the lobes of these two objects deviate from equipartition conditions, it must be in the direction of magnetic domination, requiring field strengths of $\sim$ 1-2 nT. Such magnetic domination is not found where direct measurements of magnetic field strengths have been made from X-ray inverse Compton emission."
 In no case is the field strength. significantly higher than the equipartition value: Feigelson et al. (, In no case is the field strength significantly higher than the equipartition value; Feigelson et al. (
1995) found a level of X-ray inverse Compton in the lobes of Fornax A slightly higher than. but consistent with equipartition. and Tashiro et al. (,"1995) found a level of X-ray inverse Compton in the lobes of Fornax A slightly higher than, but consistent with equipartition, and Tashiro et al. ("
1995) found the lobes of PKS 1343-601 to be particle dominated.,1995) found the lobes of PKS 1343-601 to be particle dominated.
 Our results also constrain pressure contributions from non-radiating particles., Our results also constrain pressure contributions from non-radiating particles.
 Although the presence of some entrainec material in the lobes is necessary (e.g. from models of je deceleration). the X-ray deficits rule out a signiticant contribution to pressure from a thermal gas component at the temperature of the surrounding atmosphere.," Although the presence of some entrained material in the lobes is necessary (e.g. from models of jet deceleration), the X-ray deficits rule out a significant contribution to pressure from a thermal gas component at the temperature of the surrounding atmosphere."
 The presence of sufficient cold gas woulc be expected to produce significant Faraday depolarization of the lobes. which is not observed (e.g. Feretti et al.," The presence of sufficient cold gas would be expected to produce significant Faraday depolarization of the lobes, which is not observed (e.g. Feretti et al."
 1999). although i is possible to devise magnetic field structures where such materia could be present but does not result in significant depolarization (Laing 1984).," 1999), although it is possible to devise magnetic field structures where such material could be present but does not result in significant depolarization (Laing 1984)."
 However. it is implausible that large quantities of material could be hidden in this way.," However, it is implausible that large quantities of material could be hidden in this way."
 Entrained material could be heated (by the entrainment process. or by energy transfer from interactions with the relativistie electrons). and so could provide sufficient pressure without producing detectable X-ray emission: e.g. in 3C 66B. the missing pressure might be provided by gas at —5 keV. Missing pressure could also be hidden in an extra population of low-energy electrons. producing inverse Compton emission at a level we could not detect.," Entrained material could be heated (by the entrainment process, or by energy transfer from interactions with the relativistic electrons), and so could provide sufficient pressure without producing detectable X-ray emission: e.g. in 3C 66B, the missing pressure might be provided by gas at $\sim$ 5 keV. Missing pressure could also be hidden in an extra population of low-energy electrons, producing inverse Compton emission at a level we could not detect."
 However. these electrons must have -] 200.requiring the power-law number index to steepen to 3 below  10? eV. then to drop off sharply at energies of «5...10 eV. since large populations of electrons at these energies would also," However, these electrons must have $\gamma \sim 1-200$, requiring the power-law number index to steepen to 3 below $\sim$ $^{8}$ eV, then to drop off sharply at energies of $\sim 5 \times 10^{5}$ eV, since large populations of electrons at these energies would also"
bolometric luminosity Lgg may contain a relatively small black hole accreting at a high rate or a more massive black hole accreting at a lower rate.,bolometric luminosity $L_{\rm bol}$ may contain a relatively small black hole accreting at a high rate or a more massive black hole accreting at a lower rate.
" In this work, we adopt a power-law Eddington ratio distribution with an exponential cutoff at a high ratio to derive the BHMF of AGN with a LF, with which the continuity equation for black hole number density is integrated to calculate the cosmological evolution of BHMF of AGN relics."," In this work, we adopt a power-law Eddington ratio distribution with an exponential cutoff at a high ratio to derive the BHMF of AGN with a LF, with which the continuity equation for black hole number density is integrated to calculate the cosmological evolution of BHMF of AGN relics."
 The resultant BHMF of AGN relics is constrained by the measured local BHMF., The resultant BHMF of AGN relics is constrained by the measured local BHMF.
" The conventional cosmological Ωμ=0.3, Q4=0.7, and Ho=70kms!Mpc”! haveparameters been adopted in this work."," The conventional cosmological parameters $\Omega_{\rm M}=0.3$, $\Omega_{\Lambda}=0.7$, and $H_0=70~ {\rm
km~s^{-1}~Mpc^{-1}}$ have been adopted in this work."
" Hopkins&Hernquist(2009) suggested that the quasar lightcurve can be described by where A=Lyoi/Lgaa (Lgaa=1.3x1055My/Mcergs sl), TQ is the quasar life timescale, and the parameter Apeak describes the peak luminosity of quasars."," \citet{2009ApJ...698.1550H} suggested that the quasar lightcurve can be described by where $\lambda=L_{\rm bol}/L_{\rm Edd}$ $L_{\rm Edd}=1.3\times
10^{38}M_{\rm bh}/M_\odot~{\rm ergs}~{\rm s}^{-1}$ ), $\tau_{\rm Q}$ is the quasar life timescale, and the parameter $\lambda_{\rm peak}$ describes the peak luminosity of quasars."
" This power-law lightcurve is consistent with the self-regulated black hole growth model, in which feedback produces a self-regulating j°decayj+ or j?blowout;x phase after the AGN reaches some peak luminosity and begins to expel gas and shut down accretion (e.g.,Hopkinsetal.2005a).."," This power-law lightcurve is consistent with the self-regulated black hole growth model, in which feedback produces a self-regulating ¡°decay¡± or ¡°blowout¡± phase after the AGN reaches some peak luminosity and begins to expel gas and shut down accretion \citep*[e.g.,][]{2005ApJ...630..716H}."
" This lightcurve can be translated to an observed Eddington ratio distribution ¢(A), where C; is the normalization, if the switch-on of AGN activity is balanced with switch-off of AGN activity and το is significantly shorter than the age of the universe at redshift z."," This lightcurve can be translated to an observed Eddington ratio distribution $\zeta(\lambda)$, where $C_{l}$ is the normalization, if the switch-on of AGN activity is balanced with switch-off of AGN activity and $\tau_{\rm Q}$ is significantly shorter than the age of the universe at redshift $z$."
" The power-law Eddington ratio distribution is consistent with those derived with samples of nearby AGNs (e.g.,Heckmanetal.2004;Yu2005;Hopkins&Hernquist 2009).."," The power-law Eddington ratio distribution is consistent with those derived with samples of nearby AGNs \citep*[e.g.,][]{2004ApJ...613..109H,2005ApJ...634..901Y,2009ApJ...698.1550H}."
" Such an Eddington ratio distribution has a lower cutoff at À=Amino, below which the sources are no longer regarded as AGNs."," Such an Eddington ratio distribution has a lower cutoff at $\lambda=\lambda_{\rm min,0}$, below which the sources are no longer regarded as AGNs."
" In this work, we adopt A=Amino10~ in all the calculations."," In this work, we adopt $\lambda=\lambda_{\rm
min,0}=10^{-4}$ in all the calculations."
" At high redshifts, the quasar life timescale is comparable with (or even shorter than) the age of the universeτο at redshift z."," At high redshifts, the quasar life timescale $\tau_{\rm Q}$ is comparable with (or even shorter than) the age of the universe at redshift $z$."
" In this case, the time after the birth of the first quasars is so short that most of them are still very luminous (i.e., accreting at high rates), and the lower limit onthe Eddington ratios for AGNs should be significantly higher than Amino."," In this case, the time after the birth of the first quasars is so short that most of them are still very luminous (i.e., accreting at high rates), and the lower limit onthe Eddington ratios for AGNs should be significantly higher than $\lambda_{\rm
min,0}$."
" The first quasars are predicted to have formed at ση»10 (e.g.,2003),, with which we can estimate the minimal Eddington ratio Άι for AGNs at redshift z as where ¢(z) is the age of the universe at z measured from Zfq=10 when the first quasars formed."," The first quasars are predicted to have formed at $z_{\rm
fq}\sim 10$ \citep*[e.g.,][]{2001ApJ...552..459H,2003ApJ...596...34B}, with which we can estimate the minimal Eddington ratio $\lambda_{\rm
min}^\prime$ for AGNs at redshift $z$ as where $t(z)$ is the age of the universe at $z$ measured from $z_{\rm
fq}=10$ when the first quasars formed."
" For simplicity,we adopt Amin=max[Amino;A4, in all our calculations on the black hole evolution."," For simplicity,we adopt $\lambda_{\rm min}=\max[\lambda_{\rm min,0},\lambda_{\rm
min}^\prime(z)]$ in all our calculations on the black hole evolution."
" In (z)] 1,,"," In Fig. \ref{fig_eddrat},"
 we the minimal Eddington ratiosas functions of Fig.redshift z for plotdifferent quasar life timescales το., we plot the minimal Eddington ratiosas functions of redshift $z$ for different quasar life timescales $\tau_{\rm Q}$ .
" lcm For a given black hole mass function Nagn(Mpn,z) and Eddington ratio distribution, the AGN LF ®(z,Zpo1) can be calculated with where =x10°8A), Nacn(Mpn,z) is the AGN ΒΗΜΕMyn/Moat z, andLsg/(1.3 the Eddington ratio distribution ¢(A) is given by Eq. (2))."," 1cm For a given black hole mass function $N_{\rm AGN}(M_{\rm bh},z)$ and Eddington ratio distribution, the AGN LF $\Phi(z,L_{\rm bol})$ can be calculated with where $M_{\rm bh}/M_\odot=L_{\rm bol}/(1.3\times10^{38}\lambda)$, $N_{\rm AGN}(M_{\rm bh},z)$ is the AGN BHMFat $z$, and the Eddington ratio distribution $\zeta(\lambda)$ is given by Eq. \ref{eddrat_dis}) )."
" In this work, we assume that the AGN black hole mass function has the same form as the AGN LF, where the parameters Nacno, Máy. mi and 5 are to be determined."," In this work, we assume that the AGN black hole mass function has the same form as the AGN LF, where the parameters $N_{\rm AGN,0}$, $M_{\rm bh}^*$, $\beta_{\rm
m1}$ and $\beta_{\rm m2}$ are to be determined."
 Substituting Eq. (5)), Substituting Eq. \ref{agn_bhmf}) )
" into Eq. (4),"," into Eq. \ref{agn_lf}) ),"
 we can calculate the AGN LF with a given Eddington ratio distribution ¢(\) provided the values of the four in the AGN BHMF are specified., we can calculate the AGN LF with a given Eddington ratio distribution $\zeta(\lambda)$ provided the values of the four parameters in the AGN BHMF are specified.
" In this work, weparameters tune the values of these parameters till the observed LF can be well reproduced by that calculated with Eq. (4))."," In this work, we tune the values of these parameters till the observed LF can be well reproduced by that calculated with Eq. \ref{agn_lf}) )."
" We adopt the LF given by Hopkinsetal.(2007b),, which is calculated by using a large set of observed quasar luminosity functions in various wavebands, from the IR through optical, soft and hard X-rays (seeHopkinsetal.2007b,forthe details),, with normalization ¢,., break L.., faint-end slope γι. and bright-endslope 2."," We adopt the LF given by \citet{2007ApJ...654..731H}, which is calculated by using a large set of observed quasar luminosity functions in various wavebands, from the IR through optical, soft and hard X-rays \citep*[see][for
the details]{2007ApJ...654..731H}, , with normalization $\phi_{*}$ break luminosity $L_{*}$ faint-end slope $\gamma_1$ , and bright-endslope $\gamma_2$ ."
" The break luminosity L,. evolves with redshift is given by and the two slopes γι and γ2 evolves with redshift as and", The break luminosity $L_{*}$ evolves with redshift is given by and the two slopes $\gamma_1$ and $\gamma_2$ evolves with redshift as and
Iu order to explain the activity of active galactic nuclei (ACNs) and compact X-ray sources. we consider a black hole magnetosphere in the ceuter of these objects.,"In order to explain the activity of active galactic nuclei (AGNs) and compact X-ray sources, we consider a black hole magnetosphere in the center of these objects."
 The magnetosphere is composed of a ceutral black hole with surrounding plasmias aud a large scale maeuctic field., The magnetosphere is composed of a central black hole with surrounding plasmas and a large scale magnetic field.
 The magnetic field is originated frou au accretion disk rotating aroun the black hole., The magnetic field is originated from an accretion disk rotating around the black hole.
 The οἱectrodvnaiics of the black hole maguetosphere has been discussed by many authors: force-free magneospheres were discussed in (1986) aud more general maenetospheres in Piusv(2001)., The electrodynamics of the black hole magnetosphere has been discussed by many authors; force-free magnetospheres were discussed in \citet{Membrane86} and more general magnetospheres in \citet{Punsly01}.
 Iu the black hole maenetosphere.8 because ofthe srong eravity of the black hole and the rapid rotation of the inagnetic field. both an imgoiug plasina flow (acci'etiou) and an accelerated outgoiug plasma (wind/jet) should be created.," In the black hole magnetosphere, because of the strong gravity of the black hole and the rapid rotation of the magnetic field, both an ingoing plasma flow (accretion) and an accelerated outgoing plasma (wind/jet) should be created."
 The plasiua would be provided frou the disk surface aud its corona., The plasma would be provided from the disk surface and its corona.
 When the plasma density iu the magnetosphere is somewhat large. the plasma inertia effects shotld be important.," When the plasma density in the magnetosphere is somewhat large, the plasma inertia effects should be important."
 Iu this case. the plasina would be nearly neutral aud should be treated by the ideal uaenetolivdrodyjuuic CMIID) approsimation (Phinney1983). so the plasma streaus aloug a nignetic field iue. where the magnetic field line could exterid from the disk surface to the eveut horizon or a far cdistaut region (Nita.Takahashi. ju see also Tomimatsi&Takalasli (2001))).," In this case, the plasma would be nearly neutral and should be treated by the ideal magnetohydrodynamic (MHD) approximation \citep{Phinney83}, so the plasma streams along a magnetic field line, where the magnetic field line could extend from the disk surface to the event horizon or a far distant region \cite{Nitta-TT91}; see also \cite{TT2001}) )."
 The outexune fiow effectively carries the iieular moment ront16 plasma source. aud then t1ο accretion would coutiuue ο be stationary. releasing its gravitational energy.," The outgoing flow effectively carries the angular momentum from the plasma source, and then the accretion would continue to be stationary, releasing its gravitational energy."
 The magnetic field lines comectiue the black hole with t1ο disk. which are mainly eoncrated by the disk current. may not connect directly to the distant region. but via the disks interior the energv5 and augular momentum of the black hole cau de! camied to the distant region: the energy and augular momenta transport nske the disk is uot discussed bere.," The magnetic field lines connecting the black hole with the disk, which are mainly generated by the disk current, may not connect directly to the distant region, but via the disk's interior the energy and angular momentum of the black hole can be carried to the distant region; the energy and angular momentum transport inside the disk is not discussed here."
period-change rates are used for the statistics.,period-change rates are used for the statistics.
" If variables with the most regular behaviour are only considered (stars with strictly linear period changes or variables not showing the Blazhko effect, and omitting the most extreme period decrease value of V42), the results converge to a small positive, Bzz0.01dMyr! value."," If variables with the most regular behaviour are only considered (stars with strictly linear period changes or variables not showing the Blazhko effect, and omitting the most extreme period decrease value of V42), the results converge to a small positive, $\beta \approx\, 0.01\, \textrm{d} \textrm{Myr}^{-1}$ value."
 The period-change studies of RR Lyrae stars have revealed that the period-change behaviour of stars of a GC is related to its Oosterhoff (Oo) type (Rathbun&Smith1997)., The period-change studies of RR Lyrae stars have revealed that the period-change behaviour of stars of a GC is related to its Oosterhoff (Oo) type \citep{rs97}.
. The tendency is that both the mean and median values of a (or 8) are smaller for OoI than for Ooll clusters in keeping with evolutionary models; most of the RR Lyrae stars in Ool clusters are located near their ZAHB position while most of those in OolI clusters have already left their initial position on the HB and are moving from blue to red through, The tendency is that both the mean and median values of $\alpha$ (or $\beta$ ) are smaller for OoI than for OoII clusters in keeping with evolutionary models; most of the RR Lyrae stars in OoI clusters are located near their ZAHB position while most of those in OoII clusters have already left their initial position on the HB and are moving from blue to red through
lu addition to the choice of rotation curve. Galactic kineilaties are dependent ou the parameters of solar motion and the local staudard of rest.,"In addition to the choice of rotation curve, Galactic kinematics are dependent on the parameters of solar motion and the local standard of rest."
 For the solar «listance. 2... the couseusus appears to be δ. kpe. based on orbits of 50-2 stars implying 140.1 kpe (2). aud &8.3340.35 kpe (?)..," For the solar distance, $R_{\odot}$, the consensus appears to be 8.4 kpc, based on orbits of S0-2 stars implying $\pm$ 0.4 kpc \citep{ghez08} and $\pm$ 0.35 kpc \citep{gillessen09}."
 This is consistent with the parallax observations of water masers in Ser B2 indicating 7840.8 kpc (?) aud the parallaxes of methanol masers indicating 140.6 kpe (?).., This is consistent with the parallax observations of water masers in Sgr B2 indicating $\pm$ 0.8 kpc \citep{reid09b} and the parallaxes of methanol masers indicating $\pm$ 0.6 kpc \citep{reid09}.
 The LAU standards of solar motion are unplicitly incorporated in our maser LSR veloci(les., The IAU standards of solar motion are implicitly incorporated in our maser LSR velocities.
 However. recent maser astrometric observations have prompted revision.," However, recent maser astrometric observations have prompted revision."
 Two of the parameters. solar motion towards he Galac16 centre.C... alid solar motion towards the north Galactic »ole. Woo. have remained la'gelv ο]auged land | respectively. but the solar motion in the clirection of CalactiC ICXation. V.. lias not.," Two of the parameters, solar motion towards the Galactic centre,$U_{\odot}$, and solar motion towards the north Galactic pole, $W_{\odot}$, have remained largely unchanged $^{-1}$ and $^{-1}$ respectively), but the solar motion in the direction of Galactic rotation, $V_{\odot}$, has not."
 Originally V. was chosen to be 1 (the LAU standard). ilen il was revised to 5.25+0.62 + based on stellar kitemaltics of the Hipparcos catalogue (?)..," Originally $V_{\odot}$ was chosen to be $^{-1}$ (the IAU standard), then it was revised to $\pm$ $^{-1}$ based on stellar kinematics of the Hipparcos catalogue \citep{dehnen98}."
 However tlie dataset. was re-examined. resulting in futjer revision to t+ ! (?)..," However the dataset was re-examined, resulting in further revision to $\pm$ $^{-1}$ \citep{schonrich10}."
 This higler value of V.. returning to a value close to the original LAU staucdad. is in line with the suggestious of 2. aud? based on maser proper motious.," This higher value of $V_{\odot}$, returning to a value close to the original IAU standard, is in line with the suggestions of \citet{reid09} and \citet{mcmillan10} based on maser proper motions."
 The revision toa higher value may account for tle apparent motion of star forming regious counter to Galactic rotatio 1(?).., The revision to a higher value may account for the apparent motion of star forming regions counter to Galactic rotation \citep{bobylev10}.
 Clactic cireular rotation of t1e Sun. O. has also been subject to recent revision.," Galactic circular rotation of the Sun, $\Theta_{\odot}$ has also been subject to recent revision."
" The LAU standa«d of O,. 4. has been revised toa higher value based ou the results of proper motions deduced from maser astrometry observations."," The IAU standard of $\Theta_{\odot}$ , $^{-1}$, has been revised toa higher value based on the results of proper motions deduced from maser astrometry observations."
 The revised values are 2512-16 | as estimaed by 2.. or either 2162-30 kkinss.+ or 214-13 | as estimated by ?..," The revised values are $\pm$ $^{-1}$ as estimated by \citet{reid09}, or either $\pm$ $^{-1}$ or $\pm$ $^{-1}$ as estimated by \citet{bovy09}."
 ΤΙierefore the current best estimates of the parameters are: C. = WW. = 5h = 1:0. = ts and A. — 8.1 kpe., Therefore the current best estimates of the parameters are: $U_{\odot}$ = $^{-1}$; $W_{\odot}$ = $^{-1}$; $V_{\odot}$ = $^{-1}$; $\Theta_{\odot}$ = $^{-1}$; and $R_{\odot}$ = 8.4 kpc.
 The most significant difference is the increase in Ο..., The most significant difference is the increase in $\Theta_{\odot}$.
 We adopt the 0. of &.1 kpe throughout. but explored the impact of the other variations on ot: conclusions. aud the effect is minimal.," We adopt the $R_{\odot}$ of 8.4 kpc throughout, but explored the impact of the other variations on our conclusions, and the effect is minimal."
 The adjustment of ©.. has a reasonable impact ou kinemati€ clistauce estimates. but as we are working iu the Lv domai1. it cloes uot influence our maser paraueters.," The adjustment of $\Theta_{\odot}$ has a reasonable impact on kinematic distance estimates, but as we are working in the domain, it does not influence our maser parameters."
 It does affect the location of the spiral arm loci if we transfer them with this value rather tian the LAU staudard. but this only serves to shift the loci it velocity by ~5-LOkkuiss!.," It does affect the location of the spiral arm loci if we transfer them with this value rather than the IAU standard, but this only serves to shift the loci in velocity by $\sim$ $^{-1}$."
of our metal poor population ([Fe/H|2—0.27 dex and HD). 2.. 2.. ?,"of our metal poor population $= -0.27$ dex and $=-0.04$, II). \cite{Melendez08}, \cite{Ryde09},"
 ? ? (?) (?.. 2.. 2)) (2.. 2)). ? ? ? ? ," \cite{Bensby09} \cite{AlvesBrito10} \cite{Ryde09} \citep{Bournaud09} \cite{Prugniel01}, \cite{Peletier07}, \cite{Erwin08}) \cite{Samland03}, \cite{Athanassoula05}) \cite{Nakasato03} \cite{Minniti96} \cite{Nakasato03} \cite{Samland03} "
other spectral windows (Wakker Boulanger 1986: Colgan. Salpeter Terzian 1990).,"other spectral windows (Wakker Boulanger 1986; Colgan, Salpeter Terzian 1990)."
 Initially. the prospect. of optical emission line detections of LIVCs looked bleak.," Initially, the prospect of optical emission line detections of HVCs looked bleak."
" Reynolds (1987) cid not detect any of six LIVC's in the range =0.6-lem "" pe with the Fabry-Perot ‘staring’ technique.", Reynolds (1987) did not detect any of six HVCs in the range $=0.6-1$ $^{-6}$ pc with the Fabry-Perot `staring' technique.
 jut there have since been many attempts to detect ΗΝος at wavelengths other thanHi. with sensitive oobservations having the highest success rate.," But there have since been many attempts to detect HVCs at wavelengths other than, with sensitive observations having the highest success rate."
 Wakker van Woerden (1997) list the following published ddetections of LIVCs: HIVC€. 168-43-280 (0.08 I. Ixutvrev lievnolds 1989). cloud M LL (O0.1-0.2 I: Munch Pitz 1990). complex € (0.03 It. 11989: 0.00 It. 11998) and the Magellanic Stream (AIS Ll AIS HE. and AIS IV. at. 0.37. 0.21. and 0.20 1t respectively: Weiner Williams 1996).," Wakker van Woerden (1997) list the following published detections of HVCs: HVC 168-43-280 (0.08 R, Kutyrev Reynolds 1989), cloud M II (0.1-0.2 R; Munch Pitz 1990), complex C (0.03 R, 1989; 0.09 R, 1998) and the Magellanic Stream (MS II, MS III, and MS IV, at 0.37, 0.21, and 0.20 R respectively; Weiner Williams 1996)."
 Other optical detections of HIVC'sS rely primarily on absorption line studies., Other optical detections of HVCs rely primarily on absorption line studies.
 This work can be used to constrain distances ancl determine metallicities (ic. Magellanic metallicities in 11998: see also Schwarz. Walker van Wocrden 1995).," This work can be used to constrain distances and determine metallicities (i.e. Magellanic metallicities in 1998; see also Schwarz, Wakker van Woerden 1995)."
 Most detections of visual band. and/or ultraviolet absorption by metal ions are listed in Table 3 of Wakker van Woerden (1997)., Most detections of visual band and/or ultraviolet absorption by metal ions are listed in Table 3 of Wakker van Woerden (1997).
 The ions most commonly detected areCorr.Ale. and Civ.," The ions most commonly detected are, and ."
 van ((1907) recently. used Ca Ix. absorption to determine an upper limit on the distance to complex A. giving 4. 11 kpe as the first distance bracket for an ΝΟ.," van (1997) recently used Ca K absorption to determine an upper limit on the distance to complex A, giving $-$ 11 kpc as the first distance bracket for an HVC."
 LIST is frequently used to search for the UV absorption lines. with the most recent detection by Sahu Blades (1997) of ttowards IVO 487.," HST is frequently used to search for the UV absorption lines, with the most recent detection by Sahu Blades (1997) of towards HVC 487."
 ALL CO observations of IIVC's have resulted in detections (Llulsbosch 1978: Ciovanelli 1986: 119589). indicating that some IIVC's are further than 3 kpe away.," All CO observations of HVCs have resulted in non-detections (Hulsbosch 1978; Giovanelli 1986; 1989), indicating that some HVCs are further than 3 kpc away."
 Though previous searches for far infrared: emission have been negative (Wakker Boulanger 1986: 1988: 11987). νους Christodoulou (1997) searched the LRAS point source catalog and found possible voung stellar objects in the ecores of the M cloud and complex 11. Vhere have been claims for enhanced: x-ray emission towards LVCs from ROSAT observations. towarels Complex Al near AL E anc AL LL (Llerbstmeier. 1995). and possibly from Complex € (Ixerp 1996).," Though previous searches for far infrared emission have been negative (Wakker Boulanger 1986; 1988; 1987), Ivesic Christodoulou (1997) searched the IRAS point source catalog and found possible young stellar objects in the cores of the M cloud and complex H. There have been claims for enhanced x-ray emission towards HVCs from ROSAT observations, towards Complex M near M I and M II (Herbstmeier 1995), and possibly from Complex C (Kerp 1996)."
 Blom (1997) claims extended MeV. emission is associated with ΗΝΟ Complexes Al and A. in the same location as associated dilluse soft κι...," Blom (1997) claims extended MeV emission is associated with HVC Complexes M and A, in the same location as associated diffuse soft x-rays."
 Absorption at 21 em has been more successful for LLVC' detection., Absorption at 21 cm has been more successful for HVC detection.
 It vields a measurement of the hydrogen spin temperature. Py. and can be used to determine the kinetic eas temperature (Dickey 1979: Liszt. 1983).," It yields a measurement of the hydrogen spin temperature, $_s$, and can be used to determine the kinetic gas temperature (Dickey 1979; Liszt 1983)."
 The results of this work generally vield temperatures between LOO. ((1990) Gels Ty 7 20-7Ol for the Anticentre Clouds. Ty > POW for νο 48-18-300. and Py > 101 for the Magellanic Stream.," The results of this work generally yield temperatures between $-$ 100K. (1990) finds $_s$ $>$ 20-70K for the Anticentre Clouds, $_s$ $>$ 20K for HVC 43-13-309, and $_s$ $>$ 10K for the Magellanic Stream."
 Mebold (1991) μα E; o> 501k for another position in the Magellanic Stream., Mebold (1991) find $_s$ $>$ 50K for another position in the Magellanic Stream.
 Definitive results include two components at TOL and 800K in Cloud Ro 119758: 11980) and 50Ix for complex LE 11991)., Definitive results include two components at 70K and 300K in Cloud R 1978; 1980) and 50K for complex H 1991).
 We now present the first simultaneous. detection. of more than one emission line towards an LVC., We now present the first simultaneous detection of more than one emission line towards an HVC.
 The observations presented here were first. reported. by. Blaxd- (1994)., The observations presented here were first reported by Bland-Hawthorn (1994).
 In 62. we describe the observations before sununarising the calibrations and reductions in 83.," In $\S$ 2, we describe the observations before summarising the calibrations and reductions in $\S$ 3."
 In 84. the high velocity cloud. measurements are presented. and these are discussed in the context of ionisation models in 65.," In $\S$ 4, the high velocity cloud measurements are presented, and these are discussed in the context of ionisation models in $\S$ 5."
 The observations were carried out over three long dark nights (1994 Auge 12) at the [/8 Casseerain locus of he ANT 3.9m. Follow-up observations were carried out at £15 on 1994 Oct 29-30 and 1995 Sep 27., The observations were carried out over three long dark nights (1994 Aug $-$ 12) at the f/8 Cassegrain focus of the AAT 3.9m. Follow-up observations were carried out at f/15 on 1994 Oct 29-30 and 1995 Sep 27.
 The TAUIRUS-2 interferometer was used in conjunction with three cdilferent Queensgate etalons (Lable 1)): the ΗΡΙ 405422 gap etalon rom the University of Hawaii. the UALel 444m etalon from he University of Maryland. and the UNC 197m etalon from he University of North Carolina.," The TAURUS-2 interferometer was used in conjunction with three different Queensgate etalons (Table \ref{tbl:tbl1}) ): the HIFI $\mu$ m gap etalon from the University of Hawaii, the UMd $\mu$ m etalon from the University of Maryland, and the UNC $\mu$ m etalon from the University of North Carolina."
 A sinele order of interference was isolated using -eavity blocking filters with high throughput 90%)) ancl bandpasses well matched to the ctalon free. spectral ranges., A single order of interference was isolated using 4-cavity blocking filters with high throughput $-$ ) and bandpasses well matched to the etalon free spectral ranges.
 The 50num filters were placed out of focus close to the focal plane anc ballled to give a Ποιά., The 50mm filters were placed out of focus close to the focal plane and baffled to give a field.
 The etalon was tilted by 34° to shift the optical axis to the field. edge., The etalon was tilted by $^\circ$ to shift the optical axis to the field edge.
 An in-focus. focal plane. colander mask was used to ensure that low-order ghosts fall outside the field of view.," An in-focus, focal plane, colander mask was used to ensure that low-order ghosts fall outside the field of view."
 Phe “PAURUS-2 f/s pupil diameter. is 59.0mnm which is oversized for the 50nun. diameter etalon., The TAURUS-2 f/8 pupil diameter is 59.9mm which is oversized for the 50mm diameter etalon.
 Due to uncertainties of the precise location of the optica cavity within the etalon. we placed a 45-Onun aperture stop immecdiately in front of the etalon.," Due to uncertainties of the precise location of the optical cavity within the etalon, we placed a 45.0mm aperture stop immediately in front of the etalon."
 Phe pupil stop introduce a major loss of light (50) compounded: by a Casscerain hole which is of the total pupil area., The pupil stop introduced a major loss of light ) compounded by a Cassegrain hole which is of the total pupil area.
 The full pupi was used in the [/15 observations., The full pupil was used in the f/15 observations.
 The observational set-up was the same except for a 75mm blocking filter centered a wwhich was not ballled thereby. producing a field. of view similar to the [/8 observations., The observational set-up was the same except for a 75mm blocking filter centered at which was not baffled thereby producing a field of view similar to the f/8 observations.
 Observations were made at two closely spaced positions on the Smith cloud and at a sky position 15 away (Fig. 1))., Observations were made at two closely spaced positions on the Smith cloud and at a sky position $^\circ$ away (Fig. \ref{HImom}) ).
 The ctalon was used at fixed gap spacings and the resulting ring pattern was imaged onto a Tek 10247 CCD with pixel scales of, The etalon was used at fixed gap spacings and the resulting ring pattern was imaged onto a Tek $^2$ CCD with pixel scales of
"The angle-averaged svnchrotron emission by relativistic Maxwellian electrons is given by (Pacholezvk 1970) where ry,=2r/(31402). ϱμυ is a fitting Formula (Alahadevan. Naravan. Yi 1996).","The angle-averaged synchrotron emission by relativistic Maxwellian electrons is given by (Pacholczyk 1970) where $x_M \equiv 2\nu/(3\nu_0\theta_e^2)$ , $\nu_0 \equiv eB/(2\pi m_e
c)$, and is a fitting formula (Mahadevan, Narayan, Yi 1996)."
 When absorption is not important. the cooling rate due to the optically thin svuehrotron emission is obtained by integrating the equation (D1)) a large fraction of the low energv svnchrotron photons are generally absorbed by svinchrotron sell-absorption.," When absorption is not important, the cooling rate due to the optically thin synchrotron emission is obtained by integrating the equation \ref{eq:ep_syn}) ) However, a large fraction of the low energy synchrotron photons are generally absorbed by synchrotron self-absorption."
" The svuchrotvon emission in the presence of absorption can be approximated as where is the fraction of svnchrotron emission above the svnchrotron sell-absorption frequency Lap, Which satisfies Thus. we only consider the optically Chin part of svncehrotron emission as (he cooling function for the eas and as a contribution to the preheating radiation field."," The synchrotron emission in the presence of absorption can be approximated as where is the fraction of synchrotron emission above the synchrotron self-absorption frequency $\nu_{abs}$ which satisfies Thus, we only consider the optically thin part of synchrotron emission as the cooling function for the gas and as a contribution to the preheating radiation field."
 Locally emitted svnchrotron photons are upscattered by inverse Comptonization olf hot electrons., Locally emitted synchrotron photons are upscattered by inverse Comptonization off hot electrons.
 Here. we adopt a simple estimate of Comptonized svuchrotron. which is reasonable in phvsical conditions considered inthis paper.," Here, we adopt a simple estimate of Comptonized synchrotron, which is reasonable in physical conditions considered inthis paper,"
returns entirely back to it at later times (c£.,returns entirely back to it at later times (cf.
 the middle panel of Fie. 11))., the middle panel of Fig. \ref{fig:nohi}) ).
 This explains why. despite a lower loss of angular momentum. a larger fraction of cjecta moves inward compared to RAL (bottom panel).," This explains why, despite a lower loss of angular momentum, a larger fraction of ejecta moves inward compared to RM (bottom panel)."
 In fact. on the disk the centripetal force is larger: as more angular momentum deficient. gas falls on it. a larger amount of cjecta move inward.," In fact, on the disk the centripetal force is larger; as more angular momentum deficient gas falls on it, a larger amount of ejecta move inward."
 Likewise. the fraction of cjecta moving outward increases conipared to RAL due to the lower loss of angular momentum that facilitates the spreading of the material outward the injection region.," Likewise, the fraction of ejecta moving outward increases compared to RM due to the lower loss of angular momentum that facilitates the spreading of the material outward the injection region."
 In conclusion. a smaller amount of eas (40%)) remains within 7.5«R<S.5 kpe compared to RAL because a larger fraction of it moves both outward and inwarel.," In conclusion, a smaller amount of gas ) remains within $7.5<R<8.5$ kpc compared to RM because a larger fraction of it moves both outward and inward."
 lt is known that the neutral hydrogen distribution is rather chumpy (e.g.2).. instead of smooth. as we have assumed (ef.," It is known that the neutral hydrogen distribution is rather clumpy \citep [e.g.][]{wolf03}, instead of smooth, as we have assumed (cf."
 Eq. 13)., Eq. \ref{eq:ism}) ).
 Actually. such an assumption is necessary because an unrealistic eric resolution would be needed in order to resolve spatially the LL clouds.," Actually, such an assumption is necessary because an unrealistic grid resolution would be needed in order to resolve spatially the H clouds."
 One can expect that the leacing shock wave of the bubble/fountain moving through a realistic ISAT would advance faster. because most of the volume is filled by the rarefiecd LEIE σας which allows higher shock velocities. as well as lower post-shock radiative losses.," One can expect that the leading shock wave of the bubble/fountain moving through a realistic ISM would advance faster, because most of the volume is filled by the rarefied H gas which allows higher shock velocities, as well as lower post-shock radiative losses."
 To evaluate how our assumption on the LLI distribution influences our results. we have run a mocel similar to the reference. one. but. where LL1 is absent: this is a rather extreme assumption. but allows us to establish an upper limit value on the heights reached by the fountain.," To evaluate how our assumption on the H distribution influences our results, we have run a model similar to the reference one, but where H is absent; this is a rather extreme assumption, but allows us to establish an upper limit value on the heights reached by the fountain."
 Actually. after 150 Myr the amount of the ejecta above," Actually, after 150 Myr the amount of the ejecta above"
duration of the dip: lower minimum fluxes tend to be related to longer dips.,duration of the dip: lower minimum fluxes tend to be related to longer dips.
 This link was already mentioned by Bellonietal.(1997) in the case of class κ. observations., This link was already mentioned by \citet{Belloni:1997} in the case of class $\kappa$ observations.
" Finally, a more pronounced trend is visible between the duration of the dips At and the parameters of the subsequent flares: longer dips seem to be followed by more important radio ejections (Fig. 6,,"," Finally, a more pronounced trend is visible between the duration of the dips $\Delta t$ and the parameters of the subsequent flares: longer dips seem to be followed by more important radio ejections (Fig. \ref{blob},"
 7 and 8))., \ref{blob_K} and \ref{resume}) ).
" In particular, a correlation is visible between At and the amplitude Snax of the following radio flare."," In particular, a correlation is visible between $\Delta t$ and the amplitude $S_{max}$ of the following radio flare."
 A correlation is also visible between At and the fluence L15G5; of the following radio flare., A correlation is also visible between $\Delta t$ and the fluence $L_{15GHz}$ of the following radio flare.
" To quantify this, we used the Pearson and Spearman tests of correlation."," To quantify this, we used the Pearson and Spearman tests of correlation."
" The Spearman test detects any monotonic correlation in the data, while the Pearson test detects linear correlation."," The Spearman test detects any monotonic correlation in the data, while the Pearson test detects linear correlation."
 Values of these indices are reported in Table 2 in confidence levels., Values of these indices are reported in Table \ref{correl} in confidence levels.
" The two tests show a strong correlation between the length of the X-ray dip At and the maximum of the following flare $4,454.", The two tests show a strong correlation between the length of the X-ray dip $\Delta t$ and the maximum of the following flare $S_{max}$.
 'The correlation between the length of the dips and the fluence L15Gg; is also high., The correlation between the length of the dips and the fluence $L_{15GHz}$ is also high.
 Spearman and Pearson tests are not significant in the case of length of the X-ray dip At versus width to of the flares., Spearman and Pearson tests are not significant in the case of length of the X-ray dip $\Delta t$ versus width $t_0$ of the flares.
" Note, however, that the Lisg#z vs. At and Sax vs. At correlations are less pronounced when ignoring the five points corresponding to At<200s."," Note, however, that the $L_{15GHz}$ vs. $\Delta t$ and $S_{max}$ vs. $\Delta t$ correlations are less pronounced when ignoring the five points corresponding to $\Delta t < 200 s$."
" In the case of Smax vs. At, the level of significance for the Spearman test drops to values between and98%,, for the “all data” and “Index 1” subsets, respectively."," In the case of $S_{max}$ vs. $\Delta t$, the level of significance for the Spearman test drops to values between and, for the “all data"" and “Index 1"" subsets, respectively."
" Indeed, as visible on Fig. 7,,"," Indeed, as visible on Fig. \ref{blob_K},"
 the index 1 data are still correlated when ignoring the A points., the index 1 data are still correlated when ignoring the $\lambda$ points.
" In the case of L15G54 vs. At, however, the non-A points are almost compatible with a constant."," In the case of $L_{15GHz}$ vs. $\Delta t$, however, the $\lambda$ points are almost compatible with a constant."
" During the A observations, there is no radio emission prior to the X-ray spike, so the characteristics of the flare are well constrained."," During the $\lambda$ observations, there is no radio emission prior to the X-ray spike, so the characteristics of the flare are well constrained."
 We therefore have good confidence on the robustness of these values., We therefore have good confidence on the robustness of these values.
" However, a crucial test for the reality of the Sma, vs. At and Lisamgz vs. At correlations would be to observe X-ray dips in the range 200—500 s. More observations are needed to populate this range in order to refine the link between X-ray dips and radio flares."," However, a crucial test for the reality of the $S_{max}$ vs. $\Delta t$ and $L_{15GHz}$ vs. $\Delta t$ correlations would be to observe X-ray dips in the range 200–500 s. More observations are needed to populate this range in order to refine the link between X-ray dips and radio flares."
" Looking at the fluence vs. dip-length relationship, the correlation does not seem to be linear nor affine."," Looking at the fluence vs. dip-length relationship, the correlation does not seem to be linear nor affine."
" Indeed, short X-ray dips produce much weaker radio flares than long dips (see Fig. 8))."," Indeed, short X-ray dips produce much weaker radio flares than long dips (see Fig. \ref{resume}) )."
" This is consistent with the statement of Klein-Woltetal.(2002), who mentioned that dips shorter than 100s do not seem to be followed by radio flares."," This is consistent with the statement of \citet{KleinWolt:2002}, who mentioned that dips shorter than 100s do not seem to be followed by radio flares."
" 'Therefore, we looked for other functions to describe the relationship between the (radio) fluence Ligay, and the length At of the X-ray dip than a simple linear or affine law (Fig. 8))."," Therefore, we looked for other functions to describe the relationship between the (radio) fluence $L_{\mathrm{15}Ê\textrm{ } \mathrm{GHz}}$ and the length $\Delta t$ of the X-ray dip than a simple linear or affine law (Fig. \ref{resume}) )."
" Two types of functions produced good results, which are listed in Table 3.."," Two types of functions produced good results, which are listed in Table \ref{expo}."
" Firstly, the data are well described by a function of the form Liseag,=— with 7 between 0.17 and 0.35 depending(AM) on A(Atthe subsetAto)’, considered."," Firstly, the data are well described by a function of the form $L_{\mathrm{15}Ê\textrm{ } \mathrm{GHz}}(\Delta t) = A (\Delta t-\Delta t_0)^\gamma$, with $\gamma$ between 0.17 and 0.35 depending on the subset considered."
" Then, an exponential function of the form [ερ@y,(At)=Lmax(1--eo) provided very similar x2, with a characteristic time 7T between 100 and 500 s, and a saturating fluence Lima, between 55 and 80 Jy.s."," Then, an exponential function of the form $L_{\mathrm{15}Ê\textrm{ } \mathrm{GHz}}(\Delta t) = L_{max} (1-e^{-\frac{\Delta t-\Delta t_{min}}{\tau}})$ provided very similar $\chi_\nu^2$, with a characteristic time $\tau$ between 100 and 500 s, and a saturating fluence $L_{max}$ between 55 and 80 Jy.s."
" Both models are truncated at short dip-length, as visible on the plots."," Both models are truncated at short dip-length, as visible on the plots."
" In these two cases, the quantities Ato and Atmjn correspond to the length of the X-ray dip below which no flare is detected (L,.&ay,= 0)."," In these two cases, the quantities $\Delta t_0$ and $\Delta t_{min}$ correspond to the length of the X-ray dip below which no flare is detected $L_{\mathrm{15}Ê\textrm{ } \mathrm{GHz}}=0$ )."
 They measure Ato and At; between 50 and 130 s. This is compatible with the empirical observation that no flare are detected after dips shorter than ~100 s. Our analysis extends the previous results onthe occurrenceof radio flares., They measure $\Delta t_0$ and $\Delta t_{min}$ between 50 and 130 s. This is compatible with the empirical observation that no flare are detected after dips shorter than $\sim$ 100 s. Our analysis extends the previous results onthe occurrenceof radio flares.
" Klein-Woltetal.(2002) suggested that, during /£ and v classes, long and spectrally hard State C intervals are followed by radio oscillations."," \citet{KleinWolt:2002} suggested that, during $\beta$ and $\nu$ classes, long and spectrally hard State C intervals are followed by radio oscillations."
" Rodriguezetal.(2008a) extended this connexion to A classes, and identified the X-ray spike at the end of the X-ray dips as the trigger to the ejection."," \citet{Rodriguez:2008a} extended this connexion to $\lambda$ classes, and identified the X-ray spike at the end of the X-ray dips as the trigger to the ejection."
" With an extended data set, we confirm that, during a, B, A and v classes, every X-ray dip in the lightcurve is followed by a radio flare."," With an extended data set, we confirm that, during $\alpha$ , $\beta$ , $\lambda$ and $\nu$ classes, every X-ray dip in the lightcurve is followed by a radio flare."
" Moreover, the"," Moreover, the"
"this range was extended to 1.0 pc, there was no significant change in the column density projection.","this range was extended to $1.0$ pc, there was no significant change in the column density projection."
" T'his is because the density of the gas close to the sink is so high, and covers such a large angle, that it completely dominates the column density."," This is because the density of the gas close to the sink is so high, and covers such a large angle, that it completely dominates the column density."
 The range of column densities seen by the central sink is shown in 2 as a percentage of the total core surface area and mass., The range of column densities seen by the central sink is shown in \ref{CDarea} as a percentage of the total core surface area and mass.
 For the symmetric core (a) nearly all of its area and mass is at column densities below 1?., For the symmetric core (a) nearly all of its area and mass is at column densities below $1$.
". However, the column densities reach higher values where there are filaments."," However, the column densities reach higher values where there are filaments."
 The spatial clustering in the column density projection means that a larger proportion of the mass is at higher column densities than a simple average may suggest., The spatial clustering in the column density projection means that a larger proportion of the mass is at higher column densities than a simple average may suggest.
 1 shows the percentage of the area and mass of the cores that is above a column density of 1?., \ref{area_table} shows the percentage of the area and mass of the cores that is above a column density of $1$.
". In the case of core (d), more than half of its mass is above 1?,, but this is contained within only 24% of the core's surface."," In the case of core (d), more than half of its mass is above $1$, but this is contained within only $24\%$ of the core's surface."
" This has important implications for the action of radiative feedback on the core: a large fraction of the core mass will be shielded by a high extinction, and hence will be comparatively unaffected by any feedback, while a large fraction of the surface of the core will be covered by low extinction material, allowing for the easy escape of radiation along these low extinction sightlines."," This has important implications for the action of radiative feedback on the core: a large fraction of the core mass will be shielded by a high extinction, and hence will be comparatively unaffected by any feedback, while a large fraction of the surface of the core will be covered by low extinction material, allowing for the easy escape of radiation along these low extinction sightlines."
 Similar arguments were made in ? regarding the effects of ionising winds on a star cluster., Similar arguments were made in \citet{Dale08} regarding the effects of ionising winds on a star cluster.
" As the ram pressure seen by the central sink is simply the product of the column density with the gas radial velocity, the pressure towards the centre of the core is also highly non-uniform."," As the ram pressure seen by the central sink is simply the product of the column density with the gas radial velocity, the pressure towards the centre of the core is also highly non-uniform."
" That star formation often takes place in filaments is not in itself a new result, although the impact this has on the environment ‘seen’ by the proto-stars is perhaps surprising."," That star formation often takes place in filaments is not in itself a new result, although the impact this has on the environment `seen' by the proto-stars is perhaps surprising."
" However, due to the large number of stars formed in a variety of environments within this simulation, it is possible to quantify how common this is."," However, due to the large number of stars formed in a variety of environments within this simulation, it is possible to quantify how common this is."
" Obviously it is impractical to show all the column density projections, so the cores are classified according to the shapes of their angular covariance functions."," Obviously it is impractical to show all the column density projections, so the cores are classified according to the shapes of their angular covariance functions."
 3 shows the covariance functions of the four cores shown in 1.., \ref{Corr_types} shows the covariance functions of the four cores shown in \ref{CDprojections}.
 These covariance functions are typical of the entire data-set and using these shapes it is possible to classify the cores into three types according to the number of over-densities they contain., These covariance functions are typical of the entire data-set and using these shapes it is possible to classify the cores into three types according to the number of over-densities they contain.
" have carried out a similar classification on their Class 0 sources,7? and have independently proposed a very similar scheme."," \citet{Tobin10} have carried out a similar classification on their Class 0 sources, and have independently proposed a very similar scheme."
Cloomre Toomre 1972: Foomre 1977) galaxies or to Hit-Iuminous merger remnants (Sanders Mirabel 1996).,(Toomre Toomre 1972; Toomre 1977) galaxies or to IR-luminous merger remnants (Sanders Mirabel 1996).
 ligure 6 summarizes the distribution and kinematics of gas at the end of each simulation., Figure \ref{fig06} summarizes the distribution and kinematics of gas at the end of each simulation.
" Fhese plots show logarithmic radii logr rradial velocities. c, of eas particles.", These plots show logarithmic radii $\log r$ radial velocities $v_r$ of gas particles.
" The distributions are roughly with respect to.the horizontal axis 7,= Oat small radii. but distinctlymchrie at larger radii."," The distributions are roughly with respect tothe horizontal axis $v_r = 0$ at small radii, but distinctly at larger radii."
 Phe narrow diagonal streaks seen at large radii represent. tails extracted [rom the disks before they merged., The narrow diagonal streaks seen at large radii represent tails extracted from the disks before they merged.
 Almost every. periccntric passage vields a pair of tails. but the amount of tail material and its subsequent evolution depend. on the geometry. of the passage.," Almost every pericentric passage yields a pair of tails, but the amount of tail material and its subsequent evolution depend on the geometry of the passage."
 Thus al the instants shown in Figure 6. the remnant produced by REP 3: has almost no gaseous tail material. while remnant DIR 3:1 still shows distinct. tails (ancl the remains of a fourth). each originating from a cillerent. disk at a dillerent. passage.," Thus at the instants shown in Figure \ref{fig06} the remnant produced by RET 3:1 has almost no gaseous tail material, while remnant DIR 3:1 still shows distinct tails (and the remains of a fourth), each originating from a different disk at a different passage."
 The dashed curves in the upper right of cach plot represent. the nominal escape velocity PoeAfBGM|ALr.," The dashed curves in the upper right of each plot represent the nominal escape velocity $v_{\rm esc}
\equiv \sqrt{2 G (M_1 \! + \! M_2) / r}$."
 Some tail material has chough velocity to escape. but almost all falls back eventually.," Some tail material has enough velocity to escape, but almost all falls back eventually."
 Tail material with ορ«0 has passed apogalacticon and is now falling back: as this material reenters the remnant. the gas encounters shocks and begins evolving toward closed orbits.," Tail material with $v_r < 0$ has passed apogalacticon and is now falling back; as this material reenters the remnant, the gas encounters shocks and begins evolving toward closed orbits."
 If the infalline eas has relatively Littl: angular momentum it may plunge deep into the remnant and clirectly assimilate into a disk., If the infalling gas has relatively little angular momentum it may plunge deep into the remnant and directly assimilate into a disk.
 In many cases. however. the tal gas has so much angular momentum that it initially sicle-swipes the central disk ane subsequently follows eccentric. looping paths before falling back vet again: a vivid example is provided on the right in Figure 5..," In many cases, however, the tail gas has so much angular momentum that it initially side-swipes the central disk and subsequently follows eccentric, looping paths before falling back yet again; a vivid example is provided on the right in Figure \ref{fig05}."
 The gas on these looping orbits populates transition zones between asvmametric and symmetric e distributions in Figure 6.., The gas on these looping orbits populates transition zones between asymmetric and symmetric $v_r$ distributions in Figure \ref{fig06}.
 μονο zones are labeled by the letter 7L7: the various POLar encounters all produce. clear examples. of this behavior., These zones are labeled by the letter “L”; the various POLar encounters all produce clear examples of this behavior.
 A given gas particle may. settle into a closed orbit. after executing a few loops. but the loop structures theniselves are replenished by continued infall.," A given gas particle may settle into a closed orbit after executing a few loops, but the loop structures themselves are replenished by continued infall."
 At radii where the eas distribution is nearly svnimetric with respect to ο=0 lie the gas disks formed. by. this infall process., At radii where the gas distribution is nearly symmetric with respect to $v_r = 0$ lie the gas disks formed by this infall process.
" Gas on nearlv-cireular orbits has e,20. while gas on elongated. orbits has a large c, dispersion."," Gas on nearly-circular orbits has $v_r \simeq 0$, while gas on elongated orbits has a large $v_r$ dispersion."
 Thus in ligure 6 the vertical spread of the points at a given radius gives information on the shapes of gas orbits., Thus in Figure \ref{fig06} the vertical spread of the points at a given radius gives information on the shapes of gas orbits.
" For example. remnants such as POL 1:1 C. INC 1:1 ο and INC 1:1 D have large amounts of gas with fairly narrow ve, distributions: this eas lies in rotating disks. cach labeled. 7D in the plots."," For example, remnants such as POL 1:1 C, INC 1:1 C, and INC 1:1 D have large amounts of gas with fairly narrow $v_r$ distributions; this gas lies in rotating disks, each labeled “D” in the plots."
 At smaller racii. remnants DII. 1:1 D. DIR. 3:1. POL 3:1. and INC 3:1 have zones. labeled. 77 in the plots. with large. symmetric spreads in ον.," At smaller radii, remnants DIR 1:1 D, DIR 3:1, POL 3:1, and INC 3:1 have zones, labeled “B” in the plots, with large, symmetric spreads in $v_r$."
 Fhese arise where central triaxial or bar-like structures dominate the potential and the σας consequently moves on elongated. orbits., These arise where central triaxial or bar-like structures dominate the potential and the gas consequently moves on elongated orbits.
" Albo twelve remnants have nuclear eas clouds characterized by very high. densities. often. of order poc10"" model units."," All twelve remnants have nuclear gas clouds characterized by very high densities, often of order $\rho \sim 10^6$ model units."
 These nuclei. which are labeled “NU dn Figure 6.. usually have small radial velocity. dispersions: most are supported by a combination of pressure ancl circular motion.," These nuclei, which are labeled “N” in Figure \ref{fig06}, usually have small radial velocity dispersions; most are supported by a combination of pressure and circular motion."
 But remnants DIR 3:1. REP 3:1. POL 1:1 €. and INC 1:1 € are dillerent: in these cases the nuclear gas lies in rotating elliptical disks.," But remnants DIR 3:1, RET 3:1, POL 1:1 C, and INC 1:1 C are different; in these cases the nuclear gas lies in rotating elliptical disks."
 These nuclei are. barely resolved. in the present. simulations. so their detailed dvnamics are not well-determined.," These nuclei are barely resolved in the present simulations, so their detailed dynamics are not well-determined."
 However. the total masses and angular momenta of nuclear clouds should be more reliable since these are determined. by events on somewhat larger scales.," However, the total masses and angular momenta of nuclear clouds should be more reliable since these are determined by events on somewhat larger scales."
 Several of these nuclear eas disks are kinematically decoupled with respect to the remnants they inhabit., Several of these nuclear gas disks are kinematically decoupled with respect to the remnants they inhabit.
 The gas fractions in the nuclei. bars. disks. loops. ane ails of all remnants are listed in Table 2..," The gas fractions in the nuclei, bars, disks, loops, and tails of all remnants are listed in Table \ref{tab:remnants}."
 Here and in wha ollows. cach of these components is simply. defined. as gas within an appropriate range of radii measured. from. he center of cach remnant.," Here and in what follows, each of these components is simply defined as gas within an appropriate range of radii measured from the center of each remnant."
 These radii often corresponc o obvious features in Figure 6: for example. the 7D. (disk) component in remnant DIR 1:1 € is delimited by the abrup end of the infalling tails at logrO88 on the one mand. and by à marked change in the density of points a ogre192 onthe other hand.," These radii often correspond to obvious features in Figure \ref{fig06}; for example, the “D” (disk) component in remnant DIR 1:1 C is delimited by the abrupt end of the infalling tails at $\log r \simeq -0.33$ on the one hand, and by a marked change in the density of points at $\log r \simeq -1.92$ on the other hand."
 In a few cases the divisions tween components are less obvious: in particular. its har o define the boundaries between disks. ancl outer. loops rom the data in Figure 6..," In a few cases the divisions between components are less obvious; in particular, it's hard to define the boundaries between disks and outer loops from the data in Figure \ref{fig06}."
" To fix these boundaries more accurately, E used an interactive viewing program to inspec he gas distribution in three dimensions: on such a display. as in the right-hand side of Figure 5.. the distinction between nearly circular disks and elongated loops is unmistakable."," To fix these boundaries more accurately, I used an interactive viewing program to inspect the gas distribution in three dimensions; on such a display, as in the right-hand side of Figure \ref{fig05}, the distinction between nearly circular disks and elongated loops is unmistakable."
 As ‘Table 2 shows. the initial orientation of the colliding disks has a definite effect on the distribution of gas in the remnants.," As Table \ref{tab:remnants} shows, the initial orientation of the colliding disks has a definite effect on the distribution of gas in the remnants."
 Encounters in which disks are tilted with respect to the orbital plane vield. remnants. with massive disks. while encounters in which a disk lies in the orbital plane drive more gas to the nuclear regions.," Encounters in which disks are tilted with respect to the orbital plane yield remnants with massive disks, while encounters in which a disk lies in the orbital plane drive more gas to the nuclear regions."
 Nuclei contain an average of ~85 percent of the gas in the remnants of DIBect and IZTrograde encounters: the most. massive nuclei. found in the REPrograde encounters. are. produced w violent. hvdrodynamic forces as illustrated in Figure 1..," Nuclei contain an average of $\sim 85$ percent of the gas in the remnants of DIRect and RETrograde encounters; the most massive nuclei, found in the RETrograde encounters, are produced by violent hydrodynamic forces as illustrated in Figure \ref{fig01}."
 In contrast. only 63 percent of the gas Lies in the nuclei of he POLar and INClined remnants: the balance is found in he extended bars. disks. and loops surrounding these nuclei.," In contrast, only $\sim 63$ percent of the gas lies in the nuclei of the POLar and INClined remnants; the balance is found in the extended bars, disks, and loops surrounding these nuclei."
 Figure 7 displavs rotation directions for the gas in the remnants., Figure \ref{fig07} displays rotation directions for the gas in the remnants.
 In. cach plot. an area-preserving map is used to ransform the unit sphere S of all possible spin directions onto the unit circle C: the direction of the initial orbit’s angular momentum vector Joni always maps to the origin of C.," In each plot, an area-preserving map is used to transform the unit sphere ${\bf S}$ of all possible spin directions onto the unit circle ${\bf C}$; the direction of the initial orbit's angular momentum vector ${\bf J}_{\rm orbit}$ always maps to the origin of ${\bf C}$."
 Any area-preserving map from the sphere to the plane must create some distortion: here. the direction. exactly opposite to Jona maps to the edge of the circle. and nearby regions are stretched into elongated: crescents.," Any area-preserving map from the sphere to the plane must create some distortion; here, the direction exactly opposite to ${\bf
J}_{\rm orbit}$ maps to the edge of the circle, and nearby regions are stretched into elongated crescents."
 Llowever. the area-preserving property of this map implies that an isotropic ensemble of directions is mapped. to a uniform distribution within C.," However, the area-preserving property of this map implies that an isotropic ensemble of directions is mapped to a uniform distribution within ${\bf C}$ ."
" ""The images represent. the angular momenta directions of gas particles: cach particle's angular momentum vector. measured. with respect tothe center of the remnant as defined by the peak gas density. was"," The images represent the angular momenta directions of gas particles; each particle's angular momentum vector, measured with respect tothe center of the remnant as defined by the peak gas density, was"
On Fig.,On Fig.
 8 we show the percentage of circular polarization plotted against the percentage ol linear polarization for all spots., 8 we show the percentage of circular polarization plotted against the percentage of linear polarization for all spots.
 The spots are labelled by letters as in Table 1., The spots are labelled by letters as in Table 1.
 The dashed line shows where completely polarized features could appear ou the diagram., The dashed line shows where completely polarized features could appear on the diagram.
 The majority of the spots are located close to the LOO per cent polarization line., The majority of the spots are located close to the 100 per cent polarization line.
 A notable exception is spot L (1667 MllIz transition) which is 47 per cent polarized., A notable exception is spot L (1667 MHz transition) which is 47 per cent polarized.
 There is evidence for a correlation in (hat predominantly cireularly. polarized spots are either located in the upper ancl lower left corners of the diagram. and predominantly linearly polarized spots are located in the middle right of the diagram.," There is evidence for a correlation in that predominantly circularly polarized spots are either located in the upper and lower left corners of the diagram, and predominantly linearly polarized spots are located in the middle right of the diagram."
 The numbers on the dashed line indicate an angle 8 between the line of sightex and the magneticC» field direction. accordinge to equations These equations describe polarization of the σ components in the theory by (1973) [or the case when the Zeeman splitting is larger (han the linewidth (seealsoElitzur1996).," The numbers on the dashed line indicate an angle $\theta$ between the line of sight and the magnetic field direction, according to equations These equations describe polarization of the $\sigma$ –components in the theory by \citet*{goldreich73} for the case when the Zeeman splitting is larger than the linewidth \citep[see also][]{elitzur96}."
. Most of (he maser spots occupy lwo regions on (he diagram: 9.<30° and 807«9907., Most of the maser spots occupy two regions on the diagram: $\theta <30^\circ$ and $80^\circ<\theta<90^\circ$.
 If all the spots are σ components it means Chat the line of sight is either parallel or perpendicular to the magnetic field direction. and no intermediate cases exist.," If all the spots are $\sigma$ –components it means that the line of sight is either parallel or perpendicular to the magnetic field direction, and no intermediate cases exist."
 The predominantly circularly polarized spots are almost certainly σ components. although frequently without the second member of (he pair.," The predominantly circularly polarized spots are almost certainly $\sigma$ –components, although frequently without the second member of the pair."
 The predominantly linearly polarized spots are also σ components with @ 890°. or 7 components.," The predominantly linearly polarized spots are also $\sigma$ –components with $\theta\approx$ $^\circ$, or $\pi$ –components."
 A correct atiribution is important for the determination of the direction of the magnetic field: it is parallel to E-vector lor x and perpendicular to E-vector for σ components.," A correct attribution is important for the determination of the direction of the magnetic field: it is parallel to E-vector for $\pi$ --components, and perpendicular to E-vector for $\sigma$ –components."
 As mentioned in Section 3.6 (he presence of the small circular polarization makes these components ellipticallv polarized. and therefore they must be σ components. since 7 Components can not have a circular polarization contribution.," As mentioned in Section 3.6 the presence of the small circular polarization makes these components elliptically polarized, and therefore they must be $\sigma$ –components, since $\pi$ –components can not have a circular polarization contribution."
 The only linearly polarized spot. L at 1667 MlIz. is definitely not 100 per cent polarized and is an exception among all maser spots in W75N. In the model of the weak magnetic field the percentage of linear polarization for sin9>1/3 is (Goldreich.Ixeelev.andKwan1973).," The only linearly polarized spot, L at 1667 MHz, is definitely not 100 per cent polarized and is an exception among all maser spots in W75N. In the model of the weak magnetic field the percentage of linear polarization for $\sin^2\theta>1/3$ is \citep*{goldreich73}."
". For this spot my,=41.6 per cent. and corresponds io 8=43.4."," For this spot $m_L= 41.6$ per cent, and corresponds to $\theta=43.4^\circ$."
 The percentagee of cireular polarization varies across the line profile (Fig., The percentage of circular polarization varies across the line profile (Fig.
e 9) changing the sign as predicted by the theory for the case of small Zeeman splitting, 9) changing the sign as predicted by the theory for the case of small Zeeman splitting
" >10!! z—2 formation (e.g.. 2005; 2008: Damjanov et 22009). but at redshifts z>1 a subset of thepopulation has MIPS 24,/m fluxes and near-IR colors characteristic of dust-obscured star-formation (e.g.. 2006; 2010:Brammer 2011)."," $>10^{11}$ $z\sim 2$ formation (e.g., 2005; 2008; Damjanov et 2009), but at redshifts $z>1$ a subset of thepopulation has MIPS $\mu$ m fluxes and near-IR colors characteristic of dust-obscured star-formation (e.g., 2006; 2010; 2011)."
" These galaxies mascarade as ""dead"" red sequence galaxies as they have very similar optical colors but in fact have very high inferred star formation rates.", These galaxies mascarade as “dead” red sequence galaxies as they have very similar optical colors but in fact have very high inferred star formation rates.
 These apparently star-forming. massive galaxies are progenitors of at least a subset of massive galaxies today.," These apparently star-forming, massive galaxies are progenitors of at least a subset of massive galaxies today."
" In the nearby Universe strongly star forming galaxies are typically gas-rich mergers. but several studies have argued that at higher redshift such galaxies more resemble ""scaled-up"" spiral galaxies than local mergers(Wolf 2005: 2010: 2011)."," In the nearby Universe strongly star forming galaxies are typically gas-rich mergers, but several studies have argued that at higher redshift such galaxies more resemble ``scaled-up'' spiral galaxies than local mergers 2005; 2010; 2011)."
 Interpreting these galaxies. and their relation to the compact quiescent galaxies which exist at the same epoch. has been hampered by a lack of mass-complete samples with homogeneous data at the redshifts of interest.," Interpreting these galaxies, and their relation to the compact quiescent galaxies which exist at the same epoch, has been hampered by a lack of mass-complete samples with homogeneous data at the redshifts of interest."
 Most existing samples are luminosity- rather than mass-selected. are based on photometric redshifts. lack rest-frame optical morphological information. and/or lack well-calibrated star formation diagnostics.," Most existing samples are luminosity- rather than mass-selected, are based on photometric redshifts, lack rest-frame optical morphological information, and/or lack well-calibrated star formation diagnostics."
 —1 this Letter. we construct and study a spectroscopic stellar mass-limited sample of galaxies at|<z< 1.5. in order to," In this Letter, we construct and study a spectroscopic stellar mass-limited sample of galaxies at$1<z<1.5$ , in order to"
directly to CMDs of other clusters (Figure 3).,directly to CMDs of other clusters (Figure 3).
 We compare figure 3 with the results from 17 Tuc (GIIEOL. Excinonds et al.," We compare figure 3 with the results from 47 Tuc (GHE01, Edmonds et al."
 2002a.b). 2 Cen (Rutledge ct al.," 2003a,b), $\omega$ Cen (Rutledge et al."
 Ww02. Cool et al.," 2002, Cool et al."
 2002). NGC 6397 (CUIEOLb). NGC 6752 (Pooley et al.," 2002), NGC 6397 (GHE01b), NGC 6752 (Pooley et al."
 2002a). NCC 6110 (Pooley et al.," 2002a), NGC 6440 (Pooley et al."
 20025). and M28 (Becker et al.," 2002b), and M28 (Becker et al."
 2003)., 2003).
" Quiescent LAINBs have been identified iu globular clusters by their blackbody-like spectra aud hnieh Py/Pop, values.", Quiescent LMXBs have been identified in globular clusters by their blackbody-like spectra and high $F_X/F_{Opt}$ values.
" CX2 aud CNG "" sind colors and luminosities to qLMXDs ideutified in n aeTuc (X5. NT). w Cen (4633). NOC 6397 (C21). a GLLO (CNT) bv these means. so we classify them as probable qLAINBs."," CX2 and CX6 have similar colors and luminosities to qLMXBs identified in 47 Tuc (X5, X7), $\omega$ Cen 3), NGC 6397 (U24), and NGC 6440 (CX1) by these means, so we classify them as probable qLMXBs."
 As a further check upon our classification. we plot im Fieure 3 theoretical tracks for 10 and 12 km nommagnetic bydrogen-atusosplere models 6: Llovd (2003).," As a further check upon our classification, we plot in Figure 3 theoretical tracks for 10 and 12 km nonmagnetic hydrogen-atmosphere models of Lloyd (2003)."
 These are essentially cooling tracks for neutron stars. since they show how the N-rav color of the qLMXD should change as the Iuninositv decreases for a NS of fixed radius.," These are essentially cooling tracks for neutron stars, since they show how the X-ray color of the qLMXB should change as the luminosity decreases for a NS of fixed radius."
 Clearly CX2 and CX6 are m agreement with the predictions of these tracks., Clearly CX2 and CX6 are in agreement with the predictions of these tracks.
 ILuder sources (-l<Neolor<l) associated with these clusters above 1077 ores «| secnm to be almost entirely CVs (GIIEO0Ia. GIIEOIb. Pooley et al.," Harder sources $<$ $<$ 1) associated with these clusters above $10^{32}$ ergs $^{-1}$ seem to be almost entirely CVs (GHE01a, GHE01b, Pooley et al."
" 2002a). so we identify CX2.. CN3. CNL aud. CN5 as probable CVs,"," 2002a), so we identify CX2, CX3, CX4, and CX5 as probable CVs."
 Two eclipsing CVs in l7 Tuc (AVS and W15: GIIEOL. Edimouds et al.," Two eclipsing CVs in 47 Tuc (W8 and W15; GHE01, Edmonds et al."
 2003a. b) show Neolor<-l. due to high intrinsic absorption of the X-ravs from the iuner disk and/or WD passing through the edge-on accretion disk.," 2003a, b) show $<$ -1, due to high intrinsic absorption of the X-rays from the inner disk and/or WD passing through the edge-on accretion disk."
 N-rav spectra showing these colors without hieh intrinsic absorption (from an accretion disk or other gas in the system) are highly implausible., X-ray spectra showing these colors without high intrinsic absorption (from an accretion disk or other gas in the system) are highly implausible.
 CX15 shows simular colors and Iuniinosities to these systems. so we propose it is also a CV.," CX15 shows similar colors and luminosities to these systems, so we propose it is also a CV."
" The remaining sources. below Ly=1077 eres st, are sinilar im colors aud Iuninositv to both CV and bright AD svsteiis in 17 Tuc. x Ceu. NGC 6397. and NGC 6752."," The remaining sources, below $L_X=10^{32}$ ergs $^{-1}$, are similar in colors and luminosity to both CV and bright AB systems in 47 Tuc, $\omega$ Cen, NGC 6397, and NGC 6752."
 Soft AISPs in 1? Tuc and NGC 6752 are wniformly less ταν luminous than any systems in ALSO. but the uumsual nouthermalh-cimitting MSPs in NGC6397 (GIIEOTIb) aud LF Tuc CI? Tuc-W. Ecanouds et al.," Soft MSPs in 47 Tuc and NGC 6752 are uniformly less X-ray luminous than any systems in M80, but the unusual nonthermally-emitting MSPs in NGC 6397 (GHE01b) and 47 Tuc (47 Tuc-W, Edmonds et al."
 20025) are as Iuminous as our faintest sources (, 2002b) are as luminous as our faintest sources. (
A luninous. vouug ASP like PSR B1821-21 iu M28 should probably be detected in the curent radio searches of MESO bv N. D'Amico et al.,"A luminous, young MSP like PSR B1821-24 in M28 should probably be detected in the current radio searches of M80 by N. D'Amico et al."
 We believe such objectsDude to be rare iu globular clusters. but we cannot exc such an object. as our 3.2 s readout time does not allow pulsation searches at appropriate periods.)," We believe such objects to be rare in globular clusters, but we cannot exclude such an object, as our 3.2 s readout time does not allow pulsation searches at appropriate periods.)"
 Therefore we regard our remaining sources: as probably predominantly CVs. with some ABs and perhaps MSPs ήχος in.," Therefore we regard our remaining sources as probably predominantly CVs, with some ABs and perhaps MSPs mixed in."
 We identify probable CVs. qLMXDs. aud nuidentified sources with Αα. ο. aud * sviubols respectively in Fieures 2 aud 3.," We identify probable CVs, qLMXBs, and unidentified sources with $\blacktriangle$, $\times$, and $\star$ symbols respectively in Figures 2 and 3."
 The ROSAT N-rav source #77. icdeutifed by Vorbuut (2001) as stay ΠΟ 116157 (V —8.16). is clearly detected 1/22 offaxis as CXOU J161711.6-225520.," The ROSAT X-ray source 7, identified by Verbunt (2001) as star HD 146457 $V$ =8.46), is clearly detected 2 off-axis as CXOU J161714.6-225520."
. Five other serendipitous ROSAT sources also appear in the field of view., Five other serendipitous ROSAT sources also appear in the field of view.
 No otherbright sources are πιαΙου] identified with SIMDBAD objects.wi so we use ΠΟ 116157 to define our astrometry.," No other bright sources are unambiguously identified with SIMBAD objects, so we use HD 146457 to define our astrometry."
 find au offset between the andpuedetect positions. aud the Tycho Refercuce Catalog position. of -0.002s. 17666 )). and add this offset to our nominal astrometric solution to derive a corrected astrometric solution which we use for the rest of this paper.," We find an offset between the and positions, and the Tycho Reference Catalog position, of -0.002s, 66 ), and add this offset to our nominal astrometric solution to derive a corrected astrometric solution which we use for the rest of this paper."
" The uncertainty in the pwdetect-derived position of TID 116157 is An=0r002, Ad=0733. but our absolute astrometric errors ας be slightly increased due to uncertainties in the plate scale aud off-axis poiut-spreacl function modeling."," The uncertainty in the -derived position of HD 146457 is $\Delta\alpha$ 02, $\Delta\delta$ 3, but our absolute astrometric errors may be slightly increased due to uncertainties in the plate scale and off-axis point-spread function modeling."
 Analysis of numerous point sources with optical counterparts by Feigelsou et al. (, Analysis of numerous point sources with optical counterparts by Feigelson et al. (
2002) and AIuno et al. (,2002) and Muno et al. (
2003) sugeest that typical relative astrometric uncertainties at 'off-axis are of order y!n5.,2003) suggest that typical relative astrometric uncertainties at off-axis are of order 5.
 Although classification bv color aud luminosity can identify some N-ray sources with certain populations. optical identification of counterparts is uccessary to be certain of most classifications.," Although classification by color and luminosity can identify some X-ray sources with certain populations, optical identification of counterparts is necessary to be certain of most classifications."
 The full task is bevoud the scope of this work. but we do consider previously identified possible counterparts.," The full task is beyond the scope of this work, but we do consider previously identified possible counterparts."
 Shara and Drisseu (1995) identified two fait blue stars in ALSO that are candidate CVs., Shara and Drissen (1995) identified two faint blue stars in M80 that are candidate CVs.
 They identify one. at 16:17:02.83. -22:58:31.3. (J2000. using the Cade Star Catalog D. as the probable counterpart of Nova 1860 T Sco. based ou a contemporary determination CAwwers 1862) of the nova position with respect to two bright stars and the cluster center.," They identify one, at 16:17:02.83, -22:58:31.3 (J2000, using the Guide Star Catalog I), as the probable counterpart of Nova 1860 T Sco, based on a contemporary determination (Auwers 1862) of the nova position with respect to two bright stars and the cluster center."
 Shara Drisseus preferred extrapolation of the Aiwers (1862) nova position (using offsets from bright stars) is 16:17:02.52.-22:58:32.1.," Shara Drissen's preferred extrapolation of the Auwers (1862) nova position (using offsets from bright stars) is 16:17:02.82,-22:58:32.1."
 These positions are respectively 17LE and 0766 away frou our position for CXI. the brightest candidate CV in our Πμαρσο," These positions are respectively 4 and 6 away from our position for CX1, the brightest candidate CV in our image."
", Considering the uncertainties (often 1-27) in the Cade Star Catalog I. and iu our astrometric solution above. we sugeest that CXI may be the N-ray counterpart of Nova 1860 T Sco."," Considering the uncertainties (often 1-2”) in the Guide Star Catalog I, and in our astrometric solution above, we suggest that CX1 may be the X-ray counterpart of Nova 1860 T Sco."
 IIakala et al. (, Hakala et al. (
1997) provide three argunients against the identifioeation of Nova σου. T Sco with the (confused) ROSAT ALSO N-rav. source: the positional discrepaucy. the rather high X-ray huninosity. and the rather high X-rav to optical flux ratio.,"1997) provide three arguments against the identification of Nova 1860 T Sco with the (confused) ROSAT M80 X-ray source: the positional discrepancy, the rather high X-ray luminosity, and the rather high X-ray to optical flux ratio."
 The positional discrepancy is ercatlv reduced by the resolution of the ROSAT MSO. source iuto nunierous sources by Chandra., The positional discrepancy is greatly reduced by the resolution of the ROSAT M80 source into numerous sources by Chandra.
 The N-vay Imuinosity of CX1 is only 3.1«1072 eres + (0.5-2.5. keV). compared to the total chister Ly (0.5-2.5 keVjJ~SG«1077 eres + for the ROSAT PSPC observation cited by Takala et al. (," The X-ray luminosity of CX1 is only $3.1\times10^{32}$ ergs $^{-1}$ (0.5-2.5 keV), compared to the total cluster $L_X$ (0.5-2.5 $\sim8.6\times10^{32}$ ergs $^{-1}$ for the ROSAT PSPC observation cited by Hakala et al. ("
1995).,1995).
 While lugh. this bhuniuositv is comparable to that of probable CVs in other globular clusters. e.g... LF Tuc (CGIIEO0LTa). NGC 6110 (Pooley et al.," While high, this luminosity is comparable to that of probable CVs in other globular clusters, e.g., 47 Tuc (GHE01a), NGC 6440 (Pooley et al."
 20022). aud. Terzan 5 (Πάικο et al.," 2002a), and Terzan 5 (Heinke et al."
 20035)., 2003b).
 Finally. the(absorbed atio0.5-2.5 keV) Nav to (uucorrected. V-baud) optical fiux (PyfFoy) of CNL. ifit is the counterpart of Nova 1860 T Sco. is [.5.," Finally, the (absorbed 0.5-2.5 keV) X-ray to (uncorrected V-band) optical flux ratio $F_X/F_{\rm Opt}$ ) of CX1, if it is the counterpart of Nova 1860 T Sco, is 4.5."
 While somewhat hieh for field svstenus. this is consistent with the range of Py/Fopr found for CVs in £7 Tuc by Edimouds et al. (," While somewhat high for field systems, this is consistent with the range of $F_X/F_{\rm Opt}$ found for CVs in 47 Tuc by Edmonds et al. ("
2003b). of which the brightest objects iav be maguetie DO Ter systems(GIIEOTa).,"2003b), of which the brightest objects may be magnetic DQ Her systems (GHE01a)."
 We note that a fainter undetected CNT counterpart would increase the ΕνFo ratio. aud that in any case the N-rav aud optical flux measurements are not smimltaucous.," We note that a fainter undetected CX1 counterpart would increase the $F_X/F_{\rm Opt}$ ratio, and that in any case the X-ray and optical flux measurements are not simultaneous."
 Thus we conclude that the association is plausible. but uuprovenu.," Thus we conclude that the association is plausible, but unproven."
 Further analysis is in progress to look for additional AXorav counterpart candidates and improve the aastrometry., Further analysis is in progress to look for additional X-ray counterpart candidates and improve the astrometry.
 For the six brightest sources associated with the cluster (over 50 counts). we extract source (using at least 10 counts per biu) aud (offcluster) background spectra using," For the six brightest sources associated with the cluster (over 50 counts), we extract source (using at least 10 counts per bin) and (off-cluster) background spectra using"
(w= 1).,$\omega=1$ ).
 In the three-dineusional case this property is ound again in the vertical direction (compare Fig. 6..," In the three-dimensional case this property is found again in the vertical direction (compare Fig. \ref{fig:acvsxz},"
 upper paucl. aud WRBAL 22). but now also iu the iorizontal direction. albeit with much reduced amplitude.," upper panel, and KRBM, 2), but now also in the horizontal direction, albeit with much reduced amplitude."
 The oval shape of the pressure extrema is related o the distribution. of # values in space (Fig. 2))., The oval shape of the pressure extrema is related to the distribution of $k-$ values in space (Fig. \ref{fig:vg}) ).
 As seen in Fig., As seen in Fig.
 6 (lower panel) the pressure amplitude iu he horizoutal direction has wave crests that are nearlv equidistant. consistent with the narrow distribution of ko values aud. consequently. vaveleugths. through most of he rangeC» of .e values.," \ref{fig:acvsxz} (lower panel), the pressure amplitude in the horizontal direction has wave crests that are nearly equidistant, consistent with the narrow distribution of $k-$ values and, consequently, wavelengths, through most of the range of $x-$ values."
 By contrast. the distance between oressure extrema in the vertical direction increases with distance from the head of the wave due to the corresponding increase in the phase velocity. from the sound speed at the head of the wave to larger values near the origin (Fig.," By contrast, the distance between pressure extrema in the vertical direction increases with distance from the head of the wave due to the corresponding increase in the phase velocity, from the sound speed at the head of the wave to larger values near the origin (Fig."
 2). (aud to infinitely large values in the asvinptotic limit off.> x).," 2), (and to infinitely large values in the asymptotic limit of $t\rightarrow\infty$ )."
 Since the disturbance is due to a point source. the wave starts out as a spherical wave.," Since the disturbance is due to a point source, the wave starts out as a spherical wave."
 The pulse retains that shape but as can be seen in Fig. 5..," The pulse retains that shape but as can be seen in Fig. \ref{fig:ac},"
 the amplitude of the pulse increases from the vertical direction (both positive aud neeative) towards the horizoutal direction., the amplitude of the pulse increases from the vertical direction (both positive and negative) towards the horizontal direction.
 The three-dimeusional solution allows us to imvoestieate the variatiou of the perturbation amplitude with direction relative to the vertical., The three-dimensional solution allows us to investigate the variation of the perturbation amplitude with direction relative to the vertical.
 We can look to this variation from two differeut perspectives: one possibiitv is that of considering the variation of the amplitude o a naxinuu at a fixed time and the other is that of considering it at a fixed height (see Fie. 7))., We can look to this variation from two different perspectives: one possibility is that of considering the variation of the amplitude of a maximum at a fixed time and the other is that of considering it at a fixed height (see Fig. \ref{fig:cartoon}) ).
 In an astroplivsica context this second case would correspond to looking at a fixed optica depth and therefore to a particular spectroscopic signature of he wave., In an astrophysical context this second case would correspond to looking at a fixed optical depth and therefore to a particular spectroscopic signature of the wave.
 In the first case (fixed. time). he variation of he amplitude has two parts. the intrinsic| variation of he reduced function. aud the variation of the exponcutia Cor. exp(Cz/2/I). that compensates for the! expoueutia dependence of the backeround mass density on height ae converts the reduced variables iuto the plysical variables.," In the first case (fixed time), the variation of the amplitude has two parts, the intrinsic variation of the reduced function, and the variation of the exponential factor, $\exp(z/2H)$, that compensates for the exponential dependence of the background mass density on height and converts the reduced variables into the physical variables."
 Du at a fixed height the distinction between reduced auc jisical variables is relevant., But at a fixed height the distinction between reduced and physical variables is irrelevant.
 We consider first the case of fixed height: Fig., We consider first the case of fixed height: Fig.
 8 shows he variation of the amplitude of the pulse and of the, \ref{fig:aczfix} shows the variation of the amplitude of the pulse and of the
relation.,relation.
 While we have not attempted to fit the full relation. we can infer what sshould be for reasonable values of5.," While we have not attempted to fit the full relation, we can infer what should be for reasonable values of."
. We plot iin Figure 13. under two different assumptions., We plot in Figure \ref{fig:T0} under two different assumptions.
 In the first case. we use the values of mimeasurect in our fiducial simulations 6CX15-6115). where lincreases from zzL4 at 2—5 tor& LGat 2=2.," In the first case, we use the values of measured in our fiducial simulations (A15-G15), where increases from $\gamma \approx 1.4$ at $z = 5$ to $\gamma \approx 1.6$ at $z = 2$."
 The exact values for aare given by the solid lines in the middle panelof Figure and in Table 4.., The exact values for are given by the solid lines in the middle panelof Figure \ref{fig:sim_grid} and in Table \ref{tab:temp}.
 In this case. shown by the filled circles. iis consistent with —SOO00IxIx. at 2 dd. increasing to ~120000KIN at 2=2.8. and then decreasing to ~1L0000 KIN at =2.," In this case, shown by the filled circles, is consistent with $\sim$ K at $z \ge 4.4$ , increasing to $\sim$ K at $z = 2.8$, and then decreasing to $\sim$ K at $= 2$."
 This scenario represents the minimum cease. in which there is no additional heating in the voids that would tend to flatten the temperature-density relation.," This scenario represents the minimum case, in which there is no additional heating in the voids that would tend to flatten the temperature-density relation."
 Even in this case. an increase in bbetween z=4.4 and +=2.8 is detected at the Ta level.," Even in this case, an increase in between $z = 4.4$ and $z = 2.8$ is detected at the $\sigma$ level."
 In the second case. we assume à constant 5=1.3.," In the second case, we assume a constant $\gamma = 1.3$."
 AX value of 5 in this range is suggested. by the numerical simulations of ?.., A value of $\gamma$ in this range is suggested by the numerical simulations of \citet{mcquinn2009a}.
 Lt corresponds to a mild. Uattening of the tempoerature-density relation as expected during. an extended rrelonization process., It corresponds to a mild flattening of the temperature-density relation as expected during an extended reionization process.
 iis largely insensitive to aat 229d. where the optimal overdensity at which we measure iis already close to the mean density.," is largely insensitive to at $z > 4$, where the optimal overdensity at which we measure is already close to the mean density."
 At lower redshifts. however. iis substantially higher [ους=1.3. up to ~17 KIN at ;=2.0.," At lower redshifts, however, is substantially higher for $\gamma = 1.3$, up to $\sim$ K at $z
= 2.0$."
 Following the end of rreionization. iis expected to return to its asvmiptotie value (57 1.5). and πο OUL measurements are consistent with a decline in aat 2«2S even if the temperature-densitv relation is ]attened at higher redshifts.," Following the end of reionization, is expected to return to its asymptotic value $\gamma \sim 1.5$ ), and so our measurements are consistent with a decline in at $z < 2.8$ even if the temperature-density relation is flattened at higher redshifts."
 We emphasize that the rrelevant to our study is the globallvy-averaged: value. even hough there may be significant scatter in the density relation.," We emphasize that the relevant to our study is the globally-averaged value, even though there may be significant scatter in the temperature-density relation."
 Within growing »bubbles. dense regions should ionize first and have time to cool before the voids become Lully ionized (2)...," Within growing bubbles, dense regions should ionize first and have time to cool before the voids become fully ionized \citep{furoh2008b}."
 Racliative ransfer elfects may also create additional complexity in the temperature-density relation (7)..., Radiative transfer effects may also create additional complexity in the temperature-density relation \citep{boltonohfur2009a}.
 Getting the cmperature-censity relation to fatten across the entire LGAL simultaneously. however. would require a brief. and spatially-coordinatec rreionization. which appears not to be favored on theoretical erounds (ο...2)..," Getting the temperature-density relation to flatten across the entire IGM simultaneously, however, would require a brief and spatially-coordinated reionization, which appears not to be favored on theoretical grounds \citep[e.g.,][]{mcquinn2009a}."
 Nevertheless. if the IGM is isothermal then wwould be given by the values of iin Figure 12..," Nevertheless, if the IGM is isothermal then would be given by the values of in Figure \ref{fig:T_delta}."
 Our test of the impact of thermal history in Section ?? sugeests that we may have somewhat underestimated. the increase in from zcd to z~3., Our test of the impact of thermal history in Section \ref{sec:thermal_history} suggests that we may have somewhat underestimated the increase in from $z > 4$ to $z \sim 3$.
 We emphasize. however. that since we are comparing the data to simulations with Lat hermal histories. the position of the peak in {ος} for the ~~1.5 case in Figure 12. is likely to be correct.," We emphasize, however, that since we are comparing the data to simulations with flat thermal histories, the position of the peak in $T_0(z)$ for the $\gamma \sim 1.5$ case in Figure \ref{fig:T_delta} is likely to be correct."
 Future measurements of the spatial coherence of the absorbers using vais of QSO sight lines should allow us to clisentanele the Jeans smoothing from the instantaneous temperature (?).., Future measurements of the spatial coherence of the absorbers using pairs of QSO sight lines should allow us to disentangle the Jeans smoothing from the instantaneous temperature \citep{peeples2010b}.
 For now. the detection of an increase in from zcd to z~3 is robust. since the colder simulation runs are likely to underestimate the true level of Jeans smoothing. while in the the hotter runs idt is ikely to be overestimated.," For now, the detection of an increase in from $z > 4$ to $z \sim 3$ is robust, since the colder simulation runs are likely to underestimate the true level of Jeans smoothing, while in the the hotter runs it is likely to be overestimated."
 Our analysis should. therefore attribute too little of the change in curvature to changes in the instantaneous temperature. which would lead to an underestimate of the change in wwith redshift.," Our analysis should therefore attribute too little of the change in curvature to changes in the instantaneous temperature, which would lead to an underestimate of the change in with redshift."
 We compare our results with selected vvalues from the literature in Figure 14.., We compare our results with selected values from the literature in Figure \ref{fig:T0_with_lit}.
" In the left-hand panel we overplot our values with the results of the wavelet analvsis performed. by ον,", In the left-hand panel we overplot our values with the results of the wavelet analysis performed by \citet{lidz2009}.
 Phe overall agreement is Lair. with the exception of z=3.4. where their 20 lower bound significantly exceeds our inferred value of flor ΞL3.," The overall agreement is fair, with the exception of $z = 3.4$, where their $\sigma$ lower bound significantly exceeds our inferred value of for $\gamma = 1.3$."
 To match their lower limit o£. Wkly. we would require a mildly inverted. temperature-density relation (45 0.9).," To match their lower limit of K, we would require a mildly inverted temperature-density relation $\gamma \sim 0.9$ )."
 While tentative evidence evidence Lor an inverted temperature-density relation has been found in the [ux probability distribution function (?7).. it remains a theoretical challenge to simultaneously achieve this over the entire IGM. even during rreionization (?7)..," While tentative evidence evidence for an inverted temperature-density relation has been found in the flux probability distribution function \citep{becker2007,bolton2008}, it remains a theoretical challenge to simultaneously achieve this over the entire IGM, even during reionization \citep{mcquinn2009a}."
 We are mareinally consistent with the Lidz et al., We are marginally consistent with the Lidz et al.
 lower limit at z=4.2., lower limit at $z = 4.2$.
 Thew note that. their errors in this bin are stronely allected by uncertainties in the mean Dux. and it is possible that a lower zr. such as the one we have used. would bring their numeasurementinto better agreement with ours.," They note that their errors in this bin are strongly affected by uncertainties in the mean flux, and it is possible that a lower $\tau_{\rm eff}$, such as the one we have used, would bring their measurementinto better agreement with ours."
 In. the right-hand. panel of Figure 142. we overplot our values with the results of the Voigt profile analysis by 2.., In the right-hand panel of Figure \ref{fig:T0_with_lit} we overplot our values with the results of the Voigt profile analysis by \citet{schaye2000}. .
 Phe agreement is again fair. although the Schave et al.," The agreement is again fair, although the Schaye et al."
 errors are only 10., errors are only $\sigma$ .
 AX careful measurement of, A careful measurement of
0.5 respectively) for both energy bands to enable a more detailed parameter eri search for the other parameters. and hence to obtain better constraints on these parameters.,"0.5 respectively) for both energy bands to enable a more detailed parameter grid search for the other parameters, and hence to obtain better constraints on these parameters."
 The best-fitting values are listed in Table 3.., The best-fitting values are listed in Table \ref{tab:2lor}.
 Phe Lorentzian peak £requencies are similar to. but not exactly the same as. the corresponding break frequencies. with the Lorentzian frequencies Ling closer to the centre of the bancd-limited power.," The Lorentzian peak frequencies are similar to, but not exactly the same as, the corresponding break frequencies, with the Lorentzian frequencies lying closer to the centre of the band-limited power."
 Figures 7 and S show the best-fitting two-Lorentzian models to the hard and. soft band: respectively., Figures \ref{hardpsd} and \ref{softpsd} show the best-fitting two-Lorentzian models to the hard and soft band respectively.
 In this interpretation. the increase in variability power at high [requencies in the hard. band is entirely due to the greater strength of the high frequeney Lorentzian in this band.," In this interpretation, the increase in variability power at high frequencies in the hard band is entirely due to the greater strength of the high frequency Lorentzian in this band."
 The peak frequencies in both energy. bands are consistent within the confidence limits (see contour plot in Fig.9))., The peak frequencies in both energy bands are consistent within the confidence limits (see contour plot in \ref{2lor_contour}) ).
 Note that. Figs., Note that Figs.
 7 and S show the PSD untolded hrough the distortions produce by sampling ellects., \ref{hardpsd} and \ref{softpsd} show the PSD unfolded through the distortions produced by sampling effects.
 These distortions also depend on the underlying PSD shape so he resultant unfolded PSD depends on the model being itted., These distortions also depend on the underlying PSD shape so the resultant unfolded PSD depends on the model being fitted.
 I£the two-Lorentzian model is the correct underlying SD. the strong power component around LO Ες will lead ο spurious apparent power at lower frequencies in a PSD which has not been unfolded from the distortions. and where he low frequency. part of the PSD has been derived. [rom observations which do not sample the 10. Πε region.," If the two-Lorentzian model is the correct underlying PSD, the strong power component around $10^{-5}$ Hz will lead to spurious apparent power at lower frequencies in a PSD which has not been unfolded from the distortions, and where the low frequency part of the PSD has been derived from observations which do not sample the $10^{-5}$ Hz region."
 This οσοι is known as aliasing (e.g.seeUttleyοἱal.2002.ormoredetails) and here particularly allects the long imescale cata (blue erosses in Figs 5.. 7 and 8)).," This effect is known as aliasing \citep[e.g. see][for more
 details]{uttley02} and here particularly affects the long timescale data (blue crosses in Figs \ref{bendingpsd}, \ref{hardpsd} and \ref{softpsd}) )."
 When we unfold he PSD we remove this spuriouslow frequency power., When we unfold the PSD we remove this spuriouslow frequency power.
 Thus he lowest frequeney. part of the PSDs in Figs., Thus the lowest frequency part of the PSDs in Figs.
 7. and 8 ies below the same part in the bending power law model (lig.5)). where the model did not contain so much power at higher frequencies.," \ref{hardpsd} and \ref{softpsd}
 lies below the same part in the bending power law model \ref{bendingpsd}) ), where the model did not contain so much power at higher frequencies."
 Pherefore the low break frequency. in Fig., Therefore the low break frequency in Fig.
 5 is lower than in Figs., \ref{bendingpsd} is lower than in Figs.
 7 and &.., \ref{hardpsd} and \ref{softpsd}. .
 since the normalisations of low ancl high-frequency, Since the normalisations of low and high-frequency
too much mass become unbound.,too much mass become unbound.
 This is why the lower part of the plot. below fiery.xLO vears is empty.," This is why the lower part of the plot below $t_{merge} \approx
10^8\,$ years is empty."
 With increasing the kick velocity aso the typical velocity of a system inereases anc there ayopear short livecl systems. in tight orbits., With increasing the kick velocity also the typical velocity of a system increases and there appear short lived systems in tight orbits.
 They can now survive a large mass loss when the kick velocity has a favorabe direction., They can now survive a large mass loss when the kick velocity has a favorable direction.
 Thus as the kick velocity is increased. only the tightly bound. systems (with short merger time) can survive the supernova explosions., Thus as the kick velocity is increased only the tightly bound systems (with short merger time) can survive the supernova explosions.
 Another effect of the kick veocitv is that the lone lived systems Wilh fiery much longer than the Llubble time. which were present in the case σι= ükm  disappear.," Another effect of the kick velocity is that the long lived systems with $t_{merge}$ much longer than the Hubble time, which were present in the case $\sigma_v=0\,$ km $^{-1}$ disappear."
 The typical velocity of a svsem increases with the kick velocity., The typical velocity of a system increases with the kick velocity.
" However. the population of the comapet merger binaries is not much alDected wwn the kick velocity becomes arge. e.g. changing the kick velocity distribution width from 0, =O0kms *to200kni | produces a much stronger elfect han ὃνgoinge [rom e,=400 km to SOOkm s.T."," However, the population of the comapct merger binaries is not much affected when the kick velocity becomes large, e.g. changing the kick velocity distribution width from $\sigma_v=0\,$ km $^{-1}$ to $200\,$ km $^{-1}$ produces a much stronger effect than going from $\sigma_v=400\,$ km $^{-1}$ to $800\,$ km $^{-1}$."
 Most of he systems are cisrtipted by such high. velocities. and he surviving ones are only those for which the kick are not SO arge and have a favorable direction.," Most of the systems are disrupted by such high velocities, and the surviving ones are only those for which the kick are not so large and have a favorable direction."
 Another ellect. of increasing the kick velocity is 1 he typical Lifetime o |a svstem becomes smaller., Another effect of increasing the kick velocity is that the typical lifetime of a system becomes smaller.
 When sick velocity is large «olv very tight. and/or highly eccen systems survive. henee the typical lifetime of compact obj xunaries decreases.," When the kick velocity is large only very tight, and/or highly eccentric systems survive, hence the typical lifetime of compact object binaries decreases."
 1 should be noted the typical center of mass velocity. of he compact object. binaries increases roughly linearly withi the kick velocity. while the lifetime decreases approximaοἷν exponentially.," It should be noted the typical center of mass velocity of the compact object binaries increases roughly linearly with the kick velocity, while the lifetime decreases approximately exponentially."
range 0<z«I.,range $0 < z < 1$.
 The major merger rate in the MCGat z=0.09 is RAW=0.035+0.006 Gyr'. while the confidence area is limited by the following curves (Fig. 8)).," The major merger rate in the MCGat $z = 0.09$ is $R_{\rm MM}^{\rm MGC} = 0.035\pm0.006$ $^{-1}$, while the confidence area is limited by the following curves (Fig. \ref{mrfig}) ),"
" The power law-index inferred from the fits ts 7=-—0.540.7,.", The power law-index inferred from the fits is $n = -0.5 \pm 0.7$.
 As in Sect.22.," As in Sect.\ref{ffmmevol},"
" a negative power-law index for Ry, 1mplies that the minor merger rate decreases with redshift.", a negative power-law index for $R_{\rm mm}$ implies that the minor merger rate decreases with redshift.
 Also in this case the value of 2 is compatible with a constant minor merger rate (1= 0). but again its evolution ts different than that of the major merger rate. that increases with redshift (7>0. see below).," Also in this case the value of $n$ is compatible with a constant minor merger rate $n = 0$ ), but again its evolution is different than that of the major merger rate, that increases with redshift $n > 0$, see below)."
 A local reference is needed to better constraint the evolution of Rum., A local reference is needed to better constraint the evolution of $R_{\rm mm}$.
 If we repeat this study with the volumetric merger rate. the confidence area ts limited by In this case the evolution is 7=—0.5+0.7.," If we repeat this study with the volumetric merger rate, the confidence area is limited by In this case the evolution is $n = -0.5 \pm 0.7$."
" Thefit to both major merger rates 1s estimate the volumetric major merger rate (gj> 1/4) finding. as for the merger fraction. that it evolves faster for fainter samples. with a power-law index =2.2 for M5,€-18 galaxies and 2=1.6 for My,€—18.77 galaxies. so our =0.9 follows the trend of decreasing # for brighter galaxies found by ?."," Thefit to both major merger rates is estimate the volumetric major merger rate $\mu \geq 1/4$ ) finding, as for the merger fraction, that it evolves faster for fainter samples, with a power-law index $n = 2.2$ for $M_B^{\rm e} \leq-18$ galaxies and $n = 1.6$ for $M_B^{\rm e} \leq-18.77$ galaxies, so our $n = 0.9$ follows the trend of decreasing $n$ for brighter galaxies found by ."
". On the other hand. the volumetric merger rate of My,€-18 galaxies is a factor of ~5 higher than the one of My,€—20 galaxies."," On the other hand, the volumetric merger rate of $M_B^{\rm e} \leq-18$ galaxies is a factor of $\sim5$ higher than the one of $M_B^{\rm e} \leq-20$ galaxies."
 This is because the number density ας lower for bright galaxies than for the fainter ones., This is because the number density is lower for bright galaxies than for the fainter ones.
 The same trend is observed in mass-selected samples (?)., The same trend is observed in mass-selected samples .
". We can obtain the average number of mergers per galaxy between z» and σι<zs» às where E(zj=Q4+Q,,(1+2) in a flat universe.", We can obtain the average number of mergers per galaxy between $z_2$ and $z_1 < z_2$ as where $E(z) = \sqrt{\Omega_{\Lambda} + \Omega_{m}(1+z)^3}$ in a flat universe.
 The definitions of Λη and Ninn are analogous., The definitions of $N_{\rm MM}$ and $N_{\rm mm}$ are analogous.
" Using results from the previous section. we obtain Nj,=0.73€0.21. with Num=0.37€0.13 and Man=0.36€0.17 from z=| to >=0. indicating thatones."," Using results from the previous section, we obtain $N_{\rm m} = 0.73\pm0.21$, with $N_{\rm MM} = 0.37\pm0.13$ and $N_{\rm mm} = 0.36\pm0.17$ from $z=1$ to $z=0$, indicating that."
 Note that these values and those reported in the following have an additional factor of two uncertainty due to the merger timescales derived from simulations (Sect. ??))., Note that these values and those reported in the following have an additional factor of two uncertainty due to the merger timescales derived from simulations (Sect. \ref{mrpairfull}) ).
" In their work. find that almost all the evolution in the stellar mass function since z-| is consequence of the observed star formation2).. and estimate Nj,~0.7 mergers since z~] per log(M,/M..)~10.6 galaxy. similar to the average mass of our M;x-20 galaxies. are needed to explain the remaining evolution."," In their work, find that almost all the evolution in the stellar mass function since $z \sim 1$ is consequence of the observed star formation, and estimate $N_{\rm m} \sim 0.7$ mergers since $z \sim 1$ per $\log\,(M_{\star}/M_{\odot}) \sim 10.6$ galaxy, similar to the average mass of our $M_B^{\rm e} \leq -20$ galaxies, are needed to explain the remaining evolution."
 Their result agrees with our direct estimation. but they infer Ny«0.2.," Their result agrees with our direct estimation, but they infer $N_{\rm MM} < 0.2$."
 This value is half of ours. pointing out that close pair studies are needed to understand accurately the role of major/minor mergers in galaxy evolution.," This value is half of ours, pointing out that close pair studies are needed to understand accurately the role of major/minor mergers in galaxy evolution."
 In addition to the mean number of mergers per galaxy. we have estimated the mass accreted by bright galaxies since | due to major and minor mergers.," In addition to the mean number of mergers per galaxy, we have estimated the mass accreted by bright galaxies since $z = 1$ due to major and minor mergers."
 Forthis. we take ys as a proxy of the mass ratio between the galaxies in the pair.," Forthis, we take $\mu$ as a proxy of the mass ratio between the galaxies in the pair."
" We can determine the mean merger ratio of major (µη). and minor mergers (115,5) às For jm=1/4 and μμ=1/10 we obtain fying=0.47 and fmm=0.15. values that depend slightly on s: the mean merger ratios change less than 10% 1n the range probed by our results. s€[—1.25.20.58]."," We can determine the mean merger ratio of major $\overline{\mu_{MM}}$ ), and minor mergers $\overline{\mu_{mm}}$ ) as For $\mu_{\rm MM} = 1/4$ and $\mu_{\rm mm} = 1/10$ we obtain $\overline{\mu_{\rm MM}} = 0.47$ and $\overline{\mu_{\rm mm}} = 0.15$, values that depend slightly on $s$: the mean merger ratios change less than $10$ in the range probed by our results, $s \in [-1.25,-0.58]$."
" We assume these values of Hom and di, hereafter.", We assume these values of $\overline{\mu_{\rm MM}}$ and $\overline{\mu_{\rm mm}}$ hereafter.
 Weighting the number of mergers with its corresponding merger ratio. we infer that8%.," Weighting the number of mergers with its corresponding merger ratio, we infer that."
 We further infer that the relative contribution of major and minor mergers to this mass assembly is and25%.. respectively.," We further infer that the relative contribution of major and minor mergers to this mass assembly is and, respectively."
 Because the factor of two uncertainty in the merger timescales affects in the same way major and minor mergers. this relative contribution is a robust result.," Because the factor of two uncertainty in the merger timescales affects in the same way major and minor mergers, this relative contribution is a robust result."
" In their cosmological models. predict that the relative contribution of major and minor mergers in the spheroids assembly of log(M,/M.)~10.6 galaxies ts ~80%/20%.. in good agreement with our observational result."," In their cosmological models, predict that the relative contribution of major and minor mergers in the spheroids assembly of $\log\,(M_{\star}/M_{\odot}) \sim 10.6$ galaxies is $\sim80\%$, in good agreement with our observational result."
 Therefore. we have demonstrated that minor mergers do contribute to the mass assembly of bright galaxies. at a level corresponding to about a third of the major mergers contribution.," Therefore, we have demonstrated that minor mergers do contribute to the mass assembly of bright galaxies, at a level corresponding to about a third of the major mergers contribution."
 Because the merger properties of red and blue galaxies are very different. we estimate here the role of minor and major mergers in the evolution of red galaxies since z~1.," Because the merger properties of red and blue galaxies are very different, we estimate here the role of minor and major mergers in the evolution of red galaxies since $z \sim 1$."
 We assume a constant major and minor merger rate for red galaxies from 5= Oto >=|. as found in Section ??..," We assume a constant major and minor merger rate for red galaxies from $z = 0$ to $z = 1$, as found in Section \ref{mrpair}."
 Applying Eq. (22)), Applying Eq. \ref{numm}) )
" to RS and RS. we obtain that 0.3. with Ns,= and NS=0.5€ 02."," to $R_{\rm mm}^{\rm red}$ and $R_{\rm MM}^{\rm red}$ , we obtain that , with $N_{\rm MM}^{\rm red} = 0.7\pm0.2$ and $N_{\rm mm}^{\rm red} = 0.5\pm0.2$ ."
 These values are higher than those from the globalpopulation. reflecting the higher mergerrate of red galaxies.," These values are higher than those from the globalpopulation, reflecting the higher mergerrate of red galaxies."
" We find that red galaxies of log(M,/M.)~10.8 have undergone ~1.2 merger events since z~ |. but it is important to quantify the impact of mergers in the mass assembly of these galaxies."," We find that red galaxies of $\log\, (M_{\star}/M_{\odot}) \sim 10.8$ have undergone $\sim 1.2$ merger events since $z \sim 1$ , but it is important to quantify the impact of mergers in the mass assembly of these galaxies."
 Weighting the number of mergers with their, Weighting the number of mergers with their
The second fact arises because the derivatives of the basis fuunctious are known analytically. aud so by Eq.(,"The second fact arises because the derivatives of the basis functions are known analytically, and so by Eq.,"
3). and similarly for higher derivatives., and similarly for higher derivatives.
" Iu order to compute the spectral cocficicuts a). we use where one requires The points c; are calledpoints. aud are chosen as the abscissas of the Gaussian quadrature associated with the basis set δε,"," In order to compute the spectral coefficients $\tilde u_k$ we use where one requires The points $x_i$ are called, and are chosen as the abscissas of the Gaussian quadrature associated with the basis set $\Phi_k$."
" This choice of collocation points cau be motivated by cousidering fInπιj|°dv,", This choice of collocation points can be motivated by considering $\int\left[ ({\cal N} u^{(N)})(x)\right]^2dx$.
 Evaluating this iuteeral with Gaussian quadrature. we fud by virtue of Eq.," Evaluating this integral with Gaussian quadrature, we find by virtue of Eq."
 where ay are the weielits of the quadrature., where $w_i$ are the weights of the quadrature.
 We see that A0?) quust be small throughout D aud thus the fiction 40? satisfying Eqs.," We see that ${\cal
 N}u^{(N)}$ must be small throughout $\cal D$ and thus the function $u^{(N)}$ satisfying Eqs."
 umst be close to the true solution., must be close to the true solution.
 More rigorous treatineuts of the pseudospectral collocation method can be found iu the literature|?.?.?]..," More rigorous treatments of the pseudospectral collocation method can be found in the \cite{Gottlieb-Orszag:1977,
 Canuto-Hussaini, Boyd:2001}."
 Chebyshev polynomials are widely used as basis fuuctious for spectral methods., Chebyshev polynomials are widely used as basis functions for spectral methods.
" ""They satisty the convenient analytical properties of “classical” orthogonal polwnomials.", They satisfy the convenient analytical properties of “classical” orthogonal polynomials.
 Their defining differential equation is aszeguler Sturi-Liouville problem. aud so Chebyshev expansions converge exponentially for smooth fictions 0 of the boundary couditious satisfied by « [?. ?]..," Their defining differential equation is a Sturm-Liouville problem, and so Chebyshev expansions converge exponentially for smooth functions $u$ of the boundary conditions satisfied by $u$ \cite{Gottlieb-Orszag:1977, Boyd:2001}. ."
 Chebyshev polynomials are defined. by They are defined on the interval XC|1.1| oulv: usually one needs to map the XC|1.1] to the plivsical coordinate of the problem. wc[ab].," Chebyshev polynomials are defined by They are defined on the interval $X\in [-1,1]$ only; usually one needs to map the $X\in[-1,1]$ to the physical coordinate of the problem, $x\in [a,b]$."
 We use the convention that the variable VY varies over the interval |1.1]. whereas wo is defined over arbitrary intervals.," We use the convention that the variable $X$ varies over the interval $[-1,1]$, whereas $x$ is defined over arbitrary intervals."
 We will describe our approach to mappings below in the implementation section., We will describe our approach to mappings below in the implementation section.
 For an expausion up to order JN (10. having a total of NU|1 basis functions) theassociated collocation poiuts are Define the real space values, For an expansion up to order $N$ (i.e. having a total of $N+1$ basis functions) theassociated collocation points are Define the real space values
with accurate photometric redshifts. aud may be subject to iore subtle uncertainties iu the foreground mass distribution.,"with accurate photometric redshifts, and may be subject to more subtle uncertainties in the foreground mass distribution."
" Furthermore. suce the geometric term. iu the lensing equation depends ou source aud lens redshitts separately, it is not munuediatelv clear how to stack the results from large samples of lenses in a simple wav."," Furthermore, since the geometric term in the lensing equation depends on source and lens redshifts separately, it is not immediately clear how to stack the results from large samples of lenses in a simple way."
 The analysis is thus less intuitive. making it larder to spot nuauticipated systematics in the results.," The analysis is thus less intuitive, making it harder to spot unanticipated systematics in the results."
 The COSMOS survey provides au interesting data set with which to explore ecometric lensing tests., The COSMOS survey provides an interesting data set with which to explore geometric lensing tests.
 COSMOS has an unusual combination of a ligh density of sources With accurate lensing shape measurements. and accurate ploto-zs for a laree fraction of these sources.," COSMOS has an unusual combination of a high density of sources with accurate lensing shape measurements, and accurate photo-zs for a large fraction of these sources."
 Unttortunately the COSALOS feld has πο really massive clusters in it: the largest cluster has an estimated mass of 2.5«1014AZ... (Finoguenovctal.2007). 10 times less than the largest stroug-leusimg clusters. and is at a redshift of +=0.73 (Carzzoctal.2007) where leusine is past the peak in seusitivitv. eiven the source redshift distribution.," Unfortunately the COSMOS field has no really massive clusters in it; the largest cluster has an estimated mass of $2.5\times 10^{14} M_\odot$ \citep{Finoguenov:2007}, 10 times less than the largest strong-lensing clusters, and is at a redshift of $z = 0.73$ \citep{Guzzo07} where lensing is past the peak in sensitivity, given the source redshift distribution."
 The lensing signal in the COSMOS field conies justeack from many low-significauce. eroup-sized haloes (Finoeucnoyctal.2007:Leauthaudet2010).," The lensing signal in the COSMOS field comes instead from many low-significance, group-sized haloes \citep{Finoguenov:2007,Leauthaud:2010}."
. Collectively these systems could still produce a large lensing signal to test ecometiry. however. provided the signal could be stacked.," Collectively these systems could still produce a large lensing signal to test geometry, however, provided the signal could be stacked."
 Tere we propose a simple method for stacking the sienal from τρίο leuses iuto a sinele measure of ecolctry. in effect the relation between comoving or aneular diameter distance and redshift.," Here we propose a simple method for stacking the signal from multiple lenses into a single measure of geometry, in effect the relation between comoving or angular diameter distance and redshift."
 Applving this new xtacked shear ratio test” to X-ray selected. eroups in the COSAIOS field. we obtain a clear detection of the geometric signal and derive sieuificant constraints ou the dark enerewv deusitv parameter Oy.," Applying this new `stacked shear ratio test' to X-ray selected groups in the COSMOS field, we obtain a clear detection of the geometric signal and derive significant constraints on the dark energy density parameter $\Omega_X$."
 While the COSAMIOS field is probably too small to overcome sample variance limitations. the magnitude of our statistical errors ilustrates the future promise of this technique.," While the COSMOS field is probably too small to overcome sample variance limitations, the magnitude of our statistical errors illustrates the future promise of this technique."
 The outline of paper is as follows: iu section 2 we present the basic data. including the sample of leasing eroups. and the source redshifts and shape measurements of the COSMOS lensing catalogue.," The outline of paper is as follows: in section 2 we present the basic data, including the sample of lensing groups, and the source redshifts and shape measurements of the COSMOS lensing catalogue."
 Iu section 3 we introduce the stacking technique and discuss optimal weighting for this technique., In section 3 we introduce the stacking technique and discuss optimal weighting for this technique.
 In section L| we use the stacked shear ratio test to derive parameter constraints ou the density of dark euergv «y and the equation-of-state parameter d. and discuss possible svstematics for this test.," In section 4, we use the stacked shear ratio test to derive parameter constraints on the density of dark energy $\Omega_X$ and the equation-of-state parameter $w$, and discuss possible systematics for this test."
 In section 5 we stunmarize our results aud discuss future prospects for applving the stacked shear ratio test to other weak lensing surveys., In section 5 we summarize our results and discuss future prospects for applying the stacked shear ratio test to other weak lensing surveys.
" Throughout the paper we refer our results to the WAIAP 7-vear mean parameter values derived in Larsonetal.(2011). takine a flat cosinologv with O4=0.73. Qa,=0.27. IH=TOhey kanss1L + (AVALAPT hereafter) as our bascline."," Throughout the paper we refer our results to the WMAP 7-year mean parameter values derived in \citet{WMAP7}, taking a flat cosmology with $\Omega_\Lambda = 0.73$, $\Omega_M = 0.27$, $H_0 = 70\,h_{70}$ $^{-1}$ $^{-1}$ (WMAP7 hereafter) as our baseline."
 The COSMOS survey (Scovillectal.2007a) brings together panchromatic nuagiug from X-rawv to radio wavelengths. including the lareest contiguous area observed with the Hubble Space Telescope. anc deep optical spectroscopic observations.," The COSMOS survey \citep{Scoville:2007a} brings together panchromatic imaging from X-ray to radio wavelengths, including the largest contiguous area observed with the Hubble Space Telescope, and deep optical spectroscopic observations."
 The feld covers au area of 1.61 square degrees centered at 10:00:28.6. 102:12:21.0 (32000) and contains identified groups. clusters aud larger structures spauniug a wide range in redshift (Scovilleetal.2007))..," The field covers an area of 1.64 square degrees centered at 10:00:28.6, +02:12:21.0 (J2000) and contains identified groups, clusters and larger structures spanning a wide range in redshift \citep{Scoville:2007c}. ."
 We consider the eravitational lensing signal behind a saluple of galaxy groups selected originally via their X-rav Cluission (Finogucnoyetal.2007) and updated using a combined mosaic of umaeing fromNewton (1.5Ms.Hasiueeretal.2007:Cappelluti2009). aud the observatories (1.5Ms.Elvisctal.2009).," We consider the gravitational lensing signal behind a sample of galaxy groups selected originally via their X-ray emission \citep{Finoguenov:2007} and updated using a combined mosaic of imaging from \citep[1.5 Ms,][]{Hasinger:2007,Cappelluti:2009} and the observatories \citep[1.8 Ms,][]{Elvis:2009}."
". Groups are detected from the combined X-ray mosaic using a wavelet filter, which can result iu ceutering uncertainties of up to 32""."," Groups are detected from the combined X-ray mosaic using a wavelet filter, which can result in centering uncertainties of up to $\arcsec$."
 The distribution of galaxies along the line of sight to each A-ray detection is searched for a red sequence overdcusity to determine the eroup redshift. with spectroscopic redshifts used for subsequent refinemceut (Finoguenovetal.2007).," The distribution of galaxies along the line of sight to each X-ray detection is searched for a red sequence overdensity to determine the group redshift, with spectroscopic redshifts used for subsequent refinement \citep{Finoguenov:2007}."
. Ctiroup πιοσος are selected. based ou their photometric redshift aud proxiuitv to the X-rav centroid. using au algorithm tested extensively on mock. catalogs anc spectroscopic subsamples (Georgeetal.2011).," Group members are selected based on their photometric redshift and proximity to the X-ray centroid, using an algorithm tested extensively on mock catalogs and spectroscopic subsamples \citep{George:2011}."
. Stellar 1nasses of the member galaxies are determined from uitiwaveleneth data (see Leauthaudetal.2001. for details)., Stellar masses of the member galaxies are determined from multiwavelength data (see \citealt{Leauthaud:2011} for details).
 From an initial list of members. eroup ceuters are then redefined around the most massive eroup galaxy within the NEW. scale radius of the N-rayv centroid 41). which optimizes the weak leusiug signal at small radii (Ceoree et al.," From an initial list of members, group centers are then redefined around the most massive group galaxy within the NFW scale radius of the X-ray centroid $_{\rm scale}$ ), which optimizes the weak lensing signal at small radii (George et al."
 in prep.)., in prep.).
 For the majority of our groups this gives ceuters which agree with the X-ray. centroid: a munority (approximately 20%)) of eroups show significant offsets between the most massive galaxy aud the N-ray ceutroid., For the majority of our groups this gives centers which agree with the X-ray centroid; a minority (approximately ) of groups show significant offsets between the most massive galaxy and the X-ray centroid.
 These offsets could be due to observational problems (stich as low signal-to-noise in the X-ray or optical data). or they müght indicate unrolaxed. low-conceutration eroups with poorly defined plysical centers such as recent iereers.," These offsets could be due to observational problems (such as low signal-to-noise in the X-ray or optical data), or they might indicate unrelaxed, low-concentration groups with poorly defined physical centers, such as recent mergers."
 We will consider below both the full set of groups and a restricted! set which excludes the systelus with significant offsets., We will consider below both the full set of groups and a `restricted' set which excludes the systems with significant offsets.
 The centering algorithiu will be discussed further in a forthcoming paper (Ceoree et al, The centering algorithm will be discussed further in a forthcoming paper (George et al.
 in prep.)., in prep.).
 The full X-ray eroup sample. together with derived properties. will be mace available through the NASA/TPAC Infrared Science Archive IRSA) (see Georgeetal.2011 for details).," The full X-ray group sample, together with derived properties, will be made available through the NASA/IPAC Infrared Science Archive (IRSA) (see \citealt{George:2011} for details)."
 We restrict the leus sample to groups at i<1 to iure the reliability of X-ray detections and optica associations. as well as good photometric redshifts for oechtifving mcmbers aud centers.," We restrict the lens sample to groups at $z < 1$ to ensure the reliability of X-ray detections and optical associations, as well as good photometric redshifts for identifying members and centers."
 We further cut out of je sample poor groups. groups with centroids affect wolnaskine.aud possible mergers (this corresponds ccto aking only eroups with = 1as defiue« iu Ceoreeetab 2011)).," We further cut out of the sample poor groups, groups with centroids affected by masking,and possible mergers (this corresponds to taking only groups with = 1as defined in \citealt{George:2011}) )."
 Our final sample consists of 129 systems (105 in the restricted set) spoanniug a rest-πεις 0.12.1 keV luminosity range between 101 ane 10Heyre/s. with estimated virial masses of 0.8&Lot? 2«1021 MAL... virial radii of liz: Mpc. auc xojected pataueular sizes of 1 6.," Our final sample consists of 129 systems (105 in the restricted set) spanning a rest-frame 0.1–2.4 keV luminosity range between $10^{41}$ and $10^{44}$ erg/s, with estimated virial masses of $0.8\times10^{13}$ – $2\times10^{14}\, h^{-1}_{70}$ $_\odot$, virial radii of $h^{-1}_{70}$ Mpc, and projected angular sizes of $1\arcmin$ $6\arcmin$."
 Fig., Fig.
 1. shows the mass. physical size aud augular size for the eroups in the sample (uote units have been couverted from the value fy=72 aus + tb used in the catalog to Ly=70 lan | +).," \ref{fig:xgroups} shows the mass, physical size and angular size for the groups in the sample (note units have been converted from the value $H_0 = 72$ km $^{-1}$ $^{-1}$ used in the catalog to $H_0 = 70$ km $^{-1}$ $^{-1}$ )."
" The virial radius is taken to be Royy,. the radius witlin which the mean ceusity is equal to 200 times the critical density p.(:) at the redshift of thegroup. and the virial mass is taken to be Mojo. the mass euclosed"," The virial radius is taken to be $R_{200c}$ , the radius within which the mean density is equal to 200 times the critical density $\rho_c(z)$ at the redshift of thegroup, and the virial mass is taken to be $M_{200c}$ the mass enclosed"
"If the profiles are identical (Αι=...Anjo1= on), we have S/N «WN.","If the profiles are identical $A_{1} = \ldots = A_{\rm N};
\sigma_{1} = \ldots = \sigma_{\rm N}$ ), we have S/N $\propto
\sqrt{N}$."
" Practically, however, effects like intrinsic flux variations, scintillation and system temperature variations cause the S/Ns of profiles with identical integration times to differ."," Practically, however, effects like intrinsic flux variations, scintillation and system temperature variations cause the S/Ns of profiles with identical integration times to differ."
 This causes deviations from the scaling rule in the processing of real data., This causes deviations from the scaling rule in the processing of real data.
" Therefore, we define the effective number of pulses as: where n is the number of pulses within an individual integration, S/N is calculated from Eq. (2)),"," Therefore, we define the effective number of pulses as: where $n$ is the number of pulses within an individual integration, S/N is calculated from Eq. \ref{eq:SNR_int}) ),"
 and S/Nmean is the averaged S/N for all integrations.," and $\rm S/N_{\rm
mean}$ is the averaged S/N for all integrations."
" Effectively, Νοις is a normalised pulse number, which corrects for the varying S/N of individual pulsar pulses."," Effectively, $N_{\rm efc}$ is a normalised pulse number, which corrects for the varying S/N of individual pulsar pulses."
" Consequently, the measured S/N of averaged profiles should scale linearly with the calculated vNefc, regardless of the brightness variations of the pulses involved."," Consequently, the measured S/N of averaged profiles should scale linearly with the calculated $\sqrt{N_{\rm efc}}$, regardless of the brightness variations of the pulses involved."
 The main goals of template matching are to calculate the equivalent TOA of the average profile with respect to a fiducial phase provided by the template profile; and to evaluate the corresponding uncertainty caused by the additive noise of the profile., The main goals of template matching are to calculate the equivalent TOA of the average profile with respect to a fiducial phase provided by the template profile; and to evaluate the corresponding uncertainty caused by the additive noise of the profile.
" It can be carried out both in the time-domain and (more commonly) in the frequency-domain, by cross-correlating the target profile with a high S/N standard that was either obtained at a different observing time or created analytically (?).."," It can be carried out both in the time-domain and (more commonly) in the frequency-domain, by cross-correlating the target profile with a high S/N standard that was either obtained at a different observing time or created analytically \citep{tay92}."
" Theoretically, the uncertainty of TOA measurements, induced by the white noise of the profile should be in the form of (?):: Here S/N; is the equivalent single pulse S/N and is the pulse sharpness parameter, with U(t) the normalised pulse waveform and is the noise de-correlation time scale where n(t) is the noise function."," Theoretically, the uncertainty of TOA measurements, induced by the white noise of the profile should be in the form of \citep{dr83}: Here $\rm S/N_{1}$ is the equivalent single pulse S/N and is the pulse sharpness parameter, with $U(t)$ the peak-normalised pulse waveform and is the noise de-correlation time scale where $n(t)$ is the noise function."
 It can be seen that the sharpness parameter basically relates the intrinsic profile shape to the precision of the TOA., It can be seen that the sharpness parameter basically relates the intrinsic profile shape to the precision of the TOA.
" The template matching technique produces the same result as predicted in Eq. (4)),"," The template matching technique produces the same result as predicted in Eq. \ref{eq:SNRSharp}) ),"
" but only if there is no profile shape difference between the template and the observation, which is an ideal assumption in practice."," but only if there is no profile shape difference between the template and the observation, which is an ideal assumption in practice."
" If profile distortion (as can be introduced by any of the effects discussed in Section ??)) does occur, the calculated uncertainty does not turn out to be as good as expected for high-S/N profiles."," If profile distortion (as can be introduced by any of the effects discussed in Section \ref{sec:Issues}) ) does occur, the calculated uncertainty does not turn out to be as good as expected for high-S/N profiles."
 Fig., Fig.
 1 shows a simulated example of this case., \ref{tmpl matching simulation} shows a simulated example of this case.
 Here a template is created as a Gaussian and fake observation profiles are formed by adding white noise to the template after being broadened or narrowed by 0.596., Here a template is created as a Gaussian and fake observation profiles are formed by adding white noise to the template after being broadened or narrowed by $0.5\%$.
 It is clear that the calculated TOA errors begin to deviate from the predicted uncertainty once the S/N rises to values beyond 1000., It is clear that the calculated TOA errors begin to deviate from the predicted uncertainty once the S/N rises to values beyond 1000.
" Note that the deviations are seen to be roughly equal for both the broadened and narrowed cases, which indicates that it is not the absolute pulse shape of the observation determining the reliability of its TOA uncertainty, but the relative difference between the observation and the noise-free template, stressing the importance of reliable template profiles."," Note that the deviations are seen to be roughly equal for both the broadened and narrowed cases, which indicates that it is not the absolute pulse shape of the observation determining the reliability of its TOA uncertainty, but the relative difference between the observation and the noise-free template, stressing the importance of reliable template profiles."
 The different results in the S/N—o graphs presented by ? and ? already suggested this to be the case., The different results in the $-\sigma$ graphs presented by \cite{vbb+10} and \cite{hbb+09} already suggested this to be the case.
" As their data show, even though the integrated profile for PSR J0437—4715 is supposed to be intrinsically stable at the folding time scale, this phenomenon still appears at high S/N. In Fig. 2,,"," As their data show, even though the integrated profile for PSR $-$ 4715 is supposed to be intrinsically stable at the folding time scale, this phenomenon still appears at high S/N. In Fig. \ref{timing},"
 we summarise the propagation path of pulsar timing data and identify for each stage the phenomena that can affect TOAs and their precision., we summarise the propagation path of pulsar timing data and identify for each stage the phenomena that can affect TOAs and their precision.
 Some of these are instrumental and correctable while others induce a natural limit to timing precision., Some of these are instrumental and correctable while others induce a natural limit to timing precision.
 Detailed discussions of our current knowledge about these issues together with more in-depth investigations based on our data are presented below., Detailed discussions of our current knowledge about these issues together with more in-depth investigations based on our data are presented below.
FeinsteinD.. (1995)- suggests that there are 143. known or suspected open star clusters probably related to the Carina spiral. feature.,Feinstein (1995) suggests that there are 14 known or suspected open star clusters probably related to the Carina spiral feature.
⋅ Most of⋅ them are actually. very well Nonetheless.. some remain. very poorly studied.. and our knowledge often.⋅ does not extend. beyond. the simple. identification.," Most of them are actually very well Nonetheless some remain very poorly studied, and our knowledge often does not extend beyond the simple identification."
.- As a consequence the real nature of⋅ some of these star clusterings. and their. belonging: to the Carinaev. complex| are not well mPhe region. of⋅ 5 Carinaeos on the other hand. ds. MNsince long time recognized as an ideal laboratory to study the formation. of star clusters by obtaining2. precise. photometry and age estimates (Massey and Johnson Llaving. this uuin mind.. we have undertaken a photometric. survey aimed at obtaining homogeneous high quality CCD data for⋅ all the known star clusterings. in. this. We already reported about NGC 3324 and. Locen 165 (Carraro ct al 2001). showing that Loden 165 does probably not belong to the Carina ∐⋖⋅↓⋅∢⊾∖∖⋎∢⊾↓⋅⋖⋅↓≻∪↓⋅⇂∪⊔↥⇂⊔⋅∢⋅⋖⋅↓≻∪∪↓⋅⇂∙∖⇁≱∖↿⋯⇂↓⋖⋅∠⇂∪∣⋡≯⇃⋖⋅≼∙↿≱∖∶ . . Bochum; 9. ;Bochum 10 and Bochum; 11. identified.⋠⋅ in. the seventies bv Alolfat Voet (1975).," As a consequence the real nature of some of these star clusterings and their belonging to the Carinae complex are not well The region of $\eta$ Carinae on the other hand is since long time recognized as an ideal laboratory to study the formation of star clusters by obtaining precise photometry and age estimates (Massey and Johnson Having this in mind, we have undertaken a photometric survey aimed at obtaining homogeneous high quality CCD data for all the known star clusterings in this We already reported about NGC 3324 and Loden 165 (Carraro et al 2001), showing that Loden 165 does probably not belong to the Carina Here we report on three poorly studied objects: Bochum 9, Bochum 10 and Bochum 11, identified in the seventies by Moffat Vogt (1975)."
 Only photoclectric shotometry is. available. for. these objects:. in: particular. Dochum 9 deserves special. attention. since» ib osis not clear whether it D.is a cluster or not., Only photoelectric photometry is available for these objects; in particular Bochum 9 deserves special attention since it is not clear whether it is a cluster or not.
 .The other two clusters are voung objects. with some evidence of a pre AIS population (Vitzeerald. Mehta LOST).," The other two clusters are young objects, with some evidence of a pre MS population (Fitzgerald Mehta 1987)."
my opTheir basic. parameters are eiven in Table EPhe plan of the paper is. as follows., Their basic parameters are given in Table The plan of the paper is as follows.
. In SectionEN 2 we describe. the data acquisitionZu and reduction.. while ⊀↴⊀Sections 3∙ to 5- are dedicated. to Bochum; 9. ;Bochum 10 and ;Bochum 11. respectively.," In Section 2 we describe the data acquisition and reduction, while Sections 3 to 5 are dedicated to Bochum 9, Bochum 10 and Bochum 11, respectively."
 Finally Section 6 summarizes our results. and in. the Appendix. we provide. some acdcditional.. details. on the data reduction. and photometric: errors.," Finally Section 6 summarizes our results, and in the Appendix we provide some additional details on the data reduction and photometric errors."
 Observations were conducted. at. La Silla on April 13-16.," Observations were conducted at La Silla on April 13-16,"
"The scattering cross section can be given by the single scattering albedo for small wavelengths: wy=sy""eC wy).",The scattering cross section can be given by the single scattering albedo for small wavelengths: $\omega_0=\kappa_0^{\rm sca}/(\kappa_0^{\rm abs}+\kappa_0^{\rm sca})$ .
 In this paper. we consider three cases of wo=0 (no scattering). 0.9. or 0.99.," In this paper, we consider three cases of $\omega_0=0$ (no scattering), $0.9$, or $0.99$."
 The values of wy for the last. two cases may be extreme but such a large albedo is expected for lev grains in some wavelengths., The values of $\omega_0$ for the last two cases may be extreme but such a large albedo is expected for icy grains in some wavelengths.
 Figure 1 shows Planck means of the absorption cross section and the scattering albedo assumed in this paper as a function ofthe temperature input into the Planck function., Figure 1 shows Planck means of the absorption cross section and the scattering albedo assumed in this paper as a function of the temperature input into the Planck function.
 In the panels. we show seven cases of erain size from 0.01 tto Lem.," In the panels, we show seven cases of grain size from 0.01 to 1 cm."
 We note that the absorption cross section and the scattering albedo become independent. of the temperature. ij. Terex”. when the temperature exceeds a critical one which depends on the grain size. corresponds (o the critical wavelength: Ac. and. is roughly expressed as Z5—10*(1june) Ix. In this paper. we do not consider the size distribution of the dust. grains.," We note that the absorption cross section and the scattering albedo become independent of the temperature, i.e. “grey”, when the temperature exceeds a critical one which depends on the grain size, corresponds to the critical wavelength $\lambda_{\rm c}$, and is roughly expressed as $T_{\rm c}\sim10^3(1~\micron/a)$ K. In this paper, we do not consider the size distribution of the dust grains."
" Thus. the ""grain size” of this paper means a typical grain size averaged. over a size clistribution function with a weight."," Thus, the “grain size” of this paper means a typical grain size averaged over a size distribution function with a weight."
 We here show the results of the annulus with the ractius of 1 AU obtained from our numerical radiation transfer in Figures 2 and 3., We here show the results of the annulus with the radius of 1 AU obtained from our numerical radiation transfer in Figures 2 and 3.
 The results with other radii have been confirmed. to be the same qualitatively., The results with other radii have been confirmed to be the same qualitatively.
 Phe eas column density is assumed to be 1PCR/AU)! g 7. where BR is the radial distance from the central star.," The gas column density is assumed to be $10^3(R/{\rm AU})^{-1}$ g $^{-2}$, where $R$ is the radial distance from the central star."
" The properties of the central star assumed. are the cllective temperature 7,=3.000 Ix. the radius //,=2.0 H.. and the mass Ad,=0.5 M.."," The properties of the central star assumed are the effective temperature $T_*=3,000$ K, the radius $R_*=2.0$ $R_\odot$, and the mass $M_*=0.5$ $M_\odot$."
" Other assumed. parameters are as follows: the grazing angle a=0.05. the visible fraction. of the stellar photosphere at the annuli. νε=0.5. and the mean molecular weight fa,=7/3."," Other assumed parameters are as follows: the grazing angle $\alpha=0.05$, the visible fraction of the stellar photosphere at the annuli $f_{\rm vis}=0.5$, and the mean molecular weight $\mu_{\rm m}=7/3$."
 Figure 2 shows the vertical temperature structures of annuli with | AU radius with various grain sizes., Figure 2 shows the vertical temperature structures of annuli with 1 AU radius with various grain sizes.
 We take a coordinate of the Planck mean extinction optical depth with the stellar effective temperature as the horizontal axis., We take a coordinate of the Planck mean extinction optical depth with the stellar effective temperature as the horizontal axis.
 Note that the maximum optical depth in cach curve occurs the equatorial plane., Note that the maximum optical depth in each curve occurs the equatorial plane.
 Phe grain sizes assumed are shown in each panel., The grain sizes assumed are shown in each panel.
 The solid. dotted. and dashed: curves are the cases of no scattering (Le. wy=0). ay=0.9. and ay=0.99. respectively.," The solid, dotted, and dashed curves are the cases of no scattering (i.e. $\omega_0=0$ ), $\omega_0=0.9$, and $\omega_0=0.99$, respectively."
 For no scattering cases (solid curves). the so-called two-laver structure proposed by C97 is confirmed.," For no scattering cases (solid curves), the so-called two-layer structure proposed by CG97 is confirmed."
 The dust temperature near the surface is enhanced due to the direct stellar radiation: “super-heatecl Laver”., The dust temperature near the surface is enhanced due to the direct stellar radiation: “super-heated layer”.
 The thickness of the super-heated Laver is well expressed. by the Planck mean extinction optical depth as τς~a=0.05 (erazing angle).," The thickness of the super-heated layer is well expressed by the Planck mean extinction optical depth as $\tau_{\rm P,*}^{\rm ext}\simeq\alpha=0.05$ (grazing angle)."
 The tomperature rapidly decreases if 785>a.," The temperature rapidly decreases if $\tau_{\rm P,*}^{\rm ext}>\alpha$."
 Lf the interior is optically thick against its own radiation. then. the interior reaches the thermal equilibrium and becomes isothermal.," If the interior is optically thick against its own radiation, then, the interior reaches the thermal equilibrium and becomes isothermal."
 As he grain size becomes larger. the temperature of the super-weated Laver becomes lower.," As the grain size becomes larger, the temperature of the super-heated layer becomes lower."
 In. contrast. the temperature of the interior becomes higher.," In contrast, the temperature of the interior becomes higher."
 Phe physical reason of this whenomenon will be discussed in section 3 with two analytic models: the standard two-layer moclel like CG97 and a newly developed three-laver model., The physical reason of this phenomenon will be discussed in section 3 with two analytic models: the standard two-layer model like CG97 and a newly developed three-layer model.
 Llere. we just mention the fact hat the numerical results agree with the prediction by the hree-laver model for the grain size of 0.01.1pum. whereas he results agree with that by the two-laver model for the size zLOµια.," Here, we just mention the fact that the numerical results agree with the prediction by the three-layer model for the grain size of 0.01–1, whereas the results agree with that by the two-layer model for the size $\ga10$."
 When there is scattering. some differences appear.," When there is scattering, some differences appear."
 For a—0.01 ((pancl a]). the scattering. albedo c is negligible in. the wavelength interest (e.g. an elfective temperature less than Ti.=3.000 Ix in Figure 1).," For $a=0.01$ (panel [a]), the scattering albedo $\omega$ is negligible in the wavelength interest (e.g., an effective temperature less than $T_*=3,000$ K in Figure 1)."
 Thus. scattering virtually has no elfect.," Thus, scattering virtually has no effect."
 For «=0.1 ((panel b]). we for the stellar radiation is significant. but hat for the cülfuse radiation in the annulus (its. elfective emperature is less than about 300 Ix) is still negligible (see ligure 1).," For $a=0.1$ (panel [b]), $\omega$ for the stellar radiation is significant, but that for the diffuse radiation in the annulus (its effective temperature is less than about 300 K) is still negligible (see Figure 1)."
 In this case. the temperature at the equatorial xane becomes slightly lower than that in the no scattering case. which is consistent with Dullemond&Natta(2003b).," In this case, the temperature at the equatorial plane becomes slightly lower than that in the no scattering case, which is consistent with \cite{dul03}."
. For a—1 10 ((panels ced). w becomes significant for the radiation of the super-heated laver.," For $a=1$ –10 (panels [c,d]), $\omega$ becomes significant for the radiation of the super-heated layer."
 In. this case. we observe. a uateau like structure at around τος~1 and a significant reduction of the equatorial temperature.," In this case, we observe a plateau like structure at around $\tau_{\rm P,*}^{\rm ext}\sim1$ and a significant reduction of the equatorial temperature."
 For α=100 1l mm (panels ef]. finally. & becomes. “grey” for all the radiation considered. here.," For $a\ga100$ --1 mm (panels [e,f]), finally, $\omega$ becomes “grey” for all the radiation considered here."
" In this case. the temperature structure with scattering. becomes incistinguishable [rom that without scattering: a ""σον. scattering has no cllect on the temperature structure in the optical depth coordinate."," In this case, the temperature structure with scattering becomes indistinguishable from that without scattering; a “grey” scattering has no effect on the temperature structure in the optical depth coordinate."
 The physical reasons of these features will be discussed in section 3 with an analytic model., The physical reasons of these features will be discussed in section 3 with an analytic model.
To minimize (he side-lobes. we estimated the PSD with the maximum entropy method (MEM) (Press 1989) and with a classic periodogram augmented with CLEAN.,"To minimize the side-lobes, we estimated the PSD with the maximum entropy method (MEM) (Press 1989) and with a classic periodogram augmented with CLEAN."
 The results from both approaches are completely. consistent., The results from both approaches are completely consistent.
 In order to overcome (he aliasing problem due to large gaps in (ime. we used the following procedure.," In order to overcome the aliasing problem due to large gaps in time, we used the following procedure."
 This procedure determines the period from well-sampled but small cata set. folds au irregularly-saapled but larger data set with that period and (hen searches for a new period.," This procedure determines the period from well-sampled but small data set, folds an irregularly-sampled but larger data set with that period and then searches for a new period."
 We considered three subsets of the full Bght curves: 1990-91. 1990-93 and 1911-1999(&e.. the [ull set).," We considered three subsets of the full light curves: 1990-91, 1990-93 and 1977-1999, the full set)."
 We removed a third-order polynomial from each of these data sels., We removed a third-order polynomial from each of these data sets.
 This baseline represents slow variations in the flux density of Sev A*., This baseline represents slow variations in the flux density of Sgr A*.
 In the 1990-91 subset. (he maximum sampling eap (28 days) corresponds to (he Nyquist critical frequency of f.—2.1x10* Uz.," In the 1990-91 subset, the maximum sampling gap (28 days) corresponds to the Nyquist critical frequency of $f_c=2.1\times10^{-7}$ Hz."
 Using the zero-leveled subset. 1990-91. we caleulated a PSD profile.," Using the zero-leveled subset 1990-91, we calculated a PSD profile."
 At 1.3 cm. we found a spectral peak at the frequency f=1.0710* Hz. corresponding to a period P?=101 days.," At 1.3 cm, we found a spectral peak at the frequency $f=1.07\times10^{-7}$ Hz, corresponding to a period $P=107$ days."
 This lrequeney is well within the range of Nvquist critical frequency., This frequency is well within the range of Nyquist critical frequency.
 To verily the periodic signals. we examined the 1990-93 ancl 1977-99 subsets folded into JN. evcles of period Py.," To verify the periodic signals, we examined the 1990-93 and 1977-99 subsets folded into $N_{cyc}$ cycles of period $P_{\rm in}$."
 The 1990-93 consists of 59 observations curing the period 1990.1-1993.3. containing ~1/2 of the total data points in 1977-99.," The 1990-93 consists of 59 observations during the period 1990.1-1993.8, containing $\sim1/2$ of the total data points in 1977-99."
 The maxinun gaps in (he sampling are 120 and 1350 davs for the subsets 1990-93 and 1977-99. respectively.," The maximum gaps in the sampling are 120 and 1350 days for the subsets 1990-93 and 1977-99, respectively."
 The number N15 chosen as the largest number such that the maximum sampling gap GN uu) in the new folded time series is smaller than half the value of the period., The number $N_{cyc}$ is chosen as the largest number such that the maximum sampling gap $\Delta t_{max}$ ) in the new folded time series is smaller than half the value of the period.
 Taking the new folded time series of these subsets. we calculate PSD profiles.," Taking the new folded time series of these subsets, we calculate PSD profiles."
 Table 1 and Figure 2 sunmiarize (he results., Table 1 and Figure 2 summarize the results.
 The peak frequencies (/) derived [rom these three data sets are consistent. with a mean value of 1.090x10.* Iz.," The peak frequencies $f$ ) derived from these three data sets are consistent, with a mean value of $\times10^{-7}$ Hz."
 The uncertainty 0; ~3x10? Hz (3 days) of the peak frequency is estimated from the maximum deviation of the peak [frequencies derived [rom the three data subsets., The uncertainty $\sigma_f$ $\sim 3\times 10^{-9}$ Hz (3 days) of the peak frequency is estimated from the maximum deviation of the peak frequencies derived from the three data subsets.
 The EWIIM width GV) of the PSD feature is 9x10.7 Ilz derived from both 1990-91 and 1990-93 subsets., The FWHM width $\Delta f$ ) of the PSD feature is $\times10^{-8}$ Hz derived from both 1990-91 and 1990-93 subsets.
 For the 1977-99 subset. the FWIIM," For the 1977-99 subset, the FWHM"
UST WFEPC-2 observations were obtained on 1996 January 10 of the CFRSO300+00 Ποια (Lilly et al.,$HST$ WFPC-2 observations were obtained on 1996 January 10 of the CFRS0300+00 field (Lilly et al.
 1995) during a survey of the morphology of high redshift field galaxies in CFRS fields., 1995) during a survey of the morphology of high redshift field galaxies in CFRS fields.
 The total exposure time for (he F314W images of the CEIS0300--00 Ποιά was 6100s., The total exposure time for the F814W images of the CFRS0300+00 field was 6700s.
 Even though CERS03.1071 was not located in the higher resolution PC part of the WEDPC-? field. (he are structure near the galaxy. was immediately obvious while preprocessing the data (see Figure la) and was clear in the individual frames before stacking.," Even though CFRS03.1077 was not located in the higher resolution PC part of the WFPC-2 field, the arc structure near the galaxy was immediately obvious while preprocessing the data (see Figure 1a) and was clear in the individual frames before stacking."
 The J2000 coordinates of CERS03.1077 are 03 027? 30:99 002711., The J2000 coordinates of CFRS03.1077 are $^h$ $^m$ 9 1.
 The are has a radius of 271+071 and is accurately centered (lo within 207005) on the galaxy.," The arc has a radius of $2\farcs1\pm
0\farcs1$ and is accurately centered (to within $\pm $ 05) on the galaxy."
 Special attention was paid to deriving the parameters of CERS03.1077., Special attention was paid to deriving the parameters of CFRS03.1077.
 A high S/N point spread function was determined [rom six stars located at similar locations on images of other fields (since no suitable nearby star was present) and several other fainter stars were used (o assess possible errors., A high S/N point spread function was determined from six stars located at similar locations on images of other fields (since no suitable nearby star was present) and several other fainter stars were used to assess possible errors.
" Filling was carried oul on a c""svmmeltrzed image (see Schadeetal.(1995.1996). for details) of the galaxy so that the procedure was not perturbed by the presence of the arc or any other images."," Fitting was carried out on a “symmetrized” image (see \citet{Sch95, Sch96} for details) of the galaxy so that the procedure was not perturbed by the presence of the arc or any other images."
 The best-fit value of the reduced chi-square was 0.9988 for a fit radius of 20 pixels., The best-fit value of the reduced chi-square was 0.9988 for a fit radius of 20 pixels.
 Subtraction of the model galaxy (see Figure 1b) demonstrates that the resulting fit is an extremely. good representation of the galaxys luminosity distribution., Subtraction of the model galaxy (see Figure 1b) demonstrates that the resulting fit is an extremely good representation of the galaxy's luminosity distribution.
 The parameters of (he galaxy. were measured [rom the combined F814W image with a lolal integration time of 6700s., The parameters of the galaxy were measured from the combined F814W image with a total integration time of 6700s.
" The errors in the parameters were estimated [rom the lits to the five individual //57T' images with exposure times of 1100. 1200. or 2100 s. The dispersions among these fits were 07113 in R,. 0.025 in axial ratio (b/a). 2:88 in position angle. 0.04 mag in total magnitude. and 0.06 mag in central surface brightness."," The errors in the parameters were estimated from the fits to the five individual $HST$ images with exposure times of 1100, 1200, or 2100 s. The dispersions among these fits were 13 in $R_e$, 0.025 in axial ratio (b/a), 8 in position angle, 0.04 mag in total magnitude, and 0.06 mag in central surface brightness."
 The errors in the stacked image are expected to be roughly v5 times smaller because of better ratio., The errors in the stacked image are expected to be roughly $\sqrt 5$ times smaller because of better signal-to-noise ratio.
 These errors are also likely (o be svstematically over estimated because cosmic ravs are nol properly removed in (he individual images., These errors are also likely to be systematically over estimated because cosmic rays are not properly removed in the individual images.
 Possible svstematic errors due to imperlect knowledge of the point-spread-Dunction (PSF) were estimated by repeating the lits wilh several different PSEs from different observations aud dillerent positions on the chip., Possible systematic errors due to imperfect knowledge of the point-spread-function (PSF) were estimated by repeating the fits with several different PSFs from different observations and different positions on the chip.
3C147. at the start and end of the observations.,"3C147, at the start and end of the observations."
 For the sample galaxies with low LSR velocities. particular care was taken to choose a bandpass calibrator which does not have any absorption feature in the relevant velocity range.," For the sample galaxies with low LSR velocities, particular care was taken to choose a bandpass calibrator which does not have any absorption feature in the relevant velocity range."
 The phase calibration was done once every 30 min by observing a nearby VLA phase calibrator source., The phase calibration was done once every 30 min by observing a nearby VLA phase calibrator source.
 The GMRT data were reduced in the usual way using the standard tasks in classic AIPS., The GMRT data were reduced in the usual way using the standard tasks in classic AIPS.
 For each run. bad visibility points were edited out. after which the data were calibrated.," For each run, bad visibility points were edited out, after which the data were calibrated."
 The GMRT does not do online doppler tracking — any required doppler shifts have to be applied during the offline analysis., The GMRT does not do online doppler tracking – any required doppler shifts have to be applied during the offline analysis.
 However. for all of the sample galaxies. the differential doppler shift over our observing interval was much less than the channel width. hence. there was no need to apply any offline correction.," However, for all of the sample galaxies, the differential doppler shift over our observing interval was much less than the channel width, hence, there was no need to apply any offline correction."
 The GMRT has a hybrid configuration (Swarup et al., The GMRT has a hybrid configuration (Swarup et al.
" 1991) with [4 of its 30 antennas located in a central compact array with size zc | km (z 5 KA at 2]em) and the remaining antennas distributed in a roughly ""Y"" shaped configuration. giving a maximum baseline length of = 25"," 1991) with 14 of its 30 antennas located in a central compact array with size $\approx$ 1 km $\approx$ 5 $\lambda$ at 21cm) and the remaining antennas distributed in a roughly “Y” shaped configuration, giving a maximum baseline length of $\approx$ 25"
is closer to 2= (for the upper limit on age of 20.000 years. a very low braking index of n—| is required).,"is closer to $n=2$ (for the upper limit on age of 20,000 years, a very low braking index of $n\simeq 1$ is required)."
 Here we show that an initial period of several ms (6 ms in our example) can be obtained for a braking index of 3. if the appearance of a pure quark core is considered.," Here we show that an initial period of several ms (6 ms in our example) can be obtained for a braking index of $n=3$ , if the appearance of a pure quark core is considered."
 We use the same EOS and the MO=1.551M. constant baryonic mass sequence mentioned in previous sections and numerically integrate Equation (12))., We use the same EOS and the $M0=1.551 M_\odot$ constant baryonic mass sequence mentioned in previous sections and numerically integrate Equation \ref{Omdot}) ).
 We find that the age of the pulsar can be expressed in the following integral form where Q; is the initial angular velocity. or. equivalently. where J; is the initial angular momentum.," We find that the age of the pulsar can be expressed in the following integral form where $\Omega_i$ is the initial angular velocity, or, equivalently, where $J_i$ is the initial angular momentum."
" For numerical integration, it is more convenient to introduce a dimensionless central energy density &.=(e./e7)/(10%¢/em*) as the integration parameter, and evaluate The result of the numerical integration is shown in Fig. 9.."," For numerical integration, it is more convenient to introduce a dimensionless central energy density $\tilde \epsilon_c=(\epsilon_c/c^2)/(10^{15}{\rm g/cm^3})$ as the integration parameter, and evaluate The result of the numerical integration is shown in Fig. \ref{f_age},"
 which displays the age of the pulsar as a function of the central energy density., which displays the age of the pulsar as a function of the central energy density.
 For a current spin of 16ms and a pulsar age of 5.000 years. the initial spin is obtained to be 6ms.," For a current spin of 16ms and a pulsar age of 5,000 years, the initial spin is obtained to be 6ms."
 Thus. even an 2=3 braking index can yield an initial spin that is in agreement with theoretical expectations. provided the occurrence of a pure quark core is taken into account.," Thus, even an $n=3$ braking index can yield an initial spin that is in agreement with theoretical expectations, provided the occurrence of a pure quark core is taken into account."
 In the above example. a particular choice of EOS and baryonte mass was made.," In the above example, a particular choice of EOS and baryonic mass was made."
 Different choices would lead to different initial spin period estimates., Different choices would lead to different initial spin period estimates.
 However. the qualitative effect of the presence of a pure quark core is to merease (with respect to an EOS without a phase transition) the computed initial spin period.," However, the qualitative effect of the presence of a pure quark core is to increase (with respect to an EOS without a phase transition) the computed initial spin period."
 An important parameter for the successful detection of a phase-transition signal in the braking index of spinning-down pulsars is the event rate. which is determined by several importat= factors.," An important parameter for the successful detection of a phase-transition signal in the braking index of spinning-down pulsars is the event rate, which is determined by several important factors."
 Let's assume that pulsars are born with an. initial period of only a few milliseconds., Let's assume that pulsars are born with an initial period of only a few milliseconds.
 Since normal pulsars have a magnetic field strength of ~10!°G. they would quickly spin down to much larger periods due to magnetic dipole radiation.," Since normal pulsars have a magnetic field strength of $\sim 10^{12}G$, they would quickly spin down to much larger periods due to magnetic dipole radiation."
 Thus. if the baryonic mass of a newly-borr pulsar is such that the phase transition appears at a short rotational period. then the phase transition signal will not last for an extended period of time to have a realistic chance of being detected.," Thus, if the baryonic mass of a newly-born pulsar is such that the phase transition appears at a short rotational period, then the phase transition signal will not last for an extended period of time to have a realistic chance of being detected."
 Notice that no young. Crab-like pulsar with period shorter than 16ms has been observed. which is indicative of the very small event rate that should be expected for such an observation.," Notice that no young, Crab-like pulsar with period shorter than $16$ ms has been observed, which is indicative of the very small event rate that should be expected for such an observation."
 On the other hand. if pulsars are bor with rotational periods larger than. say. 6ms. then a phase transition can occur during their lifetime only if their baryonic mass falls within an extremely small range of values.," On the other hand, if pulsars are born with rotational periods larger than, say, 6ms, then a phase transition can occur during their lifetime only if their baryonic mass falls within an extremely small range of values."
 To illustrate this point. we plot in Figure 10. the constant baryonic mass sequence considered in Sec.," To illustrate this point, we plot in Figure \ref{f_spindown} the constant baryonic mass sequence considered in Sec."
 3. and the corresponding sequence of nonrotating models., \ref{Sequence} and the corresponding sequence of nonrotating models.
 The vertical dashed line specifies the central density at which the pure quark core appears., The vertical dashed line specifies the central density at which the pure quark core appears.
 It erosses the constant-baryonic-mass sequence at a model with rotational period of 6ms and gravitational mass of 1.419M.., It crosses the constant-baryonic-mass sequence at a model with rotational period of 6ms and gravitational mass of $1.419M_\odot$.
 Notice that the gravitational mass of a nonrotating star with central energy density equal to that of the quark core appearance (1.69110 ¢/em*) is L414M..," Notice that the gravitational mass of a nonrotating star with central energy density equal to that of the quark core appearance $1.691\times10^{15}{\rm
 g/cm^3}$ ) is $1.414M_\odot$."
 Thus. a pure quark core ean appear in a spinning down pulsar with rotational period less than 6ms only if its mass falls within AM~0.0025M... of the value of 1.4165M. (the the sequence considered in this example).," Thus, a pure quark core can appear in a spinning down pulsar with rotational period less than 6ms only if its mass falls within $\Delta M\sim 0.0025 M_\odot$ of the value of $1.4165M_\odot$ (the the sequence considered in this example)."
 The probability for this to happen is obviously negligible., The probability for this to happen is obviously negligible.
 The above arguments show that the only observed population remaining. in which one could hope for a significant event rate for the considered signal. are old millisecond pulsars. spun-up by aceretion. with low magnetic field and spin-down rate.," The above arguments show that the only observed population remaining, in which one could hope for a significant event rate for the considered signal, are old millisecond pulsars, spun-up by accretion, with low magnetic field and spin-down rate."
 The actual event rate will then depend on the mass-distribution for this population and on the precise value of the central energy density at which the quark core appears., The actual event rate will then depend on the mass-distribution for this population and on the precise value of the central energy density at which the quark core appears.
 None of these parameters are currently known with sufficient accuracy to compute a reliable value for the event rate., None of these parameters are currently known with sufficient accuracy to compute a reliable value for the event rate.
 In fact. the observational determination of the braking index is itself a difficult task and no braking index has been measured for any of the known millisecond pulsars. to date.," In fact, the observational determination of the braking index is itself a difficult task and no braking index has been measured for any of the known millisecond pulsars, to date."
 However. should a millisecond pulsar become supramassive. due to mass-aceretion. then there is a realistic chance for detecting the presence of a quark core in observations of the first time-derivative. P. of the rotational period.," However, should a millisecond pulsar become supramassive, due to mass-accretion, then there is a realistic chance for detecting the presence of a quark core in observations of the first time-derivative, $\dot P$, of the rotational period."
 Once the quark core appears and if the pulsar is sufficiently massive. then P«0 for the rest of the pulsar's lifetime.," Once the quark core appears and if the pulsar is sufficiently massive, then $\dot P<0$ for the rest of the pulsar's lifetime."
 Observational constraints for the properties of compact stars are currently still too weak to determine the correct, Observational constraints for the properties of compact stars are currently still too weak to determine the correct
Iu a high-mass X-ray. binary (HMXB). a compact object. which ean be a black hole (BH) or a ueutron star (NS). accretes some portion of the wind (rom a highi-1nass (M> OAL.) uou-degenerate companion star.,"In a high-mass X-ray binary (HMXB), a compact object, which can be a black hole (BH) or a neutron star (NS), accretes some portion of the wind from a high-mass $M>5M_\odot$ ) non-degenerate companion star."
" Some HMXBs are called ""mniero-quasars! (jQSOs) when resolved. collimated radio features are observed. which are interpreted as relativistic jets."," Some HMXBs are called `micro-quasars' $\mu$ QSOs) when resolved, collimated radio features are observed, which are interpreted as relativistic jets."
 ⋯⊳∖↿↓↥∢⊾⊳∖⋜⋯↓∢⋅↓⋯⊔↓∣⋈⋅↓⋅∪⇂∎≱∖↿⋜⊔⋅⊳∖∣⋡∪↥↓↕∣⋡↓⋯⋅∖∖⊽⋜⋯⇂⋜⋯∠⇂↓⋅∢⋅∠⇂∖∖⋎⋜⊔⋅∠⇂ ∪⇂⋅⇂↓,has the same number of stars both blueward and redward of the RR Lyrae gap).
↥∢⊾∐∐∟∙∖⇁↓⋅⋯⊾⋏∙≟⋜↧↓≻↴⇀∖⊔↓∪⊔⋏∙≟⊳∖∣↿↓⊔⋅⊳∖⋜⋯↓↓≻↓⋖⊾∪⇂∎≺⊲∪∐⋖⋅⊔↙∣∣∣∕↽ ∖↓≤⋗≤⋗↖∖⊐⋠↓≱∖↥↓↥⋖⋅≺∶≺∶≺⊲↳∖↓∶⊰⋃∖⊽≺∶≺⊲⋅↱≻⇉⊤⇉∃⊳⇂⋅∪↓⋅∖∖⊽↓↥⊀⊔⇍↓↥↥⇂↥∢⋅∙∖⇁⋖≱∣⋡↿⋜↧↕↓↕ 11:35 = 2.31A. and has an extremely blue LIB.," Amongst the sample of Cohen (1998) is the GGC M3 (NGC 5272), for which they obtain $\beta$ = 2.31, and has an extremely blue HB."
 Since both of ⇂↥∢⋅≱∖⋖⋅≺∶≺∶≺⊲≱∖⇂⋯∖⇁⋖⋅↓⊲∖⋖⋅∐∿−↓⊳≼≨⋅↱≻⊳↿∐↓⊳∖∖∖⊽∪⊔↓∠⇂⊲↓⊔↓↓≻↓∙∖⇁⇂↓⋯↿∐∐ ⊔↓∪↓⋅↓≻⇂↥∪↓∪⋏∙≟∙∖⇁↓⋯⊳∖↓∐∐⋖⋅∪↓⋅⊔∪⋖⋅∐∎⋯∙↥⊔↓≻∪⊔∐⊰⊳≼∼∪⊔⇂↓⋅⋜⊔⋅∙∖⇁↿∪↿⇂↥⋖⋅ ≻↓⋅∢⊾∠⇂⊲⊔∙↿⋠↓∪⊔≱∖∪⇂∎↿∐⋖⋅⋜↧∣⋯∖⇁∢⋅∺∺↓↴," Since both of these GGCs have Fe/H $\sim$ -1.65, this would imply that HB morphology has little or no effect upon $\beta$, contrary to the predictions of the above SSP models."
⊔↓⋯⇂∢⊾↓⊳∖⊳≺⊲↓⋖⊾⋜⊔⋅↓∙∖⇁⊳⋜↧↓↕⊀↓⋏∙≟↓⊔↥⋯↧↓⊀∐∙∖⇁⊳ ↥∪⊔↓∪⋏∙≟⋖⋅⊔∢⋅∪⊔≱∖∠⇂⋜↧⋯⊳∖⋖⋅↿⊲↓⊳∖↓⋅∢⊾⊏↥⊔⊲⊔⋅∢⊾∠⇂↿∪⊀↓⊔∖⇁⋖⊾⊳∖↿⊲↓⋏∙≟⋜⋯⊾∖∖⊽↓↕∢⋅⇂↓↥∢⊾↓⋅⇂↓↕⋖⋅ ↕∪↓⋰↓∠∪⊔↿⋜↧↓∣⋡↓⋅⋜⋃⊔⇍↓↕⊔↓⋜↧∙∖⇁⋜↧∐⋅⋯∼⇂⇂↓↕⋖⋅≩⋜↧↓⊔↓⋖⋅↓⋅⊲↓⊔∠∐⊓⊾≱∖∪⇂∎⋏∙≟⇂∪∣⋡⊔⇂⋜⊔⋅ clusters at the same metallicity.," Clearly, a high quality, homogeneous data set is required to investigate whether the horizontal branch may affect the Balmer indices of globular clusters at the same metallicity."
 The model grids cover a moetallicitvy-age parameter space of -0.5 < Le/ll] 0.5 with isochrones of 1.5 <rx 17 Gyr., The model grids cover a metallicity-age parameter space of -0.5 $\leq$ [Fe/H] $\leq$ 0.5 with isochrones of 1.5 $\leq \tau \leq$ 17 Gyr.
 To cover old. metal-poor populations. they have been subsequently. extended to bracket -2.0. x ο/η] x 0.5 for ages S &rX 17 Gyr.," To cover old, metal-poor populations, they have been subsequently extended to bracket -2.0 $\leq$ [Fe/H] $\leq$ 0.5 for ages 8 $\leq \tau \leq$ 17 Gyr."
 The orthogonality of the index-index plots indicates the degree. of decoupling between age and metallicity in the mocels., The orthogonality of the index-index plots indicates the degree of decoupling between age and metallicity in the models.
 The assumption of a red clump in the Worthey (1994) nmiodels possibly explains the findings of Cohen (1998) that formally their metal-rich GGCs are than the metal-poor ones. the opposite of what one might expect.," The assumption of a red clump in the Worthey (1994) models possibly explains the findings of Cohen (1998) that formally their metal-rich GGCs are than the metal-poor ones, the opposite of what one might expect."
 This new treatment of the LLBs in the models predicts similar ages for the metal-rich and metal-poor GGCs., This new treatment of the HBs in the models predicts similar ages for the metal-rich and metal-poor GGCs.
 We calibrate the SSP models using the indices measured for the combined sample of GGCs., We calibrate the SSP models using the indices measured for the combined sample of GGCs.
 The metallicities predicted bv the models of Worthey (1994) must. first he placed. on to the metallicity scale of our GGC's., The metallicities predicted by the models of Worthey (1994) must first be placed on to the metallicity scale of our GGCs.
 We use the most widely used metallicity scale for CiCs. which is that of Zinn (1985).," We use the most widely used metallicity scale for GGCs, which is that of Zinn (1985)."
 “Phis is primarily based on a number of narrow-band photometric indices sensitive to the ultraviolet blanketing in the integrated light of the globular cluster spectral energy distribution., This is primarily based on a number of narrow-band photometric indices sensitive to the ultraviolet blanketing in the integrated light of the globular cluster spectral energy distribution.
 Whilst there is increasing evidence that this metallicity. scale. is non-linear (c.g. Carretta Cratton 1997). we adopt it since it remains self-consistent ancl the empirical calibrations of Brodic Huchra (1990) are based upon this (see below).," Whilst there is increasing evidence that this metallicity scale is non-linear (e.g. Carretta Gratton 1997), we adopt it since it remains self-consistent and the empirical calibrations of Brodie Huchra (1990) are based upon this (see below)."
 We first obtain. Fe/LH] on the Worthey (1994) scale as a function of the Fe5270. Mg 6 and Meg» indices for our entire sample of GGCs.," We first obtain [Fe/H] on the Worthey (1994) scale as a function of the Fe5270, Mg $b$ and $_{2}$ indices for our entire sample of GGCs."
 The newly assigned. metallicities for the elobular clusters are then compared to those of Zinn (1985) in order to derive a transformation function from the mocel metallicities to that of the Zinn (1985) metallicity scale., The newly assigned metallicities for the globular clusters are then compared to those of Zinn (1985) in order to derive a transformation function from the model metallicities to that of the Zinn (1985) metallicity scale.
 The C4300 and. Fe5335 indices are not used for the re-scaling of the models. since there are fewer (αι with measurements of these indices.," The G4300 and Fe5335 indices are not used for the re-scaling of the models, since there are fewer GGCs with measurements of these indices."
 For the magnesium indices. we obtain the lincar transformations: for Mg b and Ales respectively.," For the magnesium indices, we obtain the linear transformations: for Mg $b$ and $_{2}$ respectively."
 The Fe5270 index proved. to be non-linear. ancl was fit with the quadratic: with an rms of 7=0.2 dex.," The Fe5270 index proved to be non-linear, and was fit with the quadratic: with an rms of $\sigma$ =0.2 dex."
may provide a way to form young elliptical galaxies in the clusters at late times.,may provide a way to form young elliptical galaxies in the clusters at late times.
" The morphological evidence for recent and rapid evolution in the cluster galaxy population is supported by photometric and spectroscopic studies. which have found a significant increase of the number fractions of star forming and post star burst galaxies from z20 to zz1 (e.g. Butcher Oemler 1978. 1984. Dressler Gunn 1983. Couch Sharples 1987. Postman. Lubin. Oke 1998. Poggianti et 11999, van Dokkum et al 2000)."," The morphological evidence for recent and rapid evolution in the cluster galaxy population is supported by photometric and spectroscopic studies, which have found a significant increase of the number fractions of star forming and post star burst galaxies from $z=0$ to $z=1$ (e.g., Butcher Oemler 1978, 1984, Dressler Gunn 1983, Couch Sharples 1987, Postman, Lubin, Oke 1998, Poggianti et 1999, van Dokkum et al 2000)."
 Hence the evidence appears secure that many early-type galaxies in clusters were transformed from star forming galaxies at fairly recent times., Hence the evidence appears secure that many early-type galaxies in clusters were transformed from star forming galaxies at fairly recent times.
 The purpose of this paper is to produce models which can bring these apparently different lines of evidence regarding the ages into agreement., The purpose of this paper is to produce models which can bring these apparently different lines of evidence regarding the ages into agreement.
 Specifically. we analyse the effects of late morphological transformations as found by Dressler et al..," Specifically, we analyse the effects of late morphological transformations as found by Dressler et al.,"
 and others. on the observed evolution of colors and luminosities with redshift.," and others, on the observed evolution of colors and luminosities with redshift."
 We show that the effect of “progenitor bias” (Franx van Dokkum 1996; van Dokkum et 22000) can be very significant: if early-type galaxies were transformed from other galaxy types at late times. the youngest progenitors of present-day early-type galaxies drop out of the sample of early-type galaxies at high redshift.," We show that the effect of “progenitor bias” (Franx van Dokkum 1996; van Dokkum et 2000) can be very significant: if early-type galaxies were transformed from other galaxy types at late times, the youngest progenitors of present-day early-type galaxies drop out of the sample of early-type galaxies at high redshift."
 Hence the samples of galaxies at low and high redshift are not the same. and in particular. the high redshift samples might be biased towards the oldest progenitors of present-day early-type galaxies.," Hence the samples of galaxies at low and high redshift are not the same, and in particular, the high redshift samples might be biased towards the oldest progenitors of present-day early-type galaxies."
 The purpose of this paper is to quantify the effects of progenitor bias. and to estimate the corrections which are required for models which ignore morphological evolution.," The purpose of this paper is to quantify the effects of progenitor bias, and to estimate the corrections which are required for models which ignore morphological evolution."
 To that end. we construct relatively simple models for the history of star formation and morphological type of cluster early-type galaxies.," To that end, we construct relatively simple models for the history of star formation and morphological type of cluster early-type galaxies."
 We show that the observed slow luminosity evolution and low seatter in the color-magnitude relation and the Fundamental Plane are natural consequences of recent and ongoing assembly of early-type galaxies., We show that the observed slow luminosity evolution and low scatter in the color-magnitude relation and the Fundamental Plane are natural consequences of recent and ongoing assembly of early-type galaxies.
 We correct the observed evolution for the progenitor bias. and derive the corrected mean age of the stars in early-type galaxies.," We correct the observed evolution for the progenitor bias, and derive the corrected mean age of the stars in early-type galaxies."
 Our models are extensions of the earlier work by van Dokkum et al (1998b). Bower et ((1998). and Shioya Bekki (1998).," Our models are extensions of the earlier work by van Dokkum et al (1998b), Bower et (1998), and Shioya Bekki (1998)."
 These authors considered complex star formation histories of cluster galaxies. but did not investigate the effects of morphological transformations on the observed properties of early-type galaxies at high redshift.," These authors considered complex star formation histories of cluster galaxies, but did not investigate the effects of morphological transformations on the observed properties of early-type galaxies at high redshift."
 The progenitor bias is implicitly meluded in the very detailed semi-analytical models by. for example. Kauffman Charlot (1998) and Baugh. Cole. Frenk (1996).," The progenitor bias is implicitly included in the very detailed semi-analytical models by, for example, Kauffman Charlot (1998) and Baugh, Cole, Frenk (1996)."
 In these complex models it is difficult to isolate and quantify specific. effects. such as the progenitor bias.," In these complex models it is difficult to isolate and quantify specific effects, such as the progenitor bias."
 The main contribution of our work is that we use simple analytic models with only three free parameters. which allows us to provide explicit estimates for the effects of morphological evolution on the observed colors and luminosities of early-type galaxies.," The main contribution of our work is that we use simple analytic models with only three free parameters, which allows us to provide explicit estimates for the effects of morphological evolution on the observed colors and luminosities of early-type galaxies."
 We construct simple models for the evolution of early-type galaxies. which parameterize both their star formation history and morphological evolution.," We construct simple models for the evolution of early-type galaxies, which parameterize both their star formation history and morphological evolution."
 Our models allow the full history to be quantified by three parameters., Our models allow the full history to be quantified by three parameters.
 They are not based on a full physical description of the formation and evolution of galaxies as derived by. e.g.. Kauffmann. White. Guiderdoni (1993) and Baugh et ((1996).," They are not based on a full physical description of the formation and evolution of galaxies as derived by, e.g., Kauffmann, White, Guiderdoni (1993) and Baugh et (1996)."
 We assume that early-type galaxies have similar histories of star formation and morphology., We assume that early-type galaxies have similar histories of star formation and morphology.
 The history of each individual galaxy can be described by three parameters: the time when star formation starts. the time when star formation stops. and the variation of star formation between the start and end.," The history of each individual galaxy can be described by three parameters: the time when star formation starts, the time when star formation stops, and the variation of star formation between the start and end."
 The star formation is allowed to increase or decrease with time., The star formation is allowed to increase or decrease with time.
 It is assumed that the galaxy ts classified as an early-type galaxy some time after the cessation of starformation., It is assumed that the galaxy is classified as an early-type galaxy some time after the cessation of starformation.
 We assume that the galaxies do not stop their star formation at the same time. but rather have a distribution of cessation times.," We assume that the galaxies do not stop their star formation at the same time, but rather have a distribution of cessation times."
 This deseription is fairly generic for many detailed theories of galaxy formation., This description is fairly generic for many detailed theories of galaxy formation.
 We do not define the processes driving the morphological transformation and the cessation. of star formation., We do not define the processes driving the morphological transformation and the cessation of star formation.
" Various processes have been invoked. including gas stripping of spiral galaxies (e.g.. Gunn Gott 1972. Tytler Vidal 1978. Abadi. Moore. Bower 1999, Kodama Smail 2000). tidal interactions (e.g.. Fried 1988. Moore et 11996). and mergers (e.g.. Lavery et 11992, van Dokkum et 11999)."," Various processes have been invoked, including gas stripping of spiral galaxies (e.g., Gunn Gott 1972, Tytler Vidal 1978, Abadi, Moore, Bower 1999, Kodama Smail 2000), tidal interactions (e.g., Fried 1988, Moore et 1996), and mergers (e.g., Lavery et 1992, van Dokkum et 1999)."
 It does not matter in our analysis what process causes the cessation of star formation. and we allow for bursts of star formation to accompany this event.," It does not matter in our analysis what process causes the cessation of star formation, and we allow for bursts of star formation to accompany this event."
 The transition phase between star forming galaxy and early-type galaxy is assumed to last for a significant time., The transition phase between star forming galaxy and early-type galaxy is assumed to last for a significant time.
 Immediately after the cessation of star formation galaxies are likely to show tidal features (in case of an interaction or merger) or weak spiral arms.," Immediately after the cessation of star formation galaxies are likely to show tidal features (in case of an interaction or merger), or weak spiral arms."
 The morphologies of “E+A™ or post star burst galaxies seem to be consistent with this scenario., The morphologies of “E+A” or post star burst galaxies seem to be consistent with this scenario.
 They generally are classified as early-type spirals or tidally distorted systems (Poggianti et 11999; Fabricant et 22000: van Dokkum et 22000)., They generally are classified as early-type spirals or tidally distorted systems (Poggianti et 1999; Fabricant et 2000; van Dokkum et 2000).
 It is not well known how long it takes before these structures fade or disperse: we assume that early-type galaxies are first classified as such ~1.5 GGyr after star formation in their progenitors ceased.," It is not well known how long it takes before these structures fade or disperse; we assume that early-type galaxies are first classified as such $\sim
1.5$ Gyr after star formation in their progenitors ceased."
 In the current Section we do not specify whether the models apply to elliptical galaxies. SO. galaxies. or both.," In the current Section we do not specify whether the models apply to elliptical galaxies, S0 galaxies, or both."
 Observationally. the early-type galaxy fraction is more robust than the relative numbers of elliptical galaxies and SO galaxies (e.g.. Fabricant. Franx. van Dokkum 2000. van Dokkum et 22000).," Observationally, the early-type galaxy fraction is more robust than the relative numbers of elliptical galaxies and S0 galaxies (e.g., Fabricant, Franx, van Dokkum 2000, van Dokkum et 2000)."
 If different histories apply to the two classes of galaxies. two separate models will be needed for each sub-class.," If different histories apply to the two classes of galaxies, two separate models will be needed for each sub-class."
 We explore such models in Section 5., We explore such models in Section 5.
 The generic effects of late morphological transitions. are illustrated in , The generic effects of late morphological transitions are illustrated in \\ref{modeltracks.plot}.
In panel (a). the evolution of the ratio is shown for a population of galaxies with a small range in age. without any late morphological transitions.," In panel (a), the evolution of the mass-to-light ratio is shown for a population of galaxies with a small range in age, without any late morphological transitions."
 Ás can be seen. galaxies with young stellar populations evolve more rapidly than galaxies with old stellar populations. and hence the spread in M/L ratios increases with redshift (panel b).," As can be seen, galaxies with young stellar populations evolve more rapidly than galaxies with old stellar populations, and hence the spread in $M/L$ ratios increases with redshift (panel b)."
 The mean evolution is faster than that of a single age population formed at z=x. which is indicated by the dashed line in (b).," The mean evolution is faster than that of a single age population formed at $z=
\infty$, which is indicated by the dashed line in (b)."
" This type of modelling has been used extensively to constrain the ages of early-type galaxies in clusters: if there are no morphological transitions. the evolution of the mean color or luminosity constrains the mean age of early-type galaxies. and the scatter constrains the spread in ages (e.g.. Bower. Lucey. Ellis 1992, Ellis et 11997. van Dokkum et 11998(a.b). Bower et 11998. Stanford et 11998. Ferreras Silk 2000)."," This type of modelling has been used extensively to constrain the ages of early-type galaxies in clusters: if there are no morphological transitions, the evolution of the mean color or luminosity constrains the mean age of early-type galaxies, and the scatter constrains the spread in ages (e.g., Bower, Lucey, Ellis 1992, Ellis et 1997, van Dokkum et 1998(a,b), Bower et 1998, Stanford et 1998, Ferreras Silk 2000)."
 In panel (c). a model is shown in which galaxies are transformed into early-type galaxies at a constant rate.," In panel (c), a model is shown in which galaxies are transformed into early-type galaxies at a constant rate."
 The, The
"values for the parameters. α=23.5. J=126.1. 5=2.92. Αμ,=1.72«10!AF. and P,=1078.","values for the parameters, $\alpha=23.5$ , $\beta=126.1$ , $\gamma=2.92$, $M_{BH_b}=1.72\times10^4 M_{\odot}$ and $P_b=40\fdg8$."
 Also. it can be seen that as the pitch angle approaches zero. that the black hole mass increases rapidly.," Also, it can be seen that as the pitch angle approaches zero, that the black hole mass increases rapidly."
 However. it should be noted that the relationship only applies to spiral galaxies. and is therefore not applicable below pitch angles of ~7°. re. similar to the pitch angle of M31. since this is the tighest pitch angle typically seen in disk galaxies.," However, it should be noted that the relationship only applies to spiral galaxies, and is therefore not applicable below pitch angles of $\sim7^{\circ}$, i.e. similar to the pitch angle of M31, since this is the tighest pitch angle typically seen in disk galaxies."
" In Figure 2 we show a plot of bulge central velocity dispersion. 7,.. as a function of spiral arm pitch angle."," In Figure 2 we show a plot of bulge central velocity dispersion, $\sigma_c$, as a function of spiral arm pitch angle."
 Not surprisingly. a good correlation is seen.," Not surprisingly, a good correlation is seen."
" This i$ simply a result of the fact that σ,. is also an indicator of the mass of central BHs (Gebhardt et 22000a; Ferrarese Merritt 2000).", This is simply a result of the fact that $\sigma_c$ is also an indicator of the mass of central BHs (Gebhardt et 2000a; Ferrarese Merritt 2000).
 In this case. Pearson’s linear correlation coefficient is 0.92 and the significance level at which the null hypothesis of zero correlation is disproved ts also 3o.," In this case, Pearson's linear correlation coefficient is 0.92 and the significance level at which the null hypothesis of zero correlation is disproved is also $\sigma$."
" We suggest that two of the factors in the determination of supermassive BH mass could be either dark matter halo concentration (ο=Ry./R.. where P 1s the virial radius and A, is the dark matter density profile scale radius: Navarro et 1997) or the dark matter halo virial mass (see Ferrarese 2002)."," We suggest that two of the factors in the determination of supermassive BH mass could be either dark matter halo concentration $c=R_{\rm vir}/R_{\rm s}$, where $R_{\rm vir}$ is the virial radius and $R_{\rm s}$ is the dark matter density profile scale radius; Navarro et 1997) or the dark matter halo virial mass (see Ferrarese 2002)."
 One of the determining factors of spiral arm pitch angle is central mass concentration. which in turn is related to dark matter halo concentration (e.g.. Seigar et 22006).," One of the determining factors of spiral arm pitch angle is central mass concentration, which in turn is related to dark matter halo concentration (e.g., Seigar et 2006)."
 Furthermore. spiral galaxies with larger halo concentrations are more likely to have larger stellar bulges in which more massive BHs can reside.," Furthermore, spiral galaxies with larger halo concentrations are more likely to have larger stellar bulges in which more massive BHs can reside."
 Finally. the stellar velocity dispersion of the bulge. o. is an indicator of the dynamical mass within the radius at which it is measured.," Finally, the stellar velocity dispersion of the bulge, $\sigma$, is an indicator of the dynamical mass within the radius at which it is measured."
 This ts also related to halo concentration. which in turn is related to halo virial mass (e.g.. van den Bosch et 22007).," This is also related to halo concentration, which in turn is related to halo virial mass (e.g., van den Bosch et 2007)."
 It is therefore possible not only to explain the relationship between spiral arm pitch angle and supermassive BH mass (presented here). but also the relation between bulge mass and supermassive BH mass (Magorrian et 11998) and the ἁδωῃ-σ relation (Gebhardt et 22000a; Ferrarese Merritt 2000).," It is therefore possible not only to explain the relationship between spiral arm pitch angle and supermassive BH mass (presented here), but also the relation between bulge mass and supermassive BH mass (Magorrian et 1998) and the $M_{\rm BH}$ $\sigma$ relation (Gebhardt et 2000a; Ferrarese Merritt 2000)."
 However. we note that given the current evidence. it 15 impossible to tell if dark matter halo concentration is the main determinant of supermassive BH mass. or if some other quanitity 1s also important.," However, we note that given the current evidence, it is impossible to tell if dark matter halo concentration is the main determinant of supermassive BH mass, or if some other quanitity is also important."
 To determine if the dark matter halo does affect BH mass ts the subject of a more detailed study., To determine if the dark matter halo does affect BH mass is the subject of a more detailed study.
 Finally. the importance of the relationship between spiral arm pitch angle and supermassive BH mass lies in the ability to detect regular spiral structure out to intermediate redshifts.," Finally, the importance of the relationship between spiral arm pitch angle and supermassive BH mass lies in the ability to detect regular spiral structure out to intermediate redshifts."
 For example. Elmegreen et ((2004) clearly show that disk galaxies at +—1 can exhibit grand design spiral structure.," For example, Elmegreen et (2004) clearly show that disk galaxies at $z\simeq 1$ can exhibit grand design spiral structure."
 If this is true. then it may be possible to estimate the growth of supermassive BHs in disk galaxies as a function of look back time. just from imaging data and a measurement of spiral arm pitch angle.," If this is true, then it may be possible to estimate the growth of supermassive BHs in disk galaxies as a function of look back time, just from imaging data and a measurement of spiral arm pitch angle."
 In such a study. the accuracy for predicting the BH mass for an individual galaxy is +30%.. based on the scatter in Figure | and the typical errors associated with estimating spiral arm pitch angles.," In such a study, the accuracy for predicting the BH mass for an individual galaxy is $\pm$, based on the scatter in Figure 1 and the typical errors associated with estimating spiral arm pitch angles."
 Taking into account that spiral arm pitch angles for more distant galaxies will be measured with less certainty. it is likely that we will be able to determine BH masses to within +50%..," Taking into account that spiral arm pitch angles for more distant galaxies will be measured with less certainty, it is likely that we will be able to determine BH masses to within $\pm$."
 It is therefore important to note that the spiral arm pitch angle versus BH mass relation should be applied to a large sample of nearly face-on galaxies. in which case a statistical analysis of the evolution of BH masses in disk galaxies can be determined.," It is therefore important to note that the spiral arm pitch angle versus BH mass relation should be applied to a large sample of nearly face-on galaxies, in which case a statistical analysis of the evolution of BH masses in disk galaxies can be determined."
 Given the quantity of deep HST imaging of blank fields that is now available. it seems that the time is ripe to perform such as study.," Given the quantity of deep HST imaging of blank fields that is now available, it seems that the time is ripe to perform such as study."
 For example. we estimate that ~700 galaxies are available for a study of spiral structure from the Great Observatories Origins Deep Survey fields alone (see Giavalisco et 22004 for a description of this survey).," For example, we estimate that $\sim$ 700 galaxies are available for a study of spiral structure from the Great Observatories Origins Deep Survey fields alone (see Giavalisco et 2004 for a description of this survey)."
 It therefore should now be possible to determine. statistically. the evolution of SMBHs in disk galaxies. based upon spiral arm morphology.," It therefore should now be possible to determine, statistically, the evolution of SMBHs in disk galaxies, based upon spiral arm morphology."
 Support for this work was provided by the Arkansas NASA EPSCoR program., Support for this work was provided by the Arkansas NASA EPSCoR program.
 This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract withNASA.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract withNASA."
 Theauthors wish to thank the anonymous referees whose comments improved the content of this letter., Theauthors wish to thank the anonymous referees whose comments improved the content of this letter.
assumption holds also for AGN. we have plotted in. Fig.,"assumption holds also for AGN, we have plotted in Fig."
 5 the luminosity of the 10 jam silicate feature versus its rest-frame center., \ref{silum} the luminosity of the 10 $\mu$ m silicate feature versus its rest-frame center.
 Indeed. we find that stronger silicate enission is associated with a stronger reciward displacement.," Indeed, we find that stronger silicate emission is associated with a stronger redward displacement."
 Llowever. the two Iowest-Iuminosity sources (Ill Zw 2 and 3C st) do not appear to follow this trend.," However, the two lowest-luminosity sources (III Zw 2 and 3C 84) do not appear to follow this trend."
 We note that in the current literature authors often study the (emission) equivalent widths. of the silicate features rather than their luminosities., We note that in the current literature authors often study the (emission) equivalent widths of the silicate features rather than their luminosities.
 Vhis approach needs to be taken with caution. since. by definition. the equivalent width depends strongly on the continuum flux.," This approach needs to be taken with caution, since, by definition, the equivalent width depends strongly on the continuum flux."
 And. as the SEDs in Fig.," And, as the SEDs in Fig."
 show. the LO pam silicate feature is located such that its continuum (tx is given by the relative streneths of the warm and. cool blackbock components. which vary strongly between sources.," \ref{sed} show, the 10 $\mu$ m silicate feature is located such that its continuum flux is given by the relative strengths of the warm and cool blackbody components, which vary strongly between sources."
 In fact. the relation observed. in Fig.," In fact, the relation observed in Fig."
 5 is not evident we use rest-framoe equivalent. width values instead of Iuminosities. and our sample shows a trend for higher equivalent widths to be measured. the weaker the warm blackbody component is relative to the cool one.," \ref{silum} is not evident if we use rest-frame equivalent width values instead of luminosities, and our sample shows a trend for higher equivalent widths to be measured, the weaker the warm blackbody component is relative to the cool one."
 We have selected our sample. of raclio-louck AGN based on their relatively wee jet viewing angles (@7 20°)., We have selected our sample of radio-loud AGN based on their relatively large jet viewing angles $\theta \ga 20^{\circ}$ ).
 At these orientations the relativistic enhancement. of the jet emission is expected. to be verv low. ensuring that the observed. infrared. SED is dominated. by emission [rom the putative dusty torus.," At these orientations the relativistic enhancement of the jet emission is expected to be very low, ensuring that the observed infrared SED is dominated by emission from the putative dusty torus."
 In fact. based on the calculated relativistic Doppler factors 9. (Fable. 1.. column (16)). we expect relativistic beaming of the integrated jet Dux. which is proportional to 61. by [actors of <10 in three sources (LIL Zw 2. 3€ S4. and 3C 245) and relativisticdebeaming for the remainder.," In fact, based on the calculated relativistic Doppler factors $\delta$ (Table \ref{general}, column (16)), we expect relativistic beaming of the integrated jet flux, which is proportional to $\delta^4$, by factors of $\la 10$ in three sources (III Zw 2, 3C 84, and 3C 245) and relativistic for the remainder."
": .Pho ueexception(8M1 i1Ss !he ""SNsource(5 unQE3C OOT=207.. ""arfor which.Ihe. baDasned ou improved. proper motion data. we now caleulate a relatively small inclination angle (@~ 8)."," The exception is the source 3C 207, for which, based on improved proper motion data, we now calculate a relatively small inclination angle $\theta \sim 8^{\circ}$ )."
 Lts relativistic Doppler actor is Ó~3. meaning that the relativistic jet. παν enhancement is expected to be a factor of ~SO.," Its relativistic Doppler factor is $\delta \sim 3$, meaning that the relativistic jet flux enhancement is expected to be a factor of $\sim 80$."
 However. as Fig.," However, as Fig."
 6 shows. even in the strongest relativistically 2οΠΙΟ source in our sample the infrared SLED is dominated w thermal emission.," \ref{jetsed}
 shows, even in the strongest relativistically beamed source in our sample the infrared SED is dominated by thermal emission."
 An extrapolation of the core radio spectrum using a typical blazar SED that generally. peaks at a dew pm (7). predicts mid-infrared [uxes a factor of ~40 ower than observed., An extrapolation of the core radio spectrum using a typical blazar SED that generally peaks at a few $\mu$ m \citep{Gio02} predicts mid-infrared fluxes a factor of $\sim 40$ lower than observed.
 Further evidence that the infrared SEDs of all our sources are dominated by thermal rather than non-hermal emission comes from their similar. relatively bulgv appearance and the lack of strong. short-term. variability.," Further evidence that the infrared SEDs of all our sources are dominated by thermal rather than non-thermal emission comes from their similar, relatively bulgy appearance and the lack of strong, short-term variability."
 The IRS spectroscopy overlaps in wavelength with either, The IRS spectroscopy overlaps in wavelength with either
NGC 1110AÀ is the host of both a racio-loud active nucleus aud on-goiug star formation.,NGC 4410A is the host of both a radio-loud active nucleus and on-going star formation.
 The W.ar formatiol is iu the form of extremely luminous Η ΠΠ regious aligued in an arc aoug the eastern »ortion of a riug-like stellar structure sur'oundiug the active nucleus., The star formation is in the form of extremely luminous H II regions aligned in an arc along the eastern portion of a ring-like stellar structure surrounding the active nucleus.
 The westert portion of this jug contaius filamentary ionized gas wit1 optical line ratios imjplviug shock ionization., The western portion of this ring contains filamentary ionized gas with optical line ratios implying shock ionization.
 NGC LLOA is thus a nearby example of an ΑΝ with spatially-resolved evideuce for both sta: formation ancl shocks in an extenced emission line regioL, NGC 4410A is thus a nearby example of an AGN with spatially-resolved evidence for both star formation and shocks in an extended emission line region.
 Such au object leds credeuce to t hypothesis that le emission ililine regions associated wit adio galaxies auc thie central galaxies it cluster cooling lows migη also 'esult. [rom the ellects of nore than one pheomenonu. with te implicaion that 10 single physical process can explain all of the observatious.," Such an object lends credence to the hypothesis that the emission line regions associated with radio galaxies and the central galaxies in cluster cooling flows might also result from the effects of more than one phenomenon, with the implication that no single physical process can explain all of the observations."
 (GC LLLOA coulc| be an example of a disk galaxy ou its way to becoming ar elliptical. via iuteractious with its grop compatIOUS.," NGC 4410A could be an example of a disk galaxy on its way to becoming an elliptical, via interactions with its group companions."
 We thank Jaues Webb for help with the SARA observatns., We thank James Webb for help with the SARA observations.
 We are grateul to Catly Luholl (NLAST) for assisance with the NEWSIPS package aud ciscussious regarding he IUE data., We are grateful to Cathy Imhoff (MAST) for assistance with the NEWSIPS package and discussions regarding the IUE data.
 This research has made use of the NASA/IPAC Extragalactic Database (NED) whicl is operated by the Jet Propulsion Laboratory under contract with NASA., This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory under contract with NASA.
 Some of the data presented in this paper were obtained [rom the Multimission Archive at the Space Telescope Science Lisitute (MLAST)., Some of the data presented in this paper were obtained from the Multimission Archive at the Space Telescope Science Institute (MAST).
 STScl is operated by the Association for Universities for Research in Astronomy. Lic. under NASA contract. NÀS5-26555.," STScI is operated by the Association for Universities for Research in Astronomy, Inc. under NASA contract NAS5-26555."
 Support for MAST for i0n-HST data is provided by the ASA Ollice of Space Science via erant. NACO-7581 aud by other grants aud contracts., Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NAG5-7584 and by other grants and contracts.
 We woulcl also like to ackuowledge tlie use of the Double Spectrograpl at the Palomar Observatory (5-1neer). then under joint support by the Observatories of the Cartegie Institution of Washington aux the Caliornia Iustitute of Technology.," We would also like to acknowledge the use of the Double Spectrograph at the Palomar Observatory (5-meter), then under joint support by the Observatories of the Carnegie Institution of Washington and the California Institute of Technology."
 We also obtained data from facilities at the Ixitt Peak National Observatory. which is {μισά by the Natioual Science Foundaion aud operated by the Association of Unive‘sities for Research in Astronomy. Inc. B. J. 5. acknowedges support from NASA erant. AR-O837LOI-07A [rom the Space Telescope Scieuce Lustitute.," We also obtained data from facilities at the Kitt Peak National Observatory, which is funded by the National Science Foundation and operated by the Association of Universities for Research in Astronomy, Inc. B. J. S. acknowledges support from NASA grant AR-08374.01-97A from the Space Telescope Science Institute."
2007).,.
". IC 3418's disk has blue optical colors but red UV colors relative to its optical colors and no Ha, suggesting that star formation was truncated on order 100 Myr ago (Figure 2))."," IC 3418's disk has blue optical colors but red UV colors relative to its optical colors and no $\alpha$, suggesting that star formation was truncated on order 100 Myr ago (Figure \ref{SED}) )."
 The disk appears truncated in the FUV relative to the NUV (Figure 1)) and shows UV and optical color gradients (Figure 3)) consistent with star formation having ceased first in the outer disk., The disk appears truncated in the FUV relative to the NUV (Figure \ref{UV}) ) and shows UV and optical color gradients (Figure \ref{profiles}) ) consistent with star formation having ceased first in the outer disk.
" Though irregular, the disk shows no signs of tidal disturbance (no structured streams or arms of disk stars)."," Though irregular, the disk shows no signs of tidal disturbance (no structured streams or arms of disk stars)."
" IC 3418 is not detected in H (My1«109? Mo), though a diffuse component in the tail has not been excluded (Chungal. 2009).."," IC 3418 is not detected in H $M_{\rm H~\textsc{i}}<10^{6.9}~{\rm M}_{\odot}$ ), though a diffuse component in the tail has not been excluded \citep{Chung09}."
" If IC 3418 is on its first orbit through Virgo, as many cluster members appear to be, it was likely accreted on order 100 Myr ago; 500 Myr being a generic cluster infall time."," If IC 3418 is on its first orbit through Virgo, as many cluster members appear to be, it was likely accreted on order 100 Myr ago; 500 Myr being a generic cluster infall time."
" Together, these observations suggest IC 3418 was recently RP stripped by Virgo's intracluster medium (ICM)."," Together, these observations suggest IC 3418 was recently RP stripped by Virgo's intracluster medium (ICM)."
" We visually separate the tail into bright circular knots and diffuse, asymmetric, lower surface brightness regions."," We visually separate the tail into bright circular knots and diffuse, asymmetric, lower surface brightness regions."
 The resolution of limits our interpretation of these objects., The resolution of limits our interpretation of these objects.
" To measure luminosities, regions are defined using the outermost closed NUV surface brightness contour around each object, which are labeled in Figure 1.."," To measure luminosities, regions are defined using the outermost closed NUV surface brightness contour around each object, which are labeled in Figure \ref{UV}."
" A discrete set of contours was considered, but given their dense spacing on the sky this should not impact our results."," A discrete set of contours was considered, but given their dense spacing on the sky this should not impact our results."
" The bright knots have NUV luminosities (v f,) between 1.3x10°Lo and 3.4x106Lo.", The bright knots have NUV luminosities $\nu f_{\nu}$ ) between $1.3\times10^{5}~L_{\odot}$ and $3.4\times10^{6}~L_{\odot}$.
 The diffuse regions are redder in FUV-NUV than the knots; the average colors are 0.35+0.06 and —0.02+0.03 respectively (Table 1)., The diffuse regions are redder in FUV-NUV than the knots; the average colors are $0.35\pm0.06$ and $-0.02\pm0.03$ respectively (Table 1).
 The knots’ colors are consistent with ongoing star formation., The knots' colors are consistent with ongoing star formation.
" The total FUV luminosity of the tail, 3.3x107 Lo, corresponds to a star formation rate (SFR) of 6x107?Moyr- if star formation is ongoing (Salimetal. 2007)."," The total FUV luminosity of the tail, $3.3\times10^7~L_{\odot}$ , corresponds to a star formation rate (SFR) of $6\times10^{-3}~\rm{ M_{\odot}~yr^{-1}}$ if star formation is ongoing \citep{Salim07}."
. This is a lower limit; the knots may contain dust., This is a lower limit; the knots may contain dust.
 A knot is also defined (kl) using the innermost FUV contour within the streamer at the tail’s base (d1)., A knot is also defined (k1) using the innermost FUV contour within the streamer at the tail's base (d1).
" Its FUV-NUV color is —0.08+0.12, typical of the knots."," Its FUV-NUV color is $-0.08\pm0.12$, typical of the knots."
" Ha is found in the majority of the knots, indicating that star formation is ongoing."," $\alpha$ is found in the majority of the knots, indicating that star formation is ongoing."
 Ha is not observed in the three UV knots closest to IC 3418., $\alpha$ is not observed in the three UV knots closest to IC 3418.
" They may be detected in deeper Ho imaging if they have a top-light initial mass function, could be a signature of the tail's formation mechanism, or could indicate RPS of gas from the stellar knots themselves."," They may be detected in deeper $\alpha$ imaging if they have a top-light initial mass function, could be a signature of the tail's formation mechanism, or could indicate RPS of gas from the stellar knots themselves."
 Only one Ha region is observed away from a UVpeak., Only one $\alpha$ region is observed away from a UVpeak.
"the progenitor, but depend uniquely on the peculiarly low value of the CBM density.","the progenitor, but depend uniquely on the peculiarly low value of the CBM density."
" This led us to expand the traditional classification of GRBs to three classes: “genuine” short GRBs, “fake” or “disguised” short GRBs, and the remaining “long duration” ones."," This led us to expand the traditional classification of GRBs to three classes: “genuine” short GRBs, “fake” or “disguised” short GRBs, and the remaining “long duration” ones."
" A CBM density nj,~107 particles/cm? is typical of a galactic halo environment, and GRB 970228 was indeed found to be in the halo of its host galaxy (Sahuetal.1997;VanParadijsetal. 1997)."," A CBM density $n_{cbm} \sim 10^{-3}$ $^3$ is typical of a galactic halo environment, and GRB 970228 was indeed found to be in the halo of its host galaxy \citep{Sahu97,VP97}."
". We therefore proposed that the progenitors of this new class of “disguised” short GRBs are merging binary systems, formed by neutron stars and/or white dwarfs in all possible combinations, which spiraled out from their birth place into the halo (seeBernardinietal.2007;Caitoetal.2009;Kramer 2006)."," We therefore proposed that the progenitors of this new class of “disguised” short GRBs are merging binary systems, formed by neutron stars and/or white dwarfs in all possible combinations, which spiraled out from their birth place into the halo \citep[see][]{b07,c09,k06}."
. This hypothesis can also be supported by other observations., This hypothesis can also be supported by other observations.
" Assuming that the soft tail peak luminosity is directly related to the CBM density, GRBs displaying a prolonged soft tail should have a systematically smaller offset from the center of their host galaxy."," Assuming that the soft tail peak luminosity is directly related to the CBM density, GRBs displaying a prolonged soft tail should have a systematically smaller offset from the center of their host galaxy."
 Some observational evidence was found in this sense (Trojaetal. 2008)., Some observational evidence was found in this sense \citep{ta08}.
". However, the present sample of observations does not enable us to derive any firm conclusion that short GRBs with extended emission have smaller physical offsets than those without extended emission (Fongetal.2010;Berger2010)."," However, the present sample of observations does not enable us to derive any firm conclusion that short GRBs with extended emission have smaller physical offsets than those without extended emission \citep{fa10,b10}."
. We examine the possibility that GRB 071227 can also be classified as a “disguised” burst., We examine the possibility that GRB 071227 can also be classified as a “disguised” burst.
" We analyzed the observed light curves of this burst in the 15-50 keV_ bandpass, corresponding to the lowest band of the y-ray emission, detected by the BAT instrument on the satellite, and in the 0.3-10 keV energy band, corresponding to the X-ray component from the XRT instrument."," We analyzed the observed light curves of this burst in the $15$ $50$ keV bandpass, corresponding to the lowest band of the $\gamma$ -ray emission, detected by the BAT instrument on the satellite, and in the $0.3$ $10$ keV energy band, corresponding to the X-ray component from the XRT instrument."
" To model the CBM structure, we assume that r5, is a function of only the radial coordinate, rp,=Ncbm(r) (radial approximation)."," To model the CBM structure, we assume that $n_{cbm}$ is a function of only the radial coordinate, $n_{cbm}=n_{cbm}(r)$ (radial approximation)."
 The CBM is arranged in spherical shells of width ~10!°—1016 cm arranged in such a way that the corresponding modulation of the emitted flux closely resembles the observed shape., The CBM is arranged in spherical shells of width $\sim 10^{15}-10^{16}$ cm arranged in such a way that the corresponding modulation of the emitted flux closely resembles the observed shape.
 We assumed that the first short spike-like emission represents the P-GRB and the y-ray tail is the peak of the extended afterglow., We assumed that the first short spike-like emission represents the P-GRB and the $\gamma$ -ray tail is the peak of the extended afterglow.
" We therefore began the simulation in such a way that the extended afterglow light curve begins in coincidence with the peak of the P-GRB (about 1s), as shown in Fig. 2.."," We therefore began the simulation in such a way that the extended afterglow light curve begins in coincidence with the peak of the P-GRB (about $1$ s), as shown in Fig. \ref{f2}."
" To reproduce the observational data and the energetics observed for the P-GRB emission (Ej)~1.0x105! erg), we require the initial conditions E,=5.04x10?! erg and B=2.0x107."," To reproduce the observational data and the energetics observed for the P-GRB emission $E_{iso}\sim1.0\times10^{51}$ erg), we require the initial conditions $E_{tot}^{e^\pm}= 5.04\times10^{51}$ erg and $B=2.0\times10^{-4}$."
 In Figs., In Figs.
 2 and3 we plot the comparison of the GRB 071227 BAT and XRT data with the theoretical extended afterglow light curves., \ref{f2} and \ref{f3} we plot the comparison of the GRB 071227 BAT and XRT data with the theoretical extended afterglow light curves.
" We obtained a good result in the prompt emission for the 15— 50 keV bandpass (see Fig. 2)),"," We obtained a good result in the prompt emission for the $15$ $50$ keV bandpass (see Fig. \ref{f2}) ),"
" while, for 0.3-10 keV, we only succeeded in reproducing the first decaying part of the XRT light curve (see Fig. 3))."," while, for $0.3$ $10$ keV, we only succeeded in reproducing the first decaying part of the XRT light curve (see Fig. \ref{f3}) )."
" We assumed this to correspond to the possible onset of the ""plateau"" phase of the extended afterglow (Nouseketal.2006).", We assumed this to correspond to the possible onset of the “plateau” phase of the extended afterglow \citep{nu06}.
". From our simulation, the amount of energy stored in the P-GRB is found to be about 20% of the total energetics of the explosion."," From our simulation, the amount of energy stored in the P-GRB is found to be about $20$ of the total energetics of the explosion."
" Hence, this burst cannot be a short burst within the fireshell scenario."," Hence, this burst cannot be a short burst within the fireshell scenario."
 The baryon loading obtained (B=2.0x 1074) remains in the range of long duration GRBs., The baryon loading obtained $B=2.0\times10^{-4}$ ) remains in the range of long duration GRBs.
" This is a very critical value, because it is very close to the crossing point of the plot of the energetics of GRBs as a function of B (see Fig. 1))."," This is a very critical value, because it is very close to the crossing point of the plot of the energetics of GRBs as a function of $B$ (see Fig. \ref{f1}) )."
 This is the lowest baryon loading that we have ever found in our analysis within the fireshell scenario., This is the lowest baryon loading that we have ever found in our analysis within the fireshell scenario.
" From our analysis, we found a peculiar result for the average CBM density."," From our analysis, we found a peculiar result for the average CBM density."
" We obtained a density of n,=1.0x107? particles/cn? at the beginning of the process, later decreasing to m5,=1.0x107 particles/cm?."," We obtained a density of $n_{cbm}=1.0\times10^{-2}$ $^3$ at the beginning of the process, later decreasing to $n_{cbm}=1.0\times10^{-4}$ $^3$."
" This low average density, inferred from the analysis, is responsible for the strong deflation of the y-ray tail."," This low average density, inferred from the analysis, is responsible for the strong deflation of the $\gamma$ -ray tail."
" However, at the radius of about 2.0x10"" "," However, at the radius of about $2.0\times10^{17}$ "
sample 2004).. and the bright sub-sample of the Massive Cluster Survey (Bright ALACS: 2001: 2010)) we select a statistically complete. sample of 238 X-ray luminous clusters covering the redshift range 2<0.5.,"sample , and the bright sub-sample of the Massive Cluster Survey (Bright MACS; ; ) -- we select a statistically complete sample of 238 X-ray luminous clusters covering the redshift range $z<0.5$."
 OF these 238 clusters. 94 have follow-up or observations that we incorporate into the analysis.," Of these 238 clusters, 94 have follow-up or observations that we incorporate into the analysis."
 Fron the follow-up observations. we measure X-ray. Iuminositv. average Lomperature. and gas mass within roo. Phe gas mass is used as a proxy for total mass. using the finding of that the gas mass fraction. fas.=Moun. λίαν is a constant for hot. massive clusters (see also 4)).," From the follow-up observations, we measure X-ray luminosity, average temperature, and gas mass within $r_{500}$ The gas mass is used as a proxy for total mass, using the finding of that the gas mass fraction, $\fgas=\Mgas/\Mtot$ , is a constant for hot, massive clusters (see also )."
 Cluster measurements additionally provide a precise measure of cosmic distance. so we include the full data set and analysis of Allen et al.," Cluster measurements additionally provide a precise measure of cosmic distance, so we include the full data set and analysis of Allen et al."
 in this work., in this work.
 In addition to these cluster data sets. we incorporate CAMB. SNla and. BAO data.," In addition to these cluster data sets, we incorporate CMB, SNIa and BAO data."
 Our analysis of the CMD anisotropies uses S-vear data with the March 2008 version of the likelihood.2009)... as well as Areminute Cosmology Dolometer Array Receeiver (ACBAR) data at smaller angular scales ancl measurements of the CAIB polarization. from the Background maging of Cosmic Extragalactic Polarization (DICTI). instrument2010).," Our analysis of the CMB anisotropies uses 5-year data with the March 2008 version of the likelihood, as well as Arcminute Cosmology Bolometer Array Receiver (ACBAR) data at smaller angular scales and measurements of the CMB polarization from the Background Imaging of Cosmic Extragalactic Polarization (BICEP) instrument."
. The SNla results are derived from the Union compilation2008).. which includes data from a variety of sources (307 SNla in total: see references in D).," The SNIa results are derived from the Union compilation, which includes data from a variety of sources (307 SNIa in total; see references in )."
 Our analysis of BAO data uses the constraints on the ratio of the sound horizon to the distance scale at >=0.25 and z=0.35 derived by from the galaxy correlation function in 2011 and Sloan Digital Sky Survey data., Our analysis of BAO data uses the constraints on the ratio of the sound horizon to the distance scale at $z=0.25$ and $z=0.35$ derived by from the galaxy correlation function in 2dF and Sloan Digital Sky Survey data.
" Finally. we emplov in some cases a Gaussian prior on the Llubble parameter. f=0.742+0.036. based. on the results of Our results ave obtained via Markov. Chain Monte. Carlo (AICAIC). emploving the Metropolis sampler embedded. in the code of ""Phe. Alay 2008 release includes the S-vear and Union supernova data and analysis codes: an additional module implementing the analysis has also. been publicly released2005:; Further modifications were mace to include the likelihood codes for the NLP ancl BAO data."," Finally, we employ in some cases a Gaussian prior on the Hubble parameter, $h=0.742 \pm 0.036$, based on the results of Our results are obtained via Markov Chain Monte Carlo (MCMC), employing the Metropolis sampler embedded in the code of The May 2008 release includes the 5-year and Union supernova data and analysis codes; an additional module implementing the analysis has also been publicly released; Further modifications were made to include the likelihood codes for the XLF and BAO data."
 Phe CAIB and matter power spectrum calculations were performed. using the package of When analvzing the CAIB data. we marginalize over a plausible range in the amplitude of the Sunvaev-Zel'dovich signal due to galaxy clusters (0«;daz2: introduced. by 2007)).," The CMB and matter power spectrum calculations were performed using the package of When analyzing the CMB data, we marginalize over a plausible range in the amplitude of the Sunyaev-Zel'dovich signal due to galaxy clusters $0<\mysub{A}{SZ}<2$; introduced by )."
 Our analysis of the Union supernova sample of includes their treatment of svstematic uncertainties. which accounts for the cllects of Alalmeuist. bias and uncertainties in lighteurve fitting aud photometry (among others).," Our analysis of the Union supernova sample of includes their treatment of systematic uncertainties, which accounts for the effects of Malmquist bias and uncertainties in lightcurve fitting and photometry (among others)."
 The method used to analyze cluster cata is deseribed. in full by(2008)., The method used to analyze cluster data is described in full by.
.. Lt incorporates eencrous systematic allowances for instrument calibration (10 per cent). non-thermal pressure support2007).. the depletion of barvons in clusters with respect to the cosmic mean (20 per cent). and evolution with redshift) of the barvonic and stellar content of clusters (10 ancl 20 per cent).," It incorporates generous systematic allowances for instrument calibration (10 per cent), non-thermal pressure support, the depletion of baryons in clusters with respect to the cosmic mean (20 per cent), and evolution with redshift of the baryonic and stellar content of clusters (10 and 20 per cent)."
 The analwsis of the NLE data isdetailed inL., The analysis of the XLF data isdetailed in.
 The method combines cluster survey data with follow-up observations in an internally consistent way. rigorously accounting for the effects of Malmejuist ancl Eddington biases and. parameter degeneracies.," The method combines cluster survey data with follow-up observations in an internally consistent way, rigorously accounting for the effects of Malmquist and Eddington biases and parameter degeneracies."
 Conservative svstematic allowances are included to account for uncertainty in the predicted: cluster mass function. the overall cluster survey completeness ancl purity. and instrument calibration.," Conservative systematic allowances are included to account for uncertainty in the predicted cluster mass function, the overall cluster survey completeness and purity, and instrument calibration."
 As discussed in and illustrated in and 6. the ALE data. contribute to constraints on and through their measurement of ax.," As discussed in and illustrated in and \ref{sec:neffresults}, , the XLF data contribute to constraints on and through their measurement of $\sigma_8$."
 The posterior uncertainty on this measurement (from the ΧΙΙ alone) is 6 per cent. and is dominated by svstematic uncertainty. as described inL.," The posterior uncertainty on this measurement (from the XLF alone) is $\sim 6$ per cent, and is dominated by systematic uncertainty, as described in."
 Specifically. the uncertainty in ax is determined. by the accuracy with which cluster masses can be measured.," Specifically, the uncertainty in $\sigma_8$ is determined by the accuracy with which cluster masses can be measured."
 As detailed. inIL. we do no directly infer cluster masses at. που by assuming hyelrostatic equilibrium of the intracluster medium. a procedure which. when applied to a tvpical cluster. introduces a large am üghlv variable bias2007).," As detailed in, we do not directly infer cluster masses at $r_{500}$ by assuming hydrostatic equilibrium of the intracluster medium, a procedure which, when applied to a typical cluster, introduces a large and highly variable bias."
. Instead. we use the gas mass a sug. which can be measured without significant bias. as a ooxy for total mass.," Instead, we use the gas mass at $r_{500}$, which can be measured without significant bias, as a proxy for total mass."
 The proxy relation is calibrated. using 16 data of(2008).. which effectively consis X eas mass and total mass measurements for the subse X clusters where the hyclrostatic assumption is applicable (the most massive. cvnamically: relaxed: clusters)," The proxy relation is calibrated using the data of, which effectively consist of gas mass and total mass measurements for the subset of clusters where the hydrostatic assumption is applicable (the most massive, dynamically relaxed clusters)."
 Of the uvstematic allowances described above. the most relevant for us procedure are the allowances for non-thermal support and instrument calibration in the analysis.," Of the systematic allowances described above, the most relevant for this procedure are the allowances for non-thermal support and instrument calibration in the analysis."
 In addition. we account for uncertainty in the dillerence in between rosou (as measured by Allen ct al.)," In addition, we account for uncertainty in the difference in between $r_{2500}$ (as measured by Allen et al.)"
 and roo. as well as possible scatter in from cluster to cluster (see LL).," and $r_{500}$, as well as possible scatter in from cluster to cluster (see )."
 Ultimately. both our estimates of incüvidual masses and the mean cluster mass scale include a systematic error budget ol ~15 per cent.," Ultimately, both our estimates of individual masses and the mean cluster mass scale include a systematic error budget of $\sim 15$ per cent."
 We first. consider the case of a spatiallv [lat cosmology with non-zero neutrino mass., We first consider the case of a spatially flat cosmology with non-zero neutrino mass.
 For this mocdel. the joint 68.8 and 95.4 per centconfidence regions in the ax plane from the combination of CMD. fi... SNla and BAO," For this model, the joint 68.3 and 95.4 per centconfidence regions in the $\sigma_8$ plane from the combination of CMB, , SNIa and BAO"
"zero in the neutral line, because the polarity of the magnetic field changes from, e.g. positive to negative, but in spectra the V signal does not disappear completely due to the multi- penumbral structure (cf.?)..","zero in the neutral line, because the polarity of the magnetic field changes from, e.g. positive to negative, but in spectra the $V$ signal does not disappear completely due to the multi-component penumbral structure \citep[cf.][]{schlichenmaier+collados2002}."
" These profiles in the neutral line show not only two o-components in the circular polarization signal, but several local extrema (both minima and maxima)."," These profiles in the neutral line show not only two $\sigma$ -components in the circular polarization signal, but several local extrema (both minima and maxima)."
" To generate such complex patterns, the magnetic field has to be complex as well."," To generate such complex patterns, the magnetic field has to be complex as well."
 Appendix AppendixA: shows how such complex profiles can be created by the addition of two regular Stokes V profiles with opposite polarities., Appendix \ref{prof_constr} shows how such complex profiles can be created by the addition of two regular Stokes $V$ profiles with opposite polarities.
" This simple addition of profiles however does not tell, if the two magnetic field components leading to the V profiles are actually located in the same pixel."," This simple addition of profiles however does not tell, if the two magnetic field components leading to the $V$ profiles are actually located in the same pixel."
" If the spatial resolution of the polarimetric observations is insufficient to separate the flow filaments seen in high resolution observations from their surroundings, field components from two different spatial locations would be added up."," If the spatial resolution of the polarimetric observations is insufficient to separate the flow filaments seen in high resolution observations from their surroundings, field components from two different spatial locations would be added up."
" There however is an indicator that suggests that the field components are not spatially separated in the horizontal dimensions, but vertically interlaced, the Net Circular Polarization (NCP)."," There however is an indicator that suggests that the field components are not spatially separated in the horizontal dimensions, but vertically interlaced, the Net Circular Polarization (NCP)."
 A non-zero value of NCP — as observed — indicates discontinuities or at least strong gradients of field properties along the line of sight inside the formation height of spectral lines.," A non-zero value of NCP – as observed in the penumbra of sunspots \citep[e.g.][]{almeida+lites1992,solanki+montavon1993,valentin2000,mueller+etal2002,mueller+etal2006} – indicates discontinuities or at least strong gradients of field properties along the line of sight inside the formation height of spectral lines."
 Most of the observed properties of profiles in the penumbra of sunspots can be explained with theuncombed penumbra model suggested by ?.., Most of the observed properties of profiles in the penumbra of sunspots can be explained with the penumbra model suggested by \citet{solanki+montavon1993}.
" In this model, a more vertical field component winds around horizontal flow channels, which carry the Evershed flow."," In this model, a more vertical field component winds around horizontal flow channels, which carry the Evershed flow."
" The success of this model is related to the fact that it is able to explain the most prominent peculiarities of sunspots: a horizontal flow field in a non-horizontal field topology, the appearances of neutral lines in total linear polarization, L, and Stokes V, and the NCP."," The success of this model is related to the fact that it is able to explain the most prominent peculiarities of sunspots: a horizontal flow field in a non-horizontal field topology, the appearances of neutral lines in total linear polarization, $L$, and Stokes $V$, and the NCP."
" However, the model itself gives no reason, why its specific topology should exist in the penumbra."," However, the model itself gives no reason, why its specific topology should exist in the penumbra."
 The simulations of ? showed that such a configuration of embedded flow channels results from the temporal evolution of flux initially located at the boundary layer between the sunspot and the field-free surroundings., The simulations of \citet{schliche+jahn+schmidt1998} showed that such a configuration of embedded flow channels results from the temporal evolution of flux initially located at the boundary layer between the sunspot and the field-free surroundings.
 ? suggested that turbulent convection outside the spot pulls down field lines and thus produces the filamentary structure of the sunspot., \citet{thomas+weiss2004} suggested that turbulent convection outside the spot pulls down field lines and thus produces the filamentary structure of the sunspot.
" In both cases, the penumbra consists of similar embedded flow channels, but created by different mechanisms."," In both cases, the penumbra consists of similar embedded flow channels, but created by different mechanisms."
" ? and ? recently suggested a completely different model, where the intensity filaments are related to the existence of field-free gaps below the visible surface layer."," \citet{spruit+scharmer2006} and \citet{scharmer+spruit2006}
 recently suggested a completely different model, where the intensity filaments are related to the existence of field-free gaps below the visible surface layer."
" In this paper, I want to show that a rather simple uncombed model using two depth-independent magnetic components is to reproduce simultaneous observations in infrared and visible spectral lines with their different responses to magnetic fields."," In this paper, I want to show that a rather simple uncombed model using two depth-independent magnetic components is to reproduce simultaneous observations in infrared and visible spectral lines with their different responses to magnetic fields."
 The inversion setup is described after the observations and data reduction (Sect. 2))., The inversion setup is described after the observations and data reduction (Sect. \ref{sec_obs}) ).
 I study average field properties and their radial variation in Sect. 4.., I study average field properties and their radial variation in Sect. \ref{sec_results}. .
 I then deduce a geometrical model of the sunspot by integrating the surface inclination of the fields (Sect. 5))., I then deduce a geometrical model of the sunspot by integrating the surface inclination of the fields (Sect. \ref{sec_3dmodel}) ).
" The physical properties of the model like field strength, velocity, or field orientation, correspond to the best-fit model atmospheres necessary to reproduce the observed spectra."," The physical properties of the model like field strength, velocity, or field orientation, correspond to the best-fit model atmospheres necessary to reproduce the observed spectra."
" I shortly investigate the temporal evolution in Sect. 6,,"," I shortly investigate the temporal evolution in Sect. \ref{tempevol},"
 with emphasis on which parts change with time and which do not., with emphasis on which parts change with time and which do not.
" In the discussion (Sect. 7)),"," In the discussion (Sect. \ref{sec_disc}) ),"
 I address the question of penumbral heat transport in the context of the results of the previous analysis., I address the question of penumbral heat transport in the context of the results of the previous analysis.
 Appendix AppendixA: shows how complex profiles can be created with simple assumptions., Appendix \ref{prof_constr} shows how complex profiles can be created with simple assumptions.
 Appendix AppendixB: shows an example of the integration along a single cut through the penumbra and the full 3-Dmodel from different viewing angles., Appendix \ref{appa} shows an example of the integration along a single cut through the penumbra and the full 3-Dmodel from different viewing angles.
 Appendix AppendixC: describes the analysis of a time series of, Appendix \ref{appb} describes the analysis of a time series of
telescope. while Fig.,"telescope, while Fig."
 3 shows the corresponding lightcurve at the highest energy range (1.2-10 TeV)., 3 shows the corresponding lightcurve at the highest energy range (1.2-10 TeV).
 The time lag between the two energy bands ts about three minutes., The time lag between the two energy bands is about three minutes.
 The chosen flaring episode is too short to approach the stationary state corresponding to the new increased injection., The chosen flaring episode is too short to approach the stationary state corresponding to the new increased injection.
 Fig., Fig.
| shows. in addition to the pre-flare steady state. the multi-wavelength spectra at the instance where the fluence is maximum at the hard TeV band (long dashed line).,"\ref{fig1} shows, in addition to the pre-flare steady state, the multi-wavelength spectra at the instance where the fluence is maximum at the hard TeV band (long dashed line)."
 Fig., Fig.
 4 shows the the derived TeV hardness ratio (defined as ΕΕ—10TeV)/F(0.25 1TeV)) versus the TeV flux., \ref{fig4} shows the the derived TeV hardness ratio (defined as $F(1-10 \mathrm{TeV})/F(0.25-1 \mathrm{TeV})$ ) versus the TeV flux.
 This. as expected. is anti-clockwise.," This, as expected, is anti-clockwise."
 In the present paper we have attempted to explain the rapid variability as observed by the MAGIC telescope in 2005 with à one-zone model which includes particle acceleration plus radiation., In the present paper we have attempted to explain the rapid variability as observed by the MAGIC telescope in 2005 with a one-zone model which includes particle acceleration plus radiation.
 According to this particles are injected into some acceleration mechanism at low energies and subsequently they accelerated to high energies., According to this particles are injected into some acceleration mechanism at low energies and subsequently they accelerated to high energies.
 They also radiate synchrotron and SSC radiation. thus losing energy.," They also radiate synchrotron and SSC radiation, thus losing energy."
 The acceleration process saturates eventually at some particle energy where it 1s balanced by the radiative losses., The acceleration process saturates eventually at some particle energy where it is balanced by the radiative losses.
 In this picture. the basic mechanism for producing hard lags as the one observed by MAGIC (?).. could be a brief episode of enhanced particle injection.," In this picture, the basic mechanism for producing hard lags as the one observed by MAGIC \citep{albert07}, could be a brief episode of enhanced particle injection."
 As the freshly injected particles move to high energies they will radiate first soft photons and later harder ones. thus creating a hard lag flare.," As the freshly injected particles move to high energies they will radiate first soft photons and later harder ones, thus creating a hard lag flare."
 This episode occurs on top of a quasi steady state that the particles were assumed to have achieved in the pre-flare state and to which they return in post-flare., This episode occurs on top of a quasi steady state that the particles were assumed to have achieved in the pre-flare state and to which they return in post-flare.
 Thus according to this picture. MAGIC has caught electron acceleration at work.," Thus according to this picture, MAGIC has caught electron acceleration at work."
 While hard lags can be explained by increasing the particle injection at low energies. the observed spectral hardening of the flare requires that. in addition. the acceleration timescale and/or the magnetic field strength should be reduced over their pre-flare values.," While hard lags can be explained by increasing the particle injection at low energies, the observed spectral hardening of the flare requires that, in addition, the acceleration timescale and/or the magnetic field strength should be reduced over their pre-flare values."
 Even if variation in one of the above parameters can produce a spectral hardening. varying both simultaneously improves the lighteurve fit.," Even if variation in one of the above parameters can produce a spectral hardening, varying both simultaneously improves the lightcurve fit."
 Given. however. the complexity of the overall flaring activity of TeV blazars. we consider the issue to be open. requiring more detailed observations.," Given, however, the complexity of the overall flaring activity of TeV blazars, we consider the issue to be open, requiring more detailed observations."
 The parameters used here are quite similar to the ones used in ?.., The parameters used here are quite similar to the ones used in \citet{konopelkoetal03}.
 Especially we note that in both fits there was a need for a high value of the Doppler factor 9. In the present case this, Especially we note that in both fits there was a need for a high value of the Doppler factor $\delta$ In the present case this
cllicient ancl accurate. even when the tree particles are random. cistributed amongst the SCL particles.,efficient and accurate even when the tree particles are random distributed amongst the SCF particles.
 This is the Worst case scenario in terms of elliciency., This is the worst case scenario in terms of efficiency.
 During the force calculation on an SCE particle it will form a large. list of tree cell interactions., During the force calculation on an SCF particle it will form a large list of tree cell interactions.
 Now we move to a case where the tree particles formi some clistinet structure within the SCF svstem. that of a disk embedded: within a halo.," Now we move to a case where the tree particles form some distinct structure within the SCF system, that of a disk embedded within a halo."
 The study of disk evolution in a non-interacting svstem has been the focus of much research. and. requires a good. deal more attention than a mere subsection to investigate it Cully., The study of disk evolution in a non-interacting system has been the focus of much research and requires a good deal more attention than a mere subsection to investigate it fully.
 Here we content ourselves with an example of how the varving of Niue allects the stability of the disk., Here we content ourselves with an example of how the varying of $N_{\rm halo}$ affects the stability of the disk.
 We construct combined diskhalobulge models using the method. of Dubinski Ixuijken (1995)., We construct combined disk–halo–bulge models using the method of Dubinski Kuijken (1995).
 The ratio of masses of the components was disk:bulge:halo = 1.00:0.37:12.80. the scale radius of the disc was set to Ry=1.0.," The ratio of masses of the components was disk:bulge:halo = 1.00:0.37:12.80, the scale radius of the disc was set to $R_d=1.0$."
 The number of disk. particles in each case was 6000. and the number of bulge particles was 2000.," The number of disk particles in each case was 6000, and the number of bulge particles was 2000."
 In four runs the number of halo particles was varied from. 13000. to 107., In four runs the number of halo particles was varied from 13000 to $10^5$.
" Each time the disk particles were assigned to the ""Tree system and the rest to the SCE system.", Each time the disk particles were assigned to the Tree system and the rest to the SCF system.
 Fieure 12. demonstrates increased. stability as number of halo particles. Nig. is increased.," 	 Figure \ref{spiral} demonstrates increased stability as number of halo particles, $N_{\rm halo}$ is increased."
 In. particular at Nia=100000 Little structure has formed. in the disk and is unchanged apart from a slight thickening. whereas for Nie=13000 the clisk is particularly unstable to warping. and spiral structure seems to be developing.," In particular at $N_{\rm
halo}=100000$ little structure has formed in the disk and is unchanged apart from a slight thickening, whereas for $N_{\rm halo}=13000$ the disk is particularly unstable to warping, and spiral structure seems to be developing."
 The thickening of the disk shown in Figure 11.., The thickening of the disk shown in Figure \ref{zdisp}.
" Phese figures confirm what we would expect as we change the number of Nya, in a self-consistent. simulation.", These figures confirm what we would expect as we change the number of $N_{\rm halo}$ in a self-consistent simulation.
 With fewer SCE particles noise in the SCE expanded potential will cause I[uctuations in the halo potential to develop. and thus cause the disk to become unstable to warping.," With fewer SCF particles noise in the SCF expanded potential will cause fluctuations in the halo potential to develop, and thus cause the disk to become unstable to warping."
 Penetrating encounters. between stellar svstems provide many interesting scenarios which one could fruitfully model with our hybrid code., 	 Penetrating encounters between stellar systems provide many interesting scenarios which one could fruitfully model with our hybrid code.
 Representing interacting svstenis separately with the SCE anc Tree. methods. invites the question of how well SCETREE describes the behavicur of SCE and ‘Tree particles interacting with each other in οποίας wavs., Representing interacting systems separately with the SCF and Tree methods invites the question of how well SCFTREE describes the behaviour of SCF and Tree particles interacting with each other in differing ways.
 We address this issue by investigating the ability of the code to tackle dynamical friction. specifically » running a few simulations of the sinking satellite sort.," We address this issue by investigating the ability of the code to tackle dynamical friction, specifically by running a few simulations of the sinking satellite sort."
 SCF is used to model the primary. ancl Tree used. for the satellite.," SCF is used to model the primary, and Tree used for the satellite."
 Although the force on each SCE particle due to he ‘Tree particles is directly calculated: (subject. to. the olerance criterion). he Tree particles only respond. to he SCE particles indirectly. via the expanded. field.," Although the force on each SCF particle due to the Tree particles is directly calculated (subject to the tolerance criterion), the Tree particles only respond to the SCF particles indirectly via the expanded field."
 One might initially be concerned that the lack of direct. particlexwticle interactions which account for the deceleration. of he satellite will invalidate the use of this code in. such cases. however we show that so long as the SCE expansion is truncated after a reasonable number of terms dynamical Tiction is acceptably treated. Fiegure(13))," One might initially be concerned that the lack of direct particle--particle interactions which account for the deceleration of the satellite will invalidate the use of this code in such cases, however we show that so long as the SCF expansion is truncated after a reasonable number of terms dynamical friction is acceptably treated. \ref{sink}) )"
 demonstrates the dependence of dsnamical riction on the number of expansion cocllicients used. in, demonstrates the dependence of dynamical friction on the number of expansion coefficients used in
"disk. we expect it to be accompanied. by a 7rellection"" component due to Compton scattering in the disk GGoeorge Fabian 1991: Matt 11991).","disk, we expect it to be accompanied by a “reflection” component due to Compton scattering in the disk George Fabian 1991; Matt 1991)."
 The presence of such a component does not alfect our conclusions regarding the line. variability., The presence of such a component does not affect our conclusions regarding the line variability.
 Including a reflection component appropriate for a disk inclined at 21deg. with a covering fraction of 2x reduces both line Luxes by ~20 per cen to 2.10.3 and 120.2 10+ ph em 3 respectively.," Including a reflection component appropriate for a disk inclined at $27\deg$, with a covering fraction of $2\pi$ reduces both line fluxes by $\sim 20$ per cent to $2.1\pm 0.3$ and $1.2\pm 0.2$ $10^{-4}$ ph $^{-2}$ $^{-1}$ respectively."
 Clearly the change is still highly significant., Clearly the change is still highly significant.
 Note. however. that the best-fit power-law index is steeper. with E1.9. when reflection is included.," Note, however, that the best-fit power-law index is steeper, with $\Gamma\sim 1.9$, when reflection is included."
 These cllects have already. been noted by N96., These effects have already been noted by N96.
 Finally. we have investigated whether small variations in the line shape alfect our results.," Finally, we have investigated whether small variations in the line shape affect our results."
 Although πο large changes are evident in Fig., Although no large changes are evident in Fig.
 1. we have allowed for this by allowing q to be free in the fit to each dataset.," 1, we have allowed for this by allowing $q$ to be free in the fit to each dataset."
 Fig., Fig.
 3 shows the change in the confidence surfaces when we allow the line profile to vary., 3 shows the change in the confidence surfaces when we allow the line profile to vary.
 Clearly the parameter. values are not. as strongly constrained as when q was fixed. however. we still conclude that the line is variable.," Clearly the parameter values are not as strongly constrained as when $q$ was fixed, however, we still conclude that the line is variable."
 We have presented evidence for variability of the iron Ίνα emission. line in. NGC 3516., We have presented evidence for variability of the iron $\alpha$ emission line in NGC 3516.
 The line lux changes proportionately with the continuum over à; ~ vr baseline., The line flux changes proportionately with the continuum over a $\sim 1$ yr baseline.
 This sets a firm upper limit of 1 lever (ys~1045 cm) [or the extent of the line-producing region., This sets a firm upper limit of 1 lt-yr $R_{\rm max} \sim 10^{18}$ cm) for the extent of the line-producing region.
 It is likely to be much smaller than this: the duration of the individual observations is 1 d and if the D'uorescing material extended over a region much Larger than this. the fact that the line changes bv the same factor as the continuum would have to » considered as co-incidental. as it would be responding to he continuum averaged over the previous Rinasfe.," It is likely to be much smaller than this; the duration of the individual observations is $\sim 1$ d and if the fluorescing material extended over a region much larger than this, the fact that the line changes by the same factor as the continuum would have to be considered as co-incidental, as it would be responding to the continuum averaged over the previous $R_{\rm max}/c$."
 As NGC 3516 shows strong short time scale (ic. intra-dav) variability (Ixolman 11993: Nancdra 11996a) we therefore conclude that the line is most likely. xocduced in a region «1 [t day in extent.," As NGC 3516 shows strong short time scale (i.e. intra-day) variability (Kolman 1993; Nandra 1996a), we therefore conclude that the line is most likely produced in a region $<1$ lt day in extent."
 This agrees very well with the predictions of accretion disk mocels. which are required to explain the broad. asvmimetrie profiles (Tanaka 11995: NOG).," This agrees very well with the predictions of accretion disk models, which are required to explain the broad, asymmetric profiles (Tanaka 1995; N96)."
" Assuming for the moment that Pia,<1 Lt day). this corresponds to a distance of ~200/A4.Bh eravitational ασ, where A is the black hole mass in units"," Assuming for the moment that $R_{\rm max}<1$ lt day), this corresponds to a distance of $\sim 200/M_{8}\ R_{\rm g}$ gravitational radii, where $M_{8}$ is the black hole mass in units"
"motion between LIP 6445 A and B between the central llipparcos epoch and our observation: LIP 6445 A anc DB have a distance of 120415 pe and spectral types F45V and WIV. hence a total mass of ~L8 M.. so that maximum possible orbital motion (for a cireular orbit) in 18.25. ves epoch cdillerence results in a change of 25.9 mas (milli are sec) in separation and 0.28"" in PA.","motion between HIP 6445 A and B between the central Hipparcos epoch and our observation: HIP 6445 A and B have a distance of $120 \pm 15$ pc and spectral types F4.5V and K1V, hence a total mass of $\sim 1.8$ $_{\odot}$, so that maximum possible orbital motion (for a circular orbit) in 18.25 yrs epoch difference results in a change of 25.9 mas (milli arc sec) in separation and $0.28^{\circ}$ in PA."
 The measurement of the separation between LIL? 6445 A and D in the NACO images gives 629.88+0.14. pixels., The measurement of the separation between HIP 6445 A and B in the NACO images gives $629.88 \pm 0.14$ pixels.
 Compared to the Hipparcos data. and taking into account the errors from orbital motion in LID? 6445 A|D. the NACO pixel scale is 13.2724t049 mas/pixel (half the error budget from possible orbital motion in HIP. 6445 A and B) and the detector orientation for those images of 0.31d0.307. which have to be added to all PA measurements on uncorrected images (two thirds of the error budget (rom possible orbital motion in LIP 6445 A and D).," Compared to the Hipparcos data, and taking into account the errors from orbital motion in HIP 6445 A+B, the NACO pixel scale is $13.272 \pm 0.049$ mas/pixel (half the error budget from possible orbital motion in HIP 6445 A and B) and the detector orientation for those images of $0.31 \pm 0.30 ^{\circ}$, which have to be added to all PA measurements on uncorrected images (two thirds of the error budget from possible orbital motion in HIP 6445 A and B)."
 With this pixel scale. we can convert the separation measured between ELE.7329 A and B on the detector to 4199-2531 mas and obtain a true. corrected A between A and B of 166.99+0.30 ," With this pixel scale, we can convert the separation measured between HR 7329 A and B on the detector to $4199 \pm 31$ mas and obtain a true, corrected PA between A and B of $166.99 \pm 0.30 ^{\circ}$."
We retrieved. all archival UST and. ESO data. and reduced them in a similar way as above., We retrieved all archival HST and ESO data and reduced them in a similar way as above.
 In cases. where he object LR. 7329 D. was Located. within the PSE of LE 7329 A. we first subtracted the PSE of LR. 7329 A. before we measured the position anc magnitude of HIt 7329 D (using a dedicated LOL software. A. Seifahrt. priv.," In cases, where the object HR 7329 B was located within the PSF of HR 7329 A, we first subtracted the PSF of HR 7329 A, before we measured the position and magnitude of HR 7329 B (using a dedicated IDL software, A. Seifahrt, priv."
 comumn.)., comm.).
 Since no astrometric standards were observed in nights. for which we took data from archives. we used the pixel scale rom the header (fits header keyword ESO.INS.PINSCALE eives 13.26 mas/pix without error bar): for the archival SACO S13 data from. 2004 to 2008. we used the mecdians of the error bars from seven nights [rom 2004 to 2007 (Neuháuuser ct al.," Since no astrometric standards were observed in nights, for which we took data from archives, we used the pixel scale from the header (fits header keyword ESO.INS.PIXSCALE gives 13.26 mas/pix without error bar); for the archival NACO S13 data from 2004 to 2008, we used the medians of the error bars from seven nights from 2004 to 2007 (Neuhäuuser et al."
 2008). namely 0.053 mas/pix as error xw for the pixel scale. from the header.," 2008), namely $\pm 0.053$ mas/pix as error bar for the pixel scale from the header."
 For 2004. June. which is close to epoch 2004.3 in Table 1. Neuhauuser e al. (," For 2004 June, which is close to epoch 2004.3 in Table 1, Neuhäuuser et al. ("
2005) eave 13.230.00 mas/pix and Egecnhecreer et al. (,2005) gave $13.23 \pm 0.05$ mas/pix and Eggenberger et al. (
2007) gave 13.18here£0.06 mas/pix. both for NACO $13. so hat our choice of 13.26+0.053. mas/pix is consisten with both of them.,"2007) gave $13.18 \pm 0.06$ mas/pix, both for NACO S13, so that our choice here of $13.26 \pm 0.053$ mas/pix is consistent with both of them."
 For the S27 opties with the L-band cata from 2008.3. (Lable we use the pixel scale [rom he header and twice the S13 error bar. Le. 27.19+0.1 mas/pixel.," For the S27 optics with the L-band data from 2008.3 (Table 1), we use the pixel scale from the header and twice the S13 error bar, i.e. $27.19 \pm 0.11$ mas/pixel."
" For the detector orientation. we have to assume correct alignment. but use the median alignment error. of 40.291"" (Neuhauuser et al."," For the detector orientation, we have to assume correct alignment, but use the median alignment error of $\pm 0.291 ^{\circ}$ (Neuhäuuser et al."
 2008)., 2008).
 We include here the data with short individual integration time (0.36 sec). nuwhere LII. 7329 A is not saturated. for best. position measurements. and those with long individual integration time m(25 sec). where LR 7329 A is saturated for best sensitivity and dynamic range for detecting unknown further companion candidates: during the observations with the 25-sec individual integration times. the field rotated from image to image. so that we de-rotatec all images before adding them up.," We include here the H-band data with short individual integration time (0.36 sec), where HR 7329 A is not saturated, for best position measurements, and those with long individual integration time (25 sec), where HR 7329 A is saturated for best sensitivity and dynamic range for detecting unknown further companion candidates; during the observations with the 25-sec individual integration times, the field rotated from image to image, so that we de-rotated all images before adding them up."
 The LIST data were reduced in the wav: HI 7329 was observed with LIST NICMOS2 at lollowingepoch 1998.40 and 2007.75. both in coronagraphic mode placing LIU 7329 4 behind an occulting hole.," The HST data were reduced in the following way: HR 7329 was observed with HST NICMOS 2 at epoch 1998.49 and 2007.75, both in coronagraphic mode placing HR 7329 A behind an occulting hole."
 After retrieving the pre-calibrated data from the LIST archive. we subtracted the PSE of A from the images to attenuate residual speckle noise.," After retrieving the pre-calibrated data from the HST archive, we subtracted the PSF of A from the images to attenuate residual speckle noise."
" For the 1998.49. epoch we used two images available with a 29.9"" roll angle.", For the 1998.49 epoch we used the two images available with a $29.9 ^{\circ}$ roll angle.
 For the2007take5 epoch we used a reference star of similar spectral tvpe n with the same instrunient configuration for subtraction. because there were no rolled images available.," For the 2007.75 epoch we used a reference star of similar spectral type taken with the same instrument configuration for subtraction, because there were no rolled images available."
 Due to A being behind the occulting hole of the NIC2 camera. its position could. not. be measured directly. but could be caleulatecl using its position in the acquisition image and the telescope ollset to place it behind the occulting hole given in the image headers.," Due to A being behind the occulting hole of the NIC2 camera, its position could not be measured directly, but could be calculated using its position in the acquisition image and the telescope offset to place it behind the occulting hole given in the image headers."
" We corrected the positions for geometric distortion using SMAD . [ου the 1998.49 epoch and SMOV3b data for the""m 2tn5 epoch. respectively."," We corrected the positions for geometric distortion using SMOV2 data for the 1998.49 epoch and SMOV3b data for the 2007.75 epoch, respectively."
 We then calculated separation in image coordinates., We then calculated separation and PA in image coordinates.
 Since the NIC? pixel scale is stable since carly 1997. we derived it by averaging the measurements from [ate 1997 and 1998 as well as the measurements from 2002.," Since the NIC2 pixel scale is stable since early 1997, we derived it by averaging the measurements from late 1997 and 1998 as well as the measurements from 2002."
 We took into account that the NIC2 detector is sliethly tilted towards its focal plane. thus vielding slightly different pixel scales in x ancl v direction.," We took into account that the NIC2 detector is sligthly tilted towards its focal plane, thus yielding slightly different pixel scales in x and y direction."
 The results are 76.1140.15 mas/pix in x and 75.43dE0.14 mas/pix in v. The orientation of the NIC2 detector v-axis was retrieved from the individual image headers., The results are $76.11 \pm 0.15$ mas/pix in x and $75.43 \pm 0.14$ mas/pix in y. The orientation of the NIC2 detector y-axis was retrieved from the individual image headers.
 We also observed LIU 7329 with the HX imager Son OL Isaac (Soll) at the 3.5m. ESO New ‘Technology Telescope (NIL) in 2000 (see COL) ancl 2009, We also observed HR 7329 with the IR imager Son OF Isaac (SofI) at the 3.5m ESO New Technology Telescope (NTT) in 2000 (see G01) and 2009.
 We reduced the data analogously as described above lor NACO., We reduced the data analogously as described above for NACO.
" The pixel scale was determined to be 287.97£0.21 mas/pix and the detector orientation to be 0.02+0.04"" (to be added: to. clirect measurements).", The pixel scale was determined to be $287.97 \pm 0.21$ mas/pix and the detector orientation to be $0.02 \pm 0.04 ^{\circ}$ (to be added to direct measurements).
 Before measuring the position of ΕΙ 7329 D. and hence separation and PA between ΗΝ 7329 A and D. we subtracted the PSE of Ht 7329 A with LDL.," Before measuring the position of HR 7329 B, and hence separation and PA between HR 7329 A and B, we subtracted the PSF of HR 7329 A with IDL."
 All observations used here are Listed in Table 1, All observations used here are listed in Table 1.
 ‘Lo check for common proper motion ancl orbital motion. we use the ... data from Lipparcos: Proper motion fccos(0)=25.57+L21 mmas/vr and ys=82.71£014 mas/ve. distance 47> pc. both for LR 7329 A. data from Perrvman et al. (," To check for common proper motion and orbital motion, we use the astrometric data from Hipparcos: Proper motion $\mu _{\alpha} \cdot \cos (\delta) = 25.57 \pm 0.21$ mas/yr and $\mu _{\delta} = -82.71 \pm 0.14$ mas/yr, distance $47.7 \pm 1.5$ pc, both for HR 7329 A, data from Perryman et al. ("
It097) and van Leeuwen (2007). whose values dilfer slightly. from cach other. but. are. compatible within the error bars.,"1997) and van Leeuwen (2007), whose values differ slightly from each other, but are compatible within the error bars."
 We show in Figs., We show in Figs.
 1 and 2 the astrometric data from ‘Table 1. which reject the hypothesis that LIU 7329 D would have been a non-moving background object“0 with z21a. so that we can continue to regard Li A and D as common proper motion pair.," 1 and 2 the astrometric data from Table 1, which reject the hypothesis that HR 7329 B would have been a non-moving background object with $\ge 21~\sigma$, so that we can continue to regard HR 7329 A and B as common proper motion pair."
 We also show the expected maximal orbital motion for a circular orbit. of 1Η 7329 B around A. being <S.SA mas/vr change in separation for an edgc-on orbit (Fig.," We also show the expected maximal orbital motion for a circular orbit of HR 7329 B around A, being $\le 8.84$ mas/yr change in separation for an edge-on orbit (Fig."
 1) and <0.189 /vr change in PA for an pole-on orbit (Fig., 1) and $\le 0.189^{\circ}$ /yr change in PA for an pole-on orbit (Fig.
 2)., 2).
 We do not see any change in PA (Fig., We do not see any change in PA (Fig.
 2) and conclude that the (2D) orbit (on skv) is not. pole- at all., 2) and conclude that the (2D) orbit (on sky) is not pole-on at all.
 The non-reducedfi47 for the separation fit. (Fig., The non-reduced $\chi ^{2}$ for the separation fit (Fig.
 1) is lower than for the PA (Fig., 1) is lower than for the PA fit (Fig.
 2) - possibly indicating that the separation errors are overestimated. while PA errors are not overestimated.," 2) - possibly indicating that the separation errors are overestimated, while PA errors are not overestimated."
 Εις could. be due to radial NACO detector distortions. which are negligible for PA. values.," This could be due to radial NACO detector distortions, which are negligible for PA values."
 Since the separation of the astrometric calibrator is higher than for the LER 7329 svstem. increasederrors are introduced into the racial error budget (separation errors) bybackroundjittering. which has to be done in order to remove the in the LR in both cases.," Since the separation of the astrometric calibrator is higher than for the HR 7329 system, increased errors are introduced into the radial error budget (separation errors) by jittering, which has to be done in order to remove the background in the IR in both cases."
 The possibly detected. change in separation due to orbital motion (2.91+2.41 mas/vr) is much smaller than the expected maximum orbital motion for a circular edge-on orbit (Fig., The possibly detected change in separation due to orbital motion $2.91 \pm 2.41$ mas/yr) is much smaller than the expected maximum orbital motion for a circular edge-on orbit (Fig.
 1). so that we conclude that," 1), so that we conclude that"
Diving TOO3 the object further reduced its bursting activity. aud no Type II bursts were seen throughout the observation.,"During TOO3 the object further reduced its bursting activity, and no Type II bursts were seen throughout the observation."
 The bestfit model spectrum was still an absorbed 2BB (Table 1)., The best–fit model spectrum was still an absorbed 2BB (Table 1).
 As in the case of TOO2. no irou emission line at 6.5 keV was found.," As in the case of TOO2, no iron emission line at 6.5 keV was found."
 The RB was instead no louger visible in MECS/LECS images duriug TOOI., The RB was instead no longer visible in MECS/LECS images during TOO4.
 Stray light from N35LO prevented us to ect a deep observation of the source., Stray light from GX354-0 prevented us to get a deep observation of the source.
 The 3o upper lait to the RB Nray emission was 1.5.10 1 «πο 27s + : inthe A2-10 τον cnerey baud., The $\sigma$ upper limit to the RB X–ray emission was $\times$ $^{-12}$ erg $^{-2}$ $^{-1}$ in the 2-10 keV energy band.
new IRAC data force us to conclude that there is a thermal inversion in the atmosphere of IID 209458h at altitude and that we are indeed seeing water in the 4—8 gap. but ineinission.,"new IRAC data force us to conclude that there is a thermal inversion in the atmosphere of HD 209458b at altitude and that we are indeed seeing water in the $4-8$ gap, but in."
 In fact. we now expect the water absorption features of the older default theory to be (lipped into emission features throughout the entire near- (ο mid-inlrared wavelength range.," In fact, we now expect the water absorption features of the older default theory to be flipped into emission features throughout the entire near- to mid-infrared wavelength range."
 Therefore. we find that. contrary to the conclusion of Richardsonetal.(2007).. the flatness or slight rise of their IRS spectrum near ~7.8 in fact supports the presence of abundant atmospheric water. because this spectral region is at the edge of a strong water band in emission.," Therefore, we find that, contrary to the conclusion of \citet{rich07}, the flatness or slight rise of their IRS spectrum near $\sim$ 7.8 in fact supports the presence of abundant atmospheric water, because this spectral region is at the edge of a strong water band in emission."
 A temperature inversion might also naturally explain the (wo emission features tentatively identified by Richardsonetal.(2007)., A temperature inversion might also naturally explain the two emission features tentatively identified by \citet{rich07}.
. Burrowsetal.(2007b) explore the theoretical and model consequences of these new IRAC data in more depth., \citet{bur07b} explore the theoretical and model consequences of these new IRAC data in more depth.
 The idea that the spectrum ofa strongly irradiated extrasolar giant planet could manifest water emission features was presaged by IIubenyetal.(2003) and. Burrowsetal.(2006).. who discussed a bifurcation in the atmosphere solution. but we still do not know the nature of the stratospheric absorber responsible for this heating.," The idea that the spectrum of a strongly irradiated extrasolar giant planet could manifest water emission features was presaged by \citet{hub03} and \citet{bur06}, who discussed a bifurcation in the atmosphere solution, but we still do not know the nature of the stratospheric absorber responsible for this heating."
 Roweetal.(2006.2007) report a value of 0.0440.04 for the geometric albedo of the planet at visible wavelengths. indicating that the stratospheric absorber must absorb much more in the optical (han the infrared. as predicted by Hubenyetal.(2002).," \citet{rowe06,rowe07} report a value of $0.04\pm0.04$ for the geometric albedo of the planet at visible wavelengths, indicating that the stratospheric absorber must absorb much more in the optical than the infrared, as predicted by \citet{hub03}."
.. This eliminates many (vpes of clouds. which tend to be reflective at optical wavelengths.," This eliminates many types of clouds, which tend to be reflective at optical wavelengths."
 Cowanetal.(2007). placed a 26 upper limit of 0.0015 on the size of the phase variation for this planet at 8same: when compared to the eclipse depth of 0.00240£0.00026 described in this paper. Chis indicates that the flux from the night side must be at least of the flux from the day side. which would indicate relatively efficient circulation in the atmosphere at the level of the 8 photosphere.," \citet{cow07} placed a $\sigma$ upper limit of 0.0015 on the size of the phase variation for this planet at 8; when compared to the eclipse depth of $0.00240\pm0.00026$ described in this paper, this indicates that the flux from the night side must be at least of the flux from the day side, which would indicate relatively efficient circulation in the atmosphere at the level of the 8 photosphere."
 Because high-altitude clouds or other opaque lavers would shift the location of the 8 photosphere. this provides additional constraints on (he nature of (he unknown stratospheric absorber.," Because high-altitude clouds or other opaque layers would shift the location of the 8 photosphere, this provides additional constraints on the nature of the unknown stratospheric absorber."
 We estimate (he secondary eclipse depth for the transiting planet ILD 209458b al 3.6. 4.5. 5.8. and 8.0jan.," We estimate the secondary eclipse depth for the transiting planet HD 209458b at 3.6, 4.5, 5.8, and 8.0."
. These observations provide a useful complement to previous observations of this svstem. which were limited to wavelengths longer (han 3.0jun.," These observations provide a useful complement to previous observations of this system, which were limited to wavelengths longer than 8.0."
. In contrast to the results for longer wavelengths. we find that the planets emission at shorter wavelengths is Clearly inconsistent with the predictions for a stancarcl cloudless atmosphere model.," In contrast to the results for longer wavelengths, we find that the planet's emission at shorter wavelengths is clearly inconsistent with the predictions for a standard cloudless atmosphere model."
 We suggest an allernative explanation. in which a temperature inversion in (he upper atmosphere produces water emission features at 4.5 and 5.8yam.," We suggest an alternative explanation, in which a temperature inversion in the upper atmosphere produces water emission features at 4.5 and 5.8."
. Although the cause of this inversion laver is unknown. il is suggestive (hat this planet also falls into a class of hot Jupiters which appear to have radii that are significantly larger (han predicted by standard models for an," Although the cause of this inversion layer is unknown, it is suggestive that this planet also falls into a class of hot Jupiters which appear to have radii that are significantly larger than predicted by standard models for an"
"for detectable galaxies to fainter and fainter limits were the space based ""e Deep Field. North (IDEN: E in Lubble Deep Field. South """,for detectable galaxies to fainter and fainter limits were the space based Hubble Deep Field North (HDFN; ) and Hubble Deep Field South .
 Although of a limited field of view of m a onlv. the spth of the HEDEs allowed the detection of galaxies up to a redshift of 5 and even beyond.," Although of a limited field of view of about $5\sq\arcmin$ only, the depth of the HDFs allowed the detection of galaxies up to a redshift of 5 and even beyond."
" In the past vears the space based. IDEs were supplemented by many more multi-band/ photometric surveys like the MPP SUSI deep Field (NDE: 999a)). we Chandra Deep Field South (CDES: 2001a)). the William Llersehel Deep Field. (WILDE: 200123). the Subaru Deep Field/Survey (DE: 2003)). the COMDO-I7 surveyME. FIRES2003).. the FORS Deep Fie ""DeepDE: 2003)). the Great Observatories Origins Survey (GOODS: 2004b)). the Ultra Deep Field (UDE and UDE-Parallel ACS fields: 20042). the VIAMOS deep survey2004). GEMS2004).. the Ixeck. Deep Fields.2005).. and the Alultiwavelength Survey bv. Yale-Chile (MUSYC: 20073)."," In the past years the space based HDFs were supplemented by many more multi-band photometric surveys like the NTT SUSI deep Field (NDF; ), the Chandra Deep Field South (CDFS; ), the William Herschel Deep Field (WHDF; ), the Subaru Deep Field/Survey (SDF; ), the COMBO-17 survey, FIRES, the FORS Deep Field (FDF; ), the Great Observatories Origins Deep Survey (GOODS; ), the Ultra Deep Field (UDF and UDF-Parallel ACS fields; ), the VIRMOS deep survey, GEMS, the Keck Deep Fields, and the Multiwavelength Survey by Yale-Chile (MUSYC; )."
 With the advent of. all these deep multi-band photometric surveys the photometric redshift technique (essentially a ecneralisation of the drop-out technique) can be used to identify high-redshift galaxies., With the advent of all these deep multi-band photometric surveys the photometric redshift technique (essentially a generalisation of the drop-out technique) can be used to identify high-redshift galaxies.
 Photometric redshifts are often. determined. by means of. template matching algorithm that applies. Bayesian statistics and uses semi-empirical template spectra matched. to. band photometry (sec also 2006))., Photometric redshifts are often determined by means of template matching algorithm that applies Bayesian statistics and uses semi-empirical template spectra matched to broad-band photometry (see also ).
 Reclshilts of galaxies that are several magnitudes fainter than typical spectroscopic limits can be determined. reliably. with an accuracy of of 0.02 to 0.1., Redshifts of galaxies that are several magnitudes fainter than typical spectroscopic limits can be determined reliably with an accuracy of of 0.02 to 0.1.
 In this context the COSMOS survey(2007): see also http:www.astro.caltech.edu/cosmos/ for an overview) combines deep to very-cleep multiwaveband information in order to extend the analysis of deep pencil beam surveys to a much bigger volume. thus being able to drastically. increase the statistics and detect. also very rare objects.," In this context the COSMOS survey; see also http://www.astro.caltech.edu/cosmos/ for an overview) combines deep to very-deep multi-waveband information in order to extend the analysis of deep pencil beam surveys to a much bigger volume, thus being able to drastically increase the statistics and detect also very rare objects."
 For this. the survey covers an area of about 27° with imaging bw space-based telescopes (Llubble. Spitzer. GALEN. NATAL Chandra) as well as large ground based telescopes (Subaru. VLA. ESO-VET. UINXIIE. NOAO. CELT. and others).," For this, the survey covers an area of about $2\sq\degr$ with imaging by space-based telescopes (Hubble, Spitzer, GALEX, XMM, Chandra) as well as large ground based telescopes (Subaru, VLA, ESO-VLT, UKIRT, NOAO, CFHT, and others)."
 In this paper we combine publicly available u. D. V. r i. z. and Ix COSMOS data with proprietary imaging in the 1I band to derive a homogeneous multi-waveband catalogue suitable for deriving accurate photometric redshifts.," In this paper we combine publicly available u, B, V, r, i, z, and K COSMOS data with proprietary imaging in the H band to derive a homogeneous multi-waveband catalogue suitable for deriving accurate photometric redshifts."
 1n Section 2. we give an overview of the near-infrared. (NLR) data acquisition ancl we describe our 2-pass data reduction pipeline used to derive optimally (in terms of signal-to-noise for faint sources) stacked images in Section 3.., In Section \ref{sec:imaging_data} we give an overview of the near-infrared (NIR) data acquisition and we describe our 2-pass data reduction pipeline used to derive optimally (in terms of signal-to-noise for faint sources) stacked images in Section \ref{sec:imaging_reduction}.
 We also present NIIt galaxy number counts and compare them with the In Section 4 we present the deep multi-waveband i-band selected catalogue and discuss its properties. whereas the data reduction of the spectroscopic redshifts is described in Section. ??7..," We also present NIR galaxy number counts and compare them with the In Section \ref{sec:isel_catalogue} we present the deep multi-waveband i-band selected catalogue and discuss its properties, whereas the data reduction of the spectroscopic redshifts is described in Section \ref{sec:spec}."
 |n Section ο we present the photometric redshift’ catalogue. discuss the accuracy. of the latter and show the redshift distribution of the galaxies.," In Section \ref{sec:photoz} we present the photometric redshift catalogue, discuss the accuracy of the latter and show the redshift distribution of the galaxies."
 In Section 7 we derive the redshift evolution. of the restframe. UV luminosity function and luminosity density at 1500 from our i-selected catalogue before we summarise our lindings in Section &.., In Section \ref{sec:uvlf} we derive the redshift evolution of the restframe UV luminosity function and luminosity density at 1500 from our i-selected catalogue before we summarise our findings in Section \ref{sec:summary_conclusion}.
 We use AB magnitudes. and adopt a A cosmology throughout the paper with=0.8..0.7... and 1.," We use AB magnitudes and adopt a $\Lambda$ cosmology throughout the paper with, and ."
 Our observing strategy was designed. to. follow-up. the xibliely. available COSMOS observations with proprietary imaging in Ll band., Our observing strategy was designed to follow-up the publicly available COSMOS observations with proprietary imaging in H band.
 The whole area is covered by 25 »intings (15.4x15.4. each) to a depth adequate to the oublie NIR data., The whole area is covered by 25 pointings (15.4'x15.4' each) to a depth adequate to the public NIR data.
 The field. lavout and nomenclature is shown in Fig.d., The field layout and nomenclature is shown in \ref{fieldnomenclature}.
 The programme was carried out as a joint effort between three large extragalactic survey projects currently being pursued at the Centro Astronómmico llispano Alemánn (CALLA). on Calar Alto: ALILAMBRA ALANOS-wicle and. MUNICS-Doeep (€roranova et al.," The programme was carried out as a joint effort between three large extragalactic survey projects currently being pursued at the Centro Astronómmico Hispano Alemánn (CAHA), on Calar Alto: ALHAMBRA, MANOS-wide and MUNICS-Deep (Goranova et al.,"
 in »ep.)., in prep.).
 In addition. as a part of the MUNICS-Doeep project. in one of the pointings (Ole) we have already collected. deep Js- and Ix-band data.," In addition, as a part of the MUNICS-Deep project, in one of the pointings (01c) we have already collected deep Js- and K'-band data."
 The observations in. Hl. Js and Wo bands were M out. using the NIR wide-lield. imagercepe operating al u prime focus of the CALLA 3.5m te," The observations in H, Js and K' bands were carried out using the NIR wide-field imager, operating at the prime focus of the CAHA 3.5m telescope."
 OALEGA2000 is. equipped. with a LAVAL LeCdTe 2048X2048 array., OMEGA2000 is equipped with a HAWAII-2 HgCdTe 2048x2048 array.
 The instrument pixel scale is per pixel. providing afield-of-view of 15.4/x15.4*.. Llere we present the L-band observations in 15 pointines (sce LFig.4)). collected. curing 11. nights spanned over 3 observing campaigns: December 2004. February 2005. and Alarch/April 2005.," The instrument pixel scale is per pixel, providing afield-of-view of x. Here we present the H-band observations in 15 pointings (see \ref{fieldnomenclature}) ), collected during 11 nights spanned over 3 observing campaigns: December 2004, February 2005, and March/April 2005."
 Each pointing was observed for a totaΙ of at least 3 Kksec., Each pointing was observed for a total of at least 3 ksec.
 Ehe individual exposure times were 3 sec. on-chip co-acclecl to produce single frames of 60 sec each.," The individual exposure times were 3 sec, on-chip co-added to produce single frames of 60 sec each."
 Except for 05b. at least 50 such frames (depending on the weather conditions) were observed. per pointing.," Except for 05b, at least 50 such frames (depending on the weather conditions) were observed per pointing."
 In addition. observations in Js and [N bands in Ole were collected. during 7 night in the observing campaigns November 2003 and February 2006.," In addition, observations in Js and K' bands in 01c were collected during 7 night in the observing campaigns November 2003 and February 2006."
 The total exposure time in Js-band data was 8.2 ksec with the same individual exposure time scheme as for the LE band., The total exposure time in Js-band data was 8.2 ksec with the same individual exposure time scheme as for the H band.
 The Ix-band observations have a total of 7.7 ksec exposure time with individual exposures of 2 sec. co-adcded internally into single frames of 30 sec each.," The K'-band observations have a total of 7.7 ksec exposure time with individual exposures of 2 sec, co-added internally into single frames of 30 sec each."
 ALL observations were done using cithering pattern consisting of typically 20 positions shifted: with respect to one another by , All observations were done using dithering pattern consisting of typically 20 positions shifted with respect to one another by .
Phe consecutive dithering sequences, The consecutive dithering sequences
evolutionary histories of M31 and the Galaxy might be reflected in svstematic clifferences between (heir globular cluster svstems.,evolutionary histories of M31 and the Galaxy might be reflected in systematic differences between their globular cluster systems.
 Some spice is added to this problem by (he [fact that the Galaxy may have a more massive dark matter halo than. M31. even though the Andromeda galaxy has a larger stellar mass than does the Milky Way Svstem (Watkins οἱ al.," Some spice is added to this problem by the fact that the Galaxy may have a more massive dark matter halo than M31, even though the Andromeda galaxy has a larger stellar mass than does the Milky Way System (Watkins et al."
 2010)., 2010).
 To look into these questions in more detail the present paper compares available inlormation on the globular cluster systems in these (wo spiral galaxies., To look into these questions in more detail the present paper compares available information on the globular cluster systems in these two spiral galaxies.
 Data on the integrated UDV colors of the majority of galactic globular clusters have been compiled bv Harris (1996) and were updated at wwiw.phlivsics.memaster.cea/Globular.htl., Data on the integrated UBV colors of the majority of galactic globular clusters have been compiled by Harris (1996) and were updated at www.physics.mcmaster.ca/Globular.html.
 It is the purpose of the present paper to provide comparable UDV data for those clusters in the Andromeda galaxy. whieh Peacock et al. (, It is the purpose of the present paper to provide comparable UBV data for those clusters in the Andromeda galaxy which Peacock et al. (
"2010) have recently flagged as ""old elobular elusters"".",2010) have recently flagged as “old globular clusters”.
 A complete listing of information on these old clusters is given at htttp://astro.soton.ac.uk/ m.b.peacock/m3lgc.hünl., A complete listing of information on these old clusters is given at htttp://astro.soton.ac.uk/ m.b.peacock/m31gc.html.
 Peacock used the following criteria for includsion of an object in his listing of old elobular clusters: (1) All objects are previously identified in other catalogs. (2) previously published spectroscopy (or LIST observations) confirm that they are not background galaxies. (3) colors are consistent with these objects being old clusters.," Peacock used the following criteria for includsion of an object in his listing of old globular clusters: (1) All objects are previously identified in other catalogs, (2) previously published spectroscopy (or HST observations) confirm that they are not background galaxies, (3) colors are consistent with these objects being old clusters."
 This age cut is based on e-r color., This age cut is based on g-r color.
 Finally (4) preliminary spectral energy distributions obtained so far confirm that most of these objects are genuinely older than 10 Gvr., Finally (4) preliminary spectral energy distributions obtained so far confirm that most of these objects are genuinely older than 10 Gyr.
 Data for these clusters in M31. translormed to the UDV svstem. are listed in Table 1.," Data for these clusters in M31, transformed to the UBV system, are listed in Table 1."
 Color transformations from the ugr svstem to ihe UDV svstem were drawn from Jester et al. (, Color transformations from the ugr system to the UBV system were drawn from Jester et al. (
2005) and Peacock et al. (,2005) and Peacock et al. (
2010).,2010).
 Values based on color indexes that are uncertain bv more than 0.050 mag are followed by a colon €)., Values based on color indexes that are uncertain by more than 0.050 mag are followed by a colon (:).
 Applving the transformations used by Jester et al., Applying the transformations used by Jester et al.
 to the colors of globular clusters may introduce slightly larger errors than those obtained [rom objects having the οποιον distributions of single stars., to the colors of globular clusters may introduce slightly larger errors than those obtained from objects having the energy distributions of single stars.
 The actual transformation equations used were the following:," The actual transformation equations used were the following: V = g - 0.59(g-r) - 0.01, (1)"
in Appendix AppendixΑ:..,in Appendix \ref{sec:bootes_images}.
" In this section, we discuss two characteristics of the survey: number counts and spectral indices."," In this section, we discuss two characteristics of the survey: number counts and spectral indices."
 Further analyses will be done in a subsequent article., Further analyses will be done in a subsequent article.
" When properly corrected for incompleteness, the number counts are an objective measure of the 153 MHz source population, that can be compared against models and other surveys."," When properly corrected for incompleteness, the number counts are an objective measure of the 153 MHz source population, that can be compared against models and other surveys."
" For individual sources, the spectral index can help to classify sources, and identify rare sources such as HzRGs and cluster halos relics."," For individual sources, the spectral index can help to classify sources, and identify rare sources such as HzRGs and cluster halos relics."
 We derived the Euclidean-normalized differential source counts from the catalog., We derived the Euclidean-normalized differential source counts from the catalog.
" Because the source extraction criteria vary over the survey area, we used Figure 2 to correct for the missed fraction per flux bin."," Because the source extraction criteria vary over the survey area, we used Figure \ref{fig:bootes_detection} to correct for the missed fraction per flux bin."
 This mainly affects the lowest two bins., This mainly affects the lowest two bins.
" Furthermore, the combined effect of random peaks in the background noise and a peak detection criteria causes a selection bias for positively enhanced weak sources (Eddington bias)."," Furthermore, the combined effect of random peaks in the background noise and a peak detection criteria causes a selection bias for positively enhanced weak sources (Eddington bias)."
" In general, noise can scatter sources into other flux bins, most noticeably near the detection limit."," In general, noise can scatter sources into other flux bins, most noticeably near the detection limit."
 Our attempts to correct for this effect through Monte-Carlo simulations were numerically unstable due to the low number counts in the lowest flux bin., Our attempts to correct for this effect through Monte-Carlo simulations were numerically unstable due to the low number counts in the lowest flux bin.
" The effect on the higher bins was minimal, therefore we omit the Eddington bias corrections."," The effect on the higher bins was minimal, therefore we omit the Eddington bias corrections."
 The Euclidean normalized differential source counts are tabulated in Table ??.., The Euclidean normalized differential source counts are tabulated in Table \ref{tab:bootes_dif_counts}.
" Figure 4 shows our source counts in comparison with the (little) other observational data that is available for this frequency at comparable sensitivity, as well as source counts derived from two models,8030."," Figure \ref{fig:bootes_dif_source_counts} shows our source counts in comparison with the (little) other observational data that is available for this frequency at comparable sensitivity, as well as source counts derived from two models."
"29 At the high flux end (0.1—1 Jy), there is a good agreement between our source counts and those derived from part of the 7C survey at 151 MHz (?).."," At the high flux end $0.1-1$ Jy), there is a good agreement between our source counts and those derived from part of the 7C survey at 151 MHz \citep{mcgilcrist1990}."
" ? present source counts of 765 sources in a single-field, deep GMRT 153 MHz observation similar to ours, but with over twice the bandwidth (16 MHz)."," \citet{ishwara2010} present source counts of 765 sources in a single-field, deep GMRT 153 MHz observation similar to ours, but with over twice the bandwidth (16 MHz)."
 Their source counts go down to ~2.5 mJy., Their source counts go down to $\sim 2.5$ mJy.
" While their source counts are roughly equal to ours at the high flux end, they are increasingly lower towards lower flux levels."," While their source counts are roughly equal to ours at the high flux end, they are increasingly lower towards lower flux levels."
" Their source counts are well approximated by a single power-law slope of 1.01, which is steeper than the value of 0.91 from our data over the range 40-400 mJy."," Their source counts are well approximated by a single power-law slope of 1.01, which is steeper than the value of 0.91 from our data over the range 40–400 mJy."
 This suggests a non-linear flux scale difference., This suggests a non-linear flux scale difference.
 We can offer little explanation on this apparent discrepancy., We can offer little explanation on this apparent discrepancy.
" Within 2-3 times the (1e) error bars, the two source count results may still be considered consistent."," Within 2–3 times the $1\sigma$ ) error bars, the two source count results may still be considered consistent."
 ? have determined source counts from a shallower GMRT 153 MHz field (central RMS 3.1 beam-!)) centered around ε Eridanus., \citet{george2008} have determined source counts from a shallower GMRT 153 MHz field (central RMS 3.1 ) centered around $\epsilon$ Eridanus.
 From binning 113 source fluxes over a range of 20 mJy-2 Jy they derive a single power-law slope of 0.72 (not plotted)., From binning 113 source fluxes over a range of 20 mJy–2 Jy they derive a single power-law slope of 0.72 (not plotted).
 The most likely explanation for this much flatter slope is the large uncertainties in their counts due to low-number statistics., The most likely explanation for this much flatter slope is the large uncertainties in their counts due to low-number statistics.
" ? constructed a 151 MHz source count model, based on an extrapolation of source counts >0.2 Jy from the 3CRR and 6C catalogs (??).."," \citet{jackson2005} constructed a 151 MHz source count model, based on an extrapolation of source counts $> 0.2$ Jy from the 3CRR and 6C catalogs \citep{laing1983,hales1988}."
" Two cosmological scenarios are considered, namely an Ωμ=1 cosmology and a ACDM cosmology, the latter being today’s generally accepted cosmology (e.g.,?)."," Two cosmological scenarios are considered, namely an $\Omega_\mathrm{m}=1$ cosmology and a $\Lambda$ CDM cosmology, the latter being today's generally accepted cosmology \citep[e.g.,][]{komatsu2011}."
" In this model, radio sources dominate the counts above ~50 and ~20 mJy, for the two cosmologies respectively."," In this model, radio sources dominate the counts above $\sim 50$ and $\sim 20$ mJy, for the two cosmologies respectively."
" Below, sources are the most dominant population down to below our detection threshold, which causes a flattening of the counts below ~20 mJy in both cosmologies."," Below, sources are the most dominant population down to below our detection threshold, which causes a flattening of the counts below $\sim 20$ mJy in both cosmologies."
" Figure 4 shows that the source count models for both scenarios roughly match our observed source counts near 500 mJy, but increasingly underestimate the counts towards lower flux densities."," Figure \ref{fig:bootes_dif_source_counts} shows that the source count models for both scenarios roughly match our observed source counts near $500$ mJy, but increasingly underestimate the counts towards lower flux densities."
" Between 20 and 200 mJy, the approximately constant model slope for both scenarios is 0.98 and 1.19, respectively, steeper than the value of 0.91 derived from our data."," Between 20 and 200 mJy, the approximately constant model slope for both scenarios is 0.98 and 1.19, respectively, steeper than the value of 0.91 derived from our data."
 The observed source counts shows no clear evidence of flattening towards lower flux levels., The observed source counts shows no clear evidence of flattening towards lower flux levels.
" ? have generated model source counts at 151 MHz from a semi-empirical (ACDM) cosmological simulation,"," \citet{wilman2008} have generated model source counts at 151 MHz from a semi-empirical $\Lambda$ CDM) cosmological simulation,"
is (he number of clusters per unit galaxy. luminosity elal. 1991): where Αι is the total number of clusters. and AZ is the integrated absolute magnitude of the host galaxy.,"is the number of clusters per unit galaxy luminosity \citep{Har_vdB81, Har91}: : where $N_{cl}$ is the total number of clusters, and $M_V^T$ is the integrated absolute magnitude of the host galaxy."
 ον is found to difler among gE galaxies by more than an order of magnitude (Ilarris.llarris&MeLaughlin1998:ILarris.2001).," $S_N$ is found to differ among gE galaxies by more than an order of magnitude \citep{HHM98, Har01}."
. I is known that for cD-tvpe and BCG ealaxies (he specilic [requency increases systematically wilh the total galaxy. Iuminositv. the size ol the surrounding cluster of galaxies. and the X-rav. halo gas mass 1999).. albeit with a factor-ol-two scatter that is not understood in detail.," It is known that for cD-type and BCG galaxies the specific frequency increases systematically with the total galaxy luminosity, the size of the surrounding cluster of galaxies, and the X-ray halo gas mass \citep{BTM97, Bla99, HHM98, McL99, Kav99}, albeit with a factor-of-two scatter that is not understood in detail."
 We calculate the total number of clusters bv integrating the radial profiles and scaling up the result by the fraction of the area under the bright half of the GCLFs (the completeness magnitude used for the radial profiles corresponds to completeness. while for (he GCLFs it is 50%)).," We calculate the total number of clusters by integrating the radial profiles and scaling up the result by the fraction of the area under the bright half of the GCLFs (the completeness magnitude used for the radial profiles corresponds to completeness, while for the GCLFs it is )."
 Following previously established convention (Iuris2001).. the result is then doubled. which implicitly assumes that the GCLF is svimmetric about the turnover magnitude.," Following previously established convention \citep{Har01}, the result is then doubled, which implicitly assumes that the GCLF is symmetric about the turnover magnitude."
 We can therefore think of specific Lrequency as equivalent to the number of clusters in a galaxy., We can therefore think of specific frequency as equivalent to the number of clusters in a galaxy.
 Also. the value of S is fairly insensitive (ο the assumptions in the galaxy distance. because changes in distance will affect the calculated. galaxy. huminositv. and total cluster population in the same sense (see Harris&vandenBersh. (1981))).," Also, the value of $S_N$ is fairly insensitive to the assumptions in the galaxy distance, because changes in distance will affect the calculated galaxy luminosity and total cluster population in the same sense (see \citet{Har_vdB81}) )."
 The total populations along with the specific lrequencies Say are listed in Table 4., The total populations along with the specific frequencies $S_N$ are listed in Table \ref{sn_table}.
 Figure G shows our results along with Chose from other gE galaxies previously published., Figure \ref{sn_plot} shows our results along with those from other gE galaxies previously published.
 NGC 708 in A262 has the highest value lor Say. consistent with the fact that it is the only genuine cD-tvpe galaxy of the four studied.," NGC 708 in A262 has the highest value for $S_N$, consistent with the fact that it is the only genuine cD-type galaxy of the four studied."
 The other three galaxies are central ως without the extended ¢D envelope. ancl have lower values for Sy.," The other three galaxies are central BCGs without the extended cD envelope, and have lower values for $S_N$."
 Somewhat of an outlier is IC 4296 in À3565. with a ὧν value of 2.6. definitely on the low end for a such a high-Iuninositv elliptical.," Somewhat of an outlier is IC 4296 in A3565, with a $S_N$ value of 2.6, definitely on the low end for a such a high-luminosity elliptical."
 Its 5x is. however. similar to those of “field” ellipticals which are commonly thought to have formed by major mergers between relatively less cluster-rich disk galaxies.," Its $S_N$ is, however, similar to those of “field” ellipticals which are commonly thought to have formed by major mergers between relatively less cluster-rich disk galaxies."
 Even if {he merging galaxies are equite gas-rich. a hieh—Sy elliptical would not necessarily result. since new field stars star clusters both form during the merger. and the net ratio of clusters to field stars in the final merger product could either increase or decrease.," Even if the merging galaxies are quite gas-rich, a $-S_N$ elliptical would not necessarily result, since new field stars star clusters both form during the merger, and the net ratio of clusters to field stars in the final merger product could either increase or decrease."
 The final Sa would be higher only if the ellicieney of cluster formation was considerably enhanced over (he cluster formation that took place in the original protogalactie epoch., The final $S_N$ would be higher only if the efficiency of cluster formation was considerably enhanced over the cluster formation that took place in the original protogalactic epoch.
 In. actually observed cases of recentclisk/disk mergers. whatappears to be emerging in every case is an elliplical wilh Sy~2 (see Harris(2001) for more extensive discussion).," In actually observed cases of recentdisk/disk mergers, whatappears to be emerging in every case is an elliptical with $S_N \sim 2$ (see \citet{Har01} for more extensive discussion)."
As we see in Figures &.. 9.. and LO the networks output for a are concentrated on the range between2-3.,"As we see in Figures \ref{fig8}, , \ref{fig9}, , and \ref{fig10}
 the network's output for $\alpha$ are concentrated on the range between 2-3."
 The mean power law index. o. is 2.8. 2.7 and 2.6 lor intensity averaged over 3X3. 5 and 9x pixels. respectively.," The mean power law index, $\alpha$, is 2.8, 2.7 and 2.6 for intensity averaged over $3\times3$, $5\times5$ and $9\times9$ pixels, respectively."
 This confirms that. larger areas involve larger Mare evenis.," This confirms that, larger areas involve larger flare events."
 We note that (he τι values increase with binning., We note that the $\tau_d$ values increase with binning.
 For example. the average 7; Lor 3x pixels is 43 aud [or 9x pixels it is 53.," For example, the average $\tau_d$ for $3\times3$ pixels is 43 and for $9\times9$ pixels it is 53."
 The τι seems to depend on the event size., The $\tau_d$ seems to depend on the event size.
 This suggests that the larger areas as was expected have greater backeround., This suggests that the larger areas as was expected have greater background.
" The response of the STEREO/EUVI 171. as a function of plasma temperature is within the range log7,225.1—6.7 (Wüllser et al."," The response of the STEREO/EUVI 171 as a function of plasma temperature is within the range $\log
T_e\approx5.1-6.7$ (Wüllser et al."
 2004)., 2004).
 If. we suppose the plasmacooling, If we suppose the plasmacooling
so-called catastrophic ploto-z errors or outlicrs.,so-called catastrophic photo-z errors or outliers.
 The outline of the~ paper is as follows., The outline of the paper is as follows.
 In 82 we introduce the forniualisni and paraiuecterizations of cosmologv. galaxy redslitt distributions aud photometric redshift errors.," In \ref{sec:methodology}
 we introduce the formalism and parameterizations of cosmology, galaxy redshift distributions and photometric redshift errors."
 The iniplemieutatiou of the formalis is detailed in 823.., The implementation of the formalism is detailed in \ref{sec:implementation}.
 We show the dependence of the size of the calibration saiple ou he unnuber of Gaussians aud the shapes of the fiducial proto-z models in L.., We show the dependence of the size of the calibration sample on the number of Gaussians and the shapes of the fiducial photo-z models in \ref{sec:size}.
 We illustrate the effectiveness of optimizing the calibration sample iu 85.., We illustrate the effectiveness of optimizing the calibration sample in \ref{sec:optimize}.
 We cliscuss our results aud couchiucle in 86.., We discuss our results and conclude in \ref{sec:conclusion}.
 Two major generalizaions are mace to the work doue in MaMooetal.(2006)., Two major generalizations are made to the work done in \cite{Ma05}.
.. οne is that we donof assunepriovi of the true παπιντο (unobserved) ealaxy redshift distribution »(:)., One is that we do assume knowledge of the true underlying (unobserved) galaxy redshift distribution $n(z)$.
 Instead. we treat it as an unknown fiction Wwich must be coustraimed by the photo-z distribution τμ).make aud other observables.," Instead, we treat it as an unknown function which must be constrained by the photo-z distribution $n(z_{\rm ph})$ and other observables."
 The other modification we is to generalize the photo-z probability distribution to generic parametric functions. in our case multiple Ciussiaus.," The other modification we make is to generalize the photo-z probability distribution to generic parametric functions, in our case multiple Gaussians."
 Oue of the observables that a weak lensing survey wonld provide is the galaxy photo-z distribution (tpn)., One of the observables that a weak lensing survey would provide is the galaxy photo-z distribution $n(z_{\rm ph})$.
"""t The corresponding galaxy true redshift distribution . is unknown.", The corresponding galaxy true redshift distribution $n(z)$ is unknown.
 These two galaxy redshift distributions are relatedby the photo-z probability distribution P(zu:). Iu practice. we model the true 5(:) as a linear interpolation between values 2 at a discrete sot of redshifts (2/4.," These two galaxy redshift distributions are related by the photo-z probability distribution $P(z_{\rm ph}|z)$, In practice, we model the true $n(z)$ as a linear interpolation between values $n^i$ at a discrete set of redshifts $\{z^i\}$."
 The 0 becoiie free parameters iu a fit to the observables., The $n^i$ become free parameters in a fit to the observables.
 Weak-lensing tomoeraphy(Iu1999:IIuterer2002) extracts teniporal iuforiiationbv dividing ealaxic(tpn) into a fev photo-z bius.," Weak-lensing tomography \citep{Hu99, Huterer02} extracts temporal information by dividing $n(z_{\rm ph})$ into a few photo-z bins."
" The true distribution of s nil) that fall] in: the . /th photo-z bin: with: “hh(7)<tbhXMEINE""ph becomes Maotal.(2006) had taken P(zi|:) to bea Catssian. deseribed by two parameters (redshift bias aud rms) at a eiven value of z."," The true distribution of galaxies $n_i(z)$ that fall in the $i$ th photo-z bin with $z_{\rm ph}^{(i)} < z_{\rm ph} < z_{\rm ph}^{(i+1)}$ becomes \cite{Ma05} had taken $P(z_{\rm{ph}} | z)$ to be a Gaussian, described by two parameters (redshift bias and rms) at a given value of $z$ ."
 Now we allow a generic dependence on a set of photo-z parameters pj tudexed by i. Papi.," Now we allow a generic dependence on a set of photo-z parameters $p_\mu$ indexed by $\mu$, $P(z_{\rm ph} | z; p_\mu)$."
 For a inultiple Gaussian plioto-z model. ave the biases and ris values of the component Coussiaus.," For a multiple Gaussian photo-z model, $p_\mu$ are the biases and rms values of the component Gaussians."
"pj, The total παν of galaxies per steracian n=A5 Last) fixes the normalization. aud we analogously defiue for the tomographic bius."," The total number of galaxies per steradian n^A = dz n(z), fixes the normalization, and we analogously define = dz for the tomographic bins."
 We utilize information from both leusiug and redshift survevs Which inchide galaxy photo-z distribution aud the spectroscopic calibration sample for the ploto-zs., We utilize information from both lensing and redshift surveys which include galaxy photo-z distribution and the spectroscopic calibration sample for the photo-z's.
 Following Mactal.(2006).. we choose the nunuber-weighted convergence power spectra isiPRU) as leusingC» where / and j label tomographic[m bius.," Following \cite{Ma05}, we choose the number-weighted convergence power spectra $n^A_i n^A_j P_{ij}^{\kappa}(\ell)$ as lensing, where $i$ and $j$ label tomographic bins."
 From Isaiser(1992.1998). we have where /7(:) is the nibble parameter. D(z) is the augular diameter distance in comoving coordinates. Phy.+) is the three-dimeusional matter power spectrum. and hy=QD) is the wavenumber that projects outo the multipole ( at redshitt :.," From \cite{Kaiser_92, Kaiser_98}
 we have where $H(z)$ is the Hubble parameter, $D(z)$ is the angular diameter distance in comoving coordinates, $P(k_{\ell}, z)$ is the three-dimensional matter power spectrum, and $k_{\ell} = \ell /D(z)$ is the wavenumber that projects onto the multipole $\ell$ at redshift $z$."
 The weights VV are giveu by where Ώρος.) is the anenlar diameter distance between the two redshifts.," The weights $W$ are given by where $D_{LS}(z,z')$ is the angular diameter distance between the two redshifts."
 We compute a power spectruuui from the transfer function of Eiseustein&IIn(1999) with dark energy uodifications from Thi(2002).. aud the nonlinear fitting function of Peacock&Dodds(1996).," We compute a power spectrum from the transfer function of \cite{Hu_transfer} with dark energy modifications from \cite{Hu01c}, and the nonlinear fitting function of \cite{PD96}."
. Another set of observables from the redshift surveys is the galaxy. photo-z distribution. nt:2na collected iuto bius.," Another set of observables from the redshift surveys is the galaxy photo-z distribution, $n(z_{\rm ph}^i)$, collected into bins."
" The width the6,4, of these bius would typically be much finer than tomography bius aud should be at least as fine as the nodes z ou which the tue redshift distribution is defined.", The width $\delta z_{\rm ph}$ of these bins would typically be much finer than the tomography bins and should be at least as fine as the nodes $z^i$ on which the true redshift distribution is defined.
 Binning refeqmuizpuz.. we have So the observables are fuuctious of the intrinsic distribution [5$ aud the photo-z parameters py.," Binning \\ref{eq:nzpnz}, we have So the observables are functions of the intrinsic distribution $\{n^i\}$ and the photo-z parameters $p_\mu$."
 The last piece of information we utilize is the spectroscopic calibration sample., The last piece of information we utilize is the spectroscopic calibration sample.
 We presmne that a representative sample of Nis galaxies lias been drawu from the sources in redshift bin {ἐν with spectroscopic redshifts determined forοἱ of them.," We presume that a representative sample of $N_{\rm spect}^i$ galaxies has been drawn from the sources in redshift bin $i$, with spectroscopic redshifts determined for of them."
 Equivalently. we cau demand that the failure rate for obtainime redshifts iu the spectroscopic survey must be completely independent of redshift.," Equivalently, we can demand that the failure rate for obtaining redshifts in the spectroscopic survey must be completely independent of redshift."
 Thelikelihood of the jth spectroscopic survey [sealaxy with ploto-z value vIEl cine© observed to lave spectroscopic redshift+ Vds of course P(2npy) Each spectroscopic redshift hence adds a little more coustraiut to the photo-z paraueters. as quautified in," Thelikelihood of the $j$ th spectroscopic survey galaxy with photo-z value $z_{\rm ph}^j$ being observed to have spectroscopic redshift $z^j$ is of course $P(z_{\rm ph}^j|z^j; p_\mu).$ Each spectroscopic redshift hence adds a little more constraint to the photo-z parameters, as quantified in"
"The dense globular cluster ""Terzan 5 lies in the bulge of the Alilky Way Galaxy at an estimated distance. of 19—5.5 kpe (Ortolanietal.2007).",The dense globular cluster Terzan 5 lies in the bulge of the Milky Way Galaxy at an estimated distance of $D=5.5$ kpc \citep[][]{ortolani2007}.
.. Ferzan 5 contains an exceptionally large population of millisecond radio pulsars (e.g.Ransomοἱal.2005).. and high-spatial resolution oobservations have allowed for the identification of many X-rav point sources that are likely quiescent. low-mass X-ray binaries (LAINBs) or cataclysmic variables. (Lleinkectal. 2006)..," Terzan 5 contains an exceptionally large population of millisecond radio pulsars \citep[e.g.,][]{ransom2005}, and high-spatial resolution observations have allowed for the identification of many X-ray point sources that are likely quiescent low-mass X-ray binaries (LMXBs) or cataclysmic variables \citep[][]{heinke2006_terzan5}."
 Neutron stars residing in LAINBs accrete matter from a companion that has à mass 1M.., Neutron stars residing in LMXBs accrete matter from a companion that has a mass $\lesssim1~\Msun$.
 These are often transient svstems [for which the X-ray luminosity can brighten orders of magnitude due to a sudden strong increase in the mass-accretion rate onto the compact primary., These are often transient systems for which the X-ray luminosity can brighten orders of magnitude due to a sudden strong increase in the mass-accretion rate onto the compact primary.
 Such accretion outbursts generally reach 210 keV. X-ray luminosities of Ly~10777eres+. and last for several weeks.," Such accretion outbursts generally reach 2–10 keV X-ray luminosities of $L_X\sim10^{36-38}~\lum$, and last for several weeks."
" Afterwards. the svstenm returns to the quiescent state with a typical X-ray luminosity of L,~10%ores+. and remains as such for vears or decades until it enters a new outburst."," Afterwards, the system returns to the quiescent state with a typical X-ray luminosity of $L_q\sim10^{31-33}~\lum$, and remains as such for years or decades until it enters a new outburst."
 bbulge scan monitoring observations signalled X-ray activity in the direction of Terzan 5 on 2010 October 10 (Bordasetal. 2010).., bulge scan monitoring observations signalled X-ray activity in the direction of Terzan 5 on 2010 October 10 \citep[][]{bordas2010}.
 The subsequent detection of twpe-l X-ray bursts (Chenevezetal.2010) and coherent 11. Lz pulsations (Strohmaverctal.2010) demonstrated that. the active source was a neutron star LAND. whereas oobservations provided an accurate localization (Pooleyetal. 2010).," The subsequent detection of type-I X-ray bursts \citep[][]{chenevez2010_terzan5} and coherent 11 Hz pulsations \citep[][]{strohmayer2010} demonstrated that the active source was a neutron star LMXB, whereas observations provided an accurate localization \citep{pooley2010}."
. This new X-ray transient. designated: (C11748 hereafter). is the second confirmed transient neutron star LAINB in this elobular cluster (fordetailsontheotherone:seeWijnandsetal.2002:1einke 2003).," This new X-ray transient, designated (J1748 hereafter), is the second confirmed transient neutron star LMXB in this globular cluster \cite[for details on the other one; see][]{wijnands2002_terzan5,heinke2003}."
. Timing of the N-rav pulsations revealed that the neutron star orbits its 0.41.5M. donor in ~21 h (Papittoctal.2011)., Timing of the X-ray pulsations revealed that the neutron star orbits its $\sim 0.4 - 1.5 ~\Msun$ donor in $\sim21$ h \citep[][]{papitto2010}.
". The neutron star is thought to have a relatively strong magnetic Ποιά. as inferred. from the detection of a broad. iron line in the A-ray spectrum. (BLOT40.10""2011). timing of the X-ray pulsations (D.~0.2.24.10"" and burst oscillation studies (D10"" 2011)."," The neutron star is thought to have a relatively strong magnetic field, as inferred from the detection of a broad iron line in the X-ray spectrum \citep[$B\sim0.7-4.0\times10^{9}$, timing of the X-ray pulsations \citep[$B\sim0.2-24\times10^{9}$ and burst oscillation studies \citep[$B\gtrsim10^{9}$ ."
 Figure 1 displavs the lighteurve of the 2010 outburst of Terzan 5. as observed with the aall-skv X-ray monitor mounted on the International SpaceStation (Alatsuokaetal. 2009)...," Figure \ref{fig:maxi} displays the lightcurve of the 2010 outburst of Terzan 5, as observed with the all-sky X-ray monitor mounted on the International SpaceStation \citep[][]{maxi2009}. ."
 The activity commenced arounc 2010 October 10 (seealsoBoreasetal.2010) and the, The activity commenced around 2010 October 10 \citep[see also][]{bordas2010} and the
are within reach comprising low (220.2) to very high-redshift clusters (2~1).,are within reach comprising low $z\gsim0.2$ ) to very high-redshift clusters $z\sim1$ ).
 Such a sample would be ideal for evolutionary studies of galaxies ancl large-scale structures., Such a sample would be ideal for evolutionary studies of galaxies and large-scale structures.
 The ELS cluster catalog being compiled will also be of great value for many other applications and in support to VET observations as well as targets for ollow-up observations with Chandra and NMM., The EIS cluster catalog being compiled will also be of great value for many other applications and in support to VLT observations as well as targets for follow-up observations with Chandra and XMM.
 Phere is currently no comparable sample in the southern hemisphere., There is currently no comparable sample in the southern hemisphere.
boundary. the symmetry axis. are mirrored.,"boundary, the symmetry axis, are mirrored."
 The parameters. density and. temperature at the left-hand boundary are fixed and the inflow of the plasma is initialized at à constant value.," The parameters, density and temperature at the left-hand boundary are fixed and the inflow of the plasma is initialized at a constant value."
" In order to trace the condensation of the streaming material onto the cloud a new quantity. ""colour. is introduced that is set in each cell to the density fraction of hot ISM."," In order to trace the condensation of the streaming material onto the cloud a new quantity, “colour”, is introduced that is set in each cell to the density fraction of hot ISM."
" At the beginning only the cells around the cloud possess a non-zero ""colour"" of value unity.", At the beginning only the cells around the cloud possess a non-zero “colour” of value unity.
 During the calculation this quantity is advected like the others. such as mass density or energy density.," During the calculation this quantity is advected like the others, such as mass density or energy density."
 The Poisson equation for self-gravity was solved at each tenth timestep because significant density changes of the cloud structure happen on a much longer timescale than the dynamical one., The Poisson equation for self-gravity was solved at each tenth timestep because significant density changes of the cloud structure happen on a much longer timescale than the dynamical one.
 The energy equation includes heating. cooling and heat conduction: Here ο denotes the energy density. v the velocity. P the pressure. [ the heating rate. A the cooling rate and q the heat flux.," The energy equation includes heating, cooling and heat conduction: Here $e$ denotes the energy density, $\vec{v}$ the velocity, $P$ the pressure, $\Gamma$ the heating rate, $\Lambda$ the cooling rate and $\vec{q}$ the heat flux."
 The equation of state for an ideal gas is assumed to be valid: The cooling function used assumes collisional 10nisation equilibrium and is a combination of the function introduced by Bóhhringer Hensler (1989)) for T> 10!K and solar metallicity and by Dalgarno MeCray (1972)) for the lower temperature regime., The equation of state for an ideal gas is assumed to be valid: The cooling function used assumes collisional ionisation equilibrium and is a combination of the function introduced by Böhhringer Hensler \cite{bh89}) ) for $T>10^4$ K and solar metallicity and by Dalgarno McCray \cite{dm72}) ) for the lower temperature regime.
 The heating function considers cosmic rays (Black 1987)). X-rays and the photoelectric effect on dust grains (de Jong 19771 de Jong et al. 1980)).," The heating function considers cosmic rays (Black \cite{b87}) ), X-rays and the photoelectric effect on dust grains (de Jong \cite{dj77}
; de Jong et al. \cite{dj80}) )."
 The heat flux is caleulated by taking both the classical and the saturated flux into account., The heat flux is calculated by taking both the classical and the saturated flux into account.
 In order to apply a smooth transition between the classical and saturated regimes we use the analytical form by Slavin Cox (1992)) This guarantees that the lower flux is taken if both differ significantly., In order to apply a smooth transition between the classical and saturated regimes we use the analytical form by Slavin Cox \cite{sc92}) ) This guarantees that the lower flux is taken if both differ significantly.
 The heat flux due to electron diffusion is calculated separately using an implicit method which follows a scheme introduced by Crank Nicolson (1947)) and Juncosa Young (1971))., The heat flux due to electron diffusion is calculated separately using an implicit method which follows a scheme introduced by Crank Nicolson \cite{cn47}) ) and Juncosa Young \cite{jy71}) ).
 To couple the two directions in space the method of fractional steps by Yanenko (1971)) is used., To couple the two directions in space the method of fractional steps by Yanenko \cite{y71}) ) is used.
 A detailed description of the implementation of heat conduction in the existing hydro-code is given in. PaperL. as well as a comparison of analytical solutions and numerical test cases to prove the reliability of the code.," A detailed description of the implementation of heat conduction in the existing hydro-code is given in \cite{vh05}, as well as a comparison of analytical solutions and numerical test cases to prove the reliability of the code."
 The initial temperature and density profiles of the clouds are generated for hydrostatic and thermal equilibrium under the constraint of spherical symmetry: ΦΥ} is the gravitational potential., The initial temperature and density profiles of the clouds are generated for hydrostatic and thermal equilibrium under the constraint of spherical symmetry: $\Phi(r)$ is the gravitational potential.
 Setting the temperature 75. and particle density ων of the hot and tenuous outer medium. the energy density c; of the plasma ts given.," Setting the temperature $T_{\mbox{\tiny ISM}}$ and particle density $n_{\mbox{\tiny ISM}}$ of the hot and tenuous outer medium, the energy density $e_{\mbox{\tiny ISM}}$ of the plasma is given."
" The density and temperature profile of the cloud is then calculated by integrating equations (12)) and (139) from inside-out using the core temperature of the cloud as a boundary condition. and truncating the cloud’s outer border where the energy density reaches (e, ", The density and temperature profile of the cloud is then calculated by integrating equations \ref{gl10}) ) and \ref{gl11}) ) from inside-out using the core temperature of the cloud as a boundary condition and truncating the cloud's outer border where the energy density reaches $e_{\mbox{\tiny ISM}}$.
Here we present the evolution of three different models., Here we present the evolution of three different models.
 Their parameters are given in Table 2.., Their parameters are given in Table \ref{t2}.
" For all models the temperature of the HIM is fixed to 5.6-10"" K. In two models their density is set to 6.6-10.tem ? to allow for comparison with static models of Paper I and for one model (E) is increased by one order of magnitude.", For all models the temperature of the HIM is fixed to $5.6 \cdot 10^{6}$ K. In two models their density is set to $6.6 \cdot 10^{-4}$ $^{-3}$ to allow for comparison with static models of Paper I and for one model (E) is increased by one order of magnitude.
 In model U we consider a massive cloud of 6.110! M. representing à GMC or PCC., In model U we consider a massive cloud of $6.4 \cdot 10^{4}$ $_{\sun}$ representing a GMC or PCC.
 This cloud serves às a reference model for Paper I in which the fate of this cloud was investigated in an identical but static environment., This cloud serves as a reference model for Paper I in which the fate of this cloud was investigated in an identical but static environment.
 Model E with a cloud mass of [86.7 ; anda cloud radius one order of magnitude smaller than model U represents a small molecular cloud., Model E with a cloud mass of $486.7$ $_{\sun}$ and a cloud radius one order of magnitude smaller than model U represents a small molecular cloud.
 Clouds of this type can be found as remnants of larger clouds in galactic chimneys such as the one associated with the region W4 (Heyeretal.1996;; Tayloretal. 1999)) or behind shock fronts of supernovae., Clouds of this type can be found as remnants of larger clouds in galactic chimneys such as the one associated with the region W4 \cite{he96}; \cite{ta99}) ) or behind shock fronts of supernovae.
 The size of model K is similar to model E but the mass is decreased to 15.9 M: to reach an almost homogeneous density distribution that can be compared in its evaporation rate with Eq. (, The size of model K is similar to model E but the mass is decreased to $15.9$ $_{\sun}$ to reach an almost homogeneous density distribution that can be compared in its evaporation rate with Eq. (
6) which ts valid for uniform clouds.,6) which is valid for uniform clouds.
 This represents an extreme case of a small cloud that is only slightly gravitationally bound., This represents an extreme case of a small cloud that is only slightly gravitationally bound.
 All models show a typical multi-phase structure., All models show a typical multi-phase structure.
 While Model U and E possess a dense core and a density decrease outwards. Model K is homogeneous.," While Model U and E possess a dense core and a density decrease outwards, Model K is homogeneous."
 Their radial density profiles are plotted in Fig. 1.., Their radial density profiles are plotted in Fig. \ref{f1}.
 With respect to dealing with more realistic interstellar clouds with self-gravity and non-equilibrium boundary conditions. these models differ clearly from the situation implied by CM77.," With respect to dealing with more realistic interstellar clouds with self-gravity and non-equilibrium boundary conditions, these models differ clearly from the situation implied by CM77."
 For comparison all models were studied with and without heat conduction., For comparison all models were studied with and without heat conduction.
" The parameters a). Aj and 7., are therefore only defined for calculations with heat conduction."," The parameters $\sigma_0$, $\lambda_{\mbox{\tiny F}}$ and $\tau_{\mbox{\tiny eva}}$ are therefore only defined for calculations with heat conduction."
" In all models the hot gas streams subsonically with ej, = 0.3 Mach and all clouds are kept at rest so that the relative velocity. (6, important for the KH instability (see Appendix B) ts identical to c.", In all models the hot gas streams subsonically with $v_{\mbox{\tiny ISM}}$ = 0.3 Mach and all clouds are kept at rest so that the relative velocity $v_{\mbox{\tiny rel}}$ important for the KH instability (see Appendix B) is identical to $v_{\mbox{\tiny ISM}}$.
 Such a large velocity difference between clouds and the HIM ts only observed for HVCs. PCCs. and interstellar clouds overtaken by supernova shocks.," Such a large velocity difference between clouds and the HIM is only observed for HVCs, PCCs, and interstellar clouds overtaken by supernova shocks."
 Here we wish to study dynamical effects on clouds in addition to heat conduction., Here we wish to study dynamical effects on clouds in addition to heat conduction.
 For smaller relative velocities. as GMCs move through the ISM.," For smaller relative velocities, as GMCs move through the ISM,"
selected by their optical or sub-mm emission.,selected by their optical or sub-mm emission.
 Recently. there has also been a large increase in the number of potential group-scale lenses discovered that show extended gravitational ares from background blue star-forming galaxies with image separations between 6 and 16 aresec (Limousinetal.2009).," Recently, there has also been a large increase in the number of potential group-scale lenses discovered that show extended gravitational arcs from background blue star-forming galaxies with image separations between 6 and 16 arcsec \citep{limousin09}."
. The prospects of carrying out surveys for radio emitting star-forming galaxies behind clusters has become more appealing with the advent of new or upgraded radio facilities (see previous work by Garrett and BercianoAlbaetal. 20103)., The prospects of carrying out surveys for radio emitting star-forming galaxies behind clusters has become more appealing with the advent of new or upgraded radio facilities (see previous work by \citealt{garrett05} and \citealt{berciano-alba10}) ).
 Simulations by Fedeli&BercianoAlba(2009). find that over the whole sky. several 100 cluster lens systems could potentially be found from deep radio observations (~20 py arcsec7. surface-brightness sensitivity at L4 GHz) that are within the sensitivity limits of. for example. the Expanded VLA.," Simulations by \citet{fedeli09} find that over the whole sky, several 100 cluster lens systems could potentially be found from deep radio observations $\sim$ 20 $\mu$ Jy $^{-2}$ surface-brightness sensitivity at 1.4 GHz) that are within the sensitivity limits of, for example, the Expanded VLA."
 JPM would like to thank Ian Browne and Neal Jackson for useful discussions and Paul Phillips for providing the WHT data., JPM would like to thank Ian Browne and Neal Jackson for useful discussions and Paul Phillips for providing the WHT data.
 The William Herschel Telescope and its service programme are operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias., The William Herschel Telescope and its service programme are operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.
"rreeions. it is entirely possible Chat the ambient pressure around Ls is not ""tvpical of the global ISM.","regions, it is entirely possible that the ambient pressure around s is not “typical” of the global ISM."
 The second piece of evidence suggesting extreme vouth is the fraction of ionizing stars in rreeions compared to the Iraction of ionizing stars in conventional rreeions., The second piece of evidence suggesting extreme youth is the fraction of ionizing stars in regions compared to the fraction of ionizing stars in conventional regions.
 For M33. and NGC 6946 the minimum implied total Lyman continuum. photon production rate. Q. of the rregions is 1.9x10?s band 10x10?!s! respectively (provided there is no leakage from (he enshrouding cocoon that would likely result in associated Πα emission).," For M33 and NGC 6946 the minimum implied total Lyman continuum photon production rate, $Q$, of the regions is $1.9\times10^{51}~s^{-1}$ and $10\times10^{51}~s^{-1}$ respectively (provided there is no leakage from the enshrouding cocoon that would likely result in associated $\alpha$ emission)."
 The total Q lor the entire galaxy is 3x1075s+ for M33 and 1.5x107s+ for NGC 6946 (IKennicutt 1983 scaled to our adopted distance)., The total $Q$ for the entire galaxy is $3\times10^{53}~s^{-1}$ for M33 and $1.5\times10^{53}~s^{-1}$ for NGC 6946 (Kennicutt 1983 scaled to our adopted distance).
 Thus. the rregions contain and of the total ionizing photons.," Thus, the regions contain and of the total ionizing photons."
 If the star formation has been reasonably continuous in these svstems. a plausible estimate for the twpical duration of the pphase is 0.01 and 0.07 times the typical rregion lifetime (x10* vr).," If the star formation has been reasonably continuous in these systems, a plausible estimate for the typical duration of the phase is 0.01 and 0.07 times the typical region lifetime $\times10^{7}$ yr)."
 This implies a mean age of less than | Mvr for rreglons., This implies a mean age of less than 1 Myr for regions.
 The thid. and perhaps weakest. piece of evidence in favor of the extreme vouth οἱ rregions comes [rom their high visual extinctions.," The third, and perhaps weakest, piece of evidence in favor of the extreme youth of regions comes from their high visual extinctions."
 In this article. we note that many of the ionizing star clusters within the rreelons are not visible at optical wavelengths.," In this article, we note that many of the ionizing star clusters within the regions are not visible at optical wavelengths."
 Iu some cases. onlv diffuse Ja emission is seen.," In some cases, only diffuse $H\alpha$ emission is seen."
 Sans ((1994) show that in NGC 253. the extinetions due to dust reach local maxima. as high as “Ay15 mae at the positions of the radio sources we have identified as rreeions.," Sams (1994) show that in NGC 253, the extinctions due to dust reach local maxima, as high as $A_V=15$ mag at the positions of the radio sources we have identified as regions."
 This picture is consistent with UDILIIs being extremely. voune rregions still hidden from view by the clust associated with their natal molecular clouds., This picture is consistent with s being extremely young regions still hidden from view by the dust associated with their natal molecular clouds.
 llowever. one must also bear in mind that we cannot rule out screens of dust not physically associated with the regions of optically thick Iree-Iree emission.," However, one must also bear in mind that we cannot rule out screens of dust not physically associated with the regions of optically thick free-free emission."
 We expect that deliberate radio continuum searches will continue to find rregions in all galaxies with sulliciently high levels of recent star formation., We expect that deliberate radio continuum searches will continue to find regions in all galaxies with sufficiently high levels of recent star formation.
 It is becoming clear (hal we are seeing ΣΕ of sizes and huninosities for extragalactic massive star Clusters in the earliest stages of their evolution., It is becoming clear that we are seeing a of sizes and luminosities for extragalactic massive star clusters in the earliest stages of their evolution.
 We predict (hat the natal cocoons of, We predict that the natal cocoons of
abundance μυ.,"abundance $x_{\rm H_2, 0}$."
 As stated in 811. high IT» abundance as tu.2105 ean be achieved if a parent cloud uudereoes ionization prior to the collapse.," As stated in 1, high $_2$ abundance as $x_{\rm H_2, 0} \gtrsim 10^{-3}$ can be achieved if a parent cloud undergoes ionization prior to the collapse."
 Iu Paper IL we followed the collapse aud fragmentation of the primordial filaments with one-dimensional aud two-dimensional axisviuuetrie simulations.," In Paper II, we followed the collapse and fragmentation of the primordial filaments with one-dimensional and two-dimensional axisymmetric simulations."
 The umuuerical results of Paper II showed that the fragment masses derived frou the two-dimensional simulations are in good agreement with the estimate based on one-dimensional siuulatious., The numerical results of Paper II showed that the fragment masses derived from the two-dimensional simulations are in good agreement with the estimate based on one-dimensional simulations.
 Therefore. in this paper. we pursue onc-dimensional simulations on the collapse of the filaments to estimate the fragimoeut masses.," Therefore, in this paper, we pursue one-dimensional simulations on the collapse of the filaments to estimate the fragment masses."
" We calculated ore than 3000 models by choosing the model parameters vey. dy. f. and pna as logiyiveufomο).=1.00.1.33.1.67.2.00...6.00. Ty= 200. 300. 100 I, f=1.5.2.0,2.5.....6.0. and eiu=1ste3410610LI1&107...1410 ?. respectively."," We calculated more than 3000 models by choosing the model parameters $n_{\rm c,0}$ , $T_0$, $f$ and $x_{\rm H_2,0}$ as $\log _{10} (n_{\rm c,0}/{\rm cm}^{-3}) 
= 1.00, 1.33, 1.67, 2.00, \dots, 6.00$, $T_0=200$ , 300, 400 K, $f=1.5, 2.0, 2.5, \dots, 6.0$, and $x_{\rm H_2,0}= 1\times 10^{-4}, 3\times 10^{-4}, 6\times 10^{-4},
1\times 10^{-3}, \dots, 1\times 10^{-2}$ , respectively."
 Iu Papers I aud IL we studied the fragmentation of the primordial filaments incorporating IH» cooling. aud it was shown that the fragmentation is bifurcated by a threshold initial density of ο7. below which as massive stars as 2210? form. and above which less massive stars with swLAL... fona.AZ...," In Papers I and II, we studied the fragmentation of the primordial filaments incorporating $_2$ cooling, and it was shown that the fragmentation is bifurcated by a threshold initial density of $\approx 10^5{\rm cm}^{-3}$, below which as massive stars as $\approx 10^2M_\odot$ form, and above which less massive stars with $\approx 1M_\odot$ form."
 Iu this section. we reexanune the collapse of the fluneuts including the ITD cooling as well as IL cooling.," In this section, we reexamine the collapse of the filaments, including the HD cooling as well as $_2$ cooling."
 As shown below. there is a threshold initial TT. concentration. above which IID cooling predominantly reeulates the cloud evolution.," As shown below, there is a threshold initial $_2$ concentration, above which HD cooling predominantly regulates the cloud evolution."
 We also show that the IID cooling does not play an inportaut role for high-density eas., We also show that the HD cooling does not play an important role for high-density gas.
" Thus. the evolution of the flameuts is classified iuto three cases. depending upon the initial density. Ώου aud initial IT» abundance. 41,9: (1) low-density fibuneuts with high (2) low-density &kuneuts with low νο. aud (3) high-densitywy. filaments."," Thus, the evolution of the filaments is classified into three cases, depending upon the initial density, $n_{\rm c,0}$, and initial $_2$ abundance, $x_{\rm H_2, 0}$; (1) low-density filaments with high $x_{\rm H_2, 0}$, (2) low-density filaments with low $x_{\rm H_2, 0}$, and (3) high-density filaments."
 Iu the following. we first compare the WD cooling aud Il) cooling on the που«Που diagran to clarity the nuportance of ID cooliug.," In the following, we first compare the HD cooling and $_2$ cooling on the $n_{\rm c,0}-x_{\rm H_2, 0}$ diagram to clarify the importance of HD cooling."
 Next. we show the mmuerical results of one-dimensional simulations.," Next, we show the numerical results of one-dimensional simulations."
 Iu the models shown iu this section. the initial temperatures are set to be equilibrimu temperatures of the filaments which decrease with increasing ypu.," In the models shown in this section, the initial temperatures are set to be equilibrium temperatures of the filaments which decrease with increasing $x_{\rm H_2, 0}$."
 WD cooling depeuds sensitively on the initial cloud density aud Πο abundance., HD cooling depends sensitively on the initial cloud density and $_2$ abundance.
 To clarity the effect of ΠΟ cooling. we compare the ΠΟ cooling rate (ΑΠ) aud the IT» cooling rate (Aq) in Figure 6..," To clarify the effect of HD cooling, we compare the HD cooling rate $\Lambda _{\rm HD}$ ) and the $_2$ cooling rate $\Lambda _{\rm H_2}$ ) in Figure \ref{fig:1}."
 The abscissa aud ordinate indicate the initial eas clensity and the IIo abundance. respectively.," The abscissa and ordinate indicate the initial gas density and the $_2$ abundance, respectively."
" The solid lines show the contour curves of the IID-to-II» cooling ratio (Απο A, )."," The solid lines show the contour curves of the $_2$ cooling ratio $\Lambda _{\rm HD}$ $\Lambda _{\rm
H_2}$ )."
" When evaluating the cooling rates. the eas temperatures are determined iteratively to satisfy the condition of feco,=fgas. where fou Is cooling time aud tea, is fragmentation time as defined iu 2.."," When evaluating the cooling rates, the gas temperatures are determined iteratively to satisfy the condition of $t_{\rm cool}=t_{\rm frag}$, where $t_{\rm cool}$ is cooling time and $t_{\rm frag}$ is fragmentation time as defined in \ref{subsec:LowD1}."
 The resultant temperatures are also shown by dashed lines., The resultant temperatures are also shown by dashed lines.
" The WD abundance is taken to be proportional to the IT» abundance as ejfe,=1s10. which is consistent with those in the models shown in and 3.L."," The HD abundance is taken to be proportional to the $_2$ abundance as $x_{\rm HD}/x_{\rm H_2}=1\times 10^{-4}$, which is consistent with those in the models shown in \ref{subsec:LowD2} and \ref{subsec:HighD}. ."
 This feure shows that the contribution of IID cooling rate is largest around veg=105 7. which is almost comparable to the critical density of ΠΟ. bevoud which the rotational level populations achieve the LTE.," This figure shows that the contribution of HD cooling rate is largest around $n_{\rm c,0}=10^5$ $^{-3}$, which is almost comparable to the critical density of HD, beyond which the rotational level populations achieve the LTE."
 Tf the cloud has the initial Πο abundance lower than a weshold value of πω=3<107. TID cooling docs iof play a significant role iu the thermal evolution of 1ο cloud. because Agu<Aq.," If the cloud has the initial $_2$ abundance lower than a threshold value of $x_{\rm H_2, cr}=3\times 10^{-3}$ , HD cooling does not play a significant role in the thermal evolution of the cloud because $\Lambda _{\rm HD}<\Lambda _{\rm H_2}$."
 The cloud temperature is then equal to the equilibrimm temperature shown by re dashed lines., The cloud temperature is then equal to the equilibrium temperature shown by the dashed lines.
" As shown later. the Ts abundance i- a collapsing f&lhuueut stavs almost coustant before the wee-body reactions proceed at LOS9 7,"," As shown later, the $_2$ abundance in a collapsing filament stays almost constant before the three-body reactions proceed at $10^{8-9}$ $^{-3}$."
 Thos. if a- evolutionary path of such a cloud is superimposed on Figure l. then it is almost parallel to the abscissa.," Thus, if an evolutionary path of such a cloud is superimposed on Figure 1, then it is almost parallel to the abscissa."
" For 1ο filameuts with o<10° 7 aud DIS2«Ἡνιοι, the evolutionary path cuters iuto the region of App7Ai, i 16 course of contraction even if Ag, is larger than Άγιο at je initial state."," For the filaments with $n \lesssim 10^5$ $^{-3}$ and $x_{\rm H_2} \gtrsim x_{\rm H_2, cr}$, the evolutionary path enters into the region of $\Lambda _{\rm HD}>\Lambda _{\rm H_2}$ in the course of contraction even if $\Lambda _{\rm H_2}$ is larger than $\Lambda _{\rm HD}$ at the initial state."
 In actual evolution. as shown below. the xessure force retards the contraction of the filament.," In actual evolution, as shown below, the pressure force retards the contraction of the filament."
 I- uwtieubu. when the deusitv exceeds ΠΟ critical deusity. Mupe105 7. the contraction slows aud the actual cloud temperature stavs below LOO K. Consequently. IID cooling continues to control the contraction uutil the cloud vecolnes opaque to the ΠΟ lines.," In particular, when the density exceeds HD critical density, $n_{\rm HD, cr}\sim 10^{4-5}$ $^{-3}$, the contraction slows and the actual cloud temperature stays below 100 K. Consequently, HD cooling continues to control the contraction until the cloud becomes opaque to the HD lines."
" On the other hand. for he filaments with voy2LO P aud iyoνου: he evolutionary path goes iuto the region of Απο<Aq, even if App is larger than Ay, at the initial state."," On the other hand, for the filaments with $n_{\rm c,0} \gtrsim 10^5$ $^{-3}$ and $x_{\rm H_2,0} \gtrsim x_{\rm H_2, cr}$ , the evolutionary path goes into the region of $\Lambda _{\rm HD}<\Lambda _{\rm H_2}$ even if $\Lambda _{\rm HD}$ is larger than $\Lambda _{\rm H_2}$ at the initial state."
 As a result. for the initial condition i the οταν region in Figure l. the IID cooling plays an important role in the thermal evolution of the gas.," As a result, for the initial condition in the gray region in Figure 1, the HD cooling plays an important role in the thermal evolution of the gas."
" Asa typical example in which the ΠΟ cooling controls the contraction. we slow the evolution of the model with meg=lcm ον Ty= 200. f=2. and =ον10%,"," As a typical example in which the HD cooling controls the contraction, we show the evolution of the model with $n_{\rm c,0}=10$ $^{-3}$, $T_0=200$ K, $f=2$, and $x_{\rm H_2, 0} = 3 \times 10^{-3}$."
 Figures Taa. Thb. Tec. aud. τος show theyy time evolution of (a) the temperature. (b) Πο Hie} and HD linc) abundauces. (c) cooling rates by IL line) aud by ΠΟ Hnc). aud. the total linc). (d) the cooling timescale linc). the timescale of dynamical contraction line). aud the fragmentation timescaleline). respectively. as a functiou of the ceutral density [η=p(ung η.," Figures \ref{fig:2}a a, \ref{fig:2}b b, \ref{fig:2}c c, and \ref{fig:2}d d show the time evolution of (a) the temperature, (b) $_2$ ) and HD ) abundances, (c) cooling rates by $_2$ ) and by HD ), and the total ), (d) the cooling timescale ), the timescale of dynamical contraction ), and the fragmentation timescale), respectively, as a function of the central density $n_c\equiv \rho_c /(\mu m_H) $ ]."
" Since the central deusitv monotonically increases with time, the abscissa corresponds to the evolution. time."," Since the central density monotonically increases with time, the abscissa corresponds to the evolution time."
 The contraction aud cooling timescale are. respectively. defined as tay=p/p and te=Ey/(Ar). where F4 and A. are total internal energy and net cooling rate. respectively.," The contraction and cooling timescale are, respectively, defined as $t_{\rm dyn}\equiv \rho/\dot{\rho}$ and $t_{\rm cool}\equiv E_{\rm t}/(\Lambda _{\rm t})$, where $E_{\rm t}$ and $\Lambda _{\rm t}$ are total internal energy and net cooling rate, respectively."
 Thefraginentation tie. trae. is defined as 2.5 ines the inverse of the growth rate of the fastest-erowing node (eq [3s] of Nakannia. Hanawa. Nakano 1993). Les fuas—DOT(zGp)Ve.," Thefragmentation time, $t_{\rm frag}$, is defined as 2.5 times the inverse of the growth rate of the fastest-growing mode (eq [38] of Nakamura, Hanawa, Nakano 1993), i.e., $t_{\rm frag} \equiv 5.17 (2 \pi G \rho)^{-1/2}$."
 Note that this definition of fae is 2.5 times larecr than that of Paper IL, Note that this definition of $t_{\rm frag}$ is 2.5 times larger than that of Paper II.
 In xactice.a filament docs not fragment in onc-dinenusional calculations.," In practice,a filament does not fragment in one-dimensional calculations."
 Therefore. fray should be regarded as a ucasure of the fragmentation epoch as well as the frec- time-scale.," Therefore, $t_{\rm frag}$ should be regarded as a measure of the fragmentation epoch as well as the free-fall time-scale."
 At the carly stagesof the contraction. Ilocooling dominates TWD cooling. aud the equilibrium teniperature is lowered to Fo~100 E owing to thehieh ID abundance.," At the early stagesof the contraction, $_2$cooling dominates HD cooling, and the equilibrium temperature is lowered to $T\sim 100$ K owing to thehigh $_2$ abundance."
 When the deusitv reaches the critical deusitv of Ta. byec1073 7s the Ho cooling is saturated and then WD cooling becomes dominant as the density increases.," When the density reaches the critical density of $_2$ , $n_{\rm H_2, cr}\sim 10^{3-4}$ $^{-3}$ , the $_2$ cooling is saturated and then HD cooling becomes dominant as the density increases."
 When theIID cooling becomes effective. the," When theHD cooling becomes effective, the"
 , 
the inner parsec of the Galaxy.,the inner parsec of the Galaxy.
 If the dark matter is distributed. it is likely that a portion of this wind is captured by the compact cluster and that it settles within its poteutial well.," If the dark matter is distributed, it is likely that a portion of this wind is captured by the compact cluster and that it settles within its potential well."
 Although such a configuration would not include the steep eradicuts associated with a black holes gravitational field. this trapped gas (if hot and magnetized) might conceivably still account for at least some of Sey A?s radiative characteristics.," Although such a configuration would not include the steep gradients associated with a black hole's gravitational field, this trapped gas (if hot and magnetized) might conceivably still account for at least some of Sgr A*'s radiative characteristics."
 It is this possibility that we study here., It is this possibility that we study here.
 Ins 22 of this paper. we beein with a simple hydrostatic model of the eas bound to a compact dark cluster. whose mass and size are chosen to comply with the observed stellar kinematics.," In 2 of this paper, we begin with a simple hydrostatic model of the gas bound to a compact dark cluster, whose mass and size are chosen to comply with the observed stellar kinematics."
 Our subsequent 3-dimensioual sinulatious of the eas flow through this mass distribution are described iu . aud the results are presented in &1.," Our subsequent 3-dimensional simulations of the gas flow through this mass distribution are described in 3, and the results are presented in 4."
 We provide au overview of our analysis aud the iuplicatious for the nature of Ser A* in δη, We provide an overview of our analysis and the implications for the nature of Sgr A* in 5.
", Before cinbarking ou a full 3-dimensional hydrodynamical sinulation of the gas flow through the dark cluster potential. let us brieflv set up a simple hydrostatic model to examine the plivsical conditious expected for the captured plasima."," Before embarking on a full 3-dimensional hydrodynamical simulation of the gas flow through the dark cluster potential, let us briefly set up a simple hydrostatic model to examine the physical conditions expected for the captured plasma."
 For simplicity. we adopt a IKiug model poteutial for the dark cluster.," For simplicity, we adopt a King model potential for the dark cluster."
 Later. for the hydrocdwuamical simulations. we will use an i-model. described below.," Later, for the hydrodynamical simulations, we will use an $\eta$ -model, described below."
 The ceutral mass density of the cluster is where dy is a nuniber of order unity that depends on how coudeused the stellar distribution is. aud ry is the Nine scale radius.," The central mass density of the cluster is where $u_K$ is a number of order unity that depends on how condensed the stellar distribution is, and $r_K$ is the King scale radius."
 If the tidal radius ry is 2ryy. then wy=0.7ILE.," If the tidal radius $r_t$ is $2r_K$, then $u_K=0.74141$."
 In this simple tov model. we place 10°AL. of stars within 1 core radius. corresponding roughly to 07.02 in projected angular size.," In this simple toy model, we place $10^6\;M_\odot$ of stars within $1$ core radius, corresponding roughly to $0^{\prime\prime}.02$ in projected angular size."
 This constitutes a linear core size ry=170 AU's αμα thus εξ310 AU's., This constitutes a linear core size $r_K=170$ AU's and thus $r_t=340$ AU's.
 The total iuteerated mass of this cluster is then 1.22«109AL... which gives p.=1.03410* gem5m," The total integrated mass of this cluster is then $1.22\times 10^6 \;M_\odot$, which gives $\rho_*=1.43\times 10^{-7}$ g $^{-3}$."
 The eravitational poteutial per unit mass. measured relative to the ceuter of the cluster. is For the gas (ith density p) to be iu hydrostatie equilibrium within this potential. its pressure ust," The gravitational potential per unit mass, measured relative to the center of the cluster, is For the gas (with density $\rho$ ) to be in hydrostatic equilibrium within this potential, its pressure must"
clises (Itamos-C'aro.López-Suspez&González (2008))). this plot exhibits a variety of regular and. chaotic trajectories.,"discs \cite{ramos}) ), this plot exhibits a variety of regular and chaotic trajectories."
 ‘There is a regular central region conformed by two kinds of WAAL curves: the central rings made by box orbits: à πο of resonant islands chain (made by loop orbits) enclosing the rings., There is a regular central region conformed by two kinds of KAM curves: the central rings made by box orbits; a set of resonant islands chain (made by loop orbits) enclosing the rings.
 Moreover. there are two lateral regular zones of loop orbits that. as well as the central region. are enclosed by a sea of chaos.," Moreover, there are two lateral regular zones of loop orbits that, as well as the central region, are enclosed by a sea of chaos."
" In figure 7.. we show the ellect of increasing D, in model m=2."," In figure \ref{fig:PedOrbit2}, we show the effect of increasing $B_{1}$ in model $m=2$."
 Then. for the same initial conditions with &=1.245 and /=0.2. the surface of section reveals an increasing in the chaotic region along with a distortion of the WAAL curves in regular zones (for example. now the central torus are mace only by box orbits).," Then, for the same initial conditions with $E=-1.245$ and $\ell=0.2$, the surface of section reveals an increasing in the chaotic region along with a distortion of the KAM curves in regular zones (for example, now the central torus are made only by box orbits)."
" One could. expect. similar chaotic surfaces. of section for models m=3... but what really happens is that for certain values of D, all the orbits are regular."," One could expect similar chaotic surfaces of section for models $m=3,\ldots$, but what really happens is that for certain values of $B_{1}$ all the orbits are regular."
 This is the case illustrated in figure S.. where the Poincaré section. corresponding to a particle moving around the model m= 3. reveals completely regular motion.," This is the case illustrated in figure \ref{fig:PedOrbit3}, where the Poincaré section, corresponding to a particle moving around the model $m=3$ , reveals completely regular motion."
 This is a surprising [act. since in this kind of potentials chaos is the rule.," This is a surprising fact, since in this kind of potentials chaos is the rule."
" Lf one increases D, (for example. from 0.2 to 1). as in the case of figure 9.. we find again a prominent chaotic region enclosing some regular regions of WAAL curves."," If one increases $B_{1}$ (for example, from 0.2 to 1), as in the case of figure \ref{fig:PedOrbit4}, we find again a prominent chaotic region enclosing some regular regions of KAM curves."
 Thus. the free parameter D. apart from determining some relevant features in cquatorial orbits. plays an essential role in," Thus, the free parameter $B_{1}$, apart from determining some relevant features in equatorial orbits, plays an essential role in"
cluission that is observed.,emission that is observed.
 Iu this regard. dark matter annihilations have several advantages over proposed astroplivsical iechanisius.," In this regard, dark matter annihilations have several advantages over proposed astrophysical mechanisms."
 First. electrons produced hrough dark matter annihilatious vield a svuchrotron spectrin iu good agreement with the hard spectral index and turnover observed from NREs. without mandating finely tuned magnueto-hydrodvunamuc mteractions to niove electrons independently: iuto equivalent imuonoenergetic electron distributions.," First, electrons produced through dark matter annihilations yield a synchrotron spectrum in good agreement with the hard spectral index and turnover observed from NRFs, without mandating finely tuned magneto-hydrodynamic interactions to move electrons independently into equivalent monoenergetic electron distributions."
" Second. WIMPs aunihilatiug iuto eptonic final states, such as those enmploved at low nasses du order to explain the Fermu-Galactic ceuter excess (7). are predicted to inject electrous imto the Galactic center region with au energv density very siuular to the svuchrotron signal observed from NRFs."," Second, WIMPs annihilating into leptonic final states, such as those employed at low masses in order to explain the Fermi-Galactic center excess \citep{2011PhLB..697..412H}, are predicted to inject electrons into the Galactic center region with an energy density very similar to the synchrotron signal observed from NRFs."
 Lastly. as shown in Fie. 5.," Lastly, as shown in Fig. \ref{fig:5},"
 dark matter aunililations naturally explain the observed correlation between the radial distance of NRFs to the Galactic ceuter aud the inferred clectrou injection spectrum in the filaments., dark matter annihilations naturally explain the observed correlation between the radial distance of NRFs to the Galactic center and the inferred electron injection spectrum in the filaments.
 A dark matter origin of the observed radio emission roni NREs viekls several coucrete and testable xedictious., A dark matter origin of the observed radio emission from NRFs yields several concrete and testable predictions.
 In particular. the dark matter aunililation rate and corresponding flux of injected clectrous must show approximate spherical svimmetry with respect to he Galactic ceuter (7)..," In particular, the dark matter annihilation rate and corresponding flux of injected electrons must show approximate spherical symmetry with respect to the Galactic center \citep{2008Natur.454..735D},"
body above the critical Lrequency 7. where (he dust clouds become optically Chick while it is that of the v7? exev body spectrum at lower frequencies.,body above the critical frequency $\nu_c$ where the dust clouds become optically thick while it is that of the $\nu^{2+\beta}$ grey body spectrum at lower frequencies.
" Observations suggest that thermal dust emission is nearly optically thick even at A~100 jan for galaxies dominated by intense starburst regions 1997).. and we adopt v.=2x101” Iz (A,=150 jm)."," Observations suggest that thermal dust emission is nearly optically thick even at $\lambda \sim 100$ $\mu$ m for galaxies dominated by intense starburst regions , and we adopt $\nu_c = 2 \times 10^{12}$ Hz $\lambda_c = 150$ $\mu$ m)."
 Combining the Eqs., Combining the Eqs.
 1 Ὁ.. For a dust source of ϐ arcsec in diameter. expected flux density al v (in GIIz) due to thermal dust emission is The FIR. Iluminosity. L445. is derived by integrating Eq.," \ref{eq:Sd1}~ \ref{eq:Q}, For a dust source of $\theta$ arcsec in diameter, expected flux density at $\nu$ (in GHz) due to thermal dust emission is The FIR luminosity, $L_{FIR}$, is derived by integrating Eq."
" 4 over (he emitüng area Q, ancl over the frequency range corresponding to A=40—500 jm. Lepr=AxD;f[SuvjdvdQ."," \ref{eq:Sd3}
 over the emitting area $\Omega_d$ and over the frequency range corresponding to $\lambda = 40-500~\mu$ m, $L_{FIR}=4\pi D_L^2 \int \int S_d(\nu) d\nu d\Omega$."
 The massive star formation rate (SFR) lor a dustv starburst galaxy is then directly related (o its dust continuum spectrum by the FUR luminosity Thermal Bremsstrahlung (Iree-Dree) emission [rom ionized gas in the ΠΠ regions surrounding hot voung stars can be described in the same functional form as the thermal dust emission as in Eq. 3..," The massive star formation rate (SFR) for a dusty starburst galaxy is then directly related to its dust continuum spectrum by the FIR luminosity Thermal Bremsstrahlung (free-free) emission from ionized gas in the HII regions surrounding hot young stars can be described in the same functional form as the thermal dust emission as in Eq. \ref{eq:Sd2},"
 where T; is electron temperature and τει is [ree-Iree optical depth at the observed frequency., where $T_e$ is electron temperature and $\tau_{ff}$ is free-free optical depth at the observed frequency.
" In the Ravleigh-Jeanse regimee (hv< KT). B(v.T.)2ον/ο at radio frequencies. and Free-[ree optical depth is given by trp=0.082EMp.2T,9, where EM=[nzdl |! pe) is the emission measure."," In the Rayleigh-Jeans regime $h\nu\ll kT$ ), $B(\nu,T_e)=2kT_e\nu^2/c^2$ at radio frequencies, and Free-free optical depth is given by $\tau_{ff} = 0.083 EM \nu^{-2.1} T_e^{-1.35}$, where $EM \equiv \int n_e^2 dl$ $^{-6}$ pc) is the emission measure."
" In the optically thin regime. thermalDremsstrahlung emission then has the familiar p.""! dependence."," In the optically thin regime, thermalBremsstrahlung emission then has the familiar $\nu^{-0.1}$ dependence."
 A circular source of ϐ arcsec in diameter would have fIux clensity of, A circular source of $\theta$ arcsec in diameter would have flux density of
We now compare a star wilh an oscillating mountain against a star whose mountain is in equilibrium.,We now compare a star with an oscillating mountain against a star whose mountain is in equilibrium.
" We compute (10)) and (11)) directly from e(/) as generated by ZEUS-3D (see and 3.1)). ie. without assuming that h.(f) aud ο} are pure 0 fanctons al f=f,.2f.."," We compute \ref{eq:fc}) ) and \ref{eq:hc}) ) directly from $\epsilon(t)$ as generated by ZEUS-3D (see \ref{sec:burial} and \ref{sec:gwpolarization}) ), i.e. without assuming that $h_{+}(f)$ and $h_{\times}(f)$ are pure $\delta$ functions at $f = f_*, \, 2f_*$."
" Table 1. lists the SNR. and associated characteristic quantities For three M, values (and b= 10) for both the static and oscillating5 mountains.", Table \ref{table:snr} lists the SNR and associated characteristic quantities for three $\Ma$ values (and $b = 10$ ) for both the static and oscillating mountains.
 Thecase of a particular a and 7 (a=?= 7/3) is shown along with the average over a and / (Thorne 1998).," Thecase of a particular $\alpha$ and $i$ $\alpha = i = \pi/3$ ) is shown along with the average over $\alpha$ and $i$ \citep{tho87,bil98,bra98}."
". We see that the oscillations increase the SNR by up to ~15 per cent: the peaks at f=f,.2f, are the same amplitude as for a static mountain. but additional signal is contained in the sidebands."," We see that the oscillations increase the SNR by up to $\sim 15$ per cent; the peaks at $f= f_*, \, 2f_*$ are the same amplitude as for a static mountain, but additional signal is contained in the sidebands."
 At least one peak exceeds the LIGO II noise curve in Figure 3. in each polarization.," At least one peak exceeds the LIGO II noise curve in Figure \ref{fig:hplus}
 in each polarization."
 The SNR increases with M4. primarily because € increases.," The SNR increases with $\Ma$, primarily because $\bar{\epsilon}$ increases."
" The ellect of the oscillations is more complicated: although the Alfvénn sidebancds increase in amplitude as M, increases. their frequency displacement Ilrom /—f, and f/=2f. decreases. as discussed in 83.2... πο that the extra power is confined in a narrower range of /."," The effect of the oscillations is more complicated: although the Alfvénn sidebands increase in amplitude as $\Ma$ increases, their frequency displacement from $f = f_*$ and $f = 2f_*$ decreases, as discussed in \ref{sec:freeoscill}, so that the extra power is confined in a narrower range of $f$."
" ILowever. e ancl hence (he SNR plateau when A, increases above M. (see 83.1))."," However, $\epsilon$ and hence the SNR plateau when $\Ma$ increases above $\Mc$ (see \ref{sec:gwpolarization}) )."
" The net result is that increasing AL, bv a factor of 10 raises the SNR bv less than a [actor of (wo.", The net result is that increasing $\Ma$ by a factor of 10 raises the SNR by less than a factor of two.
 The SNR saturates at ~3.5 when averaged over à and / (multiple sources). but. can reach ~6 for a particular source whose orientation is favorable.," The SNR saturates at $\sim 3.5$ when averaged over $\alpha$ and $i$ (multiple sources), but can reach $\sim 6$ for a particular source whose orientation is favorable."
" For our parameters. an accreting neutron star typically becomes detectable with LIGO II once it has acereted Af,2 O.LAL.."," For our parameters, an accreting neutron star typically becomes detectable with LIGO II once it has accreted $\Ma \gtrsim 0.1\Mc$ ."
 The base of the mountain may be al a depth where (he ions are crystallized. bul an analvsis of the crystallization properties is bevond the scope of tliis paper.," The base of the mountain may be at a depth where the ions are crystallized, but an analysis of the crystallization properties is beyond the scope of this paper."
the DM annihilation produced iu our own Galactic halo (see the relevant calculation by INawasalsdetal.(20093) Note that «ue to relatively small fraction of energy released iu the orm of prompt plotous ~2UC. except for the 7r|τ channel where the prompt photon part reaches w (to ~TK. the inverse Compton part of the spectra has a higher auuplitude han the prompt portion.,"the DM annihilation produced in our own Galactic halo (see the relevant calculation by \citet{2009arXiv0904.3626K}) Note that due to relatively small fraction of energy released in the form of prompt photons $\sim 2-4 \%$, except for the $\tau^{-}+\tau^{+}$ channel where the prompt photon part reaches up to $\sim 17 \%$, the inverse Compton part of the spectrum has a higher amplitude than the prompt portion."
 As the observational )omnds are represented by a roughly iorizontal line it is ccar that in the case ofο|ε und Bodp chauncls the coustrait we obtain ou (0ye) arises roni the inverse Compton portion ouly., As the observational bounds are represented by a roughly horizontal line it is clear that in the case of $e^{-}+e^{+}$ and $\mu^{-}+\mu^{+}$ channels the constraint we obtain on $\cs$ arises from the inverse Compton portion only.
 However. for the T|r' channel ane for relatively low ρα. When the xonipt bunip of the spectrum reaches the energy range xobed by ECRET. he constraiut ou στο) is provided x the amplitude of the prompt portion. instead.," However, for the $\tau^{-}+\tau^{+}$ channel and for relatively low $m_{DM}$, when the prompt bump of the spectrum reaches the energy range probed by EGRET, the constraint on $\cs$ is provided by the amplitude of the prompt portion, instead."
 Iu Fig., In Fig.
 5 we show au exauple of the evolution of the ionization fraction {τιoper panel) aud matter temperature (lower panel) for the* modol with the annihilating DM particle with mass mipaj— TeV aud with a thermally averaged. eross-sectiou. ἐστι3°.10Flom., \ref{fig5} we show an example of the evolution of the ionization fraction (upper panel) and matter temperature (lower panel) for the model with the annihilating DM particle with mass $m_{DM}=1$ TeV and with a thermally averaged cross-section $\cs=3\times10^{-24}{\rm cm}^2$.
 The two uost extreme concentration models of Fig., The two most extreme concentration models of Fig.
 2 have been used and for clarity only the results for the e.|¢ channel are shown., \ref{fig2} have been used and for clarity only the results for the $e^{-}+e^{+}$ channel are shown.
 The lowest solid line pots the case where the structure boost has been ncelectec. Lc. Blt)=1 and the dashed line corresponds to the staudard “coucordance” cosinology without an auwihilating DAL," The lowest solid line plots the case where the structure boost has been neglected, i.e. $B(z)=1$ and the dashed line corresponds to the standard “concordance” cosmology without an annihilating DM."
 We have shown the evolution only down to τοςμιάt 2=6 hevoxd which there is a clear observational evideice that the Universe ects fully ionized (Fanetal.. 2006).., We have shown the evolution only down to redshift $z=6$ beyond which there is a clear observational evidence that the Universe gets fully ionized \citep{2006ARA&A..44..415F}. .
 In the lower 21Ο] the dotted li1ο shows the evolution of re CAIB temerature., In the lower panel the dotted line shows the evolution of the CMB temperature.
" Note that at 2~100 the power law coucentration model with Magi,=10PAL. clearly starts to deviate from the smooth model without the clustering boost. resulting 1 an order of magnitude higher ionization fraction at redshitts."," Note that at $z\sim 100$ the power law concentration model with $M_{\rm min}=10^{-9}M_{\odot}$ clearly starts to deviate from the smooth model without the clustering boost, resulting in an order of magnitude higher ionization fraction at low redshifts."
 However. if one calculates the optical depth to the last scattering then all of the nucels with DAL zunililatioi plotted in Fie.," However, if one calculates the optical depth to the last scattering then all of the models with DM annihilation plotted in Fig."
 5. eive very simular results. ie. clustering boos at low : has ατα effect.," \ref{fig5} give very similar results, i.e. clustering boost at low $z$ has minimal effect."
 Iu Dolikov&Iooper(20093) the authors discuss λοςels where the DM auuiliation is able to fully reionize tlie Universe at low redshifts., In \citet{2009arXiv0904.1210B} the authors discuss models where the DM annihilation is able to fully reionize the Universe at low redshifts.
 Iu otτ calculations we also fine that. indeed. it is possibe to fulv relonize the Universe. however. all of those models eive oo large amplitudes for he ioulzationfraction plateau af ποτον100 and thus vioate the CAIB nueasurenments.," In our calculations we also find that, indeed, it is possible to fully reionize the Universe, however, all of those models give too large amplitudes for the ionizationfraction plateau after $z\sim 100$ and thus violate the CMB measurements."
We here report the results of optical. ultraviolet aud Xταν observations of CCS 5926 aud a discussion of them. aud we conclude that this star is either an Xray variable or eclipsing SvND. or that the low-significauceROSAT detection was spurious.,"We here report the results of optical, ultraviolet and X–ray observations of CGCS 5926 and a discussion of them, and we conclude that this star is either an X–ray variable or eclipsing SyXB, or that the low-significance detection was spurious."
 The outline of the paper is as follows: iu Sect., The outline of the paper is as follows: in Sect.
 2 we deseribe our optical and Xray observations. while Sect.," 2 we describe our optical and X–ray observations, while Sect."
 3 reports the results and Sect., 3 reports the results and Sect.
 [ a discussion of them., 4 a discussion of them.
 Finally. iu Sect.," Finally, in Sect."
 5 we present the couchisious of our mnultiwaveleueth investigation of star COCS 5926., 5 we present the conclusions of our multiwavelength investigation of star CGCS 5926.
 Optical spectroscopy of CGCS 5926 was acquired ou 11 October 2009 with the L.s82-metre “Copernicus” telescope of the Asiago Astronomical Observatory (Italy) plus the AFOSC instrument (which carries a 102141021 pixel Tektrouix TR1021 CCD)., Optical spectroscopy of CGCS 5926 was acquired on 14 October 2009 with the 1.82-metre “Copernicus” telescope of the Asiago Astronomical Observatory (Italy) plus the AFOSC instrument (which carries a $\times$ 1024 pixel Tektronix TK1024 CCD).
 Using the Caism 11 and a 1726 «lit. this setup provided a dispersion of L2 A//pixel ale a nominal coverage between :3500 and 7800A.," Using the Grism 4 and a $\farcs$ 26 slit, this setup provided a dispersion of 4.2 /pixel and a nominal coverage between 3500 and 7800."
. The total exposure time was «20 min centered at 02:03 UT., The total exposure time was $\times$ 20 min centered at 02:03 UT.
" Spectroscopic observations to further explore the blue part of the optical range were secured at tle Astronomical Observatory of Bologna in Loiana (Italv) with the 1.52-metre “Cassini telescope plus the BFOSC iustriuneut carving an EEW 130041310 pixel CCD: with the use of Corin 466 and a slit width of 2"" we obtained a dispersion of 1.5 A//pixel in the nominal range 3000.5300A."," Spectroscopic observations to further explore the blue part of the optical range were secured at the Astronomical Observatory of Bologna in Loiano (Italy) with the 1.52-metre “Cassini"" telescope plus the BFOSC instrument carrying an EEV $\times$ 1340 pixel CCD: with the use of Grism 6 and a slit width of $''$ we obtained a dispersion of 1.8 /pixel in the nominal range 3000–5300."
. Precisely. two 30-1210. spectra were obtained at exposure time 02:13 UT of 9 Aueust 2011.," Precisely, two 30-min spectra were obtained at mid-exposure time 02:13 UT of 9 August 2011."
" Few additional 55008500 spectra with dispersion l.l Á//pix were moreover obtained ou 23 and 28 June 2011x and ou 1 and 7 July 2011 with the 0.6-metre aud 0.7-1netre reflector telescopes operated bv the ANS in La Polse di Coiences (Udine. Italy) aud at the Schiaparelli Observatory in Campo de Fiori (Varesc. Italv). respectively. to check for possible preseuce of IL, CLUISSIOLL. an confirming on al dates its absence."," Few additional 5500–8500 spectra with dispersion 1.1 /pix were moreover obtained on 23 and 28 June 2011 and on 1 and 7 July 2011 with the 0.6-metre and 0.7-metre reflector telescopes operated by the ANS in La Polse di Cougnes (Udine, Italy) and at the Schiaparelli Observatory in Campo de' Fiori (Varese, Italy), respectively, to check for possible presence of $_\alpha$ emission, and confirming on all dates its absence."
 The spectra. after correction for flat—field. Dias and cosnue-ray rejection. were backeround subtracted and optimally extracted (Ilorune 1986) usineIRAF?.," The spectra, after correction for flat-field, bias and cosmic-ray rejection, were background subtracted and optimally extracted (Horne 1986) using."
. Wavoleugth calibration was performed using comparison laps acquired soon after cach ou-tarect spectroscopic exposure. while fux calibration was accomplished. by observing stars HIR. STSO and IIR. 5631 from the Asiago internal list of bright spectroplotometric standard stars (Almari 2012. in preparation).," Wavelength calibration was performed using comparison lamps acquired soon after each on-target spectroscopic exposure, while flux calibration was accomplished by observing stars HR 8780 and HR 8634 from the Asiago internal list of bright spectrophotometric standard stars (Munari 2012, in preparation)."
 Wavelength calibration uncertainty was ~0.5 As: this was checked by using the positions of backeround might sky lines., Wavelength calibration uncertainty was $\sim$ 0.5; this was checked by using the positions of background night sky lines.
 The flux calibration of the Asiago spectra was verified against tle source photometry acquired or this source (see below) and we found that it is correct to better han ACTOSS he optical continua: the flax scale of the other spectra agrees with that of the Asiago oues., The flux calibration of the Asiago spectra was verified against the source photometry acquired for this source (see below) and we found that it is correct to better than across the optical continuum; the flux scale of the other spectra agrees with that of the Asiago ones.
 Spectra from a same observatory were then stacked together to increase the final signal-to-nolse ratio., Spectra from a same observatory were then stacked together to increase the final signal-to-noise ratio.
 huaegiug data of the source were obtained with he robotic Linch Celestron telescope of the Sonoita Research Observatory (New Mexico. USA) in 2009 (from 15 October to 27 December) and 2010 Grom 5 September o 1v November).," Imaging data of the source were obtained with the robotic 14-inch Celestron telescope of the Sonoita Research Observatory (New Mexico, USA) in 2009 (from 15 October to 27 December) and 2010 (from 5 September to 17 November)."
 The eutire log of these observations] is presented in Table , The entire log of these observations is presented in Table 1.
DVBele Optec photometric filters were used: the etector was a 10214102 jxel SBICG STL-LOOLE CCD camera. with a 20'420/ field of view and a plate scale of 1725 pix+.," $BVR_{\rm C}I_{\rm C}$ Optec photometric filters were used; the detector was a $\times$ 1024 pixel SBIG STL-1001E CCD camera, with a $'$$\times$ $'$ field of view and a plate scale of $\farcs$ 25 $^{-1}$."
 The frames were corrected for bias and flat-fleld and reduced by means of siniple. aperture photometry., The frames were corrected for bias and flat-field and reduced by means of simple aperture photometry.
 Photometric calibration was obtained through continuous imnonitoriug of several equatorial standards (Landolt 1992) during the nights of observations., Photometric calibration was obtained through continous monitoring of several equatorial standards (Landolt 1992) during the nights of observations.
 The field of CCGCS 5926 was observed ou 6 January 2010 in the 0.3.10 keV band with the XNRay Telescope (XRT: Burrows et al., The field of CGCS 5926 was observed on 6 January 2010 in the 0.3–10 keV band with the X–Ray Telescope (XRT; Burrows et al.
 2005) on board theSuvft satellite (Gehrels et al., 2005) on board the satellite (Gehrels et al.
 2005)., 2005).
 The NRT pointing (ID: 00031572001) started at 08:34 UT. and 137 £s of ou-source data were collected.," The XRT pointing (ID: 00031572001) started at 08:34 UT, and 4374 s of on-source data were collected."
comparison of N216L10mc and N216L10 runs clearly shows that metal cooling enhances the cosmic SFR throughout all redshifts by20—3096.,comparison of N216L10mc and N216L10 runs clearly shows that metal cooling enhances the cosmic SFR throughout all redshifts by$20-30$.
". Previously, Hernquist&Springel(2003,Fig.13) argued that the SFR density is enhanced by metal cooling mostly at lower redshifts and hardly at z, however, our simulations suggest otherwise. ("," Previously, \citet[][Fig.~13]{Hernquist.Springel:03} argued that the SFR density is enhanced by metal cooling mostly at lower redshifts and hardly at $z$, however, our simulations suggest otherwise. ("
See 6 for more discussion on this point.),See \ref{sec:summary} for more discussion on this point.)
" Metallicity needs to be higher than ~10?Zo to noticeably increase the gas cooling rate, because the metal cooling rate is much smaller than that by H and He at ZX107?Zo."," Metallicity needs to be higher than $\sim 10^{-2} \Zsun$ to noticeably increase the gas cooling rate, because the metal cooling rate is much smaller than that by H and He at $Z \leq 10^{-2} \Zsun$."
" The metallicity of diffuse IGM is generally lower than 107? at z>3, and the metal cooling effect on IGM is small."," The metallicity of diffuse IGM is generally lower than $10^{-2} \Zsun$ at $z \gtrsim 3$, and the metal cooling effect on IGM is small."
" ZoHowever the local SFR could be enhanced significantly even at high-z when the ISM is enriched to Z»107?Zo, which can be easily achieved after a few events of SN II."," However the local SFR could be enhanced significantly even at $z$ when the ISM is enriched to $Z > 10^{-2} \Zsun$, which can be easily achieved after a few events of SN II."
" Our results suggest that star formation at high-z can also be enhanced by metal cooling, and not just at low-z."," Our results suggest that star formation at $z$ can also be enhanced by metal cooling, and not just at $z$ ."
 We also find that the peak of the cosmic SF history hardly, We also find that the peak of the cosmic SF history hardly
ddiameter (see Sect. 3)).,diameter (see Sect. \ref{sec:30m}) ).
" The 18"" ?CO(1-0) bar-like structure contributes an H5 mass of ΜΗ, 2.1x10?Mo, roughly one-third of the Hy mass computed within42"", although the feature occupies an area of only ~5% of the bbeam.3627,"," The $\sim$ $^{12}$ CO(1–0) bar-like structure contributes an $_{2}$ mass of $\rm_{H_{2}}$$\sim$ $\times10^{8}~\rm{M_{\odot}}$, roughly one-third of the $_{2}$ mass computed within, although the feature occupies an area of only $\sim$ of the beam.,"
", compared to other NUGA galaxies, is not particularly massive in molecular gas, especially with respect to the extraordinary case of 11961 with an Hz mass of ~1.8x10!°Μο (Combesetal.2009)."," compared to other NUGA galaxies, is not particularly massive in molecular gas, especially with respect to the extraordinary case of 1961 with an $_{2}$ mass of $\sim$ $\times10^{10}~\rm{M_{\odot}}$ \citep{francoise09}."
. Information about the local excitation conditions of the molecular gas can be inferred from the line ratio R?j-Lj/ljo., Information about the local excitation conditions of the molecular gas can be inferred from the line ratio $_{\rm 21}$ $_{\rm 21}$ $_{\rm10}$.
" This ratio is obtained by comparing the CO maps of the two transitions, at the same resolution and with the same spatial frequency sampling."," This ratio is obtained by comparing the $^{12}$ CO maps of the two transitions, at the same resolution and with the same spatial frequency sampling."
" Figure 5 shows Ro; ratio with ""CO(1-0) contours as in Fig.", Figure \ref{fig:ratio} shows $_{\rm 21}$ ratio with $^{12}$ CO(1–0) contours as in Fig.
 4 (left panel)., \ref{fig:co10-21} (left panel).
" In the observed region, the line ratio ranges from 0.25 to 1 but the bulk of the emission has a ratio between 0.4 and 0.7."," In the observed region, the line ratio ranges from 0.25 to 1 but the bulk of the emission has a ratio between 0.4 and 0.7."
" These R», line ratio values are consistent with R2; = 0.6 obtained by Kripsetal.(2008),, and more in general with optically thick emission in spiral disks (e.g.,Braine&Combes1992;García-Burilloetal.1993)."," These $_{21}$ line ratio values are consistent with $_{21}$ = 0.6 obtained by \citet{melanie08}, and more in general with optically thick emission in spiral disks \citep[e.g.,][]{braine92,santi93}."
. The Ro; peaks of ~1 are reached in the center of aand at the southern extreme of the elongated '*CO emission region., The $_{21}$ peaks of $\sim$ 1 are reached in the center of and at the southern extreme of the elongated $^{12}$ CO emission region.
" A higher excitation of the molecular gas in the nucleus, suggested by a higher Ro; line ratio, is consistent with the HCN(1-0) emission in the same region (see Sect. 3))."," A higher excitation of the molecular gas in the nucleus, suggested by a higher $_{21}$ line ratio, is consistent with the HCN(1–0) emission in the same region (see Sect. \ref{sec:30m}) )."
" Figures 6 and 7 show the velocity-channel maps of CO(1- 0) and ?CO(-1) emission, respectively, in the central region of3627."," Figures \ref{channels10} and \ref{channels21} show the velocity-channel maps of $^{12}$ CO(1--0) and $^{12}$ CO(2–1) emission, respectively, in the central region of."
". The inner ""CO emission of the galaxy exhibits signatures of non-circular motions both at negative and positive velocities.", The inner $^{12}$ CO emission of the galaxy exhibits signatures of non-circular motions both at negative and positive velocities.
" These non-circular components are associated both with the bbar-like structure and the spiral feature detected beyond the bar-like structure and will be discussed in detail later, in Sect. 4.5,,"," These non-circular components are associated both with the bar-like structure and the spiral feature detected beyond the bar-like structure and will be discussed in detail later, in Sect. \ref{sec:corc},"
 where we analyze the rotation curve derived with our 1200 data., where we analyze the rotation curve derived with our $^{12}$ CO data.
 ?2CO(1-0) isovelocity contours (first-moment map) are superposed on the '?CO(1-0) integrated intensity in Figure 8 (left panel).," $^{12}$ CO(1–0) isovelocity contours (first-moment map) are superposed on the $^{12}$ CO(1–0) integrated intensity in Figure \ref{fig:co-vel}
 (left panel)."
" The white star indicates the dynamical center of the galaxy, assumed coincident with the phase tracking center of our observations, and the velocities are relative to the systemic heliocentric velocity, Veyshet = 744 ος] (see Sect. 4.1))."," The white star indicates the dynamical center of the galaxy, assumed coincident with the phase tracking center of our observations, and the velocities are relative to the systemic heliocentric velocity, $V_{\rm sys, hel}$ = 744 $^{-1}$ (see Sect. \ref{sec:dyncen}) )."
" The dashed line traces the position angle of the major axis of the observed region, PA = 178° + 1° (almost vertical), obtained by maximizing the symmetry in the position velocity diagrams."," The dashed line traces the position angle of the major axis of the observed region, PA = $^{\circ}$ $\pm$ $^{\circ}$ (almost vertical), obtained by maximizing the symmetry in the position velocity diagrams."
A host of estimation methods lave been proposed iu the literatureremoval.,A host of estimation methods have been proposed in the literature.
 Major contributions consist ofstabilization:: a classical solution is to preprocess the data by applying a variance 8abilizine tramsOr (VST) such as the Ansconi)o transforms utl67(?)., Major contributions consist of: a classical solution is to preprocess the data by applying a variance stabilizing transform (VST) such as the Anscombe transform .
. It Call he shown hat jo trausformie data are approximately stationary.lepencent.. aud Caussian.," It can be shown that the transformed data are approximately stationary, and Gaussian."
 However. these ranstormatioLs are only valid for α sufficieutlv large ΠΟΥ of cotits (aud of course. for even Lore counts. he Poisson distribution becomes Gaussian with equal mean aid variance) (?).," However, these transformations are only valid for a sufficiently large number of counts (and of course, for even more counts, the Poisson distribution becomes Gaussian with equal mean and variance) ."
. The necessary average number of cotits is about 20 if bias is to be avoided., The necessary average number of counts is about 20 if bias is to be avoided.
 lu tUs case. as alternative ao»proach. a filtering approach for VOYV πια munhbers of counts. includius requent zero cases. has been prop.wed iu (?).. which js base ou the popular isotropic wavelet ranstorm. a trous algorithm) and the ιutoconvolution histogram echuique for deriving the of the wavelet coefficient α," In this case, as alternative approach, a filtering approach for very small numbers of counts, including frequent zero cases, has been proposed in , which is based on the popular isotropic wavelet transform à trous algorithm) and the autoconvolution histogram technique for deriving the of the wavelet coefficient ."
νν This method is part O ‘the data reduction pipeIve ¢ot the NAIANLLSS project for detecting of clusters of galaxies (?)., This method is part of the data reduction pipeline of the XMM-LSS project for detecting of clusters of galaxies .
". This aleorithiu is obviously for LAT 2D map ialysis, bu its extensioi to 2D-1D does not exist."," This algorithm is obviously for LAT 2D map analysis, but its extension to 2D-1D does not exist."
 It is far frou beime trivial. and even if it were possible. computation time would certaiubEy be prohibitive o for LAT 2D-1Ds. Then. au alternative approach is needed.," It is far from being trivial, and even if it were possible, computation time would certainly be prohibitive to for LAT 2D-1D. Then, an alternative approach is needed."
 Several aithors laVE slgeesed that the Haar wavelet transOr IS verv well-suited or treating (ata with Poisson noise., Several authors have suggested that the Haar wavelet transform is very well-suited for treating data with Poisson noise.
 Since a [aar wavelet coefficient is just the differeice between wo random variables folkwine a Poisson distriution. it js easier fo chetive mathenatical tools for rouxwine the roise than with any other wavelet method.," Since a Haar wavelet coefficient is just the difference between two random variables following a Poisson distribution, it is easier to derive mathematical tools for removing the noise than with any other wavelet method."
 stidy. shows hat the ILIuw transform is less effective for resoring X-rav astrononical images tlal the à trous algoriluu., study shows that the Haar transform is less effective for restoring X-ray astronomical images than the à trous algorithm.
 The reason is that the wavelet shape of the isotropic wavelet raustorm is much better adapted to astronomical sources. which are nore or less Caussian-shaped ancl isotropic. hau the Haar wavelet.," The reason is that the wavelet shape of the isotropic wavelet transform is much better adapted to astronomical sources, which are more or less Gaussian-shaped and isotropic, than the Haar wavelet."
 Some papers proposed a spatial partitioning. possibly dvadic. of the image for colplicatcc ecolectrical content recovery.," Some papers proposed a spatial partitioning, possibly dyadic, of the image for complicated geometrical content recovery."
 This cdyvaclic outitiouiug concept is however again not very well suited ο astrophysical data., This dyadic partitioning concept is however again not very well suited to astrophysical data.
" Iu a receut paper. lave proposed to merec a X""uidance stabilization technique and the imultiscale decomposition. leading to the Multi-Scale./ Variance Staalization Trausform CMSVST))."," In a recent paper, have proposed to merge a variance stabilization technique and the multiscale decomposition, leading to the Multi-Scale Variance Stabilization Transform )."
 Iu the case of the isotropic undecimated wavelet trausfori. as thewavelet cocicieuts (e; derived by a simple difference of two consecutive dvadie scales of the input image (see SCCjon :k2)). wj;4dj the stabilized wavelet coeicdents are obtained by applying a stabilization on botLa; q deg. wy=A;eyi)Ajay). where A;a auk Aj ave nou-linear trausforms the Auscombe transformdetails.," In the case of the isotropic undecimated wavelet transform, as thewavelet coefficients $w_j$ derived by a simple difference of two consecutive dyadic scales of the input image (see section \ref{subsec:iuwt}) ), $\JF{w_j = a_{j-1} - a_{j}}$, the stabilized wavelet coefficients are obtained by applying a stabilization on both $\JF{a_{j-1}}$ and $\JF{a_{j}}$, $\JF{w_j= {\cal A}_{j-1} (a_{j-1}) - {\cal A}_{j} ( a_{j})}$, where $ {\cal A}_{j-1} $ and $ \JF{{\cal A}_{j}} $ are non-linear transforms the Anscombe transform;."
.. This new method is fast aud easy. to implement. alc moreImportantly... works very well at very low countations.. down to 0.1 photons perpixel.," This new method is fast and easy to implement, and more, works very well at very low count, down to $0.1$ photons per."
 Iun this paper. we present ai new nmultiscalerepresentation... derived from theMSVST.. which allows us to remove the Poisson noise in 3D datascts.. when the third dimension is not a spatial dimension. but the warcleneth. the euergv the time.," In this paper, we present a new multiscale, derived from the, which allows us to remove the Poisson noise in 3D data, when the third dimension is not a spatial dimension, but the wavelength, the energy the time."
sequel.. We show that it COUId be very useful to analyze LAT data. especially time varving sources.," We show that it could be very useful to analyze LAT data, especially time varying sources."
 Seclon describes. the LAT simulated data., Section \ref{sec_glast_data} describes the LAT simulated data.
 Section 3 reviews the method relative f| the isotropic undecinated wavelet ranstorm and section lL shows how it can be extended to the 2D-1D case., Section \ref{sect_msvst} reviews the method relative to the isotropic undecimated wavelet transform and section \ref{sect_msvst2d1d} shows how it can be extended to the 2D-1D case.
 Section 5 presets sole experiments oudata.. σοιclusions are given iu section 6.., Section \ref{sect_glast_exp} presents some experiments on Conclusions are given in section \ref{sect_ccl}.
 For a real discrete-time filter whose iupulse response is hy. hi|-h|ig.sic& is its time-reversed version.," For a real discrete-time filter whose impulse response is $h[i]$, $\bar{h}[i]=h[-i], ~ i \in \mathbb{Z}$ is its time-reversed version."
 For the sake of clarity. the notation δή] js used instead of h; for he location iudex.," For the sake of clarity, the notation $h[i]$ is used instead of $h_i$ for the location index."
 This will lighten the notation by avoiding multiple subscripts in the derivations of the paper., This will lighten the notation by avoiding multiple subscripts in the derivations of the paper.
" Tje discrete circular convolution product of two selvals will be written κ, aud the continuous convolution oftwo functions x.The term circular stands for periodic boundary conditions."," The discrete circular convolution product of two signals will be written $\star$ , and the continuous convolution of two functions $*$ .The term circular stands for periodic boundary conditions."
 The sviubol 9[/] is the Nrouccker delta., The symbol $\delta[i]$ is the Kronecker delta.
IX J1914|24 (also known as V407 Vul) is one of 3 sources discovered in recent veers which show intensity variations on periods of less than 10 mins.,RX J1914+24 (also known as V407 Vul) is one of 3 sources discovered in recent years which show intensity variations on periods of less than$\sim$ 10 mins.
 As no other periods have »en detected in these systems. and for other reasons. these »eriods have been associated with the binary orbital period.," As no other periods have been detected in these systems, and for other reasons, these periods have been associated with the binary orbital period."
 As such. these systems would have the shortest binary period of any known svstenm.," As such, these systems would have the shortest binary period of any known system."
 In addition. they would be amongst he strongest sources of constant gravitational radiation in he sky ane casily detectable using the future space mission.," In addition, they would be amongst the strongest sources of constant gravitational radiation in the sky and easily detectable using the future space mission."
 Their nature. however. remains controversial.," Their nature, however, remains controversial."
 Of the 3 svstems. ES Cet (Warner Woudt 2002). with a period. of 620 sec. has been shown to have an accretion disc.," Of the 3 systems, ES Cet (Warner Woudt 2002), with a period of 620 sec, has been shown to have an accretion disc."
 Both RN J1914|24 (Cropper et al 1998. Ramsay et al 2000. 2002) with a period of 569 sec. and WN 0506|15 (Ramsay. Llakala Cropper 2002. Israel et al 2002) with a period of 321 sec. do not show evidence for an accretion disc and share many similar properties.," Both RX J1914+24 (Cropper et al 1998, Ramsay et al 2000, 2002) with a period of 569 sec, and RX J0806+15 (Ramsay, Hakala Cropper 2002, Israel et al 2002) with a period of 321 sec, do not show evidence for an accretion disc and share many similar properties."
 Their X-ray light curves are almost identical. being “oll” for around half their evcle. showing a sharp rise to maximum Ilux and a more gradual decay.," Their X-ray light curves are almost identical, being `off' for around half their cycle, showing a sharp rise to maximum flux and a more gradual decay."
 In contrast. their optical light curves are sinusoicdal in shape. and in anti-phase with the X-ray. phase (Ramsay et al 2000. Israel et al 2003).," In contrast, their optical light curves are sinusoidal in shape, and in anti-phase with the X-ray phase (Ramsay et al 2000, Israel et al 2003)."
 Ehe period of both systems are reported to be evolving in the same direction (ie spinning up) as predicted if their binary orbit is evolving through eravitational raciiation (Llakala ct al 2003. Strohmaver 2003. Hakala. Ramsay Byekling 2004 for RA JOSOG|15. and Strohmayer 2002. 2004a for AN 1914|24).," The period of both systems are reported to be evolving in the same direction (ie spinning up) as predicted if their binary orbit is evolving through gravitational radiation (Hakala et al 2003, Strohmayer 2003, Hakala, Ramsay Byckling 2004 for RX J0806+15 and Strohmayer 2002, 2004a for RX J1914+24)."
 They do. however. diller in some respects.," They do, however, differ in some respects."
 IX JOSOG|24 shows weak optical emission lines. with Hydrogen blending with Ilelium lines (Israel οἱ al 2002. Norton. Laswell Wynn 2004).," RX J0806+24 shows weak optical emission lines, with Hydrogen blending with Helium lines (Israel et al 2002, Norton, Haswell Wynn 2004)."
 On the other hand UN. J1914|124. shows a generally [caturcless optical spectrum but with weak absorption lines which appear similar to that of a Ix star (Stecehs et al 2004)., On the other hand RX J1914+24 shows a generally featureless optical spectrum but with weak absorption lines which appear similar to that of a K star (Steeghs et al 2004).
 At present it is unclear as to how to interpret this spectrum. although a triple svstem is a possibility.," At present it is unclear as to how to interpret this spectrum, although a triple system is a possibility."
 RN J1914)24 has been observed in X-rays usingIOSAT. (Cropper et al 1998. Ramsay et al 2000. 2002) and (Strohmayer 2004a).," RX J1914+24 has been observed in X-rays using, (Cropper et al 1998, Ramsay et al 2000, 2002) and (Strohmayer 2004a)."
 With its larger cllective area. provides the possibility. of obtaining phase resolved spectroscopy through the 569 sec evele.," With its larger effective area, provides the possibility of obtaining phase resolved spectroscopy through the 569 sec cycle."
 Here. we present observations of Ν J1914|24 mace using NALAL-Neowfou.," Here, we present observations of RX J1914+24 made using ."
αἱ higher μι,at higher $N_{HI}$.
 We exclude both the very low column density [να forest. since it may not be associated with denser structures. and the verv high eolinn density. data. because star and molecular gas formation might have reduced the original ecolumn density.," We exclude both the very low column density $\alpha$ forest, since it may not be associated with denser structures, and the very high column density data, because star and molecular gas formation might have reduced the original column density."
 While simple power law fits to Αμ) fail we will show in what follows that a power law for the total hydrogen distribution ean instead well fit all the data displaved in Figure 2., While simple power law fits to $f(N_{HI})$ fail we will show in what follows that a power law for the total hydrogen distribution can instead well fit all the data displayed in Figure 2.
" As in Corbellietal.(2001)we derive a theoretical (Αμ) after applving the Ny—Nyy, conversion relation to an assumed power law distribution for the total gas column densitv. οΑν=ἂν"," As in \citet{cor01} we derive a theoretical $f(N_{HI})$ after applying the $N_H-N_{HI}$ conversion relation to an assumed power law distribution for the total gas column density, $g(N_{H})=K N_{H}^{-\alpha}$."
" The use of 2l-cm data eliminates the problem of having large errors in Nyy in the region where Lyman limit svstems become saturated and therefore we can salelv use [μι binned over small Ny), intervals.", The use of 21-cm data eliminates the problem of having large errors in $N_{HI}$ in the region where Lyman limit systems become saturated and therefore we can safely use $f(N_{HI})$ binned over small $N_{HI}$ intervals.
" We consider (wo possible Vy,Ἁμι conversion models for 1047<Ng,«6x10?""20) 2. (a) (he model used by Corbellietal.(2001) to fit the data on Lyman limit and Damped Lya systems. as described in (heir Section 3. extended (to lower column density svstems."," We consider two possible $N_{H}-N_{HI}$ conversion models for $10^{14}\le N_{HI}<6\times 10^{20}$ $^{-2}$: $(a)$ the model used by \citet{cor01} to fit the data on Lyman limit and Damped $\alpha$ systems, as described in their Section 3, extended to lower column density systems."
 This model is valid fora dark matter confined gas with ionization fractions which increasesteadily as (he total gas column density decreases., This model is valid for a dark matter confined gas with ionization fractions which increasesteadily as the total gas column density decreases.
" (5) the model used by Corbellietal.(2001) only [or Nyy>Ny: for Ny< we keep constant the II ionization [raction. equal to that reached [or Nj,=N,."," $(b)$ the model used by \citet{cor01} only for $N_{H}\ge N_*$; for $N_{H} < N_*$ we keep constant the H ionization fraction, equal to that reached for $N_{H}=N_*$."
" A constant ionization Traction for Vy,<AN, is achieved if the average gas volume density stays constant as Ny, clecreases below Αν.", A constant ionization fraction for $N_{H}< N_*$ is achieved if the average gas volume density stays constant as $N_{H}$ decreases below $N_*$.
 A constant gas volume density might imply either that a constant external pressure is confining (he gas or that dark matter and turbulence are distributed in such a wav as (o give a gas vertical dispersion which does not depend on the eas column density., A constant gas volume density might imply either that a constant external pressure is confining the gas or that dark matter and turbulence are distributed in such a way as to give a gas vertical dispersion which does not depend on the gas column density.
 For both (a) and (5) we find the best fitting value of à and of Jp/i)., For both $(a)$ and $(b)$ we find the best fitting value of $\alpha$ and of $J_L/\eta_0$.
 This is the ratio between the intensitv of the background fIux al 912 nnormalized to 1077 eres 7s ! t 4. and the gas compression factor my due to eravitv from matter other than the gas (e.g.dark matter).," This is the ratio between the intensity of the background flux at 912 normalized to $10^{-22}$ ergs $^{-2}$ $^{-1}$ $^{-1}$ $^{-1}$, and the gas compression factor $\eta_0$ due to gravity from matter other than the gas (e.g.dark matter)."
" The constant oj adds to the gas self eravily in vertical scale height expression (Corbellietal. 200111 where M, is the total mass surface density per 7 of gas. c; is the thermal sound speed and ὃς is the value of ce; for T—10! K. For model (a) theminimum value ol VO (1.3) corresponds to a=3.32 and to logJjην= —0.25."," The constant $\eta_0$ adds to the gas self gravity in vertical scale height expression \citep{cor01}: : where $M_g$ is the total mass surface density per $^{-2}$ of gas, $c_s$ is the thermal sound speed and $\tilde c_s$ is the value of $c_s$ for $T=10^4$ K. For model $(a)$ theminimum value of $\chi^2$ (1.3) corresponds to $\alpha=3.32$ and to $\log J_L/\eta_0=-0.25$ ."
 The 3-6 uncertainties on a are 40.4. on logSL!Jj/1g ave &0.6.," The $\sigma$ uncertainties on $\alpha$ are $\pm 0.4$, on $\log J_L/\eta_0$ are $\pm0.6$ ."
 An a=3 power law is therefore compatible with the data., An $\alpha=3$ power law is therefore compatible with the data.
" This is important since there have been often claims (hat /CN4,) for disk like structures shouldfollow an Αη power law (Milgrom 1988).. but /(N4,,) observed in galaxies strongly"," This is important since there have been often claims that $f(N_{HI})$ for disk like structures shouldfollow an $N_{HI}^{-3}$ power law \citep{mil88}, , but $f(N_{HI})$ observed in galaxies strongly"
"by Galactic latitude /=260"" aand Galactic longitule b=25""357.",by Galactic latitude $l$ and Galactic longitude $b$.
 The galaxies are drawn from the the ool (1990:2002).," The galaxies are drawn from the the of \shortcite{somak:1990,somak:2002}."
. Phe PLAS survey region is richly structured. and includes the aane Lvelra cluster. as well as many other Abell clusters. and thePlane.," The FLASH survey region is richly structured, and includes the and Hydra cluster, as well as many other Abell clusters, and the."
. The ELAIL fibre spectrograph at the UINST was used to obtain redshifts accurate to 100 [for 1896 ealaxics., The FLAIR-II fibre spectrograph at the UKST was used to obtain redshifts accurate to $\sim$ 100 for 1896 galaxies.
 A further 1245 recshifts were obtained from the NED and ZCAT catalogues. bringing the total number of galaxies with redshifts in the survey to.," A further 1245 redshifts were obtained from the NED and ZCAT catalogues, bringing the total number of galaxies with redshifts in the survey to."
. The overall redshift’ completeness of the sample is 68 per cent., The overall redshift completeness of the sample is 68 per cent.
 Although the completeness varies with apparent magnitude. dropping almost to 50 per cent at the [faint survey limit. follow-up observations show that there is no explicit redshift bias.," Although the completeness varies with apparent magnitude, dropping almost to 50 per cent at the faint survey limit, follow-up observations show that there is no explicit redshift bias."
" ""This magnitude-dependent incompleteness can therefore be corrected in a straightforward manner.", This magnitude-dependent incompleteness can therefore be corrected in a straightforward manner.
 ὃν selection. the FLASLI survey region is not a [air sample of the universe.," By selection, the FLASH survey region is not a fair sample of the universe."
 The redshift wedge plot for the whole survey region (Figure. 10)) reveals a remarkable amount of structure., The redshift wedge plot for the whole survey region (Figure \ref{fig:wedge_all}) ) reveals a remarkable amount of structure.
 The dominant structures are galaxy clusters. shown as iin the wedge plot. with the largest structure being theSupercluster.," The dominant structures are galaxy clusters, shown as in the wedge plot, with the largest structure being the."
. Walls and. filaments connect the various clusters. forming in the vicinity of the aa structure similar to the stick-man! structure observed around the Coma cluster in the CLA survey. but on a much larger scale.," Walls and filaments connect the various clusters, forming in the vicinity of the a structure similar to the `stick-man' structure observed around the Coma cluster in the CfA survey, but on a much larger scale."
 Dilferent structures can be seen in the wedge plots for the early and late morphological types in the ΕΤΑΡΗ survey., Different structures can be seen in the wedge plots for the early and late morphological types in the FLASH survey.
 The most representative tracer of large-scale structure are, The most representative tracer of large-scale structure are
"the mass number of the clement ἐν,",the mass number of the element $i$.
" The integration with respect to energy is carried out between the minima aud niaxinmuu euereies per uucleou iu the ejecta obtained from our nuuerical calculations. which are denoted as ej4,5, aud €x respectively,"," The integration with respect to energy is carried out between the minimum and maximum energies per nucleon in the ejecta obtained from our numerical calculations, which are denoted as $\epsilon_{\rm min}$ and $\epsilon_{\rm max}$, respectively."
 We use the empirical formula given by Read&Viola(1981). for the cross sectious., We use the empirical formula given by \citet{Read_84} for the cross sections.
 Table 6.2. stnunarizes the results., Table \ref{tbl-yields} summarizes the results.
 Since the ratios of elements are determined solely by the energy distribution of the injected materials aud the energy distributions of all the calculated models have a similar shape. the models eivesimilar isotopic ratios: * Li/Li-1.2 ο.," Since the ratios of elements are determined solely by the energy distribution of the injected materials and the energy distributions of all the calculated models have a similar shape, the models givesimilar isotopic ratios: $^7$ $^6$ $\sim$ 1.2 and $^{11}$ $/^{10}$ $\sim 2.8$."
 The D isotopic ratio observed in meteorites is [.05-250.05 (Shima1962:Chaussidou&Robert1995).," The B isotopic ratio observed in meteorites is $\pm0.05$ \citep{Shima_62, Chaussidon_95}."
. Thus neutrino spallation processes m core-collapse SNe may contribute to the enhancement of +B., Thus neutrino spallation processes in core-collapse SNe may contribute to the enhancement of $^{11}$ B .
 On the other hand. this ratio observed in the local ISAL is around. 3.140.7 (Lambertetal. 1998).. which can be mareiually reproduced by the mechanism discussedhere.," On the other hand, this ratio observed in the local ISM is around $3.4\pm 0.7$ \citep{Lambert_98}, , which can be marginally reproduced by the mechanism discussedhere."
Gucliding wncertainty) and the evolutionary models of Burrowsetal.(1997)...,(including uncertainty) and the evolutionary models of \citet{1997ApJ...491..856B}.
 The lack of a clearLil line may also indicate that Πα is depleted iu the secondary as well: alternately. the liue iav be obscured by the relatively bright coutiuuun from the primary.," The lack of a clear line may also indicate that lithium is depleted in the secondary as well; alternately, the line may be obscured by the relatively bright continuum from the primary."
 Using as a template spectral data for the L3 spectral staudard 2MASS JI116315|223053. a source which exhibits absorption (Iirkpatricketal. 1999.. Fiewre 2)). and assuming a c1 mas brightuess difference in the 6708 reeion. we cleteruuued that a signal-to-noise ratio of 20 or better is required to detectL| absorption from the secondary alone.," Using as a template spectral data for the L3 spectral standard 2MASS J1146345+223053, a source which exhibits absorption \citealt{1999ApJ...519..802K}, , Figure \ref{fig_optspec}) ), and assuming a $\sim$ 1 mag brightness difference in the 6708 region, we determined that a signal-to-noise ratio of 20 or better is required to detect absorption from the secondary alone."
 Iu coutrast. SDSS data for have a signal-to-noise of roughly 5 in this region.," In contrast, SDSS data for have a signal-to-noise of roughly 5 in this region."
 Heuce. we cannot rule out the presence of the line in the secondary.," Hence, we cannot rule out the presence of the line in the secondary."
 Tf this liue is present. it would indicate a bounded age constraint of 0.55 S 7 = 0.8 Cur for the system (the corresponudiug coustraint based on the Daraffeetal.2003. evolutionary models are r Z αντ). 06," If this line is present, it would indicate a bounded age constraint of 0.55 $\lesssim$ $\tau$ $\lesssim$ 0.8 Gyr for the system (the corresponding constraint based on the \citealt{2003A&A...402..701B} evolutionary models are 0.6 $\lesssim$ $\tau$ $\lesssim$ 1.1 Gyr)."
SSuch a vouug age is uot incousistent with the kinematics of1155., Such a young age is not inconsistent with the kinematics of.
 The inferred space velocities [ELVIN] = (2646. 041 evaluated in the local standard of rest (Dehuen&Binney 1998).. are nominally consistent with that of a voung. thin disk svstem.," The inferred space velocities, $U, V, W$ ] = $\pm$ 6, $\pm$ 4, $\pm$ 7] evaluated in the local standard of rest \citep{1998MNRAS.298..387D}, are nominally consistent with that of a young, thin disk system."
" The JAK, colors of the primary is slightly blue for its inferred twpe. since GFNj zm 1.6 mag for L3 dwarts (INirkpatricketal.2000:Fahertyetal. 2009).."," The $J-K_s$ colors of the primary is slightly blue for its inferred type, since $\langle{J-K_s}\rangle$ $\approx$ 1.6--1.7 mag for L3 dwarfs \citep{2000AJ....120..447K, 2009AJ....137....1F}."
" This could be an indication of au older age. since uumsuallvy blue wear-infrared colors for VEM cdwiufs have been associated with both older kinematics aud ligher surface gravities οι, Knappetal.20014:Falertyetal. 20093)."," This could be an indication of an older age, since unusually blue near-infrared colors for VLM dwarfs have been associated with both older kinematics and higher surface gravities (e.g., \citealt{2004AJ....127.3553K, 2009AJ....137....1F}) )."
 ILowever. variatious in cloud propertics can also produce variations dn nemr-infrared color. au effect most pronounced iu iid-type L dwarfs (Chiuetal.2006:Durgasser 2008b)..," However, variations in cloud properties can also produce variations in near-infrared color, an effect most pronounced in mid-type L dwarfs \citep{2006AJ....131.2722C, 2008ApJ...674..451B}."
 Resolved. optical spectroscopy would settle this issue. aud could ideutifv as an important age standard for VLM studies.," Resolved optical spectroscopy would settle this issue, and could identify as an important age standard for VLM studies."
 We lave resolved the L dwarf into a (79 visual binary with L3.5 and LI componcuts., We have resolved the L dwarf into a $\farcs$ 9 visual binary with L3.5 and L4 components.
 Evidence based on the common proper motion. Common spectroplotometric distance and low probability of rvaudom alieniment confirms this svstem as a plysically bound pair.," Evidence based on the common proper motion, common spectrophotometric distance and low probability of random alignment confirms this system as a physically bound pair."
" While has the widest projected. plivsieal separation of auv L dwartL dwarf binary identified to date, 3043 AU at an estimated distance of 3343 pc. it is not unusual for VLM multiples in the field."," While has the widest projected physical separation of any L dwarf-L dwarf binary identified to date, $\pm$ 3 AU at an estimated distance of $\pm$ 3 pc, it is not unusual for VLM multiples in the field."
 The effective temperatures of its conrponeuts aud lack of absorption iu its combined light spectrin identify as a eood candidate for determining a precise svstenic age through the binary ήπια aee-dating techuique of Liu&Leeectt(2005).. necessitating resolved optical spectroscopy. that is Cluineutly feasible for this well-separated pair.," The effective temperatures of its components and lack of absorption in its combined light spectrum identify as a good candidate for determining a precise systemic age through the binary lithium age-dating technique of \citet{2005ApJ...634..616L}, necessitating resolved optical spectroscopy that is eminently feasible for this well-separated pair."
 The authors would like to thank telescope operator Paul Sears and instrmucut specialists John Ravuer for their assistance during the IRTF observations. RReid aud CCruz for their helpful input in the preparation of the imuauuscript. aud CCaballero for his thorough aud expert review.," The authors would like to thank telescope operator Paul Sears and instrument specialists John Rayner for their assistance during the IRTF observations, Reid and Cruz for their helpful input in the preparation of the manuscript, and Caballero for his thorough and expert review."
 This publication makes use of data from the Two Micron All Sky Survey. which is a joint project of the University of Massachusetts aud the Infrared Processing and Analysis Center. and funded by the National Aeronautics and Space Adiuinistrationo and the Natioual Science Foundation.," This publication makes use of data from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center, and funded by the National Aeronautics and Space Administration and the National Science Foundation."
 2\IASS data were obtained fou the NASA/TPAC Infrared Science Archive. which is operated by the Jet Propulsion Laboratory. California Tustitute of Technology. uncer contract with the National Acronauties and Space Administration.," 2MASS data were obtained from the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."
 Funding for the SDSS aud SDSS-II has been provided by the Alfred P. Sloan Foundation. the Participating Institutions. the National Science Foundation. the U.S. Departineut of Energv the National Acronautics and Space Achuinistration. the Japanese Moubukaealusho. the Max Planck Society. and the Iüeher Education Funding Council for Euglaud.," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."
 The SDSS is managed by the Astrophysical Research Consortium for the participating institutions /www.sdss.ore))., The SDSS is managed by the Astrophysical Research Consortium for the participating institutions ).
 This research has made use of the SIMDBAD database. operated at CDS. Strasbourg. France: tle Very-Low-Mass. Binarics Archive housed at) and maintained by Nick Siegler. Chris Celine. aud Adam Durgasser: aud the M. L. aud T dwarf compeudiunm housed at DwirfArchives.org and maintained bv Chris Celino. Davy Kirkpatriek. and Adam Bureasser.," This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France; the Very-Low-Mass Binaries Archive housed at and maintained by Nick Siegler, Chris Gelino, and Adam Burgasser; and the M, L, and T dwarf compendium housed at DwarfArchives.org and maintained by Chris Gelino, Davy Kirkpatrick, and Adam Burgasser."
 The authors wish to recoguize and acknowledge the very sjenificaut cultural role aud reverence that the sunuuit of Mauna Kea has always lad within the indigenous Hawaiian comunity., The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community.
We are most fortunate to have the opportunity to conduct observations frou this wowntain.,We are most fortunate to have the opportunity to conduct observations from this mountain.
 Facilities:, Facilities:
such relations may be very dillieult to be detect just. by inspection.,such relations may be very difficult to be detect just by inspection.
 With this strategy. good results may. still. be obtained even when a large portion of the data is missing or when the number of examples in each category is biased.," With this strategy, good results may still be obtained even when a large portion of the data is missing or when the number of examples in each category is biased."
 Fuzzy logic accommodates soft computing bv allowing for an imprecise representation of the real world., Fuzzy logic accommodates soft computing by allowing for an imprecise representation of the real world.
 In crisp logic à clear boundary is considered to separate the various classes and cach element is categorised into one group such that samples in sets οἱ and noc represents the entire dataset., In crisp logic a clear boundary is considered to separate the various classes and each element is categorised into one group such that samples in sets $A$ and $not A$ represents the entire dataset.
 Fuzzy logic extends on this by giving all sample a degree of membership in each set hence also caters for situations in which simple boolean logic is not enough., Fuzzy logic extends on this by giving all sample a degree of membership in each set hence also caters for situations in which simple boolean logic is not enough.
 Hf classically set membership was denoted by 0 (False) or 1 (true). now we can also have 0.25 or 0.75.," If classically set membership was denoted by 0 (false) or 1 (true), now we can also have $0.25$ or $0.75$."
 In fuzzy logic. the truth of any statement becomes à matter of degree.," In fuzzy logic, the truth of any statement becomes a matter of degree."
 The mathematical function that maps each input to the corresponding membership value between O and | is known as the membership function., The mathematical function that maps each input to the corresponding membership value between $0$ and $1$ is known as the membership function.
 Although this can be arbitrary. such function is normally chosen with computation efficiency and simplicity kept in mind.," Although this can be arbitrary, such function is normally chosen with computation efficiency and simplicity kept in mind."
 Various common membership unctions include the triangular function. the trapezoidal 'unction. the eaussian function and the bell function.," Various common membership functions include the triangular function, the trapezoidal function, the gaussian function and the bell function."
 The alter are the most popular and although they are smooth. concise and can attain non-zero values anywhere. they aul in specifving asvometric membership functions.," The latter are the most popular and although they are smooth, concise and can attain non-zero values anywhere, they fail in specifying asymmetric membership functions."
 Such imitation is elevated through the use of sigmoid. functions hat can either open left or right., Such limitation is elevated through the use of sigmoid functions that can either open left or right.
" For an inference system. #f(hen rules that deal with ""zzv consequents and fuzzy antecedents are defined."," For an inference system, $if-then$ rules that deal with fuzzy consequents and fuzzy antecedents are defined."
 An ageraced fuzzy set is then outputted after these conditional rules are compared and. combined by standard. logical operators equivalents., An aggraded fuzzy set is then outputted after these conditional rules are compared and combined by standard logical operators equivalents.
 Since the degree of membership can now attain anv value between 0 and 1. the AND and OR operators are replaced. by the mer and mn functions respectively.," Since the degree of membership can now attain any value between $0$ and $1$ , the $AND$ and $OR$ operators are replaced by the $max$ and $min$ functions respectively."
 Ehe resulting output is then defuzzified: to obtain one output value., The resulting output is then defuzzified to obtain one output value.
 Fuzzy inference svstems are easily understood and can even be applied. when dealing with imprecise data., Fuzzy inference systems are easily understood and can even be applied when dealing with imprecise data.
 Like decision tree classifiers. they provide a penetrative mocel that experts can analyze and even add other information to it.," Like decision tree classifiers, they provide a penetrative model that experts can analyze and even add other information to it."
 Such inference approaches have already been successfully applied. in a number of applications that range from integration in consumer produces to industrial process control. medical instrumentation ancl decision support πμο...," Such inference approaches have already been successfully applied in a number of applications that range from integration in consumer produces to industrial process control, medical instrumentation and decision support systems."
 In all machine learning algorithms. the set of input parameters strongly. determine the overall accuracy of the classifier.," In all machine learning algorithms, the set of input parameters strongly determine the overall accuracy of the classifier."
 Ideally. a minimum number of attributes that can differentiate between the three galaxy morphology classes are required.," Ideally, a minimum number of attributes that can differentiate between the three galaxy morphology classes are required."
 For this work. photometric and spectra values downloaded from the SDSS and tables. were used.," For this work, photometric and spectra values downloaded from the SDSS and tables, were used."
 Data for which classification information is available in the Galaxy Zoo catalogue were downloaded and used to test the various machine learning algorithms used., Data for which classification information is available in the Galaxy Zoo catalogue were downloaded and used to test the various machine learning algorithms used.
 In this study. the set of 13 parameters as taken by 2? which are based. on colour. profile fitting and. adaptive moments were used.," In this study, the set of 13 parameters as taken by \cite{banerji09} which are based on colour, profile fitting and adaptive moments were used."
 Llowever. we did not limit the evaluation to the band but also aimed at testing whether the values derived rom the band give equal or better classification accuracies.," However, we did not limit the evaluation to the band but also aimed at testing whether the values derived from the band give equal or better classification accuracies."
 The input parameters used are presented in Table 2.., The input parameters used are presented in Table \ref{parametersTable}.
 The DeVaucouleurs law provides a measure of how he surface brightness of an elliptical galaxy varies with apparent distance from the centre., The DeVaucouleurs law provides a measure of how the surface brightness of an elliptical galaxy varies with apparent distance from the centre.
 This should. provide a good element of discrimination between spiral and elliptical xofiles., This should provide a good element of discrimination between spiral and elliptical profiles.
 The parameter also helps to separate galaxy [rom star objects., The parameter also helps to separate galaxy from star objects.
 The concentration parameter is eiven by the ratios of radii containing and of he Petrosian flux in a given band., The concentration parameter is given by the ratios of radii containing and of the Petrosian flux in a given band.
 The parameter compares the range of Iuctuations in the surface brightness X the object to the full dynamic range of the surface rightness., The parameter compares the range of fluctuations in the surface brightness of the object to the full dynamic range of the surface brightness.
 Leis expected that this is negligible for smooth xoliles but becomes significant in high variance regions such as spiral armis., It is expected that this is negligible for smooth profiles but becomes significant in high variance regions such as spiral arms.
 The other parameters used. are based. on the object's shape., The other parameters used are based on the object's shape.
 Particularly. the adaptive moments derived. from the SDSS photometric pipeline are. second. moments of the object intensity. measured using a particular scheme designed to have an optimal signal to noise ratio.," Particularly, the adaptive moments derived from the SDSS photometric pipeline are second moments of the object intensity, measured using a particular scheme designed to have an optimal signal to noise ratio."
 These moments are caleulatecl by using a radial weight. function that adopts to the shape and size of the object., These moments are calculated by using a radial weight function that adopts to the shape and size of the object.
 Although theoretically there exists an optimal radial shapefor the, Although theoretically there exists an optimal radial shapefor the
correlation at a fixed angular separation and setting the redshift of two correlated halos to be equal for all other purposes.,correlation at a fixed angular separation and setting the redshift of two correlated halos to be equal for all other purposes.
 We calculate the shear signal of off-center halos on annuli 7f(h) by integrating the surface density of the halo inside and on the annulus and applying Eqn. 3.., We calculate the shear signal of off-center halos on annuli $\gamma_t^k(\bmath{h})$ by integrating the surface density of the halo inside and on the annulus and applying Eqn. \ref{eqn:gammatkappa}.
" We take into account the width A=0.1 of our annuli k with r€[1—A):τε,(14-A):ri] by calculating and tabulating where γι,h) and &(x,h) are the average tangential shear and convergence a halo with properties h introduces to an annulus of radius x."," We take into account the width $\Delta=0.1$ of our annuli $k$ with $r\in[(1-\Delta)\cdot r_k,(1+\Delta)\cdot r_k]$ by calculating and tabulating where $\gamma_t(x,\bmath{h})$ and $\kappa(x,\bmath{h})$ are the average tangential shear and convergence a halo with properties $\bmath{h}$ introduces to an annulus of radius $x$."
 The integral is numerically not more demanding than the simpler one required for zero-width rings., The integral is numerically not more demanding than the simpler one required for zero-width rings.
" As a simplification for numerical integration, we truncate the projected surface density of NFW halos (?7) at a radius rtrunc=20-Τε>T200m, which does not change the signal significantly."," As a simplification for numerical integration, we truncate the projected surface density of NFW halos \citep{1996A&A...313..697B,2000ApJ...534...34W} at a radius $r_{\mathrm{trunc}}=20\cdot r_s>r_{200m}$, which does not change the signal significantly."
" When doing thefinal integrations over dz to get the covariance matrices, we leave out the range 0.162<z0.338 as it is already included in the simulations."," When doing thefinal integrations over $dz$ to get the covariance matrices, we leave out the range $0.162 < z < 0.338$ as it is already included in the simulations."
 We limit the mass range of halos included to 10*McXMseoom<10 , We limit the mass range of halos included to $10^8\Msol\leq M_{200m}\leq 10^{14}\Msol$ .
"This lowers the overall variance because of the lack of more Mo.massive halos, which can be expected to be modelled separately in real-world weak lensing analyses (?).."," This lowers the overall variance because of the lack of more massive halos, which can be expected to be modelled separately in real-world weak lensing analyses \citep{2010arXiv1011.1084H}."
 We apply the approximation in which the uncorrelated LSS noise can simply be added to the reduced shear signal of the clusters., We apply the approximation in which the uncorrelated LSS noise can simply be added to the reduced shear signal of the clusters.
 Formally taking into account the effect of multiple lensing planes on reduced shears requires more complex calculations., Formally taking into account the effect of multiple lensing planes on reduced shears requires more complex calculations.
" Shear dispersions as a function of radius compared with shape noise for our binning scheme are shown in Figure A,, together with covariances between the signal at different radii."," Shear dispersions as a function of radius compared with shape noise for our binning scheme are shown in Figure \ref{fig:hmvar}, together with covariances between the signal at different radii."
 The inner peak is dominated by the one-halo term while the slowly decreasing outer range is mostly due to two- contributions., The inner peak is dominated by the one-halo term while the slowly decreasing outer range is mostly due to two-halo contributions.
" The results from our calculation agree with those presented in ??.. A1,,"," The results from our calculation agree with those presented in \citet{2001A&A...370..743H,2010arXiv1011.1084H}. . \ref{eqn:gtk},"
 A4 A10 , \ref{eqn:dp11} \ref{eqn:covc} 
2008. Vernazza οἱ al.,"2008, Vernazza et al."
 2009) because this slightly longer timescale leads to mD diy., 2009) because this slightly longer timescale leads to $r^*\approx 5$ -7 $R_{\rm pl}$.
 Note that these 7 values are plausible because the opticallv-active thin surface laver may be vulnerable to even tiniest tidal perturbations that were not considered in (he simulations ol Büchardson et al. (, Note that these $r^*$ values are plausible because the optically-active thin surface layer may be vulnerable to even tiniest tidal perturbations that were not considered in the simulations of Richardson et al. (
1998). and Walsh ancl Richardson (2003).,"1998), and Walsh and Richardson (2008)."
 Values /4.>1 Mv are also plausible (based on the NEA constraint only) but we are not able to deal with these longer timescales with the method described in this section., Values $t_{\rm sw}>1$ My are also plausible (based on the NEA constraint only) but we are not able to deal with these longer timescales with the method described in this section.
 The method described in the previous section is only approximate because it is difficult. even in the statistical sense. to reconstruct the history of past planetary. encounters by nunmerical integrations of present orbits into the past.," The method described in the previous section is only approximate because it is difficult, even in the statistical sense, to reconstruct the history of past planetary encounters by numerical integrations of present orbits into the past."
 It is even more problematic to trv to extend (hese numerical integrations bevond 1 My. (0 times comparable with the average orbital lifetime of NEAs (5 My: Bottke et al.," It is even more problematic to try to extend these numerical integrations beyond 1 My, to times comparable with the average orbital lifetime of NEAs $\approx$ 5 My; Bottke et al."
 2002)., 2002).
 This is because the statistical results obtained from these integrations cannot be used to retrace the real orbital evolution of individual objects from their source locations in the main belt to NEA space., This is because the statistical results obtained from these integrations cannot be used to retrace the real orbital evolution of individual objects from their source locations in the main belt to NEA space.
 Consecuently. ihe encounter statistic obtained from such integrations would be incorrect.," Consequently, the encounter statistic obtained from such integrations would be incorrect."
 A clilferent method needs {ο be used to circumvent this problem (and check on the results obtained in the previous section)., A different method needs to be used to circumvent this problem (and check on the results obtained in the previous section).
 We used the method developed in Bottke et al. (, We used the method developed in Bottke et al. (
2002: herealter DO2).,2002; hereafter B02).
 DO2 constructed the NEA model by tracking orbits originating from various locations in the main belt. such as the rj and 3:1 resonances. and the population known as the Intermediate source Mars Crossers (IAICs for short).," B02 constructed the NEA model by tracking orbits originating from various locations in the main belt, such as the $\nu_6$ and 3:1 resonances, and the population known as the Intermediate source Mars Crossers (IMCs for short)."
 IMCs have marginally unstable orbits that are leaking from more stable locations in (he inner main belt but have not vel reached. \lars-crossing: space (Migliorini et al., IMCs have marginally unstable orbits that are leaking from more stable locations in the inner main belt but have not yet reached Mars-crossing space (Migliorini et al.
 1998. Morbidelli and Nesvorny -—," 1998, Morbidelli and Nesvorný 1999)."
 By calibrating the orbital distribution obtained in the model tothat of known NEÀs. D02 was able to set constraints on the contribution of each source to the NEA population as a function of absolute magnitude 17.," By calibrating the orbital distribution obtained in the model to that of known NEAs, B02 was able to set constraints on the contribution of each source to the NEA population as a function of absolute magnitude $H$."
 Apparently. the three most important sources are (he 4; resonance. 3:1 resonance and IMCs. which contribute by37%.. and27%.. respectivelv. for 11<18. {," Apparently, the three most important sources are the $\nu_6$ resonance, 3:1 resonance and IMCs, which contribute by, and, respectively, for $H<18$. ["
The outer main belt resonances and Jupiter-family comets provide the remaining 16%..,The outer main belt resonances and Jupiter-family comets provide the remaining .]
.) We conducted numerical simulations similar (o (hose reported in BO2 onlv this time focusing on the statistics :ose encounters ofNEAs with the terrestrial planets., We conducted numerical simulations similar to those reported in B02 only this time focusing on the statistics of close encounters of NEAs with the terrestrial planets.
 Specifically. we tracked orbits of --.71000 test particles (per source) as thev evolve from their source regions into space.," Specifically, we tracked orbits of $\sim$ 1000 test particles (per source) as they evolve from their source regions into planet-crossing space."
 These integrations included seven planets (Venus to Neptune)., These integrations included seven planets (Venus to Neptune).
 Thermal effects on orbits (such as the Yarkovsky effect) were neglected because NEA dynamics is mainly controlled by planetary encounters and powerbul resonances., Thermal effects on orbits (such as the Yarkovsky effect) were neglected because NEA dynamics is mainly controlled by planetary encounters and powerful resonances.
 We used a variant of the Wisdom-IHolman map (Wisdom aud Lolman 1991) known as rrmvs3 (Levison and Duncan 1994)., We used a variant of the Wisdom-Holman map (Wisdom and Holman 1991) known as rmvs3 (Levison and Duncan 1994).
 We modified the Swill integrator so that it records all encounters of model NEAs with planets up to a distance of 20 £25., We modified the Swift integrator so that it records all encounters of model NEAs with planets up to a distance of 20 $R_{\rm pl}$.
 These cata were used in a statistical that follows the orbital evolution of each object estimates ils spectral index al any modelgiven moment., These data were used in a statistical model that follows the orbital evolution of each object and estimates its spectral index at any given moment.
 We define (he spectral index. I. as 0 jailfor a fresh Q-tvpe object andL for a fully space weathered S tvpe object.," We define the spectral index, $I_s$, as 0 for a fresh Q-type object and1 for a fully space weathered S type object."
" The inlemmedlicte values 1/3<I,2/3 are used (o represent the Sq-tvpe asteroids.", The intermediate values $1/3<I_s<2/3$ are used to represent the Sq-type asteroids.
" The model has (wo parameters: 7* and ἐν, ", The model has two parameters: $r^*$ and $t_{\rm sw}$.
"Each object is assumed (o be initially fullv space weathered with J,=1.", Each object is assumed to be initially fully space weathered with $I_s = 1$.
" I£ an encounter with r«i5 occurs. we set {ς=0 at the corresponding time. and let a simple SW algorithm5 increase /,."," If an encounter with $r<r^*$ occurs, we set $I_s = 0$ at the corresponding time, and let a simple SW algorithm increase $I_s$ ."
 Therefore. assuming5 that no additional encounters," Therefore, assuming that no additional encounters"
strength below 10 G. This result is in agreement with the development of a three-dimensional cascade (see Sect.,strength below 10 G. This result is in agreement with the development of a three-dimensional cascade (see Sect.
 2)., 2).
 The one-generation approximation for the cascade is good in this case since for high magnetic field (B>5 G). the contribution from extra-generations can be ignored (see Sect. 4.4)).," The one-generation approximation for the cascade is good in this case since for high magnetic field $B>5~$ G), the contribution from extra-generations can be ignored (see Sect. \ref{sect_mag}) )."
 Note that the synchrotron peak energy emitted by secondary pairs barely changes with increasing magnetic field (ej=| MeV. see Fig. 11)).," Note that the synchrotron peak energy emitted by secondary pairs barely changes with increasing magnetic field $\epsilon_1\approx 1~$ MeV, see Fig. \ref{mag_orb}) )."
 This is due to the effect of synchrotron losses on the cooled energy distribution of the radiating pairs in the cascade., This is due to the effect of synchrotron losses on the cooled energy distribution of the radiating pairs in the cascade.
 Synchrotron cooling dominates over Compton cooling (fy€ fj) at high energies and depletes the most energetic pairs in the steady-state distribution (see Eq. 6))., Synchrotron cooling dominates over Compton cooling $t_{syn}<t_{ic}$ ) at high energies and depletes the most energetic pairs in the steady-state distribution (see Eq. \ref{cool}) ).
 In consequence. the mean energy of cooled pairs in the cascade diminishes with increasing magnetic field (for a fixed stellar radiation field).," In consequence, the mean energy of cooled pairs in the cascade diminishes with increasing magnetic field (for a fixed stellar radiation field)."
 The non-trivial combination of both effects results in a (almost) constant synchrotron peak (the critical energy in synchrotron radiation is proportional to y7B)., The non-trivial combination of both effects results in a (almost) constant synchrotron peak (the critical energy in synchrotron radiation is proportional to $\gamma_e^2 B$ ).
 Three-dimensional pair cascade can be initiated in. gamma-ray binaries provided that pairs are confined and tsotropized by the ambient magnetic field in the system., Three-dimensional pair cascade can be initiated in gamma-ray binaries provided that pairs are confined and isotropized by the ambient magnetic field in the system.
 In LS 5039. a three-dimensional pair cascade contributes significantly in the formation of the VHE radiation at every orbital phase.," In LS 5039, a three-dimensional pair cascade contributes significantly in the formation of the VHE radiation at every orbital phase."
 In particular. the cascade radiation prevails over the primary source of gamma rays close to superior conjunction where the yy-opacity is high) and gives a lower flux than the ID cascade at this phase.," In particular, the cascade radiation prevails over the primary source of gamma rays close to superior conjunction where the $\gamma\gamma$ -opacity is high) and gives a lower flux than the 1D cascade at this phase."
 The 3D cascade radiation 1s modulated differently compared with the 1D cascade and preserves the modulation of the primary absorbed flux because the pairs stay localized., The 3D cascade radiation is modulated differently compared with the 1D cascade and preserves the modulation of the primary absorbed flux because the pairs stay localized.
 In addition. the 3D cascade radiation decreases the amplitude of the observed TeV modulation.," In addition, the 3D cascade radiation decreases the amplitude of the observed TeV modulation."
 The amplitude of the HESS light curve is correctly reproduced for an melination of|=40°., The amplitude of the HESS light curve is correctly reproduced for an inclination of $i\approx 40\degr$.
 The ambient magnetic field in LS 5039 cannot exceed 106 (if uniform) or synchrotron radiation from pairs in the cascade would overestimate X-ray observations., The ambient magnetic field in LS 5039 cannot exceed 10 G (if uniform) or synchrotron radiation from pairs in the cascade would overestimate X-ray observations.
 This is a reasonable constraint as most of massive stars are probably non-magnetic. even though strong magnetic fields (>100 G) have been measured for a few O stars at their surface (see ? for a recent review and references therein).," This is a reasonable constraint as most of massive stars are probably non-magnetic, even though strong magnetic fields $>100~$ G) have been measured for a few O stars at their surface (see \citealt{2009ARA&A..47..333D} for a recent review and references therein)."
 The VHE emitter should also remain very close to the compact object location. possibly at the collision site between both star winds. otherwise the TeV light curve shape is not reproduced although this does not rule out complex combinations.," The VHE emitter should also remain very close to the compact object location, possibly at the collision site between both star winds, otherwise the TeV light curve shape is not reproduced although this does not rule out complex combinations."
 The model described in this paper is not fully satisfying., The model described in this paper is not fully satisfying.
 The spectral shape of VHE gamma rays ts still not reproduced close to superior conjunction., The spectral shape of VHE gamma rays is still not reproduced close to superior conjunction.
 In addition. the light curve amplitude tends to be overestimated except for low inclinations but then the shape is not perfect.," In addition, the light curve amplitude tends to be overestimated except for low inclinations but then the shape is not perfect."
 It remains difficult to explain both the shape and the amplitude of the modulation in LS 5039., It remains difficult to explain both the shape and the amplitude of the modulation in LS 5039.
 A possible solution would be to consider a more complex injection of fresh pairs along the orbit or additional effects such as adiabatic losses or advection., A possible solution would be to consider a more complex injection of fresh pairs along the orbit or additional effects such as adiabatic losses or advection.
 A Doppler-boosted emission in the primary source can also change the spectrum seen by the observer. especially around superior conjunction (?)..," A Doppler-boosted emission in the primary source can also change the spectrum seen by the observer, especially around superior conjunction \citep{2010arXiv1004.0511D}."
algorithm to allow simulation of the effects of multiple ionizing sources.,algorithm to allow simulation of the effects of multiple ionizing sources.
" In the case that no two HII regions overlap, no changes to the algorithm would be required, but if the ionized regions excited by two or more different sources overlap, a given particle may be receiving flux from more than one source."," In the case that no two HII regions overlap, no changes to the algorithm would be required, but if the ionized regions excited by two or more different sources overlap, a given particle may be receiving flux from more than one source."
" For an ionized particle, the recombination rate per unit volume of the ionized gas making up the particle is apn’, where n is the number density of ions and op is the case-B recombination coefficient."," For an ionized particle, the recombination rate per unit volume of the ionized gas making up the particle is $\alpha_{\rm B}n^{2}$, where $n$ is the number density of ions and $\alpha_{\rm B}$ is the case–B recombination coefficient."
" To keep the particle ionized, ionizing photons must be subtracted from radiation beams passing through the particle."," To keep the particle ionized, ionizing photons must be subtracted from radiation beams passing through the particle."
 The problem that must be solved is to determine how many photons should be subtracted from each beam., The problem that must be solved is to determine how many photons should be subtracted from each beam.
 We solve this problem in a crude way by assuming that all sources illuminating a given ionized particle are equally responsible for keeping it ionized., We solve this problem in a crude way by assuming that all sources illuminating a given ionized particle are equally responsible for keeping it ionized.
" Strictly, the global ionization state of the whole cloud should then be found by iteration, but this is time-consuming."," Strictly, the global ionization state of the whole cloud should then be found by iteration, but this is time–consuming."
" Instead, at a given timestep, if a gas particle is receiving radiation from N ionizing sources, when the particle's ionization state is next updated, we assume that the volume recombination rate subtracted from the radiation beam of each source passing through the particle is apn?/N."," Instead, at a given timestep, if a gas particle is receiving radiation from $N$ ionizing sources, when the particle's ionization state is next updated, we assume that the volume recombination rate subtracted from the radiation beam of each source passing through the particle is $\alpha_{\rm B} n^{2}/N$."
 We therefore assume that the recombination load is shared equally among all the sources illuminating a given Both the low resolution and the high resolution clouds evolve in a similar fashion over the 4.3 Myr that the evolutions were followed (without feedback)., We therefore assume that the recombination load is shared equally among all the sources illuminating a given Both the low resolution and the high resolution clouds evolve in a similar fashion over the 4.3 Myr that the evolutions were followed (without feedback).
 The turbulence in the gas generates significant internal structure in the form of filaments., The turbulence in the gas generates significant internal structure in the form of filaments.
" Regions within the filamentary structure become self-gravitating and collapse to be replaced by sink particles (which represent stars in the high-resolution simulation, and small clusters in the low-resolution run)."," Regions within the filamentary structure become self-gravitating and collapse to be replaced by sink particles (which represent stars in the high–resolution simulation, and small clusters in the low–resolution run)."
" Larger-scale regions become gravitationally bound due to the shock dissipation of kinetic energy, allowing clusters or groups of clusters to form at the junctions of the filaments."," Larger-scale regions become gravitationally bound due to the shock dissipation of kinetic energy, allowing clusters or groups of clusters to form at the junctions of the filaments."
 These forming clusters continue to grow by accreting infalling gas and other sink particles., These forming clusters continue to grow by accreting infalling gas and other sink particles.
" The clustering properties of the model are of intrinsic interest for comparison to real massive star forming regions, but also since the distribution of clusters and massive stars determines to a large extent the influence of The low resolution run created 601 sink-particles whereas the high-resolution simulation created 5750 sinks."," The clustering properties of the model are of intrinsic interest for comparison to real massive star forming regions, but also since the distribution of clusters and massive stars determines to a large extent the influence of The low resolution run created 601 sink-particles whereas the high-resolution simulation created 5750 sinks."
" In Figure 1, we plot the location of all stars at a time of 43Myr in this simulation."," In Figure \ref{fig:OBclus}, we plot the location of all stars at a time of 4.3Myr in this simulation."
 Amongst the sinks are several very significant clusterings including the most massive cluster with a mass density in excess of 10° Mo pc? inside 0.25 pc., Amongst the sinks are several very significant clusterings including the most massive cluster with a mass density in excess of $10^5$ $_{\odot}$ $^{-3}$ inside 0.25 pc.
" Figures 2 and 3 show the mass density for each sink in the high-resolution computation computed from the mass within lpc of that sink, and from the distance to its tenth nearest neighbouring sink respectively."," Figures \ref{fig:clus_1pc} and \ref{fig:clus_10neigh} show the mass density for each sink in the high–resolution computation computed from the mass within 1pc of that sink, and from the distance to its tenth nearest neighbouring sink respectively."
 We see from these figures that most of the more massive sinks are in highly clustered regions with local mass densities reaching 10° Mo pe’., We see from these figures that most of the more massive sinks are in highly clustered regions with local mass densities reaching $10^8$ $_{\odot}$ $^{-3}$.
" In addition to the high clustering of most of the massive sinks, we see a number of relatively massive sinks with masses >100 Mo that are in low density regions as measured from the distance to their tenth nearest neighbour."," In addition to the high clustering of most of the massive sinks, we see a number of relatively massive sinks with masses $\ge 100$ $_{\odot}$ that are in low density regions as measured from the distance to their tenth nearest neighbour."
 Such sinks likely represent small clusters that may contain what appear to be isolated massive stars in the context of the whole, Such sinks likely represent small clusters that may contain what appear to be isolated massive stars in the context of the whole
as |IK approaches zero.,as $\mid \!{\mathbf{K}}\!\mid$ approaches zero.
 For self gravitational systems the small |IK limit is unphysical. due to the absence of screening.," For self gravitational systems the small $\mid \!{\mathbf{K}}\!\mid$ limit is unphysical, due to the absence of screening."
 The distance between interacting particles is limited in this case by the inhomogeneity of the system. a feature which is lost in the local approximation.," The distance between interacting particles is limited in this case by the inhomogeneity of the system, a feature which is lost in the local approximation."
" If one were to insist on the quasi-homogeneous approximation. the integration over wave vectors in equation (48)) would have to be artificially limited from below to some minimum modulus A,,;,2x/I. where His a characteristic size of the system."," If one were to insist on the quasi-homogeneous approximation, the integration over wave vectors in equation \ref{colltensorhomograv}) ) would have to be artificially limited from below to some minimum modulus $K_{min} \sim 2\pi/R$, where $R$ is a characteristic size of the system."
 Little would then be gained over a more traditional Fokker-Planck approximation. but for the fact that equation (47) still accounts for the collective dressing of the colliding particles.," Little would then be gained over a more traditional Fokker-Planck approximation, but for the fact that equation \ref{LAequationhomograv}) ) still accounts for the collective dressing of the colliding particles."
 When these collective effects. are themselves. neglected. which amounts to take ς=1 in equation. (48)). the usual local Fokker-Planck equation (49)) is recovered. with braking and diffusion coctlicicnts given hy expressions (50)) and (51)). 5 now supposedly being equal to unity.," When these collective effects are themselves neglected, which amounts to take $\varepsilon = 1$ in equation \ref{colltensorhomograv}) ), the usual local Fokker-Planck equation \ref{formeFP}) ) is recovered, with braking and diffusion coefficients given by expressions \ref{Ahomogene}) ) and \ref{Bhomogene}) ), $\varepsilon$ now supposedly being equal to unity."
 As above. the integral on wavevectors in equation (48)) should limited to a lower cutolf at [KK|2Ay. to account for the finite size of the system. and to an upper cutoll[IK|=Ayia. to account for strong collisions (section 5.3)).," As above, the integral on wavevectors in equation \ref{colltensorhomograv}) ) should limited to a lower cutoff at $\mid \! {\mathbf{K}}\! \mid = K_{min}$, to account for the finite size of the system, and to an upper cutoff$\mid \! {\mathbf{K}}\! \mid = K_{max}$, to account for strong collisions (section \ref{strongcoll}) )."
" The coulomb logarithm is InA. where X—A,,,""/1I,,;,."," The coulomb logarithm is $\ln \Lambda$, where $\Lambda = K_{max}/K_{min}$."
 When s equals unity. the integration over wave vectors in equation (48)) can easily be performed.," When $\varepsilon$ equals unity, the integration over wave vectors in equation \ref{colltensorhomograv}) ) can easily be performed."
 The result. which involves the relative velocity of the colliding particles ο-νv. is: where Tis the unit second rank tensor.," The result, which involves the relative velocity of the colliding particles ${\mathbf{g}} = {\mathbf{v}} - {\mathbf{v}}'$, is: where ${\overline{\overline{ {\mathbf{I}} }}}$ is the unit second rank tensor."
 his is identical to the Pokker-Planek equation presented. for example. in (1987).. equations (8.4.10).," This is identical to the Fokker-Planck equation presented, for example, in \citet{BinneyTremaine}, equations (8A.10)."
 The collective dressing becomes important when |=?dn equation (48)) largely differs from unity., The collective dressing becomes important when $\mid\varepsilon\mid^{-2}$ in equation \ref{colltensorhomograv}) ) largely differs from unity.
 As shown by Weinberg(1993).. this happens when the system is not far from being unstable. for example when its size becomes of order of the Jeans length. the complex zeroes of £(IKc) Iving close. but below. the real axis.," As shown by \citet{Weinberg93}, this happens when the system is not far from being unstable, for example when its size becomes of order of the Jeans length, the complex zeroes of $\varepsilon({\mathbf{K}}, \omega)$ lying close, but below, the real axis."
 Equation (38)) satisfies an Ll theorem which states that the statistical entropy: increases with time., Equation \ref{LAequation}) ) satisfies an H theorem which states that the statistical entropy: increases with time.
" Because the relaxing distribution functions depend on actions only. the integral over angles reduces to a mere multiplication bv a factor Sx"". so that: The time derivative of f"" is given by equation. (38)) which can be svmmetrized by substituting to the first operator ΚιV5,1 the operator ΚιV31ΚωVs."," Because the relaxing distribution functions depend on actions only, the integral over angles reduces to a mere multiplication by a factor $8\pi^3$, so that: The time derivative of $f^a$ is given by equation \ref{LAequation}) ) which can be symmetrized by substituting to the first operator ${\mathbf{k}}_1\! \cdot\! {\mathbf{\nabla}}_{ {\mathbf{J}}_1}$ the operator ${\mathbf{k}}_1\! \cdot\! {\mathbf{\nabla}}_{ {\mathbf{J}}_1} 
-\, {\mathbf{k}}_2\! \cdot\! {\mathbf{\nabla}}_{ {\mathbf{J}}_2 }$."
" The contribution associated with the added operatorKo»Vy, vanishes on integration> over Jo.", The contribution associated with the added operator $\! {\mathbf{k}}_2\! \cdot\! {\mathbf{\nabla}}_{ {\mathbf{J}}_2 }$ vanishes on integration over ${\mathbf{J}}_2$.
 This can be seen by using the Dux divergence theorem in action space. recognizing that the surface integral over the boundary of the physical Jz domain vanishes.," This can be seen by using the flux divergence theorem in action space, recognizing that the surface integral over the boundary of the physical ${\mathbf{J}}_2$ domain vanishes."
" Indeed. the expression on the right of the first operator ΚιV3, in equation (38)) represents. up to its sign. the Dux in action space at Jy caused by collisions with particles having action Je or the Lux at Jo caused by collisions with particles of action Jy."," Indeed, the expression on the right of the first operator ${\mathbf{k}}_1\! \cdot\! {\mathbf{\nabla}}_{ {\mathbf{J}}_1}$ in equation \ref{LAequation}) ) represents, up to its sign, the flux in action space at ${\mathbf{J}}_1$ caused by collisions with particles having action ${\mathbf{J}}_2$ or the flux at ${\mathbf{J}}_2$ caused by collisions with particles of action ${\mathbf{J}}_1$."
 The physical domain is limited in action space by a boundary at a finite distance and extends to infinity in certain directions., The physical domain is limited in action space by a boundary at a finite distance and extends to infinity in certain directions.
 Phe llux through the boundary at finite distance vanishes because the action vector of no particle can evolve through this boundary from the physical to the unphysical domain., The flux through the boundary at finite distance vanishes because the action vector of no particle can evolve through this boundary from the physical to the unphysical domain.
 The Ilux at infinity vanishes. because f(J2)«dh decreases fast⋅ enough., The flux at infinity vanishes because $f^b({\mathbf{J}}_2)$ decreases fast enough.
" This wesjustifiesIp the above-sugeested, substitution.", This justifies the above-suggested substitution.
". usThe expression. of t.0;f£""""(1) given. by equation (38)). modified as described. when inserted in equation (55)). gives the following expression for ds/dl: This expression is further svnimetrizecl by combining it with the equivalent expression obtained by exchanging species indices e and b. actions J, and Jo and Fourier variables Κι and ke."," The expression of $\partial_t f^a(1)$ given by equation \ref{LAequation}) ), modified as described, when inserted in equation \ref{evolentropystat}) ), gives the following expression for $ds/dt$: This expression is further symmetrized by combining it with the equivalent expression obtained by exchanging species indices $a$ and $b$, actions ${\mathbf{J}}_1$ and ${\mathbf{J}}_2$ and Fourier variables ${\mathbf{k}}_1$ and ${\mathbf{k}}_2$ ."
 The resulting expression is then integrated by parts. using the flux divergence theorem in either Jy or Jo space.," The resulting expression is then integrated by parts, using the flux divergence theorem in either ${\mathbf{J}}_1$ or ${\mathbf{J}}_2$ space."
 As explained above. the contribution of the integral on the boundary of the action domain or at infinity vanishes.," As explained above, the contribution of the integral on the boundary of the action domain or at infinity vanishes."
 We are eventually left with the positive expression:, We are eventually left with the positive expression:
sentimental reasons we shall keep the contribution due to the slow resonance.,sentimental reasons we shall keep the contribution due to the slow resonance.
 The modified version of the ideal dispersion relation GEL) is F is given by (16)) and G is defined as When we combine the TT approximation with TB approximation. the dispersion relation is reduced to The zero order solution to (50)) without taking into account the effect of the resonance 15 of course (18)).," The modified version of the ideal dispersion relation \ref{DRInC1}) ) is $F$ is given by \ref{F}) ) and $G$ is defined as When we combine the TT approximation with TB approximation, the dispersion relation is reduced to The zero order solution to \ref{DRInC4}) ) without taking into account the effect of the resonance is of course \ref{Freqkink}) )."
 The effect of the resonance is contained in G., The effect of the resonance is contained in $G$.
 In order to take that effect into account we proceed as before and approximate c with ως+2{ωιγ., In order to take that effect into account we proceed as before and approximate $\omega^2$ with $\omega_{\mathrm k} ^2 + 2 i \omega_{\mathrm k} \gamma$.
 The solution for the damping decrement is If the variation of ως is solely due to the variation of density p a8 is the case here since the vertical magnetic field is constant. the equation can be rewritten às From here on we shall specialise to a=1.," The solution for the damping decrement is If the variation of $\omega_{\mathrm A}^2$ is solely due to the variation of density $\rho$ as is the case here since the vertical magnetic field is constant, the equation can be rewritten as From here on we shall specialise to $m=1$."
 For a linear profile of density For a sinusoidal profile of density For all practical purposes we can neglect the contribution proportional to (&-R) and conclude that the damping due to resonant absorption of the kink mode in an incompressible plasma is the same as that in a pressureless plasma (see equations (32)) and (33)))., For a linear profile of density For a sinusoidal profile of density For all practical purposes we can neglect the contribution proportional to $(k_z R)^2$ and conclude that the damping due to resonant absorption of the kink mode in an incompressible plasma is the same as that in a pressureless plasma (see equations \ref{GammaNoPr3}) ) and \ref{GammaNoPr4}) )).
 If we forget about differences proportional to (Κ.Α then the conclusion is that kink MHD waves in pressureless plasmas and incompressible plasmas are the same., If we forget about differences proportional to $(k_z R)^2$ then the conclusion is that kink MHD waves in pressureless plasmas and incompressible plasmas are the same.
 In view of that conclusion it is difficult to understand why a kink mode can be called fast as fast waves are absent from incompressible plasmas., In view of that conclusion it is difficult to understand why a kink mode can be called fast as fast waves are absent from incompressible plasmas.
 The eigenfunctions in the thin dissipative layer can be described by the functions F(t) and G(r) which were first introduced by Rudemanetal.(1995) for non-stationary incompressible resonant Alfvénn waves in planar plasmas., The eigenfunctions in the thin dissipative layer can be described by the functions $\tilde{F}(\tau)$ and $\tilde{G}(\tau)$ which were first introduced by \cite{Ruderman1995} for non-stationary incompressible resonant Alfvénn waves in planar plasmas.
 The conclusion is the same as in the previous section., The conclusion is the same as in the previous section.
 The kink MHD waves are highly Alfvénnie in the dissipative layer., The kink MHD waves are highly Alfvénnic in the dissipative layer.
 So far we have seen that kink MHD waves in the thin tube approximation do not care about propagating (body wave) or evanescent (surface wave) behaviour in the internal part of the flux tube., So far we have seen that kink MHD waves in the thin tube approximation do not care about propagating (body wave) or evanescent (surface wave) behaviour in the internal part of the flux tube.
 The behaviour in the exterior plasma was until now evanescent., The behaviour in the exterior plasma was until now evanescent.
 Here we take the next step and consider leakage of energy due to MHD radiation., Here we take the next step and consider leakage of energy due to MHD radiation.
 MHD radiation causes the frequencies to be complex even in absence of resonant damping., MHD radiation causes the frequencies to be complex even in absence of resonant damping.
 MHD waves in the presence of MHD radiation were studied for uniform flux tubes by Spruit(1982). in the TT approximation and by Cally(1985.2003) forarbitrary values of the radius.," MHD waves in the presence of MHD radiation were studied for uniform flux tubes by \cite{Spruit1982}
 in the TT approximation and by \cite{Cally1985, Cally2003} forarbitrary values of the radius."
 Stenuitetal.(1998) and Stenuitetal.(1999) determined MHD waves undergoing resonant absorption and/or leakage for photospheric flux tubes embedded in a non-magnetic surrounding., \cite{Stenuit1998} and \cite{Stenuit1999} determined MHD waves undergoing resonant absorption and/or leakage for photospheric flux tubes embedded in a non-magnetic surrounding.
 Stenuitetal.(1999) pointed out which Hankel function to use for leaky and non-leaky waves., \cite{Stenuit1999} pointed out which Hankel function to use for leaky and non-leaky waves.
 We use the equations for linear MHD waves on a I-dimensional cylinder with a straight field., We use the equations for linear MHD waves on a 1-dimensional cylinder with a straight field.
 Effects due to plasma pressure and compressibility are taken into account., Effects due to plasma pressure and compressibility are taken into account.
 The equations are The coefficient functions D and C» are now As before we rewrite the two first order differential equations of (56)) as a second order ordinary differential equation for P': where [(w7) is now defined as We have solved the set of equations (560) under general conditions allowing for non-zero plasma pressure and compressibility. see Spruit(1982);Cally(1985). for uniform plasmas and Goossens&Hollweg(1993) for nonuniform plasmas.," The equations are The coefficient functions $D$ and $C_2$ are now As before we rewrite the two first order differential equations of \ref{MHDwavesMHDR1}) ) as a second order ordinary differential equation for $P'$: where $\Gamma(\omega^2)$ is now defined as We have solved the set of equations \ref{MHDwavesMHDR1}) ) under general conditions allowing for non-zero plasma pressure and compressibility, see \citet
[]{Spruit1982,Cally1985} for uniform plasmas and \citet[]{Goossens1993} for nonuniform plasmas."
 Here we present the results for à pressureless plasma with vs=0., Here we present the results for a pressureless plasma with $v_{\mathrm S}=0$.
 Equations (56)) are then reduced to equation (1)) and equation (59)) is reduced to equation (8))., Equations \ref{MHDwavesMHDR1}) ) are then reduced to equation \ref{MHDwavesNoPressure1}) ) and equation \ref{GammaMHDR}) ) is reduced to equation \ref{Gamma}) ).
 On one hand. sine we aim to study MHD waves that are propagating in the external medium we require that co—wi.» 0.," On one hand, sine we aim to study MHD waves that are propagating in the external medium we require that $\omega^2 - \omega_{\mathrm {Ae}}^2 >0$ ."
 On the other, On the other
In this section. we apply our technique to two particular cases of observed. binaries and triples containing merger products.,"In this section, we apply our technique to two particular cases of observed binaries and triples containing merger products."
 The first is an observed. triple system: in the old open cluster M67 that is thought to contain two ος (vandenBerectal.2001:Sandequistet2003).," The first is an observed triple system in the old open cluster M67 that is thought to contain two BSs \citep{vandenberg01,
 sandquist03}."
.. Phe second is the period-eccentricity clistribution of the Bs binary population of the OC NGC 155. which bears a remarkable resemblance to M67. (Alathicu&Celler2009).," The second is the period-eccentricity distribution of the BS binary population of the OC NGC 188, which bears a remarkable resemblance to M67 \citep{mathieu09}."
. After determining the most probable qualitative formation scenarios. we obtain quantitative constraints for. suitable initial conditions that could. have produced. the observed orbital parameters.," After determining the most probable qualitative formation scenarios, we obtain quantitative constraints for suitable initial conditions that could have produced the observed orbital parameters."
 51082 is believed to be a triple svstem in the old OC M67 (vandenBerectal.2001:Sandequistet2003).," S1082 is believed to be a triple system in the old OC M67 \citep{vandenberg01, sandquist03}."
.. The observations suggest that a distant triple companion orbits à close binary containing a BS and another peculiar star., The observations suggest that a distant triple companion orbits a close binary containing a BS and another peculiar star.
 The companion to the BS has a photometric appearance that puts it close to the MSTO in the CMD ane vet. curiously. its derived mass is significantly &reater than that of the ol.," The companion to the BS has a photometric appearance that puts it close to the MSTO in the CMD and yet, curiously, its derived mass is significantly greater than that of the turn-off."
 The outer companion is a BS in its own right. so that $1082 is thought to be composed of two BSs.," The outer companion is a BS in its own right, so that S1082 is thought to be composed of two BSs."
 Although both the inner and outer components of this. suspected triple have systemic velocites that sugeest they are. both cluster members. it is important to note that there is no direct evidence proving a dynamical link between the two (Sandquistetal.2003).," Although both the inner and outer components of this suspected triple have systemic velocites that suggest they are both cluster members, it is important to note that there is no direct evidence proving a dynamical link between the two \citep{sandquist03}."
. Assumine for the time being that a dvnamical link does exist. we can apply the procedure outlined in Section 2.2. to the case of SI082:," Assuming for the time being that a dynamical link does exist, we can apply the procedure outlined in Section \ref{general} to the case of S1082:"
Isothermal simulations are relatively cheap. so an encounter survey can be performed with modest computational resources.,"Isothermal simulations are relatively cheap, so an encounter survey can be performed with modest computational resources."
 For ease of comparison. | adopted the same set of four encounter geometries. used. in previous studies (c.g. Barnes 1992: Barnes Lernquist 1996).," For ease of comparison, I adopted the same set of four encounter geometries used in previous studies (e.g. Barnes 1992; Barnes Hernquist 1996)."
 Table. 1 lists clisk inclinations ὁ and pericentric arguments w for the passages used in this paper., Table \ref{tab:geometries} lists disk inclinations $i$ and pericentric arguments $\omega$ for the passages used in this paper.
 Each combination was used in three different encounters: first. a close passage of galaxies with a 1:1 mass ratio: second. a more distant. passage. again with a 1:1 ratio: and third. a close passage with a 3:1 mass ratio.," Each combination was used in three different encounters: first, a close passage of galaxies with a 1:1 mass ratio; second, a more distant passage, again with a 1:1 ratio; and third, a close passage with a 3:1 mass ratio."
 Vhus there are 12 simulations in this survey., Thus there are $12$ simulations in this survey.
 For convenience. E designate cach simulation by specifying the disk geometry. (rom Table 1)). the mass ratio (either door 3:1). and optionally the pericentric separation (C or DJ).," For convenience, I designate each simulation by specifying the disk geometry (from Table \ref{tab:geometries}) ), the mass ratio (either 1:1 or 3:1), and optionally the pericentric separation (C or D)."
 Thus DIR 1:1 € specifies a direct. close passage of equal-mass galaxies. DIR 1:1 D is a more distant version of he same encounter. and INC 3:1 is an inclined. passage of ealaxies with a 3:1 mass ratio.," Thus DIR 1:1 C specifies a direct, close passage of equal-mass galaxies, DIR 1:1 D is a more distant version of the same encounter, and INC 3:1 is an inclined passage of galaxies with a 3:1 mass ratio."
 The galaxy models in these experiments are the same as hose used in earlier studies (Barnes 1998: Dendo Barnes 2000)., The galaxy models in these experiments are the same as those used in earlier studies (Barnes 1998; Bendo Barnes 2000).
 Driellv. each. moclel contains a bulge with a shallow cusp (Llernquist. 1990). an exponential disk with constant scale height (Freeman 1970: Spitzer 1942). and a dark halo with a constant-densitv core (Dehnen 1993: Tremaine et al.," Briefly, each model contains a bulge with a shallow cusp (Hernquist 1990), an exponential disk with constant scale height (Freeman 1970; Spitzer 1942), and a dark halo with a constant-density core (Dehnen 1993; Tremaine et al."
 1994)., 1994).
 Density profiles for these components are where ris the spherical radius. £2 is the cvlindrical radius in the disk plane. and z is the distance from the disk plane.," Density profiles for these components are where $r$ is the spherical radius, $R$ is the cylindrical radius in the disk plane, and $z$ is the distance from the disk plane."
 The gas is initially clistributec like the clisk component and amounts to 12.5 percent of the disk mass., The gas is initially distributed like the disk component and amounts to $12.5$ percent of the disk mass.
 Initial velocities and velocity dispersions for the collisionless components were determined from the Jeans equations (e.g. Llernquist 1993): the disk gas was set rotating at the local circular velocity., Initial velocities and velocity dispersions for the collisionless components were determined from the Jeans equations (e.g. Hernquist 1993); the disk gas was set rotating at the local circular velocity.
 Unless otherwise indicated. the results below are given in simulation units with CG=I.," Unless otherwise indicated, the results below are given in simulation units with $G = 1$."
" In these units. the galaxies in the equal-mass encounters had total masses Aly=AloΑμα|Maaμα=mn.|1-i and length scales (audae= 0.04168. Raia=0.08333. ngu=0.0007. and hal,= OL. "," In these units, the galaxies in the equal-mass encounters had total masses $M_1 = M_2 = M_{\rm bulge} \! + \! M_{\rm
disk} \! + \! M_{\rm halo} = \frac{1}{16} \! + \! \frac{3}{16} \! +
\! 1 = \frac{5}{4}$ and length scales $a_{\rm bulge} = 0.04168$ , $R_{\rm disk} = 0.08333$, $z_{\rm disk} = 0.007$, and $a_{\rm halo} =
0.1$ ."
These choices viekd a model with half-mass radius rpg20.28. rotation period fyor(ruan)z1.2. and binding energv {—1.07.," These choices yield a model with half-mass radius $r_{\rm half}
\simeq 0.28$, rotation period $t_{\rm rot}(r_{\rm half}) \simeq 1.2$, and binding energy $E \simeq -1.07$."
 The same model was used. for the larger galaxy in the simulations with a 3:1 mass ratio. while the smaller model was simply scaled down bv a factor of 3 in mass and a factor of \/3 in radius. thereby following a Moxet relation. similar to the observed. luminosity-rotation velocity relation for disk galaxies.," The same model was used for the larger galaxy in the simulations with a 3:1 mass ratio, while the smaller model was simply scaled down by a factor of $3$ in mass and a factor of $\sqrt{3}$ in radius, thereby following a $M \propto v^4$ relation similar to the observed luminosity-rotation velocity relation for disk galaxies."
 Phe large galaxy model may be roughly scaled to the Milky Way by equating the simulation units of length. mass. and time to 40kpe. LOM.. and 2.5107vr. respectively.," The large galaxy model may be roughly scaled to the Milky Way by equating the simulation units of length, mass, and time to $40 {\rm\,kpc}$, $2.2 \times 10^{11} {\rm\,M_\odot}$, and $2.5
\times 10^8 {\rm\,yr}$, respectively."
 Gravitational forces were calculated after smoothing the mass distribution using a Plummer kernel with «—0.0125., Gravitational forces were calculated after smoothing the mass distribution using a Plummer kernel with $\epsilon = 0.0125$.
 The gas had. an isothermal equation of state. P?= where the sound: speed. is fixed at ὃς=0.0966 velocity units.," The gas had an isothermal equation of state, $P = c_{\rm s}^2 \rho$, where the sound speed is fixed at $c_{\rm s} = 0.0966$ velocity units."
 The simulation code evaluates the heating ἡ of each eas particle due to adiabatie compression and shocks: this energy is assumed to be racdiated instantly. so the gas stays at a constant temperature.," The simulation code evaluates the heating $\dot{u}$ of each gas particle due to adiabatic compression and shocks; this energy is assumed to be radiated instantly, so the gas stays at a constant temperature."
 The sound speed ὃς is an order of magnitude smaller than typical circular velocities in these models: thus gas pressure forces are relatively small. and the gas travels on roughly ballistic trajectories except where civerted by shocks.," The sound speed $c_{\rm s}$ is an order of magnitude smaller than typical circular velocities in these models; thus gas pressure forces are relatively small, and the gas travels on roughly ballistic trajectories except where diverted by shocks."
" Lo the large galaxy moclel is scaled to the AIW. the sound speed is e,15.5kms.!. corresponding to a gas temperature of 20000Ix."," If the large galaxy model is scaled to the MW, the sound speed is $c_{\rm s} \simeq
15.5 {\rm\,km\,s^{-1}}$, corresponding to a gas temperature of $\sim
20000 {\rm\,K}$."
 I chose this value to take account of non-thermal pressures due to magnetic fields aud turbulence. but the more conventional choice of 103IX swvould vield nearly identical results.," I chose this value to take account of non-thermal pressures due to magnetic fields and turbulence, but the more conventional choice of $10^4 {\rm\,K}$ would yield nearly identical results."
 Initial conditions for the encounters were generated by building pairs of galaxy models. placing them on the chosen orbits. and rotating them to the desired orientations.," Initial conditions for the encounters were generated by building pairs of galaxy models, placing them on the chosen orbits, and rotating them to the desired orientations."
" The initial center-of-mass position and velocity of cach galaxy were determined from a parabolic orbit of two point masses Ad, and Ale with pericentric separation rji; and time of pericenter Fio."," The initial center-of-mass position and velocity of each galaxy were determined from a parabolic orbit of two point masses $M_1$ and $M_2$ with pericentric separation $r_{\rm
peri}$ and time of pericenter $t_{\rm peri}$."
 For the 1:1 encounters the close passages had ria;—0.2. while the distant. passage had mes=0.4.," For the 1:1 encounters the close passages had $r_{\rm peri} = 0.2$, while the distant passage had $r_{\rm peri} = 0.4$."
 The 3:1 encounters used rie=0.2.," The 3:1 encounters used $r_{\rm peri} =
0.2$."
 In all cases fei=1. so point masses on these orbits would reach pericenter exactly one time unit after the start of the simulation.," In all cases $t_{\rm peri} = 1$, so point masses on these orbits would reach pericenter exactly one time unit after the start of the simulation."
 Of course. the actual trajectories deviate from the Keplerian ideal as soon as the galaxy models begin to interpenetrate (c.g. Barnes 1955. 1992).," Of course, the actual trajectories deviate from the Keplerian ideal as soon as the galaxy models begin to interpenetrate (e.g. Barnes 1988, 1992)."
 At passage. these deviations are moclest the close encounters come within roi20.25 at dye&1.03. while the distant ones reach me2OAS at bye01.04.," At passage, these deviations are modest – the close encounters come within $r_{\rm peri} \simeq
0.25$ at $t_{\rm peri} \simeq 1.03$, while the distant ones reach $r_{\rm peri} \simeq 0.45$ at $t_{\rm peri} \simeq 1.04$."
 Each simulation used Nas.|NecaNude=2457620696|32768=STOLO particles.," Each simulation used $N_{\rm gas} \! + \! N_{\rm star} \! + \! N_{\rm
halo} = 24576 \! + \! 29696 \! + \! 32768 = 87040$ particles."
 Collisionless components were followed. using standard N-bods techniques. while the eas was simulated using Smoothed Particle Hycdrodynamies or SPL (e.g. Monaghan 1992): the code uses a hierarchica algorithm to compute gravitational forces. adaptive smoothing to resolve a fixed mass scale in the gas. zux adaptive time-steps determined. by a Courant condition.," Collisionless components were followed using standard N-body techniques, while the gas was simulated using Smoothed Particle Hydrodynamics or SPH (e.g. Monaghan 1992); the code uses a hierarchical algorithm to compute gravitational forces, adaptive smoothing to resolve a fixed mass scale in the gas, and adaptive time-steps determined by a Courant condition."
 ‘To take maximum advantage of a cluster of eight 333MIIz processors. E ran multiple calculations simultaneously.," To take maximum advantage of a cluster of eight $333 {\rm\,MHz}$ processors, I ran multiple calculations simultaneously."
 Mos runs required between 400 ancl SOO processor hours. largely spent in the later stages where high eas densities demzux very short time-steps.," Most runs required between $400$ and $800$ processor hours, largely spent in the later stages where high gas densities demand very short time-steps."
 Enerey and angular momentum were conserved to a fraction ofa percentin all cases., Energy and angular momentum were conserved to a fraction ofa percentin all cases.
 The resolution of these simulations is comparable to that available in earlier. SPILL studies of dissipative encounters involving disk galaxies (e.g. Llerncuist 1989: Barnes Llernquist 1991. 1996: Mihos llernequist 1994. 1996).," The resolution of these simulations is comparable to that available in earlier SPH studies of dissipative encounters involving disk galaxies (e.g. Hernquist 1989; Barnes Hernquist 1991, 1996; Mihos Hernquist 1994, 1996)."
 Gravitational forces were, Gravitational forces were
A proxy for the dust production rate can be calculated using the expression derived by ALearnetal.(1984): where cL is the ond. albedo. f is the filling factor of the erains in the field of view. and p is the circular radius of the telescope aperture at. the comet fem).,"A proxy for the dust production rate can be calculated using the expression derived by \citet{A1984}: where $A$ is the Bond albedo, $f$ is the filling factor of the grains in the field of view, and $\rho$ is the circular radius of the telescope aperture at the comet (cm)."
 £\ is the mean cometary [lux in the range of 62306270Α.. and fois the solar flux in the same wavelength range (both in erg cm.2S ΣΑ 1j. calculated. here using the values in Arvesen.Πα&Pearson(1969).," $F_{\lambda}$ is the mean cometary flux in the range of $6230-6270$, and $F_{\odot}$ is the solar flux in the same wavelength range (both in erg $^{-2}$ $^{-1}$ $^{-1}$ ), calculated here using the values in \citet{A1969}."
. The beliocentric aud geocentric distances are in au and cm. respectively.," The heliocentric and geocentric distances are in au and cm, respectively."
 Ll the cometary cust is assumed. to flow away [rom the nucleus in a uniform manner. without breakup. acceleration. or darkening. then the quantity. cAfp (em) is proportional to the dust production rate CXLearnctal.1984:Storrs 1992).," If the cometary dust is assumed to flow away from the nucleus in a uniform manner, without breakup, acceleration, or darkening, then the quantity $Af\rho$ (cm) is proportional to the dust production rate \citep{A1984,S1992}."
. The continuum flux is measured in the range of 62306270 of the solar-corrected spectra. where there are. no known lines (Fink1994:Fink&Licks1996).," The continuum flux is measured in the range of 6230--6270 of the solar-corrected spectra, where there are no known lines \citep{F1994,FH1996}."
. The circular radius. p. is assumed to be half the width of the rectangular slit (1 aresec).," The circular radius, $\rho$, is assumed to be half the width of the rectangular slit (1 arcsec)."
 This approximation introduces a conversion, This approximation introduces a conversion
where z is the altitude on the Galactic plane.,where z is the altitude on the Galactic plane.
 We plot the different major morphological (vpes: Ro (round). E (elliptical). BC! (bipolar core). and D (bipolar) in different panels. with all distances calculated with the Magellanic Cloud calibrated CIXS scale.," We plot the different major morphological types: R (round), E (elliptical), BC (bipolar core), and B (bipolar) in different panels, with all distances calculated with the Magellanic Cloud calibrated CKS scale."
 Using the most discordant distance scale. for example the Magellanic Cloud-calibrated: Aly px. scale. eives a verv similar distribution for all morphological types. with the exception of bipolar PNe. whose statistical distances are not very acciurate anvway.," Using the most discordant distance scale, for example the Magellanic Cloud-calibrated $_{\rm ion}$ $_{\rm PN}$ scale, gives a very similar distribution for all morphological types, with the exception of bipolar PNe, whose statistical distances are not very accurate anyway."
 From Fig., From Fig.
 1 we confirm that the bipolar sample is confined close to the Galactic plane (again the distance bias for (his class should be taken into account) aud the bipolar core PNe are intermediately distributed between elliptical and bipolar. as found in previous analvses (Stanghellini et al.," 1 we confirm that the bipolar sample is confined close to the Galactic plane (again the distance bias for this class should be taken into account) and the bipolar core PNe are intermediately distributed between elliptical and bipolar, as found in previous analyses (Stanghellini et al."
 1993. 2002).," 1993, 2002)."
 In Figure 2 we plot on the same plane all the PNe. and then those of Peimbert Tvpe I. Il. ancl HI.," In Figure 2 we plot on the same plane all the PNe, and then those of Peimbert Type I, II, and III."
 This plot has distances calculated in the same way Chan in Fig., This plot has distances calculated in the same way than in Fig.
 1. and includes bipolar PNe.," 1, and includes bipolar PNe."
" In order to assess the (vpe of distance calibration we plot in Figure 3 the Re 2 locus of all PNe with distances calculated with the method above. and then with the Tí Rex. Mi, Rex. ad Rpy relations. using in all cases (he superior Magellanic Cloud calibrations (Eq."," In order to assess the type of distance calibration we plot in Figure 3 the $_{\rm G}$ –z locus of all PNe with distances calculated with the method above, and then with the $_{\rm b}$ $_{\rm PN}$, $_{\rm ion}$ $_{\rm PN}$, and $_{\rm PN}$ relations, using in all cases the superior Magellanic Cloud calibrations (Eq."
 5. 6. and 7 in SSV).," 5, 6, and 7 in SSV)."
 These samples of 728 PNe include bipolar PNe., These samples of 728 PNe include bipolar PNe.
 We can see (hat the dillerent (Magellanie Cloud-calibrated) scales give broad agreement in the PN Galactic distribution. but there are differences. in that PNe are significantly more clustered around the Sun when using Magellanic Cloud-calibrated CIS distances.," We can see that the different (Magellanic Cloud-calibrated) scales give broad agreement in the PN Galactic distribution, but there are differences, in that PNe are significantly more clustered around the Sun when using Magellanic Cloud-calibrated CKS distances."
 The variation of the radiallvy-binned a-elemental abundances in disk galaxies is eenerallv indicated as thegradient. and it is a measure of the composition of," The variation of the radially-binned $\alpha$ -elemental abundances in disk galaxies is generally indicated as the, and it is a measure of the composition of"
ime [roi1 one such survey. the Supernova Legacy Survey (SNLS.Astieretal.(2006))).,"time from one such survey, the Supernova Legacy Survey \citet{Astier:06}) )."
 The desien of this (aud some other moderni surveys) results in a dramatic increase in the anmouut of early-time shotometry available when compared with previous generations of surveys. as detailedin 83..," The design of this (and some other modern surveys) results in a dramatic increase in the amount of early-time photometry available when compared with previous generations of surveys, as detailedin \ref{sec:data}."
 We first describe the basic problem (82)). then present the data on which our measurement is based. 3)). followed by a description of our analysis procedures (81)).," We first describe the basic problem \ref{sec:parameterization}) ), then present the data on which our measurement is based \ref{sec:data}) ), followed by a description of our analysis procedures \ref{sec:analysis}) )."
 Finally. we compare our heasttleljents against nearby SNe Ia. as well as between cdiffereut subsets of our data (85)).," Finally, we compare our measurements against nearby SNe Ia, as well as between different subsets of our data \ref{sec:results}) )."
 Iu order to measure the rise time of our sample we require a mechanism lor combining data [rom clifferent SNe Ia. correcting for the dilferences iu light-curve shape aud peak flux. aud a model for the early-time flux as a fiction of time.," In order to measure the rise time of our sample we require a mechanism for combining data from different SNe Ia, correcting for the differences in light-curve shape and peak flux, and a model for the early-time flux as a function of time."
 Considerable effort aud iugeuuity have been devoted to developing techniques for parameterizing SNe Ia ligit curves near aud after maximum light (Riess 11996. GOL. Guy 22005).," Considerable effort and ingenuity have been devoted to developing techniques for parameterizing SNe Ia light curves near and after maximum light (Riess 1996, G01, Guy 2005)."
 Here we Lollow the stretel inetlod as described iu. for example. GOL.," Here we follow the stretch method as described in, for example, G01."
 The flux as a fuuctiou ol time after the rise-time region is represented as where fj is the flux at maximum. aud o is some normalized [ιν template appropriate to the passbaud wader consideration.," The flux as a function of time after the rise-time region is represented as where $f_0$ is the flux at maximum, and $\psi$ is some normalized flux template appropriate to the passband under consideration."
 7 is the effective date defined by 7=(E—lnax)/sτσ]. wliere hax is the date of rnaxiuimumn flux tn some arbitrary filter (usually B). s is the stretel. aud z is the redshift.," $\tau$ is the effective date defined by $\tau = \left(t - t_{\mbox{max}}\right)/ s \left(1+z\right)$, where $t_{\mbox{max}}$ is the date of maximum flux in some arbitrary filter (usually $B$ ), $s$ is the stretch, and $z$ is the redshift."
 Conventionally. s=1 is deliued to represent an average SN Ia. Ouce s. fy. aud {μας are fited to the data. we can combine data [rom different SNe Ia by converting [rom observed epoch | to 7 aud dividiug by fy to normalize the flux. values relative to each other.," Conventionally, $s=1$ is defined to represent an average SN Ia. Once $s$, $f_0$, and $t_{\mbox{max}}$ are fited to the data, we can combine data from different SNe Ia by converting from observed epoch $t$ to $\tau$ and dividing by $f_0$ to normalize the flux values relative to each other."
 We must also apply a sso that the 'esulting data are a| expressed iu the sane rest-[ralje. filter., We must also apply a so that the resulting data are all expressed in the same rest-frame filter.
" Note that diΠο observatious roni the same SN are correlated by this p""OCecCure. all ilat in addition estle of the light-crve fit parameters aὁ generally (quite stroiply correlaed."," Note that different observations from the same SN are correlated by this procedure, and that in addition estimates of the light-curve fit parameters are generally quite strongly correlated."
 We must take bo a account in our analysis., We must take both into account in our analysis.
" For our purposes we limit the fit to his tmoclel o the ""core"" light οι between —10dp<39 days.", For our purposes we limit the fit to this model to the “core” light curve between $-10 < \tau < 35$ days.
 The lower limit arises because we fit the ‘ise-time moclel in tliis range. aud we want to prevent the fit from suppressing uuusual rise-time behavior.," The lower limit arises because we fit the rise-time model in this range, and we want to prevent the fit from suppressing unusual rise-time behavior."
 The upper limit arises because after this effective epoch the SNe Ia enter the so-called nebular plpliase. in which the stretch prescription no longer works (GOL).," The upper limit arises because after this effective epoch the SNe Ia enter the so-called nebular phase, in which the stretch prescription no longer works (G01)."
 Iu the rise-time regiou (7uw —10). we follow earlier work (ROD. AIXNOO. GOL) in makiug use oL a simple quadratic model and Oat earlier times.," In the rise-time region $\tau < -10$ ), we follow earlier work (R99, AKN00, G01) in making use of a simple quadratic model for $\tau > -\tr$ , and 0 at earlier times."
Note that. as for IGR J13149+4422. the position of IGR J14579—4308 reported in Bodagheeetal.(2007) and in SIMBAD is that of the pair of interacting galaxies. while we identify here one of the components of this double system as the best counterpart to the ssource thanks to the refined position.,"Note that, as for IGR J13149+4422, the position of IGR $-$ 4308 reported in \citet{bodaghee07} and in SIMBAD is that of the pair of interacting galaxies, while we identify here one of the components of this double system as the best counterpart to the source thanks to the refined position."
 The best positions for the other sources are reported in Table 5.., The best positions for the other sources are reported in Table \ref{tab:pos}.
 Only source 2 on Fig., Only source 2 on Fig.
 2. has an infared counterpart reported in 2MASS., \ref{fig:14579} has an infared counterpart reported in 2MASS.
 2MASS J14570433—4300187 indeed lies 1755 fromJ145704., 2MASS $-$ 4300187 indeed lies 5 from.
4—430020.. No UVOT data are available from any of the observing sequences., No UVOT data are available from any of the observing sequences.
 We combined the three observations to perform a spectral analysis., We combined the three observations to perform a spectral analysis.
 The average spectrum of IGR J14579—4308 has 703 cts for a total of 21685 s exposure., The average spectrum of IGR $-$ 4308 has 703 cts for a total of 21685 s exposure.
 A simple absorbed power law does not fit the data well (yz;=2.88 for 29 DOF)., A simple absorbed power law does not fit the data well $\chi_\nu^2=2.88$ for 29 DOF).
 A large excess is visible below 2 keV. Adding a black body to the model improves the fit to y;=1.25 for 27 DOF., A large excess is visible below 2 keV. Adding a black body to the model improves the fit to $\chi_\nu^2=1.25$ for 27 DOF.
 The black body radiation is not absorbed and has a temperature of 0.28701! keV. The best parameters of the other spectral components (power law and Ny)) are reported in Table 2.., The black body radiation is not absorbed and has a temperature of $0.28_{-0.06}^{+0.11}$ keV. The best parameters of the other spectral components (power law and ) are reported in Table \ref{tab:res}.
 Replacing the black body by a dise model in XSPEC) provides a good description of the spectrum (y;=1.28 for 27 DOF)., Replacing the black body by a disc model in XSPEC) provides a good description of the spectrum $\chi_\nu^2=1.28$ for 27 DOF).
 The inner dise temperature is 0.5705 keV. The high value of the absorption indicates that the object is intrinsically highly absorbed. as would be expected in a Sey 2 AGN.," The inner disc temperature is $_{-0.2}^{+0.7}$ keV. The high value of the absorption indicates that the object is intrinsically highly absorbed, as would be expected in a Sey 2 AGN."
 Further spectral results will be reported in Kalemcei et al. (, Further spectral results will be reported in Kalemci et al. (
in prep.).,in prep.).
 ΙΙ 16385-2057 Was first reported by Birdetal.(2007)., IGR $-$ 2057 was first reported by \citet{bird07}.
.. Based on a positional coincidence with IRXS J163830.9-205520 and Oph 1163830—2055. it was suggested to be the X-ray counterpart to those objects.," Based on a positional coincidence with 1RXS $-$ 205520 and Oph $-$ 2055, it was suggested to be the X-ray counterpart to those objects."
 Optical spectra allowed Masettietal.(2006a) to tentatively classify it as a Sey | at z=0.027.," Optical spectra allowed \citet{masetti06}
 to tentatively classify it as a Sey 1 at z=0.027."
 The Swift//XRT position is aaway from the position of 2MASX J16383091-—2055246 an AGN at z=0.026 (Hasegawaetal..2000)., The /XRT position is away from the position of 2MASX $-$ 2055246 an AGN at z=0.026 \citep{hwm00}.
. This object is also compatible Oph J163830—-2055. and therefore the tentative identification as a Sey | seems confirmed by the refined XRT position.," This object is also compatible Oph $-$ 2055, and therefore the tentative identification as a Sey 1 seems confirmed by the refined XRT position."
 Note that the pposition is also from IRXS J163830.9—205520. well within the ROSAT error box (7).," Note that the position is also from 1RXS $-$ 205520, well within the ROSAT error box )."
 No UVOT data are available for this We combined the two observations to perform a spectral analysis., No UVOT data are available for this We combined the two observations to perform a spectral analysis.
 The average spectrum of IGR J16385—2057 has 2195 cts for a total of 9168 s exposure., The average spectrum of IGR $-$ 2057 has 2195 cts for a total of 9168 s exposure.
 An absorbed power law fits the data well (yz=1.27 for 85 DOF)., An absorbed power law fits the data well $\chi_\nu^2=1.27$ for 85 DOF).
 The value of the absorption is a factor of two higher than the total absorption along the line of sight., The value of the absorption is a factor of two higher than the total absorption along the line of sight.
 This may indicate that a part of the absorbing material is intrinsic to the object., This may indicate that a part of the absorbing material is intrinsic to the object.
 IGR J18490—0000 was first. reported by Molkovetal.(2004) from a survey of the Sagittarius Arm tangent region., IGR $-$ 0000 was first reported by \citet{molkov03} from a survey of the Sagittarius Arm tangent region.
 Nothing more is known about this source., Nothing more is known about this source.
 There is a single 2MASS point source within the Swifr//XRT error box., There is a single 2MASS point source within the /XRT error box.
 2MASS J18490182-0001190lies ffrom the centre of the eerror box., 2MASS J18490182-0001190	lies from the centre of the error box.
 It has a well-measured magnitude only in the K-band. while it is not detected in the UVOT We extracted an average spectrum from the two pointings.," It has a well-measured magnitude only in the K-band, while it is not detected in the UVOT We extracted an average spectrum from the two pointings."
 The spectrum has 441 counts for a total of 12208 s and is well fitted by an absorbed power law (yz=0.40 for 17 DOF)., The spectrum has 441 counts for a total of 12208 s and is well fitted by an absorbed power law $\chi_\nu^2=0.40$ for 17 DOF).
 The value of iis about 34 times higher than the average value of the absorption. along the line of sight., The value of is about 3 times higher than the average value of the absorption along the line of sight.
 Thismay indicate. that IGR J18490—0000 is intrinsically absorbed., Thismay indicate that IGR $-$ 0000 is intrinsically absorbed.
 This source is likely a Galactic X-ray binary because of the presence of, This source is likely a Galactic X-ray binary because of the presence of
resampling.,resampling.
 ?. also tabulate the space density of each sample. so it is straightforward for us to select corresponding samples of semi-analytic galaxies.," \citet{ZEH05} also tabulate the space density of each sample, so it is straightforward for us to select corresponding samples of semi-analytic galaxies."
" Our cosmological constraints will use samples with a galaxy space density n,=0.003085Mpe.. corresponding to galaxies with AJ,5log,yh<20.5 in the SDSS."," Our cosmological constraints will use samples with a galaxy space density $\bar{n}_g=0.00308\ h^3\ \mathrm{Mpc}^{-3}$, corresponding to galaxies with $M_r-5\log_{10}h<-20.5$ in the SDSS."
 Our semi-analytic catalogues have approximately twice the effective volume of the observational sample. so when calculating how well our models fit the data we use only the covariance matrix of the observational correlation function to compute our errors. neglecting the statistical errors on the simulated function.," Our semi-analytic catalogues have approximately twice the effective volume of the observational sample, so when calculating how well our models fit the data we use only the covariance matrix of the observational correlation function to compute our errors, neglecting the statistical errors on the simulated function."
 We use the sample of this space density since it provides a good compromise between volume and space density. giving relatively small errors. and since most of the constraining power then comes from the galaxies of intermediate luminosity which are modelled best by the semi-analytic code.," We use the sample of this space density since it provides a good compromise between volume and space density, giving relatively small errors, and since most of the constraining power then comes from the galaxies of intermediate luminosity which are modelled best by the semi-analytic code."
 We will. though. briefly discuss the effect of using samples of a different space density or selected in a different waveband.," We will, though, briefly discuss the effect of using samples of a different space density or selected in a different waveband."
 We compare the clustering in our synthetic catalogues and in the SDSS in Fig. 3.., We compare the clustering in our synthetic catalogues and in the SDSS in Fig. \ref{fig:rwgrid1}.
" We plot the quantity ΓΙ) since this scales out much of the +, dependence and makes differences in shape easier to see.", We plot the quantity $r_\mathrm{p}w_\mathrm{p}(r_\mathrm{p})$ since this scales out much of the $r_\mathrm{p}$ dependence and makes differences in shape easier to see.
 Fig., Fig.
 3. shows our results for a grid of nine cosmologies spaced regularly in σε such that they lie on the curve, \ref{fig:rwgrid1} shows our results for a grid of nine cosmologies spaced regularly in $\sigma_8$ such that they lie on the curve
AL. where 0.0017 is the fraction of iron bv mass in the solar photosphere.,$M_{\odot}$ where 0.0017 is the fraction of iron by mass in the solar photosphere.
" If all the iron is created in Type Ia supernovac, each having energv 1075 eres and providing 0.7 AZ. in iron. the total feedback energy frou, Type Ia superiovae cannot exeeed about Es,2(0.3.1.0)«1002 eres. Which are also less than APE(r.)5,4 in Table 2."," If all the iron is created in Type Ia supernovae, each having energy $10^{51}$ ergs and providing 0.7 $M_{\odot}$ in iron, the total feedback energy from Type Ia supernovae cannot exceed about $E_{SnIa} \approx (0.3,1.0)\times 10^{62}$ ergs, which are also less than $\Delta PE(r_v)$ in Table 2."
 While ACN feedback dominates cluster cnerectics. supernovae may nevertheless contribute of the total feedback energy.," While AGN feedback dominates cluster energetics, supernovae may nevertheless contribute of the total feedback energy."
 Nagai et al. (, Nagai et al. (
2007a.b) computed a varicty of gaseous atimospheres iu clusters iucludiug superuovae of all types but without AGN feedback. as commonly assumed.,"2007a,b) computed a variety of gaseous atmospheres in clusters including supernovae of all types but without AGN feedback, as commonly assumed."
 Iu their clusters the barvou fraction and eutropy profiles are iu reasonably eood agreecimeut with those observed by Vikhliniu et al. (, In their clusters the baryon fraction and entropy profiles are in reasonably good agreement with those observed by Vikhlinin et al. (
2006) outside the central region. rZΟδ.,"2006) outside the central region, $r \gta 0.2r/r_v$."
" But ceutral overcooling iurτςοfry, isa serious problem.", But central overcooling in $r \lta 0.2r/r_v$ is a serious problem.
 At zero redshift inthe models of Nagai et al., At zero redshift in the models of Nagai et al.
" about of the barvous within rowO.5r, ave in the form of a centrally concentrated lass of stars and cold eas.", about of the baryons within $r \approx 0.5r_v$ are in the form of a centrally concentrated mass of stars and cold gas.
 The mass of this central concentration of radiatively cooled birvons causes the eas density aud temperature to peak up near the cluster centers unlike the observations., The mass of this central concentration of radiatively cooled baryons causes the gas density and temperature to peak up near the cluster centers unlike the observations.
 A large amount of ACN feedback energy. similar to that estimated here. is essential to remove this overcooling gas before it forms iuto stars aud relocate it to distant regions of the cluster.," A large amount of AGN feedback energy, similar to that estimated here, is essential to remove this overcooling gas before it forms into stars and relocate it to distant regions of the cluster."
 The outward flow of cluster eas that results from the creation of X-rav cavities is described bv Mathews Drieheuti (2008) and Mathews (2009)., The outward flow of cluster gas that results from the creation of X-ray cavities is described by Mathews Brighenti (2008) and Mathews (2009).
 AGN feedback has just begun to be included ii receut cosmological cluster caleulatious where the overcooling problemi is ereatly alleviated (Tevssicr et al., AGN feedback has just begun to be included in recent cosmological cluster calculations where the overcooling problem is greatly alleviated (Teyssier et al.
 2010: Puchwein et al., 2010; Puchwein et al.
 2010: MeCartliy et al., 2010; McCarthy et al.
 2010)., 2010).
 The approximate rate that mass cools in the two composite clusters in the absence of feedback cau be estimated from the bolometric X-ray Iuninositv at the cooling racius. (n cre 13 where the cooling radius ρω] 18 defined as that radius at which the local gas cooling time is equal to a typical cluster age f4~7 Cis.," The approximate rate that mass cools in the two composite clusters in the absence of feedback can be estimated from the bolometric X-ray luminosity at the cooling radius, (in erg $^{-1}$ ) where the cooling radius $r_{cool}$ is defined as that radius at which the local gas cooling time is equal to a typical cluster age $t_{cl}\sim 7$ Gyrs."
" For cluster (1.2) with ρω=(98.120) kpe and νι)=(1.36.1011 σος l (determined with Poos(t)) we find M,zm(225.165) AL. 1."," For cluster (1,2) with $r_{cool} = (98, 120)$ kpc and $L_x(r_{cool}) = (1.36,4.96)\times 10^{44}$ erg $^{-1}$ (determined with $\rho_{obs}(r)$ ) we find ${\dot M}_{cf} \approx (225,465)$ $M_{\odot}$ $^{-1}$."
 This is the approximate rate that the cluster gas would cool in the absence of feedback cenerey., This is the approximate rate that the cluster gas would cool in the absence of feedback energy.
" The ratio for the two clusters M44/M.4»=0.[8 is comparable to but larger than the ratio of total feedback enereies. APE/APE,~0.29 for gas initially at ry, mm the ""no core” solutions."," The ratio for the two clusters ${\dot M}_{cf,1}/{\dot M}_{cf,2} = 0.48$ is comparable to but larger than the ratio of total feedback energies, $\Delta PE_1/\Delta PE_2 \approx 0.29$ for gas initially at $r_v$ in the “no core” solutions."
 As shown in Mathews (2009). feedback. energv can create cluster outflows that balance aud arrest cooling inflows caused bv radiation losses.," As shown in Mathews (2009), feedback energy can create cluster outflows that balance and arrest cooling inflows caused by radiation losses."
" For this to happen within a stronely radiating cluster core. the tinme-averaged rate that cluster gas flows out due to feedback expansion unust be equal to the average mass inflow rate AZ, due to radiative losses."," For this to happen within a strongly radiating cluster core, the time-averaged rate that cluster gas flows out due to feedback expansion must be equal to the average mass inflow rate ${\dot M}_{cf}$ due to radiative losses."
 First imagine the expanding flow of cluster gas duc to feedback. ignoring energv losses due to radiation.," First imagine the expanding flow of cluster gas due to feedback, ignoring energy losses due to radiation."
" Iu this limiting case the niass of gas within any radius rk decreases because of feedback expansion from ο) to Mister) as the initial adiabatic atmosphere evolves to the observed one duriug the cluster lifetime £,4.", In this limiting case the mass of gas within any radius $r$ decreases because of feedback expansion from $M_{ad}(r)$ to $M_{ob}(r)$ as the initial adiabatic atmosphere evolves to the observed one during the cluster lifetime $t_{cl}$.
 The mean positive feedback mass flow past radius r. AAL(r)/ty—Alon.)ta. is plotted in Figure 5 for both compositeMoate) clusters.," The mean positive feedback mass flow past radius $r$ , $\Delta M(r)/t_{cl} \equiv [M_{ad}(r) - M_{obs}(r)]/t_{cl}$, is plotted in Figure 5 for both composite clusters."
" At the other anit when radiative losses are present but feedback is absent. the rate that gas cools within radius r. AM,g(r) is related. by equation (8) to the total rate that energv is radiated within this radius. νι"," At the other limit when radiative losses are present but feedback is absent, the rate that gas cools within radius $r$, ${\dot M}_{cf}(r)$ is related by equation (8) to the total rate that energy is radiated within this radius, $L_x(r)$."
 In particular. the nass of eas within the cooling radius in the observed cluster atmosphere. by definition of ρω. Is expected to flow inward at an average rate ALy(oor).," In particular, the mass of gas within the cooling radius in the observed cluster atmosphere, by definition of $r_{cool}$, is expected to flow inward at an average rate ${\dot M}_{cf}(r_{cool})$."
" Consequently. in the presence of both radiative losses and feedback eas. feedback from the central black hole is expected o increase until the time-averaged rate that sas mass is driven outward past renee balances the average rate hat mass would cool aud flow inward past ru, over the cluster lifetime."," Consequently, in the presence of both radiative losses and feedback gains, feedback from the central black hole is expected to increase until the time-averaged rate that gas mass is driven outward past $r_{cool}$ balances the average rate that mass would cool and flow inward past $r_{cool}$ over the cluster lifetime."
" This balance is shown in Figure 5 where the total time-averaged rate that mass flows out past the cooling radius. AArao)μι verv early matches the approximate micau míflow rate AM.4(7,,,) expected (frou equ."," This balance is shown in Figure 5 where the total time-averaged rate that mass flows out past the cooling radius, $\Delta M(r_{cool})/t_{cl}$ very nearly matches the approximate mean inflow rate ${\dot M}_{cf}(r_{cool})$ expected (from eqn."
" 8) at radius £2, during tine f,43f£ radiative cooling within this radius is uninhibited by feedback.", 8) at radius $r_{cool}$ during time $t_{cl}$ if radiative cooling within this radius is uninhibited by feedback.
" Since inflow M,ytr) (estimated. from Lí(r) without feedback). aud outflow ΔΑ (estimated without radiation losses) have opposite signs. the near equality of their magnitudes at r=ρω In Figure 5 indicates that feedback. aud cooling are balanced within r4,,;."," Since inflow ${\dot M}_{cf}(r)$ (estimated from $L_x(r)$ without feedback) and outflow $\Delta M(r)/t_{cl}$ (estimated without radiation losses) have opposite signs, the near equality of their magnitudes at $r = r_{cool}$ in Figure 5 indicates that feedback and cooling are balanced within $r_{cool}$."
 A quasi-steady. state is established with little or no net eas flow across regu Although feedback outflow continues dir 252444 unaffected by radiation losses.," A quasi-steady state is established with little or no net gas flow across $r_{cool}$, although feedback outflow continues in $r > r_{cool}$ unaffected by radiation losses."
 The important agrecinent between opposing mass flows at roo) shown in Figure 5 is a further coufirmation of the selfconsistency our simple feedback estimates., The important agreement between opposing mass flows at $r_{cool}$ shown in Figure 5 is a further confirmation of the self-consistency our simple feedback estimates.
 Less than 1 percent of the total feedback euergy is stored as potential energy witlin the cooling radius., Less than 1 percent of the total feedback energy is stored as potential energy within the cooling radius.
 Nevertheless. central black holes iu their over-zealous. over-reaching efforts to feed back to the cluster atinosphiere the energy acquired from eas cooling in their imuuediate vicinity dive huge flows of gas out bevond the virial radius. but iu the process necessuilv provide enoush nass outfiow within the relatively small cooling radius to shut down the large cooling inflow that would otherwise occur in this critical central region.," Nevertheless, central black holes – in their over-zealous, over-reaching efforts to feed back to the cluster atmosphere the energy acquired from gas cooling in their immediate vicinity -- drive huge flows of gas out beyond the virial radius, but in the process necessarily provide enough mass outflow within the relatively small cooling radius to shut down the large cooling inflow that would otherwise occur in this critical central region."
 Although we do not consider the detailed time evolution of the initial adiabatic cluster eas profile as it transforms iuto the eas density profiles observed today. we imagine that this occurs in a quasi-steady imiauner. as explained above. m which feedback cucrey is widely distributed as PE in the cluster eas.," Although we do not consider the detailed time evolution of the initial adiabatic cluster gas profile as it transforms into the gas density profiles observed today, we imagine that this occurs in a quasi-steady manner, as explained above, in which feedback energy is widely distributed as $PE$ in the cluster gas."
 By this means the feedback outflow always nearly balances the raciative inflow. avoiding auv larec ceutral gas concentration (and eventual overdensity due to star formation) or other excursious verv far from the eas density profiles currently observed.," By this means the feedback outflow always nearly balances the radiative inflow, avoiding any large central gas concentration (and eventual overdensity due to star formation) or other excursions very far from the gas density profiles currently observed."
 It is likely that feedback consists of jets aud jet- cavities thatare filled mostly with cosmic ravs., It is likely that feedback consists of jets and jet-produced cavities thatare filled mostly with cosmic rays.
 If so. it is interesting to compare the total feedback enerev iu our composite clusters. ~10575 ores. with that expected from other cluster cosmic ray sources.," If so, it is interesting to compare the total feedback energy in our composite clusters, $\sim10^{63}$ ergs, with that expected from other cluster cosmic ray sources."
 For, For
"the SF model using another, more efficient AGN feedback scheme.","the SF model using another, more efficient AGN feedback scheme."
" Recently, ? have simulated a large number of groups and clusters with the SPH code GADGET, using a mass resolution that is only about a factor 2 lower than ours and a spatial resolution of 2.5kpc (compared to 1 kpc at low res."," Recently, \cite{Puchwein:2010p763} have simulated a large number of groups and clusters with the SPH code GADGET, using a mass resolution that is only about a factor 2 lower than ours and a spatial resolution of 2.5kpc (compared to 1 kpc at low res."
 or 0.5 kpc at high res., or 0.5 kpc at high res.
 here)., here).
" Nevertheless, they also found that with AGN feedback, the total baryon fraction was below the universal value."," Nevertheless, they also found that with AGN feedback, the total baryon fraction was below the universal value."
" More interestingly, using a high universal baryon fraction (Q%/Qm= 0.165), they report a stellar mass fraction of f.~0.05, quite independent of the parent halo mass."," More interestingly, using a high universal baryon fraction $\Omega_b/\Omega_m=0.165$ ), they report a stellar mass fraction of $f_* \simeq 0.05$, quite independent of the parent halo mass."
" In our case, for our Virgo-like cluster with Myc1014 Mo, we obtained f.~0.01 in the low resolution case and f.-0.02 in our high resolution simulation."," In our case, for our Virgo-like cluster with $M_{\rm vir} \simeq 10^{14}$ $_\odot$, we obtained $f_* \simeq 0.01$ in the low resolution case and $f_* \simeq 0.02$ in our high resolution simulation."
" Our value is in better agreement with the observational estimate proposed by ??,, while the higher value found by ? is in better agreement with the observations reported in ?.."," Our value is in better agreement with the observational estimate proposed by \cite{Lin:2003p1820, Lin:2004p1817}, while the higher value found by \cite{Puchwein:2010p763} is in better agreement with the observations reported in \cite{Gonzalez:2007p916}."
" Using the COSMOS survey, ? have estimated stellar mass fractions for a large sample of galaxy clusters and groups."," Using the COSMOS survey, \cite{Giodini:2009p4283} have estimated stellar mass fractions for a large sample of galaxy clusters and groups."
" For our simulated halo mass, Msouc~8x10? Mo, they report stellar mass fraction ranging from to5%."," For our simulated halo mass, $M_{500c} \sim 8 \times 10^{13}$ $_\odot$, they report stellar mass fraction ranging from to."
". Using the original feedback model of ? in the GADGET code, ? have also computed the predicted baryon and stellar mass fraction of a large sample of groups extracted from a cosmological simulation."," Using the original feedback model of \cite{Booth:2009p501} in the GADGET code, \cite{Duffy:2010p568} have also computed the predicted baryon and stellar mass fraction of a large sample of groups extracted from a cosmological simulation."
" Although they report a similar baryon deficit within the virial radius, they obtained fsc0.03 for an even larger universal baryon fraction Q,/€,,=0.18."," Although they report a similar baryon deficit within the virial radius, they obtained $f_* \simeq 0.03$ for an even larger universal baryon fraction $\Omega_b/\Omega_m=0.18$."
 We see that there is a consensus about a strong reduction of the stellar mass fraction in groups and clusters thanks to AGN feedback., We see that there is a consensus about a strong reduction of the stellar mass fraction in groups and clusters thanks to AGN feedback.
" The extent of this reduction seems to depend quite sensitively of the details of each implementation, and possibly to the nature of the code (SPH versus AMR)."," The extent of this reduction seems to depend quite sensitively of the details of each implementation, and possibly to the nature of the code (SPH versus AMR)."
" As suggested by observations also, we note that the exact stellar and baryon fraction probably varies from halo to halo."," As suggested by observations also, we note that the exact stellar and baryon fraction probably varies from halo to halo."
" We would like also to stress that all the reported simulations, including ours, are probably not fully converged yet."," We would like also to stress that all the reported simulations, including ours, are probably not fully converged yet."
 We have simulated the formation of a Virgo-sized galaxy cluster to study the effects of feedback on the overcooling problem., We have simulated the formation of a Virgo–sized galaxy cluster to study the effects of feedback on the overcooling problem.
" The impact of AGN feedback on the distribution of the baryonic mass is strong, and in good agreement with previous SPH simulations: star formation in massive galaxies is drastically reduced."," The impact of AGN feedback on the distribution of the baryonic mass is strong, and in good agreement with previous SPH simulations: star formation in massive galaxies is drastically reduced."
" At the same time, left-over gas is very efficiently removed from the core of the parent halos, where it would have otherwise accumulated."," At the same time, left-over gas is very efficiently removed from the core of the parent halos, where it would have otherwise accumulated."
" In order to quantify the effect of AGN feedback, we have run two other reference simulations: one model with only star formation and supernovae feedback (the standard scenario) and one model for which we have artificially prevented star formation to occur in massive enough spheroids (the quenching scenario)."," In order to quantify the effect of AGN feedback, we have run two other reference simulations: one model with only star formation and supernovae feedback (the standard scenario) and one model for which we have artificially prevented star formation to occur in massive enough spheroids (the quenching scenario)."
" A detailed comparison of the three models clearly demonstrates that AGN feedback is needed to control star formation in the central BCG, but also to unbind the overcooling gas from the cluster core."," A detailed comparison of the three models clearly demonstrates that AGN feedback is needed to control star formation in the central BCG, but also to unbind the overcooling gas from the cluster core."
 We also clearly identify the effect of the baryon dynamics on the dark matter mass distribution on large scale., We also clearly identify the effect of the baryon dynamics on the dark matter mass distribution on large scale.
" Interestingly enough, in case of AGN feedback, we observe the adiabatic expansion of the dark halo, an effect well modeled by the AC theory of ?.."," Interestingly enough, in case of AGN feedback, we observe the adiabatic expansion of the dark halo, an effect well modeled by the AC theory of \cite{Gnedin:2004p569}."
" A comparison of our simulation results with observational data for Virgo and its central galaxy M87 rules out the standard model, but also the quenching model."," A comparison of our simulation results with observational data for Virgo and its central galaxy M87 rules out the standard model, but also the quenching model."
" On the contrary, our simulation with AGN feedback, although not fully converged yet, shows a much better agreement with M87 data in term of mass distribution."," On the contrary, our simulation with AGN feedback, although not fully converged yet, shows a much better agreement with M87 data in term of mass distribution."
" In particular, we obtain a significantly reduced baryon fraction within the virial radius, in agreement with observations compiled by ? and ?.."," In particular, we obtain a significantly reduced baryon fraction within the virial radius, in agreement with observations compiled by \cite{Lin:2003p1820} and \cite{Gonzalez:2007p916}."
" We clearly identify in our simulation that gas is removed from the core of the cluster by convective motions and/or strong shocks, and accumulates in a region just"," We clearly identify in our simulation that gas is removed from the core of the cluster by convective motions and/or strong shocks, and accumulates in a region just"
at high frequencies. as also found in. blazar objects.,"at high frequencies, as also found in blazar objects."
 The lack of pe-seale morphology information does not allow us to unambiguously determine the origin of this complex Following the approach by Tintietal.(2005). and. Orientietal.(2007) we investigate the presence of Dux. density variability. by computing the variability index V: where 5; is the Dux density at the Hth frequency. measured at one epoch. S; is the mean value of the tlux density computed. averaging the tux density at the Hth frequency nmieasured at all the available epochs. 0; is the rms on hiS0δν anc m is the number of sampled frequencies.," The lack of pc-scale morphology information does not allow us to unambiguously determine the origin of this complex Following the approach by \citet{tinti05} and \citet{mo07} we investigate the presence of flux density variability, by computing the variability index $V$: where $S_{i}$ is the flux density at the -th frequency measured at one epoch, $\overline S_{i}$ is the mean value of the flux density computed averaging the flux density at the -th frequency measured at all the available epochs, $\sigma_{i}$ is the rms on $S_{i}-
\overline S_{i}$, and $m$ is the number of sampled frequencies."
 We prefer to compute the variability index for cach new epoch (see Table 5)) instead of considering all the epochs together in order to better detect the presence of a possible burst., We prefer to compute the variability index for each new epoch (see Table \ref{variability}) ) instead of considering all the epochs together in order to better detect the presence of a possible burst.
 As in Tintietal.(2005)... we consider variable those sources with a variability index V.9. From the comparison of the multi-epoch spectral properties ancl variability we - 24 objects maintain the convex spectrum without showing significant [lux density variability (V< 9).," As in \citet{tinti05}, we consider variable those sources with a variability index $V > 9$ From the comparison of the multi-epoch spectral properties and variability we - 24 objects maintain the convex spectrum without showing significant flux density variability $V<9$ )."
 They are labelled “LY in Column 9 of Table 5:: - 2] sources preserve the convex spectrum at the various epochs. although with some amount of [lux density variability (V7 9).," They are labelled “H” in Column 9 of Table \ref{variability}; - 21 sources preserve the convex spectrum at the various epochs, although with some amount of flux density variability $V>9$ )."
" They are labelled °W"" in column 9 of", They are labelled “V” in column 9 of
The parameter € is and Zep=2 is fixed.,The parameter $\xi$ is and $z_{\rm ref}=2$ is fixed.
" The other parameters of this LF are as follows: log9.(Mpc?)=—4.825+ 0.060, [logL.(3.9x 0.043, ky,=0.632+0.077, kj»= 0.38, kj.=—14.25+0.80, (1)o0.417+0.055, kJ,=—0.6230.132, (2)o=2.174+0.055, 0.096, and ky,+5=—0.7930.057 (seeHopkinsky,etal.20070,forthe details)."," The other parameters of this LF are as follows: $\log \phi_{*}({\rm Mpc}^{-3})=-4.825\pm 0.060$ , $[\log
L_{*}(3.9\times 10^{33} {\rm erg~s}^{-1})]_{0}=13.036\pm 0.043$ , $k_{L,1}=0.632\pm 0.077$ , $k_{L,2}=-11.76\pm 0.38$ , $k_{L,3}=-14.25\pm 0.80$, $(\gamma_1)_{0}=0.417\pm 0.055$, $k_{\gamma_1}=-0.623\pm 0.132$, $(\gamma_2)_{0}=2.174\pm 0.055$, $k_{{\gamma_2},1}=1.460\pm 0.096$ , and $k_{{\gamma_2},2}=-0.793\pm
0.057$ \citep*[see][for the details]{2007ApJ...654..731H}."
. This LF includes both the Compton-thin and thick sources., This LF includes both the Compton-thin and thick sources.
 We give some examples of the AGNBHMFs derived from an AGN LF with a given Eddington ratio distribution at different redshits z in Fig. 2.., We give some examples of the AGNBHMFs derived from an AGN LF with a given Eddington ratio distribution at different redshits $z$ in Fig. \ref {Fig_bhmf_lf}.
 It is found that the AGN LF can be well reproduced by the calculations from the AGN BHMF with the form given in Eq. (5))., It is found that the AGN LF can be well reproduced by the calculations from the AGN BHMF with the form given in Eq. \ref{agn_bhmf}) ).
" t). It was suggested that the standardpn, thin accretion disk will transit to an advection dominated accretion flow (ADAF) when the dimensionless mass accretion rate ri is lower than a critical value Merit (m=M/Meaa; Mgaa=1.3.x (Narayan&Yi1995).", 1cm It was suggested that the standard thin accretion disk will transit to an advection dominated accretion flow (ADAF) when the dimensionless mass accretion rate $\dot{m}$ is lower than a critical value $\dot{m}_{\rm crit}$ $\dot{m}=\dot{M}/\dot{M}_{\rm Edd}$; $\dot{M}_{\rm Edd}=1.3\times 10^{38}M_{\rm bh}/0.1M_\odot c^2$ ) \citep{1995ApJ...452..710N}.
" The radiative efficiency for ADAFs is lower than that for standard thin disks, and itsignificantly decreases with decreasing mass accretion rate m."," The radiative efficiency for ADAFs is significantly lower than that for standard thin disks, and it decreases with decreasing mass accretion rate $\dot{m}$."
" It was suggested that the radiative efficiency Tad can be described with where ri=0.01 is adopted in this work (seeNarayan2002,forthedetaileddiscussionandreferences therein),, and the parameter s=1 is suggested in Narayan&Yi(1995).."," It was suggested that the radiative efficiency $\eta_{\rm rad}$ can be described with where $\dot{m}_{\rm crit}=0.01$ is adopted in this work \citep*[see][for the detailed discussion and the references
therein]{2002luml.conf..405N}, and the parameter $s=1$ is suggested in \citet{1995ApJ...452..710N}."
 The calculations of the ADAFs surrounding rotating black holes in the general relativistic frame showed that the value of s is in the range of ~0.2—1.1 depending on the value of black hole spin parameter a (Xu&Cao2010).., The calculations of the ADAFs surrounding rotating black holes in the general relativistic frame showed that the value of $s$ is in the range of $\sim 0.2-1.1$ depending on the value of black hole spin parameter $a$ \citep{2010ApJ...716.1423X}.
" In all our calculations, we adopt s=0.5 (e.g.,Merloni&Heinz2008;Draper&Ballantyne 2010).."," In all our calculations, we adopt $s=0.5$ \citep*[e.g.,][]{2008MNRAS.388.1011M,2010ApJ...715L..99D}."
" The mean mass accretion rate for the blackholes with My, at redshift z can be calculated with where Nacn(Mpn,z) is the AGN BHMF at z, and the radiative efficiency rjaq is given by Eq. (13))."," The mean mass accretion rate for the blackholes with $M_{\rm bh}$ at redshift $z$ can be calculated with where $N_{\rm AGN}(M_{\rm bh},z)$ is the AGN BHMF at $z$, and the radiative efficiency $\eta_{\rm rad}$ is given by Eq. \ref{etarad}) )."
" The black hole evolution equation can be rewritten as As described in §2, the AGN BHMF Nacn(Mpn,z) can be calculated with a given Eddington ratio distribution (2)) and the AGN LF (6)), and the mean mass accretion rate can be calculated with Eq. (14))."," The black hole evolution equation can be rewritten as As described in 2, the AGN BHMF $N_{\rm AGN}(M_{\rm bh},z)$ can be calculated with a given Eddington ratio distribution \ref{eddrat_dis}) ) and the AGN LF \ref{lf}) ), and the mean mass accretion rate can be calculated with Eq. \ref{mdot_aver}) )."
 IntegratingEq. (15)), IntegratingEq. \ref{bhmf_evolz}) )
" over z from Zmaxwith derived AGN BHMF Nacn(Mpn,z) and suitable initial conditions at Zmax, the cosmological evolution of massive black holes is available."," over $z$ from $z_{\rm max}$with derived AGN BHMF $N_{\rm AGN}(M_{\rm bh},z)$ and suitable initial conditions at $z_{\rm max}$, the cosmological evolution of massive black holes is available."
 The duty cycle 6 of AGN is defined as which isrequired to be less than unity., The duty cycle $\delta$ of AGN is defined as which isrequired to be less than unity.
" In all our calculations, we assume that the duty cycle 6=0.5 at Zmax =5."," In all our calculations, we assume that the duty cycle $\delta=0.5$ at $z_{\rm max}=5$ ."
" There are three free parameters, 7raqo, 9, and Apeak, in our calculations, which are tuned to let the BHMF of theAGN relicsat z=0 fit the measured local BHMF given in"," There are three free parameters, $\eta_{\rm rad,0}$ , $\beta_l$ , and $\lambda_{\rm peak}$ , in our calculations, which are tuned to let the BHMF of theAGN relicsat $z=0$ fit the measured local BHMF given in"
The most exciting cosmological discovery in recent vears has been the observed latetime acceleration of the expansion of the Universe (Riess et al.,The most exciting cosmological discovery in recent years has been the observed late–time acceleration of the expansion of the Universe (Riess et al.
 1998: Perlmutter et αἱ., 1998; Perlmutter et al.
 1999)., 1999).
" When this observation is combined with other cosmological data from the Cosmic Microwave Dackground (CAIB) and ealaxy redshift surveys. the best fit mocdoel to all these data is a [lat Universe with 230% of its energy density in the form of dark matter and ~70% in the form of ""dark energy: a mysterious component of the Universe with an effective negative pressure."," When this observation is combined with other cosmological data from the Cosmic Microwave Background (CMB) and galaxy redshift surveys, the best fit model to all these data is a flat Universe with $\simeq 30$ of its energy density in the form of dark matter and $\simeq 70$ in the form of “dark energy”; a mysterious component of the Universe with an effective negative pressure."
 The simplest explanation for dark energy is a “cosmological constant” (CA) as introduced by Einstein in his General Theorv of Relativity to create a static Universe., The simplest explanation for dark energy is a “cosmological constant” $\Lambda$ ) as introduced by Einstein in his General Theory of Relativity to create a static Universe.
" In recent times. the cosmological constant has been interpreted as the ""vacuum energv. but the observed value. of (X ds a factor of ~107"" smaller than its natural value [rom particle physies (Ixrauss “Turner 1995: Carroll 2001)."," In recent times, the cosmological constant has been interpreted as the “vacuum energy”, but the observed value of $\Lambda$ is a factor of $\sim10^{120}$ smaller than its natural value from particle physics (Krauss Turner 1995; Carroll 2001)."
 Alternatives to the cosmological constant include. timeevolving dark energy models. such as quintessence (Ratra Peebles 1988: Wetterich 1988). ancl modifications of gravity," Alternatives to the cosmological constant include time--evolving dark energy models, such as quintessence (Ratra Peebles 1988; Wetterich 1988), and modifications of gravity"
"weighted relations are g—2=—0.014Mj+0.642 and g—2=—0.053Mj+0.225 [or the blue and red GC's. respectively,","weighted relations are $g-z = -0.014 \, 
M_B + 0.642$ and $g-z = -0.053 \, M_B + 0.225$ for the blue and red GCs, respectively."
 The plotted error bars are standard errors of (he mean., The plotted error bars are standard errors of the mean.
 The fils exclude the ος NGC 4365. whose anomalous GC svstem has been discussed in detail elsewhere (Larsen. Drodie. Strader 2005. Drodie 2005. Larsen 2003. Puzia 2002).," The fits exclude the gE NGC 4365, whose anomalous GC system has been discussed in detail elsewhere (Larsen, Brodie, Strader 2005, Brodie 2005, Larsen 2003, Puzia 2002)."
 For the red GC's there is a hint that the slope may flatten out for the faintest ealaxies. but a runs test on the red residuals gave p=0.33 (and p=0.45 for the blue GC's). sugeesting reasonable model fits.," For the red GCs there is a hint that the slope may flatten out for the faintest galaxies, but a runs test on the red residuals gave $p=0.33$ (and $p=0.45$ for the blue GCs), suggesting reasonable model fits."
 Many. possible systematic errors could affect the faintest ealaxies. e.g.. the larger effects of contamination. aud the uncertainty in the distances to individual galaxies. which could change their Àj by ~0.2—0.3 mag.," Many possible systematic errors could affect the faintest galaxies, e.g., the larger effects of contamination, and the uncertainty in the distances to individual galaxies, which could change their $M_B$ by $\sim 0.2-0.3$ mag."
 Thus. one cannot conclude that the GC color-galaxy luminosity relations are well-constrained at the faint end of our sample.," Thus, one cannot conclude that the GC color-galaxy luminosity relations are well-constrained at the faint end of our sample."
 However. (μον are consistent wilh extrapolations from brighter galaxies.," However, they are consistent with extrapolations from brighter galaxies."
 Our results are also consistent wilh previous slope measurements: Larsen (2001) and Stvacler (2004) found that the V—7 rec:blue ratio of slopes is ~2. while we find ~3.7 ing-z.," Our results are also consistent with previous slope measurements: Larsen (2001) and Strader (2004) found that the $V-I$ red:blue ratio of slopes is $\sim 2$, while we find $\sim 3.7$ in $g-z$."
 This is consistent wilh g—zx2(V—£D). a rough initial estimate of color conversion (Drodie 2005).," This is consistent with $g-z \propto 2 \, (V-I)$, a rough initial estimate of color conversion (Brodie 2005)."
 There is al least one ongoing program to study Galactic GCs in the Sloan filter set which should improve this (xd similar) conversions considerably., There is at least one ongoing program to study Galactic GCs in the Sloan filter set which should improve this (and similar) conversions considerably.
 It does appear that (the residuals of the blue and red peak values are correlated: this is probably unavoidable when fitting heteroscedastic mixture models to populations which are not well-separated., It does appear that the residuals of the blue and red peak values are correlated; this is probably unavoidable when fitting heteroscedastic mixture models to populations which are not well-separated.
 Since the red and blue GC subpopulations clearly have clilferent dispersions where this can be tested in detail. fitting homoscedastc models does not make sense.," Since the red and blue GC subpopulations clearly have different dispersions where this can be tested in detail, fitting homoscedastic models does not make sense."
 We experimented with filling two-component models with the variances fixed to the mean value for the brightest galaxies. for which the large number of GCs (at least partiallv) breaks the degeneracy between peak location and dispersion.," We experimented with fitting two-component models with the variances fixed to the mean value for the brightest galaxies, for which the large number of GCs (at least partially) breaks the degeneracy between peak location and dispersion."
 The slopes of the resulting blue and red relations ave similar to those found using the above approach: —0.012 ancl —0.057. respectively.," The slopes of the resulting blue and red relations are similar to those found using the above approach: $-0.012$ and $-0.057$, respectively."
 However. the blue peak values for many of (he galaxies appear to be artificially hiehthis max be because galaxies less massive (han gEs have smaller intra-subpopulation metalliitv spreads.," However, the blue peak values for many of the galaxies appear to be artificially high—this may be because galaxies less massive than gEs have smaller intra-subpopulation metallicity spreads."
 Thus we have chosen to leave the original [its as our final values., Thus we have chosen to leave the original fits as our final values.
 The very existence of red GC's in faint galaxies with Mg~—15 to —16 is an interesting and somewhat unexpected result., The very existence of red GCs in faint galaxies with $M_B \sim -15$ to $-16$ is an interesting and somewhat unexpected result.
 In massive earlv-tvpe galaxies and many spiral bulges. the number of red GC's normalized to spheroid luminosity is approximately constant. (Forbes. Drodie. Larsen 2001).," In massive early-type galaxies and many spiral bulges, the number of red GCs normalized to spheroid luminosity is approximately constant (Forbes, Brodie, Larsen 2001)."
 This suggests that red GCS formed along with the spheroidal field stars al ~ constant efficiency., This suggests that red GCs formed along with the spheroidal field stars at $\sim$ constant efficiency.
 Ilowever. many properties of clEs (e.g.. surlace brightness profiles. M/L ratios. spatial/velocity distribution. stellar populations) suggest that (heir formation mechanism was different [rom massive Es (e.g.. IXormendy. 1985. though see Graham Guzmánn 2003 for a different view).," However, many properties of dEs (e.g., surface brightness profiles, M/L ratios, spatial/velocity distribution, stellar populations) suggest that their formation mechanism was different from massive Es (e.g., Kormendy 1985, though see Graham Guzmánn 2003 for a different view)."
 A continuity of red GC properties between Es and at least some of the dEs in our sample could imply either that (their formation mechanisms were more similar than expected or that red GCs are formed by a sell-regulating.," A continuity of red GC properties between Es and at least some of the dEs in our sample could imply either that their formation mechanisms were more similar than expected or that red GCs are formed by a self-regulating,"
"primordial non-CGaussiauities frou, observations of larec-scale structures.",primordial non-Gaussianities from observations of large-scale structures.
 Iu particular. as discussed above for Eq.(L18)). the method. presented in this article is quite eeneral aud cau be applied to a large class of nodels.," In particular, as discussed above for \ref{chi_i}) ), the method presented in this article is quite general and can be applied to a large class of models."
 Aloreover. since it provides results iu botji real space and Fourier space (io. fi6 halo two-point correlation and power spectrum) it eielves a complete aud consistcut description of halo clusterig.," Moreover, since it provides results in both real space and Fourier space (i.e. the halo two-point correlation and power spectrum) it gives a complete and consistent description of halo clustering."
 B.As for previous approaches. the most reliable use of these inodels to constrain cosmology is to take advuitage of the specific sitpe of the dependence on lass {or the mass function) or scale (for the bias) brought ba> primordial nou-Ciuussiauitv to constrain νι (rather tha1 the chauge in the amplitude at a given mass or scale).," As for previous approaches, the most reliable use of these models to constrain cosmology is to take advantage of the specific shape of the dependence on mass (for the mass function) or scale (for the bias) brought by primordial non-Gaussianity to constrain $\fNL$ (rather than the change in the amplitude at a given mass or scale)."
shown in Fig.,shown in Fig.
 | provides an opportunity to reconstruct the so-called one-dimensional. projectior image. which is obtained by integrating the object's two-dimensional intensity distribution along the direction perpendicular to the linear av coverage on the sky (central slice theorem or Fourier slice theorem).," \ref{uvcoverage} provides an opportunity to reconstruct the so-called one-dimensional projection image, which is obtained by integrating the object's two-dimensional intensity distribution along the direction perpendicular to the linear $uv$ coverage on the sky (central slice theorem or Fourier slice theorem)."
 In other words. this one-dimensional projection image represents the two-dimensional intensity distribution compressed or squashed onto the linear uv coverage on the sky.," In other words, this one-dimensional projection image represents the two-dimensional intensity distribution compressed or squashed onto the linear $uv$ coverage on the sky."
 For example. the one-dimensional projection image of a uniform. disk is a semi-circle (see also. the. dimensional image of a limb-darkened disk and its one-dimensional projection image shown in Figs.," For example, the one-dimensional projection image of a uniform disk is a semi-circle (see also the two-dimensional image of a limb-darkened disk and its one-dimensional projection image shown in Figs."
 Blaa and Blec)., \ref{simdata_ldd}a a and \ref{simdata_ldd}c c).
 The reconstruction of one-dimensional projection images was first proposed for radio interferometry by Bracewell (1956))., The reconstruction of one-dimensional projection images was first proposed for radio interferometry by Bracewell \cite{bracewell56}) ).
 Whereas the information Ἡ the direction perpendicular to the baseline vector is lost in one-dimensional projection images. they still provide model-independent information about the geometrical extent and asymmetry of the object.," Whereas the information in the direction perpendicular to the baseline vector is lost in one-dimensional projection images, they still provide model-independent information about the geometrical extent and asymmetry of the object."
 The reconstruction of one-dimensional projection images from IR interferometric data or lunar occultation data has been carried out (e.g.. Navarro et al. 1990::," The reconstruction of one-dimensional projection images from IR interferometric data or lunar occultation data has been carried out (e.g., Navarro et al. \cite{navarro90};"
 Leinert et al. 1991::, Leinert et al. \cite{leinert91};
 Tatebe et al. 2006:;, Tatebe et al. \cite{tatebe06};
 Chandler et al. 2007))., Chandler et al. \cite{chandler07}) ).
 We used the MiRA package ver. (, We used the MiRA package ver. (
Thiébbaut et al. 2008)),Thiébbaut et al. \cite{thiebaut08}) )
 to reconstruct one-dimensional projection images at each spectral channel (details of our image reconstruction procedure are described i1 Appendix Appendix B:)., to reconstruct one-dimensional projection images at each spectral channel (details of our image reconstruction procedure are described in Appendix \ref{appendix_simtests}) ).
 We first carried out the image reconstruction using computer-simulated data to examine effects of the mv coverage and reconstruction parameters such as the initial model. prior. and regularization scheme on the reconstructed images.," We first carried out the image reconstruction using computer-simulated data to examine effects of the $uv$ coverage and reconstruction parameters such as the initial model, prior, and regularization scheme on the reconstructed images."
 These tests with simulated data are crucial for examining the credibility of aperture synthesis imaging particularly for objects with complex structures., These tests with simulated data are crucial for examining the credibility of aperture synthesis imaging particularly for objects with complex structures.
 With appropriate reconstruction. parameters. determined from these tests. we attempted to reconstruct one-dimensional projection images from the observed 162 visibility amplitudes and 54 CPs.," With appropriate reconstruction parameters determined from these tests, we attempted to reconstruct one-dimensional projection images from the observed 162 visibility amplitudes and 54 CPs."
 While this worked well for the continuum. the reconstruction 1 the CO lines turned out to be very sensitive to the reconstruction parameters.," While this worked well for the continuum, the reconstruction in the CO lines turned out to be very sensitive to the reconstruction parameters."
 For example. depending on the size of the uniform disk used as the initial. model. the recostructed one-dimensional projection image in the CO lines shows a faint region on the eastern or western side.," For example, depending on the size of the uniform disk used as the initial model, the reconstructed one-dimensional projection image in the CO lines shows a faint region on the eastern or western side."
 Therefore. we used the self-calibration technique. which has recently been successfully applied to AMBER data for the first time by Millour et al. (2011)).," Therefore, we used the self-calibration technique, which has recently been successfully applied to AMBER data for the first time by Millour et al. \cite{millour11}) )."
 We added modifications to their technique to deal with some Issue specific to our data of Betelgeuse as described in Appendix AppendixC:.., We added modifications to their technique to deal with some issue specific to our data of Betelgeuse as described in Appendix \ref{appendix_selfcal}.
 This technique allows us to restore the phase of the complex Fourier transform of the object's intensity distribution from the DP measurements., This technique allows us to restore the phase of the complex Fourier transform of the object's intensity distribution from the DP measurements.
 Image reconstruction with the complex visibility (1e... visibility amplitude and phase) removes the ambiguity of the solution derived with the visibility amplitude and CP alone.," Image reconstruction with the complex visibility (i.e., visibility amplitude and phase) removes the ambiguity of the solution derived with the visibility amplitude and CP alone."
 To compare with the A-band continuum visibilities from the 2008 data that were derived from the binned data with a spectral resolution 4800. we also derived the visibilities from the 2009 data binned with the same spectral resolution.," To compare with the $K$ -band continuum visibilities from the 2008 data that were derived from the binned data with a spectral resolution 4800, we also derived the visibilities from the 2009 data binned with the same spectral resolution."
 As in Paper I. we selected continuum points shortward of the CO band head at 2.294jm.," As in Paper I, we selected continuum points shortward of the CO band head at 2.294."
.. For each data set. we averaged the visibilities over the selected continuum points.," For each data set, we averaged the visibilities over the selected continuum points."
 We took the simple mean of the errors as the errors in the average continuum visibilities without reducing by VNo4. where Neon is the number of the selected continuum points.," We took the simple mean of the errors as the errors in the average continuum visibilities without reducing by $\sqrt{N_{\rm cont}} $, where $N_{\rm cont}$ is the number of the selected continuum points."
 The reason is that the measurement errors are dominated by the systematic error i the absolute visibility calibration and do not become smaller by the averaging., The reason is that the measurement errors are dominated by the systematic error in the absolute visibility calibration and do not become smaller by the averaging.
 We applied this averaging to the 2008 data as well., We applied this averaging to the 2008 data as well.
 Since the different continuum spectral channels correspond to slightly different spatial frequencies. we also averaged the spatial frequencies from the selected continuum points.," Since the different continuum spectral channels correspond to slightly different spatial frequencies, we also averaged the spatial frequencies from the selected continuum points."
 Figure 5 shows the K-band continuum visibilities measured in 2008 and 2009 as a function of spatial frequency., Figure \ref{vis_continuum} shows the $K$ -band continuum visibilities measured in 2008 and 2009 as a function of spatial frequency.
 The figure reveals that the nearly linear wv coverage shown in Fig., The figure reveals that the nearly linear $uv$ coverage shown in Fig.
 | enabled us to sample the visibility functio quite densely from the first to the fifth visibility lobe., \ref{uvcoverage} enabled us to sample the visibility function quite densely from the first to the fifth visibility lobe.
 Uniform-disk fitting to the 2009 data results in a diameter of 42.05+0.05 mas with a reduced y of 3.8., Uniform-disk fitting to the 2009 data results in a diameter of $42.05 \pm 0.05$ mas with a reduced $\chi^2$ of 3.8.
 Fitting with a power-law-type limb-darkend disk (Hestroffer et al. 1997)), Fitting with a power-law-type limb-darkend disk (Hestroffer et al. \cite{hestroffer97}) )
 results in à limb-darkened disk diameter of 42.49+0.06 mas and a limb-darkening parameter of (9.7+0.5)x107 with a better reduced y of 2.5.," results in a limb-darkened disk diameter of $42.49 \pm 0.06$ mas and a limb-darkening parameter of $(9.7 \pm 0.5) \times 
10^{-2}$ with a better reduced $\chi^2$ of 2.5."
 While the reduced y value is still higher than |. Fig.," While the reduced $\chi^2$ value is still higher than 1, Fig."
 2. shows that the deviation from the limb-darkened disk is not strong. as found for the 2008 data.," \ref{vis_continuum} shows that the deviation from the limb-darkened disk is not strong, as found for the 2008 data."
 Only at the highest spatial frequency (1.e.. the smallest spatial scale) is the deviation noticeable. but the errors are also large there.," Only at the highest spatial frequency (i.e., the smallest spatial scale) is the deviation noticeable, but the errors are also large there."
 The limb-darkened disk diameter derived from the K- band continuum data and a bolometric flux of (111.67+6.49)x10-7 W oem? (Perrin et al. 2004) , The limb-darkened disk diameter derived from the $K$ -band continuum data and a bolometric flux of $(111.67 \pm 6.49) \times 10^{-13}$ W $^{-2}$ (Perrin et al. \cite{perrin04}) )
lead to an effective temperature of 3690+54 K. We propose this value as ar effective temperature of the continuum-forming layer. approximately free from the effects of molecular lines.," lead to an effective temperature of $3690 \pm 54$ K. We propose this value as an effective temperature of the continuum-forming layer, approximately free from the effects of molecular lines."
 Perrin et al. (20049) , Perrin et al. \cite{perrin04}) )
modeled K-broadband interferometric measurements of Betelgeuse with a continuum-forming blackbody sphere and an extended molecular shell., modeled $K$ -broadband interferometric measurements of Betelgeuse with a continuum-forming blackbody sphere and an extended molecular shell.
 They derived 3690+50 K for the continuum-forming sphere., They derived $3690 \pm 50$ K for the continuum-forming sphere.
 This value excellently agrees with our effective temperature of the continuum-forming layer., This value excellently agrees with our effective temperature of the continuum-forming layer.
 Our effective temperature ts slightly higher than the 3600+66 K recently derived by Haubots et al. (20095) , Our effective temperature is slightly higher than the $3600 \pm 66$ K recently derived by Haubois et al. \cite{haubois09}) )
from the the H-band observations with the Infrared Optical Telescope Array (IOTÀ). but both agree within the uncertainties.," from the the $H$ -band observations with the Infrared Optical Telescope Array (IOTA), but both agree within the uncertainties."
 Figure 2. reveals that the continuum visibilities show no or only marginal time variations between 2008 (green dots) and 2009 (red and blue dots) within the measurement errors., Figure \ref{vis_continuum} reveals that the continuum visibilities show no or only marginal time variations between 2008 (green dots) and 2009 (red and blue dots) within the measurement errors.
 We compare this observational result with the current three- convection simulation for RSGs by Chiavassa et, We compare this observational result with the current three-dimensional convection simulation for RSGs by Chiavassa et
variables is explained in the Appendix.),variables is explained in the Appendix.)
" The orbital phase clistribution. w5. is narrow because the guiding centres of all stars in the sample are close to the Sun's azimuth in the Galaxy. which was arbitrarily chosen to lie at ay,=0."," The orbital phase distribution, $w_\phi$, is narrow because the guiding centres of all stars in the sample are close to the Sun's azimuth in the Galaxy, which was arbitrarily chosen to lie at $w_\phi = 0$."
 The clistribution of radial phases. ay. is non-uniform also. reflecting the substructure in phase space (Fig. 5)).," The distribution of radial phases, $w_R$, is non-uniform also, reflecting the substructure in phase space (Fig. \ref{contall}) )."
 As explained more fully in Paper Ll a new peak that appears in any of the distributions of simple. linear combinations of these phase angles may indicate a group of stars trapped in. or recently scattered by. a resonance.," As explained more fully in Paper I, a new peak that appears in any of the distributions of simple linear combinations of these phase angles may indicate a group of stars trapped in, or recently scattered by, a resonance."
" The appropriate combination is mus,|Peg.", The appropriate combination is $mw_\phi + lw_R$.
 Phis test is insensitive to corotation. where /=Q0. but a new concentration of stars at. some value of one of. these combinations with |/|=1 is an indicator of a Lindblad resonance.," This test is insensitive to corotation, where $l = 0$, but a new concentration of stars at some value of one of these combinations with $|l|=1$ is an indicator of a Lindblad resonance."
" MeMallan(2011). Bas shown that selection ellects in any local sample. together with a small amount of scatter about the expected constant value of mus,|Pig. conspire to frustrate this test."," \citet{McM11} has shown that selection effects in any local sample, together with a small amount of scatter about the expected constant value of $mw_\phi
+ lw_R$, conspire to frustrate this test."
 In the light of his finding. our more limited. objective here is to show that the features. that appeared in the tests in Paper E have their counterparts in the present sample.," In the light of his finding, our more limited objective here is to show that the features that appeared in the tests in Paper I have their counterparts in the present sample."
 Fig., Fig.
 S shows the distributions of four combinations of the angle variables of stars in the combined sample., \ref{restest} shows the distributions of four combinations of the angle variables of stars in the combined sample.
 Lhe top panel shows the case for an flor m=2. while the lower three panels are for various LLRs. The overall shapes of the distributions cdiller in detail from those found for sstars in Paper 1. However. Sellwood identified clear peaks in the ceases [or m=2 and m=3 (his Fig.," The top panel shows the case for an for $m=2$, while the lower three panels are for various s. The overall shapes of the distributions differ in detail from those found for stars in Paper I. However, Sellwood identified clear peaks in the cases for $m=2$ and $m=3$ (his Fig."
 7). and for m=4 in Fig.," 7), and for $m=4$ in Fig."
 A3. of this paper., \ref{restest4} of this paper.
 These features. at the abscissac markecl by arrows. can also be identified in Fie.," These features, at the abscissae marked by arrows, can also be identified in Fig."
 S. in this independent sample., \ref{restest} in this independent sample.
 Although the significance of the peaks at the indicated abscissae is not high. they do lie at the same ohases as those in the ssample.," Although the significance of the peaks at the indicated abscissae is not high, they do lie at the same phases as those in the sample."
 Phe peak near zero. that becomes more prominent as om ds increased. is à selection clleet that is explained in he Appendix.," The peak near zero, that becomes more prominent as $m$ is increased, is a selection effect that is explained in the Appendix."
" A peak is also visible in the deistribution. in the top panel. near 2a,|wg~Ls hat also has a counterpart at the indicated position in the corresponding distribution from the ssample in. Paper 1. although in that case the dillerence xetween the distributions of Puy,|wy and of te, alone was ess pronounced."," A peak is also visible in the distribution, in the top panel, near $2w_\phi+w_R \sim -1.8$ that also has a counterpart at the indicated position in the corresponding distribution from the sample in Paper I, although in that case the difference between the distributions of $2w_\phi+w_R$ and of $w_R$ alone was less pronounced."
 The peaks in these new data are far from compelling. out. they provide a valuable confirmation of the far more significant peaks that were found. from the higher quality ssanmiple.," The peaks in these new data are far from compelling, but they provide a valuable confirmation of the far more significant peaks that were found from the higher quality sample."
 Measurement errors. must always smooth away features on the scale of the uncertainty anc the above estimates of the uncertainties suggest. broadening on the scale of σ~0.2 radians., Measurement errors must always smooth away features on the scale of the uncertainty and the above estimates of the uncertainties suggest broadening on the scale of $\sigma \sim 0.2$ radians.
 In. particular. it is reassuring that the most significant peak in Fig.," In particular, it is reassuring that the most significant peak in Fig."
 6 lies at the same frequency. and the peaks in the lower three panels of Fig.," \ref{actplt} lies at the same frequency, and the peaks in the lower three panels of Fig."
 S. lie at the same phases. as in the corresponding Figures from the ssample.," \ref{restest} lie at the same phases, as in the corresponding Figures from the sample."
 Taken together. this is strong evidence in support of a Lindblad: resonance from this completely independent sample.," Taken together, this is strong evidence in support of a Lindblad resonance from this completely independent sample."
Active galactic nuclei (AGN) are commonly assumed. to be super massive black holes in the centre of galaxies. in which accretion processes give rise to emission throughout the electromagnetic spectrum.,"Active galactic nuclei (AGN) are commonly assumed to be super massive black holes in the centre of galaxies, in which accretion processes give rise to emission throughout the electromagnetic spectrum."
 AGN are observed to date up to redshifts ofς~6.4 (Willott et al., AGN are observed to date up to redshifts of$z \sim 6.4$ (Willott et al.
 2007). showing that super massive black holes with masses of Mg;~10°M. must have been formed as early as <0.7 Gyrs after the formation of the first stars (Kashlinskyetal. 2005)).," 2007), showing that super massive black holes with masses of $M_{BH} \sim 10^8 \rm \, M_\odot$ must have been formed as early as $< 0.7$ Gyrs after the formation of the first stars \cite{Kashlinsky05}) )."
 In order to be able to form super massive black holes at this early stage of the Universe. merging events and high accretion rates are required.," In order to be able to form super massive black holes at this early stage of the Universe, merging events and high accretion rates are required."
 This black hole evolution is closely tied to the growth of the bulge of the AGN's host galaxy. as both seem to be correlated with May=107Mputec (Gebhardtetal. 2000)).," This black hole evolution is closely tied to the growth of the bulge of the AGN's host galaxy, as both seem to be correlated with $M_{BH} \simeq
10^{-3} M_{Bulge}$ \cite{Gebhardt00}) )."
 Recent studies intend to not only find unification models for the different AGN types but also probe whether their central engines andsuper massive black holes are simply scaled versions of Galactic black holes likeX-1..J1655—40.. or GX 339-4.," Recent studies intend to not only find unification models for the different AGN types but also probe whether their central engines andsuper massive black holes are simply up-scaled versions of Galactic black holes like, or GX 339–4."
 In this context. models of black hole accretion can be tested using objects showing extreme physical properties. like luminosity. accretion rate. or Eddington ratio.," In this context, models of black hole accretion can be tested using objects showing extreme physical properties, like luminosity, accretion rate, or Eddington ratio."
 The Seyfert 1.9 galaxy presented here resides in an extreme end of the known parameter space of AGN., The Seyfert 1.9 galaxy presented here resides in an extreme end of the known parameter space of AGN.
 X-ray observations give a direct view on matter close to the super massive black hole. providing insights into the geometry and the state of the matter.," X-ray observations give a direct view on matter close to the super massive black hole, providing insights into the geometry and the state of the matter."
 The flux andspectral variability of the sources in the hard X- reflect the size and physical state of the regions involved in the emission processes (see Uttley McHardy 2004 for a brief review)., The flux andspectral variability of the sources in the hard X-rays reflect the size and physical state of the regions involved in the emission processes (see Uttley McHardy 2004 for a brief review).
 MCG-05-23-016 is one of the brightest Seyfert galaxies in the X-rays., MCG–05–23–016 is one of the brightest Seyfert galaxies in the X-rays.
 This Seyfert 1.9 galaxy at redshift z=0.0085 has not only been studied in the 2—1O0keV band by most X-ray missions so far. but has also been detected in hard X- above 20 keV with BeppoSAX/PDS (e.g. Balestra et al.," This Seyfert 1.9 galaxy at redshift $z=0.0085$ has not only been studied in the $2 - 10 \rm \, keV$ band by most X-ray missions so far, but has also been detected in hard X-rays above 20 keV with /PDS (e.g. Balestra et al."
 2004). INTEGRAL/IBIS (Soldi et al.," 2004), /IBIS (Soldi et al."
 2005). and. Swift/BAT (Beckmann et al.," 2005), and /BAT (Beckmann et al."
 2007. Tueller et al.," 2007, Tueller et al."
 2008)., 2008).
" With a bolometric luminosity of Ly,=2x10eres! this Seyfert is a moderately luminous object. with a comparably small central black hole of Μι=2xI0M4 (Wang&Zhang 2007)."," With a bolometric luminosity of $L_{bol} \simeq 2 \times 10^{44} \rm \, erg \,
s^{-1}$ this Seyfert is a moderately luminous object, with a comparably small central black hole of $M_{BH} = 2 \times 10^6 \rm \,
M_\odot$ \cite{BHmass}) )."
 Wang Zhang used the width of the OIII line (Greene&Ho2005)) to obtain the black hole mass from the Mp;—o relation (Tremaineetal. 2002)) and give the error of the measurement with 0.7 dex., Wang Zhang used the width of the OIII line \cite{Greene05}) ) to obtain the black hole mass from the $M_{BH} - \sigma$ relation \cite{Tremaine02}) ) and give the error of the measurement with 0.7 dex.
 Balestra et al. (, Balestra et al. (
2004) derived fromASCA.BeppoSAX. and data that the iron Ke line apparent in the spectrum seems to be a superposition of a narrow and a broad component. that a reflection component of R=O45 is detectable. and that the continuum can be modeled by a photo: index of [=17 and à cut-off at Ec=lIOkeV.,"2004) derived from, and data that the iron $\alpha$ line apparent in the spectrum seems to be a superposition of a narrow and a broad component, that a reflection component of $R = 0.45$ is detectable, and that the continuum can be modeled by a photon index of $\Gamma \simeq 1.7$ and a cut-off at $E_C = 110 \rm \, keV$."
 The observations covered a time span from 1994 to 2001. during which the object showed little flux variation and a stable spectrum as well as constant iron line and reflection component.," The observations covered a time span from 1994 to 2001, during which the object showed little flux variation and a stable spectrum as well as constant iron line and reflection component."
 A recent re-analysis of theBeppoSAX data by Dadina (2007) indicates a slightly steeper spectrum (I=1.79—(0.08 O0) with higher cut-off energy (Ec=191B keV). and stronger reflection component (R= 0.747075).," A recent re-analysis of the data by Dadina (2007) indicates a slightly steeper spectrum $\Gamma = 1.79 {+0.07 \atop -0.08}$ ) with higher cut-off energy $Ec = 191 {+110 \atop -60} \rm \, keV$ ), and stronger reflection component $R = 0.74 {+0.22 \atop -0.52}$ )."
" An analysis of data by Mattson Weaver (2004) using a fixed underlying power law slope of I=1.88 led to a variable reflection component in the range R=0.85—0.57 and iron Ke line flux (fg,=(1.55-1.99)x107photonskeV-!cme? s7!)."," An analysis of data by Mattson Weaver (2004) using a fixed underlying power law slope of $\Gamma = 1.88$ led to a variable reflection component in the range $R = 0.35 - 0.57$ and iron $K\alpha$ line flux $f_{K\alpha} =
 (1.55 - 1.99) \times 10^{-4} \rm \, photons \, keV^{-1} \, cm^{-2}
 \, s^{-1}$ )."
 Recently. observations on MCG-05-23-016 by showed a 0.4—I00keV spectrum which appeared tobe a cut-off power law of [=1.9 and Ec>170keV plus a dual reflector with R~0.9 and R~ 0.5. respectively (Reevesetal. 2007)).," Recently, observations on MCG–05–23–016 by showed a $0.4-100 \rm \, keV$ spectrum which appeared tobe a cut-off power law of $\Gamma = 1.9$ and $E_C > 170 \rm \, keV$ plus a dual reflector with $R \sim 0.9$ and $R \sim 0.5$ , respectively \cite{Reeves07}) )."
 and data confirmed that the iron Ka line complex consists, and data confirmed that the iron $\alpha$ line complex consists
surface of the NS has been located. geodesics connecting the surface to the observer are computed.,"surface of the NS has been located, geodesics connecting the surface to the observer are computed."
 We discretize the surface into small patches and calculate the zenith angleοἱ between the local normal and initial photon direction in the locally comoving frame for each patch., We discretize the surface into small patches and calculate the zenith angle$\alpha$ between the local normal and initial photon direction in the locally comoving frame for each patch.
 We also calculate the solid angle dQ subtended by the patch as seen by the observer and the redshift =... The redshift. z. includes both the gravitational redshift and Doppler-like terms resulting from rotation.," We also calculate the solid angle $d\Omega$ subtended by the patch as seen by the observer and the redshift $z_*$ The redshift, $z_*$ includes both the gravitational redshift and Doppler-like terms resulting from rotation."
 Since the intensity. 7. is both a function of energy and cos. the observed flux due to the patch is The observed spectrum is found by summing over all visible patches.," Since the intensity, $I$, is both a function of energy and $\cos\alpha$, the observed flux due to the patch is The observed spectrum is found by summing over all visible patches."
 The technical details of the fully relativistic computational method are presented by Cadeau et al. (, The technical details of the fully relativistic computational method are presented by Cadeau et al. (
2005b).,2005b).
 We also use the simpler S+D approximation (Miller Lamb 1998; Braje. Romant. Rauch 2000: also see Cadeau et al 2005a and Poutanen Gierlinski 2003) to independently compute the spectrum.," We also use the simpler S+D approximation (Miller Lamb 1998; Braje, Romani, Rauch 2000; also see Cadeau et al 2005a and Poutanen Gierlinski 2003) to independently compute the spectrum."
 In the S+D approximation the metric is approximated by the non-rotating Schwarzschild metric. and appropriate Doppler factors correct for the rotation.," In the S+D approximation the metric is approximated by the non-rotating Schwarzschild metric, and appropriate Doppler factors correct for the rotation."
" To lowest order in v/c. the redshift factor reduces to (1z.)=+21—6) where à=isincsina sini, !22zRi/G/1-26M/(QIc7)) is the scale of rotational broadening. ως 1s the observed spin of the NS. and z2(1—2GM(ΝΟΤΙ-1."," To lowest order in $v/c$ , the redshift factor reduces to $(1+z_*) = (1+z)(1-\delta) $ where $\delta = \beta {\sin \zeta \sin
\alpha \sin i}$ , $\beta = 2 \pi R \nu_{\rm s}/(c\sqrt{1-2GM/(Rc^2)})$ is the scale of rotational broadening, $\nu_{\rm s}$ is the observed spin of the NS, and $z = (1-2GM/(Rc^2))^{-1/2} -1$."
 The angle ¢ is the azimuthal angle of the emitting patch about the vector pointing from the center of the star towards the observer., The angle $\zeta$ is the azimuthal angle of the emitting patch about the vector pointing from the center of the star towards the observer.
 This angle is zero if the patch is in the plane defined by the spin axis and this vector., This angle is zero if the patch is in the plane defined by the spin axis and this vector.
 A further simplification is the use of the Beloborodov (2002) approximation. 1—cosa2(IH2)7(1—cosc). where cis the bending angle.," A further simplification is the use of the Beloborodov (2002) approximation, $ 1-\cos\alpha = (1+z)^{-2} (1-\cos\psi), $ where $\psi$ is the bending angle."
 This allows the total observed flux to be written as the integral over all possible initial photon zenith and azimuthal angles. where RK is the NS radius and « is the distance.," This allows the total observed flux to be written as the integral over all possible initial photon zenith and azimuthal angles, where $R$ is the NS radius and $d$ is the distance."
 The results for emission from the entire NS surface with CBW's intrinsic line profile of the fully relativistic calculation and the S+D approximation are shown in Figure 1.., The results for emission from the entire NS surface with CBW's intrinsic line profile of the fully relativistic calculation and the S+D approximation are shown in Figure \ref{fig:Sharon}.
 They are in excellent agreement and the tiny deviations are mainly due to our neglect of relativistic aberation., They are in excellent agreement and the tiny deviations are mainly due to our neglect of relativistic aberation.
 The linear change to the metric in v/c due to frame dragging (Hartle 1967. Hartle Thorne 1968) suggests observable effect on the line at spin frequencies near 300 Hz as }~0.1.," The linear change to the metric in $v/c$ due to frame dragging (Hartle 1967, Hartle Thorne 1968) suggests observable effect on the line at spin frequencies near 300 Hz as $\beta \sim
0.1$."
 However. the frame-drageing term enters into the line broadening calculation as a second order effect in v/c. preserving the validity of the simple S+D approximation.," However, the frame-dragging term enters into the line broadening calculation as a second order effect in $v/c$, preserving the validity of the simple S+D approximation."
 Only at very high spin frequencies does frame dragging have the potential of producing observable effects (Bhattacharyya et al 2004)., Only at very high spin frequencies does frame dragging have the potential of producing observable effects (Bhattacharyya et al 2004).
 Of greater relevance is the relative size of the fine structure splitting and the scale of rotational broadening., Of greater relevance is the relative size of the fine structure splitting and the scale of rotational broadening.
 At 45 Hz. the scale of rotational broadening is 24 eV for a 10 km NS. which is similar to the fine structure splitting of 20.7 eV for the Fe Πα line.," At 45 Hz, the scale of rotational broadening is 24 eV for a 10 km NS, which is similar to the fine structure splitting of 20.7 eV for the Fe $\alpha$ line."
 At slower and faster rotation rates. fine structure splitting dominates rotational broadening and vice versa.," At slower and faster rotation rates, fine structure splitting dominates rotational broadening and vice versa."
 Hence the line profile can change dramatically near 45 Hz., Hence the line profile can change dramatically near 45 Hz.
 We illustrate this effect in Figure 1. where we plot the line profile for isin;=20 Hz (long-short dashed line). which is dominated by fine structure splitting.," We illustrate this effect in Figure \ref{fig:Sharon} where we plot the line profile for $\nu_{\rm s}\sin i
= 20$ Hz (long-short dashed line), which is dominated by fine structure splitting."
 The simplicity and accuracy of the S+D approximation allows for a rapid and detailed exploration of parameter space., The simplicity and accuracy of the S+D approximation allows for a rapid and detailed exploration of parameter space.
 We assume emission from the entire surface., We assume emission from the entire surface.
 Emission concentrated near the spin axis would also give narrow line profiles (Bhattacharyya. Miller Lamb 2004). but we do not consider this possibility.," Emission concentrated near the spin axis would also give narrow line profiles (Bhattacharyya, Miller Lamb 2004), but we do not consider this possibility."
 We fit our models to the co-added spectra and continuum model from CPM., We fit our models to the co-added spectra and continuum model from CPM.
 We focus on a narrow range between παπα aand plot these points in Figure 2.., We focus on a narrow range between and and plot these points in Figure \ref{fig:fitSpectra}.
 The 13.25 ffeature in the continuum fit is due to à Ne IX resonant transition m the circumstellar model., The 13.25 feature in the continuum fit is due to a Ne IX resonant transition in the circumstellar model.
 Taking the continuum model as the background flux. we overlay some models for v=0. 45. 100 and 300 Hz for R=10 km.," Taking the continuum model as the background flux, we overlay some models for $\nu_{\rm s} = 0$, $45$, 100 and 300 Hz for $R=10$ km."
" To set the scale of Stark broadening. we take a background density of n,=10em. which is appropriate for a uniform Fe abundance above the continuum photosphere (CBW)."," To set the scale of Stark broadening, we take a background density of $n_p = 10^{23}\,{\rm cm}^{-3}$, which is appropriate for a uniform Fe abundance above the continuum photosphere (CBW)."
" From these models. large spins Le. 7,sin?=300 Hz are ruled out."," From these models, large spins i.e. $\nu_{\rm s}\sin i = 300$ Hz are ruled out."
 Secondly. the intrinsically broad line profile which is similar to the width of the observed line. prohibits a meaningful limit on R for i4=44.7 Hz.," Secondly, the intrinsically broad line profile which is similar to the width of the observed line, prohibits a meaningful limit on $R$ for $\nu_{\rm s} = 44.7$ Hz."
 We also performed a detailed exploration. of. parameter space., We also performed a detailed exploration of parameter space.
 Using the data between 12.6 aand 13.3A.. we overlay our line profiles on the continuum model to test the goodness of fit.," Using the data between 12.6 and 13.3, we overlay our line profiles on the continuum model to test the goodness of fit."
 Varying iusincR/IOKkm). I+z. and Ny4-5. the best fit gives a ES-]1.01 for degrees of freedom.," Varying $\nu_{\rm
s}\sin i (R/10\,{\rm km})$, 1+z, and $N_{\rm Fe, n=2}$, the best fit gives a $\chi^2 = 11.01$ for 17 degrees of freedom."
 By itself. the continuum model gives 17(=24.9.," By itself, the continuum model gives $\chi^2 = 24.9$."
 The best fit parameters are r4sini(R/IOkm)=32+19Hz. Iz1.345c 0.004. and logyg(Men=2em)=17.9£ 0.2.The errors indicated are one sigma values derived from the covariance matrix.," The best fit parameters are $\nu_{\rm s}\sin i (R/10\,{\rm km}) = 32 \pm 19\,{\rm Hz}$, $1 + z =
1.345 \pm 0.004$ , and ${\rm log}_{10} (N_{\rm Fe, n=2}/{\rm cm^{-2}}) =
17.9 \pm 0.2$ .The errors indicated are one sigma values derived from the covariance matrix."
 To develop a more detailed understanding of parameter space. we marginalize our three parameter joint probability distribution function (PDF) over two parameters at a timeand," To develop a more detailed understanding of parameter space, we marginalize our three parameter joint probability distribution function (PDF) over two parameters at a timeand"
helt curve was usec.,light curve was used.
 Thus the use of the full light curve produces sole improvement in tiniug., Thus the use of the full light curve produces some improvement in timing.
 We nav also ask how accurately the theoretical model cau determine the outburst timine., We may also ask how accurately the theoretical model can determine the outburst timing.
 Iu the iupact model a typical disk crossing time of the SCondary black hole is one week., In the impact model a typical disk crossing time of the secondary black hole is one week.
 However. eveuts at auch shorter time scale cau make a difference to the outburst timine. as illustrated by Ivanov ct al. (," However, events at much shorter time scale can make a difference to the outburst timing, as illustrated by Ivanov et al. ("
1998).,1998).
 They show that there is a factor of two pressure change over the distance of 1/30 of the disk width aliead of the secondary black hole., They show that there is a factor of two pressure change over the distance of 1/30 of the disk width ahead of the secondary black hole.
 Thus we may consider tie steps of 1/30 of a week as physically meauineful. i.e. the relevant time step is ~OQ0005 vi.," Thus we may consider time steps of $\sim 1/30$ of a week as physically meaningful, i.e. the relevant time step is $\sim 0.0005$ yr."
 Also in the gas bubble bursting out of the disk this sue time scale produces a sienificant amount of evolution. as shown in their Figure 1.," Also in the gas bubble bursting out of the disk this same time scale produces a significant amount of evolution, as shown in their Figure 4."
 We consider this the minima time step that has astroplivsical relevance., We consider this the minimum time step that has astrophysical relevance.
 Another limitation to the timing accuracy cones from the influence of the secoudary on the level of the accretion disk., Another limitation to the timing accuracy comes from the influence of the secondary on the level of the accretion disk.
 The approaching secondary lifts the disk wp. aud cause au iipact earlier than predicted in a rigid disk model (Ivanov ot al.," The approaching secondary lifts the disk up, and cause an impact earlier than predicted in a rigid disk model (Ivanov et al."
 1998)., 1998).
 The calculation of this effect by particle disk siuulatious was carried out by Valtonen (2007)., The calculation of this effect by particle disk simulations was carried out by Valtonen (2007).
 In Figure 5 we show the profile of the accretion disk mauediatelv after the napact in the sununucr of 1912., In Figure 5 we show the profile of the accretion disk immediately after the impact in the summer of 1912.
 We notice that the disk is lifted towards the approaching secondary and is bent., We notice that the disk is lifted towards the approaching secondary and is bent.
 In the model we need to know the raised level of the accretion disk at the time of the aupact., In the model we need to know the raised level of the accretion disk at the time of the impact.
 The orbit of the secondary is marked by ticks at the intervals of 0.01 vr., The orbit of the secondary is marked by ticks at the intervals of 0.01 yr.
 We estimate that the timing accuracy in this occasion is 0.005 vy., We estimate that the timing accuracy in this occasion is $\pm 0.005$ yr.
 This is the typical accuracy that we may use for mipacts at the outer disk (7c. the 1913. 1957. 1973. 2005. POLS aud 2022 outbursts).," This is the typical accuracy that we may use for impacts at the outer disk $i.e.$ the 1913, 1957, 1973, 2005, 2015 and 2022 outbursts)."
 For the inner disk the effect is negligible., For the inner disk the effect is negligible.
 For example. the 2005 outburst lav be timed within —O.00L vr from observations. but such accuracy is uot justified by theoretical considerations.," For example, the 2005 outburst may be timed within $\pm0.001$ yr from observations, but such accuracy is not justified by theoretical considerations."
 The PN approximation provides the equations of motion of a compact binary as corrections to he Newtonian equations of motion in powers of (ofc)?~GALAR). where c. M. and R are he characteristic orbital velocity. the total mass. and the typical orbital separation of the binary. respectively.," The PN approximation provides the equations of motion of a compact binary as corrections to the Newtonian equations of motion in powers of $(v/c)^2 \sim G M / (c^2 R)$, where $v$, $M$, and $R$ are the characteristic orbital velocity, the total mass, and the typical orbital separation of the binary, respectively."
 In Valtonen et al. (, In Valtonen et al. (
2010). the binary lack hole was modeled using à spiuuiug primary lack hole with an accretion disk and a non-spiuuniug companion.,"2010), the binary black hole was modeled using a spinning primary black hole with an accretion disk and a non-spinning companion."
 The calculation of the orbit included all the 2PN-accurate nou-spiuniug finite nass contributions as well as the leading order eeneral relativistic (1.5PN order) aud classical spin-orbit (2PN order) spinning contributions. and radiation reaction effects (2.5PN order).," The calculation of the orbit included all the 2PN-accurate non-spinning finite mass contributions as well as the leading order general relativistic (1.5PN order) and classical spin-orbit (2PN order) spinning contributions, and radiation reaction effects (2.5PN order)."
 ere the terminology 2PN. for example. refers to corrections to Newtonian dyvnanuces dn powers of (efe).," Here the terminology 2PN, for example, refers to corrections to Newtonian dynamics in powers of $(v/c)^4 $ ."
(e.g.. Grindlay1993:οἱal. 2001)).,"(e.g., \citealt{grind93,grind01}) )."
 It has also been pointed out that these often occur in clusters clesignated as core collapse svstems. supporting the general picture that enhanced stellar interactions lead to LAINBs.," It has also been pointed out that these often occur in clusters designated as core collapse systems, supporting the general picture that enhanced stellar interactions lead to LMXBs."
 Also. it was noted that the metal-rich svstems are more likely to host an LMXD (Grindlay1993).. an effect that is seen in elobular cluster svslenms in earlv-tvpe galaxies (Xundu.Maccarone.&Zepf2002).," Also, it was noted that the metal-rich systems are more likely to host an LMXB \citep{grind93}, an effect that is seen in globular cluster systems in early-type galaxies \citep{kund02}."
. An important advantage of analvzing LMXDs in Galactic globular clusters is that there js à vast database available for the globular cluster svstem (ILaurris1996).. including structural parameters. metallicities. velocities. ancl often. ages (SalarisandWeiss2002).," An important advantage of analyzing LMXBs in Galactic globular clusters is that there is a vast database available for the globular cluster system \citep{harris96}, including structural parameters, metallicities, velocities, and often, ages \citep{sala02}."
. With the availability of this extensive data set. we examine the LMXD host svstems in detail. where we test basic model predictions and quantify various correlations in the data.," With the availability of this extensive data set, we examine the LMXB host systems in detail, where we test basic model predictions and quantify various correlations in the data."
 Our goal is to estimate a quantity representative of the rate of stellar interactions (hat lead to LMXDs over the lifetime of the globular cluster., Our goal is to estimate a quantity representative of the rate of stellar interactions that lead to LMXBs over the lifetime of the globular cluster.
 This quantity can be compared to the properties of globular clusters with Iuminous LAINBs to determine i£ it is a useful predictor., This quantity can be compared to the properties of globular clusters with luminous LMXBs to determine if it is a useful predictor.
 As is well-known. the relevant quantities are the density of single stars. the density of binary stars. and the velocity dispersion of the elobular cluster.," As is well-known, the relevant quantities are the density of single stars, the density of binary stars, and the velocity dispersion of the globular cluster."
 Equivalentlv. a stellar density can be determined [rom the globular cluster luminosity auc hall-light radius.," Equivalently, a stellar density can be determined from the globular cluster luminosity and half-light radius."
 In principle. one would like to know these quantities at the time that the elobular clusters were formed. rather (han today. as these can evolve with (nme.," In principle, one would like to know these quantities at the time that the globular clusters were formed, rather than today, as these can evolve with time."
 In practice. models show that the hall-mass radius of the majority of the single stars does not evolve strongly with time until the final destruction ol the cluster (see Fig.," In practice, models show that the half-mass radius of the majority of the single stars does not evolve strongly with time until the final destruction of the cluster (see Fig."
 8 in Fregeauetal. 2003)). unlike the core radius. whieh can change considerably and is à poor indicator of the initial properties of the cluster.," 8 in \citealt{freg03}) ), unlike the core radius, which can change considerably and is a poor indicator of the initial properties of the cluster."
 Also. although ihe number of stars decreases with time as the cluster evolves. the number of stars changes by only about at the time of the first core collapse.," Also, although the number of stars decreases with time as the cluster evolves, the number of stars changes by only about at the time of the first core collapse."
 These evolutionary variations are smaller than the range of values between globular clusters in the \lilky Wav: more than two orders of magnitude lor and a factor of 30 forη., These evolutionary variations are smaller than the range of values between globular clusters in the Milky Way: more than two orders of magnitude for and a factor of 30 for.
 Therefore. ancl should be extremely useful inclicators of the initial size ancl mass of a globular cluster.," Therefore, and should be extremely useful indicators of the initial size and mass of a globular cluster."
 There may be some globular clusters presently in (he final stages of destruction (e.g.. NGC 6112: deMarchietal.1999:Andrenzzietal.2001:Paltrinieri 2001)). in which case there are no good measures of (heir original properties. but such clusters should comprise only a small fraction of the total cluster population.," There may be some globular clusters presently in the final stages of destruction (e.g., NGC 6712; \citealt{demar99,andr01,palt01}) ), in which case there are no good measures of their original properties, but such clusters should comprise only a small fraction of the total cluster population."
 The above relationship for the interaction rate has the advantage (hat ib can be applied to globular clusters in nearby ealaxies as well as in the Milkv. Was. since the half-leht radius can be fit for galaxies asdistant as the Virgo cluster (using the Telescope: Jordanetal. 2005)).," The above relationship for the interaction rate has the advantage that it can be applied to globular clusters in nearby galaxies as well as in the Milky Way, since the half-light radius can be fit for galaxies asdistant as the Virgo cluster (using the ; \citealt{jord05}) )."
Swift correspouds to a fux of 1.5«10Herecni2S ld the 0.3-10 keV. baud using the spectral model inTable 1 and a huninosity of 2.8«I0σος| at the disance of 3.6 Mpc to IIlohuberg IN. assumiug isotropic οnission.,"Swift corresponds to a flux of $1.8 \times 10^{-11} \rm \,
erg \, cm^{-2} \, s^{-1}$ in the 0.3-10 keV band using the spectral model inTable \ref{hardtable} and a luminosity of $2.8 \times 10^{40}
\rm \, erg \, s^{-1}$ at the distance of 3.6 Mpc to Holmberg IX assuming isotropic emission."
 Correcting for absorption iucreases this huuinositv by., Correcting for absorption increases this luminosity by.
. Stellar-iass black hole binaries cau stav in thihard state for extended periods at Iuninosities below around Z0.05ga. where Zgga is the Eddiuston hIuuinositv.," Stellar-mass black hole binaries can stay in the hard state for extended periods at luminosities below around $0.05 L_{\rm Edd}$, where $L_{\rm Edd}$ is the Eddington luminosity."
 Iu particular. CX 2339-1 has been observed to remain in the hard state for mtervals of more than one vear (Remillard&MeChlintock2006:Mivakawaetal. 2008).," In particular, GX 339-4 has been observed to remain in the hard state for intervals of more than one year \citep{Remillard06,Miyakawa08}."
". Tlis, the behavior observed from Holuberg EX. N-1 παν be snuila to that observed from CON 339-1. but with a jeher Iuninositv threshold for the trausition out of tlie hard state inuplvius a hierer Eddiugtou huninuosity."," Thus, the behavior observed from Holmberg IX X-1 may be similar to that observed from GX 339-4, but with a higher luminosity threshold for the transition out of the hard state implying a higher Eddington luminosity."
 If so. then an unusually massive black hole is required for ITolubere IX X-1l.," If so, then an unusually massive black hole is required for Holmberg IX X-1."
 We uote that some stellaranass black holes have been observed iu the hard state at IuninosilOS as hich as 0πια (Rodriguez.Corbel.&Tousick2003: 2008).," We note that some stellar-mass black holes have been observed in the hard state at luminosities as high as $0.3 L_{\rm Edd}$ \citep{Rodriguez03,Zdziarski04,Yuan07,Miyakawa08}."
. ILowever. such biel harcd-state Iuninosities are soon followed by a transition to a softer spectral stato. which is not observed in Hoblubere IN. X-1.," However, such high hard-state luminosities are soon followed by a transition to a softer spectral state, which is not observed in Holmberg IX X-1."
 The behavior of Hohuberg EX. N-1 is simular to that observed frou a nuuber of other particuarly huaduous ULXs that remain 1 the hard state even at the highest DIunuuosifies (Soriaetal.2007:Dergheaoet2008: 2009)..," The behavior of Holmberg IX X-1 is similar to that observed from a number of other particularly luminous ULXs that remain in the hard state even at the highest luminosities \citep{Soria07,Berghea08,Kaaret09m82,Soria09,Feng09}. ."
 These ULXNs with hard spectra at hnunuinosities, These ULXs with hard spectra at luminosities
either line-emission active star-forming galaxies or passivelv-evolving continuum emission galaxies.,either line-emission active star-forming galaxies or passively-evolving continuum emission galaxies.
 These details have not changed from the previous paper., These details have not changed from the previous paper.
 Since we found in POT that the active star-forming galaxies. whose redshifts are to be obtained by measuring the OL1] emission line doublet at low redshift and Lyman-a at high redshift. are the preferred targets. we adopt these as standard for all the analysis in this paper.," Since we found in P07 that the active star-forming galaxies, whose redshifts are to be obtained by measuring the O[II] emission line doublet at low redshift and $\alpha$ at high redshift, are the preferred targets, we adopt these as standard for all the analysis in this paper."
 We also set à somewhat arbitrary lower limit of 15 minutes for the exposure time. representing a reasonable compromise when taking into account a rather pessimistic estimate of a LO minute overhead time between exposures.," We also set a somewhat arbitrary lower limit of 15 minutes for the exposure time, representing a reasonable compromise when taking into account a rather pessimistic estimate of a 10 minute overhead time between exposures."
 We further assume that the galaxies are targeted so as to generate a sample of uniform number density. across each redshift bin., We further assume that the galaxies are targeted so as to generate a sample of uniform number density across each redshift bin.
 We also include an estimate of the bias of these galaxies. and its evolution with redshift.," We also include an estimate of the bias of these galaxies, and its evolution with redshift."
 Xt low redshift we take Wake et ((2008) as our guide. assuming the bias (weakly) tracks the linear growth function. using the following formula LiDin)... where (20 is the growth funetion.," At low redshift we take Wake et (2008) as our guide, assuming the bias (weakly) tracks the linear growth function, using the following formula ) = 1 +, where $D(z0$ is the growth function."
" Here we take 2;= and b(z2,;)=1.9 At high redshift we use the result. of Alvers et ((2007) that the bias grows as (1|2z)7.", Here we take $z_{hi}=0.55$ and $b(z_{hi})=1.3$ At high redshift we use the result of Myers et (2007) that the bias grows as $(1+z)^2$.
 Once the redshift ranges and number of galaxies have been determined. the cosmological parameter analvsis can proceed.," Once the redshift ranges and number of galaxies have been determined, the cosmological parameter analysis can proceed."
 Here we slice the redshift bins into a number of sub-bins. where the width of these sub-bins is fixed and the number is determined by the redshift range (as shown in Figure 1)).," Here we slice the redshift bins into a number of sub-bins, where the width of these sub-bins is fixed and the number is determined by the redshift range (as shown in Figure \ref{fig:surveyschematic}) )."
 We take the width of the redshift slices to be constant. dz=0.05. with the redshift range always being an integer number of these slices and the minimum. and masini redshifts discretized in the same units.," We take the width of the redshift slices to be constant, $dz=0.05$, with the redshift range always being an integer number of these slices and the minimum and maximum redshifts discretized in the same units."
 In computing the BAO errors on each slice. we do not include the possible correlations between slices that may oe caused by large-scale. modes in the power spectrum.," In computing the BAO errors on each slice, we do not include the possible correlations between slices that may be caused by large-scale modes in the power spectrum."
 Our slice width dz is chosen to be fairly wide to reduce such correlations., Our slice width $dz$ is chosen to be fairly wide to reduce such correlations.
 Vhese will have the elfect of decreasing he constraining power of the survey ancl so lowering the LloM. We do not necessarily expect including these effects o change the optimal survey. as they will not change the redshifts at which the measurements are being made. only he accuracy of the measurements.," These will have the effect of decreasing the constraining power of the survey and so lowering the FoM. We do not necessarily expect including these effects to change the optimal survey, as they will not change the redshifts at which the measurements are being made, only the accuracy of the measurements."
 Once the area. redshift range and slices. and galaxy number of the survey have been determined. we can use fitting formulae to estimate how well the BAO will be measured. and what clistance information will be returned.," Once the area, redshift range and slices, and galaxy number of the survey have been determined, we can use fitting formulae to estimate how well the BAO will be measured, and what distance information will be returned."
 La Rassat et ((2008) a comparison was made between cillerent methods for extracting information from a future galaxy survey., In Rassat et (2008) a comparison was made between different methods for extracting information from a future galaxy survey.
 Here. following on from POT. we only use the oscillatory part of the power spectrum (the wigeles). as we consider this the most robust source of distance information hat can be extracted.," Here, following on from P07, we only use the oscillatory part of the power spectrum (the 'wiggles'), as we consider this the most robust source of distance information that can be extracted."
 Phe full power spectrum is degenerate with primordial power spectrum parameters (tilt. running) ancl also details of the growth of structure on laree scales (nonlinear bias. non-linear growth).," The full power spectrum is degenerate with primordial power spectrum parameters (tilt, running) and also details of the growth of structure on large scales (nonlinear bias, non-linear growth)."
 The anisotropy of the power spectrum can be used as an AlcockPaczvnski (AL) est. but this require details of the non-linear behavior of 10 recishift-space distortions.," The anisotropy of the power spectrum can be used as an Alcock–Paczynski (AP) test, but this require details of the non-linear behavior of the redshift-space distortions."
 In POT we used the formula published by Blake et 106). but this has been superseded by those of Seo Eisenstein (2007).," In P07 we used the formula published by Blake et (2006), but this has been superseded by those of Seo Eisenstein (2007)."
 We use the formula derived. [rom a Fisher matrix approach. using a 2-D approximation of only 10 oscillatory part of the power spectrum (equation 26 in their paper).," We use the formula derived from a Fisher matrix approach, using a 2-D approximation of only the oscillatory part of the power spectrum (equation 26 in their paper)."
 These fitting formula estimate the errors in the position of the barvonic features along ancl across 1e line of sight. as well as the correlation between them.," These fitting formula estimate the errors in the position of the baryonic features along and across the line of sight, as well as the correlation between them."
" Thev also have the added advantage that they can simulate 1ο effect of ""reconstruction. of the linear oscillations in the =1on-linear regime (though we do not use reconstruction in js paper).", They also have the added advantage that they can simulate the effect of `reconstruction' of the linear oscillations in the non-linear regime (though we do not use reconstruction in this paper).
 This can lead to increased accuracy at lower redshifts. where non-linear elfects on the power spectra are oesent at the same scales as the BAO.," This can lead to increased accuracy at lower redshifts, where non-linear effects on the power spectra are present at the same scales as the BAO."
 The accuracies of 10 BAO measurements leads to the calculation of the FoM. In POT. as in the DITE report. the CPL xwameterization (Chevallier Polarski 2001: Lincder 2003) of the dark energy equation yal state was used. given hy wa)— wg | willoa)... where wy and dq are adjustable constants.," The accuracies of the BAO measurements leads to the calculation of the FoM. In P07, as in the DETF report, the CPL parameterization (Chevallier Polarski 2001; Linder 2003) of the dark energy equation of state was used, given by w(a) = w_0 + w_a(1-a), where $w_0$ and $w_a$ are adjustable constants."
" The FoM. we used in the previous paper was the D-optimal criterion. the inverse of the determinant of the (uo. 0) covariance maltrix. —det: 1(C) 2 lere we have switched to the ""aasquaree, root of DOTEMthe inverse of the determinant. bringing us into lino with the DEVE FoM. = =- where ty ds the equation. of state at the “pivot” redshift."," The FoM we used in the previous paper was the D-optimal criterion, the inverse of the determinant of the $w_0$, $w_a$ ) covariance matrix, = ) = Here we have switched to the square root of the inverse of the determinant, bringing us into line with the DETF FoM, = =, where $w_{\rm p}$ is the equation of state at the `pivot' redshift."
 llence our new FoM is the square root of our old FOAL. We use this new definition of the FoM throughout., Hence our new FoM is the square root of our old FoM. We use this new definition of the FoM throughout.
 The FoM is computed using a Fisher matrix approach., The FoM is computed using a Fisher matrix approach.
 Details are laid out in Appendix A.., Details are laid out in Appendix \ref{Fisher:appendix}.
 We have expanded our cosmological parameter space from DOT. by including the effect of curvature on our analysis.," We have expanded our cosmological parameter space from P07, by including the effect of curvature on our analysis."
 The importance of doing so has been emphasized by Clarkson. Cortes Bassett (2007). who showed than even a small curvature can seriously bias dark energy measurements.," The importance of doing so has been emphasized by Clarkson, Cortes Bassett (2007), who showed than even a small curvature can seriously bias dark energy measurements."
 Our cosmological parameter space (0) is now defined to be 9— fut OQ one ©," Our cosmological parameter space $\Theta$ ) is now defined to be = w_0, w_a, _k, h, h^2, ."
in energv range of 0.1-10. GeV are almost the same as in the case of à=apa.,in energy range of 0.1-10 GeV are almost the same as in the case of $a = a_{\text{peri}}$.
 When the compact object is located far from the companion star. (he stellar radiation field at the compact object becomes thinner. so that IC cooling Gime of electrons becomes longer because of less reaction rate of IC scattering.," When the compact object is located far from the companion star, the stellar radiation field at the compact object becomes thinner, so that IC cooling time of electrons becomes longer because of less reaction rate of IC scattering."
 Thus. if the injection rate of electrons is constant. the electron munber densitv at the same energy becomes larger.," Thus, if the injection rate of electrons is constant, the electron number density at the same energy becomes larger."
 On the other hand. the GeV {hax is proportional to the number density of electrons because in 0.1-10 GeV energy range. photons are not absorbed in the thermal radiation field.," On the other hand, the GeV flux is proportional to the number density of electrons because in 0.1-10 GeV energy range, photons are not absorbed in the thermal radiation field."
 Therelore. the [Iux. which is equivalent to the product of the power by IC. process per one electron and (he electron number. is as large as that al periastron in spite of thinner field.," Therefore, the flux, which is equivalent to the product of the power by IC process per one electron and the electron number, is as large as that at periastron in spite of thinner field."
 Llowever. the GeV [lux is actually subject to the cascade process as stated above.," However, the GeV flux is actually subject to the cascade process as stated above."
 This means that the amplitude of [Iux variation in GeV band can change with (he amount of energv moving to lower energv band by cascade process. which changes with the separation because the amount of energv of absorbed photons ehanges with the separation.," This means that the amplitude of flux variation in GeV band can change with the amount of energy moving to lower energy band by cascade process, which changes with the separation because the amount of energy of absorbed photons changes with the separation."
 Nevertheless. the amplitude of GeV. [hix in the case e=apa (dashed line in Figure 4I) is almost the same as In the case e=apa (dashed line in Figure tee).," Nevertheless, the amplitude of GeV flux in the case $a=a_{\text{apa}}$ (dashed line in Figure \ref{spe}f f) is almost the same as in the case $a=a_{\text{peri}}$ (dashed line in Figure \ref{spe}e e)."
 This implies less impact of cascade on variation of GeV fhux., This implies less impact of cascade on variation of GeV flux.
 Thus. flux variation in that energy range is determined. alinost exclusively by the anisotropic IC radiation.," Thus, flux variation in that energy range is determined almost exclusively by the anisotropic IC radiation."
 Bi contrast. TeV flix becomes larger than the case Οἱ a=Apexi. because the optical depth becomes smaller by thinner radiation field. but (here is almost no change in the amplitude of flix variation.," In contrast, TeV flux becomes larger than the case of $a=a_{\text{peri}}$, because the optical depth becomes smaller by thinner radiation field, but there is almost no change in the amplitude of flux variation."
 Observing the svstem with the inclination angle 7=60° (Figures 4ec and ο). one nolices that the amplitudes of flux variations in both TeV and GeV range become larger than the case of /=30°.," Observing the system with the inclination angle $i = 60^{\circ}$ (Figures \ref{spe}c c and g), one notices that the amplitudes of flux variations in both TeV and GeV range become larger than the case of $i = 30^{\circ}$."
 The increasing amplitudes of flux in GeV range ancl TeV range are explained by anisotropic IC process (Figure 2aa) and 55 absorption (Figure 3)) which are dependent on the angle a (Fieure 1))., The increasing amplitudes of flux in GeV range and TeV range are explained by anisotropic IC process (Figure \ref{noabs}a a) and $\gamma \gamma$ absorption (Figure \ref{tau}) ) which are dependent on the angle $\alpha $ (Figure \ref{modpic}) ).
 When the inclination angle becomes larger. the photon path [rom the compact object passes through the thicker radiation field at SUPC phase. aud the thinner field al INFC. so that the amplitude of TeV flux becomes larger.," When the inclination angle becomes larger, the photon path from the compact object passes through the thicker radiation field at SUPC phase, and the thinner field at INFC, so that the amplitude of TeV flux becomes larger."
or Ποιά TS. with 33 V measurements we can detect. periods of up to dd for the same variability amplitude and the imit period graph shows the expected behaviour.,"for field 78, with 33 V measurements we can detect periods of up to d for the same variability amplitude and the limit period graph shows the expected behaviour."
 A similar number of measurements over à shorter time span will only allow us to measure shorter variability timescales., A similar number of measurements over a shorter time span will only allow us to measure shorter variability timescales.
 I5.g. for ield. 26. with 29 measurements over 5dd. the maximum »eriod. we can reconstruct (for variability amplitude of 1.5 mags) is dd. We want to remind the reader at this point. that. by using the Iloating mean periodogram we are fitting the data with sinusoidal curves.," E.g. for field 26, with 29 measurements over d, the maximum period we can reconstruct (for variability amplitude of 1.5 mags) is d. We want to remind the reader at this point, that by using the floating mean periodogram we are fitting the data with sinusoidal curves."
 Any non-sinusoidal. or indeed. any non-periodic variability present in the data will be poorly ilted.," Any non-sinusoidal, or indeed any non-periodic variability present in the data will be poorly fitted."
 The maximum period that can be reconstructed for al he fields in the FSWS simultaneously is plotted in Fig. 4.., The maximum period that can be reconstructed for all the fields in the FSVS simultaneously is plotted in Fig. \ref{an:fmp:fig3}.
 For an amplitude of the variability of 70.25 mags (equivalen o an amplitude to niagnitude error ratio of 78.3). we can reconstruct variability periods of up to dd for 717.58 ddeg?E out of the ddeg? available for search (66 fields out of he GS with more wn + V band measurements). we can reconstruct variabilities of up to Seld for 713.31 ddeg? (50 ields).," For an amplitude of the variability of $\sim$ 0.25 mags (equivalent to an amplitude to magnitude error ratio of $\sim$ 8.3), we can reconstruct variability periods of up to d for $\sim$ $^2$ out of the $^2$ available for search (66 fields out of the 68 with more than 4 V band measurements), we can reconstruct variabilities of up to d for $\sim$ $^2$ (50 fields)."
 For amplitudes of 1.5 mag (magnitude error ratio of 50) we can reconstruct periods of up to 11 davs for a region of dades? (25 [ields) and so on., For amplitudes of 1.5 mag (magnitude error ratio of 50) we can reconstruct periods of up to 11 days for a region of $^2$ (25 fields) and so on.
 We can only search [or »eriods of the order of 20 davs in 2 fields., We can only search for periods of the order of 20 days in 2 fields.
 We are also interested. in detecting small amplitude and short. period. variability. the limits of the data being a mmin sampling and the photometric accuracy of ~3 millimags for the brightest. objects (Grootetal.2003).," We are also interested in detecting small amplitude and short period variability, the limits of the data being a min sampling and the photometric accuracy of $\sim$ 3 millimags for the brightest objects \cite{groot03}."
. The right panel of Fig., The right panel of Fig.
 4— zooms into the the short timescale. small amplitude variability region.," \ref{an:fmp:fig3} zooms into the the short timescale, small amplitude variability region."
 We reconstruct successfully (Le. with less than a 3q dillerence between the true and calculated period) the minimum searchable period in all fields., We reconstruct successfully (i.e. with less than a $\sigma$ difference between the true and calculated period) the minimum searchable period in all fields.
 Some interesting astronomical objects such as Cataclysmic Variables (CVs) and RR Lye show characteristic variability timescales., Some interesting astronomical objects such as Cataclysmic Variables (CVs) and RR Lyr show characteristic variability timescales.
 CW periods range from SOmmin to —6hh (although some of them show longer orbital periods such as Gly Per with a 2dd orbit)., CV periods range from min to $\sim$ h (although some of them show longer orbital periods such as GK Per with a d orbit).
 The variability of RR. Lyrae ranges from 6 hh to about lded. Other interesting svstenis such as AM CVn binaries show orbital periods of the order of tens of minutes. too short to be detected in the FSVS.," The variability of RR Lyrae ranges from $\sim$ h to about d. Other interesting systems such as AM CVn binaries show orbital periods of the order of tens of minutes, too short to be detected in the FSVS."
 On the other hand. orbital periods of mmin will be detected in the full area of the FSVS. as long as the ratio of the amplitude of the variability and the error in the V magnitude is at least 10. Le. we would be able to detect all mimin variables down to V — 24 if their variability amplitude is at least 2 mag. down to V = 23 if the variability amplitude is ab least O.7 mag. and down to V — 22 if the variability amplitude is at least 0.36 mag.," On the other hand, orbital periods of min will be detected in the full area of the FSVS, as long as the ratio of the amplitude of the variability and the error in the V magnitude is at least 10, i.e. we would be able to detect all min variables down to V = 24 if their variability amplitude is at least 2 mag, down to V = 23 if the variability amplitude is at least 0.7 mag, and down to V = 22 if the variability amplitude is at least 0.36 mag."
 CVs show characteristic orbital variability amplitudes of the order of 0.1 mag thus we will be able to detect a fraction at least down to Vo = 22., CVs show characteristic orbital variability amplitudes of the order of 0.1–0.4 mag thus we will be able to detect a fraction at least down to V = 22.
 For certain fields. when looking at the short period region. the calculated period underestimates the value of the true period.," For certain fields, when looking at the short period region, the calculated period underestimates the value of the true period."
 This will most probably happen also for the real lightcurves., This will most probably happen also for the real lightcurves.
 Orbital periods of up to 6 hours. and between 6 hours and | day (this last period range is twpical of RIS Lyr) will be detected in ddeg? (all fields but two) as long as the ratio of the amplitude of the variability and the V error is at least 20. Le. we would be able to detect. all variables with periods of up to 1 day in this area down to V = 24 if the variability amplitucle is larger than 4 mag. and down to V = 23 if the variability amplitude is at least 1.4 mag.," Orbital periods of up to 6 hours, and between 6 hours and 1 day (this last period range is typical of RR Lyr) will be detected in $^2$ (all fields but two) as long as the ratio of the amplitude of the variability and the V error is at least 20, i.e. we would be able to detect all variables with periods of up to 1 day in this area down to V = 24 if the variability amplitude is larger than 4 mag, and down to V = 23 if the variability amplitude is at least 1.4 mag."
 The variability amplitudes typical of RR Lyr range between ~0.5 and Z1 mag. which indicates that we are sensitive to RR Lyr down to V = 23as long as the variability amplitude is at least 1.4 mag.," The variability amplitudes typical of RR Lyr range between $\sim$ 0.5 and $>$ 1 mag, which indicates that we are sensitive to RR Lyr down to V = 23 as long as the variability amplitude is at least $\sim$ 1.4 mag."
 Other pulsating stars such as ? DDoraclus stars. 0 SScuti stars. slowly pulsating B stars. Cep stars ancl short »eriod. Cepheids show pulsation periods and. amplitudes in he detectable range of this survey.," Other pulsating stars such as $\gamma$ Doradus stars, $\delta$ Scuti stars, slowly pulsating B stars, $\beta$ Cep stars and short period Cepheids show pulsation periods and amplitudes in the detectable range of this survey."
 Some of them. [ike OSSculi stars. show very complicated: oscillation patterns hat are far from sinusoidal which means that. although they would be detected as variables with the 47 test. the periods reconstructed with the Dloating mean periodogram will most xobabls be incorrect.," Some of them, like $\delta$ Scuti stars, show very complicated oscillation patterns that are far from sinusoidal which means that, although they would be detected as variables with the $\chi^2$ test, the periods reconstructed with the floating mean periodogram will most probably be incorrect."
 Short period pulsators such as rapidly oscillating Ap stars. PG1159 stars. pulsating subedwarf. B stars ancl pulsating white chwarfs. and lone period pulsators such as RV ‘Tauristars ancl Mira stars will not be detected in he FSVS as their pulsating periods lie outside the range we are sensitive to.," Short period pulsators such as rapidly oscillating Ap stars, PG1159 stars, pulsating subdwarf B stars and pulsating white dwarfs, and long period pulsators such as RV Tauri stars and Mira stars will not be detected in the FSVS as their pulsating periods lie outside the range we are sensitive to."
 Solar-like stars show very small amplitude xulsations that cannot be detected in the FESVS., Solar-like stars show very small amplitude pulsations that cannot be detected in the FSVS.
 Asteroids show rotational periods of the order of a few rours and also lie in the detectable range of the ESVS., Asteroids show rotational periods of the order of a few hours and also lie in the detectable range of the FSVS.
 We see a number of asteriod tracks in the FSVS images but hese asteroids do not stay in the same position [rom image o image and are discarded during data reduction., We see a number of asteriod tracks in the FSVS images but these asteroids do not stay in the same position from image to image and are discarded during data reduction.
 We will use these results again in Section 4.3. to estimate how reliable our detections and non-detections for variability are at given timescales and amplitudes., We will use these results again in Section \ref{res:timeamp} to estimate how reliable our detections and non-detections for variability are at given timescales and amplitudes.
 In the entire FSVS. using the 47 test. after. discarding problematic points. we find a total of 7713 short timescale variable V-band. point sources that have been detected. also in the D and L bands.," In the entire FSVS, using the $\chi^2$ test, after discarding problematic points, we find a total of 713 short timescale variable V-band point sources that have been detected also in the B and I bands."
 The number of non variable sources founcl (after applying the same criteria as for the variables sources. Le. account for problematic points ancl positive detections in D and 1) is 1732276 (~1 percent of all point sources detected are short termi variables).," The number of non variable sources found (after applying the same criteria as for the variables sources, i.e. account for problematic points and positive detections in B and I) is 276 $\sim$ 1 percent of all point sources detected are short term variables)."
 Inthe top eft panel of Fig., In the top left panel of Fig.
 5. we present the distribution of sources in the FSVS in the form of a grev-scale. plot. which shows that most objects fall along the main sequence with the largest. numbers at its blue end.," \ref{res:varnovar:fig1} we present the distribution of sources in the FSVS in the form of a grey-scale plot, which shows that most objects fall along the main sequence with the largest numbers at its blue end."
 The top right panel presents the same plot for the variable sources in the IFSVS as determined by the 47 test., The top right panel presents the same plot for the variable sources in the FSVS as determined by the $\chi^2$ test.
 Again. most. sources," Again, most sources"
Pollacketal.(1996) and collaborators (Bocenheimeretal.2000:IIubickvj]2005). and inlorm the reader of important model assumptions.,"\citet{Pollack96} and collaborators \citep{Bodenheimer00, Hubickyj05} and inform the reader of important model assumptions."
 The newborn planets delivered by this modeling approach are (hen used as initial conditions to our own evolution calculations as described in Section 3., The newborn planets delivered by this modeling approach are then used as initial conditions to our own evolution calculations as described in Section 3.
 Bodenheimeretal.(2000). describe (he core aceretion-gas capture process., \citet{Bodenheimer00} describe the core accretion-gas capture process.
 The stages described below are chosen for clarity. and do not match the accretion phases as defined in Dodenheimeretal.(2000).," The stages described below are chosen for clarity, and do not match the accretion phases as defined in \citet{Bodenheimer00}."
. Each stage is keved to Figure 1. which illustrates the luminosity evolution of an accreting 1Mj planet.," Each stage is keyed to Figure 1, which illustrates the luminosity evolution of an accreting $1\,\rm M_J$ planet."
only the viscosity but also introduce new scales into the problem (see2).,only the viscosity but also introduce new scales into the problem \citep[see][]{lazarian06a}.
 This means that a range of studies are necessary. either by explicitly adding physical viscosity terms to reach a desired (low) R.. or by seeking to minimise numerical viscosity to reach very high A...," This means that a range of studies are necessary, either by explicitly adding physical viscosity terms to reach a desired (low) $\mathcal{R}_{\rm e}$, or by seeking to minimise numerical viscosity to reach very high $\mathcal{R}_{\rm e}$."
 A minimum condition for production of turbulent flow in both simulations and reality is that the Reynolds numbers should at least be high enough for the development of turbulence tie. Ry. 107)., A minimum condition for production of turbulent flow in both simulations and reality is that the Reynolds numbers should at least be high enough for the development of turbulence (i.e. $\mathcal{R}_{\rm e} \gtrsim 10^{3}$ ).
 In their study. ? compare the moving-mesh code (run in both moving and fixed-grid modes) and the Smoothed Particle Hydrodynamics (SPH) codeGADGET-3.," In their study, \citet{bs11} compare the moving-mesh code (run in both moving and fixed-grid modes) and the Smoothed Particle Hydrodynamics (SPH) code."
". The main conclusion of he paper is that. despite good results in the supersonic regime (inagreementwith 2).. ""the widely employed standard formulation of SPH fails quite badly in the subsonic regime"". because of a ""ilure to build up a ""Kolmogorov-like turbulent cascade"" which is apparent in the moving and fixed mesh calculations at the resolutions employed and is expected on theoretical grounds (2) ο occur at high Reynolds number."," The main conclusion of the paper is that, despite good results in the supersonic regime \citep[in agreement with][]{pf10}, “the widely employed standard formulation of SPH fails quite badly in the subsonic regime”, because of a failure to build up a “Kolmogorov-like turbulent cascade” which is apparent in the moving and fixed mesh calculations at the resolutions employed and is expected on theoretical grounds \citep{kolmogorov41} to occur at high Reynolds number."
" ?.— attribute the disagreement between the codes to ""large errors in SPH's. gradient estimate and the associated subsonic velocity noise"". producing ""essentially unphysical results in the subsonic regime""."," \citet{bs11} attribute the disagreement between the codes to “large errors in SPH's gradient estimate and the associated subsonic velocity noise”, producing “essentially unphysical results in the subsonic regime”."
" This ""casts doubt on the reliability of SPH for simulations of cosmic structure formation”.", This “casts doubt on the reliability of SPH for simulations of cosmic structure formation”.
 However. the Reynolds number is neither fixed nor estimated in any of the calculations.," However, the Reynolds number is neither fixed nor estimated in any of the calculations."
 In this Letter show how the Reynolds numbers in SPH urbulence calculations can be determined (Sec. 29., In this Letter show how the Reynolds numbers in SPH turbulence calculations can be determined (Sec. \ref{sec:reynolds}) ).
 This suggests hat in fact the main issue in the SPH calculations employed by ? is that they employ constant — and thus large — viscosity »ameters for their simulations. which in turn leads to low Reynolds numbers at subsonic velocities. explaining the failure o produce a Kolmogorov-like spectrum.," This suggests that in fact the main issue in the SPH calculations employed by \citet{bs11} is that they employ constant — and thus large — viscosity parameters for their simulations, which in turn leads to low Reynolds numbers at subsonic velocities, explaining the failure to produce a Kolmogorov-like spectrum."
 To demonstrate this. we dave rerun their calculations (Sec. 3)).," To demonstrate this, we have rerun their calculations (Sec. \ref{sec:av}) ),"
 adopting the standard SPH viscosity switch of ? which increases the effective Reynolds number by roughly an order of magnitude and correspondingly eads to results in much better agreement with the grid-based simulations shown in their preprint and with Kolmogorov's scaling relations., adopting the standard SPH viscosity switch of \citet{mm97} which increases the effective Reynolds number by roughly an order of magnitude and correspondingly leads to results in much better agreement with the grid-based simulations shown in their preprint and with Kolmogorov's scaling relations.
 The results are discussed and summarised in Sec. 4.., The results are discussed and summarised in Sec. \ref{sec:discussion}.
 An advantage of SPH. being a Hamiltonian method. is that the only dissipation present in the system is that which is explicitly added.," An advantage of SPH, being a Hamiltonian method, is that the only dissipation present in the system is that which is explicitly added."
 This means that it is straightforward to derive Reynolds numbers for SPH calculations. since any terms added can be directly translated into their physical equivalents.," This means that it is straightforward to derive Reynolds numbers for SPH calculations, since any terms added can be directly translated into their physical equivalents."
 The standard SPH artificial viscosity term in 3D corresponds to Navier-Stokes viscosity terms with shear 67) and bulk (C) viscosity parameters given by (c.f.22) where / is the smoothing length and à is the SPH artificial viscosity parameter (Note that in 2D the parameters are 1/58 and 5/24. respectively. c.f. 2223).," The standard SPH artificial viscosity term in 3D corresponds to Navier-Stokes viscosity terms with shear $\nu$ ) and bulk $\zeta$ ) viscosity parameters given by \citep[c.f.][]{lp10,price12}
 where $h$ is the smoothing length and $\alpha$ is the SPH artificial viscosity parameter (Note that in 2D the parameters are $1/8$ and $5/24$, respectively, c.f. \citealt{murray96,monaghan05,price12}) )."
 For low Mach number calculations we can expect that the V(V.«v) terms represent only a small contribution to the overall dissipation rate. such that the dissipation is mainly controlled by the shear viscosity term.," For low Mach number calculations we can expect that the $\nabla (\nabla\cdot {\bf v})$ terms represent only a small contribution to the overall dissipation rate, such that the dissipation is mainly controlled by the shear viscosity term."
" Furthermore the maximum signal velocity ej.2e, at low Mach number. such that the effective Revnolds number can be easily computed according to where © is the Mach number."," Furthermore the maximum signal velocity $v_{\rm sig} \approx c_{\rm s}$ at low Mach number, such that the effective Reynolds number can be easily computed according to where $\mathcal{M}$ is the Mach number."
 Note that. with ΝΤ fixed. the Revnolds number is determined entirely by two parameters: the value of à and the numerical resolution /L.," Note that, with $\mathcal{M}$ fixed, the Reynolds number is determined entirely by two parameters: the value of $\alpha$ and the numerical resolution $h/L$."
" For simulations in a periodic box using the parameters employed by ? we have where n is the number of particles along the box length £ and IN, is the neighbour number parameter inGADGET-3.. which corresponds to where /? is the kernel truncation radius in units of h (i.e. /?=2 for the cubic spline kernel) and 7 is the usual parameter specifying the smoothing length in units of the particle spacing (.=nanp “diay "," For simulations in a periodic box using the parameters employed by \citet{bs11} we have where $n_{\rm x}$ is the number of particles along the box length $L$ and $N_{\rm ngb}$ is the neighbour number parameter in, which corresponds to where $R$ is the kernel truncation radius in units of h (i.e. $R=2$ for the cubic spline kernel) and $\eta$ is the usual parameter specifying the smoothing length in units of the particle spacing $h = \eta [m/\rho]^{1/n_{\rm dim}}$ )."
Referring to the neighbour number is in general misleading since it is not independent of the resolution length / meaning that increasing Nya also corresponds to increasing / (see discussion in 25)., Referring to the neighbour number is in general misleading since it is not independent of the resolution length $h$ meaning that increasing $N_{\rm ngb}$ also corresponds to increasing $h$ (see discussion in \citealt{price12}) ).
 In this Letter we use jj=1.2 corresponding to 58 neighbours in a uniform particle distribution., In this Letter we use $\eta = 1.2$ corresponding to $\sim 58$ neighbours in a uniform particle distribution.
 From Eq., From Eq.
 4 it is easy to see why simulations are difficult at low Mach number CM 0.5) in SPH with constant viscosity parameters., \ref{eq:Re} it is easy to see why simulations are difficult at low Mach number $\mathcal{M} \lesssim 0.5$ ) in SPH with constant viscosity parameters.
" For the resolutions employed by ?.. namely n»,=64. 128 and 256 the Reynolds numbers are given by A,=154. R.R=307 and RRe=6146 respectively."," For the resolutions employed by \citet{bs11}, namely $n_{x} = 64$, $128$ and $256$ the Reynolds numbers are given by $\mathcal{R}_{\rm e} = 154$, $\mathcal{R}_{\rm e} = 307$ and $\mathcal{R}_{\rm e} = 614$ respectively."
"cti. By comparison. the Reynolds numbers that would be reached even with a=1 at Mach 10 would be approximately 30 times higher. giving R.e18.000 at 256 and R,=37.000 at 512° particles."," By comparison, the Reynolds numbers that would be reached even with $\alpha=1$ at Mach 10 would be approximately 30 times higher, giving $\mathcal{R}_{\rm e} \approx 18,000$ at $256^{3}$ and $\mathcal{R}_{\rm e} \approx 37,000$ at $512^{3}$ particles."
 2? also employed viscosity switches that decrease the viscosity away from shocks by up to an order of magnitude. meaning that they obtain Reynolds numbers of —10 and higher in practice (a plot of the Reynolds number in the ?. calculations is shown in Fig.," \citet{pf10} also employed viscosity switches that decrease the viscosity away from shocks by up to an order of magnitude, meaning that they obtain Reynolds numbers of $\sim 10^{5}$ and higher in practice (a plot of the Reynolds number in the \citealt{pf10} calculations is shown in Fig."
" 2 of 2: {νι of up to 10"" are achieved in the densest regions where the SPH resolution is highest).", 2 of \citealt{pf10b}; $\mathcal{R}_{\rm e}$ of up to $10^{6}$ are achieved in the densest regions where the SPH resolution is highest).
 Note also that the situation regarding numerical viscosity is very different in SPH compared to grid-based codes., Note also that the situation regarding numerical viscosity is very different in SPH compared to grid-based codes.
 The intrinsic numerical dissipation in a grid-based code is in general linearly proportional to the advection velocity relative to the grid (e.g.2). whereas in SPH the artificial viscosity term is linearly proportional to the resolution and largely independent of the velocity except at high Mach number where the «2 term comes into play.," The intrinsic numerical dissipation in a grid-based code is in general linearly proportional to the advection velocity relative to the grid \citep[e.g.][]{robertsonetal10}, whereas in SPH the artificial viscosity term is linearly proportional to the resolution and largely independent of the velocity except at high Mach number where the $\beta$ term comes into play."
 This means that Reynolds numbers are roughly constant in Eulerian schemes over a range of Mach numbers — because the increase in V is correspondingly offset by the increase in the numerical viscosity. whereas the Reynolds number in SPH has a linear Mach number dependence.," This means that Reynolds numbers are roughly constant in Eulerian schemes over a range of Mach numbers — because the increase in V is correspondingly offset by the increase in the numerical viscosity, whereas the Reynolds number in SPH has a linear Mach number dependence."
 Given that good agreement was found between grid and SPH codes in the power spectra in the ? calculations. it is likely that the Reynolds number achievable in the fixed and moving grid schemes employed in are of similar magnitude (i.e. ~LO” at 512° and slightly lower at 2567).," Given that good agreement was found between grid and SPH codes in the power spectra in the \citet{pf10} calculations, it is likely that the Reynolds number achievable in the fixed and moving grid schemes employed in are of similar magnitude (i.e. $\sim 10^{5}$ at $512^{3}$ and slightly lower at $256^{3}$ )."
 ? do not use any viscosity switches for their main calculations. despite the fact that most of these switches are at least 15 years," \citet{bs11} do not use any viscosity switches for their main calculations, despite the fact that most of these switches are at least $\sim 15$ years"
than 300s were emploved.,than 300s were employed.
 Our broadband filter covers the combined wavelength range of Cousins V and BR. giving a significant increase in signal-to-noise while maintaining the image degradation due to atmospheric dispersion at an undetectable level.," Our broadband filter covers the combined wavelength range of Cousins V and R, giving a significant increase in signal-to-noise while maintaining the image degradation due to atmospheric dispersion at an undetectable level."
" From: previous experience with this filler. [or a star of V=18.5 in 2"" seeing. the photon noise S/N decreases from 220 at 7-day moon to 165 at bright moon."," From previous experience with this filter, for a star of V=18.5 in $''$ seeing, the photon noise S/N decreases from 220 at 7-day moon to 165 at bright moon."
" The globular cluster 47 Tueanae was observed for a total of 33 nights [rom 2002 August 22 to 2002 September 24 with a field centre of RA=00h24m05.2s ——7127*04'51.0"".", The globular cluster 47 Tucanae was observed for a total of 33 nights from 2002 August 22 to 2002 September 24 with a field centre of RA=00h24m05.2s $-$ $^{\circ}$ $'$ $''$.
 Approximately 80% of the observing time was useful for the main planetary (ransit project. with mean seeing of 2.2 arcsec.," Approximately $\%$ of the observing time was useful for the main planetary transit project, with mean seeing of 2.2 arcsec."
 The temporal coverage of the cluster was maxinised as much as possible: and averaged an image every 6 minutes for around LO hours per night., The temporal coverage of the cluster was maximised as much as possible; and averaged an image every 6 minutes for around 10 hours per night.
 Each image was checked lor quality independently after readout., Each image was checked for quality independently after readout.
 Unsuitable images caused by satellite trails. bad seeing periods. ete. were discarded.," Unsuitable images caused by satellite trails, bad seeing periods, etc, were discarded."
 1n total we have 1220 images of the same field centered on 47 Tuc. which have been used to produce time-series lighteurves for 109.866 unsaturated stars. wilh apparent magnitude 14.5x:22.5.," In total we have 1220 images of the same field centered on 47 Tuc, which have been used to produce time-series lightcurves for 109,866 unsaturated stars, with apparent magnitude $\leqslant$ $\leqslant$ 22.5."
 This covers a large range of stellar mass and type. encompassing most of the red giant branch (RGB) the subgiant branch. the cluster turn-off. and the cluster main sequence down to a magnitude of V—22.5.," This covers a large range of stellar mass and type, encompassing most of the red giant branch (RGB) the subgiant branch, the cluster turn-off, and the cluster main sequence down to a magnitude of V=22.5."
 This dataset therefore covers a large range of variable (vpes., This dataset therefore covers a large range of variable types.
 Initial reduction of the raw images was undertaken using (he MSCRED package of IRAF|., Initial reduction of the raw images was undertaken using the MSCRED package of IRAF.
.. A significant number of calibration images were obtained over the 33-night run. and allowed [or correction of time-dependent variations. eg..," A significant number of calibration images were obtained over the 33-night run, and allowed for correction of time-dependent variations, eg.,"
 differences in flat fields, differences in flat fields
Our entire dataset consist of about 20—30 frames for each filter (see in Tab. 1)).,Our entire dataset consist of about $20-30$ frames for each filter (see in Tab. \ref{tab:log}) ).
 To increase the signal to noise ratio. we computed an average of all our images for each photometric band.," To increase the signal to noise ratio, we computed an average of all our images for each photometric band."
 In all our V. R and / averaged frames we clearly detect an object inside the 0.6 aresec radius Chandra error box (Paizisetal. 2005)). while in our J and H—band averaged frame we only have a marginal detection for this object.," In all our $V$, $R$ and $I$ averaged frames we clearly detect an object inside the 0.6 arcsec radius Chandra error box \cite{Pa05}) ), while in our $J$ and $H-$ band averaged frame we only have a marginal detection for this object."
 A finding chart is reported in Fig. l.., A finding chart is reported in Fig. \ref{fig:fc}.
 The position of the detected source IS R.A. = 00:29:03.07. Dec. = +59:34:19.12 (J2000) with an uncertainty of 0.4’.," The position of the detected source is R.A. = 00:29:03.07, Dec. = +59:34:19.12 (J2000) with an uncertainty of $0.4''$."
" This position is coincident with the one of the optical counterpart of IGR JO0291+5934 detected by Fox&Kulkarni2004 during the December 2004 outburst (with an error of 0.5"") and by Torres et al. (", This position is coincident with the one of the optical counterpart of IGR J00291+5934 detected by \cite{Fo04} during the December 2004 outburst (with an error of $0.5''$ ) and by Torres et al. (
"2007) during both Cutburst and quiescence (with an error of 0.05"") and consistent with the radio position reported by Rupenetal.2004... with ο.£o uncertainty of less than 0.1"".","2007) during both outburst and quiescence (with an error of $0.05''$ ) and consistent with the radio position reported by \cite{Ru04}, with an uncertainty of less than $0.1''$."
 Results of PSF-photometry for this source in our optical and NIR averaged frames are reported in Tab. 2.., Results of PSF-photometry for this source in our optical and NIR averaged frames are reported in Tab. \ref{tab:phot}.
 We note that our R-band magnitude value. as expected. is consistent with the one reported by Torres et al. (," We note that our $R-$ band magnitude value, as expected, is consistent with the one reported by Torres et al. ("
2007) measured during quiescence. in late 2005 (about two months after our observations).,"2007) measured during quiescence, in late 2005 (about two months after our observations)."
 On the other hand. as reported in Tab. 2..," On the other hand, as reported in Tab. \ref{tab:phot},"
 we did not detect any NIR counterpart of IGR J00291+5934 in K-band down to a limiting value of 19.3 mag (3c confidence level)., we did not detect any NIR counterpart of IGR J00291+5934 in $K-$ band down to a limiting value of 19.3 mag $\sigma$ confidence level).
 We note that Torres et al. (, We note that Torres et al. (
2007) reported a detection at K=19.0+0.1 for the 2005 Jan 24 observation. about fifty days after the discovery of the source in outburst and about twenty days after its return to quiescence (Jonkeretal. 2005)).,"2007) reported a detection at $K = 19.0 \pm 0.1$ for the 2005 Jan 24 observation, about fifty days after the discovery of the source in outburst and about twenty days after its return to quiescence \cite{Jo05}) )."
 A possible explanation of this discrepancy is that the K—band observations of Torres et al. (, A possible explanation of this discrepancy is that the $K-$ band observations of Torres et al. (
2007) took place when the source was in the tail of the outburst. and quiescence had not been reached yet.,"2007) took place when the source was in the tail of the outburst, and quiescence had not been reached yet."
 Once we identified the candidate. we searched for variability given that. as reported in Sec.," Once we identified the candidate, we searched for variability given that, as reported in Sec."
 3. we cover about 80—90% of the orbital period with each optical filter.," 3, we cover about $80-90$ of the orbital period with each optical filter."
 As a first check. we performed image subtraction with the ISIS package (Alard2000:; Alard&Lupton 1998)) on our 7—band images coadded into seven bins.," As a first check, we performed image subtraction with the ISIS package \cite{Al00}; \cite{Al98}) ) on our $I-$ band images coadded into seven bins."
 We chose the /-band frames because they were those taken under better seeing conditions., We chose the $I-$ band frames because they were those taken under better seeing conditions.
 The ISIS subtraction routine accounts for variation in the stellar PSF., The ISIS subtraction routine accounts for variation in the stellar PSF.
" A ""reference frame"" (in our case an average of two Images taken at orbital phases 0.11 and 0.15) is subtracted to all the available images and photometry is performed on the residual images.", A “reference frame” (in our case an average of two images taken at orbital phases 0.11 and 0.15) is subtracted to all the available images and photometry is performed on the residual images.
 For any variable object in the field the variation in flux. with respect to the reference frame. is given as output.," For any variable object in the field the variation in flux, with respect to the reference frame, is given as output."
 Performing photometry on the reference frame. it is possible to calibrate in magnitudes the flux variations.," Performing photometry on the reference frame, it is possible to calibrate in magnitudes the flux variations."
 The result of the image subtraction analysis is that our candidate was variable (Fig.s 2.. 3). with an indication of a sinusoidal modulation of semiamplitude 0.28+0.17 mag confidence level) at the 2.46 hr orbital period (Fig. 3)).," The result of the image subtraction analysis is that our candidate was variable (Fig.s \ref{fig:isis1}, \ref{fig:isis2}) ), with an indication of a sinusoidal modulation of semiamplitude $0.28 \pm 0.17$ mag confidence level) at the 2.46 hr orbital period (Fig. \ref{fig:isis2}) )."
 The light curve shows a single minimum at phase 0. ie. at superior conjunction (when the neutron star is behind the companion) and a maximum at phase 0.5 (based on the X-ray ephemerides of Gallowayetal. 2005)).," The light curve shows a single minimum at phase $0$, i.e. at superior conjunction (when the neutron star is behind the companion) and a maximum at phase $0.5$ (based on the X–ray ephemerides of \cite{Ga05}) )."
 However. an F-test gives a probability of with respect to a constant (period and phase constrained) so this represents only a marginal indication of variability of the source.," However, an $-$ test gives a probability of with respect to a constant (period and phase constrained) so this represents only a marginal indication of variability of the source."
 In light of this. to improve our light curve. we tried to perform a more accurate phase-resolved photometry of our candidate 1n all our optical bands. where we have a clearer detection than in the NIR filters.," In light of this, to improve our light curve, we tried to perform a more accurate phase-resolved photometry of our candidate in all our optical bands, where we have a clearer detection than in the NIR filters."
 Unfortunately. in none of the single optical frames our target was detected with signal-to-noise ratio high enough to look for variability with PSF—photometry and. considering," Unfortunately, in none of the single optical frames our target was detected with signal-to-noise ratio high enough to look for variability with $-$ photometry and, considering"
meridional flow has little effect on the polar field peak in the cycle immediately following the change.,meridional flow has little effect on the polar field peak in the cycle immediately following the change.
" Thus in a flux-transport dynamo model, a change in peak polar fields of as much as several tens of percent between one cycle and the next can not come from a change in meridional flow speed."," Thus in a flux-transport dynamo model, a change in peak polar fields of as much as several tens of percent between one cycle and the next can not come from a change in meridional flow speed."
" It must come from a significant change in the amplitude of the source of polar fields, namely the eruption and decay of active region magnetic flux."," It must come from a significant change in the amplitude of the source of polar fields, namely the eruption and decay of active region magnetic flux."
" (Pa,zd €(7) (Zehavictal.2005) (Eiseusteiuetal.2005).", $\Rvir\lesssim 1$ $\xi(r)$ \citep{york00a} \citep{zehavi05b} \citep{eisenstein05b}.
.. iment (7) ~15hUspe. (Wangetal.2006:Li&White2009)... ΑΠΟ). Zehavictal.(2005) licae he correlation function for 35.000 LRGs.," $\xi(r)$ $\sim 15\hkpc$ \citep{wang06, li09}, ), \citet{zehavi05b} measured the two-point correlation function for 35,000 LRGs."
 Zhengetal.(2008) inodeled this data using the halo occupation distribution (IIOD: sec. e.g. Peacock&σημ2000:Coorav&Sheth 2002)) framework and found a nice fit.," \citet{zheng08} modeled this data using the halo occupation distribution (HOD; see, e.g., \citealt{peacock00a, scoccimarro01a, berlind02a, cooray02}) ) framework and found a nice fit."
 However. the extrapolation of their best-fit model to sanaller separations docs not agree with the ALOG6 smallscale data: it predicts a correlation fiction that is too low (see ALOG. Fie.," However, the extrapolation of their best-fit model to smaller separations does not agree with the M06 small-scale data: it predicts a correlation function that is too low (see M06, Fig."
 D)., 4).
 Our motivation is to model these inucrinost data poiuts (0.0160.12h1 Ape) to see if we can fud a model that works., Our motivation is to model these innermost data points $0.016-0.42h^{-1}$ Mpc) to see if we can find a model that works.
 The paper is laid out as follows., The paper is laid out as follows.
 In ??.. we review the ALOG measurement.," In \ref{data}, we review the M06 measurement."
 Iu 77. awe neelationdiscuss our method for modeling the s12all-scale ος function.," In \ref{method}, we discuss our method for modeling the small-scale correlation function."
 lu ?7.. we discuss our results ina sequential format: in L.1.. we use four free from the probability distribution. PCV|A): inpuriueters ??.. we introduce the couccutration of satellite LRGs §as a new free parameter: in 77.. we allow the inner slope of the density profile of satellite LRGs to vary.," In \ref{results}, , we discuss our results in a sequential format: in \ref{varyHOD}, we use four free parameters from the probability distribution, $P(N|M)$; in \ref{varyCONC}, we introduce the concentration of satellite LRGs as a new free parameter; in \ref{varyPROFILE}, we allow the inner slope of the density profile of satellite LRGs to vary."
 Finally. in ?7.. we discuss the implications of our results.," Finally, in \ref{discussion}, we discuss the implications of our results."
 AIOG ineasured the sinalbscale (0.016Sh Mp) xojected. two-point correlation function for a voluimc-iuited sample of 21.520 hunuinous red galaxics in the SDSS.," M06 measured the small-scale $0.016-8\hmpc$ ) projected two-point correlation function for a volume-limited sample of 24,520 luminous red galaxies in the SDSS."
" The huuimnositv range of LRGs iu the sample was 23.2A,21.2 aud the vedshitt range was 16«—oc0.36.", The luminosity range of LRGs in the sample was $-23.2<M_g<-21.2$ and the redshift range was $0.16<z<0.36$.
 Measuring the correlation function on such πα. scales is non-trivial. aud requires overcomiug wo inan observational hurdles: fiber collisious aud debleudiug.," Measuring the correlation function on such small scales is non-trivial, and requires overcoming two main observational hurdles: fiber collisions and deblending."
 The SDSS spectroscopic sample is incomplete due o the physical size of the fiber-optic cables used to ake spectra of targeted ealaxics., The SDSS spectroscopic sample is incomplete due to the physical size of the fiber-optic cables used to take spectra of targeted galaxies.
Iftwoealaxies are closer than 55 arcsec on the sky. they cannot bothect ueasured spectra.,"Iftwogalaxies are closer than 55 $\arcs$ on the sky, they cannot bothget measured spectra."
These“fiber collisions”thusresult in a nuninmun possible pair separation of55 arcsec.,These“fiber collisions”thusresult in a minimum possible pair separation of55 $\arcs$ .
thes are being exposed. to mass transfer. giving. them atmospheres of solar-composition.,"they are being exposed to mass transfer, giving them atmospheres of solar-composition."
 The white cdwarls in CVs are therefore hotter and are also found to be spinning faster compared. to. isolated. ones (2))., The white dwarfs in CVs are therefore hotter and are also found to be spinning faster compared to isolated ones \citealt{2009ASPC..404..229S}) ).
 Studying these svstenis will provide important information of how the process of acecretion is affecting the evolution of the white dwarf., Studying these systems will provide important information of how the process of accretion is affecting the evolution of the white dwarf.
 In isolated WDs. pulsations are only. observed. in stars with temperatures located within a so-called in the logg μμ plane. spanning the temperature range Tia 10900 IW 12200 Ix (see Figure 3 of 2)).," In isolated WDs, pulsations are only observed in stars with temperatures located within a so-called in the $\log g$ – $T_{\text{eff}}$ plane, spanning the temperature range $T_{\text{eff}}$ = 10900 K – 12200 K (see Figure 3 of \citealt{2006AJ....132..831G}) )."
 However. there is no clear instability strip for the GW Lib stars (see Figure 13 of 2)). and. pulsations are found. in systems with WD effective temperatures up to at least. 15000 Ix. Our theoretical. understanding of the mechanism. for exciting non-racial pulsations in CVs is still limited.," However, there is no clear instability strip for the GW Lib stars (see Figure 13 of \citealt{2010ApJ...710...64S}) ), and pulsations are found in systems with WD effective temperatures up to at least 15000 K. Our theoretical understanding of the mechanism for exciting non-radial pulsations in CVs is still limited."
 The observed: pulse amplitudes are quite variable. and in some ZZ Ceti stars this is known to be the result of the beating of two signals closely spaced in frequeney. a classic ancl highly informative signature of non-raclial pulsations.," The observed pulse amplitudes are quite variable, and in some ZZ Ceti stars this is known to be the result of the beating of two signals closely spaced in frequency, a classic and highly informative signature of non-radial pulsations."
" But the CW Lib stars have not vet clearly revealed this kind of behaviour (although a hint of it emerged in the V3S6G Ser campaign reported κ P)),", But the GW Lib stars have not yet clearly revealed this kind of behaviour (although a hint of it emerged in the V386 Ser campaign reported by \citealt{2010ApJ...714.1702M}) ).
 We here present. tinie-series photometry of two more CVs which are probably members of the GW Lib. class., We here present time-series photometry of two more CVs which are probably members of the GW Lib class.
 Both systems have very low acerction luminosity. and show signatures from the white dwarf in their optical spectra.," Both systems have very low accretion luminosity, and show signatures from the white dwarf in their optical spectra."
 Also. both svstems show double-humped orbital signals. ancl non-conumensurate periodic signals. suggesting non-raclial pulsations.," Also, both systems show double-humped orbital signals, and non-commensurate periodic signals, suggesting non-radial pulsations."
 One is SDSS J145751 which has a photometric wave suggesting an orbital period of 77.885dE0.007 minutes., One is SDSS J1457+51 which has a photometric wave suggesting an orbital period of $77.885 \pm 0.007$ minutes.
 The other is DW Sculptoris. with {μην=18.22639+0.00003 minutes.," The other is BW Sculptoris, with $P_{\text{orb}} = 78.22639 \pm 0.00003$ minutes."
 Both stars show main pulsations near LO ancl 20 minutes., Both stars show main pulsations near 10 and 20 minutes.
 These rapid signals αρ slightly in. frequeney. and may consist of several. finely. spaced components.," These rapid signals drift slightly in frequency, and may consist of several, finely spaced components."
 BW Sculptoris also shows a remarkable photometric variation at Ny? münutes. which could. be explained as asuperhump.. possibly arising from a 2:1 orbital resonance in the accretion disc.," BW Sculptoris also shows a remarkable photometric variation at 87 minutes, which could be explained as a, possibly arising from a 2:1 orbital resonance in the accretion disc."
 SDSS J145751 (hereafter J1457) was first identified in the Sloan Digital Sky Survey by ?.., SDSS J1457+51 (hereafter J1457) was first identified in the Sloan Digital Sky Survey by \cite{2005AJ....129.2386S}.
 They obtained spectroscopy that showed the broad absorption characteristics of a white chvarl. inclicating a svstem of low accretion rate.," They obtained spectroscopy that showed the broad absorption characteristics of a white dwarf, indicating a system of low accretion rate."
 Lhe source was found to be faint (gz 19.5)., The source was found to be faint $g \approx 19.5$ ).
 Due to the double-peaked nature of the emission lines. they suggested the system to be of high inclination.," Due to the double-peaked nature of the emission lines, they suggested the system to be of high inclination."
 ‘Time-resolved photometry of J1457. was obtained with the 1.3 m and. 2.4 m. ALDAL telescopes at the Witt) Peak observatory. Arizona. during April and. Alay 2010.," Time-resolved photometry of J1457 was obtained with the 1.3 m and 2.4 m MDM telescopes at the Kitt Peak observatory, Arizona, during April and May 2010."
 The star was observed during 1 nights in total. spread over 47 clays.," The star was observed during 14 nights in total, spread over 47 days."
 With all data coming from the same terrestrial longituce. we were not immune from aliasing problems and therefore strove to obtain the longest: possible nightly time series (generally ~ 4-7 hours).," With all data coming from the same terrestrial longitude, we were not immune from aliasing problems and therefore strove to obtain the longest possible nightly time series (generally $\sim$ 4 - 7 hours)."
 Weather conditions such as clouds. snow ancd full moon prevented us from obtaining times series over more than 4 consecutive nights at a time.," Weather conditions such as clouds, snow and full moon prevented us from obtaining times series over more than 4 consecutive nights at a time."
 The time resolution was in the range of 208) 30 s. Table Lo presents a log of the observations., The time resolution was in the range of 20 s – 30 s. Table \ref{tab:obs1} presents a log of the observations.
 A clear filter with a blue eutoff was used to minimise differential-extinction effeets and allow for a good throughput., A clear filter with a blue cutoff was used to minimise differential-extinction effects and allow for a good throughput.
 The cata reduction was cone in real time during the observations. using standard. routines.," The data reduction was done in real time during the observations, using standard routines."
 The data consisted of differential photometry with respect to the Lele star USNO A2.0:1350-08528847., The data consisted of differential photometry with respect to the field star USNO A2.0:1350-08528847.
. The search for. periodic signals was initially clone for single nights separately. anc Lomb-Scarele periodograms (2)) were constructed.," The search for periodic signals was initially done for single nights separately, and Lomb-Scargle periodograms \citealt{1982ApJ...263..835S}) ) were constructed."
 Forma lux errors were rescaled so that the yn2 IL., Formal flux errors were rescaled so that the $\chi^{2}_{\nu} \approx$ 1.
 Εμίν was done by fitting a fake light curve to the original data. compose of multiple sine waves with periods corresponding to the strongest signals found in the sinele-night power spectrum.," This was done by fitting a fake light curve to the original data, composed of multiple sine waves with periods corresponding to the strongest signals found in the single-night power spectrum."
 Alonte-Carlo simulations were performed on every peak of interest. in the power spectrum. to find the period. ancl its error., Monte-Carlo simulations were performed on every peak of interest in the power spectrum to find the period and its error.
 In this method. the peak errors are found by randomly re-distributing the points in the light curve within their errors. à repeated number of times. and. constructing a Lomb-Scargle periodogram cach time.," In this method, the peak errors are found by randomly re-distributing the points in the light curve within their errors, a repeated number of times, and constructing a Lomb-Scargle periodogram each time."
 Ehe Iz260 error is then bound by fitting a Craussian to the output distribution of the »aks found in the periodograms., The $\sigma$ error is then found by fitting a Gaussian to the output distribution of the peaks found in the periodograms.
 Data from several nights were then combined to allow the search for signals with lower amplitude. and also to improve the frequeney.: resolution.," Data from several nights were then combined to allow the search for signals with lower amplitude, and also to improve the frequency resolution."
 Bootstrap analysis was performed. to distinguish. between he most likely alias ancl was also used to find errors on the »aks.," Bootstrap analysis was performed to distinguish between the most likely alias, and was also used to find errors on the peaks."
 In this method. the sampling pattern of the data is changed by creating a mock dataset where every point from. he original dataset is randomised.," In this method, the sampling pattern of the data is changed by creating a mock dataset where every point from the original dataset is randomised."
 “Vhis is done to efficiently destroy. or weaken the aliases pattern., This is done to efficiently destroy or weaken the aliases pattern.
 The mean power spectrum. averaged over the six best nights is shown in Figure L(a)..," The mean power spectrum, averaged over the six best nights is shown in Figure \ref{fig:s_avpow}."
 Phe 15.45 (77.9 min) and 36.97 + (38.9 min) signals are almost. certainly the orbital frequeney (a) and its first harmonic (2a)., The 18.48 $^{-1}$ (77.9 min) and 36.97 $^{-1}$ (38.9 min) signals are almost certainly the orbital frequency $\omega_{\text{o}}$ ) and its first harmonic $2\omega_{\text{o}}$ ).
" This kind of variation at δω, is commonly seen in the orbital light curves of CVs with low accretion rates (for instance in WZ See: see 7)).", This kind of variation at $2\omega_{\text{o}}$ is commonly seen in the orbital light curves of CVs with low accretion rates (for instance in WZ Sge; see \citealt{2002PASP..114..721P}) ).
 We find that the signals in the range 1242 + Hs edd.+ (z 10 min) are non-conimensurate with, We find that the signals in the range 142 $^{-1}$ – 148 $^{-1}$ $\approx$ 10 min) are non-commensurate with
"to the relation between p, and AZ.",to the relation between $\bar\rho_1$ and $M_*$.
 The right-hand. panel of Figure 6 shows that this relation is very shallow., The right-hand panel of Figure \ref{fig:comp2} shows that this relation is very shallow.
 We find While the mass varies by 2 orders of magnitude (from 104 AL. to 5107 A/.). the central density remains constant at about L8«1077 AZ.kpe7.," We find While the mass varies by 2 orders of magnitude (from $10^{11}$ $M_{\odot}$ to $5 \times 10^{12}$ $M_{\odot}$ ), the central density remains constant at about $1.8 \times 10^{10}$ $M_{\odot}\,{\rm kpc}^{-3}$."
" The left-hancl panel of Figure 6 shows another way of presenting this information: while p, varies by 32 orders of magnitude. pj varies by less than a factor of 2."," The left-hand panel of Figure \ref{fig:comp2} shows another way of presenting this information: while $\rho_e$ varies by 3 orders of magnitude, $\bar\rho_1$ varies by less than a factor of 2."
 We find Thus the central density is approximately constant for all the galaxies of our samplo., We find Thus the central density is approximately constant for all the galaxies of our sample.
 Lt is quite remarkable that they show the same relation as in the samples of Mancini ct al., It is quite remarkable that they show the same relation as in the samples of Mancini et al.
 and. Longhetti et al., and Longhetti et al.
 at 2ol5 as well as of Bezanson et al. (, at $z \sim 1.5$ as well as of Bezanson et al. (
2000) at z~2.3.,2009) at $z\sim 2.3$.
" Although p, is orders of magnitude larger in the 2~2.3 sample than at z—0. py is dillerent by only a factor of two OP SO."," Although $\bar\rho_e$ is orders of magnitude larger in the $z\sim 2.3$ sample than at $z=0$, $\bar\rho_1$ is different by only a factor of two or so."
 We analvzed a sample of 23 giant. elliptical galaxies., We analyzed a sample of 23 giant elliptical galaxies.
 They are verv massive (A>100AZ. ) with large central velocity clispersions =330 km 1o which suggests old stellar populations (Bernardi et al.," They are very massive $M>10^{11} M_{\odot}$ ) with large central velocity dispersions $\gsim 330$ km $^{-1}$, which suggests old stellar populations (Bernardi et al."
 2005)., 2005).
 We estimated dynamical masses for each of these svstems by using the observed light profiles and central velocity dispersions. by solving the Jeans Equation. under the assumptions of spherical symmetry. no tangential velocity. clispersions. no radial dependence of the stellar mass-to-light ratio. and that each svstem has 30 times more dark matter than stellar matter within the virial radius. with the dark matter following an NEW profile (ec. no accounting for aciabatic contraction).," We estimated dynamical masses for each of these systems by using the observed light profiles and central velocity dispersions, by solving the Jeans Equation, under the assumptions of spherical symmetry, no tangential velocity dispersions, no radial dependence of the stellar mass-to-light ratio, and that each system has 30 times more dark matter than stellar matter within the virial radius, with the dark matter following an NFW profile (i.e. no accounting for adiabatic contraction)."
 We found that the total stellar masses of these systems vary [from about. 1085A7. 10 5=1022AL. (lable 23)., We found that the total stellar masses of these systems vary from about $10^{11} M_{\odot}$ to $5\times 10^{12} M_{\odot}$ (Table \ref{tab:results}) ).
 In such models. the contribution of the dark matter modilies the central velocity cüspersion by less than 5X (Figure 1).," In such models, the contribution of the dark matter modifies the central velocity dispersion by less than $5\%$ (Figure \ref{fig:disp}) )."
 Thus. for these objects. the observed ay provides a good estimator of the luminous mass (equation 16)).," Thus, for these objects, the observed $\sigma_0$ provides a good estimator of the luminous mass (equation \ref{eq:lam}) )."
 We compared. the masses we derive to estimates of the stellar mass from stellar population models (Figure 4))., We compared the masses we derive to estimates of the stellar mass from stellar population models (Figure \ref{fig:MdynMvis}) ).
 We find. good agreement using a composite mocel with high age and a small (by mass) metal-poor sub-component., We find good agreement using a composite model with high age and a small (by mass) metal-poor sub-component.
 This model fits well the colors of Luminous Rec Galaxies in SDSS., This model fits well the colors of Luminous Red Galaxies in SDSS.
 AX major result of this study is that we compute the mass-to-light ratio for massive elliptical galaxies., A major result of this study is that we compute the mass-to-light ratio for massive elliptical galaxies.
" This ratio is roughly constant for all the sample (Figure 3)). we find AZ,/L~5x1 in the i-band. for θεκοκος."," This ratio is roughly constant for all the sample (Figure \ref{fig:Li}) ), we find $M_\star/L\sim5 \pm 1$ in the i-band, for $0.7< g-r < 0.9$."
 We also studied. dillerent/ ways. ο presenting. the correlation between size and mass (Figure 5))., We also studied different ways of presenting the correlation between size and mass (Figure \ref{fig:comp1}) ).
 The correlation we find. r.xALE. is slightly steeper than that reported. by Bernardi et al. (," The correlation we find, $r_e\propto M_*^{1.07}$, is slightly steeper than that reported by Bernardi et al. ("
2008).,2008).
 We suggest that this is because our estimate of Ad. is less noisy., We suggest that this is because our estimate of $M_*$ is less noisy.
 For similar reasons. we find that the density within à. is a more strongly decreasing function of M; than reported by Bernardi ct al. (," For similar reasons, we find that the density within $r_e$ is a more strongly decreasing function of $M_*$ than reported by Bernardi et al. ("
2008).,2008).
 We find poxAL;BoxMO compared. to their Ls., We find $\bar\rho_e\propto M_*/r_e^3 \propto M_*^{-2.2}$ compared to their $-1.8$.
 A notable result is that galaxies at z  2.3 (Bezanson et al.), A notable result is that galaxies at z $\sim$ 2.3 (Bezanson et al.)
 and z  1.5 (Mancini ct al.), and z $\sim$ 1.5 (Mancini et al.)
 appear to follow the same relation that we find at z  0., appear to follow the same relation that we find at z $\sim$ 0.
 If each sample correctly eather the most massive galaxies for each range of redshift. the evolution between the size and the stellar mass shoulebe meaningful.," If each sample correctly gather the most massive galaxies for each range of redshift, the evolution between the size and the stellar mass shouldbe meaningful."
" Vhe small scatter associated with our dynamica estimator of AZ, means that. in the space of rj. p, ane AL. the objects in our sample trace out à one-dimoensiona curve (although we have argued. as did Bernardi et al."," The small scatter associated with our dynamical estimator of $M_*$ means that, in the space of $r_e$, $\bar{\rho}_e$ and $M_\star$ , the objects in our sample trace out a one-dimensional curve (although we have argued, as did Bernardi et al."
 2008. that the roxAM. scaling. we find is consistent with the simplest virial theorem scaling. once we account Lor the fac that these objects have essentially fixed 0).," 2008, that the $r_e\propto M_*$ scaling we find is consistent with the simplest virial theorem scaling, once we account for the fact that these objects have essentially fixed $\sigma$ )."
 This is also true in the space of ry. σ and ALL.," This is also true in the space of $r_e$ , $\sigma$ and $M_\star$."
 We show this explicitly in Figure 7.., We show this explicitly in Figure \ref{fig:plot3d}.
 Hac we used the stellar population-based estimate oM. these curves would have been broadened into a plane.," Had we used the stellar population-based estimate of $M_*$, these curves would have been broadened into a plane."
" Since the (7.05.M,) projection is similar to that of the Fundamental Plane. our results suggest that scatter in the relation between L£ and. M. or uncertainties in estimating Al. serve to enhance the impression of a plane rather than a curvo."," Since the $r_e, \sigma_0, M_\star$ ) projection is similar to that of the Fundamental Plane, our results suggest that scatter in the relation between $L$ and $M_*$, or uncertainties in estimating $M_*$ serve to enhance the impression of a plane rather than a curve."
 On the other hand. some of the decreased. scatter in our analysis is due to our neglect of anisotropic velocity dispersion. profiles.," On the other hand, some of the decreased scatter in our analysis is due to our neglect of anisotropic velocity dispersion profiles."
 We explore. this in the Appenclix., We explore this in the Appendix.
" Nevertheless. it is likely that the scaling relation between rm and Al, of giant ellipticals is significantly steeper than for spirals (which have r,xAH ?y "," Nevertheless, it is likely that the scaling relation between $r_e$ and $M_*$ of giant ellipticals is significantly steeper than for spirals (which have $r_e\propto M_{\star}^{1/2}$ )."
Understanding why is à challenge for models in which ellipticals form from mergers of spirals., Understanding why is a challenge for models in which ellipticals form from mergers of spirals.
" Although p, decreases strongly with A;. the average density on smaller. scales. (we chose 1 kpe) is almost independent of AZ; (Figure 6))."," Although $\bar\rho_e$ decreases strongly with $M_*$, the average density on smaller scales (we chose 1 kpc) is almost independent of $M_*$ (Figure \ref{fig:comp2}) )."
 Moreover. it is remarkably similar to that. founc by Bezanson ct al. (," Moreover, it is remarkably similar to that found by Bezanson et al. ("
2009). in their analysis of z2.3 galaxies.,"2009), in their analysis of $z\sim 2.3$ galaxies."
 Phe mean density within 1 kpc seems to be independent. of the redshift ancl of the mass on an object by object basis., The mean density within 1 kpc seems to be independent of the redshift and of the mass on an object by object basis.
 Le. since z2. as these ealaxies grew in mass. the mass in the inner kpe remained unchanged.," I.e., since $z\sim 2$, as these galaxies grew in mass, the mass in the inner kpc remained unchanged."
 Understanding why is an interesting challenge., Understanding why is an interesting challenge.
 Although this is most. easily. accomplished. in. models where the mass is added to the outer regions only (e.g. Lapi Cavaliere 2009. Cook et al 2009) so i is tempting to conclude that minor mergers were the dominant. growth mode since 2~ (e.g. Bezanson et al.," Although this is most easily accomplished in models where the mass is added to the outer regions only (e.g. Lapi Cavaliere 2009, Cook et al 2009) – so it is tempting to conclude that minor mergers were the dominant growth mode since $z\sim 2$ (e.g. Bezanson et al."
 2009) there is a direct counterexample to this conclusion in the literature., 2009) – there is a direct counterexample to this conclusion in the literature.
 1n numerical simulations of hierarchical structure formation. Gao et al. (," In numerical simulations of hierarchical structure formation, Gao et al. ("
2004) find that although the mass in the central regions of what becomes a massive cluster at 2=0 has remained Constant since z6. the particles which make up this mass changed: dramatically as the objects. assembled.,"2004) find that although the mass in the central regions of what becomes a massive cluster at $z=0$ has remained constant since $z\sim 6$, the particles which make up this mass changed dramatically as the objects assembled."
 ‘This assembly occurred through a sequence of major mergers ab 2o>ld: with minor mergers beginning to dominate the mass growth only at z«1., This assembly occurred through a sequence of major mergers at $z>1$; with minor mergers beginning to dominate the mass growth only at $z<1$.
 Note that in hierarchical models. what is true for cluster mass halos is also true for galaxy mass halos.," Note that in hierarchical models, what is true for cluster mass halos is also true for galaxy mass halos."
 While gastrophysies may complicate the discussion. we raise this as an example where mass growth due to major mergers does not lead. to increased: density in the central regions.," While gastrophysics may complicate the discussion, we raise this as an example where mass growth due to major mergers does not lead to increased density in the central regions."
 This appears to be in remarkable agreement with what we see. s," This appears to be in remarkable agreement with what we see. ,"
ample. thenthe required mass growth is abouta factor of 5 (Piewe 6)) this is larger than most minor merger mociels can accommocate., thenthe required mass growth is abouta factor of 5 (Figure \ref{fig:comp2}) ) – this is larger than most minor merger models can accommodate.
 It may well be that major mergers were, It may well be that major mergers were
The technique of Fourier interrelations. as described in Section 4. are (he linear relations between the Fourier parameters in equation (1) in dillerent wave bands.,"The technique of Fourier interrelations, as described in Section 4, are the linear relations between the Fourier parameters in equation (1) in different wave bands."
 Similarly. (here exist another group of linear relations between the Fourier parzuneters in (he same wave band. known as (he Fourier intrarelations.," Similarly, there exist another group of linear relations between the Fourier parameters in the same wave band, known as the Fourier intrarelations."
 The reason lor developing the Fourier intravelations is same as in Fourier interrelation. mainiv to reconstruct the I band light curves that only contain 4 epochs.," The reason for developing the Fourier intrarelations is same as in Fourier interrelation, mainly to reconstruct the I band light curves that only contain 4 epochs."
 Therefore. the Fourier intrarelations are the linear relation between the 1 order Fourier parameter ancl the higher order Fourier parameters in one particular wave band. since 4 data points only permit the 1? order Fourier expansion.," Therefore, the Fourier intrarelations are the linear relation between the $1^{st}$ order Fourier parameter and the higher order Fourier parameters in one particular wave band, since 4 data points only permit the $1^{st}$ order Fourier expansion."
" The Fourier intrarelations have the following expression for either V or I bands: As in the case of Fourier interrelations. the coefficients are determined from the ""calibration sel” Cepheids."," The Fourier intrarelations have the following expression for either V or I bands: As in the case of Fourier interrelations, the coefficients are determined from the “calibration set” Cepheids."
 The results of the fits to the data with equation (Al) (A2) are presented in Table 7.. which only listed out the 34 and 4 order Fourier intrarelations.," The results of the fits to the data with equation (A1) (A2) are presented in Table \ref{tab7}, which only listed out the $3^{rd}$ and $4^{th}$ order Fourier intrarelations."
" The 2"" order Fourier intrarelations were omitted because for sparse. 12 epoch V band data. we can fit the data with 2"" order Fourier expansion and expand to 4"" order with Fourier intrarelations {ο reconstruct. V. band light curves."," The $2^{nd}$ order Fourier intrarelations were omitted because for sparse, 12 epoch V band data, we can fit the data with $2^{nd}$ order Fourier expansion and expand to $4^{th}$ order with Fourier intrarelations to reconstruct V band light curves."
 Then we can use the Fourier interrelations (o reconstruct the I band light curves from the V band light curves., Then we can use the Fourier interrelations to reconstruct the I band light curves from the V band light curves.
 The plots for the Fourier intrarelations in “calibrating set Cepheids are presented in Figure 21 22 lor Fourier amplitudes and phases. respectively.," The plots for the Fourier intrarelations in “calibrating set” Cepheids are presented in Figure \ref{fig:fig21} \ref{fig:fig22} for Fourier amplitudes and phases, respectively."
 From these figures. (hough a relation clearly exists. it may not be linear though we show the best fit linear relation.," From these figures, though a relation clearly exists, it may not be linear though we show the best fit linear relation."
" In the plots of sl, against Ay for both V and I band. there are some stars which lie well below the best fit linear relation."," In the plots of $A_3$ against $A_1$ for both V and I band, there are some stars which lie well below the best fit linear relation."
 The 41; verses ly plots also show some evidence of a non-linearity., The $A_4$ verses $A_1$ plots also show some evidence of a non-linearity.
 since (he error bars have been plotted on these diagrams. the trends described here are real.," Since the error bars have been plotted on these diagrams, the trends described here are real."
 This non-linearity may due to differences in long anc short period Cepheids., This non-linearity may due to differences in long and short period Cepheids.
 As in the case of Fourier interrelations. the Fourier intrarelations in OGLE LAIC Cepheids have also been found. aud presented in Table &..," As in the case of Fourier interrelations, the Fourier intrarelations in OGLE LMC Cepheids have also been found, and presented in Table \ref{tab8}."
 The corresponding plots of the Fourier amplitudes and phases are given in Figure A 25.. respectively.," The corresponding plots of the Fourier amplitudes and phases are given in Figure \ref{fig:fig23} \ref{fig:fig24}, respectively."
 The possible non-linearity of the Fourier intrarelations (hat seem on the “calibrating set Cepheids also show up in these figures. as some stars which lie below the best fit linear regression 14 vs. 14) and the indications of non-linearity in (he ο vs. Ay plots.," The possible non-linearity of the Fourier intrarelations that seem on the “calibrating set” Cepheids also show up in these figures, as some stars which lie below the best fit linear regression $A_3$ vs. $A_1$ ) and the indications of non-linearity in the $A_4$ vs. $A_1$ plots."
 Furthermore. by comparing the Fourier intrarelations in the “calibrating set and OGLE LAIC Cepheids. we see clearly that the slope," Furthermore, by comparing the Fourier intrarelations in the “calibrating set” and OGLE LMC Cepheids, we see clearly that the slope"
The radial velocity curve (Fig. 18)),The radial velocity curve (Fig. \ref{fig:radvel}) )
 has been obtained bv coaddiug radial velocity curves of individual lines. aud the zero radial velocity of all lines on 11.05.2003 (the orbital phase 0.018). was adopted.," has been obtained by coadding radial velocity curves of individual lines, and the zero radial velocity of all lines on 11.05.2003 (the orbital phase 0.048) was adopted."
 If a lue was not detected on 11.05.2003. the zero radial velocity was assunied for 28.01.2003 as well (the orbital phase 0.051).," If a line was not detected on 11.05.2003, the zero radial velocity was assumed for 28.04.2003 as well (the orbital phase 0.054)."
 If the ueasured radial velocity ou 11.05.2003 disagreed with the whole radial velocity curve of a eiven liue. au additional shift for the curve was applied.," If the measured radial velocity on 11.05.2003 disagreed with the whole radial velocity curve of a given line, an additional shift for the curve was applied."
 However no VAufts in excess of 20 kiné/s were doue., However no shifts in excess of 20 km/s were done.
 This is the reason why the radial velocity error ii 11.05.2003 is zuall. but not zero.," This is the reason why the radial velocity error in 11.05.2003 is small, but not zero."
 Thus. the radial velocity curve for absorption Lincs in Fie.," Thus, the radial velocity curve for absorption lines in Fig."
 Ls cousists of individual radial velocity curves.," \ref{fig:radvel}
 consists of individual radial velocity curves."
 Each point of the curve iucludes youn LO to 17 individual lmucasturements., Each point of the curve includes from 10 to 17 individual measurements.
 Most miecasurements were carried out at the primary nuuimuun as there the absorption lines are deeper., Most measurements were carried out at the primary minimum as there the absorption lines are deeper.
" The derived radii velocity seii-unplitude of the donor star is A,=132+9 kms. the gmunic-velocity of the binary svstem is c,=Ll kms with a formal fit uncertaintv of 2 kms. The absorption line radial velocity transition through the +-velocity occurs at the iuiddle of the optical eclipse (o,= 0.07). confrnüug that the lines actually beloug to the donor star."," The derived radial velocity semi-amplitude of the donor star is $K_v=132\pm 9$ km/s, the gamma-velocity of the binary system is $v_\gamma=14$ km/s with a formal fit uncertainty of $2$ km/s. The absorption line radial velocity transition through the $\gamma$ -velocity occurs at the middle of the optical eclipse $\phi_b=0.07$ ), confirming that the lines actually belong to the donor star."
" Note that iu the eanune-velocitv c4 aud in the transition phase co, some systematic errors can be present because of the method used.", Note that in the gamma-velocity $v_\gamma$ and in the transition phase $\phi_b$ some systematic errors can be present because of the method used.
 However they are less than 30 kis (no bigecr shifts were applied to radial velocity curves of mdividual lines) and 0.05 correspondingly., However they are less than 30 km/s (no bigger shifts were applied to radial velocity curves of individual lines) and 0.05 correspondingly.
 The main observational bias iu studving radial velocities of the donor star is the faintucss of absorption lines outside the primary ninimua aud strong iutriusic spectral variability of SS133., The main observational bias in studying radial velocities of the donor star is the faintness of absorption lines outside the primary minima and strong intrinsic spectral variability of SS433.
 To coufinui the derived radial velocity curve further spectral observations are needed., To confirm the derived radial velocity curve further spectral observations are needed.
" Qur results confirma the earlicr determination of A, by Cües et al. (", Our results confirm the earlier determination of $K_v$ by Gies et al. (
2002) which was carried out also at the mani disk opening phases.,2002) which was carried out also at the maximum disk opening phases.
 Note that spectroscopic observations by Charles et al. (, Note that spectroscopic observations by Charles et al. (
2001) were performed. at the crossover phase of SS133 when the accretion disk is seen edee-ou.,2004) were performed at the crossover phase of SS433 when the accretion disk is seen edge-on.
 Such a ράσο is disfavored for the donor star radial velocity analysis as strong σας outflows contaminate the disk plane: selective absorption iu this eas affects the true radial velocity of the donor star., Such a phase is disfavored for the donor star radial velocity analysis as strong gas outflows contaminate the disk plane; selective absorption in this gas affects the true radial velocity of the donor star.
 The heating effect of the donor star also distorts the radial velocity seiuiuuplitude., The heating effect of the donor star also distorts the radial velocity semi-amplitude.
 The analysis (Wade aud Horne 1988. Autoklina et al.," The analysis (Wade and Horne 1988, Antokhina et al."
 2005) indicates that the true value of he seii-uuplitude of the racial velocity curve as derived frou these absorption mes cau be reduced to 85 aufs (see below)., 2005) indicates that the true value of the semi-amplitude of the radial velocity curve as derived from these absorption lines can be reduced to $\sim 85$ km/s (see below).
 Recently Willwie e al. (, Recently Hillwig et al. (
2001) obtained au estimate of he racdia velocity amplitude of the douor star Ay.=LotG kis aud the eanuna-velocity ο-=6543ro kms. In our opinion. sole strong lines (which actually are shell-like ines onthe background of fait emission) could contribute o the radial velocity cross-correlatious of IHlblwie et al. (,"2004) obtained an estimate of the radial velocity amplitude of the donor star $K_v=45 \pm 6$ km/s and the gamma-velocity $v_\gamma=65\pm 3$ km/s. In our opinion, some strong lines (which actually are shell-like lines on the background of faint emission) could contribute to the radial velocity cross-correlations of Hillwig et al. ("
2001).,2004).
" For example. the two strongest lines iu their 55 FoIIA1550 aud Fell,[5s are qnm enudssion m our spectra du he micelle of eclipse."," For example, the two strongest lines in their 5 $\lambda 4550$ and $\lambda 4584$ are in emission in our spectra in the middle of eclipse."
 The KPNO-2003 observations of Tilhwig et al. (, The KPNO-2003 observations of Hillwig et al. (
2001) were made in the orbital shases O.85-1.07.,2004) were made in the orbital phases 0.85-1.07.
 Absorption lines ormed in the rotating aud extended cuvelope of the donor could be probably observed., Absorption lines formed in the rotating and extended envelope of the donor could be probably observed.
" In these orbital phases. the side of the envelope projected onto the strong cout,un source (the accretion disk) moves away from the observer."," In these orbital phases, the side of the envelope projected onto the strong continuum source (the accretion disk) moves away from the observer."
 Then the amplitude of the Ine shift can be expected to be l1/2Vq44;~OO kis. This mielt explain the positive shift of the system velocity. |65 |au/s fouud bv those authors., Then the amplitude of the line shift can be expected to be $\sim 1/2 V_{equat} \sim 60$ km/s. This might explain the positive shift of the system velocity +65 km/s found by those authors.
 Comparison of radial velocities of the accretion disk (Jv).= km/s. Fabrika and Bychkova 1990) and optical star (hy=132 lau/s) vields the mass ratio in the SS133 SVSTCLLL oq—HyfHNON.=0.75 (here nmi aud," Comparison of radial velocities of the accretion disk $K_x=175$ km/s, Fabrika and Bychkova 1990) and optical star $K_v=132$ km/s) yields the mass ratio in the SS433 system $q=m_x/m_v=K_v/K_x=0.75$ (here $m_x$ and"
"independent likelihood and L’, the combined likelihood distribution Ldistributions,L is just the product of the two Which then allows us to simply reweight each point in the chain Now likelihood contours drawn in the parameter space will represent the combined likelihood.","independent likelihood $L$ and $L'$, the combined likelihood distribution $\tilde{L}$ is just the product of the two Which then allows us to simply reweight each point in the chain Now likelihood contours drawn in the parameter space will represent the combined likelihood."
" It is worth noting that the ‘Metropolis Hastings’ and ‘Nested sampling’ algorithms use different weighting schemes, MCMC points have integer weights whilst the sum of the weights in a Multinest chain is one."," It is worth noting that the `Metropolis Hastings' and `Nested sampling' algorithms use different weighting schemes, MCMC points have integer weights whilst the sum of the weights in a Multinest chain is one."
 For ease of comparison it is necessary to normalise the weights accordingly., For ease of comparison it is necessary to normalise the weights accordingly.
 We took a WMAP chain which allowed for a time varying dark energy equation of state and then calculated the likelihood that each point fitted the galaxy power spectrum using equation 23.., We took a WMAP chain which allowed for a time varying dark energy equation of state and then calculated the likelihood that each point fitted the galaxy power spectrum using equation \ref{pk_like}.
 We then reweighted each point using equation 26 and the WMAP weight., We then reweighted each point using equation \ref{reweight} and the WMAP weight.
" The Alcock-Pazcynski and redshift space distortion β parameters were then cj,c;calculated for each point in the chain by comparing with the fiducial parameter values."," The Alcock-Pazcynski $c_\parallel, c_\bot$ and redshift space distortion $\beta$ parameters were then calculated for each point in the chain by comparing with the fiducial parameter values."
 This allows us to draw constraints in these planes (figure 5))., This allows us to draw constraints in these planes (figure \ref{fig:all_impsamp.eps}) ).
 To include a prior on the sound horizon in our toy model we assume the likelihood distribution around the true value of rs is a Gaussian of the same width as the prior used in the Fisher analysis., To include a prior on the sound horizon in our toy model we assume the likelihood distribution around the true value of $r_s$ is a Gaussian of the same width as the prior used in the Fisher analysis.
" This is then importance sampled with the toy model, giving rise to the black contours in figures 2 and 3.."," This is then importance sampled with the toy model, giving rise to the black contours in figures \ref{fig:toy_model_error_ellipses_LRG.eps} and \ref{fig:toy_model_error_ellipses_DESpec.eps}."
 To include the Gaussian prior in the CAMB model we calculatedΤε for each point in the chain using the prescription given in ??..," To include the Gaussian prior in the CAMB model we calculated$r_s$ for each point in the chain using the prescription given in \citet{1996ApJ...471..542H,1998ApJ...496..605E}."
" We then drew a probability for this value from a Gaussian distribution peaked at the fiducial value for Τε calculated using our fiducial parameter set in table 1, with the same standard deviation as before."," We then drew a probability for this value from a Gaussian distribution peaked at the fiducial value for $r_s$ calculated using our fiducial parameter set in table 1, with the same standard deviation as before."
" Each point was then reweighted using equation 26,, giving rise to the black contours in figure 5.."," Each point was then reweighted using equation \ref{reweight}, giving rise to the black contours in figure \ref{fig:all_impsamp.eps}."
 When comparing the 68% confidence limits in figure 2 from the Fisher (blue) and nested sampling (green) of the toy model we can see that for smaller survey areas there is some tension between the two methods., When comparing the $68 \%$ confidence limits in figure \ref{fig:toy_model_error_ellipses_LRG.eps} from the Fisher (blue) and nested sampling (green) of the toy model we can see that for smaller survey areas there is some tension between the two methods.
" The areas bounded by the contours are similar, with the exception of the constraints around f, but the two sets of contours do not cover exactly the same part of parameter space."," The areas bounded by the contours are similar, with the exception of the constraints around $\beta$, but the two sets of contours do not cover exactly the same part of parameter space."
" The larger survey (figure 3)) is, however, in better agreement."," The larger survey (figure \ref{fig:toy_model_error_ellipses_DESpec.eps}) ) is, however, in better agreement."
" Although in the 8—cj,c; planes the areas covered by the contours still differ by about a factor of two."," Although in the $\beta-c_\parallel,c_\bot$ planes the areas covered by the contours still differ by about a factor of two."
" By design the maximum likelihood is the same in both cases, so the question arises, what is causing the disagreement?"," By design the maximum likelihood is the same in both cases, so the question arises, what is causing the disagreement?"
 The answer can be found by examining the likelihood space in more detail., The answer can be found by examining the likelihood space in more detail.
" Let us look at the normalised 1d profile of the parallel Alcock-Paczynski parameter, cj."," Let us look at the normalised 1d profile of the parallel Alcock-Paczynski parameter, $c_\parallel$."
" We can see that for a 1(h!Gpc)? survey the likelihood is not Gaussian (figure 6)), being skewed."," We can see that for a $1(h^{-1} {\rm Gpc})^3$ survey the likelihood is not Gaussian (figure \ref{fig:1dplot_LRG.eps}) ), being skewed."
 This puts asymmetric error bars on our parameters., This puts asymmetric error bars on our parameters.
 When we look at the contours for a larger 20(h!Gpc) survey (the kind of volume expected for future spectroscopic surveys such as DESpec and BigBoss) we see that the spaces covered by the two sets of contours are more similar., When we look at the contours for a larger $20(h^{-1} {\rm Gpc})^3$ survey (the kind of volume expected for future spectroscopic surveys such as DESpec and BigBoss) we see that the spaces covered by the two sets of contours are more similar.
 If we look at the 1d probability distribution around cj again we can see that it is more Gaussian than in the 1(h~'Gpc)? case since the marginalised probabilities and mean likelihoods are more similar., If we look at the 1d probability distribution around $c_\parallel$ again we can see that it is more Gaussian than in the $1(h^{-1} {\rm Gpc})^3$ case since the marginalised probabilities and mean likelihoods are more similar.
 This is a pattern which is repeated for all the parameters in our toy model., This is a pattern which is repeated for all the parameters in our toy model.
" The larger survey enables us to look closer into the peak of the distribution, which is more Gaussian."," The larger survey enables us to look closer into the peak of the distribution, which is more Gaussian."
" As anticipated, prior knowledge of the location and uncertainty in the sound horizon at last scattering improves our ability to constrain the shape of the power spectrum and geometric distortions."," As anticipated, prior knowledge of the location and uncertainty in the sound horizon at last scattering improves our ability to constrain the shape of the power spectrum and geometric distortions."
" By adding a 196 prior onto the sound horizon of Or,=14Mpch-! in a Fisher matrix analysis we can see how calibrating with the CMB improves constraints in our οι—cj parameter space for a small 1(h!Gpc)? survey by a factor of several and larger 20(h!Gpc)? survey by more than a factor of two."," By adding a $~1 \%$ prior onto the sound horizon of $\sigma_{r_s} = 1.4 {\rm Mpc}\,h^{-1}$ in a Fisher matrix analysis we can see how calibrating with the CMB improves constraints in our $c_\bot - c_\parallel$ parameter space for a small $1(h^{-1}{\rm Gpc})^3$ survey by a factor of several and larger $20(h^{-1}{\rm Gpc})^3$ survey by more than a factor of two."
 We then conducted a likelihood analysis using nested sampling on our numerically produced power spectrum., We then conducted a likelihood analysis using nested sampling on our numerically produced power spectrum.
" A Gaussian prior on the sound horizon improves these constraints by a factor of two for the 20(h!Gpc), ‘DESpec/BigBOSS’-like survey."," A Gaussian prior on the sound horizon improves these constraints by a factor of two for the $20(h^{-1}{\rm Gpc})^3$, `DESpec/BigBOSS'-like survey."
 The combined constraints from the 20(h!Gpc)? survey + WMAP are nearly a factor of 10 times better than the constraints from the survey alone., The combined constraints from the $20(h^{-1}{\rm Gpc})^3$ survey + WMAP are nearly a factor of 10 times better than the constraints from the survey alone.
 The WMAP prior contains considerably more information and is more orthogonal than the Gaussian prior On Ts., The WMAP prior contains considerably more information and is more orthogonal than the Gaussian prior on $r_s$ .
warp propagation in the thick dise case have been performed by? and ?..,warp propagation in the thick disc case have been performed by\citet{nelson99} and \citet{nelson00}.
 Numerical simulations of warp propagation for thin. and viscous discs are much more challenging. because in order to properly catch the warp dynamics it is essential to accurately resolve the vertical structure of the disc. which for very thin disces can be difficult.," Numerical simulations of warp propagation for thin and viscous discs are much more challenging, because in order to properly catch the warp dynamics it is essential to accurately resolve the vertical structure of the disc, which for very thin discs can be difficult."
 A first attempt at testing the analytical theory with numerical simulations in the thin dise regime has been performed by ? (hereafter 23). using SPH.," A first attempt at testing the analytical theory with numerical simulations in the thin disc regime has been performed by \citet{LP07} (hereafter \citetalias{LP07}) ), using SPH."
 The results of ? showed some unexpected results: while for large values of the dise viscosity the warp diffusion coefficient. appeared to seale inversely with viscosity. as predicted analytically. such behaviour was not found at low viscosities.aniplitudes.," The results of \citetalias{LP07} showed some unexpected results: while for large values of the disc viscosity the warp diffusion coefficient appeared to scale inversely with viscosity, as predicted analytically, such behaviour was not found at low viscosities,."
. In. this case. the diffusion coefticient appeared to be much smaller than theoretically predicted. implying (as discussed extensively by 2) some additional dissipation.," In this case, the diffusion coefficient appeared to be much smaller than theoretically predicted, implying (as discussed extensively by \citetalias{LP07}) ) some additional dissipation."
 Additionally. the internal precession induced by the warp and predicted analytically was found to be strongly dependent on the specitic implementation of viscosity and was not found to match the theoretical expectations.," Additionally, the internal precession induced by the warp and predicted analytically was found to be strongly dependent on the specific implementation of viscosity and was not found to match the theoretical expectations."
 ? discuss different possible explanations for such disagreement., \citetalias{LP07} discuss different possible explanations for such disagreement.
 On the one hand. it is quite possible that the limited numerical resolution of their simulations might have affected their results.," On the one hand, it is quite possible that the limited numerical resolution of their simulations might have affected their results."
 On the other hand.strong supersonie motions were found in the 2. simulations. which might result into shocks in the resulting flow and thus provide the required additional dissipation.," On the other hand,strong supersonic motions were found in the \citetalias{LP07} simulations, which might result into shocks in the resulting flow and thus provide the required additional dissipation."
 In this paper. we want to systematically address all the issues left open by 3.. by checking both the numerical aspects of the problem and the physical effects involved.," In this paper, we want to systematically address all the issues left open by \citetalias{LP07}, by checking both the numerical aspects of the problem and the physical effects involved."
 With regards to the numerical aspects. first of all we have used a different SPH code with respect to ?.. therefore validating one code against the other.," With regards to the numerical aspects, first of all we have used a different SPH code with respect to \citetalias{LP07}, therefore validating one code against the other."
 Secondly. we have checked numerical convergence by running simulations using 20 million particles. that isa of factorten larger than ? (note that such simulations are among the largest SPH simulations of accretion discs performed to date).," Secondly, we have checked numerical convergence by running simulations using 20 million particles, that is a factor of ten larger than \citetalias{LP07} (note that such simulations are among the largest SPH simulations of accretion discs performed to date)."
 Since some of the effects reported by ? appeared to depend on the viscosity formulation. we have here tested two different possible implementations of dise viscosity.," Since some of the effects reported by \citetalias{LP07} appeared to depend on the viscosity formulation, we have here tested two different possible implementations of disc viscosity."
 Finally. we have moditied our analysis procedure. so as to obtain a more quantitative evaluation of the uncertainties in the measured parameters.," Finally, we have modified our analysis procedure, so as to obtain a more quantitative evaluation of the uncertainties in the measured parameters."
 In order to test the physical effects which might determine the ? results. we have paid attention to shocks. which were argued by ? to be responsible for the additional dissipation.," In order to test the physical effects which might determine the \citetalias{LP07} results, we have paid attention to shocks, which were argued by \citetalias{LP07} to be responsible for the additional dissipation."
 We have checked the importance of shocks by running simulations with different levels of bulk viscosity — varied independently of the shear viscosity — which is directly connected with shock dissipation., We have checked the importance of shocks by running simulations with different levels of bulk viscosity — varied independently of the shear viscosity — which is directly connected with shock dissipation.
 The paper is organised as follows., The paper is organised as follows.
 In section 2. we discuss the basic features of the analytic theory of warp propagation in both the linear and non-linear regime., In section \ref{sec:theory} we discuss the basic features of the analytic theory of warp propagation in both the linear and non-linear regime.
 In section 3. we detail the numerical method that we have used to simulate the system. including the different implementations of dise viscosity that we use.," In section \ref{sec:numerics} we detail the numerical method that we have used to simulate the system, including the different implementations of disc viscosity that we use."
 In section j we describe the procedure we have used to analyse our results and extract from the simulations the warp diffusion parameters., In section \ref{sec:analysis} we describe the procedure we have used to analyse our results and extract from the simulations the warp diffusion parameters.
 In section 5. we present and discuss our main results for the warp diffusion and precession in both the linear and non-linear regime., In section \ref{sec:results} we present and discuss our main results for the warp diffusion and precession in both the linear and non-linear regime.
 Finally. in section 6 we draw our conclusions.," Finally, in section \ref{sec:conclusions} we draw our conclusions."
 We consider here. as in ?.. the propagation of warps in thin Keplerian aecretion dises. rotating with angular velocity O(/?). with surface density X(/7) and angular momentum per unit area L(/?).," We consider here, as in \citetalias{LP07}, the propagation of warps in thin Keplerian accretion discs, rotating with angular velocity $\Omega(R)$, with surface density $\Sigma(R)$ and angular momentum per unit area ${\bf L}(R)$ ."
" Here // should be interpreted as a ""spherical! coordinate.", Here $R$ should be interpreted as a `spherical' coordinate.
 The local direction of L can be oriented arbitrarily in space. and the unit vector 10/2)=LGWUO/L(GR) defines its direction.," The local direction of ${\bf L}$ can be oriented arbitrarily in space, and the unit vector ${\bf l}(R)={\bf L}(R)/L(R)$ defines its direction."
 If the dise is rotating around a central point mass AZ. then its rotation is Keplerian. with Q=J/CALI and LOR)=VODNVCM19.," If the disc is rotating around a central point mass $M$, then its rotation is Keplerian, with $\Omega=\sqrt{GM/R^3}$ and $L(R)=\Sigma(R)\sqrt{GMR}$ ."
 The dise is warped whenever the direction identified by 1 changes with radius., The disc is warped whenever the direction identified by ${\bf l}$ changes with radius.
" The warp amplitude may be characterised using the dimensionless parameter c. where The dise thickness is //=¢,/Q. where c, is the sound speed. and is the scale over which density and pressure change in the local 2 direction."," The warp amplitude may be characterised using the dimensionless parameter $\psi$ , where The disc thickness is $H=c_{\rm s}/\Omega$, where $c_{\rm s}$ is the sound speed, and is the scale over which density and pressure change in the local $z$ direction."
 The dise aspect ratio is ///22. and we shall assume that Hf.," The disc aspect ratio is $H/R$, and we shall assume that $H/R\ll 1$."
 We use the standard ?/— prescription for the dise viscosity ο. assumed here to be a standard. isotropic. Navier-Stokes viscosity: Warping disturbances ean propagate in accretion dises in two different regimes. depending on the relative importance of pressure forces and viscous forces.," We use the standard \citet{shakura73} prescription for the disc viscosity $\nu$, assumed here to be a standard, isotropic, Navier-Stokes viscosity: Warping disturbances can propagate in accretion discs in two different regimes, depending on the relative importance of pressure forces and viscous forces."
 If the dise is sufficiently thick. such that IHfIc0.then the warp propagates as a dispersive wave (2)..," If the disc is sufficiently thick, such that $H/R>\alpha$, then the warp propagates as a dispersive wave \citep{paplin95}."
 The equations of motion for a wave in the case where the dise is Keplerian and nearly inviscid are (2? where G is the disc internal torque in the horizontal plane (only).," The equations of motion for a wave in the case where the disc is Keplerian and nearly inviscid are \citep{lubow00,lubow02}
 where ${\bf G}$ is the disc internal torque in the horizontal plane (only)."
 Note that these equations are valid only in the linear approximation for small warps. and that no general non-linear theory for the wave-like regime exists as yet (but see 2)).," Note that these equations are valid only in the linear approximation for small warps, and that no general non-linear theory for the wave-like regime exists as yet (but see \citealt{ogilvie06}) )."
 Here. we are mostly interested in the case where the dise is thin and viscous. such that ////7.«a.," Here, we are mostly interested in the case where the disc is thin and viscous, such that $H/R <«\alpha$."
 In this ease. the warp propagates diffusively (2).. and can be approximately described by the equation (2) ↕⋂↾∣∏⊰∁≰↿⋯∣⊓∩⋂⋅⊓∁↾∁∏∏⊰⇂≯⇂⊾∩⇂≯⋯⊾⊓⋯⊤∙∣∣↾∩∕∕⊥↳∣∁⊰∁∏∣↴∁↾∣↧∁ standard viscous evolution of a thin and flat disc.," In this case, the warp propagates diffusively \citep{pappringle83}, and can be approximately described by the equation \citep{pringle92}
 In this equation, the terms proportional to $\nu_1$ describe the standard viscous evolution of a thin and flat disc."
" For small amplitude warps. 7,=f (and thus a,= a). but for large amplitudes 77, can be affected by the warp."," For small amplitude warps, $\nu_1=\nu$ (and thus $\alpha_1=\alpha$ ), but for large amplitudes $\nu_1$ can be affected by the warp."
 The terms proportional to vo arise whenever the disc is warped and |O1/OR|σὲ 0., The terms proportional to $\nu_2$ arise whenever the disc is warped and $|\partial{\bf l}/\partial R|\neq 0$ .
 According to Equation (5)) the warp diffuses with a diffusion coefficient #2.By analogy with the viscosity prescription (Eq. (200), According to Equation \ref{eq:pringle}) ) the warp diffuses with a diffusion coefficient $\nu_2$ .By analogy with the viscosity prescription (Eq. \ref{eq:shakura}) ))
we can define a second parameter a» sothat It is clear that thenature of theevolution of a warped accretion dise is determined mainly by the relative values of àand o».,we can define a second parameter $\alpha_2$ sothat It is clear that thenature of theevolution of a warped accretion disc is determined mainly by the relative values of $\alpha$and $\alpha_2$.
 In the case of small warp amplitude. c:« 7/2. and for viscosity such that ///Sa 1. ? have found the following relation between the two coefficient a and ae:," In the case of small warp amplitude, $\psi \ll H/R$ , and for viscosity such that $H/R \lesssim \alpha \ll 1$ \citet{pappringle83} have found the following relation between the two coefficient $\alpha$ and $\alpha_2$ :"
Ganma-Ray Dursts (GRBs) are potentially powerful probes of the early universe (e.g...1998:Mészáros&Rees2003:Darkana&Loeb 2004).,"Gamma-Ray Bursts (GRBs) are potentially powerful probes of the early universe \citep[e.g.,][]{miralda98,meszaros03,barkana04}."
. The substantial evidence that massive stellar collapses lead to long duration GRBs suggests (hat. these outbursts probably occur up to the highest redshifts of the first generation of stars (c.L.Meészáros 2003).," The substantial evidence that massive stellar collapses lead to long duration GRBs suggests that these outbursts probably occur up to the highest redshifts of the first generation of stars \citep[c.f.,][]{meszaros02,zhang03}."
. Their hieh Iumninosities make (hem detectable inprinciple out to redshifis z~100 (Lamb&Reichart 2000).. while their alterelows may be," Their high luminosities make them detectable inprinciple out to redshifts $z \sim 100$ \citep{lamb00}, , while their afterglows may be"
our Sevtert 2 sample.,our Seyfert 2 sample.
 In fact. Mackeuty.1990. las found redder disks than nuclei for |Us sample of Markarian aud NGC Sevterts. in particular for objects with amorphous or peculiar morphologies (see also Figure 16)).," In fact, \cite{kenty90} has found redder disks than nuclei for his sample of Markarian and NGC Seyferts, in particular for objects with amorphous or peculiar morphologies (see also Figure \ref{f9}) )."
 The range of his colours ancd nieciaus are comparable to our results for the IR Wari Sevferts., The range of his colours and medians are comparable to our results for the IR Warm Seyferts.
 We computed the meanο (Disk-Nucleus) colour gradients for MacIyeutys data auc find mean (5b VjeUull. (B Ry=0.09. (V.1 j-0.05.," We computed the mean (Disk-Nucleus) colour gradients for MacKenty's data and find mean $(B-V)$ =0.14, $(B-R)$ =0.09, $(V-R)$ :-0.05."
 These are coniparable with our data for the Waun Sevfert 1 aperture colour gracicuts (Table 1))., These are comparable with our data for the Warm Seyfert 1 aperture colour gradients (Table \ref{tab1}) ).
 However. M.aclveuty’s definition of nuclear and total apertiue colours ds different than ours; which makes this οςnuparison less mieanineful.," However, MacKenty's definition of nuclear and total aperture colours is different than ours, which makes this comparison less meaningful."
 Tt is dificult to quantitatively interpr‘ot our results. even the multiplicity of factors that can affect the colours within a galaxy.," It is difficult to quantitatively interpret our results, given the multiplicity of factors that can affect the colours within a galaxy."
 Colour eracdicuts that are omnuauiv due to dust extinction are positive inwards at any given waveleueth. but their uxphology iux nagnitude will depend ou the amount aud distribution of the dust.," Colour gradients that are primarily due to dust extinction are positive inwards at any given wavelength, but their morphology and magnitude will depend on the amount and distribution of the dust."
 Assmniug some eiven dust properties. he colour eradieuts should then have simular overal uorphologies at all wavelengths. but the slopes wil vouch steeper at shorter waveleugths (larger optica depths).," Assuming some given dust properties, the colour gradients should then have similar overall morphologies at all wavelengths, but the slopes will be much steeper at shorter wavelengths (larger optical depths)."
 Moreover. because these slopes are likely to je stronglv affected by stellar populalon (age ae uetallicitv) eradieuts as well the latter effects are setter explored in the ucar-IR where coour eracicuts are lnore insensitive to dust.," Moreover, because these slopes are likely to be strongly affected by stellar population (age and metallicity) gradients as well, the latter effects are better explored in the near-IR where colour gradients are more insensitive to dust."
 Withoit such near-IR data it is impossible to discrimimate between stellar population aud dust as sources o ‘the observed optical colour eradicuts., Without such near-IR data it is impossible to discriminate between stellar population and dust as sources of the observed optical colour gradients.
 Even with jcmr-IR. data. metallicitv aud extinetion could still o degenerate and other types of data. such as hieh resolution spectra and/or resolved images recdwarels of the uear-IB. are necessary to settle the question nambignously.," Even with near-IR data, metallicity and extinction could still be degenerate and other types of data, such as high resolution spectra and/or resolved images redwards of the near-IR, are necessary to settle the question unambiguously."
" Many systematic studies of star formation rates (SER) in spiral galaxies show that the variation of optical colours aud Ho properties through the ITubble sequence is due to different birthrate hiistorics in the ealactic disks: carly type (50-50). σαaxies formed. most of their stars in less than fjr,blle- but late type systems (Sce-hr) form stars in a constaut rate since thei birth aud will continue to orn stars for several Cyr I&euuicuttetal.1991. aud references therein)."," Many systematic studies of star formation rates (SFR) in spiral galaxies show that the variation of optical colours and $\alpha$ properties through the Hubble sequence is due to different birthrate histories in the galactic disks: early type (S0-Sb) galaxies formed most of their stars in less than $_{Hubble}$, but late type systems (Sc-Irr) form stars in a constant rate since their birth and will continue to form stars for several Gyr \cite{kennicutt94} and references therein)."
 Modeling of the broad baud colours is a very useful tool in this respect. providing hat one uses disk colours that are unaffected by the old spheroidal component. rather than inteerated colours.," Modeling of the broad band colours is a very useful tool in this respect, providing that one uses disk colours that are unaffected by the old spheroidal component, rather than integrated colours."
 This approach was used by a uunber of workers. m order to study normal galaxies.," This approach was used by a number of workers, in order to study normal galaxies."
 Ieunicuttetal.L99L aud Devereux&YoungL991 sugeested that chanecs in photometric properties along the IIubble sequence are purely due to the evolutionary (star formation) historv of disks and nearly independent of the chaneing B/D ratio.," \cite{kennicutt94} and \cite{devereux91}
 suggested that changes in photometric properties along the Hubble sequence are purely due to the evolutionary (star formation) history of disks and nearly independent of the changing $B/D$ ratio."
 Ikeunicuttetal.1991 found that the observed properties of disks involve au initial mass function (AIF) which is enriched im massive stars by factors 2-3 over the solar neighborhood IMEs of Miller&Scalo1979 aud Scalo1986.., \cite{kennicutt94} found that the observed properties of disks involve an initial mass function (IMF) which is enriched in massive stars by factors 2-3 over the solar neighborhood IMFs of \cite{miller79} and \cite{scalo86}.
 Te also found that a finite-time reevchue of the eas (returned from stars or/aud through interactions) increases the life-time of the eas up to 5-15 Cor (compared to 3 Corr for instantaneous reevcling)., He also found that a finite-time recycling of the gas (returned from stars or/and through interactions) increases the life-time of the gas up to 5-15 Gyr (compared to 3 Gyr for instantaneous recycling).
 Au important conchision reached by IKeuuicutt was that the disk SFR per unit luminosity changes dramatically through the Iubble sequence (0.01-0.1 in Sa-Sb. 0.5-2 in Sc). while this change is much VAmaller within individual disks.," An important conclusion reached by Kennicutt was that the disk SFR per unit luminosity changes dramatically through the Hubble sequence (0.01-0.1 in Sa-Sb, 0.5-2 in Sc), while this change is much smaller within individual disks."
 The opposite however was fod to be true for the (icaiaud radial respectively) isk surface densitics., The opposite however was found to be true for the (mean and radial respectively) disk surface densities.
 These two fiudiugs sugecst that what determines the SFR in galactic disks is not nerely the local eas surface density., These two findings suggest that what determines the SFR in galactic disks is not merely the local gas surface density.
 DeJong1996 found for his sample of face-ou spirals. that their radial colour gradients are matched by cdiffercuces in je star formation (SFIT) within a galaxy.," \cite{jong96c} found for his sample of face-on spirals, that their radial colour gradients are matched by differences in the star formation (SFH) within a galaxy."
 The outer parts are populated by voung stars. while 1e red colours of the central regions require a range of -yetallicities iu a relatively old stellar population.," The outer parts are populated by young stars, while the red colours of the central regions require a range of metallicities in a relatively old stellar population."
 Bell&DeJong1999. have reached a different couclusiou iin Ixeunicuttetal.199[.. sugecstingOO that. in spiral ealaxies. the local surface density is tle most iuportant xuwanmeter in determining the star formation historv and together with the ealaxy mass. the ealaxws chemical evolution.," \cite{jong99} have reached a different conclusion than \cite{kennicutt94}, suggesting that, in spiral galaxies, the local surface density is the most important parameter in determining the star formation history and together with the galaxy mass, the galaxy's chemical evolution."
 Iu this section we are goiug to investigate the stellar. population- content of our sample galaxies. based ou their IR properties aud our optical photomietry results.," In this section we are going to investigate the stellar population content of our sample galaxies, based on their IR properties and our optical photometry results."
" Optical aud IR huuinositics measure star formation over slightly different time periods: the Πα emission is nudnlv due to ionization by voung stars (El vi) while the IR huwinosity is a measure of star formation over the past 105-10), ", Optical and IR luminosities measure star formation over slightly different time periods: the $\alpha$ emission is mainly due to ionization by young stars $\leq$ $^{7}$ yr) while the IR luminosity is a measure of star formation over the past $^{8}$ $^{9}$ yr.
We have calculated approximate SFRs for our objects. based on their far-IR (260 421) hinunosities.," We have calculated approximate SFRs for our objects, based on their far-IR $\geq$ 60 $\mu$ m) luminosities."
 We use the standard formula, We use the standard formula
"automatically in the marginalization procedure, its effect will be present in any model selection calculation.","automatically in the marginalization procedure, its effect will be present in any model selection calculation."
 Note: no Occam factors arise in parameter estimation problems., Note: no Occam factors arise in parameter estimation problems.
 Parameter estimation can be viewed as model selection where the competing models have the same complexity so the Occam penalties are identical and cancel out., Parameter estimation can be viewed as model selection where the competing models have the same complexity so the Occam penalties are identical and cancel out.
 The MCMC algorithm produces samples which are in proportion to the posterior probability distribution which is fine for parameter estimation but one needs the proportionality constant for estimating the model marginal likelihood., The MCMC algorithm produces samples which are in proportion to the posterior probability distribution which is fine for parameter estimation but one needs the proportionality constant for estimating the model marginal likelihood.
 Clydeetal.(2006) recently reviewed the state of techniques for model selection from a statistics perspective and Ford&Gregory(2006) have evaluated the performance of a variety of marginal likelihood estimators in the extrasolar planet context., \citet{Clyde2006} recently reviewed the state of techniques for model selection from a statistics perspective and \citet{FordGregory2006} have evaluated the performance of a variety of marginal likelihood estimators in the extrasolar planet context.
pprofiles.,profiles.
 These include the effect of pointing offsets and baseline fitting., These include the effect of pointing offsets and baseline fitting.
" Flux loss due to this effect must be somewhere between € (GBT, ?)) and (Arecibo circular feed, ?))."," Flux loss due to this effect must be somewhere between $\lesssim$ (GBT, \citealt{1998AJ....115...62H}) ) and (Arecibo circular feed, \citealt{1984AJ.....89..758H}) )."
" If the profile were initially symmetric, then the induced asymmetry parameter by this effect would be in the range Arrratio < 1.02 — 1.11, if all flux loss is located either in the receding or approaching sides."," If the profile were initially symmetric, then the induced asymmetry parameter by this effect would be in the range $A_{flux~ratio}$ $<$ 1.02 – 1.11, if all flux loss is located either in the receding or approaching sides."
" Because we have data from different telescopes, our situation is probably intermediate between both cases."," Because we have data from different telescopes, our situation is probably intermediate between both cases."
" We assume that the resulting Ayj,;atio distribution of a sample with symmetric pprofiles observed under similar conditions as our sample is likely well represented by a half-Gaussian with a c = 0.04.", We assume that the resulting $A_{flux~ratio}$ distribution of a sample with symmetric profiles observed under similar conditions as our sample is likely well represented by a half-Gaussian with a $\sigma$ = 0.04.
 The baseline fitting process can also produce artificial asymmetries in the pprofiles (?).., The baseline fitting process can also produce artificial asymmetries in the profiles \citep{1998AJ....115...62H}.
 ? indicate that different order fits show flux differences of about3%., \citet{1998AJ....115...62H} indicate that different order fits show flux differences of about.
". As a result, the asymmetry parameter for symmetric pprofiles can be altered up to Afxratio = 1.06."," As a result, the asymmetry parameter for symmetric profiles can be altered up to $A_{flux~ratio}$ = 1.06."
 A half-Gaussian curve with c: = 0.02 would mimic this effect well., A half-Gaussian curve with $\sigma$ = 0.02 would mimic this effect well.
" Given the random nature of these two effects, we cannot estimate their values individually, but their overall effect is taken into account in Sect."," Given the random nature of these two effects, we cannot estimate their values individually, but their overall effect is taken into account in Sect."
" f| to discuss the actual shape of the Ajj,ratio distribution in isolated galaxies because they can broaden the resulting distribution.", \ref{sec:discussion} to discuss the actual shape of the $A_{flux~ratio}$ distribution in isolated galaxies because they can broaden the resulting distribution.
 We list in Table[I] the following information: The Ανratio distribution is shown in Figure , We list in Table \ref{tab:tests-coeff} the following information: The $A_{flux~ratio}$ distribution is shown in Figure \ref{fig:lops-visual-sample}.
The best half-Gaussian to the asymmetry parameter distributionBI. is characterized by ff]a c = 0.15., The best half-Gaussian to the asymmetry parameter distribution is characterized by a $\sigma$ = 0.15.
" However, this half-Gaussian fit is not able to reproduce the Ay;,,;ario distribution both at the high and low ends."," However, this half-Gaussian fit is not able to reproduce the $A_{flux~ratio}$ distribution both at the high and low ends."
" First there is an excess of high values of Arj,ratio with respect to the Gaussian curve, and second, the peak of the distribution is too flat for Afixratio « 1.15."," First there is an excess of high values of $A_{flux~ratio}$ with respect to the Gaussian curve, and second, the peak of the distribution is too flat for $A_{flux~ratio}$ $<$ 1.15."
" We show in a and b the AA(rms) and AA(mean distributions, Figurerespectively."," We show in Figure \ref{fig:uncertainty} $a$ and $b$ the $\Delta A$ and $\Delta A$ distributions, respectively."
"[6] The combined effect of all the previous uncertainties, AAfiuxratio (including the small contribution of AA(pointingof f'set)), is shown in Figure 6 c."," The combined effect of all the previous uncertainties, $ \Delta A_{flux~ratio}$ (including the small contribution of $\Delta A (pointing~offset)$ ), is shown in Figure \ref{fig:uncertainty} $c$."
 We show the best Gaussian fits to the distributions., We show the best Gaussian fits to the distributions.
 We compare the asymmetry visual classification of the pprofiles (Sect. p-Tp , We compare the asymmetry visual classification of the profiles (Sect. \ref{sub:visual}) )
with the gj;ratio in Figure [I3]., with the $_{flux~ratio}$ in Figure \ref{fig:lops-visual-sample-histo-symmetry}.
" Three clearly distinct ΑΙratio distributions are seen for those galaxies visually classified as symmetric, slightly asymmetric, and strongly asymmetric (Sect. B-Tp)."," Three clearly distinct $_{flux~ratio}$ distributions are seen for those galaxies visually classified as symmetric, slightly asymmetric, and strongly asymmetric (Sect. \ref{sub:visual}) )."
" The Afiyxratio distribution of pprofiles visually classified as symmetric has a mean value equal to 1.08, with a standard deviation of 0.065."," The $A_{flux~ratio}$ distribution of profiles visually classified as symmetric has a mean value equal to 1.08, with a standard deviation of 0.065."
" The distribution for the slightly asymmetric pprofiles is characterized by a larger mean of 1.13 and a similar standard deviation, 0.09."," The distribution for the slightly asymmetric profiles is characterized by a larger mean of 1.13 and a similar standard deviation, 0.09."
" The distribution of strongly asymmetric profiles is characterized by a mean of 1.37 and a considerably larger scatter, 0.17, with values as high as Aftuxratio = 1.8."," The distribution of strongly asymmetric profiles is characterized by a mean of 1.37 and a considerably larger scatter, 0.17, with values as high as $A_{flux~ratio}$ $=$ 1.8."
 The Afinxratio distribution for the slightly asymmetric subsample partially overlaps with those of the symmetric and asymmetric distributions., The $A_{flux~ratio}$ distribution for the slightly asymmetric subsample partially overlaps with those of the symmetric and asymmetric distributions.
" The large overlap that exhibits the Afj.ratio distribution for each visually classified subsample is not surprising, because this visual classification is of course subjective, and because the Afixratio parameter misses a few cases where the shape of a real asymmetric profile does not correspond to different areas in the approaching and receding sides."," The large overlap that exhibits the $A_{flux~ratio}$ distribution for each visually classified subsample is not surprising, because this visual classification is of course subjective, and because the $A_{flux~ratio}$ parameter misses a few cases where the shape of a real asymmetric profile does not correspond to different areas in the approaching and receding sides."
 Future work would require to inspect other asymmetry parameters that are sensitive to flag these profiles as asymmetric., Future work would require to inspect other asymmetry parameters that are sensitive to flag these profiles as asymmetric.
 The shape of the Afiyxratio distribution might be affected by artificially induced values from the effects explained in Sect. B.2.T]., The shape of the $A_{flux~ratio}$ distribution might be affected by artificially induced values from the effects explained in Sect. \ref{sec:meanvel}.
" By reducing the net uncertainty in the asymmetry measurement, we reduce errors that might bias our results."," By reducing the net uncertainty in the asymmetry measurement, we reduce errors that might bias our results."
 We show in Figure[I9] hhow the Arj;ratio distribution changes for different AAfiyxratio limits., We show in Figure \ref{fig:cleaning} how the $A_{flux~ratio}$ distribution changes for different $\Delta$$A_{flux~ratio}$ limits.
" The smaller the limit (i.e, only including accurate values of Ayi, ratio), the better a half-Gaussian reproduces the distribution."," The smaller the limit (i.e., only including accurate values of $A_{flux~ratio}$ ), the better a half-Gaussian reproduces the distribution."
" From now on we choose those pprofiles with AAfixpatio < 0.05, namely the rrefined subsample, to remove from our statistical analysis those profiles with an uncertain determination of the asymmetry index."," From now on we choose those profiles with $\Delta$$A_{flux~ratio}$ $<$ 0.05, namely the refined subsample, to remove from our statistical analysis those profiles with an uncertain determination of the asymmetry index."
 With this criterion we still have a large sample of N = 166 galaxies., With this criterion we still have a large sample of $N$ = 166 galaxies.
" The basic property distributions (velocity, morphological type, Lg and Lr;g) of the rrefined subsample are shown in Figure[I] as (blue) solid lines, in comparison to those of the ssample."," The basic property distributions (velocity, morphological type, $L_B$ and $L_{FIR}$ ) of the refined subsample are shown in Figure \ref{fig:characterization} as (blue) solid lines, in comparison to those of the sample."
 In order to characterize the intrinsic scatter of the asymmetry parameter distribution in a sample of isolated galaxies with minor contamination of artificially asymmetric pprofiles we fitted a half-Gaussian function to the rrefined subsample (Fig D0))., In order to characterize the intrinsic scatter of the asymmetry parameter distribution in a sample of isolated galaxies with minor contamination of artificially asymmetric profiles we fitted a half-Gaussian function to the refined subsample (Fig \ref{fig:GaussFit}) ).
 The fit yields a width of σ =, The fit yields a width of $\sigma$ =
The LS periodogram is now increasingly being used in Doppler velocity. planet searches where. however. circular orbits (giving rise to sinusoidal velocity curves) are not common (?)..,"The LS periodogram is now increasingly being used in Doppler velocity planet searches where, however, circular orbits (giving rise to sinusoidal velocity curves) are not common \citep{BWM06}."
 Ht therefore makes more sense to fit Ixeplerians ο data instead. of sinusoids as discussed by 2., It therefore makes more sense to fit Keplerians to data instead of sinusoids as discussed by \citet{Cumming04}.
7 As orbital eccentricity is. an important parameter in a Weplerian function. we have expanded the traditional LS periodogram. o include two dimensions — that is. to examine power as a 'unction of both period and eccentricity.," As orbital eccentricity is an important parameter in a Keplerian function, we have expanded the traditional LS periodogram to include two dimensions – that is, to examine power as a function of both period and eccentricity."
 We call this the 2D Ixeplerian LS (2DIXLS) periodogram., We call this the 2D Keplerian LS (2DKLS) periodogram.
 The method we use to calculate the 2DIXLS periodogram was brielly discussed in 7 and is described in more detail below., The method we use to calculate the 2DKLS periodogram was briefly discussed in \citet{OBT07} and is described in more detail below.
 The 2DILS is an extension of the traditional Lomb-Scargle periodosram. where we vary period.and eccentricity in the calculation of power. (," The 2DKLS is an extension of the traditional Lomb-Scargle periodogram, where we vary period eccentricity in the calculation of power. ("
While the argument of. pericenter. w. ds also important in cetermuining the of the velocity. curve. it does impact the orbital period measurement in the same way as eccentricity.),"While the argument of pericenter, $\omega$, is also important in determining the of the velocity curve, it does impact the orbital period measurement in the same way as eccentricity.)"
" This is also an extension of the one dimensional Keplerian Lomb-Scarele periodogram introduced hy ον,", This is also an extension of the one dimensional Keplerian Lomb-Scargle periodogram introduced by \citet{Cumming04}.
 We find. however. that not fixing cecentricity. while more. ellicient computationally. allows for possible non-physical values (ic. outside the range 0-1).," We find, however, that not fixing eccentricity, while more efficient computationally, allows for possible non-physical values (i.e. outside the range 0-1)."
" Phe ""smoothness"" of the periodogram also depends a lot more on the initial guesses for the free. parameters.", The “smoothness” of the periodogram also depends a lot more on the initial guesses for the free parameters.
" We use a erid of fixed. periods and eccentricities to calculate the 2DIXLS. with e=O0.98 in steps of 0.01. ancl periods on a logarithmic scale from 1 day up to the maximum possible period of interest for that data sequence (in most cases 4500 days for current AAPS data) onaspacingof 10.? in log,P."," We use a grid of fixed periods and eccentricities to calculate the 2DKLS, with $e=0-0.98$ in steps of 0.01, and periods on a logarithmic scale from 1 day up to the maximum possible period of interest for that data sequence (in most cases 4500 days for current AAPS data), on a spacing of $10^{-3}$ in $\log_{\mathrm{10}}P$."
 A Weplerian described by Equation 1 is then fitted to the data using a non-linear least squares fitting routine with Levenberg-Mrequardt minimisation from ?.., A Keplerian described by Equation \ref{eq:kepler} is then fitted to the data using a non-linear least squares fitting routine with Levenberg-Marquardt minimisation from \citet{Press86}.
 Llere A is the semi-amplitude. v(f) is the true anomaly involving implicit dependence on the orbital period 7? and the time of periastron passage {νι and Yo is the velocity zero-point.," Here $K$ is the semi-amplitude, $\nu(t)$ is the true anomaly involving implicit dependence on the orbital period $P$ and the time of periastron passage $T_{\mathrm{p}}$, and $V_{\mathrm{0}}$ is the velocity zero-point."
 The true anomaly is derived by solving Kepler's equation AZ(/)=E(I)esinfe(P) where E(1) is the eccentric anomaly and AZ(/)=2sz//P is the mean anomaly., The true anomaly is derived by solving Kepler's equation $M(t)=E(t)-e\sin E(t)$ where $E(t)$ is the eccentric anomaly and $M(t)=2\pi t/P$ is the mean anomaly.
 The oower. 2(2ο). is determined. using (1ο=AY?t=(NunVies) 4. where Vike is the eoocness-ol-Lit for the yest fit Keplerian model. and. xiu is the equivalent for a constant fit to the data.," The power, $z(P,e)$, is determined using $z(P,e)=\Delta\chi^2/4=(\chi^2_{\mathrm{mean}}-\chi^2_{\mathrm{Kep}})/4$ , where $\chi^2_{\mathrm{Kep}}$ is the goodness-of-fit for the best fit Keplerian model, and $\chi^2_{\mathrm{mean}}$ is the equivalent for a constant fit to the data."
 For cach value of 2 and e we find he values of the remaining parameters that minimise T and therefore maximise (12.ο).," For each value of $P$ and $e$ we find the values of the remaining parameters that minimise $\chi^2_{\mathrm{Kep}}$ and therefore maximise $z(P,e)$."
 As discussed by. 2.. when he noise level is not known in advance (1.6. for observations) z(P.60) must be normalised. in the 2DINLS case by Mise," As discussed by \citet{Cumming04}, when the noise level is not known in advance (i.e. for observations) $z(P,e)$ must be normalised, in the 2DKLS case by $\chi^2_{\mathrm{Kep}}$."
 This orm of the 2DINLS was implemented by 2? and is used in he next section., This form of the 2DKLS was implemented by \citet{OBT07} and is used in the next section.
 For the purposes of the simulations in this xaper (described in Section 3)). the power is not normalised. »ecause the noise level is an input parameter and is therefore known in advance.," For the purposes of the simulations in this paper (described in Section \ref{sec:simul}) ), the power is not normalised, because the noise level is an input parameter and is therefore known in advance."
 The 2DIXLS has several advantages over the traditional LS periodogram., The 2DKLS has several advantages over the traditional LS periodogram.
 First. it is sensitive to high-eccentricity Xanets. which the traditional LS periodogram is not (as we show with an example in Section 2.2)).," First, it is sensitive to high-eccentricity planets, which the traditional LS periodogram is not (as we show with an example in Section \ref{sub:hd20782}) )."
 Second because the Ixeplerian functional form fitted bv the 2DINLS is a better representation of real orbits. the peak in the 2DINLS power," Second because the Keplerian functional form fitted by the 2DKLS is a better representation of real orbits, the peak in the 2DKLS power"
Dark enerev (DE) is arguably the most important physics problem of the 21st century. with major implications for astronomy. fundamental physics. and perhaps even philosophy.,"Dark energy (DE) is arguably the most important physics problem of the 21st century, with major implications for astronomy, fundamental physics, and perhaps even philosophy."
 Unfortunately. a variety of bureaucratic and sociological [orees on several continents are now driving toward a dark energv mega-mission that would simullaneously attack this problem on 3 fronts: weak lensing (WL). baryon acoustic oscillations (DAO) and supernovae (SN).," Unfortunately, a variety of bureaucratic and sociological forces on several continents are now driving toward a dark energy mega-mission that would simultaneously attack this problem on 3 fronts: weak lensing (WL), baryon acoustic oscillations (BAO) and supernovae (SN)."
 If adopted. (his course of action. will produce an utter disaster. delaving progress on a crucial frontier of science for many decades.," If adopted, this course of action will produce an utter disaster, delaying progress on a crucial frontier of science for many decades."
 While the science goals of these 3 experiments are complementary. (he instrumentation is not. and hence the costs and engineering complexity are bound (ο spiral out of control.," While the science goals of these 3 experiments are complementary, the instrumentation is not, and hence the costs and engineering complexity are bound to spiral out of control."
 Moreover. we are entering an era of severe financial crisis when such exponentiating costs simply will not be tolerated.," Moreover, we are entering an era of severe financial crisis when such exponentiating costs simply will not be tolerated."
 The siren call leading to this disaster is that only by obtaining agreement among 3 independent DE measurements. each with its own systematics. will it be possible to solve the DE problem.," The siren call leading to this disaster is that only by obtaining agreement among 3 independent DE measurements, each with its own systematics, will it be possible to solve the DE problem."
" This is nonsense: DE will not be ""solved"" by (his meea-mission. nor 2 or 3 of them."," This is nonsense: DE will not be “solved” by this mega-mission, nor 2 or 3 of them."
 It will dominate 21st century physics., It will dominate 21st century physics.
 The missions currently conceived will at best olfer some initial clues., The missions currently conceived will at best offer some initial clues.
WALAP offers a lar better model for attacking such a scientifically compelling ancl technologically challenging problem: faster. cheaper. “better”.," offers a far better model for attacking such a scientifically compelling and technologically challenging problem: faster, cheaper, “better”."
" I have put. ""better"" in quotes", I have put “better” in quotes
The presence of a cold gas embedded in a hot gas is a common phenomenon.,The presence of a cold gas embedded in a hot gas is a common phenomenon.
 This situation occurs in many astrophysical systems. such as the interstellar medium (ISAT). the intracluster gas in galaxy clusters (ICAL). AGNs and Lyman à systems.," This situation occurs in many astrophysical systems such as the interstellar medium (ISM), the intracluster gas in galaxy clusters (ICM), AGNs and Lyman $\alpha$ systems."
 “Phese multi temperature-density configurations were and still are the subject. of intensive heoretical stuck., These multi temperature-density configurations were and still are the subject of intensive theoretical study.
 Field (1965) carried out a linear stability analvsis of optically thin. collision dominated: magnetized jxasma.," Field (1965) carried out a linear stability analysis of optically thin, collision dominated magnetized plasma."
 He found the critical wavelength (the Field length) hat distinguishes perturbation wavelengths that form cold clumps from those that don't., He found the critical wavelength (the Field length) that distinguishes perturbation wavelengths that form cold clumps from those that don't.
 Perturbation wavelengths shorter than the Field length are heated by heat-conduction and fail to form cold clumps whereas the longer perturbation wavelengths. are cooled. enough bv. radiation losses to condense into cold. clumps., Perturbation wavelengths shorter than the Field length are heated by heat-conduction and fail to form cold clumps whereas the longer perturbation wavelengths are cooled enough by radiation losses to condense into cold clumps.
 The Field length retains its qualitative role in the non-linear regime (Cowie Songaila 1977: Cowie Melxee 1977: Melxee Cowie 1977)., The Field length retains its qualitative role in the non-linear regime (Cowie Songaila 1977; Cowie McKee 1977; McKee Cowie 1977).
 At large Ixnudsen numbers there is heat-Iiux saturation., At large Knudsen numbers there is heat-flux saturation.
 This is considered by Cowie Melxee. (1977)... Balbus Melee (1982). Slavin Cox (1992). and. Dalton 3albus (1993).," This is considered by Cowie McKee (1977), Balbus McKee (1982), Slavin Cox (1992), and Dalton Balbus (1993)."
 Chun Rosner (1993) consider the effects of a non-local Alaxwellian electron. distribution on Fields analysis. anc Bandiera Chan (1994a.b) generalize their work and emphasize the role of the non-local thermoclectric ellect in thermal evaporation processes.," Chun Rosner (1993) consider the effects of a non-local Maxwellian electron distribution on Field's analysis, and Bandiera Chan (1994a,b) generalize their work and emphasize the role of the non-local thermoelectric effect in thermal evaporation processes."
 Apart from. the details considered. in these works. the Field length retains is qualitative and quantitative role.," Apart from the details considered in these works, the Field length retains its qualitative and quantitative role."
 MI. the collision dominated plasma theories predict that scales smaller than the Field. leneth evaporate (heated)., All the collision dominated plasma theories predict that scales smaller than the Field length evaporate (heated).
 For typical SM. or ICM. parameters. the thermal evaporation theory precicts a hotter ISM and ICM than what is actually observed.," For typical ISM or ICM parameters, the thermal evaporation theory predicts a hotter ISM and ICM than what is actually observed."
 This is also the case for Lyman-a systems and the standard AGN model., This is also the case for $\alpha$ systems and the standard AGN model.
 For the 1981. Melxee. Ostriker (1977). proposed that the observed. gas is constantly replenished by supernovae explosions.," For the ISM, McKee Ostriker (1977) proposed that the observed gas is constantly replenished by supernovae explosions."
 Llowever. this does not necessarily apply to other astrophysical environments in. which cold and hot gas are observed to co-exist.," However, this does not necessarily apply to other astrophysical environments in which cold and hot gas are observed to co-exist."
 In broad line emission regions surrounding quasistcllar objects. (Begcleman AMelxee 1990: Melxee DBegeleman 1990) cold and hot σας coexist. bu the presence of a small scale replenishment," In broad line emission regions surrounding quasistellar objects (Begeleman McKee 1990; McKee Begeleman 1990) cold and hot gas coexist, but the presence of a small scale replenishment"
Taking the spatial correlation funcüon of the intensity scintillation to be a simple [function of a equadratie form in orthogonal transverse coordinates. the resulting ISS time scale is: where lor the ellipse specified as above. the coefficients of the quadratic form are a= ≸↽↔↴≼↲∪∐∐↲∏⋅↥≺∢∐∐↲≀↧↴∐⊳∖⇁↕↽≻≀↧↴∐≀↧↴↥⊳∖⇁≺∢≀↧↴↥≼↲∪∐∖∖↽∐↕≺∢∐⊔∐↲↥∐∥↲∐⊳∖⊽∐⋡∖↽≺∢∪↕⋅↕⋅≼↲↥≀↧↴∐∪∐↓⋟≀↧↴∐⊳∖⊽↥∪⊥∕∕∕≼↲⋅⊏≺↥∏≀↧↴∐∪∐⊔↕⋝↕⊔⊳∖⇁-9/2 ⋅∙∕⊾ ∙ ∐⋯↴↥↥∐↲∐↓≀↧↴∐≺∢≀↧↴∐∡∖↽⊔∐↲⋝∖⊽≀↧↴∐∐↲≀↧↪∖⇁≼↲≺⇂∏≀↧↴∐∪∐≼⋝⊑↽⊰↕⋟∪↓⋡∐↕≸≟∐≀↧↴∐≼↲↥≀↧↴↥⋅⋜⋝∃∩∪≺≨⇄⋝⋅⋅ ↴∏∐↲↕⋅⋯∐∪∪∣↽≻⊳∖⇁≼↲↕⋅∖↽≀↧↴∐∪∐⋝∖⊽≀⋯↲↥⋡∖↽↕↽≻↕≺∢≀↧↴∐∡∖↽≀↧⊔∖⇁≼↲↥∪↓≯∣↥⋝∖∖∖↽≼↲↕⋅⊳∖⇁∏⊳∖⇁≼⇂≀⋯↲∐∐↲≀↧↪∖⊽⋯⋅≼↲∐,"Taking the spatial correlation function of the intensity scintillation to be a simple function of a quadratic form in orthogonal transverse coordinates, the resulting ISS time scale is: where for the ellipse specified as above, the coefficients of the quadratic form are $a = {\cos}^2 \theta_{A}/A + A {\sin}^2 \theta_{A}$ , $b = {\sin}^2 \theta_{A}/A + A {\cos}^2 \theta_{A}$ , $c = 2{\sin}\theta_{A} {\cos}\theta_{A}(1/A - A)$, and $s_{\rm iss}$ is the geometric mean spatial scale on which the intensity correlation falls to 1/e. Equation \ref{eq:tiss}) ) is mathematically the same as equation (3) of \citet{Bignall2006}."
∐↲↕∐⋝∖⊽⋅≀↧↪∖⊽⊳∖⊽∐⋯∖↽∐∣↽≻∡∖⇁ ⊔∐↲↕↽≻∪↕∐↥⋟∖⊽↕∐⊔∐↲↥≼↲∐↥⋯↴∐≼⇂↕↽≻≀↕↴∐≼↲↥⋟∖⊽∪↓⋟∏≸↽↔↴⋯⋅≼↲⋟∖⊽⊑⊰⋅⋅∔≀↧↴∐≼⇂↱≻⋅⋅↴⊺∐≼↲⇂∎↓⊔↕∐≸≟↥≀↧⊔∖⊽↳↽↕⋟∖⊽↥∪⇂∎↓∐≺⊔↥∐↲⊔∐⋅≼↲≼↲ ↕⊳↔⊲⊳↔⊲↕↽≻≀↧↴↕⋅≀↧↴∐∐↲∥↲↕⋅⊳∖⊽≼⋝⇀∣↥⋅∣⇥↼↘⋅↼⇁⋅↥⋝∖∖⇄⋝≀↧," The radio observations are typically a set of $t_{\rm iss}$ versus date measurements, as shown by the points in the left hand panels of Figures \ref{fig:1257}, \ref{fig:1519} and \ref{fig:1819}."
↴∐≼⇂⊔∐↲↥∖∖⊽∪↕↽≻↥≀↧⊔∖⇁∐↓≀↧↴∖↽≼↲↥∪≺∢∐↕≼↲⊳∖⇁≼⋝⊔⋝∖↓⊔∡⊓⋅↖⊽↥⊓↓⊔∡∪⋅↕⋝⊔↥≀↧↴↥≸↽↔↴↥∖↽≼↲⊔∐↲∣↽≻≼↲⋝∖⊽↥ ∐↥∏⊳∖⊽↕∐↖⊂↽↔↴⊔∐⋝∖⊽∐↓⋯⇂≼↲↥≼↲≺↥∏≀↧↴∐∪∐⋅∐≺∢≀↧↴∐∣↽≻≼↲⊳∖⊽∐⋯∖↽∐⊔⋯↴↥⊔∐↲↕⋅≼↲≀↧↴↕⋅≼↲↓∎↓∖↽≼↲↕∐≼⇂≼↲↕↽≻≼↲↕∐⇂≼↲↕∐≺∢∪≼↲∐∎↓≺∢↕≼↲∐↥⊳∖⊽↕∐," .The fitting task is to find the three ISS parameters $A$, $\theta_{A}$, $s_{\rm iss}$ ) and the two plasma velocities $V_{{\rm ism},\alpha},V_{{\rm ism},\delta}$ ) that give the best fit using this model equation."
 ⊔∐↲≸↽↔↴≼↲↕∐↲↕⋅≀↧↴↥≺∢≀↧↪∖⊽≼↲⋅∣↽≻⋯⊔⋯↴↥⊔∐↲↓∎↓∖↽≼↲↕↽≻∐∡∖⇁⊳∖⊽↕≺∢≀↧↴↥↕↽≻≀↧↴↕⋅≀↧↴↕∐≼↲∥↲↕⋅⊳∖⇁≺⇂≼↲↕↽≻≼↲∐≼⇂∐∪∐∐∐≼↲≀↧↴↕⋅↥∡∖↽∪∐⊔∐↲∣↥⋝∖∖≼⇂≀↧↴↥≀↧↴ aad so cannot be estimated independently.," It can be shown that there are five independent coefficients in the general case, but that the five physical parameters depend nonlinearly on the $t_{\rm iss}$ data and so cannot be estimated independently."
 Thus. while we fitted for the best of these five parameters. we also investigated the error surface by stepping through a grid of values for (Viana Vias) and at each step fitting for the remaining three ISS parameters: we constrained (he axial ratio to be less than 10. since the fit becomes degenerate for very large axial ratios. in a fashion similar to that used by Dennett-Thorpe&deDruvn(2003).," Thus, while we fitted for the best of these five parameters, we also investigated the error surface by stepping through a grid of values for $V_{{\rm ism},\alpha},V_{{\rm ism},\delta}$ ) and at each step fitting for the remaining three ISS parameters; we constrained the axial ratio to be less than 10, since the fit becomes degenerate for very large axial ratios, in a fashion similar to that used by \citet{Dennett2003}."
. The right hand panels of the same figures show that for all three sources there is a satisfactory. Π in an extended vallev in ISM velocity space., The right hand panels of the same figures show that for all three sources there is a satisfactory fit in an extended valley in ISM velocity space.
 PIS Bl257326 is a flat spectrum. radio-loud quasar al 2=1.256 that exhibits HIV al frequencies of several Gllz (Bienalletal.2003.2006).," PKS B1257–326 is a flat spectrum, radio-loud quasar at $z = 1.256$ that exhibits IHV at frequencies of several GHz \citep{Bignall2003, Bignall2006}."
. Figure 3. (left) shows the Iss lime scales for PINS D1257326 observed on different. davs in 20002003 at 4.8 Gllz bv Dignalletal.(2006). (kixdly. provided by Dr. Havlev Bignall)," Figure \ref{fig:1257} (left) shows the ISS time scales for PKS B1257–326 observed on different days in 2000–2003 at 4.8 GHz by \citet{Bignall2006}
 (kindly provided by Dr. Hayley Bignall)."
 The contours in the rieht panel show the range in (transverse velocities that lead to fits with reduced 4?—1.4., The contours in the right panel show the range in transverse velocities that lead to fits with reduced $\chi^2 < 1.4$.
 With 26 observations and fitting for three parameters. the good lit correspond to 4?<1.2.," With 26 observations and fitting for three parameters, the good fits correspond to $\chi^2 \lesssim 1.2$."
" In their analvsis of the same time scale data but also including the ISS time delays between two widely separated radio telescopes. Dignalletal.(2006). found a best combined fit at velocities V;4,,,=—49.2 aand V;,,5=11.5I. where the axial ratio was constrained to be less than 12.0."," In their analysis of the same time scale data but also including the ISS time delays between two widely separated radio telescopes, \citet{Bignall2006} found a best combined fit at velocities $V_{iss,\alpha}=-49.2$ and $V_{iss,\delta}=11.5$, where the axial ratio was constrained to be less than 12.0."
 Thev concluded that the scintillation pattern is highly elongated with anaxialratio >12. and the scattering screen is located within LO pe of the Earth.," They concluded that the scintillation pattern is highly elongated with anaxialratio $A \ge 12$, and the scattering screen is located within 10 pc of the Earth."
 We also find large axial ratios for the ISS pattern., We also find large axial ratios for the ISS pattern.
that efficient particle acceleration is possible.,that efficient particle acceleration is possible.
 The distance of 0.25 pe of the blast wave from uused here is motivated bv (he conclusion of Smith(2008) that parts of the Outer Ejecta are currently being overrun by the blast wave and by X-ray. observations. where used a ring with the same radius to describe the soft N-rav shell coincicent with the Outer Ejecta.," The distance of 0.25 pc of the blast wave from used here is motivated by the conclusion of \citet{EtaCar:Smith08} that parts of the Outer Ejecta are currently being overrun by the blast wave and by X-ray observations, where \citet{EtaCar:Seward01} used a ring with the same radius to describe the soft X-ray shell coincident with the Outer Ejecta."
 On the other hand. for a steady shock speed of 3500 km/s and an age of 161 vears. the expected distance of the blast wave to iis 0.6 pe.," On the other hand, for a steady shock speed of 3500 km/s and an age of 167 years, the expected distance of the blast wave to is 0.6 pc."
 A wind solution of the fast moving material. whieh would result in an increasing velocily with lime. could explain such a difference.," A wind solution of the fast moving material, which would result in an increasing velocity with time, could explain such a difference."
 To account for the different. distance estimates. (he spectral energy distributions (SEDs) for both values are shown in Section ??..," To account for the different distance estimates, the spectral energy distributions (SEDs) for both values are shown in Section \ref{sec:SED}."
 Dhelativistic electrons and protons will eain energy when crossing the shock front οἱ Carinass blast wave., Relativistic electrons and protons will gain energy when crossing the shock front of s blast wave.
" In the limit of a strong shock. the particle crossing time Al is determined by the diffusion coefficient &. expressed in terms of the Dohm diffusion coefficient: the shock speed vc. the particle enerev3 Ec;M and the magnetic— field in the shock region5 Brac, as: The energy gain per shock crossing is given bv NE/E=v,/c and. hence. the acceleration timescale Ty.=E/GNE/IM)gis]et: No magnetic field measurements are available in the region of the blast wave."," In the limit of a strong shock, the particle crossing time $\Delta t$ is determined by the diffusion coefficient $\kappa$, expressed in terms of the Bohm diffusion coefficient: the shock speed $v_{s}$, the particle energy $E_{\rm GeV}$ and the magnetic field in the shock region $B_{\rm \mu G}$ as: The energy gain per shock crossing is given by $\Delta E/E = v_{s}/c$ and, hence, the acceleration timescale $\tau_{\rm acc} = E/(\Delta E/\Delta t) \approx \eta\kappa / v_{s}^2$: No magnetic field measurements are available in the region of the blast wave."
 However. for theNebula different estimates exist and are used in the following as a rough euide for the magnetic field strength in the region of interest.," However, for the different estimates exist and are used in the following as a rough guide for the magnetic field strength in the region of interest."
 Aitkenetal.(1995). derived from polarization measurements. which were based on dust grain alignment. magnetic field strengths of Q((jQi mG) in theNebula. depending on the underlying process.," \citet{EtaCar:Bfield} derived from polarization measurements, which were based on dust grain alignment, magnetic field strengths of $\mu$ $m$ G) in the, depending on the underlying process."
 llowever. the dust shell of the appears to be neutralaud is likely composed of silicates and Fe rather than twpical ISM dust grains (Gailetal.2005).," However, the dust shell of the appears to be neutraland is likely composed of silicates and Fe rather than typical ISM dust grains \citep{EtaCar:Gail05}."
. Hence. for the purpose of this work. a lower magnetic field strength of 10 7G is assumed.," Hence, for the purpose of this work, a lower magnetic field strength of $10\, \mu$ G is assumed."
 In the Bobi limit and without energy losses. it would (take about a vear to accelerate an electron or proton {ο an energv of LOO GeV in a LOG field given a shock speed of 3500 km !.," In the Bohm limit and without energy losses, it would take about a year to accelerate an electron or proton to an energy of 100 GeV in a $10\,\mu G$ field given a shock speed of 3500 km $^{-1}$ ."
 This acceleration, This acceleration
reactions. such as IL + OIL,"reactions, such as H + OH."
 At? >10! vr. IHE atoms are mainly formed by cosmic ray induced photodissociation of hvdrogen molecules.," At $t > 10^{4}$ yr, H atoms are mainly formed by cosmic ray induced photodissociation of hydrogen molecules."
 At this stage the absolute abundance of the I] atom is 1 7oE independent of the gas density., At this stage the absolute abundance of the H atom is $\sim$ 1 $^{-3}$ independent of the gas density.
 We also checked the dependence of our resulis on the initial IE atom abundance: if the initial abundance is lowered by an order of magnitude. the isolopomer ratio varies only slightly.," We also checked the dependence of our results on the initial H atom abundance; if the initial abundance is lowered by an order of magnitude, the isotopomer ratio varies only slightly."
 Figure 5 shows density dependence of the CECITL/PCCIH ratio., Figure 5 shows density dependence of the $^{13}$ $^{13}$ CCH ratio.
 As the density increases. both the abundauces of electron and II atom decrease.," As the density increases, both the abundances of electron and H atom decrease."
 While the electron abundance is: proportional: to my)0.5.°. the II atom abundance- is: proportional: to Wy ," While the electron abundance is proportional to $n_{\rm H_2}^{-0.5}$, the H atom abundance is proportional to $n_{\rm H_2}^{-1}$."
:Then the peak isolopomer ratio decreases with density., Then the peak isotopomer ratio decreases with density.
 The isotopomer fractionation also affects the Isotope ratios. i.e. the CCIL/PCCII and CCIL/CUCI ratios (Figure 6).," The isotopomer fractionation also affects the isotope ratios, i.e. the $^{13}$ CCH and $^{13}$ CH ratios (Figure 6)."
 The reaction (9) enhances FC in CE CIL. while it dilutes PC in PCCIT.," The reaction (9) enhances $^{13}$ C in $^{13}$ CH, while it dilutes $^{13}$ C in $^{13}$ CCH."
 For comparison. the dashed line in Figure 6 shows the isotope ratios of CCIL in (he model without the isotopomer Iractionation: the model without the reaction (3). (4). (5). (6). (9) and (10).," For comparison, the dashed line in Figure 6 shows the isotope ratios of CCH in the model without the isotopomer fractionation: the model without the reaction (3), (4), (5), (6), (9) and (10)."
 Figure 7 shows the temporal evolution of the CÉCS/P CCS ratio., Figure 7 shows the temporal evolution of the $^{13}$ $^{13}$ CCS ratio.
 The isotopomer ratio of CCS is lower than unity in the model without the exchange reaction (10) (dashed line)., The isotopomer ratio of CCS is lower than unity in the model without the exchange reaction (10) (dashed line).
 The reactions (5) and (6) are not the main formation reactions of CCS and CCS in our model., The reactions (5) and (6) are not the main formation reactions of $^{13}$ CS and $^{13}$ CCS in our model.
 Instead. CCS is mainlv formed by the electron recombination of larger ions. such as Πορ (Figure 4).," Instead, CCS is mainly formed by the electron recombination of larger ions, such as ${\rm HC_2S^+}$ (Figure 4)."
 These reactions tend to make (he isotopomer ratio of CCS unity., These reactions tend to make the isotopomer ratio of CCS unity.
 The reaction (7) ancl (8) decreases the isotopomer ratio of CCS. because (he isolopomer ratio of CCTI is larger than unity.," The reaction (7) and (8) decreases the isotopomer ratio of CCS, because the isotopomer ratio of CCH is larger than unity."
 In the fiducial model (solid line). the isotopomer ratio is lower than unity except for very. limited periods.," In the fiducial model (solid line), the isotopomer ratio is lower than unity except for very limited periods."
 The isolopomer ratio reaches a maximum, The isotopomer ratio reaches a maximum
2.,2.
 The electron temperature of the Ile! zoue is varied in the range (Πο = (0.95 «ΤΟ 11D)., The electron temperature of the $^+$ zone is varied in the range $T_e$ $^+$ ) = (0.95 – $\times$$T_e$ (O ).
 We lave chosen this range following the work of Ciusevactal.(2006). aud Caisevactal.(2007) who have derived the electron temperature in the II! zone from the Baluer and Paschen discoutiuuties in the spectra of more than 100 II regions. and showed that 7; (OI!) differs from T.CO n) by not more than 5%.," We have chosen this range following the work of \citet{G06} and \citet{G07} who have derived the electron temperature in the $^+$ zone from the Balmer and Paschen discontinuities in the spectra of more than 100 H regions, and showed that $T_e$ $^+$ ) differs from $T_e$ (O ) by not more than ."
. We also asstuue that Te!) = Z4II!) because the I! and Ue! zones in our objects are nearly coicicent., We also assume that $T_e$ $^+$ ) = $T_e$ $^+$ ) because the $^+$ and $^+$ zones in our objects are nearly coincident.
 3., 3.
 Oxveen abundances are calculated by cousideriug two possible values of the electron temperature: 1) τν = T. (ie!) aud 2) T. = Το ur)., Oxygen abundances are calculated by considering two possible values of the electron temperature: 1) $T_e$ = $T_e$ $^+$ ) and 2) $T_e$ = $T_e$ (O ).
 L., 4.
NCCGITe |) aud £CA3889) are varied respectively iu the ranges lO — 150 P aud O 5. typical for extragalactic II regions.," $N_e$ $^+$ ) and $\tau$ $\lambda$ 3889) are varied respectively in the ranges 10 – 450 $^{-3}$ and 0 – 5, typical for extragalactic H regions."
 5., 5.
 The fraction of Πα emission due to collisional excitation is varied in the range 55... in accordance with Stasiüska&Izotov(2001) aud Luriciana (2009)..," The fraction of $\alpha$ emission due to collisional excitation is varied in the range –, in accordance with \citet{SI01} and \citet{L09a}. ."
 The fraction of IL}. IT5 aud IIó ciission due to collisional excitation Is adopted to be that of the Πα ceuission. in accordance with Luvidiana(2009)..," The fraction of $\beta$, $\gamma$ and $\delta$ emission due to collisional excitation is adopted to be that of the $\alpha$ emission, in accordance with \citet{L09a}."
 We note that Izotovetal.(2007). underestimated that fraction for jJ. adopting a value of only 1/3. and neglected. altogether to correct the Ts and IIó enüssion lines for collisional excitation.," We note that \citet{I07} underestimated that fraction for $\beta$, adopting a value of only 1/3, and neglected altogether to correct the $\gamma$ and $\delta$ emission lines for collisional excitation."
 6., 6.
 Luridiauactal.(2009) have shown that thefraction of ID) cunission due to fluorescent excitation bv the far-UV nowionizing stellar coutimmin could be as high as2%... aud somewhat lower for the Πα e1iission (their case D).," \citet{L09b} have shown that thefraction of $\beta$ emission due to fluorescent excitation by the far-UV non-ionizing stellar continuum could be as high as, and somewhat lower for the $\alpha$ emission (their case D)."
 We have adopted the conservative value of for the fraction of Πα. IDs. Tl. and Ud emission due to fluorescent excitation. since a simular effect could affect the He cussion lines aud partly compensate the effect for the Balhuer II lines (the We abundance is calculated relative to that of II).," We have adopted the conservative value of for the fraction of $\alpha$, $\beta$ , $\gamma$ and $\delta$ emission due to fluorescent excitation, since a similar effect could affect the He emission lines and partly compensate the effect for the Balmer H lines (the He abundance is calculated relative to that of H)."
 τν, 7.
 The equivalent width of the Te1i ALL absorption line is chosen to be yas(ALIT1) =LAL. following Izotovetal(2007) and GouzálezDel-eadootal. (2005).," The equivalent width of the He $\lambda$ 4471 absorption line is chosen to be $_{abs}$ $\lambda$ 4471) =, following \citet{I07} and \citet{G05}."
" The equivalent widthsof the other absorption lines are fixed according to the ratios EW,,CAMNSO) EWLLLAMITI) = 1.0. yp.(A5876) EWGLGAMITI) /= 058. ΤΝ λος) / yf ALLL) = (hl and EW,4(AT0G5) / GG CALITI) = 0.1."," The equivalent widthsof the other absorption lines are fixed according to the ratios $_{abs}$ $\lambda$ 3889) / $_{abs}$ $\lambda$ 4471) = 1.0, $_{abs}$ $\lambda$ 5876) / $_{abs}$ $\lambda$ 4471) = 0.8, $_{abs}$ $\lambda$ 6678) / $_{abs}$ $\lambda$ 4471) = 0.4 and $_{abs}$ $\lambda$ 7065) / $_{abs}$ $\lambda$ 4471) = 0.4."
" The 4,(AbSTO) pc ALLTL) and EW, ,4(AG678)} ΤΣΗΤΙ) ratios were set equal to the values mwecdicted for these ratios bv a Starburst99 (Leithercretal.1999). instantaneous burst model with an age 3%Ll Myr and a heavy clement iuass fraction Z = 001 ,00L OS and O.L respectively,"," The $_{abs}$ $\lambda$ 5876) / $_{abs}$ $\lambda$ 4471) and $_{abs}$ $\lambda$ 6678) / $_{abs}$ $\lambda$ 4471) ratios were set equal to the values predicted for these ratios by a Starburst99 \citep{L99} instantaneous burst model with an age 3-4 Myr and a heavy element mass fraction $Z$ = 0.001 – 0.004, 0.8 and 0.4 respectively."
 These values are sienificautlv higher than the corresponding ratios of 0.3 and 0.1. adopted bv Izotovetal.(2007)., These values are significantly higher than the corresponding ratios of 0.3 and 0.1 adopted by \citet{I07}.
". We vote that the value chosen for the EW,4;CADSTG) vas(A LIF1) vatio is also consistent with the one eiven w GonzálezDelgadoetal.(2005).", We note that the value chosen for the $_{abs}$ $\lambda$ 5876) / $_{abs}$ $\lambda$ 4471) ratio is also consistent with the one given by \citet{G05}.
. Since the output ielh-resolution. spectra dà Starburst99 are calculated only for wavelengths T000AÀ.. we do not have a xedictiou for the EW4:CtA7065) / ENVGLICALITI) ratio.," Since the output high-resolution spectra in Starburst99 are calculated only for wavelengths $\leq$, we do not have a prediction for the $_{abs}$ $\lambda$ 7065) / $_{abs}$ $\lambda$ 4471) ratio."
" We sot it to be equal to 0.1. the value of the DEWnCAGG78) / 4, CALITIE) ratio."," We set it to be equal to 0.4, the value of the $_{abs}$ $\lambda$ 6678) / $_{abs}$ $\lambda$ 4471) ratio."
 N., 8.
 The Ie lonization correction factor TCF(Ue! Welly is adopted from (2007).., The He ionization correction factor $ICF$ $^+$ $^{++}$ ) is adopted from \citet{I07}. .
 Two Y ΟΠ linear regresious for the IIeDCD ealaxv smuple of Izotovetal.(2007).. with the above set of paramcters. are shown in Fig. 5.," Two $Y$ – O/H linear regressions for the HeBCD galaxy sample of \citet{I07}, with the above set of parameters, are shown in Fig. \ref{fig1}."
 The two reeression lines differ iu the way oxvecn abundances have con. calculated., The two regression lines differ in the way oxygen abundances have been calculated.
 For the first regression line (Fie., For the first regression line (Fig.
" 5aa). oxveen abundances have been derived bw setting the cluperature of the O!! zone equal to T, (Ie! ). while or the second (Fie."," \ref{fig1}a a), oxygen abundances have been derived by setting the temperature of the $^{++}$ zone equal to $T_e$ $^+$ ), while for the second (Fig."
 bbb). they have been derived bx adopting the temperature 00 111) derived from the 10 I| A 1363/(A1959 ADOOT) line flux ratio.," \ref{fig1}b b), they have been derived by adopting the temperature $T_e$ (O ) derived from the [O ] $\lambda$ $\lambda$ $\lambda$ 5007) line flux ratio."
" The primordial values obtained from the two reeressions in Fig. 5.. 3,"," The primordial values obtained from the two regressions in Fig. \ref{fig1},"
" = 0.2565 + 0.0010 aud Y, = 1,2560 4 0.0011. are very simular but are siguificautly ugher than the value Y,, = 0.2516 + 0.0011 obtained by Izotovetal.(2007) for the same galaxy sample."," $Y_p$ = 0.2565 $\pm$ 0.0010 and $Y_p$ = 0.2560 $\pm$ 0.0011, are very similar but are significantly higher than the value $Y_p$ = 0.2516 $\pm$ 0.0011 obtained by \citet{I07}
 for the same galaxy sample."
 The difference is due to the inclusion of the correction or fluorescent excitation of IT lines. the correction for a arecr correction for collisional excitation to the IT./ fiux and larger adopted equivalent widths of the stellar Ie D876. 6678 and 7065 absorption lines.," The difference is due to the inclusion of the correction for fluorescent excitation of H lines, the correction for a larger correction for collisional excitation to the $\beta$ flux and larger adopted equivalent widths of the stellar He 5876, 6678 and 7065 absorption lines."
" We adopt the value of 3, from Fig.", We adopt the value of $Y_p$ from Fig.
 Saa. where both O/T aud Y are calculated with the same temperature T. = T; (He! ).," \ref{fig1}a a, where both O/H and $Y$ are calculated with the same temperature $T_e$ = $T_e$ $^+$ )."
" We have varied the ranges of some paramcters to study how the value of Y, is affected by these variations.", We have varied the ranges of some parameters to study how the value of $Y_p$ is affected by these variations.
" We have found that varviug the fraction of fluorescent excitation of the lydrogen lines between and2%.. and/or setting (Πο ) = Το ut) or changing T,.(Ie ! ) in the rauge (0.9 — «. ο 111) Gustead of malkine it change between 0.95 and LO « (ο n). result iu a change of Y, between 0.251 aud 0.258."," We have found that varying the fraction of fluorescent excitation of the hydrogen lines between and, and/or setting $T_e$ $^+$ ) = $T_e$ (O ) or changing $T_e$ $^+$ ) in the range (0.9 – $\times$ $T_e$ (O ) (instead of making it change between 0.95 and 1.0 $\times$ $T_e$ (O )), result in a change of $Y_p$ between 0.254 and 0.258."
" Additionally. adding a systematic error of caused by. uncertainties iu the We1 cuussivities (Porteretal.2009)... gives 1,— 4,2565 +4 O.00L0(stat.)"," Additionally, adding a systematic error of caused by uncertainties in the He emissivities \citep{P09}, gives $Y_p$ = 0.2565 $\pm$ 0.0010(stat.)"
 + O.0050(svst.).," $\pm$ 0.0050(syst.),"
" where ""stat? aud “syst” refer to statistical aud systematic errors. respectively,"," where “stat” and “syst” refer to statistical and systematic errors, respectively."
" Thus. the value of Y, derived iu this oper. is excater than the value of 0.2182 obtained roni the 3vr WALIAP data. assuming SBBN (Sperecletal. 2007)."," Thus, the value of $Y_p$ derived in this paper, is greater than the value of 0.2482 obtained from the 3yr WMAP data, assuming SBBN \citep{S07}. ."
" Mowever. if is cousisteut with the Y, 19 obtained by Ichikewaetal.(2008). fromthe available WATAP. ACBAR. CBI. andBOOMERANG data actually. the peak value in their ouc-dimeusional narginalized distribution of Y,(their Fig.3) isequal to 12511."," However, it is consistent with the $Y_p$ = $^{+0.10}_{-0.07}$ obtained by \citet{Ich08} fromthe available WMAP, ACBAR, CBI, andBOOMERANG data [actually, the peak value in their one-dimensional marginalized distribution of $Y_p$(their Fig.3) isequal to 0.254]."
 Using Eq. 3. ," Using Eq. \ref{eq:dO}, ,"
we derivefrom the Y O/T inear reeression (Fie., we derivefrom the $Y$ – O/H linear regression (Fig.
 aa) the slopes αἱ /dO = GEO.L(stat.), \ref{fig1}a a) the slopes $Y$ /dO = $\pm$ 0.45(stat.)
 and dY /dZ = 1.624:0.29(stat.)., and $Y$ $Z$ = $\pm$ 0.29(stat.).
 These slopes are shallower than the ones of L3340.75 aud 250.19 derived by Izotovctal.(2007)., These slopes are shallower than the ones of $\pm$ 0.75 and $\pm$ 0.49 derived by \citet{I07}.
. We now use our derived value of the priuordial Ue abundance along with the observedprimordial abundances of other dight clemeuts to check the consistency of SBBN., We now use our derived value of the primordial He abundance along with the observedprimordial abundances of other light elements to check the consistency of SBBN.
 Deviations from the standard rate of IIubble expansion iu the carly Universe can be caused by an extra contribution to the total enerevdensity. for example by additional flavors of neutrinos.," Deviations from the standard rate of Hubble expansion in the early Universe can be caused by an extra contribution to the total energydensity, for example by additional flavors of neutrinos."
" The total uuuboer of different species of weakly interacting light relativistic particles can be convenicutly be paraiucterized by N,. the ""effective nuber of light"," The total number of different species of weakly interacting light relativistic particles can be conveniently be parameterized by $N_\nu$ , the “effective number of light"
Iu order to interpret the Ar emissions. we lirst converted the signal brightness B in Rayleiehs into a slit-average column deusity No alone the line of sieht for each Ar The conversion to columa densities in the slit was performed according to the optically thin approximation: (10°.B;)/g;. where Bj is the brightuess of line 7. aud g; is the photon fluorescence rate (Le. ph s.) of that emission at the comet.,"In order to interpret the Ar emissions, we first converted the signal brightness $B$ in Rayleighs into a slit-average column density $\bar{N}$ along the line of sight for each Ar The conversion to column densities in the slit was performed according to the optically thin approximation: $\bar{N_i} = (10^6
B_i)/g_i$ , where $B_i$ is the brightness of line $i$, and $g_i$ is the photon fluorescence rate (i.e., ph $^{-1}$ ) of that emission at the comet."
 We adopted resonance fluorescence efficiencies at 1 AU of 5.3x10  Land 22x10 7 | for the 1018 and 1066 llines (after adjustinent for the variation in solar FUV uxiug the daily. ΕΟΤ solar {lux index at the time of our)H: these e-values (derived (rom (Meier1991:Parkeretal.1905) were then adjusted to reflect Hale-Bopp’s 0.915 AU heliocentric clistance.," We adopted resonance fluorescence efficiencies at 1 AU of $\times$ $^{-8}$ $^{-1}$ and $\times$ $^{-8}$ $^{-1}$ for the 1048 and 1066 lines (after adjustment for the variation in solar FUV using the daily F10.7 solar flux index at the time of our; these g-values (derived from \citep{M91, Pea98} were then adjusted to reflect Hale-Bopp's 0.915 AU heliocentric distance."
" To derive an Ar production rate (Q4,). we constructed a simple model of the coma’s Ar distribution. asstuning a spherically sviunetric. steady-state radial outflow divergiug from a point source."," To derive an Ar production rate $Q_{Ar}$ ), we constructed a simple model of the coma's Ar distribution, assuming a spherically symmetric, steady-state radial outflow diverging from a point source."
 To calculate 4. we assumed an argou outflow velocity in equilibrium with the HoO outflow. Le. ej21.25 kins 1 at 0.915 AU.," To calculate $_{Ar}$, we assumed an argon outflow velocity in equilibrium with the $_2$ O outflow, i.e., $v_i$ =1.25 km $^{-1}$ at 0.915 AU."
 Based on the MRES slit brightnesses (and coumting-+backeround brightness. errors) ofJ the two argon lines.. an error-weighted: average Ar production: rate of⋅↽↽ 1.1220.3:x 107?Mi Lowas derived.," Based on the MRES slit brightnesses (and counting+background brightness errors) of the two argon lines, an error-weighted average Ar production rate of $\pm$ $\times$ $^{29}$ $^{-1}$, was derived."
 To interpret the physical meaning of the EUVS Ar production rate obtained above. we ratio the derived. Ar production rates to the O production rate of the comet.," To interpret the physical meaning of the EUVS Ar production rate obtained above, we ratio the derived Ar production rates to the O production rate of the comet."
" HoO is the dominant molecule in cometary ices. so we derived the O production rate Qo ou the established Lixo""! ! perihelion HeO production rate (Biveretal.1997:Colom1997)."," $_2$ O is the dominant O-bearing molecule in cometary ices, so we derived the O production rate $Q_O$ on the established $\times$ $^{31}$ $^{-1}$ perihelion $_2$ O production rate \citep{Bea97, Cea97}."
. To account for the oxygen in other O-bearing species (CO. COs. CHONs. 510.) when deriving the Ar production ratio [Ar/O]. we adopt Quan=1.50 (based on Giotto NMS data adjusted for the higher CO abundance of Hale-Bopp: W. Huebner. pers.," To account for the oxygen in other O-bearing species (CO, $_2$ , CHONs, $_x$ ) when deriving the Ar production ratio [Ar/O], we adopt $Q_{\rm
oxygen}=1.5Q_{\rm H_2O}$ (based on Giotto NMS data adjusted for the higher CO abundance of Hale-Bopp; W. Huebner, pers."
 couun.)., comm.).
" Based ou this aud the Qa, estimate eiven above. we thus derive an estimate of [Àr/O]—0.0058-0.0017 in Hale-Bopp's coma."," Based on this and the $Q_{Ar}$ estimate given above, we thus derive an estimate of $\pm$ 0.0017 in Hale-Bopp's coma."
 In what follows we assume that this ratio of production rates is incicative of the comas Ar/O abundance ratio., In what follows we assume that this ratio of production rates is indicative of the coma's Ar/O abundance ratio.
 The nost recent cosmogonic (i.e.. solar) [Ar/O] abundance ratio gives [Àr/O].. 20.00372 (CirevesseSauval 1995).," The most recent cosmogonic (i.e., solar) [Ar/O] abundance ratio gives $_{\odot}$ =0.00372 \citep{GS98}."
. Figure 2 preseuts the derived correspoudeuce between tlie error-weighted average wightuess B of the two Ar lines. and the quantity Q νο. ratioed to its cosimogouic value.," Figure 2 presents the derived correspondence between the error-weighted average brightness $B$ of the two Ar lines, and the quantity $Q_{Ar}$ $Q_O$, ratioed to its cosmogonic value."
 Although we recognize the difficulty of connecting coma to nuclear abundances with precision )ecause oue does iot at preseut know exactly how gases are stored iu theuucleus?.. we interpret our 'esults at their[ace value: Hale-Bopp’s coma appears to be enriched in Ar relative to cosmogouic," Although we recognize the difficulty of connecting coma to nuclear abundances with precision because one does not at present know exactly how gases are stored in the, we interpret our results at theirface value: Hale-Bopp's coma appears to be enriched in Ar relative to cosmogonic"
"A great deal of progress has been made in our understanding of gamma-ray bursts (GRBs), thanks to the launch of a number of dedicated satellites (BeppoSAX, HETE-2, Swift and Integral).","A great deal of progress has been made in our understanding of gamma-ray bursts (GRBs), thanks to the launch of a number of dedicated satellites (BeppoSAX, HETE-2, Swift and Integral)."
" These satellites rapidly communicate burst locations to ground-based optical and radio telescopes, which has enabled detailed follow up study of the GRB afterglow emission."," These satellites rapidly communicate burst locations to ground-based optical and radio telescopes, which has enabled detailed follow up study of the GRB afterglow emission."
" It is now known that GRBs produce highly relativistic and beamed jets containing energy ~10"" ceredevelopments).", It is now known that GRBs produce highly relativistic and beamed jets containing energy $\sim10^{51}$ erg.
 It is also well established that there are two classes of GRBs., It is also well established that there are two classes of GRBs.
" One class, called long-GRBs — those lasting for more than a few seconds — is produced when a massive star collapses at the end of its nuclear burning life (see for a review)."," One class, called long-GRBs — those lasting for more than a few seconds — is produced when a massive star collapses at the end of its nuclear burning life (see for a review)."
" For the other class, called short-GRBs — those lasting for less than a few seconds — at least some members are believed to result from mergers of compact stars in binary systems(Gehrelsal-2009], and references therein)."," For the other class, called short-GRBs – those lasting for less than a few seconds – at least some members are believed to result from mergers of compact stars in binary systems, and references therein)."
" Despite thiset impressive progress, several fundamental questions remain unanswered."," Despite this impressive progress, several fundamental questions remain unanswered."
 Foremost among these is the composition of the relativistic jets that power GRBs., Foremost among these is the composition of the relativistic jets that power GRBs.
 We do not know whether GRB jets consist of a normal proton-electron plasma or if they are dominated by electron-positron pairs., We do not know whether GRB jets consist of a normal proton-electron plasma or if they are dominated by electron-positron pairs.
" Furthermore, it is uncertain whether the jets are dominated by matter or magnetic fields (Poynting outflow)."," Furthermore, it is uncertain whether the jets are dominated by matter or magnetic fields (Poynting outflow)."
 The related question of how the observed y-ray radiation is produced is also poorly understood., The related question of how the observed $\gamma$ -ray radiation is produced is also poorly understood.
" A popular model for converting jet energy to particle thermal energy andet thereby to Rees,radiation is the internalSari shock model", A popular model for converting jet energy to particle thermal energy and thereby to radiation is the internal shock model.
" According to this (Narayanaf][1992}model, the Meszaros|1994,relativistic wind from& Piran|T997).the central engine of a GRB has a variable Lorentz factor, which leads to collisions between faster and slower moving ejecta."," According to this model, the relativistic wind from the central engine of a GRB has a variable Lorentz factor, which leads to collisions between faster and slower moving ejecta."
 A fraction of the kinetic energy of the jet is converted to thermal energy in these “internal” shocks., A fraction of the kinetic energy of the jet is converted to thermal energy in these “internal” shocks.
 A fraction of this thermal energy then goes into electrons and is rapidly radiated away as y-ray photons via synchrotron and inverse-Compton processes., A fraction of this thermal energy then goes into electrons and is rapidly radiated away as $\gamma$ -ray photons via synchrotron and inverse-Compton processes.
 The internal shock model naturally produces the rapid variability observed in the y-ray emission of GRBsPiran|1997)., The internal shock model naturally produces the rapid variability observed in the $\gamma$ -ray emission of GRBs.
. This is one of its principal virtues., This is one of its principal virtues.
" The internal shock model, however, has a problem, viz.,"," The internal shock model, however, has a problem, viz.,"
" the efficiency e, (see eq.", the efficiency $\epsilon_\gamma$ (see eq.
[I7] for the definition) for converting jet energy to radiation is relatively lowMeszaros|1999)., \ref{egamma} for the definition) for converting jet energy to radiation is relatively low.
". The efficiency depends on the relative Lorentz factor of the colliding blobs, and also, in the case of magnetized ejecta, on the jet magnetization parameter o (defined in eq. p»."," The efficiency depends on the relative Lorentz factor of the colliding blobs, and also, in the case of magnetized ejecta, on the jet magnetization parameter $\sigma$ (defined in eq. \ref{sigma}) )."
" Since the efficiency e, of a GRB can be measured directly from observations of the prompt and", Since the efficiency $\epsilon_\gamma$ of a GRB can be measured directly from observations of the prompt and
ofnormal SNel-a (e.g. Branch. Fisher. Nugent 1993).,"of SNeI-a (e.g. Branch, Fisher, Nugent 1993)."
 In addition. Patat ct al. (," In addition, Patat et al. ("
1996) have shown. in a convincing way (see their Fig.,"1996) have shown, in a convincing way (see their Fig."
 8 ). that the spectroscopic evolution (at early stages) of SN. 1992 is almost identical to that of the spectroscopically normal SN. 1994D. The photometric data ον]ο a quite contradictory picture.," 8 ), that the spectroscopic evolution (at early stages) of SN 1992A is almost identical to that of the spectroscopically normal SN 1994D. The photometric data provide a quite contradictory picture."
 SN 1994D achieved at maximum D-—11.60 and V—11.72 after the small correction o the apparent magnitude at maximum to account for an E(BV)o0.06., SN 1994D achieved at maximum B=11.60 and V=11.72 after the small correction to the apparent magnitude at maximum to account for an E(B–V)=0.06.
 Unfortunately the distance to its early tvpe (127) parent. galaxy. NGC 4526. has not been measured directly.," Unfortunately the distance to its early type (E7) parent galaxy, NGC 4526, has not been measured directly."
 One might tentatively assume that the distance of NGC 4526. afide member of the Virgo cluster (Sandage. Bingeeli ct Tanimann 1985). presumably ranges οποσα 17.1 Alpe of NGC 4321 (Freedman ct al.," One might tentatively assume that the distance of NGC 4526, a member of the Virgo cluster (Sandage, Binggeli et Tammann 1985), presumably ranges between 17.1 Mpc of NGC 4321 (Freedman et al."
 1994) ancl 25.5 Alpe of 4639 (Sandage ct al., 1994) and 25.5 Mpc of 4639 (Sandage et al.
 1996)., 1996).
 3othi measures are rasecl on the P-L relationship of Cepheids., Both measures are based on the P-L relationship of Cepheids.
 After applying hese distance moduli (with the attached errors) to the D mae at maximum of SN 1994D. one concludes that the absolute magnitude at maximum of SN 1994D. presumably falls between Mg=19.34 and Mg=20.65.," After applying these distance moduli (with the attached errors) to the B mag at maximum of SN 1994D, one concludes that the absolute magnitude at maximum of SN 1994D presumably falls between $_B=-19.34$ and $_B=-20.65$."
 Although his rangee of magnitudeo is quitei large.ὃν this result. woutlel indicate that the magnitude at maximum of SN 1994D is consistent with either the average absolute at. maxinium derived above for SNel-a in earlv-type galaxies or with the possibility that this SN could have been unusually bright at maximum.," Although this range of magnitude is quite large, this result would indicate that the magnitude at maximum of SN 1994D is consistent with either the average absolute at maximum derived above for SNeI-a in early-type galaxies or with the possibility that this SN could have been unusually bright at maximum."
 In all cases (assuming that NGC 4526 is à member ofthe Virgo cluster) the peak of light of SN 1994D is than that exhibited by SN 1992. This implies that SNel-a which appear almostidentical (at carly stages). can still span a range of maximum brightness of A10.5 mag.," In all cases (assuming that NGC 4526 is a member of the Virgo cluster) the peak of light of SN 1994D is than that exhibited by SN 1992A. This implies that SNeI-a which appear almost (at early stages), can still span a range of maximum brightness of $\gsim 0.5$ mag."
 Dillerences in the photometric evolution of type LSNe were first. pointed. out by Barbon ct al. (, Differences in the photometric evolution of type I SNe were first pointed out by Barbon et al. (
1973) and. Pskoyskii (1967).,1973) and Pskovskii (1967).
 The latter author also suggested that the absolute magnitude at maximum of type L SNe correlates with the rate of decline 67) in such a wav that: the faster the carly decline of a SN the fainter its absolute magnitude at niaximum., The latter author also suggested that the absolute magnitude at maximum of type I SNe correlates with the rate of decline $\beta$ ) in such a way that: the faster the early decline of a SN the fainter its absolute magnitude at maximum.
 However. owing to the dillicultics in measuring 3 even in the best observed objects (e.g. Hamus et al.," However, owing to the difficulties in measuring $\beta$ even in the best observed objects (e.g. Hamuy et al."
 1991). such a relationship has been the subject of debate for some time.," 1991), such a relationship has been the subject of debate for some time."
 Phillips (1993). bv using as a tracer of dillerent. rates of decline the total drop in magnitude that à SN undergoes [rom its peak brightness until 15 days after maximum light ΑΗ]. has considerably. improved. the situation (see also Maza et al.," Phillips (1993), by using as a tracer of different rates of decline the total drop in magnitude that a SN undergoes from its peak brightness until 15 days after maximum light $\Delta m_{15}(B)$ ], has considerably improved the situation (see also Maza et al."
 1994 and Llamuy ct al., 1994 and Hamuy et al.
 1995)., 1995).
 From his lig., From his Fig.
 1 (top) a clear relationship between 2xn45CD) and the absolute magnitude at maximum seems to exist., 1 (top) a clear relationship between $\Delta m_{15}(B)$ and the absolute magnitude at maximum seems to exist.
 However. Sandage et al. (," However, Sandage et al. ("
1996). by studying the absolute magnitude at maximum and the rates of decline of a sample of tvpe Ia SNe occurring in late-tvpe galaxies concluded thatrates (see also Holllich et al.,"1996), by studying the absolute magnitude at maximum and the rates of decline of a sample of type Ia SNe occurring in late-type galaxies concluded that (see also Höfflich et al."
 1996)., 1996).
 The existence of this discrepancy motivates our analysis., The existence of this discrepancy motivates our analysis.
 We have collected from the literature (Lab., We have collected from the literature (Tab.
 5) the following data for SNel-a fulfilling the following requirements: a) to have been observed at maximum (or near maximum) with a reasonable xhotometric error: b) the distances to the parent ealaxies to be measurable via Cepheids (for spirals) and GCLE (for carly types)., 5) the following data for SNeI-a fulfilling the following requirements: a) to have been observed at maximum (or near maximum) with a reasonable photometric error; b) the distances to the parent galaxies to be measurable via Cepheids (for spirals) and GCLF (for early types).
 In addition we have determined (from the original cata) the apparent magnitude and. the rates of decline of 3 ‘historical’ SNe (SN 1919. 19394 and 1957B) because the PO magnitudes of the GCLE of their xwent galaxies have been determined. in recent vears (see Whitmore 1997 and references therein)," In addition we have determined (from the original data) the apparent magnitude and the rates of decline of 3 `historical' SNe (SN 1919A, 1939A and 1957B) because the TO magnitudes of the GCLF of their parent galaxies have been determined, in recent years (see Whitmore 1997 and references therein)."
 The selected objects are listed in Tab., The selected objects are listed in Tab.
 5 which gives the SN designation with the parent galaxy (col., 5 which gives the SN designation with the parent galaxy (col.
 1): the apparent magnitude at maximum (col., 1); the apparent magnitude at maximum (col.
 2): the rate of decline. (col., 2); the rate of decline (col.
 3): the adopted turn-over magnitude (col., 3); the adopted turn-over magnitude (col.
 4): the distance mocdulus derived by using our TO value. see Tab.," 4); the distance modulus derived by using our TO value, see Tab."
 3. (col.," 3, (col."
 5): the absolute D at maximum (col., 5); the absolute B at maximum (col.
 6) and the references (col., 6) and the references (col.
 7)., 7).
 For SNe Ia calibrated by Cepheids. ic. 1937€ (Sandage et al.," For SNe Ia calibrated by Cepheids, i.e. 1937C (Sandage et al."
 1992. Saha et al.," 1992, Saha et al."
 1994). SN LOTZE (Saha οἱ al.," 1994), SN 1972E (Saha et al."
 1995). SN 105110 (Saha et al.," 1995), SN 1981B (Saha et al."
 1996a). SN 1960E (Saha et al.," 1996a), SN 1960F (Saha et al."
 1996b). SN 1990N (Leibundgut et al.," 1996b), SN 1990N (Leibundgut et al."
 1991. Sandage ct al 1996). we have extracted the B absolute magnitude at maximum from Tammann (1996) for 1981DB we have used the re-calibrated apparent magnitude at maximum (Patat et al.," 1991, Sandage et al 1996), we have extracted the B absolute magnitude at maximum from Tammann (1996) [for 1981B we have used the re-calibrated apparent magnitude at maximum (Patat et al."
 1996). for SN 1990N the new data come from Lira et al. (," 1996), for SN 1990N the new data come from Lira et al. ("
1998)]. the,"1998)], the"
The galaxy spatial distribution fuuctioun fV.V) is a simple but powerful statistic which characterizes the locatious of galaxies in space.,"The galaxy spatial distribution function $f(N,V)$ is a simple but powerful statistic which characterizes the locations of galaxies in space."
 It includes statistical information ou voids aud other uuderdeuse regions. on clusters of all shapes ancl sizes. ou filaments. on the probability of [finding an arbitrary number of neighbors around raudomly located positious. on counts of galaxies iu cells of arbitrary shapes aid sizes raudomly located. aud ou galaxy correlation fuuctious of all orders.," It includes statistical information on voids and other underdense regions, on clusters of all shapes and sizes, on filaments, on the probability of finding an arbitrary number of neighbors around randomly located positions, on counts of galaxies in cells of arbitrary shapes and sizes randomly located, and on galaxy correlation functions of all orders."
 These are just some of its representations (??).. ," These are just some of its representations \citep{2000gpsg.book.....S, 2009arXiv0902.0747S}."
Moreover it is also closely related to the distribution fuuction of the peculiar velocities of galaxies around theHubble flow (??)..," Moreover it is also closely related to the distribution function of the peculiar velocities of galaxies around theHubble flow \citep{1990ApJ...365..419S, 2004ApJ...608..636L}. ."
angles from the Cygnus X-1 system. as shown in the Figure I.,"angles from the Cygnus X-1 system, as shown in the Figure 1."
 The complex X-ray spectrum of Cygnus X-1 revealed by the observation reported in Miller et al (2002) implies that the detection of minute variations in the Fe line shape will require a high spectral resolution instrument with large throughput., The complex X-ray spectrum of Cygnus X-1 revealed by the observation reported in Miller et al (2002) implies that the detection of minute variations in the Fe line shape will require a high spectral resolution instrument with large throughput.
 In what follows. we discuss the feasibility of detecting the precession of the accretion disk withASTRO-E2. and specifically with the X-ray Spectrometer (XRS) consisting of an array of semiconductor-based calorimeters delivering the best spectral resolution to date at 6 keV (pre-flight value of 6.5 eV).," In what follows, we discuss the feasibility of detecting the precession of the accretion disk with, and specifically with the X-ray Spectrometer (XRS) consisting of an array of semiconductor-based calorimeters delivering the best spectral resolution to date at 6 keV (pre-flight value of 6.5 eV)."
 is a JAXA/NASA mission to observe X-rays with unprecedented high spectral resolution imaging detectors. which ts scheduled for launch by Summer 2005.," is a JAXA/NASA mission to observe X-rays with unprecedented high spectral resolution imaging detectors, which is scheduled for launch by Summer 2005."
 The Science Working Group target list includes two observations of Cygnus X-I., The Science Working Group target list includes two observations of Cygnus X-1.
 The underlying assumption is that the X-ray spectrum of Cyg X-I can be well described by the best-fit model obtained by Miller et al (2002)., The underlying assumption is that the X-ray spectrum of Cyg X-1 can be well described by the best-fit model obtained by Miller et al (2002).
 Indeed. at higher spectral resolution. other -so far undetected- spectral components might appear.," Indeed, at higher spectral resolution, other -so far undetected- spectral components might appear."
 Examples include the presence of blue-shifted edges due to high velocity ejecta., Examples include the presence of blue-shifted edges due to high velocity ejecta.
 Should these. or other. features impact strongly either on the Fe line region itself or in the energy ranges where the underlying continuum is estimated. the specific methodology proposed here will need to be revised.," Should these, or other, features impact strongly either on the Fe line region itself or in the energy ranges where the underlying continuum is estimated, the specific methodology proposed here will need to be revised."
 Fortunately the instrument selected will deliver spectra with a very high signal to noise at a spectral resolution so high that many of these putative components might be resolved and modeled out., Fortunately the instrument selected will deliver spectra with a very high signal to noise at a spectral resolution so high that many of these putative components might be resolved and modeled out.
 That would certainly. complicate. but not invalidate. the proposed analysis.," That would certainly complicate, but not invalidate, the proposed analysis."
 As argued by Miller et al (2002) the spectrum of Cygnus X-l] is complex below 3 keV. where they did not succeed in fitting an appropriate model.," As argued by Miller et al (2002) the spectrum of Cygnus X-1 is complex below 3 keV, where they did not succeed in fitting an appropriate model."
 All our discussion assumes the Be filter is on at the XRS., All our discussion assumes the Be filter is on at the XRS.
 This removes low energy photons which are not needed for our purposes., This removes low energy photons which are not needed for our purposes.
 In our analysis. we ighore photons below 3 keV and above 9 keV. In addition. we do not use the X-ray Imaging Spectrometers (XIS) on boardASTRO-E2. which have less spectral resolution at the Fe line energy range.," In our analysis, we ignore photons below 3 keV and above 9 keV. In addition, we do not use the X-ray Imaging Spectrometers (XIS) on board, which have less spectral resolution at the Fe line energy range."
 A typical 50 ks exposure is assumed. and the background is assumed to be negligible for such an strong source (see below) and not included in the simulations.," A typical 50 ks exposure is assumed, and the background is assumed to be negligible for such an strong source (see below) and not included in the simulations."
 Pre-launch calibration redistribution matrices. and. efficiency curves have been downloaded from the web site atNASA!., Pre-launch calibration redistribution matrices and efficiency curves have been downloaded from the web site at.
. The simulated model is that fitted by Miller et al. (, The simulated model is that fitted by Miller et al. (
2002) to the data.,2002) to the data.
 The continuum ts a power law with T=1.8. absorbed by a Galactic column of Ny28.1«107!em™ which is absorbed by a smeared edge at 7.2 keV. with a width of 7 keV and a depth of 1.2.," The continuum is a power law with $\Gamma=1.8$, absorbed by a Galactic column of $N_H=8.1\times 10^{21}\, {\rm
cm}^{-2}$ which is absorbed by a smeared edge at 7.2 keV, with a width of 7 keV and a depth of 1.2."
 The narrow line component at 6.415 keV. believed to arise from the irradiated outer disk. has been simulated as a gaussian of width pare.=30 eV. The broad line component has been simulated using the numerical models explained in the previous section. for a fixed equivalent width of 140 eV and a variety of disk inclination angles.," The narrow line component at 6.415 keV, believed to arise from the irradiated outer disk, has been simulated as a gaussian of width $\sigma_{\rm narrow}=30$ eV. The broad line component has been simulated using the numerical models explained in the previous section, for a fixed equivalent width of 140 eV and a variety of disk inclination angles."
 As expected. this model produces a very high count rate in the XRS. of the order of 60 counts s!.," As expected, this model produces a very high count rate in the XRS, of the order of 60 counts $^{-1}$."
 This count rate will be distributed among several XRS pixels. according to the PSF.," This count rate will be distributed among several XRS pixels, according to the PSF."
 Although the overall count rate 1s below the telemetry limit. the fraction of events that will be measured by the software as medium or low resolution will be large (~405€).," Although the overall count rate is below the telemetry limit, the fraction of events that will be measured by the on-board software as medium or low resolution will be large $\sim 30-40\%$ )."
 There are two possibilities to deal with this: either using the neutral density filter (which will decrease the overall count rate to an acceptable level of ~6 counts s! ) or to ignore the few pixels with the higher count rates and work only with the pixels which have count rates below a few counts s7!., There are two possibilities to deal with this: either using the neutral density filter (which will decrease the overall count rate to an acceptable level of $\sim 6$ counts $^{-1}$ ) or to ignore the few pixels with the higher count rates and work only with the pixels which have count rates below a few counts $^{-1}$.
 Both of these procedures will result in an overall loss of throughput., Both of these procedures will result in an overall loss of throughput.
 This is why we consider of 10 and 5 Ks., This is why we consider of 10 and 5 ks.
 To analyze the simulated data. we follow Miller et al (2002) to fit the continuum. by excluding the range from 4.0 to 7.2 keV. A single power law leaves enormous residuals which can be well fitted by the smeared absorption edge.," To analyze the simulated data, we follow Miller et al (2002) to fit the continuum, by excluding the range from 4.0 to 7.2 keV. A single power law leaves enormous residuals which can be well fitted by the smeared absorption edge."
 In general. the edge energy is well reproduced by the fit (statistical errors in the range of 50-150 eV depending on the effective exposure time). although there is substantial degeneracy between the width of the edge and its depth.," In general, the edge energy is well reproduced by the fit (statistical errors in the range of 50–150 eV depending on the effective exposure time), although there is substantial degeneracy between the width of the edge and its depth."
 This does not affect the continuum in the Fe emission line region., This does not affect the continuum in the Fe emission line region.
 Once the continuum ts fitted. we include all data in the 3.0- energy band. and add a narrow gaussian emission line and a relativistic emission line (see Figure 2. left).," Once the continuum is fitted, we include all data in the 3.0-9.0 energy band, and add a narrow gaussian emission line and a relativistic emission line (see Figure 2, left)."
 Thanks to the superb spectral resolution of this instrument. the narrow line is very well characterized. with errors in its centroid actually limited by systematics (2 eV) rather than by statistics. even in à 5 ks exposure.," Thanks to the superb spectral resolution of this instrument, the narrow line is very well characterized, with errors in its centroid actually limited by systematics (2 eV) rather than by statistics, even in a 5 ks exposure."
 The relativistic line model returns the disk inclination angle with a error of 0.3 deg for a 50 ks exposure and 0.7 deg for a 5 ks exposure., The relativistic line model returns the disk inclination angle with a error of 0.3 deg for a 50 ks exposure and 0.7 deg for a 5 ks exposure.
 This is due to the fact that the sharp drop in the blue edge of the line is very clearly marked by the XRS., This is due to the fact that the sharp drop in the blue edge of the line is very clearly marked by the XRS.
 Figure 2 (right panel) shows the differences in these sharp edges for a 50 ks exposure and various disk inclination angles., Figure 2 (right panel) shows the differences in these sharp edges for a 50 ks exposure and various disk inclination angles.
 Note that these changes amount to about 50 eV per degree of disk inclination. and therefore the claimed limit in the systematics for line centering of 2 eV is really not an issue for this purpose.," Note that these changes amount to about 50 eV per degree of disk inclination, and therefore the claimed limit in the systematics for line centering of 2 eV is really not an issue for this purpose."
 Table ] summarizes the results of the fits to simulated data with 5. 10 and 50 ks net exposure and disk melination of 35°.," Table 1 summarizes the results of the fits to simulated data with 5, 10 and 50 ks net exposure and disk inclination of $35^{\circ}$."
 This work suggests a diagnostic tool to investigate whether the aceretion disk of Cygnus X-1 (and of other microquasar systems) precesses. and if so. what is the period and precession angle.," This work suggests a diagnostic tool to investigate whether the accretion disk of Cygnus X-1 (and of other microquasar systems) precesses, and if so, what is the period and precession angle."
 We have shown that the study of the periodic variations of the Fe Ka line. that would be unavoidably produced in the putatively precessing disk of the system. are observable in short (5-10 ks) exposures of the satellite.," We have shown that the study of the periodic variations of the Fe $\alpha$ line, that would be unavoidably produced in the putatively precessing disk of the system, are observable in short (5–10 ks) exposures of the satellite."
 The degree of precision and confidence level up to which we will be able to determine the inclination angle of disk for each short observations. thus. the magnitude of the precession. was shown to be sufficiently high as to allow a clear determination of these parameters even when the precession angle is of only a few degrees.," The degree of precision and confidence level up to which we will be able to determine the inclination angle of disk for each short observations, thus, the magnitude of the precession, was shown to be sufficiently high as to allow a clear determination of these parameters even when the precession angle is of only a few degrees."
 The work of DFT was performed under the auspices of the U.S. DOE-NNSA by U. of California LLNL under contract No., The work of DFT was performed under the auspices of the U.S. DOE–NNSA by U. of California LLNL under contract No.
 W-7405-Eng-48., W-7405-Eng-48.
 GER is supported by the research grant PICT 03-1329] (ANPCT)., GER is supported by the research grant PICT 03-13291 (ANPCT).
 XB acknowledges financial support by the Spanish Ministerio de Educaciónn y Ciencia. under project ESP 2003-00852.," XB acknowledges financial support by the Spanish Ministerio de Educaciónn y Ciencia, under project ESP 2003-00852."
redshifts of the lenses. τι. are taken (o be the observed. spectroscopic redshifts. and the positions of the lenses in the field (RA and DEC) are taken to be the observed positions on the skv.,"redshifts of the lenses, $z_l$, are taken to be the observed spectroscopic redshifts, and the positions of the lenses in the field (RA and DEC) are taken to be the observed positions on the sky."
 The Monte Carlo simulation then proceeds by computing the weak lensing shear. . (hat is induced as the light ravs emanating [rom the background sources encounter the foreground lenses.," The Monte Carlo simulation then proceeds by computing the weak lensing shear, $\vec{\gamma}$, that is induced as the light rays emanating from the background sources encounter the foreground lenses."
 In (he case of single-deflection caleulations. the lensing of each source is computed solely for the lens which is nearest to the source in projection on (he sky.," In the case of single-deflection calculations, the lensing of each source is computed solely for the lens which is nearest to the source in projection on the sky."
 That is. the “closest” lenses are the only lenses that are used in the single deflection caleulations. and the resulting shear for each source is simply the shear induced by the closest lens.," That is, the “closest” lenses are the only lenses that are used in the single deflection calculations, and the resulting shear for each source is simply the shear induced by the closest lens."
 In the case of full. multiple-deflection calculations. the lensing of each source by all foreground lenses is computed.," In the case of full, multiple-deflection calculations, the lensing of each source by all foreground lenses is computed."
 The resulting shear for each source is (hen the net shear due to all [oreground lenses., The resulting shear for each source is then the net shear due to all foreground lenses.
 This is straightforward (ο compute in the weak lensing regime since all weak deflections may be considered to be independent (e.g.. Barlelmann Schneider 2001).," This is straightforward to compute in the weak lensing regime since all weak deflections may be considered to be independent (e.g., Bartelmann Schneider 2001)."
 Each source galaxy is assigned a random intrinsic position angle and an intrinsic ellipticity that ds drawn at random from (he observed ellipticity distribution of the IIDE-N galaxies., Each source galaxy is assigned a random intrinsic position angle and an intrinsic ellipticity that is drawn at random from the observed ellipticity distribution of the HDF-N galaxies.
" The intrinsic shape parameters of (he source galaxies are (hen given bv where ej,=(¢—6)/(a+6) is the intrinsic ellipticity of (he source and oj, is its intrinsic position angle.", The intrinsic shape parameters of the source galaxies are then given by where $\epsilon_{in} = (a-b)/(a+b)$ is the intrinsic ellipticity of the source and $\phi_{in}$ is its intrinsic position angle.
 Since we are dealing only with the weak lensing regime. the final image shape of each source galaxy in the multiple-deflection calculations is given by where 5; is the shear induced by foreground lens galaxy. j.," Since we are dealing only with the weak lensing regime, the final image shape of each source galaxy in the multiple-deflection calculations is given by where $\vec{\gamma}_j$ is the shear induced by foreground lens galaxy, $j$."
" In the case of the full. nmultiple-deflection calculations. the net shear due to all lenses with z;<2, is used to obtain y lor each source galaxy."," In the case of the full, multiple-deflection calculations, the net shear due to all lenses with $z_l < z_s$ is used to obtain $\vec{\gamma}_f$ for each source galaxy."
 In the case of the single deflection caleulations. the sum over all [oreground lenses is simply replaced by Foose. the shear induced by the lens that is closest to (he source in projection on the sky.," In the case of the single deflection calculations, the sum over all foreground lenses is simply replaced by $\vec{\gamma}_{\rm close}$, the shear induced by the lens that is closest to the source in projection on the sky."
 Shown in Figure | is a zoomed-in image of one of the simulations., Shown in Figure 1 is a zoomed-in image of one of the simulations.
 The image is centered on the IIDF-N. and (he locations of chips 2. 3. and 4 on WEPC-2 are shown by (he black lines.," The image is centered on the HDF-N, and the locations of chips 2, 3, and 4 on WFPC-2 are shown by the black lines."
 Here a fiducial lens halo model with o;=150 km ! and s=1005! kpe has been adopted. and the source galaxies have been distributed in redshift space according to equation (6) above.," Here a fiducial lens halo model with $\sigma_v^\ast = 150$ km $^{-1}$ and $s = 100h^{-1}$ kpc has been adopted, and the source galaxies have been distributed in redshift space according to equation (6) above."
" A flat A-dominated cosmology with Ly=τὸ km ! 1. Q,,=0.3 and O44=0.7 has been also been adopted."," A flat $\Lambda$ -dominated cosmology with $H_0 = 70$ km $^{-1}$ $^{-1}$, $\Omega_{m0} = 0.3$ and $\Omega_{\Lambda 0} = 0.7$ has been also been adopted."
 The left panel of Figure 1 shows the magnitude of the net shear. ancl for clarity (he orientation of the net shear is not shown.," The left panel of Figure 1 shows the magnitude of the net shear, and for clarity the orientation of the net shear is not shown."
 Rec peaks in the shear field (ie.. locations of the largest net shear) correspond to the locations of ihe most important weak galaxy lenses in the field.," Red peaks in the shear field (i.e., locations of the largest net shear) correspond to the locations of the most important weak galaxy lenses in the field."
 The right panel of Figure 1 shows the, The right panel of Figure 1 shows the
Some of the reaction rates involving H» depend on the ortho-to-para ratio of molecular hydrogen.,Some of the reaction rates involving $\H2$ depend on the ortho-to-para ratio of molecular hydrogen.
" For this ratio and other thermodynamic quantities (y(T), U(T), etc) we use exact expressions computed from quantum-mechanical statistical sums (Turk et al, 2010, in preparation)."," For this ratio and other thermodynamic quantities $\gamma(T)$, $U(T)$, etc) we use exact expressions computed from quantum-mechanical statistical sums (Turk et al, 2010, in preparation)."
 Examples of cooling functions from our simulations are given in Figure [ATO]., Examples of cooling functions from our simulations are given in Figure \ref{fig:cf}.
" The cooling function, in general, is a function of gas temperature only, but also depends on the gas metallicity Z, the energy density of the incident radiation field U,, the number density of baryons n; (although for n;€104cm? the dependence on the last two parameters always enters as U,,/np), and abundances of all atomic and molecular species X;= "," The cooling function, in general, is a function of gas temperature only, but also depends on the gas metallicity $Z$, the energy density of the incident radiation field $U_\nu$ , the number density of baryons $n_b$ (although for $n_b\lesssim10^4\dim{cm}^{-3}$ the dependence on the last two parameters always enters as $U_\nu/n_b$ ), and abundances of all atomic and molecular species $X_j\equiv n_j/n_b$."
"Therefore, when plotted as a function of temperature, the cooling function takes a range of values (depending on the values of n;/np.other gas properties) rather than a single, unique value."," Therefore, when plotted as a function of temperature, the cooling function takes a range of values (depending on the values of other gas properties) rather than a single, unique value."
" Interestingly, Figure shows that the cooling rate at T«10*K is dominated by cooling due to molecular hydrogen, rather than by low ionization metal species such as OI or CII."," Interestingly, Figure \ref{fig:cf} shows that the cooling rate at $T<10^4\dim{K}$ is dominated by cooling due to molecular hydrogen, rather than by low ionization metal species such as OI or CII."
 Molecular hydrogen cooling is often assumed to be negligible due to lower cooling rates?)., Molecular hydrogen cooling is often assumed to be negligible due to lower cooling rates.
". However, we use the updated H» cooling rates of?,, which are considerably higher than the previous estimates."," However, we use the updated $\H2$ cooling rates of, which are considerably higher than the previous estimates."
" As Figure[AT0] shows, the new H cooling rates dominate over the low ionization metal species at T€5000K."," As Figure \ref{fig:cf} shows, the new $\H2$ cooling rates dominate over the low ionization metal species at $T\lesssim 5000\dim{K}$."
" The two shielding factors, Sp and Sy,, together with the clumping factor C,, are important parameters of our empirical model."," The two shielding factors, $\SD$ and $S_\H2$, together with the clumping factor $C_\rho$, are important parameters of our empirical model."
" As explain, we use an ansatz similar in spirit to the Sobolev approximation to estimate dust shielding: where Dyw is the dust-to-gas ratio in units of its Milky Way value (see p)». σος2x10?!cm?, and Note that the value for o that we use in this paper is twice lower than the one listed in?;; the new value is a commonly adopted value for this parameter for the Milky Way type dust, and provides a better quantitative fit to the existing observational constraints."," As explain, we use an ansatz similar in spirit to the Sobolev approximation to estimate dust shielding: where $\D$ is the dust-to-gas ratio in units of its Milky Way value (see \ref{sec:sims}) ), $\sigma_0 = 2\times 10^{-21} \dim{cm}^2$, and Note that the value for $\sigma_0$ that we use in this paper is twice lower than the one listed in; the new value is a commonly adopted value for this parameter for the Milky Way type dust, and provides a better quantitative fit to the existing observational constraints."
" In addition, a factor of 2 in the denominator of the expression for Lsoy was missing in - this was a typo, and the correct was used when simulations were run."," In addition, a factor of 2 in the denominator of the expression for $L_{\rm Sob}$ was missing in - this was a typo, and the correct expression was used when simulations were run."
 The major expressionchange between our current model and the model of is in the form of the molecular hydrogen self-shielding factor., The major change between our current model and the model of is in the form of the molecular hydrogen self-shielding factor.
" In this form was modified from the commonly used formula of?,, because the FUV flux in? was much higher than the Draine value."," In this form was modified from the commonly used formula of, because the FUV flux in was much higher than the Draine value."
" In our presenttests, we find that we can use either the original formula or their simpler and more approximate expression,"," In our presenttests, we find that we can use either the original formula or their simpler and more approximate expression,"
length (the scale-height corresponding to a typical temperature of | MK is 47 Mm).,length (the scale-height corresponding to a typical temperature of 1 MK is 47 Mm).
 Another variable in our problem is the ratio of scale-heights (1.6. temperatures). so y will be varied in the interval 0 to 1.," Another variable in our problem is the ratio of scale-heights (i.e. temperatures), so $\chi$ will be varied in the interval 0 to 1."
 The dependence of the P)/P2 period ratio on y and the ratio L/zH; for coronal conditions (£= 2) is shown in Fig., The dependence of the $P_1/P_2$ period ratio on $\chi$ and the ratio $L/\pi H_i$ for coronal conditions $\xi=2$ ) is shown in Fig.
 |] with the case discussed earlier by. e.g. Andries et al. (," 1 with the case discussed earlier by, e.g. Andries et al. ("
2005) corresponding to the value y= 1.,2005) corresponding to the value $\chi=1$ .
 In addition to the ratio L/zH; our model prescribes a possible diagnostic of the temperature difference between the loop and its environment., In addition to the ratio $L/\pi H_i$ our model prescribes a possible diagnostic of the temperature difference between the loop and its environment.
 The importance of changes when the different temperature of the environment is taken into account can be shown in a relative percentage plot shown in Figure 2., The importance of changes when the different temperature of the environment is taken into account can be shown in a relative percentage plot shown in Figure 2.
 The relative change was calculated as the percentage change of the results of our investigation compared to the case when y=|., The relative change was calculated as the percentage change of the results of our investigation compared to the case when $\chi=1$.
 As we can see. the changes in the domain corresponding to values of y close to | are not significant.," As we can see, the changes in the domain corresponding to values of $\chi$ close to 1 are not significant."
 However. as the temperature of the environment becomes lower than the temperature inside the loop. this difference. shows changes of the order of 10-20 for values of y of up to 0.5. while for the cases with y near zero. the difference can be even 40 (for y=0.2 and L/xH;=2).," However, as the temperature of the environment becomes lower than the temperature inside the loop, this difference shows changes of the order of 10-20 for values of $\chi$ of up to 0.5, while for the cases with $\chi$ near zero, the difference can be even 40 (for $\chi=0.2$ and $L/\pi H_i=2$ )."
 Since the relative change Is negative. it means that for the same value of P|/P> calculated assuming the same temperature the ratio. L/7H; 1s overestimated.," Since the relative change is negative, it means that for the same value of $P_1/P_2$ calculated assuming the same temperature the ratio, $L/\pi H_i$ is overestimated."
 A change of in the period ratio occurring at approximative values of L/zH;=0.8 and y=0.65 would mean that for environment temperature that is 35 less than the loop temperature. the scale-height is underestimated by about25%.," A change of in the period ratio occurring at approximative values of $L/\pi H_i=0.8$ and $\chi=0.65$ would mean that for environment temperature that is 35 less than the loop temperature, the scale-height is underestimated by about."
. It is important to note that the density ratio. &. does have an important effect of the variation of period ratio.," It is important to note that the density ratio, $\xi$, does have an important effect of the variation of period ratio."
 An increase of é to the value of 10 would result in relative percentage change reduction and the maximum value of the change is attaining its maximum value at 33 (for y=0.2 and L/xH;= 1).," An increase of $\xi$ to the value of 10 would result in relative percentage change reduction and the maximum value of the change is attaining its maximum value at 33 (for $\chi=0.2$ and $L/\pi
H_i=1$ )."
 The same analysis was repeated for prominence structures., The same analysis was repeated for prominence structures.
 These structures are known to be of chromospheric origin and show rather long stability., These structures are known to be of chromospheric origin and show rather long stability.
 Prominence fibrils are surrounded by much hotter and less denser corona., Prominence fibrils are surrounded by much hotter and less denser corona.
 For these structure we suppose that the density of the prominence two orders of magnitude times higher. Le. we take &=100.," For these structure we suppose that the density of the prominence two orders of magnitude times higher, i.e. we take $\xi=100$."
 The typical temperature of prominences varies between 5x10? and 107 K. while the temperature of the surrounding corona can be even two orders of magnitude higher.," The typical temperature of prominences varies between $5\times 10^3$ and $10^4$ K, while the temperature of the surrounding corona can be even two orders of magnitude higher."
 That is why. the value of y is chosen to change in the interval 50-150.," That is why, the value of $\chi$ is chosen to change in the interval 50-150."
 As we can see in Fig., As we can see in Fig.
 3. the changes of the period ratio P\/P> for prominences does not show large variation with y and an analysis of the relative change (compared to the case corresponding to y= 50) would reveal that these changes are of the order of 0.1%.," 3, the changes of the period ratio $P_1/P_2$ for prominences does not show large variation with $\chi$ and an analysis of the relative change (compared to the case corresponding to $\chi=50$ ) would reveal that these changes are of the order of 0.1."
. Strictly speaking the form of equilibrium densities given by Eq. (7) , Strictly speaking the form of equilibrium densities given by Eq. \ref{eq:2.7}) )
is obtained after Imposing an. equilibrium. of forces along the vertical direction (considering that the loop is vertical) whenthe forces created by pressure gradients are balanced by gravitational forces., is obtained after imposing an equilibrium of forces along the vertical direction (considering that the loop is vertical) whenthe forces created by pressure gradients are balanced by gravitational forces.
 Moreover. the density scale-heights given before are connected to the gravitational," Moreover, the density scale-heights given before are connected to the gravitational"
Large crustal currents associated with the magnetic field of magnetars may lead to a thermo-resistive instability in the crust.,Large crustal currents associated with the magnetic field of magnetars may lead to a thermo-resistive instability in the crust.
 Calculations of the instability growth time for a model neutron star crust give typical growth times of weeks to months., Calculations of the instability growth time for a model neutron star crust give typical growth times of weeks to months.
 These timescales are short compared to the ohmic diffusion timescale of the magnetic field., These timescales are short compared to the ohmic diffusion timescale of the magnetic field.
 We conclude that the instability identified in this paper may operate in neutron star crusts for a wide range of physical parameters relevant to magnetars., We conclude that the instability identified in this paper may operate in neutron star crusts for a wide range of physical parameters relevant to magnetars.
" Heating may be located anywhere in the outer crust, while magnetic length scales need only be comparable to the crust thickness or smaller."," Heating may be located anywhere in the outer crust, while magnetic length scales need only be comparable to the crust thickness or smaller."
" Instability occurs for crust temperatures Terust~5x105 K or lower, characteristic of relatively young magnetars, Tage~10* yrs (?).."," Instability occurs for crust temperatures $T_{\rm{crust}} \sim 5 \times 10^8 $ K or lower, characteristic of relatively young magnetars, $\tau_{\rm{age}} \sim 10^4 $ yrs \citep{aguilera}."
 This result coincides with the inferred age of magnetar candidates associated with supernova remnants (see ? for a review)., This result coincides with the inferred age of magnetar candidates associated with supernova remnants (see \citet{mereghetti} for a review).
" Additionally, we find that only heating models that produce large magnetic fields (B>1015 G) will produce instability, so this instability is specific to magnetars."," Additionally, we find that only heating models that produce large magnetic fields $B > 10^{15} $ G) will produce instability, so this instability is specific to magnetars."
 The characteristic temperatures and magnetic fields at which the thermo-resistive instability occurs suggest and intriguing connection between this instability and magnetars., The characteristic temperatures and magnetic fields at which the thermo-resistive instability occurs suggest and intriguing connection between this instability and magnetars.
 We note that our simplified treatment of the current sheet is likely to overestimate the critical field required for instability by a factor of order unity., We note that our simplified treatment of the current sheet is likely to overestimate the critical field required for instability by a factor of order unity.
 A stable current sheet necessarily has a more complicated structure than assumed here., A stable current sheet necessarily has a more complicated structure than assumed here.
 The components of the current that we have neglected will lead to further heating., The components of the current that we have neglected will lead to further heating.
" While we restrict our models to heating in the outer crust, instability in the inner crust could arise in the same way."," While we restrict our models to heating in the outer crust, instability in the inner crust could arise in the same way."
" Heat and charge transport mechanisms are no different, and we expect the scaling of eq. (27))"," Heat and charge transport mechanisms are no different, and we expect the scaling of eq. \ref{eq:gamma}) )"
 for the growth rate to apply to inner crust heating., for the growth rate to apply to inner crust heating.
" However, because of the larger thermal conductivity in the inner crust, deeper crustal currents would have to be larger to produce similar instability growth rates to those calculated here."," However, because of the larger thermal conductivity in the inner crust, deeper crustal currents would have to be larger to produce similar instability growth rates to those calculated here."
" As the heating is moved to deeper layers, the minimum magnetic field required for instability becomes greater than 1015 G. The magnetic energy in the crust for our higher heating models is sufficient to power even the largest giant flares."," As the heating is moved to deeper layers, the minimum magnetic field required for instability becomes greater than $10^{16} $ G. The magnetic energy in the crust for our higher heating models is sufficient to power even the largest giant flares."
 The magnetic energy contained in the magnetic field in the crust is given by, The magnetic energy contained in the magnetic field in the crust is given by
energy distribution (SED) forG3359.95—0.04 with IC on a FIR field.,energy distribution (SED) for$-$ 0.04 with IC on a FIR field.
 The injection spectrum of electrons is assumed to begin at 1 GeV and be of the form dN/dE«xE~%e®/®o with a = 2 and Eg=100 TeV. A source age of 104 years is assumed and a total power of 6.7x1055 erg/s injected into relativistic electrons is required to match the measured X-ray flux (assuming a distance to the galactic centre of 7.6+0.4 pc (Eisenhaueretal. 2005)), The injection spectrum of electrons is assumed to begin at 1 GeV and be of the form $dN/dE \propto E^{-\alpha} e^{-E/E_{0}}$ with $\alpha$ = 2 and $E_{0} = 100$ TeV. A source age of $10^{4}$ years is assumed and a total power of $6.7 \times 10^{35}$ erg/s injected into relativistic electrons is required to match the measured X-ray flux (assuming a distance to the galactic centre of $7.6\pm0.4$ pc \citep{gc_distance}) ).
") As the cooling time of the electrons responsible for the observed X-ray and y-ray emission is much shorter than the age of the pulsar in this scenario, possible evolutionary effects on the injection power (related to the breaking of the pulsar spin) can safely be neglected, we therefore assume a constant injection rate in the simulations presented here."," As the cooling time of the electrons responsible for the observed X-ray and $\gamma$ -ray emission is much shorter than the age of the pulsar in this scenario, possible evolutionary effects on the injection power (related to the breaking of the pulsar spin) can safely be neglected, we therefore assume a constant injection rate in the simulations presented here."
 Fig., Fig.
" 3 demonstrates an important aspect of IC cooling: the KN effect acts twice on the IC spectrum (firstly by distortion of the electron spectrum through cooling, and secondly in the production of IC emission), but only once on the Synchrotron spectrum."," \ref{f3} demonstrates an important aspect of IC cooling: the KN effect acts twice on the IC spectrum (firstly by distortion of the electron spectrum through cooling, and secondly in the production of IC emission), but only once on the Synchrotron spectrum."
 This means that the hardening effect of cooling in the KN regime is masked in the IC spectrum but clearly visible in the Synchrotron emission., This means that the hardening effect of cooling in the KN regime is masked in the IC spectrum but clearly visible in the Synchrotron emission.
 The effect of adding different temperature components to the GC radiation field is shown in Fig. 4.., The effect of adding different temperature components to the GC radiation field is shown in Fig. \ref{f4}.
" Optical (kT=0.3 eV), and ultraviolet (kT=3.0 eV) energy densities of 5x10* ccm? are assumed, consistent with the values expected within the central parsec of our galaxy (Davidsonetal. 1992)."," Optical $kT = 0.3$ eV), and ultraviolet $kT = 3.0$ eV) energy densities of $5\times10^{4}$ $^{-3}$ are assumed, consistent with the values expected within the central parsec of our galaxy \citep{davidson}."
. The injected electron spectrum is identical to that in Fig. 3.., The injected electron spectrum is identical to that in Fig. \ref{f3}.
" On such a compound field, low energy electrons are cooled by IC scattering on optical seed photons, with higher energies cooled by IC on the FIR."," On such a compound field, low energy electrons are cooled by IC scattering on optical seed photons, with higher energies cooled by IC on the FIR."
 This effect leads to rather different shapes for the IC spectra from these two components., This effect leads to rather different shapes for the IC spectra from these two components.
 It can be seen in this figure that the contribution of UV is likely to be small because of strong KN suppression., It can be seen in this figure that the contribution of UV is likely to be small because of strong KN suppression.
" This optical/UV domain can in principle be explored by the GLAST satellite (Thompson2004), but such measurements may be rather difficult due to the strong diffuse background and the modest angular resolution of the instrument."," This optical/UV domain can in principle be explored by the GLAST satellite \citep{glast}, but such measurements may be rather difficult due to the strong diffuse background and the modest angular resolution of the instrument."
" As is clear from Fig. 1,,"," As is clear from Fig. \ref{f1},"
 Bremsstrahlung losses are unlikely to be important in the PWN as the ambient density is likely <1000 cm7°., Bremsstrahlung losses are unlikely to be important in the PWN as the ambient density is likely $\ll 1000$ $^{-3}$.
 The spectral and spatial distribution of low energy electrons in the PWN can in principle be traced using radio observations., The spectral and spatial distribution of low energy electrons in the PWN can in principle be traced using radio observations.
" However, no point-like or extended source is observed at the position of G3359.95-0.04 in 6 cm observations and a three sigma energy flux upper limit of 5x10-1"" erg cm? s! has been derived (Yusef-Zadeh 2006)."," However, no point-like or extended source is observed at the position of 359.95-0.04 in 6 cm observations and a three sigma energy flux upper limit of $5 \times 10^{-17}$ erg $^{-2}$ $^{-1}$ has been derived \citep{yusefzadeh_pc}. ."
. This limit lies almost three orders of magnitude below the curve shown in Fig. 3.., This limit lies almost three orders of magnitude below the curve shown in Fig. \ref{f3}.
 T'here are two factors which may both act to mitigate this apparent contradiction:, There are two factors which may both act to mitigate this apparent contradiction:
"unknown for + Cep, and it is likely that these values evolved over time, so we explore a range of values for both M and α to determine which, if any, set of parameters allows for planet formation to occur.","unknown for $\gamma$ Cep, and it is likely that these values evolved over time, so we explore a range of values for both $\dot{M}$ and $\alpha$ to determine which, if any, set of parameters allows for planet formation to occur."
" As in Paper 1, we calculate a grid of disk models, with a€{0.001,0.01,0.1} and M€{10-°,10-8,10-7,10-°,10,104}Mo yr!."," As in Paper 1, we calculate a grid of disk models, with $\alpha\in\{0.001, 0.01,0.1\}$ and $\dot{M}\in\{10^{-9},10^{-8},10^{-7},10^{-6},10^{-5},10^{-4}\}\:\msunperyr$ ."
" These parameters are roughly consistent with observations of T Tauri stars (e.g. ?2),, including the extremely high and transient accretion rates of FU Ori phenomena (??).."," These parameters are roughly consistent with observations of T Tauri stars \citep[e.g.][]{gullbring,hartmann}, including the extremely high and transient accretion rates of FU Ori phenomena \citep{2000CalvetHartmannStrom, 1996HartmannKenyon}."
" In practice, the models are calculated out to 256 AU, but we consider only the material interior to the truncation radius to be available for planet formation."," In practice, the models are calculated out to 256 AU, but we consider only the material interior to the truncation radius to be available for planet formation."
" We refer to a given disk model by the coordinate pair (a,M), so that Model 1077) refers to the run with a=0.01 and Μ-107Μαν]."," We refer to a given disk model by the coordinate pair $(\alpha,\dot{M})$ , so that Model } refers to the run with $\alpha = 0.01$ and $\dot{M}=10^{-7}\:\msunperyr$."
" The truncation radii of gaseous disks depend on the and temperature of the (?,henceforthAL),, as viscosityopposed to planetesimal disks, gaswhose truncation radii can be calculated from last stable orbits of test particles (?).."," The truncation radii of gaseous disks depend on the viscosity and temperature of the gas \citep[henceforth AL]{1994ArtymowiczLubow}, as opposed to planetesimal disks, whose truncation radii can be calculated from last stable orbits of test particles \citep{pichardo}."
" The truncation radius of each disk model is calculated following AL, as in Paper 1."," The truncation radius of each disk model is calculated following AL, as in Paper 1."
" In AL, the truncation radius of a circumstellar disk in a close binary is where resonant and viscous torques balance."," In AL, the truncation radius of a circumstellar disk in a close binary is where resonant and viscous torques balance."
" This depends on the mass ratio of the binary (14), the semimajor axis of the orbit (a), the eccentricity of the orbit (6). and the Reynolds number of the disk (Re)."," This depends on the mass ratio of the binary $\mu$ ), the semimajor axis of the orbit $a$ ), the eccentricity of the orbit $e$ ), and the Reynolds number of the disk (Re)."
" For ""y Cep, µ. a, and e have all been determined observationally."," For $\gamma$ Cep, $\mu$, $a$, and $e$ have all been determined observationally."
" The remaining parameter, Re, depends on the structure of the disk, which has since dissipated."," The remaining parameter, Re, depends on the structure of the disk, which has long since dissipated."
" The Reynolds longnumber is defined as Re= rv; /v where is distance from the star, vg=/GM./r is the orbital velocity,r and v=ac;h is the viscosity of the disk."," The Reynolds number is defined as = r / where $r$ is distance from the star, $v_{\phi}\equiv\sqrt{GM_*/r}$ is the orbital velocity, and $\nu\equiv\alpha c_s h$ is the viscosity of the disk."
" Since c,/v=h/r and c,=/KT /m, Setting e=0.41 for Υ Cep, we read off truncation radii in units of semi-major axis of the circumprimary disk versus Re from Figs."," Since $c_s/v_{\phi} = h/r$ and $c_s= \sqrt{kT/\bar{m}}$ , Setting $e=0.41$ for $\gamma$ Cep, we read off truncation radii in units of semi-major axis of the circumprimary disk versus Re from Figs."
" 5 and 6 in AL, for µΞ0.3 and 0.1, respectively."," 5 and 6 in AL, for $\mu=0.3$ and $0.1$, respectively."
" For Cep, 44=0.22, so we in to find the final truncationy radius versus Re relation."," For $\gamma$ Cep, $\mu=0.22$, so we interpolate in $\mu$ to find the final truncation radius versus Re relation."
" interpolateThis µrelation is plotted as long-dashed black line in2,, for a semi-major axis of 20.18 AU."," This relation is plotted as long-dashed black line in, for a semi-major axis of 20.18 AU."
 We assume that the disks are dynamically truncated and that irradiation from the stellar companion is negligible compared to heating from viscous accretion and the central star., We assume that the disks are dynamically truncated and that irradiation from the stellar companion is negligible compared to heating from viscous accretion and the central star.
" This irradiation would most likely further decrease the likelihood of planet formation since it would provide an additional heat source at the outer edge of the disk, inhibiting planet formation by either core accretion or disk instability."," This irradiation would most likely further decrease the likelihood of planet formation since it would provide an additional heat source at the outer edge of the disk, inhibiting planet formation by either core accretion or disk instability."
" In the absence of additional accretion of material past the companion's orbit onto the disk, the disk should be viscously spreading both inwards and outwards."," In the absence of additional accretion of material past the companion's orbit onto the disk, the disk should be viscously spreading both inwards and outwards."
" Thus, the calculated truncated disk masses should be considered upper limits."," Thus, the calculated truncated disk masses should be considered upper limits."
In we plot the mass profiles of the disk models.,In we plot the mass profiles of the disk models.
" The line colors and types (solid/dotted/dashed) indicate M and q@ parameter for each disk model, respectively (see legend for details)."," The line colors and types (solid/dotted/dashed) indicate $\dot{M}$ and $\alpha$ parameter for each disk model, respectively (see legend for details)."
 Disk mass increases with M and decreasing o., Disk mass increases with increasing $\dot{M}$ and decreasing $\alpha$.
" The truncation radius for each disk increasingmodel is indicated by a symbol on the line, which also indicates the maximum disk mass for each model."," The truncation radius for each disk model is indicated by a symbol on the line, which also indicates the maximum disk mass for each model."
" shows Re versus radius for each disk model, coded the same as inl."," shows Re versus radius for each disk model, coded the same as in."
" The Reynolds number in each disk model depends on the input parameters, but stays fairly flat with radius."," The Reynolds number in each disk model depends on the input parameters, but stays fairly flat with radius."
 The black long-dashed line shows the truncation radius versus Re relation calculated followingAL., The black long-dashed line shows the truncation radius versus Re relation calculated following.
". From the intersection of the long-dashed line with each model profile, we determine a unique truncation radius for each disk model, marked "," From the intersection of the long-dashed line with each model profile, we determine a unique truncation radius for each disk model, marked bysymbols."
"The truncationby symbols.radii are in the range of 4-7 AU, roughly consistentwith the4-5 AU truncation radius assumed by ?,, albeit a bit larger."," The truncation radii are in the range of 4-7 AU, roughly consistentwith the4-5 AU truncation radius assumed by \citet{2004Thebault_gcep}, , albeit a bit larger."
 This is expected because viscous torques, This is expected because viscous torques
are about. 9.5 and 3.3 times higher than at 15 Gvyrs. respectively. assuming a Miller-9calo IME.,"are about 9.5 and 3.3 times higher than at 15 Gyrs, respectively, assuming a Miller-Scalo IMF."
 For solar metallicity. the TMDBO2 models predict an Ils equivalent width of2.91A.. and aat 2 Gvis. 5 Gvrs and 15 Gvrs. respectively.," For solar metallicity, the TMB02 models predict an $\beta$ equivalent width of, and at 2 Gyrs, 5 Gyrs and 15 Gyrs, respectively."
 We can now estimate the IL? equivalent width for any mix of the 2 Gyr. 5 Gyr and 15 Gyr populations by properly weighting each component.," We can now estimate the $\beta$ equivalent width for any mix of the 2 Gyr, 5 Gyr and 15 Gyr populations by properly weighting each component."
 For a 15 Gyr population mixed with a 5 Gvr population constituting of the total mass. the IL2 EW is1.6LÀ. about mmore (han for a pure 15 Gyr population.," For a 15 Gyr population mixed with a 5 Gyr population constituting of the total mass, the $\beta$ EW is, about more than for a pure 15 Gyr population."
 According to the TAIBO2 models. this corresponds to an age of 13 Gris instead of 15 Gvrs inferred Grom (he integrated spectrum.," According to the TMB02 models, this corresponds to an age of 13 Gyrs instead of 15 Gyrs inferred from the integrated spectrum."
 If the 15 Gyr population is mixed with a 2 Gyr population. again constituting of the mass. the IL5 EW would increase to1.98À. corresponding to an age of 7 Gvrs instead of 15 Gvrs.," If the 15 Gyr population is mixed with a 2 Gyr population, again constituting of the mass, the $\beta$ EW would increase to, corresponding to an age of 7 Gyrs instead of 15 Gyrs."
 In order io limit the increase in IL? to0.1À.. only about of the mass could be in the 2 Gyr population.," In order to limit the increase in $\beta$ to, only about of the mass could be in the 2 Gyr population."
 For the other Balmer lines we find very. similar results., For the other Balmer lines we find very similar results.
 While in reality the effects of different metallicities. IMFEs. changes in integrated colors nneed to be investigated in a more rigorous wav. it is clear that only a small number of vounger stars could be present in NGC 4365 without noticable effects on the integrated spectrum.," While in reality the effects of different metallicities, IMFs, changes in integrated colors need to be investigated in a more rigorous way, it is clear that only a small number of younger stars could be present in NGC 4365 without noticable effects on the integrated spectrum."
 The above considerations suggest that a mass fraction of in a 25 Gvr population would lead (to a decrease of about. 2 Gyrs in the Iuninositv-weighted age estimates (based on Dalmer lines). aud (hus a mass fraction of this order could plausibly remain undetected.," The above considerations suggest that a mass fraction of in a 2–5 Gyr population would lead to a decrease of about 2 Gyrs in the luminosity-weighted age estimates (based on Balmer lines), and thus a mass fraction of this order could plausibly remain undetected."
 Ht is important to point out. however. that (his caleulation applies to the integrated light at any given. position within (he galaxy if. for example. the voung population were more centrally concentrated. its relative contribution (to the mass would have to remain below a few percent even within the central regions. and thus constitute a much smaller fraction of the total mass globally.," It is important to point out, however, that this calculation applies to the integrated light at any given position within the galaxy — if, for example, the young population were more centrally concentrated, its relative contribution to the mass would have to remain below a few percent even within the central regions, and thus constitute a much smaller fraction of the total mass globally."
 With current data. the relative numbers of intermediate-age and old are poorly constrained. but P02 estimated that about 150 clusters in NGC 4365 [out of a total ~2500: Ashman&Zepf (1993)]]| might belong to the younger population.," With current data, the relative numbers of intermediate-age and old are poorly constrained, but P02 estimated that about 150 clusters in NGC 4365 [out of a total $\sim2500$; \citet{az98}] ] might belong to the younger population."
 This corresponds to about of the clusters being voung., This corresponds to about of the clusters being young.
 While the formation efficiency. of clusters relative (o field stars might vary lor the dillerent populations. it is conceivable that anv field stars associated with the intermecdiate-age clusters could be “hidden”. with the requirement (hat these stars are uniformly distributed throughout the galaxy.," While the formation efficiency of clusters relative to field stars might vary for the different populations, it is conceivable that any field stars associated with the intermediate-age clusters could be “hidden”, with the requirement that these stars are uniformly distributed throughout the galaxy."
 PO? also estimated that of the clusters in their sample wwithin a 2:5x275 field near the center) are voung. but because of their color-dependent detection limit. they estimate a biasing factor of 1.5 in the detected nunbers of metal-xich. (II-bright) numetal-poor clusters.," P02 also estimated that – of the clusters in their sample within a $2\farcm5\times2\farcm5$ field near the center) are young, but because of their color-dependent detection limit, they estimate a biasing factor of 1.8 in the detected numbers of metal-rich (IR-bright) metal-poor clusters."
 ILowever. even a mass [fraction as high as ~25% in 25 Gyr old field stars in the central regions would," However, even a mass fraction as high as $\sim25\%$ in 2–5 Gyr old field stars in the central regions would"
This work is concerned with the abundance matching (AAI) relations between σ and Ado; and between σ and AL.,This work is concerned with the abundance matching (AM) relations between $\sigma$ and $\Mvir$ and between $\sigma$ and $\Mstars$.
 The AM is intended: to recover the true median. relation., The AM is intended to recover the true median relation.
 1Η there were not any intrinsic scatter in the relation between two parameters. the JM by equation (2)) of two statistical Functions would recover the true relation exactly.," If there were not any intrinsic scatter in the relation between two parameters, the AM by equation \ref{AM}) ) of two statistical functions would recover the true relation exactly."
 In reality the distribution of two observables in a plane has intrinsic scatters around the median relation., In reality the distribution of two observables in a plane has intrinsic scatters around the median relation.
 When there are such intrinsic scatters. the AAL by equation. (2)) will give a biased median relation that is different from the true median relation.," When there are such intrinsic scatters, the AM by equation \ref{AM}) ) will give a biased median relation that is different from the true median relation."
 Here we estimate the bias and correct the AAI relation by equation (2)) to obtain the corrected. relation., Here we estimate the bias and correct the AM relation by equation \ref{AM}) ) to obtain the corrected relation.
 The bias-correetecl AM. relation is then checked. for selt-consistency through a Monte-Carlo. simulation., The bias-corrected AM relation is then checked for self-consistency through a Monte-Carlo simulation.
 In. other words. we estimate the bias so that the corrected relation reproduces from one statistical function to the other through a Monte-Carlo simulation based on the intrinsic scatter.," In other words, we estimate the bias so that the corrected relation reproduces from one statistical function to the other through a Monte-Carlo simulation based on the intrinsic scatter."
 For our purpose a knowledge of the intrinsic scatter is required., For our purpose a knowledge of the intrinsic scatter is required.
 There has been no measurement or simulation for the intrinsic scatter in the A-e relation., There has been no measurement or simulation for the intrinsic scatter in the $\Mvir$ $\sigma$ relation.
 On the other hand. there have been measurements for the relation," On the other hand, there have been measurements for the relation"
((22 ppixels FWHLIAL) in the wavelength rangeAA.,"$\simeq
2$ pixels FWHM) in the wavelength range."
.. Phe observations were carried out curing two observing runs in November 2003 and February 2004., The observations were carried out during two observing runs in November 2003 and February 2004.
 Typical exposure times for both the D&CCh and the ορ were Lhh per target., Typical exposure times for both the Ch and the LFOSC were h per target.
 Phe observations were reduced Following standard: procedures using LRA tasks resulting in wavelength: and flux calibrated: spectra., The observations were reduced following standard procedures using IRAF tasks resulting in wavelength and flux calibrated spectra.
 Iecdshifts: were determined. by visual inspection., Redshifts were determined by visual inspection.
 Optical spectra of the galaxies from these observations are presented in Appendix 1., Optical spectra of the galaxies from these observations are presented in Appendix 1.
 Our own follow-up spectroscopy. is complemented: with publicly available data. from either. the SDSS or. the literature., Our own follow-up spectroscopy is complemented with publicly available data from either the SDSS or the literature.
 Out of the 30 sources classified extended bv APAL one is the prime target of the pointing 3184) and one has unresolved. optical light. profile in the SDSS CCD quality data ancl therefore is most. Likely associated with a Galactic star., Out of the 30 sources classified extended by APM one is the prime target of the pointing 3184) and one has unresolved optical light profile in the SDSS CCD quality data and therefore is most likely associated with a Galactic star.
 Of the remaining 28 sources a total of 26 are assigned spectroscopic redshifts from either our own campaign (17) or the literature (9)., Of the remaining 28 sources a total of 26 are assigned spectroscopic redshifts from either our own campaign (17) or the literature (9).
 Pwo sources in the sample have no recshilts., Two sources in the sample have no redshifts.
 From the sources classified optically unresolved by the APAL a total of 18 have either spectroscopic. data from our own campaign or CCD quality star/galaxy separation from the SDSS., From the sources classified optically unresolved by the APM a total of 18 have either spectroscopic data from our own campaign or CCD quality star/galaxy separation from the SDSS.
 ALL these sources are indeed: confirmed. to be Galactic stars suggesting that the APAI classification is reliable., All these sources are indeed confirmed to be Galactic stars suggesting that the APM classification is reliable.
 Finally. all 3 ambiguous sources are associated with Galactic stars on the basis of the optical spectra or SDSS photometric data.," Finally, all 3 ambiguous sources are associated with Galactic stars on the basis of the optical spectra or SDSS photometric data."
 In the analysis that. follows. we exclude all Galactic stars on the basis of either. optical spectroscopy or the ADPM/SDSS star/galaxy separation., In the analysis that follows we exclude all Galactic stars on the basis of either optical spectroscopy or the APM/SDSS star/galaxy separation.
 Our final normal galaxy sample comprises a total of 28 sources. 26 spectroscopically identified. galaxies ancl 2 sources without spectra classified extended by APAL," Our final normal galaxy sample comprises a total of 28 sources, 26 spectroscopically identified galaxies and 2 sources without spectra classified extended by APM."
 This is. presented in. Table 1., This is presented in Table 1.
 For completeness we also show the 4 sources with extended (1) or ambiguous (3) APSM classification that turned out to be Galactic stars., For completeness we also show the 4 sources with extended (1) or ambiguous (3) APM classification that turned out to be Galactic stars.
 A number of sources in our sample are classified AGNs on the basis of their optical spectroscopic properties., A number of sources in our sample are classified AGNs on the basis of their optical spectroscopic properties.
 These include source X063. which is a BAL-QSO at >=0.49 (Gallagher et al., These include source A063 which is a BAL-QSO at $z=0.149$ (Gallagher et al.
 1999) and source. #AAILO 44156) suggested to harbor AGN activity by Elvis et al. (, 1999) and source A140 4156) suggested to harbor AGN activity by Elvis et al. (
1951).,1981).
 Pwo of the svstems for which we obtained optical spectroscopic observations. #AAQOL ancl A035. (see Fig.," Two of the systems for which we obtained optical spectroscopic observations, A001 and A035 (see Fig."
 AL). show evidence for broad Hla. emission-line with EWLIAL 90z1600 and. 2000kms respectively.," A1), show evidence for broad $\rm H\alpha$ emission-line with FWHM $\delta
v\approx1600$ and $2000 \rm \, km \, s^{-1}$ respectively."
 In. both cases the measured broad: width may be partly due to the low resolution spectrum that does not allow separation of the Lo from the., In both cases the measured broad width may be partly due to the low resolution spectrum that does not allow separation of the $\rm H\alpha$ from the.
AGAS Nevertheless. we conservatively classify these sources AGN.," Nevertheless, we conservatively classify these sources AGN."
 Source AO1I9 has narrow optical emission. lines but the fine ratios log(511]6716|31/1la)x—Q4. log(OLLY5007/1137)z|0.5: see Fig.," Source A019 has narrow optical emission lines but the line ratios $\rm \log ([S\,II]\,6716+31/H\alpha) \approx -0.4$, $\rm
\log ([O\,III]\,5007/H\beta) \approx +0.5$; see Fig."
 AI] place it in the AGN region of the diagnostic diagrams of Wewley et al. (, A1] place it in the AGN region of the diagnostic diagrams of Kewley et al. (
"2001) first introduced. bv. Baldwin. Phillips ""Terlevich (1981) ancl Veilleux Osterbrock (1987).","2001) first introduced by Baldwin, Phillips Terlevich (1981) and Veilleux Osterbrock (1987)."
 Here we adopt 1e theoretical lower bound for starburst galaxy. emission-ine ratios [rom Ixewley et al. (, Here we adopt the theoretical lower bound for starburst galaxy emission-line ratios from Kewley et al. (
2001: see their Figure 16) to iscriminate between LEE anc AGN dominated svstems.,2001; see their Figure 16) to discriminate between II and AGN dominated systems.
 All rese sources are excluded. from the analysis., All these sources are excluded from the analysis.
 Additionally wo of our normal galaxies (sources #AALOG. A149: see Fig.," Additionally two of our normal galaxies (sources A106, A149; see Fig."
 Al) are Coma cluster members identified in fields targeting js cluster and. are excluced from. statistical studies. (c.g. ogN—logS. Luminosity function).," A1) are Coma cluster members identified in fields targeting this cluster and are excluded from statistical studies (e.g. $\log N - \log
S$, luminosity function)."
 ‘Table 1 presents our sample including ACGNs., Table 1 presents our sample including AGNs.
 We list: l., We list: 1.
 Identification number and the NED name of that source if available., Identification number and the NED name of that source if available.
 2. 3.," 2, 3."
 Right ascension ancl cleclination of the optical source in «2000., Right ascension and declination of the optical source in J2000.
 4., 4.
 B-band magnitude from the USNO-2 version À2.0., $B$ -band magnitude from the USNO-2 version A2.0.
 5., 5.
 K-band magnitude from the 2ALASS All Sky Data Release (Skrutskie ct al., $K$ -band magnitude from the 2MASS All Sky Data Release (Skrutskie et al.
 1997)., 1997).
 Either the extended or the point source catalogue was used., Either the extended or the point source catalogue was used.
 6., 6.
 Olfset in areseconds between the X-ray. and optical source position., Offset in arcseconds between the X-ray and optical source position.
 7., 7.
 0.5-2kkeV X-ray flux corrected. for Cialactic absorption in units of 1014ergsbom2," keV X-ray flux corrected for Galactic absorption in units of $10^{-14}\, \rm erg \, s^{-1} \, cm^{-2}$."
 S., 8.
 Hardness ratio using the 0.5-2kkoV ancl the kkeV. spectral bands corrected for vignetting., Hardness ratio using the keV and the keV spectral bands corrected for vignetting.
 9., 9.
 X-raytooptical Dux ratio defined in equation 1.., X-ray–to–optical flux ratio defined in equation \ref{eq1}.
 10., 10.
 GCLIz racio lux densitv in mJy from either the FIRST (Becker et al., GHz radio flux density in mJy from either the FIRST (Becker et al.
 1995: White et al., 1995; White et al.
 1997) or the NVSS (Condon et al., 1997) or the NVSS (Condon et al.
 1998) surveys., 1998) surveys.
 11., 11.
 Redshift of the source., Redshift of the source.
 In the appendix we present he optical spectra of the normal galaxy candidates in he IXMÁM sample obtained at the ΟΛΗ and OXN-SPM Alexican telescopes as part of this project., In the appendix we present the optical spectra of the normal galaxy candidates in the 1XMM sample obtained at the OAGH and OAN-SPM Mexican telescopes as part of this project.
 2., 12.
 kkeV X-ray luminosity in units of eres +.," keV X-ray luminosity in units of $\rm erg \, s^{-1}$ ."
 For he k-correction a power-law spectral energy. distribution was adopted with photon index E—1.5., For the k-correction a power-law spectral energy distribution was adopted with photon index $\Gamma=1.8$.
 3., 13.
 Ho. luminosity in units of eres+.," $\rm H\alpha$ luminosity in units of $\rm erg \, s^{-1}$."
 This is measured rom the optical spectra after correcting for intrinsic dust obscuration using the Balmer decrement Lo/ll3., This is measured from the optical spectra after correcting for intrinsic dust obscuration using the Balmer decrement $\rm H\alpha / H\beta $.
 For more etails see section ??.., For more details see section \ref{sec_correlation}.
 4., 14.
 GClIIz radio luminosity., GHz radio luminosity.
 For the k-correction a power-law spectral energy. distribution was adopted. with spectral index à=0.8., For the k-correction a power-law spectral energy distribution was adopted with spectral index $\alpha=0.8$.
 5., 15.
 Classification on the basis of the optical spectroscopic observations: ILILE for starformine ealaxies. ADS for absorption line spectra and ACN for. systems showing evidence for central black hole accretion.," Classification on the basis of the optical spectroscopic observations: II for starforming galaxies, ABS for absorption line spectra and AGN for systems showing evidence for central black hole accretion."
" “Phere is no spectrum available for source #1142 with the redshift, estimate. showing both emission. and absorption line features. coming from Arp (1977)."," There is no spectrum available for source 142 with the redshift estimate, showing both emission and absorption line features, coming from Arp (1977)."
 In the analysis that follows this is assumed to beHEILE type system., In the analysis that follows this is assumed to beII type system.
 16., 16.
 APM star/galaxy separation., APM star/galaxy separation.
(2) the intrinsic timing noise of the 20 monitored millisecond. pulsars.,(2) the intrinsic timing noise of the 20 monitored millisecond pulsars.
 We assume that the timing noise of each of the pulsars is the random. Gaussian noise. with a variety of possible spectra described in the previous section.," We assume that the timing noise of each of the pulsars is the random Gaussian noise, with a variety of possible spectra described in the previous section."
 We shall refer to the variables parametrizine the timing noise spectral shape as LN. (3)., We shall refer to the variables parametrizing the timing noise spectral shape as $TN_a$ (3).
 Phe quadratic spin-downs. parametrised for cach of the pulsars by chi. clus. and clog. ef," The quadratic spin-downs, parametrised for each of the pulsars by $A_{a1}$, $A_{a2}$, and $A_{a3}$, cf."
 leq. (2)), Eq. \ref{Qa})
. With these assumptions. we shall write down below the expression. for. the probability distribution P(data|parameters) of the cata. as a function. of the parameters.," With these assumptions, we shall write down below the expression for the probability distribution $P({\rm data}|{\rm parameters})$ of the data, as a function of the parameters."
 By Baves theorem. we can then compute the posterior distribution function: the probability. distribution of theparameters given a certain dataset: Llere PCparameters) is the prior probability. of the unknown parameters. which represents all our current knowledge about these parameters. and (data) is the Davesian evidence. which we will use here as à normalisation actor to. ensure. that PCLNG.chop.iasμοιαι) integrates to unity over the parameter space.," By Bayes theorem, we can then compute the posterior distribution function; the probability distribution of theparameters given a certain dataset: Here $P_0({\rm parameters})$ is the prior probability of the unknown parameters, which represents all our current knowledge about these parameters, and $P({\rm data})$ is the Bayesian evidence, which we will use here as a normalisation factor to ensure that $P(A,\gamma, TN_a,
 A_{a1}, A_{a2}, A_{a3}| {\rm data})$ integrates to unity over the parameter space."
 We note here hat the Bayesian evidence is in essence a goodness of fit measure that can be used for model selection., We note here that the Bayesian evidence is in essence a goodness of fit measure that can be used for model selection.
 However. we will ignore the Bayesian evidence in this work and postpone he model selection part of the algorithm to future work.," However, we will ignore the Bayesian evidence in this work and postpone the model selection part of the algorithm to future work."
 For our purposes. we are only interested in zd and 72. which means hat we have to integrate PCAsNLclap.edie.ciusdata) over all of the other parameters.," For our purposes, we are only interested in $A$ and $\gamma$, which means that we have to integrate $P(A,\gamma, TN_a, A_{a1}, A_{a2}, A_{a3}| {\rm data})$ over all of the other parameters."
 Luckily. as weshow below. or à uniform prior the integration over vi... cds. and idus can be performed analytically.," Luckily, as weshow below, for a uniform prior the integration over $A_{a1}$, $A_{a2}$, and $A_{a3}$ can be performed analytically."
 This amounts to theremoval of the quadratic spin-down component to the pulsar data., This amounts to the of the quadratic spin-down component to the pulsar data.
 We emphasise that this removal technique is quite general. and can be readily applied to unwanted signal of any known functional form (i.e. annual modulations. jumps. ete.see Sec. 3.2)).," We emphasise that this removal technique is quite general, and can be readily applied to unwanted signal of any known functional form (i.e., annual modulations, jumps, etc.—see Sec. \ref{sec:qsdremoval}) ),"
 even if those parameters have already been fit for while calculating the timing residuals., even if those parameters have already been fit for while calculating the timing residuals.
" Phe integration over TN, must be performed. numerically.", The integration over $TN_a$ must be performed numerically.
 In this work we shall use ALCALC simulation as a multi dimensional integration technique., In this work we shall use MCMC simulation as a multi dimensional integration technique.
 Desides Hat priors for most of the parameters. we will use slightly peakecl priors for parameters which have non-normaltisable likelihood functions.," Besides flat priors for most of the parameters, we will use slightly peaked priors for parameters which have non-normalisable likelihood functions."
 This ensures that the Markov Chain can converge., This ensures that the Markov Chain can converge.
 In the rest of the paper. we detail the implementation and. tests of our algorithm.," In the rest of the paper, we detail the implementation and tests of our algorithm."
 While this subsection is written with the PTA in mind. it may well be useful for other applications in pulsar astronomy.," While this subsection is written with the PTA in mind, it may well be useful for other applications in pulsar astronomy."
 We thus begin with a fairly general discussion. and then make it more specific for the PPA case.," We thus begin with a fairly general discussion, and then make it more specific for the PTA case."
" Consider a random Gaussian process O47 with a coherence matrix C'(o). which is contaminated by several systematic signals with known functional forms f,(;) but priori unknown amplitudes £,;."," Consider a random Gaussian process $\delta x^{\rm G}_i$ with a coherence matrix $C(\sigma)$, which is contaminated by several systematic signals with known functional forms $f_p(t_i)$ but a-priori unknown amplitudes $\xi_p$."
 Here σ is a set of interesting parameters which we want to determine from the data dur., Here $\sigma$ is a set of interesting parameters which we want to determine from the data $\delta x$ .
" The resulting signal is given by or. in the vector form. by Llere the components. of the vectors dr. Sr. and € are given by dr. 941. and £j. respectively. and. £ is the non-square matrix with the elements A5,=f,(1;)."," The resulting signal is given by or, in the vector form, by Here the components of the vectors $\vec{\delta x}$ , $\vec{\delta x}^{\rm
 G}$, and $\vec{\xi}$ are given by $\delta x_i$, $\delta x^{\rm G}_i$, and $\xi_p$, respectively, and $F$ is the non-square matrix with the elements $F_{ip}=f_p(t_i)$."
 Note that the dimensions of 5r and £ are dilferent., Note that the dimensions of $\vec{\delta x}$ and $\vec{\xi}$ are different.
 The Bavesian probability cistribution for the parameters is given by where £4 is the prior probability. and AL is. the normalisation., The Bayesian probability distribution for the parameters is given by where $P_0$ is the prior probability and $M$ is the normalisation.
 Since we are only interested. in 6. we can intcerate Plo.£a) over the variables £.," Since we are only interested in $\sigma$, we can integrate $P(\sigma,
 \vec{\xi}|\vec{\delta x})$ over the variables $\vec{\xi}$."
" This process is referred to as marginalisation: it can be done analytically if we assume a [at prior forEe. if Lule.£j is independent]. since £, enter at most. quacratically into the exponential above."," This process is referred to as marginalisation; it can be done analytically if we assume a flat prior for$\vec{\xi}$ [i.e., if $P_0(\sigma,\vec{\xi})$ is $\vec{\xi}$ -independent], since $\xi_p$ enter at most quadratically into the exponential above."
 After some straightforward. mathematics which we have detailed in Appendix A. we get where AL’ is the normalisation. and and the Z-superseript stands for the transposed matrix.," After some straightforward mathematics which we have detailed in Appendix A, we get where $M'$ is the normalisation, and and the $T$ -superscript stands for the transposed matrix."
 Equation (18)) is one of the main equations of the paper. since it provides a statistically rigorous wav to remove (i.c. marginalise over) the unwanted systematic signals [rom random CGaussian processes.," Equation \ref{premoved}) ) is one of the main equations of the paper, since it provides a statistically rigorous way to remove (i.e., marginalise over) the unwanted systematic signals from random Gaussian processes."
" One can check directly that the above expression for Plalor) is insensitive to the values £, of the amplitudes of the svstematic signals in the Eq. (15)).", One can check directly that the above expression for $ P(\sigma|\vec{\delta x})$ is insensitive to the values $\xi_p$ of the amplitudes of the systematic signals in the Eq. \ref{deltareal1}) ).
 We now apply this formalism to account for the quadratic spin-downs in the PX., We now apply this formalism to account for the quadratic spin-downs in the PTA.
 As in Sec. 2..," As in Sec. \ref{sec:theory},"
 it will be convenient to use the 2-index notation for the timing-residiuals. Of; measured at the time μεν where e is the pulsar index. and 7 is the number of the timing residual measurcment for pulsar e.," it will be convenient to use the 2-index notation for the timing-residuals, $\delta t_{ai}$ measured at the time $t_{ai}$, where $a$ is the pulsar index, and $i$ is the number of the timing residual measurement for pulsar $a$ ."
" The space of the spin-down parameters ;1,;. j=1.2.3 has ΑΝ dimensions. where JN is the number of pulsarsin the array."," The space of the spin-down parameters $A_{aj}$ , $j=1,2,3$ has $3N$ dimensions, where $N$ is the number of pulsarsin the array."
 In the componentlanguage. we write where AU annis the part of the timingM residual. due to à random Gaussian process (i.c... GWD. timing noise. etc).," In the componentlanguage, we write where $\delta t^G$ is the part of the timing residual due to a random Gaussian process (i.e., GWB, timing noise, etc.),"
 and j= 1.2.3.," and $j=1,2,3$ ."
" The quantities /5,;,5;, are components of the matrix"," The quantities $
 F_{(ai)(bj)}$ are components of the matrix"
" rr0.055. baud ↑∐∖≼↧⋅↖∐⋜⋯∐↸⊳↴∖∪↕↑↕∐↴∖↸⊳↕∏↴∖↑↸∖↥⋝⋅↖⋜⋯⋜↧↕⋅↖∠∐↕∶↴∙↜ lar ⊢↴⋝↸∖↕∶↴∙⊾⋜↧↕⋜⋯⋅↖⇁∐⋜↧↖⇁↸∖↴⋝↸∖↸∖∐↕∐↑↸∖∏∐⋅↸∖↑↸∖≺∏⋝∙↖↽≼≥↕⊰↖↖ veceut ≼∐⋯↸∖∐↴∖↕∪∐⋜↧↕⋯⋜∏≻∪↕⊀≚⇝−∢⋔∙↖↖↸∖⋜↧↕↴∖∪↻⊓∖↴∖↸∖∐↑↑∐↸∖∐↴∖↑ ∙⋅first ~ )j 6.201 ↴∢ 1.5 ]↜⋅↜ ealaxics ↓↸∖↸∖⋆⊔∏∐≺⋪⋯↸⊳↸∖∪⇀⋅−⊓∙ fa ∖∙↴↽⊀≻⊂∢⊽∙ ⋡⋅≻⊀≻⋅⋅ IL,-50 INpe: 1 q;20.5. 2I Dgat ", $=$ $\sim$ $\beta$ $^{+0.5}_{-0.4}$ $\sim$ $\sim$ $\sim$ $\pm$ $_{o}$ $^{-1}$ $^{-1}$ $_{o}$ $^{th}$ $^{st}$ 
variability. while the hard X-rays fade for a few days before recovering.,"variability, while the hard X-rays fade for a few days before recovering."
 In terms of the x-ray spectral states. several works have verified that the radio flares of this source occur during the SPLS (e.g.. Fender et al..," In terms of the x-ray spectral states, several works have verified that the radio flares of this source occur during the SPLS (e.g., Fender et al.,"
 2004) and the x-ray emission of both the plateau and the flare state are different manifestations of the SPLS (e.g.. Reig et al..," 2004) and the x-ray emission of both the plateau and the flare state are different manifestations of the SPLS (e.g., Reig et al.,"
 2003)., 2003).
 The examination of radio and x-ray observations for other microquasars (e.g.. XTE 118594226. ΧΤΕ J1550-564) also suggests that the ejection of relativistic matter happens when the source is very active and in the SPLS (e.g.. Hannikeainen et.," The examination of radio and x-ray observations for other microquasars (e.g., XTE J1859+226, XTE J1550-564) also suggests that the ejection of relativistic matter happens when the source is very active and in the SPLS (e.g., Hannikeainen et."
 al. 2001; Brocksopp et.," al, 2001; Brocksopp et."
 al. 2002: Fender et al.," al, 2002; Fender et al.,"
 2004: McClintock et., 2004; McClintock et.
 al. 2007).," al, 2007)."
 According to Fender et al. (, According to Fender et al. (
2004). the origin of the optically thin emission in radio is due to shock waves that are formed in the jet when the system passes from a chard’ SPLS to a soft SPLS.,"2004), the origin of the optically thin emission in radio is due to shock waves that are formed in the jet when the system passes from a `hard' SPLS to a `soft' SPLS."
 However. what generates these shock waves or the triggering mechanism for the ejections of matter is unclear.," However, what generates these shock waves or the triggering mechanism for the ejections of matter is unclear."
 In. 2005. de Gouveia Dal Pino Lazarian (see also de Gouveia Dal Pino 2006) proposed à mechanism that can be responsible for the initial acceleration of the plasma jet to relativistic speeds in the case of the microquasar. GRS1I915+105.," In 2005, de Gouveia Dal Pino Lazarian (see also de Gouveia Dal Pino 2006) proposed a mechanism that can be responsible for the initial acceleration of the plasma jet to relativistic speeds in the case of the microquasar GRS1915+105."
 Their scenario 1s. related. to violent reconnection episodes between the magnetic field lines of the inner disk region and those that are anchored in the black hole., Their scenario is related to violent reconnection episodes between the magnetic field lines of the inner disk region and those that are anchored in the black hole.
" We here revisit this model and argue that it could be responsible for the transition from the ""hard? SPLS to the ""soft SPLS seen in other microquasars.", We here revisit this model and argue that it could be responsible for the transition from the `hard' SPLS to the `soft' SPLS seen in other microquasars.
 We also extend it to the AGN Jets and briefly discuss its role for thermal YSO jets (see also de Gouveia Dal Pino 2006 and de Gouveia Dal Pino et al., We also extend it to the AGN jets and briefly discuss its role for thermal YSO jets (see also de Gouveia Dal Pino 2006 and de Gouveia Dal Pino et al.
 2009 for earlier discussions)., 2009 for earlier discussions).
 We note that an interesting correlation between the radio and the (hard) X-ray luminosity has been reported by Laor Behar (2008) for sources spanning 10! orders of magnitude in mass (from magnetically active stars to some galactic black holes and radio quiet AGNs). and recently extended to dwarf nova outbursts by Soker Vrtilek (2009).," We note that an interesting correlation between the radio and the (hard) X-ray luminosity has been reported by Laor Behar (2008) for sources spanning $10^{10}$ orders of magnitude in mass (from magnetically active stars to some galactic black holes and radio quiet AGNs), and recently extended to dwarf nova outbursts by Soker Vrtilek (2009)."
 This correlation holds only for sources for which Lg/Ly«107 and suggests that a common mechanism may be responsible for the radio emission in these highly different objects., This correlation holds only for sources for which $L_R/L_X < 10^{-5}$ and suggests that a common mechanism may be responsible for the radio emission in these highly different objects.
 Because in magnetically active stars the emission is related to the coronae. these authors have argued that the same might be occurring in some BHXRBs and radio quiet AGNS. 1e.. the radio emission could also come from magnetic activity in the coronae above the accretion disk. just like in the scenario that we Investigate here in detail (and which was previously suggested in de Gouveia Dal Pino 2006. and de Gouveia Dal Pino et al.," Because in magnetically active stars the emission is related to the coronae, these authors have argued that the same might be occurring in some BHXRBs and radio quiet AGNs, i.e., the radio emission could also come from magnetic activity in the coronae above the accretion disk, just like in the scenario that we investigate here in detail (and which was previously suggested in de Gouveia Dal Pino 2006, and de Gouveia Dal Pino et al."
 2010a. 201050.," 2010a, 2010b)."
 Earlier studies have also revealed a correlation between the radio and the X-ray luminosity of BHXRBs in their quiescent “low/hard™ state and low-luminosity AGNs with nuclear radio emission or weak radio jets (Gallo et al.," Earlier studies have also revealed a correlation between the radio and the X-ray luminosity of BHXRBs in their quiescent ""low/hard"" state and low-luminosity AGNs with nuclear radio emission or weak radio jets (Gallo et al."
 2003: Merloni et al., 2003; Merloni et al.
 2003: Falcke et al., 2003; Falcke et al.
 2004)., 2004).
 As also remarked by Soker Vrtilek. suggestions for the presence of coronae above accretion disks are not new (e.g.. Liang Price 1977. Liang 1979. Galeev et al.," As also remarked by Soker Vrtilek, suggestions for the presence of coronae above accretion disks are not new (e.g., Liang Price 1977, Liang 1979, Galeev et al."
 1979; Done Osborne 1997; Wheatley Mauche 2005; Cao 2009). and the connection between coronae and jets were previously proposed as well (e.g.. Fender et al.," 1979; Done Osborne 1997; Wheatley Mauche 2005; Cao 2009), and the connection between coronae and jets were previously proposed as well (e.g., Fender et al."
 1999: Markoff et al., 1999; Markoff et al.
 2005: de Gouveia Dal Pino Lazarian 2000. 2001. 2005).," 2005; de Gouveia Dal Pino Lazarian 2000, 2001, 2005)."
 If the magnetic activity in erupting accreting disks is similar to that in stars. then coronal mass ejections. as 1 the Sun. could be expected.," If the magnetic activity in erupting accreting disks is similar to that in stars, then coronal mass ejections, as in the Sun, could be expected."
 Hence magnetic flares similar to those in active stars might be à potential mechanism operating at the jet launching region in à variety of systems. from young stellar objects to BHs (de Gouveia Dal Pino 2006. de Gouveia Dal Pino et al.," Hence magnetic flares similar to those in active stars might be a potential mechanism operating at the jet launching region in a variety of systems, from young stellar objects to BHs (de Gouveia Dal Pino 2006, de Gouveia Dal Pino et al."
 2009: Soker 2007; Soker Vrtilek 2009)., 2009; Soker 2007; Soker Vrtilek 2009).
 This paper is organized as follows: in Sect., This paper is organized as follows: in Sect.
 2 we briefly describe de Gouveia Dal Pino Lazarian’s model., 2 we briefly describe de Gouveia Dal Pino Lazarian's model.
 In Sect., In Sect.
 3 we discuss it in the context of the microquasars and in Sect., 3 we discuss it in the context of the microquasars and in Sect.
 4 we propose its generalization to other classes of relativistic jets. extending it to low-luminosity AGN jets.," 4 we propose its generalization to other classes of relativistic jets, extending it to low-luminosity AGN jets."
 In Sect., In Sect.
 5 we briefly discuss the reconnection model in the context of the YSO jets and finally. in Sect.," 5 we briefly discuss the reconnection model in the context of the YSO jets and finally, in Sect."
 6. we draw our conclusions.," 6, we draw our conclusions."
 We consider à magnetized accretion disk around a rotating (Kerr) BH as schematized in Fig., We consider a magnetized accretion disk around a rotating (Kerr) BH as schematized in Fig.
 1., 1.
 A detailed description of the scenario adopted is given in de Gouveia Dal Pino Lazarian (2005)., A detailed description of the scenario adopted is given in de Gouveia Dal Pino Lazarian (2005).
 Here we briefly present the assumptions made., Here we briefly present the assumptions made.
 A magnetosphere around the central BH may be formed from the drag of magnetic field lines by the aceretion disk (e.g.. MacDonald et al.," A magnetosphere around the central BH may be formed from the drag of magnetic field lines by the accretion disk (e.g., MacDonald et al."
 1986: Wang et al., 1986; Wang et al.
 2002)., 2002).
 The disk large-scale poloidal magnetic field could be established by the action of à turbulent dynamo inside the accretion disk (Livio et al., The disk large-scale poloidal magnetic field could be established by the action of a turbulent dynamo inside the accretion disk (Livio et al.
 2003; King et al., 2003; King et al.
 2004; Uzdensky Goodman 2008) driven. e.g.. by the magnetorotatioal instability (Balbus Hawley 1998) and disk differential rotation.," 2004; Uzdensky Goodman 2008) driven, e.g., by the magnetorotational instability (Balbus Hawley 1998) and disk differential rotation."
 Although this scenario remains speculative and nothi5 definitive has been revealed yet by global disk numerical simulations. the action of a turbulent dynamo followed by the advection of the magnetic flux with the gas towards the iner disk region could result in à gradual increase of the magnetic flux in this region (e.g.. Merlont 2003: Livio et al.," Although this scenario remains speculative and nothing definitive has been revealed yet by global disk numerical simulations, the action of a turbulent dynamo followed by the advection of the magnetic flux with the gas towards the inner disk region could result in a gradual increase of the magnetic flux in this region (e.g., Merloni 2003; Livio et al."
 2003: Tagger et al., 2003; Tagger et al.
 2004: de Gouveia Dal Pino Lazarian 2005: McKinney Blandford 2009)., 2004; de Gouveia Dal Pino Lazarian 2005; McKinney Blandford 2009).
 Even without any dynamo action. a net poloidal field could be built in the," Even without any dynamo action, a net poloidal field could be built in the"
chemical maps 1s presented in Sect. 8..,chemical maps is presented in Sect. \ref{DI}.
 The paper ends with a summary of the main results and discussion in Sect. 9.., The paper ends with a summary of the main results and discussion in Sect. \ref{disc}.
 Using the newly built polarimeter HARPSpol (??) attached tothe HARPS spectrometer (?) at the ESO 3.6-m telescope we have obtained high-quality observations at ten phases. covering the full orbital period of 66 Ert.," Using the newly built polarimeter HARPSpol \citep{HARPSpol, Snik:2010} attached tothe HARPS spectrometer \citep{HARPS} at the ESO 3.6-m telescope we have obtained high-quality observations at ten phases, covering the full orbital period of 66 Eri."
 The resolution of spectra is R 11150000 and a typical S/N is 200—300 at 2=5200A., The resolution of spectra is $R$ 000 and a typical $S/N$ is 200–300 at $\lambda\approx5200$.
. The HARPS detector is a mosaic of two 2K x 4K CCDs. allowing to record 45 and 26 polarimetric echelle orders on the blue and red CCD. respectively.," The HARPS detector is a mosaic of two 2K $\times$ 4K CCDs, allowing to record 45 and 26 polarimetric echelle orders on the blue and red CCD, respectively."
 The calibration set included 20 bias exposures. 20 flat fields and two ThAr frames for each night.," The calibration set included 20 bias exposures, 20 flat fields and two ThAr frames for each night."
 The flat fields and comparison spectra were recorded using the circular polarization mode., The flat fields and comparison spectra were recorded using the circular polarization mode.
 All science frames of 66 Eri were obtained in circular polarization. covering the wavelength range of 3780-6913 wwith a small gap at 5259-533A.," All science frames of 66 Eri were obtained in circular polarization, covering the wavelength range of 3780–6913 with a small gap at 5259–5337."
". Each observation of the star was split into four sub-exposures corresponding to the 45°. 1357, 225° or 315° position of the quarter-wave plate relative to the beam-splitter."," Each observation of the star was split into four sub-exposures corresponding to the $\degr$, $\degr$, $\degr$ or $\degr$ position of the quarter-wave plate relative to the beam-splitter."
" The length of individual sub-exposures varied between 200 and 300 s. depending on the weather conditions,"," The length of individual sub-exposures varied between 200 and 300 s, depending on the weather conditions."
 The ESO reduction pipeline was not available at that time. so we employed REDUCE package (?).. written in IDL. to perform a number of standard steps to reduce and calibrate our cross-dispersed echelle spectra.," The ESO reduction pipeline was not available at that time, so we employed REDUCE package \citep{reduce}, written in IDL, to perform a number of standard steps to reduce and calibrate our cross-dispersed echelle spectra."
 We average and subtract bias images from the master flat and science frames., We average and subtract bias images from the master flat and science frames.
 To locate spectral orders. REDUCE uses a cluster analysis method in conjunction. with the master flat image.," To locate spectral orders, REDUCE uses a cluster analysis method in conjunction with the master flat image."
 For the correction of pixel-to-pixel sensitivity variations in the science images the code normalizes the master flat field., For the correction of pixel-to-pixel sensitivity variations in the science images the code normalizes the master flat field.
 Finally. REDUCE removes the scattered light and performs the optimal extraction of the stellar spectra as described by ?..," Finally, REDUCE removes the scattered light and performs the optimal extraction of the stellar spectra as described by \citet{reduce}."
 HARPS spectrometer is well-known for its stability. which is of the order of | !.," HARPS spectrometer is well-known for its stability, which is of the order of 1 $^{-1}$."
 Taking this into account. it is sufficient for our study to use only one ThAr spectrum obtained during each night to do the wavelength calibration.," Taking this into account, it is sufficient for our study to use only one ThAr spectrum obtained during each night to do the wavelength calibration."
 Employing ~ 7700-900 ThAr lines we constructed a 2-D wavelength solution with an internal wavelength calibration accuracy of 18-21 m s!., Employing $\sim$ 700–900 ThAr lines we constructed a 2-D wavelength solution with an internal wavelength calibration accuracy of 18–21 m $^{-1}$.
 The final step prior to the Stokes parameters derivation is continuum normalization., The final step prior to the Stokes parameters derivation is continuum normalization.
 The continuum level is set by dividing each spectrum by a smooth. slowly varying function. obtained by fitting the upper envelope of the blaze shape corrected. spliced spectrum.," The continuum level is set by dividing each spectrum by a smooth, slowly varying function, obtained by fitting the upper envelope of the blaze shape corrected, spliced spectrum."
 For the derivation of Stokes V parameter we use the ratio method described by ?.., For the derivation of Stokes $V$ parameter we use the ratio method described by \citet{Bagnulo:2009}.
 This method minimizes spurious polarization effects by an appropriate combination of the two physical beams recorded for four different retarder quarter-wave plate positions., This method minimizes spurious polarization effects by an appropriate combination of the two physical beams recorded for four different retarder quarter-wave plate positions.
 Along with the polarization we also derive a diagnostic null spectrum., Along with the polarization we also derive a diagnostic null spectrum.
 It is obtained by combining the polarization signal in. individual sub-exposures destructively. thus showing the residual instrumental polarization remaining after application of the ratio method.," It is obtained by combining the polarization signal in individual sub-exposures destructively, thus showing the residual instrumental polarization remaining after application of the ratio method."
 We use the null spectrum in the same analysis steps as the Stokes V spectrum. thus providing a realistic estimate of possible errors.," We use the null spectrum in the same analysis steps as the Stokes $V$ spectrum, thus providing a realistic estimate of possible errors."
 Combination of eight spectra in four individual sub-exposures provided a convenient possibility to detect and remove remaining cosmic hits that otherwise seriously distort the final Stokes spectra., Combination of eight spectra in four individual sub-exposures provided a convenient possibility to detect and remove remaining cosmic hits that otherwise seriously distort the final Stokes spectra.
 Affected pixels are identified by their large deviation from the median and are substituted by the latter., Affected pixels are identified by their large deviation from the median and are substituted by the latter.
 Since our exposure times were relatively short. only 1—2 pixels required correction in each echelle order.," Since our exposure times were relatively short, only 1–2 pixels required correction in each echelle order."
 Previous attempts to find magnetic fields in. HgMn stars set an upper limit on the longitudinal magnetic field. below 100 G (22222)..," Previous attempts to find magnetic fields in HgMn stars set an upper limit on the longitudinal magnetic field below 100 G \citep{Shorlin:2002, Wade:2006, Auriere:2010, Folsom:2010, Makaganiuk:2011}."
 The fields of this strength are undetectable in individual spectral lines., The fields of this strength are undetectable in individual spectral lines.
 In this case the sensitivity of magnetic field search can be increased by adding information from many spectral lines., In this case the sensitivity of magnetic field search can be increased by adding information from many spectral lines.
 Such a multi-line method has been implemented by ? imn the so-called least-squares deconvolution (LSD)., Such a multi-line method has been implemented by \citet{Donati:1997} in the so-called least-squares deconvolution (LSD).
 This technique assumes identical shape of spectral lines and represents observations as a superposition of profiles scaled by appropriate weight., This technique assumes identical shape of spectral lines and represents observations as a superposition of profiles scaled by appropriate weight.
 With this method it becomes possible to derive à high-precision average profile. increasing the to-noise ratio by a factor of up to 1000.," With this method it becomes possible to derive a high-precision average profile, increasing the signal-to-noise ratio by a factor of up to 1000."
 The latest studies of weak magnetic fields proved the LSD technique to be very effective in detecting fields weaker than | G (??)..," The latest studies of weak magnetic fields proved the LSD technique to be very effective in detecting fields weaker than 1 G \citep{Auriere:2009, Lignieres:2009}."
 To construct a line mask required by LSD. we extracted the line list from VALD (?) using an atmospheric model with the effective temperature of 10900 K and abundance of chemical elements according to the results of ?. for the more massive star.," To construct a line mask required by LSD, we extracted the line list from VALD \citep{VALD} using an atmospheric model with the effective temperature of 10900 K and abundance of chemical elements according to the results of \citet{Yuschenko:1999} for the more massive star."
 We note that LSD analysis is very weakly sensitive to the choice of aand abundances adopted for the mask., We note that LSD analysis is very weakly sensitive to the choice of and abundances adopted for the mask.
 A line mask is a set of the laboratory line wavelengths and corresponding weights., A line mask is a set of the laboratory line wavelengths and corresponding weights.
 In the case of the Stokes / spectra. the weight ts a residual depth of individual line. given by VALD.," In the case of the Stokes $I$ spectra, the weight is a residual depth of individual line, given by VALD."
 Por the Stokes V spectra the weight is the product of central depth. the line wavelength normalized by .t=4800Á.. and an effective Landé factor of a given spectral line.," For the Stokes $V$ spectra the weight is the product of central depth, the line wavelength normalized by $\lambda=4800$, and an effective Landé factor of a given spectral line."
 Spectral lines with the central depth lower than a given cutoff factor are excluded from the line mask., Spectral lines with the central depth lower than a given cutoff factor are excluded from the line mask.
 By setting the cutoff criterion to 0.1. we produced the line mask containing 717 spectral lines.," By setting the cutoff criterion to 0.1, we produced the line mask containing 717 spectral lines."
 We use the LSD code by ?. to compute LSD Stokes 7. V. and null profiles.," We use the LSD code by \citet{Kochukhov:2010} to compute LSD Stokes $I$, $V$, and null profiles."
 Profiles were computed in the velocity range from -170 to 200 wwith a step of 0.8kms!., Profiles were computed in the velocity range from $-170$ to 200 with a step of 0.8.
. This value corresponds to the average pixel scale of HARPSpol spectra., This value corresponds to the average pixel scale of HARPSpol spectra.
 The errors of LSD profiles were calculated by propagating the uncertainties of individual pixels obtained at the reduction stage., The errors of LSD profiles were calculated by propagating the uncertainties of individual pixels obtained at the reduction stage.
 In general there is à mismatch between a model LSD spectrum and real observations due to coarse assumptions of the LSD technique., In general there is a mismatch between a model LSD spectrum and real observations due to coarse assumptions of the LSD technique.
 To account for these systematic errors we scale uncertainties of the calculated LSD profiles by the reduced y as described by ?.., To account for these systematic errors we scale uncertainties of the calculated LSD profiles by the reduced $\chi^2$ as described by \citet{Wade:2000}. .
 The re-scaled LSD profile uncertainties are used for the estimation of the longitudinal magnetic field measurements., The re-scaled LSD profile uncertainties are used for the estimation of the longitudinal magnetic field measurements.
Several views of the light curve of WH 15D are provided i1 Figures 1 to 5..,Several views of the light curve of KH 15D are provided in Figures \ref{figh} to \ref{fig2a}.
 The I inagniuce is usecl becaise most epochs included Lbaucl observations wlere the system is relatively bright., The I magnitude is used because most epochs included I-band observations where the system is relatively bright.
 Figure 1 provides tlie couext for this study by showing all of the banc photometry avalable for the star siuce 1950. wlich iicludes the photographic photouetry (some of it trausformect rom optical meastrelents 1lace al shorter wavelengths) from Johuson&Winn(2001) arn| al.(2005) ald the CCD photometry.," Figure \ref{figh} provides the context for this study by showing all of the I-band photometry available for the star since 1950, which includes the photographic photometry (some of it transformed from optical measurements made at shorter wavelengths) from \citet{J04} and \citet{J05} and the CCD photometry."
 It is clear that. as predicted. the object lias eutered iitoa uew phase. oie in whic1 neither star is directly. visible at any Tme.," It is clear that, as predicted, the object has entered into a new phase, one in which neither star is directly visible at any time."
 We may expect. therefore. that the system brightuess will remain below about I = 16.7 lor awule. perhaps even ceuturies.," We may expect, therefore, that the system brightness will remain below about I = 16.7 for awhile, perhaps even centuries."
" Or he other haud. it is euirey possible that the object will brieltel again much sooner than tliat with tlie reappearauce of eiteither star A or star B. Nothing in the «""urrent moclels allows us to predict |OW long the total oceulation of the binary orbit will persist. otier than to say that after a inilleunium or so we should be bacς to the current state."," On the other hand, it is entirely possible that the object will brighten again much sooner than that with the reappearance of either star A or star B. Nothing in the current models allows us to predict how long the total occultation of the binary orbit will persist, other than to say that after a millennium or so we should be back to the current state."
 Figure 2 shows al of the CCD photometric daa obtaiied by our group since late 1995 versus time., Figure \ref{fig1} shows all of the CCD photometric data obtained by our group since late 1995 versus time.
 The one brielt point in 1995 represents the ouly detection in the mocleru CCD era of star B and indicates that the star is more luminous than star Frou 1996 to 2006 the system hiada peak brightuess of around 11.5 mae (Hamiltonetal.2005)., The one bright point in 1995 represents the only detection in the modern CCD era of star B and indicates that the star is more luminous than star From 1996 to 2006 the system had a peak brightness of around 14.5 mag \citep{Ham05}.
. Since 2006 there has been a steady decline in the systetis brielituess at rnaxiuinun (see Fig. 2))., Since 2006 there has been a steady decline in the system's brightness at maximum (see Fig. \ref{fig1}) ).
 In Figure κ)+)3. we ὀκραμά the tiije axis to illustrate the cletailec behavior of the star during the last five observing seasons., In Figure \ref{fig} we expand the time axis to illustrate the detailed behavior of the star during the last five observing seasons.
 Accoring to the models of Chiang&lurray-Clay.(2001).. Wi(2001.2006) aud Silvia&σιJl(2008.. the decrease it inaxiiu system brightuess is due t| the steady advauce of the occultitο edge across the projection of ie binary. orbit oi the sky.," According to the models of \citet{CM04}, \citet{w04,w06} and \citet{sa08}, the decrease in maximum system brightness is due to the steady advance of the occulting edge across the projection of the binary orbit on the sky."
 While a decline such as this was pre(licted i1 all of the above models. its timiug aud the exter ol the decline was not correctly preicted in any of them.," While a decline such as this was predicted in all of the above models, its timing and the extent of the decline was not correctly predicted in any of them."
 Substaule [acing has occurred inaM7 years earlier than precicted by Chia[n]SA&Muwrayv-Clay(2001) auc about a year later tLan predicted by Winnetal.(2006) or, Substantial fading has occurred many years earlier than predicted by \citet{CM04} and about a year later than predicted by \citet{w06} or
au error on the estimate of b has almost no effect on the result.,an error on the estimate of $b$ has almost no effect on the result.
 Iu fact. 6 is well-cetermuned by the very bottom of the strongest lines where the level is clearly less than 110therecm ((Fig. 1)).," In fact, $b$ is well-determined by the very bottom of the strongest lines where the level is clearly less than $1\cdot 10^{-14}$ (Fig. \ref{plot_feii}) )."
 However. apparent enüssious due to the addition of the statistical noise aud a bad estimate of the backerounudo level might be possible.," However, apparent emissions due to the addition of the statistical noise and a bad estimate of the background level might be possible."
 But. although not excluded. it is very unlikely that this coincidence cam coutribu| fo give apparent emissions iu he two sides of the two strougest ]lines.," But, although not excluded, it is very unlikely that this coincidence can contribute to give apparent emissions in the two sides of the two strongest lines."
 The most inportau alternative to enission bv lis a time variation of the sspectrun between the observations of the template (the star) aud he disk spectra., The most important alternative to emission by is a time variation of the spectrum between the observations of the template (the star) and the disk spectra.
 If the absorption component iu he lines had significantly decreased during the acquisition of he data. hen the result is au apparent excess of enission in the second spectrmm obtained with the sli off the star.," If the absorption component in the lines had significantly decreased during the acquisition of the data, then the result is an apparent excess of emission in the second spectrum obtained with the slit off the star."
 Although the time between both spectra las been minimized. this possibility cannot be excluded without iw observations. for example ou the other side of the disk where the emissiou should be stronger in the blue.," Although the time between both spectra has been minimized, this possibility cannot be excluded without new observations, for example on the other side of the disk where the emission should be stronger in the blue."
 Tf this detection is really due to emission by Hous. the lines width nmst be explained through the dynamics of these Hous iu the disk.," If this detection is really due to emission by ions, the lines width must be explained through the dynamics of these ions in the disk."
" The Hons must be ejected from the sxvsteni by the radiation pressure which is stronger than the eravitation bv a factor Jp,j;75 (Laeranec ct al."," The ions must be ejected from the system by the radiation pressure which is stronger than the gravitation by a factor $\beta_{FeII}\approx 5$ (Lagrange et al.,"
 1998)., 1998).
 After ejection. they rapidly reach a coustaut asviuptotic velocity ox.," After ejection, they rapidly reach a constant asymptotic velocity $v_{\infty}$."
 Tf they are ejected from a body on a circular orbit. ex~IEjoDOGMAfay). where ay is the radius of the orbit of the pareut body.," If they are ejected from a body on a circular orbit, $v_{\infty}\sim \sqrt{(2\beta-1)(GM/a_0)}$, where $a_0$ is the radius of the orbit of the parent body."
 If they are ejected roni a colet on a parabolic orbit. the final velocity is ος7VIE.GMfag).," If they are ejected from a comet on a parabolic orbit, the final velocity is $v_{\infty}\sim \sqrt{(2\beta GM/a_0)}$."
 Tn this simaple scheme. the observed final velocity of about 100 lan + (Fig. 3))," In this simple scheme, the observed final velocity of about 100 km $^{-1}$ (Fig. \ref{vel_feii}) )"
 corresponds to a production at about 1.5 AU from the star. or similarly o the absence of gas drag bevoud that clistance.," corresponds to a production at about 1.5 AU from the star, or similarly to the absence of gas drag beyond that distance."
 The emission lines are strougcr in the red than iu the due., The emission lines are stronger in the red than in the blue.
 This is similar to the asvuuuetry already observed iui he cometary absorption lines which are mainly redshiftec (Beust et al., This is similar to the asymmetry already observed in the cometary absorption lines which are mainly redshifted (Beust et al.
 1996)., 1996).
 This last asvuuuetry is well-explained wv the evaporation of comets with a simall range of ongitude of periastron (DBeust et al., This last asymmetry is well-explained by the evaporation of comets with a small range of longitude of periastron (Beust et al.
 1998)., 1998).
 Au alternative explanation for the observed asviuuetry in the emission, An alternative explanation for the observed asymmetry in the emission
subsets.,subsets.
 Seasons were considered as follows. winter: January. February and. March: spring: Abril. May and June: summer: July. August and September and autumn: October. November and December.," Seasons were considered as follows, winter: January, February and March; spring: Abril, May and June; summer: July, August and September and autumn: October, November and December."
 Lt is clear that curing the summer the conditions are more variable than at any other epoch of the vear., It is clear that during the summer the conditions are more variable than at any other epoch of the year.
 In the other seasons the conditions are very stable., In the other seasons the conditions are very stable.
 lig., Fig.
 14 shows a grey level plot of the median percentage of clear time for a given combination of month and hour of day., \ref{month_hour} shows a grey level plot of the median percentage of clear time for a given combination of month and hour of day.
 Squares are drawn when more than LO h of data are available: crosses indicate less than 10 h of data., Squares are drawn when more than 10 h of data are available; crosses indicate less than 10 h of data.
 Clear conditions are present in the colder ancl drier months. from October to June.," Clear conditions are present in the colder and drier months, from October to June."
 Dark squares show cloudy weather. clearly dominant in the afternoons ofthe summer months. from July to September.," Dark squares show cloudy weather, clearly dominant in the afternoons of the summer months, from July to September."
 We repeated. the analysis for airmass lower than 2., We repeated the analysis for airmass lower than 2.
 An equivalent histogram to that shown in Fig. 9.. ," An equivalent histogram to that shown in Fig. \ref {histograma},"
was created by computing the fraction of f(elear) for every hour. adding 5211 h. As expected. it also has an almost unimocdal distribution: 82.5 per cent have f(elear) = 1 while 6.7 per cent of hours f(clear) = 0.," was created by computing the fraction of f(clear) for every hour, adding 5211 h. As expected, it also has an almost unimodal distribution: 82.5 per cent have f(clear) = 1 while 6.7 per cent of hours f(clear) = 0."
 The remaining fraction of data have intermediate values., The remaining fraction of data have intermediate values.
 Phe values of ((clear) obtained for the periodicities presented in this section are. very. similar but with less dispersion., The values of f(clear) obtained for the periodicities presented in this section are very similar but with less dispersion.
 In fact. in the analvsis per hour the dillerence in median. values are within 0.1. per cent.," In fact, in the analysis per hour the difference in median values are within 0.1 per cent."
 For the analysis per month the dillerences are also in that range except for July and August with dillerences between 0.3 to 13 per cent. with a maximum of 20 per cent for July 2006.," For the analysis per month the differences are also in that range except for July and August with differences between 0.3 to 13 per cent, with a maximum of 20 per cent for July 2006."
 The lower values obtained for the global distribution and for dillerent. periods can be explained by the presence of, The lower values obtained for the global distribution and for different periods can be explained by the presence of
lt has been several vears since. the announcement of. the discovery. that some subdwarl. B stars. pulsate (Ixilkenny.etal.. 1997).,It has been several years since the announcement of the discovery that some subdwarf B stars pulsate \cite{k97}.
". Photometric;. variationsD. in. sdDV"" stars. or “EC 14026 stars” after. the prototype. are measured in huncdredths of. a magnitude. and generally have periods. of 100200 s. “Phey appear to be due to low-order stellar pulsations."," Photometric variations in sdBV stars, or “EC 14026 stars” after the prototype, are measured in hundredths of a magnitude and generally have periods of 100–200 s. They appear to be due to low-order stellar pulsations."
 When the pulsations are better understood. it will be possible to use asteroseismology το obtain more information about the stars. including their size. mass. and structure. as has been done with some other classes ol pulsating stars.," When the pulsations are better understood, it will be possible to use asteroseismology to obtain more information about the stars, including their size, mass, and structure, as has been done with some other classes of pulsating stars."
 This will probably require multi-site photometric ancl spectroscopic Observations., This will probably require multi-site photometric and spectroscopic observations.
 PCO 16051072 has the largest. photometric pulsation amplitudes and the richest [requeney spectrum of all studied SIBVs., PG $+072$ has the largest photometric pulsation amplitudes and the richest frequency spectrum of all studied sdBV's.
 Hs light curve shows more than. 50. frequencies. though it Wois dominatedinate by τς5 frequenciesfrenee betweenπο 159NO and; 2.74 mllz (periods between 529 anc 365 5) (xoenetal.1998:Ixilkennyetal. 1999).," Its light curve shows more than 50 frequencies, though it is dominated by 5 frequencies between 1.89 and 2.74 mHz (periods between 529 and 365 s) \cite{ko98,k99}."
.. It has an effective temperature of 323004 Ix (Lieber. Reid. Werner 1999).," It has an effective temperature of $32\,300 \pm 300$ K (Heber, Reid, Werner 1999)."
 Ht has a lower gravity (logg= 5.25) and longer pulsation periods than any other sdDV. studied. which Ixilkennv et al.," It has a lower gravity $\log g = 5.25$ ) and longer pulsation periods than any other sdBV studied, which Kilkenny et al."
 (1999) say indicatesM that it. has evolved away from⋅ the core helium. burning. horizontal. branch where the shorter-period. sdDBV'sy» are found., \shortcite{k99} say indicates that it has evolved away from the core helium burning horizontal branch where the shorter-period sdBV's are found.
. Lt is. expected to be evolving. more rapidly. than other known sdDV's., It is expected to be evolving more rapidly than other known sdBV's.
M Ixawaler (1999) and Wilkenny et al., Kawaler \shortcite{kw99} and Kilkenny et al.
 (1999) report comparisons of the large-amplitude pulsations of Ρα 16051072 to those of a model with similar. physical parameters., \shortcite{k99} report comparisons of the large-amplitude pulsations of PG 1605+072 to those of a model with similar physical parameters.
" They suggest that what are observed. are most likely low-order nonradial pulsations in. ""trapped: modes."" though it was not possible to make individual mode identifications."," They suggest that what are observed are most likely low-order nonradial pulsations in “trapped modes,” though it was not possible to make individual mode identifications."
 An earlier study. O'Toole et al 2000).," An earlier study, O'Toole et al. \shortcite{o00},"
. used. time-resolved spectroscopy of PC. 1072 to look for evidence of pulsation in the radial velocities., used time-resolved spectroscopy of PG $+$ 072 to look for evidence of pulsation in the radial velocities.
 Their. observations provided. 38.65. hours of. data over a LO day period., Their observations provided 38.65 hours of data over a 10 day period.
. Spectra. within a data series were generally separated by 61 to 75 seconds., Spectra within a data series were generally separated by 61 to 75 seconds.
 “Phey detected: velocity. variations. with the three largest amplitudes having frequencies similar to those found in the photometric data by Iilkenny et al. (1999).," They detected velocity variations, with the three largest amplitudes having frequencies similar to those found in the photometric data by Kilkenny et al. \shortcite{k99}."
.. “Phe combination of the fairly slow repetition of observations. noise in the velocity spectrum caused. by the use of small Tκber 2m) tel1 n ‘ ∠↓⊳⋯↓⋖⋅⋖⊾↓⋅∖∕−−⊔↓⋖⋅⋖⊾⋡∖≼⇍∪≻≺⋅⋡∖⋡⊳⋯∠⊳↧⋡↓⋅∪⊳⊔≺∩⋡∖⋖⊾↓⋅∖⇁⊳↧↓∪⊔⊳↧⊳↧↓⊳↧⊳∖ial: Lolü oesLali signature .in comparison.. with the spacing of the [requencies observed in the photometry meant that only the strongest pulsations could be detected with any certainty.," The combination of the fairly slow repetition of observations, noise in the velocity spectrum caused by the use of small diameter $< 2$ -m) telescopes, and a broad observational alias signature in comparison with the spacing of the frequencies observed in the photometry meant that only the strongest pulsations could be detected with any certainty."
The redshift distribution of all the 925 ealaxics iu the photometric sample shows a peak at τνσε1 aud a moderate decrease at 21 without any other peak.,The redshift distribution of all the 925 galaxies in the photometric sample shows a peak at $z\simeq 1$ and a moderate decrease at $z>1$ without any other peak.
 The £(BV) value of galaxies remains almost constant for 2=06 with a possible weak peak at 2=3)L which is consisteut with the model of a constant cosuic SFR eiven by Calzetti Heckman (1999).," The $E(B-V)$ value of galaxies remains almost constant for $z=0-6$ with a possible weak peak at $z=3-4$, which is consistent with the model of a constant cosmic SFR given by Calzetti Heckman (1999)."
 We would like to express our gratiude to T. Ihodamia N. Avimoto for kindly allowing 1s to use them new population svuthesis code and to ixunvnious referee for constructive couuneuts., We would like to express our gratitude to T. Kodama N. Arimoto for kindly allowing us to use their new population synthesis code and to anonymous referee for constructive comments.
 ILE. wishes to thank the Japan Society for the Promotion of Science for a financial support., H.F. wishes to thank the Japan Society for the Promotion of Science for a financial support.
 This work is supported iu part bv Caauts-iu-Aid (O7CE2002. 116lO22s8. 10110062) from the Ministrv of Education. Science. Sports aud Cuture of Japan.," This work is supported in part by Grants-in-Aid (07CE2002, 11640228, 10440062) from the Ministry of Education, Science, Sports and Culture of Japan."
the field structure is unaffected by à switch to hyperdiffusion (see 4)). but the locality of the dissipation operator probably does matter (see remarks at the end of 3.1)).,"the field structure is unaffected by a switch to hyperdiffusion (see ), but the locality of the dissipation operator probably does matter (see remarks at the end of )."
 Further investigation of the universality of the statistics of the small-scale magnetic turbulence with respect to the form of the UV regularization ts also left for the future., Further investigation of the universality of the statistics of the small-scale magnetic turbulence with respect to the form of the UV regularization is also left for the future.
" We have found that the folding structure of subviscous-scale magnetic fluctuations that is formed via the kinematic ""stretch-and-fold"" small-scale-dynamo mechanism remains the essential feature of the nonlinear regime.", We have found that the folding structure of subviscous-scale magnetic fluctuations that is formed via the kinematic “stretch-and-fold” small-scale-dynamo mechanism remains the essential feature of the nonlinear regime.
 The scale separation is of crucial importance here: while small-scale structure can be generated and maintained in large-scale random flows. these flows lack the ability to coherently undo the structure even when acting in concert with the magnetic back reaction.," The scale separation is of crucial importance here: while small-scale structure can be generated and maintained in large-scale random flows, these flows lack the ability to coherently undo the structure even when acting in concert with the magnetic back reaction."
 Both our theoretical arguments and our numerical experiments were based on viewing the turbulent velocity field as à single-scale random flow., Both our theoretical arguments and our numerical experiments were based on viewing the turbulent velocity field as a single-scale random flow.
 In real turbulence. Re is. of course. fairly large (107 in the ISM). so many hydrodynamic scales come into play.," In real turbulence, $\Re$ is, of course, fairly large $10^4$ in the ISM), so many hydrodynamic scales come into play."
 Unfortunately. the resulting scale ranges are too broad to be adequately simulated.," Unfortunately, the resulting scale ranges are too broad to be adequately simulated."
 It is interesting. however. that the results presented above appear to hold in simulations with more realistic Re (up to 10°) but relatively small Pr (down to values of order one). in accordance with the arguments presented at the beginning of3.," It is interesting, however, that the results presented above appear to hold in simulations with more realistic Re (up to $10^3$ ) but relatively small Pr (down to values of order one), in accordance with the arguments presented at the beginning of."
". We believe. therefore. that the physics and the numerics we have laid out provide at least a semiquantitative description of the statistical properties of the small-scale MHD turbulence in high-Pr,, plasmas."," We believe, therefore, that the physics and the numerics we have laid out provide at least a semiquantitative description of the statistical properties of the small-scale MHD turbulence in $\Pr$ plasmas."
 The implications for astrophysical objects can be significant., The implications for astrophysical objects can be significant.
 For the large-scale galactic dynamo. small-scale fields must be taken into consideration if a nonlinear a@ theory is to be constructed.," For the large-scale galactic dynamo, small-scale fields must be taken into consideration if a nonlinear $\alpha\Omega$ theory is to be constructed."
 If the net effect of the accumulated. small-scale magnetic energy is to suppress o. an alternative theory will have to be sought.," If the net effect of the accumulated small-scale magnetic energy is to suppress $\alpha$, an alternative theory will have to be sought."
 The nonlinear evolution of the magnetic turbulence in. protogalaxies (Kulsrudetal. and in the early Universe (see.e.g..Son1999:Chris-tensson.Hindmarsh.&Brandenburg2001) determines the energy and the coherence scale of the seed field inherited by newly formed galaxies.," The nonlinear evolution of the magnetic turbulence in protogalaxies \citep{Kulsrud_etal_proto} and in the early Universe \citep[see, e.g.,][]{Son,Christensson_Hindmarsh_Brandenburg} determines the energy and the coherence scale of the seed field inherited by newly formed galaxies."
 The structure of tangled magnetic fields in the intracluster gas crucially affects thermal conduction in the galaxy clusters (see.e.g.Chandran&Cowley1998;Malyshkin2001:Narayan&Medvedev2001).," The structure of tangled magnetic fields in the intracluster gas crucially affects thermal conduction in the galaxy clusters \citep[see, e.g.,][]{Chandran_Cowley,Malyshkin_cond,Narayan_Medvedev}."
. In the aceretion-disk physics. presence of large amounts of small-scale magnetic energy could lead to new models for the angular-momentum transport (Balbus&Hawley1905) and for the acceleration of jets (see.e.g..Heinz&Begelman2000).," In the accretion-disk physics, presence of large amounts of small-scale magnetic energy could lead to new models for the angular-momentum transport \citep{Balbus_Hawley_review} and for the acceleration of jets \citep[see, e.g.,][]{Heinz_Begelman}."
. In the solar astrophysics. the possibility was recently raised that a substantial part of the magnetic energy in the quiet photosphere of the Sun resides in small-scale magnetic fluctuations (Cattaneo1999b)..," In the solar astrophysics, the possibility was recently raised that a substantial part of the magnetic energy in the quiet photosphere of the Sun resides in small-scale magnetic fluctuations \citep{Cattaneo_solar}."
 Indeed. it is natural to expect that. just as turbulence itself. small-scale random magnetic fields are ubiquitous in the Universe.," Indeed, it is natural to expect that, just as turbulence itself, small-scale random magnetic fields are ubiquitous in the Universe."
 Finally. constructing a self-consistent physical theory of the small-scale magnetic turbulence constitutes a fascinating task in its own right.," Finally, constructing a self-consistent physical theory of the small-scale magnetic turbulence constitutes a fascinating task in its own right."
 Though fifty years have passed since Batchelor(1950) took the first steps down this road. an inquisitive researcher will still find surprises at every turn. and it might well be short-sighted to claim that we are able to discern the contours of the final destination.," Though fifty years have passed since \citet{Batchelor} took the first steps down this road, an inquisitive researcher will still find surprises at every turn, and it might well be short-sighted to claim that we are able to discern the contours of the final destination."
 It is a pleasure to thank E. Blackman. S. Boldyrev. W. Dorland. P. Goldreich. G. Hammett. Κ. Kulsrud. L. Malyshkin. A. Shukurov. and D. Uzdensky for stimulating discussions.," It is a pleasure to thank E. Blackman, S. Boldyrev, W. Dorland, P. Goldreich, G. Hammett, R. Kulsrud, L. Malyshkin, A. Shukurov, and D. Uzdensky for stimulating discussions."
 Our work was supported by the UKAEA Agreement No., Our work was supported by the UKAEA Agreement No.
 QS06992. the EPSRC Grant Νο.," QS06992, the EPSRC Grant No."
 GR/RS5344/01. the NSF Grants No.," GR/R55344/01, the NSF Grants No."
 AST 97-13241 and AST 00-98670. and the USDOE Grant No.," AST 97-13241 and AST 00-98670, and the USDOE Grant No."
 DE-FGO03- 224., DE-FG03-93ER54 224.
 Simulations were run on the supercomputers of the National Center for Supercomputing Applications and of the UK Astrophysical Fluids Facility., Simulations were run on the supercomputers of the National Center for Supercomputing Applications and of the UK Astrophysical Fluids Facility.
For example. the SER. can be determined from the luminosity of the [Ne IH] and [Ne I} lines (HoandNeto.2007).,"For example, the SFR can be determined from the luminosity of the [Ne II] and [Ne III] lines \citep{ho07}."
. By empirically comparing luminosities of the Neon lines with those of PAIT features. Farrahοἱal.(2007). relate the SFR as given by (2007) to the luminosities of the 6.2sau plus 11.3;an PAIL features in a starburst.," By empirically comparing luminosities of the Neon lines with those of PAH features, \citet{far07} relate the SFR as given by \citet{ho07} to the luminosities of the $\mu$ m plus $\mu$ m PAH features in a starburst."
 The result in Farrahetal.(2007). is log(SFR) = log|L(6.2jm + μυ) - 40.9., The result in \citet{far07} is log(SFR) = $\mu$ m + $\mu$ m)] - 40.9.
" If we use our transformation discussed in section 2.3. 7L,.(7.7 um)) = 46) L(G.2;au+11.3san). our equation (3) becomes log(SER) = log/L(6.2;an + L1L.8yan)) - 41.1."," If we use our transformation discussed in section 2.3, $\nu$$_{\nu}$ ) = $\pm$ 6) $\mu$ $\mu$ m), our equation (3) becomes log(SFR) = $\mu$ m + $\mu$ m)] - 41.1."
 To within the uncertainties. this is the same result as derived by from the Neon lines.," To within the uncertainties, this is the same result as derived by \citet{far07} from the Neon lines."
 For now. therefore. we consider the relations in equations (2) and (3) for determining bolometric huminositv. and SFR to be as accurate as other methods. currently available. alihough we certainly expect refinements in the future.," For now, therefore, we consider the relations in equations (2) and (3) for determining bolometric luminosity and SFR to be as accurate as other methods currently available, although we certainly expect refinements in the future."
" Using these translormations along with equation (1) for the change of vL,(7.7 mn)) with redshift as shown in Figure 3. we then have {for Lj, in eres +. [or SFR in|."," Using these transformations along with equation (1) for the change of $\nu$ $_{\nu}$ ) with redshift as shown in Figure 3, we then have for $L_{ir}$ in ergs $^{-1}$ , for SFR in."
 The most Iuminous starburst in the sample is MIPS 506 (Yanetal.2007).. no.," The most luminous starburst in the sample is MIPS 506 \citep{yan07}, no."
" 192 in Table L. with log[vL, τμ) = 46.10. which gives a SFR = 3.4 x 10*J|."," 192 in Table 1, with $\nu$ $_{\nu}$ $\mu$ m)] = 46.10, which gives a SFR = 3.4 x $^{3}$."
 We emphasize again that these results are based strictly on the measurement of PAII ]uminositv in starburst sources., We emphasize again that these results are based strictly on the measurement of PAH luminosity in starburst sources.
 It is useful. therefore. to compare with previous results for maximum SET derived [rom completely independent selection and measurement criteria.," It is useful, therefore, to compare with previous results for maximum SFR derived from completely independent selection and measurement criteria."
 The most Iuminous starburst galaxies previously reported are those in the submillimeter galaxy population., The most luminous starburst galaxies previously reported are those in the submillimeter galaxy population.
 While this population contains both AGN andl starbursts. sources with cooler dust are attributed primarily to starbursts.," While this population contains both AGN and starbursts, sources with cooler dust are attributed primarily to starbursts."
 The upper envelope for L;.) for starbursts is » 46.5 al z e 2 (Chapmanοἱal. 2005)..., The upper envelope for $L_{ir}$ ) for submm-discovered starbursts is $\sim$ 46.5 at z $\sim$ 2 \citep{cha05}. .
 This result is very. similar to the maximumliminosity of 46.6 which we would [md for starbursts at z= 2 [rom equation, This result is very similar to the maximumluminosity of 46.6 which we would find for starbursts at z = 2 from equation
with and Finally. the total Hamiltonian of the problem reads: where the index Hh stands for Saturn.,"with and Finally, the total Hamiltonian of the problem reads: where the index $\saturn$ stands for Saturn."
 We will use this Hamiltonian for a numerical study of the rotation., We will use this Hamiltonian for a numerical study of the rotation.
" An analytical study can show that the Hamiltonian (25)) can be reduced to where 2) represents a perturbation. and the three constants C4. €), and c, are the periods of the free oscillations around the equilibrium defined by the Cassini Laws."," An analytical study can show that the Hamiltonian \ref{equ:Htotal}) ) can be reduced to where $\mathcal{P}$ represents a perturbation, and the three constants $\omega_u$, $\omega_v$ and $\omega_w$ are the periods of the free oscillations around the equilibrium defined by the Cassini Laws."
" This last Hamiltonian is obtained after several canonical transformations. the first one consisting in expressing the resonant arguments «e2p—,l4s and p=r+$2 respectively associated with the 1:1 spin-orbit resonance and with the orientation of the angular momentum. οἱ and $2 being the orbital variables defined above."," This last Hamiltonian is obtained after several canonical transformations, the first one consisting in expressing the resonant arguments $\sigma=p-\lambda+\pi$ and $\rho=r+\ascnode$ respectively associated with the 1:1 spin-orbit resonance and with the orientation of the angular momentum, $\lambda$ and $\ascnode$ being the orbital variables defined above."
 The complete calculation is beyond the scope of this paper. the reader can find details in (Henrard.2005a.b:Noyellesetal..2005).," The complete calculation is beyond the scope of this paper, the reader can find details in \citep{h05io,h05eu,nlv08}."
 In order to integrate numerically the system. we first express the coordinates of the perturber (vg.ΥΕ) with the numerical ephemerides and the rotations given in (Eg.22)). in the body frame APA.," In order to integrate numerically the system, we first express the coordinates of the perturber $(x_{\saturn},y_{\saturn})$ with the numerical ephemerides and the rotations given in \ref{equ:passage}) ), in the body frame $(\vec{f_1},\vec{f_2},\vec{f_3})$."
 As explained before. the ephemerides are given by the TASSI.6 ephemerides (Vienne&Duriez.1995).," As explained before, the ephemerides are given by the TASS1.6 ephemerides \citep{vd95}."
. This way. we get coordinates depending of the canonical variables.," This way, we get coordinates depending of the canonical variables."
" Then we derive the equations coming from. the Hamiltonian (259): We an,integrated over Ry200 years using the Adams-Bashforth-Moulton IOth order predictor-corrector integrator.", Then we derive the equations coming from the Hamiltonian \ref{equ:Htotal}) ): We integrated over 200 years using the Adams-Bashforth-Moulton 10th order predictor-corrector integrator.
 The solutions consist of two parts. the forced one. directly due to the perturbation. and the free one. that depends on the initial conditions.," The solutions consist of two parts, the forced one, directly due to the perturbation, and the free one, that depends on the initial conditions."
 The initial conditions should be as close as possible to the exact equilibrium. that is assumed to be the Cassini State | in 1:1 spin-orbit resonance. to have low amplitudes of the free librations.," The initial conditions should be as close as possible to the exact equilibrium, that is assumed to be the Cassini State $1$ in 1:1 spin-orbit resonance, to have low amplitudes of the free librations."
 For that. we have used the iterative algorithm NAFFO (Noyellesetal..2011) to remove the free librations from the initial conditions. after they have been identified by frequency analysis.," For that, we have used the iterative algorithm NAFFO \citep{ndc11} to remove the free librations from the initial conditions, after they have been identified by frequency analysis."
 The frequency analysis algorithm we used is based on Laskar’s original idea. named NAFF as Numerical Analysis of the Fundamental Frequencies (see for instance Laskar(1993) for the method. and Laskar(2005) for the convergence proofs).," The frequency analysis algorithm we used is based on Laskar's original idea, named NAFF as Numerical Analysis of the Fundamental Frequencies (see for instance \citet{l93} for the method, and \citet{l05} for the convergence proofs)."
 It aims at identifying the coefficients o; and cy of a complex signal 11) obtained numerically over a finite time span [-7:T] and verifying where c are real frequencies and o; complex coefficients., It aims at identifying the coefficients $a_k$ and $\omega_k$ of a complex signal $f(t)$ obtained numerically over a finite time span $[-T;T]$ and verifying where $\omega_k$ are real frequencies and $a_k$ complex coefficients.
 If the signal f(r) is real. its frequency spectrum is symmetric and the complex amplitudes associated with the frequencies ωι and —c are complex conjugates.," If the signal $f(t)$ is real, its frequency spectrum is symmetric and the complex amplitudes associated with the frequencies $\omega_k$ and $-\omega_k$ are complex conjugates."
 The frequencies and amplitudes associated are found with an iterative. scheme., The frequencies and amplitudes associated are found with an iterative scheme.
" To determine the first frequency «c. one searches for the maximum of the amplitude of where the scalar product <f(t).g(4)> is defined by and where y(£) is à weight function. 1.8. a positive function with Once the first periodic. term exp(wy,f) is found. its complex amplitude a) is obtained by orthogonal projection. and the process is started again on the remainder f|(f)=f(t)—aj expict)."," To determine the first frequency $\omega_1$, one searches for the maximum of the amplitude of where the scalar product $<f(t),g(t)>$ is defined by and where $\chi(t)$ is a weight function, i.e. a positive function with Once the first periodic term $\exp(\imath\omega_1t)$ is found, its complex amplitude $a_1$ is obtained by orthogonal projection, and the process is started again on the remainder $f_1(t)=f(t)-a_1\exp(\imath\omega_1t)$ ."
 The algorithm stops when two detected frequencies are too close to each other. which alters their determinations. or when the number of detected terms reaches a maximum set by the user.," The algorithm stops when two detected frequencies are too close to each other, which alters their determinations, or when the number of detected terms reaches a maximum set by the user."
 This algorithm is very efficient. except when two frequencies are too close to each other.," This algorithm is very efficient, except when two frequencies are too close to each other."
 In, In
 ofa of~50% 30%. (1:2)..," $\sim 50\%$ $30\%$ \cite{gri03,gil04}."
" z1.6 L, logCL,.) ~39.5ΕΗ.5 (10Afpy210°) z1 log(L,)237.5. loe(L,.)~39.0.59.5. (3))). (1).. (5:63)). lo"," $\approx 1.6$ $(L_x) \sim 35.5-40.5$ $L_x$ $(L_x)$ $\sim 39.5 - 41.5$ $10 \lesssim M_{BH} \lesssim 10^5$ $\approx 1$ $(L_x) \lesssim 37.5$ $(L_x) \sim 39.0-39.5$ \cite{sar03}) \cite{vos07}. \cite{whi02,vos09})"
"g(L,)~37 ", $(L_x) \sim 37$ 
As a simple preliminary test. we Lave isolated the 375 stars in tle final sample with [Fe/H] between —0.05 aud +0.05 aud T; between 1250 Is aud 7150 Ix. Exelucit& three stars with residuals between the calculated ancl observed B—V ereater than 0.10 mag. a fit between 75. defined as (T. - 9770)/5770. aud B—V welgied by the inve‘se square of the uicertainty in B—V for the remaining 372 stars produ“eS? Iuclusion of a cubic term does uot lead to a statistically siguificant. improvemeit in the fit.,"As a simple preliminary test, we have isolated the 375 stars in the final sample with [Fe/H] between $-0.05$ and +0.05 and $T_e$ between 4250 K and 7150 K. Excluding three stars with residuals between the calculated and observed $B-V$ greater than 0.10 mag, a fit between $T_n$, defined as $T_e$ - 5770)/5770, and $B-V$ weighted by the inverse square of the uncertainty in $B-V$ for the remaining 372 stars produces: Inclusion of a cubic term does not lead to a statistically significant improvement in the fit."
 The nicertalnty estimates for B-V iucluded the photometric uicertainty aud the dispersion iu Ti. translated to an error in B8—V aud combined in quadrature with the photometric eror.," The uncertainty estimates for $B-V$ included the photometric uncertainty and the dispersion in $T_e$, translated to an error in $B-V$ and combined in quadrature with the photometric error."
 TIe staleard deviatiou among the residuals in 8—V is 0.021 mag., The standard deviation among the residuals in $B-V$ is 0.021 mag.
 Siice the solar temiperatu'e of te models used to derive the spectroscopic abundances is set at 577!O Ix (Valenti&Fix‘her2002).. the iuplied B—V color o ‘the Sun fo ‘this combination of stella| parameters aid p1010uetry |W. B-—V — 0.651.," Since the solar temperature of the models used to derive the spectroscopic abundances is set at 5770 K \citep{vf}, the implied $B-V$ color of the Sun for this combination of stellar parameters and photometry is $B-V$ = 0.651."
 ext. the stellar sampe was sOrtec in bius 0.1 dex wide raugiiο [rom [Fe/H] = 0.55 to —0.95 auc a quadratic polvyuouia fi Was lace for each biL usiug the same teu»erature paanmeterizatlon as above.," Next, the stellar sample was sorted in bins 0.1 dex wide ranging from [Fe/H] = +0.55 to $-0.95$ and a quadratic polynomial fit was made for each bin using the same temperature parameterization as above."
" For these fits sta ""were inclded if they fell in the temperature range [roi17, = 1000 lv to 75900 Ix: points were welehted iu he sane manner as above.", For these fits stars were included if they fell in the temperature range from $T_e$ = 4000 K to 7500 K; points were weighted in the same manner as above.
 F1g., Fig.
 2) ilustrates the morphology of he mean relations plotted cillereiially relative o the color relation for solar meallicity. in the seline (B— Vous11| - (B—- Vuuo.," 3 illustrates the morphology of the mean relations plotted differentially relative to the color relation for solar metallicity, in the sense $B-V$ $_{[Fe/H]}$ - $B-V$ $_{0.00}$."
 FoI ¢‘lariy. neal 'elatious are plotted or every other metallicity startiug with [Fe/H] — +0.10 at le 10x," For clarity, mean relations are plotted for every other metallicity bin starting with [Fe/H] = +0.40 at the top."
 The curves are plotec Louly over the T; range covered : the sample used to celine he curve., The curves are plotted only over the $T_e$ range covered by the sample used to define the curve.
 The reallons exhibit reasouable morphological cousisteucy weell [Fe/H] = +0.5 aud -0.5. witl he p'ecdomiuait chauge bei ngaregUar shift iu the zero-poiut the erves as the metallicity declines.," The relations exhibit reasonable morphological consistency between [Fe/H] = +0.5 and -0.5, with the predominant change being a regular shift in the zero-point of the curves as the metallicity declines."
 However. he cliflerentjal relatiOLs for stars with [Fe/H] ow -0.5 exhijted slenificaut deviations rou linearity. as illustIied by ie bottom curve in Fig.," However, the differential relations for stars with [Fe/H] below -0.5 exhibited significant deviations from linearity, as illustrated by the bottom curve in Fig."
 3., 3.
 Ht shoud be emphasized that this is not a procct of st1all nunber statistics: while the color ange is decliniug among the lower metalicity stars. the bins centered o1 [Fe/H] = —0.5. —0.6. and —0.7 contained 59. 51. aud 31 stars. respectively.," It should be emphasized that this is not a product of small number statistics; while the color range is declining among the lower metallicity stars, the bins centered on [Fe/H] = $-0.5$, $-0.6$, and $-0.7$ contained 59, 54, and 34 stars, respectively."
 Whetler this is aneIect tied o real changes iu the color-teiiperature relations at lower [Fe/H] or an artiLact of the 7; 1ierger p‘ocess for stars of kpw metallicity. remaius uetshown aud. for our purposes. irrelevant.," Whether this is an effect tied to real changes in the color-temperature relations at lower [Fe/H] or an artifact of the $T_e$ merger process for stars of low metallicity remains unknown and, for our purposes, irrelevant."
" To define ot ‘final color-T;, 'elajon. we have restricted te metallicity range to [Fe/H] = +0.6 to —0.5. incluling ouly stars witl T. between 1200 Kk aud TOOO Ix. Using 7,, as defined above. polyuomial fits oB-V were uade to 1759 points usiug lultiple combinations of Τη and [Fe/H]."," To define our final $T_n$ relation, we have restricted the metallicity range to [Fe/H] = +0.6 to $-0.5$ , including only stars with $T_e$ between 4200 K and 7000 K. Using $T_n$ as defined above, polynomial fits to $B-V$ were made to 1759 points using multiple combinations of $T_n$ and [Fe/H]."
" As expected roni the earlier discussion. no terms above acuadratie in T, were found to be statistically siguilicaut."," As expected from the earlier discussion, no terms above a quadratic in $_n$ were found to be statistically significant."
" For [Fe/H]. ouly the linear terin aud no ¢‘oss terms involving [Fe/H] and T,, were retained."," For [Fe/H], only the linear term and no cross terms involving [Fe/H] and $_n$ were retained."
" ATer removing 13 stars with final residuals in B—V ereater than 0.10 mae. the remaining 1716 stars produce thefollowing color - TA, relation:"," After removing 13 stars with final residuals in $B-V$ greater than 0.10 mag, the remaining 1746 stars produce thefollowing color - $T­_n$ relation:"
calculated from is Lass. distance. ad age using the Burrowsetal.(200: moclels.,"calculated from its mass, distance, and age using the \citet{bur} models."
 Two further random choices coiplete the determination of wheher the simulated. planet. is detected., Two further random choices complete the determination of whether the simulated planet is detected.
 First. oue of the ten percerαυ.les given in tle sensitivity Liles is rauclouly selected.," First, one of the ten percentiles given in the sensitivity files is randomly selected."
 Combiued with the separation in aresecouds. is selection specifies the seusitivity of our observation at the location oL the simulated planet.," Combined with the separation in arcseconds, this selection specifies the sensitivity of our observation at the location of the simulated planet."
 The second rand1n choice is needed )ecause plauets appearing at low sigificauce in our images would ave a less tha1 chance of beiug confidentlvy deected., The second random choice is needed because planets appearing at low significance in our images would have a less than chance of being confidently detected.
 Our bliud seusitivity ests using fake planets placed in our raw data showed hat we could confirm of Ἰ0σ soi‘ces. of To. sources. ali of 5o sou‘ces. where o is a measure of the PSE-scale noise iu a given region of the image (see Heinzeetal.(2010) for details).," Our blind sensitivity tests using fake planets placed in our raw data showed that we could confirm of $\sigma$ sources, of $\sigma$ sources, and of $\sigma$ sources, where $\sigma$ is a measure of the PSF-scale noise in a given region of the image (see \citet{obspaper} for details)."
 This secoud ancl final raucdom choice in our Monte Carlo simulations is thereloὁ arranged to ensure that a raudonmly selected of plauets with To. significanee. and. of planets with 7-106 sienilicance. are recorded in the simulation as detected «)bjects.," This second and final random choice in our Monte Carlo simulations is therefore arranged to ensure that a randomly selected of planets with $\sigma$ significance, and of planets with $\sigma$ significance, are recorded in the simulation as detected objects."
 Although vve liave conmipleteness at 100. we choose to consider of simulated plajets with 106 or greater signiicauce to be detected. because at only slightly above 106 the true coiipleteuess certainly becomes for all practical purposes.," Although we have completeness at $\sigma$ , we choose to consider of simulated planets with $\sigma$ or greater significance to be detected, because at only slightly above $\sigma$ the true completeness certainly becomes for all practical purposes."
 Note that we iive Couservatively alowed the cetectic1 probabiities {ο Increase sepwise. rather than in a continuous curve. [rom 5 o 10o: that is. in our Monte Carlo siumlatious. planets with 5-To significauce are detected at the 5o rate [rom ot: blind sensitivity ests. while those with 7-10e significauce are detected at the To rate.," Note that we have conservatively allowed the detection probabilities to increase stepwise, rather than in a continuous curve, from 5 to $\sigma$: that is, in our Monte Carlo simulations, planets with $\sigma$ significance are detected at the $\sigma$ rate from our blind sensitivity tests, while those with $\sigma$ significance are detected at the $\sigma$ rate."
 The low completeness (1656)) at 5o. as deternined fro1 our blind seusitivity tests using fake plauets. uay seeur surprising.," The low completeness ) at $\sigma$, as determined from our blind sensitivity tests using fake planets, may seem surprising."
 Iu these tests we clistiuguished between plauets that were suggested by a concentration of unusually bright pixels CNoiced). or else coulideutly ideified as real sources CConfiriuec.," In these tests we distinguished between planets that were suggested by a concentration of unusually bright pixels (`Noticed'), or else confidently identified as real sources (`Confirmed')."
 Many more planets were noticed tan were confirmed: for uoticed planets. tle rates are at 10σ. at To. and at 5o.," Many more planets were noticed than were confirmed: for noticed planets, the rates are at $\sigma$, at $\sigma$, and at $\sigma$."
 However. very uauv false positives were also 10ticed. so sources that are merely j0ticed. but not colirmecl do not represent. usable detections.," However, very many false positives were also noticed, so sources that are merely noticed but not confirmed do not represent usable detections."
 The cotupleteness levels we used in our Monte Carlo simulations at 5o and at τσ) refer to confirmed sources., The completeness levels we used in our Monte Carlo simulations at $\sigma$ and at $\sigma$ ) refer to confirmed sources.
 No [alse positives were coufirmed iu auy of our bliud tests., No false positives were confirmed in any of our blind tests.
 Followup observations of suspected sources are costy in terms of telescope time. so a detection strategy with a low rate is imyortant.," Followup observations of suspected sources are costly in terms of telescope time, so a detection strategy with a low false-positive rate is important."
 Though seusiivity estimaors (aud therefore the exact meaning of 56) diller among planet imagine survevs. «MUS Was cquite couservative. as is explained in Heinzeetal.(2010)..," Though sensitivity estimators (and therefore the exact meaning of $\sigma$ ) differ among planet imaging surveys, ours was quite conservative, as is explained in \citet{obspaper}."
 The completeness we fiud at 5o. wuch has often been taken as a higli-completeuess seusitivity Limit. should serve as a warnlug to uture workers iu this field. and. au encouragement to establish a definitive significa1ce-couipleteless relation through blind sensitivity tests as we ave clone.," The low completeness we find at $\sigma$, which has often been taken as a high-completeness sensitivity limit, should serve as a warning to future workers in this field, and an encouragement to establish a definitive significance-completeness relation through blind sensitivity tests as we have done."
 Note that our bliud seusitivity tests. covered in Heinzeetal.(2010).. are completely distinct from he Monte Carlo sinulatious covered herein.," Note that our blind sensitivity tests, covered in \citet{obspaper}, are completely distinct from the Monte Carlo simulations covered herein."
 The blind tests involved insertsig a little over a hundred fake planets int«) our raw image cata to establish our point-source sensitivity., The blind tests involved inserting a little over a hundred fake planets into our raw image data to establish our point-source sensitivity.
 In our Monte Carlo work we simulatec the orbits. masses. aud briglituessesof miullious of planes. aud compared them to our previously-established seusitivity limits to see which planets our srvey could have," In our Monte Carlo work we simulated the orbits, masses, and brightnessesof millions of planets, and compared them to our previously-established sensitivity limits to see which planets our survey could have"
 , 
were performed using internal flat-field aud are latap exposures which were taken alter each science expostiire.,were performed using internal flat-field and arc lamp exposures which were taken after each science exposure.
 Iu practice. about 130 spectra were acquired per cluster field. with 100 vielding measurable redshifts.," In practice, about 130 spectra were acquired per cluster field, with $\sim 100$ yielding measurable redshifts."
 A redshift measurement. procedure which relies. in part. on. visual inspection was used.," A redshift measurement procedure which relies, in part, on visual inspection was used."
 The quality of the redshift ideutification was rauked with a number [rom l to L which roughly corresponds to the number of features used to identify the redshift.," The quality of the redshift identification was ranked with a number from 1 to 4, which roughly corresponds to the number of features used to identify the redshift."
 A quality of 1 means that the redshift is certain: a quality of 1 means that ouly oue emission line was observed. aud the recdshift is only possible.," A quality of 4 means that the redshift is certain; a quality of 1 means that only one emission line was observed, and the redshift is only possible."
 Because the fore/backgrouud contamination rate is so large at our cluster redshilts. approximately 50 — of the galaxies turn out to be field galaxies. rather thau cluster members (Oke 1998: Postinan 1998. 2000).," Because the fore/background contamination rate is so large at our cluster redshifts, approximately 50 – of the galaxies turn out to be field galaxies, rather than cluster members (Oke 1998; Postman 1998, 2000)."
 Deep iulrared imagine of the cluster sample was taken with IRIM whic1 contalns a 256x ICMOS3 HeCdTe array and has a resolution of 0.60 arcsecoucl per pixel on the Lin telescope., Deep infrared imaging of the cluster sample was taken with IRIM which contains a $256 \times 256$ NICMOS3 HgCdTe array and has a resolution of 0.60 arcsecond per pixel on the 4-m telescope.
 The field-of-view (151151 arcseconds) covers the central region of each chster., The field-of-view $154 \times 154$ arcseconds) covers the central region of each cluster.
 Iu order to make he deepest possible observations over this region the entire LRIS field-of-view was Dot Iuosaicec., In order to make the deepest possible observations over this region the entire LRIS field-of-view was not mosaiced.
 Observationsn were mace inn the 2.25HA.-f band., Observations were made in the $2.2\mu\ K^{'}$ band.
" Each central field)"" was observed usiugnOm a Lx| clithern yattern with a stepsize of 10 and a total extent of H30°.", Each central field was observed using a $4 \times 4$ dither pattern with a stepsize of $10^{''}$ and a total extent of $30^{''}$.
 Each exposure hac an ellective exposure tune of 1 ininute. with [ co-additious of individual backgrouud-limited 15 secoud integrations.," Each exposure had an effective exposure time of 1 minute, with 4 co-additions of individual, background–limited 15 second integrations."
 The otal integratiou time on au iudividual cluster varied between 3 auc LL hous., The total integration time on an individual cluster varied between 3 and 4.4 hours.
 Because the fields were uot excessively crowded. we were able to use iu-fiekl dithering to create a global sky flat.," Because the fields were not excessively crowded, we were able to use in-field dithering to create a global sky flat."
" The A"" cluster data were reduced uxing the Deep Infrared Mosaicing Software (DIMSUM)J). a publicly available package of IRAF seripts."," The $K^{'}$ cluster data were reduced using the Deep Infrared Mosaicing Software (DIMSUM), a publicly available package of IRAF scripts."
 This software generates not only a final stacked image but also a correspondinge exposure image.e where each pixel encodes the total number of seconds in the correspoudiug stacked image.," This software generates not only a final stacked image but also a corresponding exposure image, where each pixel encodes the total number of seconds in the corresponding stacked image."
 This exposure image was appropriately scaled aud used as a weight image by SExtractor during the catalog generation (see 82.2)., This exposure image was appropriately scaled and used as a weight image by SExtractor during the catalog generation (see 2.2).
 The data were linearizecl. triuuned to exclude masked columus and rows ou the edges of the arrays. and dark-subtracted using dark [rames of the same exposure leneth as the observations.," The data were linearized, trimmed to exclude masked columns and rows on the edges of the arrays, and dark–subtracted using dark frames of the same exposure length as the observations."
 All ünages of a given night were fattened by a super flat mace from a series of dome flats taken during the previous day., All images of a given night were flattened by a super flat made from a series of dome flats taken during the previous day.
 As part of the DIMSUM procedure. sky subtraction was done by subtracting a scaled mecian of nine temporally adjacent exposures for each [raiue.," As part of the DIMSUM procedure, sky subtraction was done by subtracting a scaled median of nine temporally adjacent exposures for each frame."
 A first-pass reduction was used to create an object mask for each frame., A first-pass reduction was used to create an object mask for each frame.
 This mask was created from a fully stacked mosaic image., This mask was created from a fully stacked mosaic image.
 It therefore excluded not only the bright objects. but also those objects too [aint to be detected in au individual exposure.," It therefore excluded not only the bright objects, but also those objects too faint to be detected in an individual exposure."
 In the second pass. the object mask was used to avoid object coutamiuatiou ol the sky flat in the production of sky [rames.," In the second pass, the object mask was used to avoid object contamination of the sky flat in the production of sky frames."
 Final mosaicing of the images of each cluster were mace with a replication of each pixel by a [actor of Lin both dimensions., Final mosaicing of the images of each cluster were made with a replication of each pixel by a factor of 4 in both dimensions.
 This procedure couserves flux while eliminating the need for interpolation when the individual frames are co-aligued., This procedure conserves flux while eliminating the need for interpolation when the individual frames are co-aligned.
 A bad, A bad
"The differential emission measure, along the path of the beam, is: Both Eqs. (C2))","	The differential emission measure, along the path of the beam, is: 	 	Both Eqs. \ref{eq:kT}) )"
" and (C3)) can be used to compute the total thermal spectrum generated by beam heating, by integrating over the whole path of the beam (or at least the portion within the instruments field of view)."," and \ref{eq:dEM}) ) can be used to compute the total thermal spectrum generated by beam heating, by integrating over the whole path of the beam (or at least the portion within the instrument's field of view)."
 This has been done in Section 3.4.., 	This has been done in Section \ref{sect:beamheating}.
" The problem is carried a little bit further than as in Appendix C:: the energy flux due to heat conduction in the direction parallel to the magnetic field is: where &=o1? keV s! K! cm! is the Spitzer conductivity(??),, with a=537.5 keV s! cm! K77, "," 	The problem is carried a little bit further than as in Appendix \ref{appendix:openloopheating}: 	the energy flux due to heat conduction in the direction parallel to the magnetic field is: 	where $\kappa= \alpha T^{5/2}$ keV $^{-1}$ $^{-1}$ $^{-1}$ is the Spitzer conductivity, with $\alpha$ =537.5 keV $^{-1}$ $^{-1}$ $^{-7/2}$ ."
Heat conduction perpendicular tothe magnetic field is negligible., 	Heat conduction perpendicular tothe magnetic field is negligible.
" Ja by SLdEndt~1EnD3kgTneV SLi,and thea ‘by tri, where L ans S are respectively the length Replacingand section of the flux tube, V— is volume, n, the average electron density, kg Boltzmann's constant, one finds the heat conductivity energy loss time-scale: In a volume V=SL, at equilibrium, the amount of thermal energy loss due to heat conductivity is the same as the amount of non-thermal power dumped: (assuming Teond«€Trad, the radiative loss timescale, which is usually the case in hot flare plasmas near the impulsive phase of the flare)."," 	 	Replacing $j_Q$ by $\frac{1}{S}\frac{dE_{th}}{dt} \approx \frac{1}{S} \frac{E_{th}}{\tau_{cond}} \approx \frac{1}{S} \frac{3k_BTn_eV}{\tau_{cond}} $ and $\frac{dT}{dz}$ by $\frac{T}{L}$, where $L$ ans $S$ are respectively the length and section of the flux tube, $V=SL$ is the volume, $n_e$ the average electron density, $k_B$ Boltzmann's constant, one finds the heat conductivity energy loss time-scale: 	In a volume $V=SL$, at equilibrium, the amount of thermal energy loss due to heat conductivity is the same as the amount of non-thermal power dumped: 	 	(assuming $\tau_{cond} \ll \tau_{rad}$, the radiative loss timescale, which is usually the case in hot flare plasmas near the impulsive phase of the flare)."
" Hence: Notice that this equilibrium temperature Τει is independentof density and filling factor, and that a factor 2 on any one parameter translates into a errorin Tyg."," 	Hence:	 	Notice that this equilibrium temperature $T_{eq}$ is independentof density and filling factor, and that a factor 2 error on any one parameter translates into a errorin $T_{eq}$ ."
" For example,taking P, T.,-4.6Mk,errorFi —5-2E\= 6.5x107? erg/s-Ax10*"" keV/s, S=10'7 cm?, and L=10° cm, one finds or kgT,,—4.2 keV."," 	For example,taking $P_{nth}$ $\frac{\delta-1}{\delta-2} F_1 E_1$ = $\times$ $^{28}$ $\times$ $^{37}$ keV/s, $S$ $^{17}$ $^2$ , and $L$ $^9$ cm, one finds $T_{eq}$ =47.6MK, 	or $k_BT_{eq}$ =4.2 keV."
The magnetic field near (he rim of SNRs may not be fully turbulent. for example if the maenetic-field amplification saturates at an amplitude 04522By.,"The magnetic field near the rim of SNRs may not be fully turbulent, for example if the magnetic-field amplification saturates at an amplitude $\delta B \approx B_0$."
 We can model a mixture of turbulent and homogeneous fields by adding to our models of fully turbulent magnetic field a homogeneous field that is orientedin the x-direction., We can model a mixture of turbulent and homogeneous fields by adding to our models of fully turbulent magnetic field a homogeneous field that is oriented in the x-direction.
 In Fig., In Fig.
 d we show the degree of polarization as a function of lrequeney. [or mixtures of turbulent ancl homogeneous fields of varying strength., \ref{f4} we show the degree of polarization as a function of frequency for mixtures of turbulent and homogeneous fields of varying strength.
 The polarized intensity has been “beam-averaged” over 50x50 cells. or of the line-oE-sight length. ancl therefore the curve for a fully turbulent field is smoother at low Irequency compared wilh (hose shown in Fig. 2..," The polarized intensity has been ""beam-averaged"" over 50x50 cells, or of the line-of-sight length, and therefore the curve for a fully turbulent field is smoother at low frequency compared with those shown in Fig. \ref{f2}."
 Largely independent of the choice of turbulence model. a homogeneous magnetic field of the same strength as the rms turbulence amplitude. Dj=0B. drives the degree of polarization into the range 30% to 35%.," Largely independent of the choice of turbulence model, a homogeneous magnetic field of the same strength as the rms turbulence amplitude, $B_0=\delta B$, drives the degree of polarization into the range $30\%$ to $35\%$ ."
 A --- magnetic field αἱ By=29D gives a degree of polarization at the level 55% to 6056.," A homogeneous magnetic field at $B_0=2\,\delta B$ gives a degree of polarization at the level $55\%$ to $60\%$."
 polarizationHowever. at low frequencies where internal Faraday rotation is important the degree of remains below 1056. and for models. ie. a very small effective turbulence wavelength. the polarization degree [alls below 3%.," However, at low frequencies where internal Faraday rotation is important the degree of polarization remains below $10\%$, and for flat-spectrum models, i.e. a very small effective turbulence wavelength, the polarization degree falls below $3\%$."
 Table 1. gives the observed magnetic-polarzation angles at high frequency for different relative amplitudes of (he homogeneous field. which is oriented in the x-direction (zero angle}.," Table \ref{tab:homofield} gives the observed magnetic-polarization angles at high frequency for different relative amplitudes of the homogeneous field, which is oriented in the x-direction (zero angle)."
 Recall thatthe magnetic-polarization angle differs bv 90° [rom the electric polarization, Recall thatthe magnetic-polarization angle differs by $90^\circ$ from the electric polarization
The search for the predicted effects of gamma-ray bursts (GRBs) on their environments is key to understanding the properties of their host galaxies. found both nearby and in the early Universe.,"The search for the predicted effects of gamma-ray bursts (GRBs) on their environments is key to understanding the properties of their host galaxies, found both nearby and in the early Universe."
 lonisation by the powerful GRB and afterglow emission has now been seen in the form of optical absorptior line variability (e.g. 0020813. Dessauges-Zavadsky et al..," Ionisation by the powerful GRB and afterglow emission has now been seen in the form of optical absorption line variability (e.g. 020813, Dessauges-Zavadsky et al.,"
 2006: 0060418. Vreeswiyk et al..," 2006; 060418, Vreeswijk et al.,"
 2007) and hinted at from several reports of low significance variations in X-ray columi density for some GRBs. for example 0011121 (Piroetal.. 2005).. 0050730 (Starlingetal.. 2005).. GRB 050904 (Boéretal..2006;Campana2007:Gendre2007) and GRB 060729 (Grupeetal..2007) and from comparisor of optical and X-ray hydrogen column densities (Watsonetal.. 2007).," 2007) and hinted at from several reports of low significance variations in X-ray column density for some GRBs, for example 011121 \citep{piro}, , 050730 \citep{050730}, , GRB 050904 \citep{boer,campana,gendre2} and GRB 060729 \citep{grupe} and from comparison of optical and X-ray hydrogen column densities \citep{watson}."
. Optical extinction should also decrease as we expect dust to be destroyed by the GRB jet out to 10-30 pc (Draine&Perna&Lazzati. 2002)..," Optical extinction should also decrease as we expect dust to be destroyed by the GRB jet out to 10–30 pc \citep{drainesal,waxdraine,fruchter,perna}."
 This should occur very shortly after the onset of the GRB. but so far only one such GRB had potentially shown this effect. 9980703. and the decrease in extinction would have occurred from approximately | day after the GRB onwards (e.g.Vreeswyketal..1999;Hol-landetal..2001;Starling 2007).," This should occur very shortly after the onset of the GRB, but so far only one such GRB had potentially shown this effect, 980703, and the decrease in extinction would have occurred from approximately 1 day after the GRB onwards \citep[e.g.][]{vreeswijk1,holland,columnsI}."
. The evidence of this comes from two sources., The evidence of this comes from two sources.
 Firstly the suggestion by Castro-Tiradoetal.(1999). that the spectral slope estimated from their R- and H-band photometric data from around | day after the burst indicated a redder value than would normally be expected for GRBs. translating into Ay ~ 2.2.," Firstly the suggestion by \cite{castrotirado} that the spectral slope estimated from their $R$ - and $H$ -band photometric data from around 1 day after the burst indicated a redder value than would normally be expected for GRBs, translating into $A_V$ $\sim$ 2.2."
 This is large when compared with the average value of Ay=1.07 found from afterglow studies at later times., This is large when compared with the average value of $A_V= 1.07$ found from afterglow studies at later times.
 Secondly. Vreeswijketal.(1999) compiled spectral energy distributions (SEDs) at four epochs covering 2.2-5.2 days after the burst and derive a potential decrease in the intrinsic optical extinction at the 2-307 level.," Secondly, \cite{vreeswijk1} compiled spectral energy distributions (SEDs) at four epochs covering 2.2–5.2 days after the burst and derive a potential decrease in the intrinsic optical extinction at the $\sigma$ level."
 There have been optical extinction neasurements of 9980703 by five groups using a number of different methods and instrumentation. and measurements of Ay at different times are far from consistent (Figure 1: Table 1)).," There have been optical extinction measurements of 980703 by five groups using a number of different methods and instrumentation, and measurements of $A_{V}$ at different times are far from consistent (Figure \ref{literature}; Table \ref{tab:literature}) )."
 There is. therefore. a need to return to the apparent variability of Ay in 9980703. which if confirmed would be the first observational evidence of this kind.," There is, therefore, a need to return to the apparent variability of $A_V$ in 980703, which if confirmed would be the first observational evidence of this kind."
 We do this via broadband spectral energy distributions. where possible combining an X-ray spectrum with early near-infrared (nIR) and optical data. and thereby discuss the observational manifestations of dust destruction by GRBs.," We do this via broadband spectral energy distributions, where possible combining an X-ray spectrum with early near-infrared (nIR) and optical data, and thereby discuss the observational manifestations of dust destruction by GRBs."
 This issue is particularly important to re-examine in the current era of rapid follow-up by the satellite (Gehrelsetal..2004).. robotic telescopes (e.g. Liverpool Telescope and Faulkes Telescopes. 2m in diameter) and rapid response mode on larger ground-based telescopes such as the 4m William Herschel Telescope and the 8m Very Large Telescopes.," This issue is particularly important to re-examine in the current era of rapid follow-up by the satellite \citep{gehrels}, robotic telescopes (e.g. Liverpool Telescope and Faulkes Telescopes, 2m in diameter) and rapid response mode on larger ground-based telescopes such as the 4m William Herschel Telescope and the 8m Very Large Telescopes."
 We use a broadband dataset to create a spectral energy distribution at early times when a high value of Ay Is reported from optical data., We use a broadband dataset to create a spectral energy distribution at early times when a high value of $A_V$ is reported from optical data.
 We took the earliest magnitudes reported in Castro-Tiradoetal.(1999) (R and H band) which were taken at 0.94 days sinceburst (and used for their estimatesof Ay)., We took the earliest magnitudes reported in \cite{castrotirado} $R$ and $H$ band) which were taken at 0.94 days sinceburst (and used for their estimatesof $A_V$ ).
 We converted the observed magnitudes into fluxes assuming, We converted the observed magnitudes into fluxes assuming
given by the models are the “true” instantaneous SFR.,given by the models are the “true” instantaneous SFR.
 The ones in assumed given star formation history., The ones published in assumed a given star formation history.
 We notice publishedthat the model stronglya underestimates the SFR from the observations for VCC 2062 if we assume single recent burst., We notice that the model strongly underestimates the SFR from the observations for VCC 2062 if we assume a single recent burst.
 This is most likely due to several factors:a the lack of observations in near-infrared beyond the z' band and a star formation history that is not properly reproduced by our set of models., This is most likely due to several factors: the lack of observations in near-infrared beyond the z' band and a star formation history that is not properly reproduced by our set of models.
" An older age of about 300 Myr with a timescale around 100 which is not ruled out by the model is probably more Myr,realistic as it would take into account more accurately a long term low level star formation."," An older age of about 300 Myr with a timescale around 100 Myr, which is not ruled out by the model is probably more realistic as it would take into account more accurately a long term low level star formation."
" For the other models, except for NGC 5291N, SFR(FUV) underestimates SFR(model)."," For the other models, except for NGC 5291N, SFR(FUV) systematically underestimates SFR(model)."
" In the case of SQ-5, systematicallySFR(model)/SFR(FUV) even reaches ~32."," In the case of SQ-5, SFR(model)/SFR(FUV) even reaches $\sim32$."
 This is chiefly an attenuation effect: spectroscopic observations of NGC 5291N show that the attenuation is very small and SQ-5 is particularly at 8 um compared to FUV and has a relatively high brightattenuation., This is chiefly an attenuation effect: spectroscopic observations of NGC 5291N show that the attenuation is very small and SQ-5 is particularly bright at 8 $\mu$ m compared to FUV and has a relatively high attenuation.
" Regarding ionized gas, SFR(model)/SFR(Ho) is comprised between 0.73 for NGC 7252 and 2.8 for SQ-5."," Regarding ionized gas, $\alpha$ ) is comprised between 0.73 for NGC 7252 and 2.8 for SQ-5."
 No trend can be seen with the star formation history or the attenuation hinting at a complex combination of several factors., No trend can be seen with the star formation history or the attenuation hinting at a complex combination of several factors.
" Finally, SFR(model) and SFR(8.0) — the star formation rate obtained from the PAH emission in the 8.0 um band — similar results with two exceptions: SpitzerSQ-5 reaches ratio of provide~4.5 and Arp 245N presents a strong mid-infrared emissiona with a ratio of 0.28."," Finally, SFR(model) and SFR(8.0) – the star formation rate obtained from the PAH emission in the Spitzer 8.0 $\mu$ m band – provide similar results with two exceptions: SQ-5 reaches a ratio of $\sim4.5$ and Arp 245N presents a strong mid-infrared emission with a ratio of 0.28."
" Even though the standard SFR estimators often yield results that have the correct order of magnitude, an error of several times is common with extreme cases of up to"," Even though the standard SFR estimators often yield results that have the correct order of magnitude, an error of several times is common with extreme cases of up to"
studying the tonized stellar wind of the B supergiant with X-ray line spectroscopy. as has been done with Vela X-1 (Sako et al.,"studying the ionized stellar wind of the B supergiant with X-ray line spectroscopy, as has been done with Vela X-1 (Sako et al."
 1999; Schulz et al., 1999; Schulz et al.
 2002)., 2002).
"ISOCAM 60.7,m data. lie in the range ALL1T2>2.7 and 0.2«II.N,0.8 refmsxxxxsable.olours)).","ISOCAM $\mu$ m data, lie in the range $K_{\rm s} - LW2 > 2.7$ and $0.2 < H - K_{\rm s} < 0.8$ \\ref{msxxxx_table_colours}) )."
l13oftheilicbelowandsabovcH. - overlapping with the range of the PG/3CR AGN., 13 of them lie below and 8 above $H - K_{\rm s} = 0.5$ overlapping with the range of the PG/3CR AGN.
 In refmsxxxxy/qglonlytheword SB isplacedattheirmeantlocation," In \\ref{msxxxx_fig1} only the word ""SB-ULIRGs"" is placed at their mean location."
" Outheotherhand, tn)Aannsy. ULIBGswith?warn’ Fys/Fs5 colours (like 2231 and 005189-2524) clearly fall into the colour range of the PG/3CR AGN refmsxxxx;able,olours))."," On the other hand, the AGN-ULIRGs with ""warm"" $F_{12}/F_{25}$ colours (like 231 and 05189-2524) clearly fall into the colour range of the PG/3CR AGN \\ref{msxxxx_table_colours}) )."
 In following we discuss. whether the ISOCP excess sources could be explained in terms of pure starburst IR galaxies.," In following we discuss, whether the ISOCP excess sources could be explained in terms of pure starburst IR galaxies."
 We will argue that such starforming galaxies would be either too bright or too distant to match the observed fluxes at A... LW2 and at 605m the corresponding colours of the ISOCP excess sources.," We will argue that such starforming galaxies would be either too bright or too distant to match the observed fluxes at $K_{\rm s}$, $LW2$ and at $\mu$ m the corresponding colours of the ISOCP excess sources."
" Our argumentation is essentially based upon the following empirical facts: First. we make use of the PAH bands and discuss the ISOCP excess sources with 755,4,"" Lmmiy."," Our argumentation is essentially based upon the following empirical facts: First, we make use of the PAH bands and discuss the ISOCP excess sources with $F_{2.2\,\mu{\rm m}} \la
1$ mJy."
" In order to match this limit. a typical SB-ULIRG. like e.g. 117208-0014. with P55,,,zc 20mmJy at 0.012. would have to lie at :=0.15δ."," In order to match this limit, a typical SB-ULIRG, like e.g. 17208-0014, with $F_{2.2\,\mu{\rm m}} \approx 20$ mJy at $z = 0.042$ , would have to lie at $z = 0.188$."
" In this case. however. Jv,LW2 would attain values below 2.7. see point (2.)"," In this case, however, $K_{\rm s}-LW2$ would attain values below 2.7, see point (2.)"
 above., above.
 The same argument applies to other SB-ULIRGs (like 2273. 2220. 14348-1447 and 22336543604).," The same argument applies to other SB-ULIRGs (like 273, 220, 14348-1447 and 23365+3604)."
 Hence. a pure starburst counterpart of thefaint ISOCP excess sources must have a lower luminosity. Le. being at most an SB-LIRG.," Hence, a pure starburst counterpart of the ISOCP excess sources must have a lower luminosity, i.e. being at most an SB-LIRG."
 Second. we make use of the Foy/Fw» ratio. which attains typically values above 230 for SB-ULIRGs.," Second, we make use of the $F_{60}/F_{LW2}$ ratio, which attains typically values above 230 for SB-ULIRGs."
 A similar flux ratio is expected for highly dust-enshrouded SB-LIRGs with J7A.>0.5 (down-sized SB-ULIRGs). if they exist.," A similar flux ratio is expected for highly dust-enshrouded SB-LIRGs with $H-K_{\rm s}>0.5$ (down-sized SB-ULIRGs), if they exist."
 In order to match Fripo71mJy for the ISOCP sources. the expected flux at j/m would have to be at least FoyZ230...510 mmJy. which is above the IRAS detection threshold at low-cirrus high-galactic latitudes.," In order to match $F_{LW2}>1\,$ mJy for the ISOCP sources, the expected flux at $\mu$ m would have to be at least $F_{60} \ga 230 \ldots 570$ mJy, which is above the IRAS detection threshold at low-cirrus high-galactic latitudes."
 For ISOCP sources with fluxes Fpwogillamnimn-Jgwecepeetusef ul, For ISOCP sources with fluxes $F_{LW2}$ $<$ mJy we expect useful IRAS upper limits.
l ΓΡ Εμμ ΕΟΓ. toplindicidually onlycightofthemshowamarginaldetcction inth eediim IRAS ADDSCAN data. the remaining sources have 30 upper limits between 90 and ," We have examined the 70 unclassified ISOCP excess sources \\ref{msxxxx_fig1}, top) individually: only eight of them show a marginal detection in the $60\,\mu$ m IRAS ADDSCAN data, the remaining sources have $3\sigma$ upper limits between 90 and mJy."
"No of the detected sources exhibit ΤουFrwasi2 ""n 230. aMoftheremaining"," Two of the detected sources exhibit $F_{60}/F_{LW2}$ $<$ 230, all of the remaining sources have $F_{60}/F_{LW2}$ $<$ 180 and at least 40 of them even have $F_{60}/F_{LW2}$ $<$ 100."
"sourceshaccEogo/ Frye. δα) estarburstgalavies withH-K, (00.5."," These low limits show that most of the 70 ISOCP sources are characterized by a high MIR/NIR flux ratio, which is not accompanied by a high FIR/MIR ratio as expected for known dust-enshrouded pure starburst galaxies with $H-K_{\rm s}$ $>$ 0.5."
 If the ISOCP excess sources are not a new population of star-forming galaxies. which are highly dust-enshrouded (with red ZZ AK). rich in PAH emission (with bright F7») and have cool FIR colours (with low 60j/m flux). then the arguments above favour a significant AGN contribution in these sources.," If the ISOCP excess sources are not a new population of star-forming galaxies, which are highly dust-enshrouded (with red $H-K$ ), rich in PAH emission (with bright $_{LW2}$ ) and have cool FIR colours (with low $\mu$ m flux), then the arguments above favour a significant AGN contribution in these sources."
 Furthermore. the four AGN-ULIRGs show an Foy/Fr» ratio between 10 and 50. consistent with the 60j/m upper limits found for the ISOCP excess sources.," Furthermore, the four AGN-ULIRGs show an $F_{60}/F_{LW2}$ ratio between 10 and 50, consistent with the $\mu$ m upper limits found for the ISOCP excess sources."
 Based on the comparison with known object types we predict that most of the 80 ISOCP excess sources house an AGN and have Seyfert luminosities. but could be more powerful if at:zc0.2.," Based on the comparison with known object types we predict that most of the 80 ISOCP excess sources house an AGN and have Seyfert luminosities, but could be more powerful if at $z \ga
0.2$."
 Therefore. we consider the ISOCP excess sources as promising AGN candidates.," Therefore, we consider the ISOCP excess sources as promising AGN candidates."
" At redshift about » (.8. when the AGN-typical SED bump shifts. the colours of the sources may become bluer than ΔΝ.=00.5, and a refined analysis using other filters has to be applied in order to identify all AGN."," At redshift about $z > 0.8$ , when the AGN-typical SED bump shifts, the colours of the sources may become bluer than $H - K_{\rm s} =0.5$, and a refined analysis using other filters has to be applied in order to identify all AGN."
 Remarkably. the new method ts - á priori - not biased against optical-UV selected QSOs.," Remarkably, the new method is - á priori - not biased against optical-UV selected QSOs."
" For comparison. the 2MASS AGN search catches only the range J7IN,>0.7 (roughly corresponding to the JIvy>].2 eriterion used by Franeis et al."," For comparison, the 2MASS AGN search catches only the range $H - K_{\rm s} > 0.7$ (roughly corresponding to the $J-K_{\rm s} > 1.2$ criterion used by Francis et al."
 2004). hence may ignore more of the known AGN - even among the local ones.," 2004), hence may ignore more of the known AGN - even among the local ones."
 Obviously. our predictions about the nature of the ISOCP excess sources have to be verified by optical spectroscopy.," Obviously, our predictions about the nature of the ISOCP excess sources have to be verified by optical spectroscopy."
 Ten of our 80 AGN candidates are already listed in the NED as QSOs., Ten of our 80 AGN candidates are already listed in the NED as QSOs.
 None ts listed as a star (in SIMBAD) or starburst galaxy., None is listed as a star (in SIMBAD) or starburst galaxy.
 Twelve sources have GGHz radio detections. 4 being radio loud.," Twelve sources have GHz radio detections, 4 being radio loud."
 Only one source (3C345. Sandage Wyndham 1965) has also been identified spectroscopically as QSO in the Sloan Survey (SDSS DRI. Abazajian et al.," Only one source (3C345, Sandage Wyndham 1965) has also been identified spectroscopically as QSO in the Sloan Survey (SDSS DR1, Abazajian et al."
 2003) while SDSS DR2 contains only one more spectrum of an ISOCP excess source (RA.Decyoaygy = 13:25:07.8. 405:41:07) — it is a QSO at 7 00.2.," 2003) while SDSS DR2 contains only one more spectrum of an ISOCP excess source $_{\rm J2000}$ = 13:25:07.8, +05:41:07) – it is a QSO at $z$ 0.2."
 Because of the marginalspectroscopic classification of the ISOCP sources. we have started a spectroscopic survey for the 70 unknown ISOCP excess sources εδ.EIT2>2.7 and JFWN.> 0.2).," Because of the marginalspectroscopic classification of the ISOCP sources, we have started a spectroscopic survey for the 70 unknown ISOCP excess sources $K_{\rm s} - LW2 > 2.7$ and $H - K_{\rm s} >
0.5$ )."
 First results obtained at the 1.9mm, First results obtained at the m
Luminous blue variables are the most massive stars during the final stage of evolution. 2].,Luminous blue variables are the most massive stars during the final stage of evolution \cite{HD1994_LBVreview}] ].
 It is a rather. short- stage characterized by high mass-Ioss rate and. mass ejections into the interstellar medium. during. outbursts., It is a rather short-lived stage characterized by high mass-loss rate and mass ejections into the interstellar medium during outbursts.
 The bolometric Iuminosities of such stars are close to the Eddington limit. below which radiation pressure can still be balanced by gravity. forces.," The bolometric luminosities of such stars are close to the Eddington limit, below which radiation pressure can still be balanced by gravity forces."
 Alodern model computations often. involve. explicitly preset time of the beginning of the LBW evolution. and the curation of this stage (see. eg... ?]]. because. these parameters are impossible to infer via self-consistent modeling.," Modern model computations often involve explicitly preset time of the beginning of the LBV evolution and the duration of this stage (see, e.g., \cite{Meynet2007}] ]), because these parameters are impossible to infer via self-consistent modeling."
 The input parameters in these cases are based on the most recent observational data., The input parameters in these cases are based on the most recent observational data.
 Moceling is further complicated. due to the lack of a consensus concerning the evolutionary sequence of massive stars e... even the LBV WR. transition remains an open issue— ?]. ?]. η.," Modeling is further complicated due to the lack of a consensus concerning the evolutionary sequence of massive stars – e.g., even the LBV $\to$ WR transition remains an open issue \cite{Smith_Owocki06}] ], \cite{ContiWNHstars}] ], \cite{Smith08}] ])."
 The number of known LBV stars in our Galaxy is too small to test the agreement between the model tracks and observational data., The number of known LBV stars in our Galaxy is too small to test the agreement between the model tracks and observational data.
 The number of known and well-studied massive stars ab. the μπα stages of evolution LBV stars. WR. stars. Je]ltvepe supergiants. anc supergiants and hvpergiants with various temperatures should be increased: considerably.," The number of known and well-studied massive stars at the final stages of evolution — LBV stars, WR stars, B[e]-type supergiants, and supergiants and hypergiants with various temperatures — should be increased considerably."
 These objects have very dilferent observational manifestations., These objects have very different observational manifestations.
 Only with a sullicient number of stars with known parameters it will be possible to reliably identify the results of modcling of the evolution of massive stars with observed objects., Only with a sufficient number of stars with known parameters it will be possible to reliably identify the results of modeling of the evolution of massive stars with observed objects.
 On the other hand. a considerably: increased. sample will make the interpretation of model computations more reliable.," On the other hand, a considerably increased sample will make the interpretation of model computations more reliable."
 Ehe discovery. aud study of new massive stars at the final stages of evolution (hereafter referred to as 7LDBV-like stars) would lav down the necessary basis for linking theory with observation so that the studies of LBV stars will no longer remain mostly descriptive., The discovery and study of new massive stars at the final stages of evolution (hereafter referred to as “LBV-like” stars) would lay down the necessary basis for linking theory with observation so that the studies of LBV stars will no longer remain mostly descriptive.
 The main goal of this paper is to search for and identify LBY candidates., The main goal of this paper is to search for and identify LBV candidates.
 In the Milky: Way such objects are hidden by strong interstellar extinction in the Galactic disk., In the Milky Way such objects are hidden by strong interstellar extinction in the Galactic disk.
 They are currently discovered. in LR. sky surveys (eg. 2]p.lts fortunate orientation and. sullicientE arge population of earlv-tvpe stars makes the M333 galaxy of the Local Group an ideal object to be searched for LBV-like stars. ?]].," They are currently discovered in IR sky surveys (e.g., \cite{IRsearchMS}] ]).Its fortunate orientation and sufficiently large population of early-type stars makes the 33 galaxy of the Local Group an ideal object to be searched for LBV-like stars \cite{M33Ivanov}] ]."
 Here we adopt an M33 distance modulus of 24799 (c.g... ΤΠ. which corresponds to a distance of 950 kpe.," Here we adopt an M33 distance modulus of 9 (e.g., \cite{M33Distance}] ]), which corresponds to a distance of 950 kpc."
 In their. review. llumphrevs and Davidson ?]] summarize all the data known about LBV stars by —that time: their list of confirmed LBV stars in M333 MEM DD. CC. . and. NS3. and 5532 229(Lov the “Romano star” ?]]) was considered. to be an candidate.," In their review, Humphreys and Davidson \cite{HD1994_LBVreview}] ] summarize all the data known about LBV stars by that time: their list of confirmed LBV stars in 33 included B, C, 2, and 83, and 532 290, the “Romano star” \cite{Romano78}] ]) was considered to be an LBV candidate."
 Later. the latter had its LBV status confirmed both spectroscopicallv 2] ancl photometrically ?]].," Later, the latter had its LBV status confirmed both spectroscopically \cite{Fabrika2000}] ] and photometrically \cite{Kurtev_etal2001}] ]."
 It was studied in more detail by MN et al. ?]], It was studied in more detail by Fabrika et al. \cite{Fabrika_etal2005}] ]
 and. Viotti et al. ??..," and Viotti et al. \cite{Viotti2006, Viotti2007}."
 Phe star AA in 333 is now commonly classified as a cool hypergiant ?]]. ?]]. ?]].," The star A in 33 is now commonly classified as a cool hypergiant \cite{Humph_etal1987}] ], \cite{Humphreys_etal2006}] ], \cite{Viotti2006}] ]."
" Although this object exhibits all the features ""nteristie for LBV stars it sucldenly brightenedin L950N1953 ?]] to become one of the most luminous stars in 333 with a spectral tvpe IB its current spectral type (M) is untvpical for classical LBY stars.", Although this object exhibits all the features characteristic for LBV stars — it suddenly brightened in 1950–1953 \cite{HubbleSandage53}] ] to become one of the most luminous stars in 33 with a spectral type F — its current spectral type (M) is untypical for classical LBV stars.
 However. given the fewness of LBV stars hitherto studied. it is possible that the known classical LBV states ?]] do not cover all possible properties of these objects.," However, given the fewness of LBV stars hitherto studied, it is possible that the known classical LBV states \cite{HD1994_LBVreview}] ] do not cover all possible properties of these objects."
 The AA star meets the eriteria of LBV class bothin terms of Luminosity (mass) and photometric variability ? |]., The A star meets the criteria of LBV class both in terms of luminosity (mass) and photometric variability \cite{NewLBVinM33}] ].
 Spectroscopic observations of LBV-like star candidates [rom our list allowed us to discover a new (the seventh) LBY star N93351 in the 122333 galaxy T]., Spectroscopic observations of LBV-like star candidates from our list allowed us to discover a new (the seventh) LBV star N93351 in the 33 galaxy \cite{NewLBVinM33}] ].
 We use very limited archival data to construct the light curve of the star and find it to be variable with the light variations of about 0744 a vear., We use very limited archival data to construct the light curve of the star and find it to be variable with the light variations of about 4 a year.
 Further observations of N93351 both photometric and spectroscopic are needed to confirm the evolutionary status of the star., Further observations of N93351 both photometric and spectroscopic are needed to confirm the evolutionary status of the star.
 Various groups of authors ?]. ?]. ?]. ?]. ?]] ?|. ?]. ?]] used various methods to search for LBV. stars in 333.," Various groups of authors \cite{
Neeseetal91}] ], \cite{Spiller1992}] ], \cite{Calzetti1995}] ], \cite{FabShol95}] ], \cite{MasseyUIT}] ], \cite{
Shol_etal97}] ], \cite{Shol_Fab2000}] ], \cite{Corral_Herrero03}] ] used various methods to search for LBV stars in 33."
 The principal method. consists in searching for sources coincident with early-type stars., The principal method consists in searching for sources coincident with early-type stars.
 Although LBV, Although LBV
"~LO—L2"". with the smaller values found in the Ix-band.","$\sim 1.0-1.2\arcsec$, with the smaller values found in the K-band."
 The average sampling of the light curves was ~4.5 days with a period of intensive (~ daily) monitoring during the second vear of observations for both sources., The average sampling of the light curves was $\sim 4.5$ days with a period of intensive $\sim$ daily) monitoring during the second year of observations for both sources.
 Simultaneous optical observations in the B ancl V-bands were also obtained and reduced as outlined above., Simultaneous optical observations in the B and V-bands were also obtained and reduced as outlined above.
 The data reduction followed. the. standard steps of dark subtraction. lat felding. and sky subtraction using consecutive jitterecl frames.," The data reduction followed the standard steps of dark subtraction, flat fielding, and sky subtraction using consecutive jittered frames."
 The light) curves were constructed. from relative photometry obtained through a fixed aperture of 2.7 and 3.6 arc-seconds in diameter for 33783 ancl 22251-178. respectively. after all images were taken to a common seeing by convolving cach image with a Gaussian of width =6%a7). where ay is the width corresponding to some of the worst secing conditions (dates with even poorest seeing were discarded) and σ is the width of each individual image.," The light curves were constructed from relative photometry obtained through a fixed aperture of 2.7 and 3.6 arc-seconds in diameter for 3783 and 2251-178, respectively, after all images were taken to a common seeing by convolving each image with a Gaussian of width $=\sqrt(\sigma_0^2-\sigma^2)$, where $\sigma_0$ is the width corresponding to some of the worst seeing conditions (dates with even poorest seeing were discarded) and $\sigma$ is the width of each individual image."
 For. NGC 3783. [ive different comparison stars were used to obtain the relative photometry whenever available., For NGC 3783 five different comparison stars were used to obtain the relative photometry whenever available.
 ALR. 2251-178 however. had only one comparison star within the field of view.," MR 2251-178 however, had only one comparison star within the field of view."
 Photometric errors were computed as the squared. sum. of the standard. deviation due to the Poissonian noise of the source ane sky flux within the aperture. plus. the uncertainty of obtaining the measurement itself," Photometric errors were computed as the squared sum of the standard deviation due to the Poissonian noise of the source and sky flux within the aperture, plus the uncertainty of obtaining the measurement itself."
 This last error was estimated as the dispersion in the photometry of the stars available in the field of view between two consecutive exposures and it was found to range [rom 0.02 to 0.05 in fractional lux., This last error was estimated as the dispersion in the photometry of the stars available in the field of view between two consecutive exposures and it was found to range from 0.02 to 0.05 in fractional flux.
 One component that should. be taken into account. when studying AGN variability is the light contribution within the used aperture from the stellar population of the host galaxy., One component that should be taken into account when studying AGN variability is the light contribution within the used aperture from the stellar population of the host galaxy.
 Ligh mass sources might be spared from this correction if they have high accretion rates. but for svstems with massive black holes anc low aceretion rates it is now known that the host will also contain a massive spheroid which should be accounted for since the emission from the active nuclei might not completely dominate the total observed. Dux.," High mass sources might be spared from this correction if they have high accretion rates, but for systems with massive black holes and low accretion rates it is now known that the host will also contain a massive spheroid which should be accounted for since the emission from the active nuclei might not completely dominate the total observed flux."
 In the Following subsections we will estimate this contribution for NGC 3783 and. AUR 2251-178., In the following subsections we will estimate this contribution for NGC 3783 and MR 2251-178.
" NGC 3783 was studied using the ACS camera on board the Llubble Space ""Telescope by Bentz et ((2006) ancl the galaxy was mocelled as a combination of a bulge. disc and bar in the E550M filter (~ 5100.0)."," NGC 3783 was studied using the ACS camera on board the Hubble Space Telescope by Bentz et (2006) and the galaxy was modelled as a combination of a bulge, disc and bar in the F550M filter $\sim
5100$ )."
 The amount of host light in our ooptical apertures at this wavelength corresponds to 1.99.107 /sfenr /A.. while for the nnear-lkR apertures it corresponds to 1.510P ergs/s/cm? BBentz. private communication). with more than of this flux coming from the bulge.," The amount of host light in our optical apertures at this wavelength corresponds to $1.9 \times 10^{-15}$ $^2$ , while for the near-IR apertures it corresponds to $1.5 \times 10^{-15}$ $^2$ Bentz, private communication), with more than of this flux coming from the bulge."
 To extrapolate this measurement at tto near-H3 wavelengths we will assume that only the bulge contributes significantly to the measured [Duxes and will use the spectral energy. distribution of the appropriate stellar population., To extrapolate this measurement at to near-IR wavelengths we will assume that only the bulge contributes significantly to the measured fluxes and will use the spectral energy distribution of the appropriate stellar population.
 The stellar populations in bulges vary às a function of their luminosity., The stellar populations in bulges vary as a function of their luminosity.
 Massive bulges are characterised by old stellar populations which are well represented. by a single poch. of star formation (Peletier et ab.," Massive bulges are characterised by old stellar populations which are well represented by a single epoch of star formation (Peletier et al.,"
 1999: Peletier Daleells. 1997). while the colours of less massive bulges found in late tvpe galaxies are better characterised when vounger stellar populations are also included. (Carollo et al..," 1999; Peletier Balcells, 1997), while the colours of less massive bulges found in late type galaxies are better characterised when younger stellar populations are also included (Carollo et al.,"
. 2007)., 2007).
 From the determination of the black hole mass in NGC 3783 e mass of the bulge is found to be ~2.LOMA7. (Lurring lux. 2004). at the lower limit of the range in the Peletier's sample. and therefore it. should. be well represented. by a stellar population with 1 to 2 times solar metallicities and ges around 9-12 Cave.," From the determination of the black hole mass in NGC 3783 the mass of the bulge is found to be $\sim
2\times 10^{10} M_{\odot}$ (Härring Rix, 2004), at the lower limit of the range in the Peletier's sample, and therefore it should be well represented by a stellar population with 1 to 2 times solar metallicities and ages around 9-12 Gyr."
 We have used the simple stellar population mocels from. yw work of Alaraston et ((2005). sealed to the LIST measurement at5100AX.. to determine the host contributions o the near-Ht fluxes.," We have used the simple stellar population models from the work of Maraston et (2005), scaled to the HST measurement at, to determine the host contributions to the near-IR fluxes."
 A correction is introduced to accoun or the cillerent apertures used. during the photomoetric measurcments in the optical and near-LHt images., A correction is introduced to account for the different apertures used during the photometric measurements in the optical and near-IR images.
 Lt is fou hat. after scaling. the single stellar population model with Z-—1Z. and 9 Gye contributes less to the near-LB. Lux han the model with Z=2Z. and 12 Gye by a factor of 1.41.5. while the contributions are nearly. equal in the B and V bands.," It is found that, after scaling, the single stellar population model with $Z=1 Z_{\odot}$ and 9 Gyr contributes less to the near-IR flux than the model with $Z=2 Z_{\odot}$ and 12 Gyr by a factor of 1.4–1.5, while the contributions are nearly equal in the B and V bands."
 The final B-band value reported in Table corresponds to the average from these two extreme values and agrees within wwith the value derived by Alloin et ((1995) using a similar aperture., The final B-band value reported in Table 1 corresponds to the average from these two extreme values and agrees within with the value derived by Alloin et (1995) using a similar aperture.
 For a visualisation of the contributions. see Section 5.4.1.," For a visualisation of the contributions, see Section 5.4.1."
 For AIR 2251-178 there is no studs of the host galaxy. except or Ho imaging of the very extended ionised nebula around he quasar (see Shopbell. Veilleux Bland-LElawthorn. 1999. and references therein).," For MR 2251-178 there is no study of the host galaxy, except for $\alpha$ imaging of the very extended ionised nebula around the quasar (see Shopbell, Veilleux Bland-Hawthorn, 1999, and references therein)."
 We have therefore. estimated. the lost contribution to our photometry in an indirect way., We have therefore estimated the host contribution to our photometry in an indirect way.
 Alarconi Lunt (2003) have determined a tight correlation »etween the black hole mass and the total bulge luminosity in the D and near-Hi bands which can allow us to infer the xulee light contribution to our photometry., Marconi Hunt (2003) have determined a tight correlation between the black hole mass and the total bulge luminosity in the B and near-IR bands which can allow us to infer the bulge light contribution to our photometry.
 Using the estimate of the black hole mass in δι 2251- we can determine the total bulge near-Hi Dux., Using the estimate of the black hole mass in MR 2251-178 we can determine the total bulge near-IR flux.
 Next it is necessary to interpolate to the Dux within our aperture., Next it is necessary to interpolate to the flux within our aperture.
 ‘To do this we need to assume a characteristic bulge elfective racidus (7) and Sersic index (2)., To do this we need to assume a characteristic bulge effective radius $r_e$ ) and Sersic index $n$ ).
 Marconi Hunts samplesuggests that for a ~I07AL. black hole 5.73.25 kpe is," Marconi Hunt's samplesuggests that for a $\sim 10^8\
M_{\odot}$ black hole $r_e \sim 3-5$ kpc is"
IGR J19140+0951 and a very bright southern source (see Fig 5-),IGR J19140+0951 and a very bright southern source (see Fig 2).
 Using the magnitudes given in CHAOS. as well as the fluxes from GLIMPSE and our observations with VISIR. we fitted its SED. and the best-fitting parameters are Ay=16.5. T.222500 K. E--192x 1079. and the reduced y7 is 1.4/6.," Using the magnitudes given in CHA08, as well as the fluxes from GLIMPSE and our observations with VISIR, we fitted its SED, and the best-fitting parameters are $\textrm{A}_\textrm{v}$ =16.5, $\textrm{T}_*$ =22500 K, $\frac{\textrm{R}_\ast}{\textrm{D}_{\ast}}$ $1.92\times10^{-{10}}$ , and the reduced $\chi^2$ is 14.4/6."
 The best fit with the additional component gives a larger reduced y of 20.2/4 and Tp<200 K. We do not need any additional component to fit the SED. and the parameters derived from our fit are in good agreement with IGR J19140+0951 to be an BIT supergiant star. as initially reported in ?..," The best fit with the additional component gives a larger reduced $\chi^2$ of 20.2/4 and $\textrm{T}_{\rm D}\,<\,200$ K. We do not need any additional component to fit the SED, and the parameters derived from our fit are in good agreement with IGR J19140+0951 to be an B1I supergiant star, as initially reported in \citet{2007Nespoli}."
 All SEDs were best-fitted without any dust component (even the very absorbed one like IGR J16320-4751). except three of them (GR J16195-4945. IGR J16318-4848. and IGR J16358-4726. see Fig.," All SEDs were best-fitted without any dust component (even the very absorbed one like IGR J16320-4751), except three of them (IGR J16195-4945, IGR J16318-4848, and IGR J16358-4726, see Fig."
 3) that exhibit a MIR excess likely due to the presence of dust in their stellar wind., 3) that exhibit a MIR excess likely due to the presence of dust in their stellar wind.
 Blue supergiants are known to exhibit a very strong but sparse stellar wind of high velocity (~ 1000-2000 km s! )., Blue supergiants are known to exhibit a very strong but sparse stellar wind of high velocity $\sim$ 1000-2000 km $^{-1}$ ).
 This has been explained through the so-called radiation line-driven CAK model (?) in which the wind ts driven by absorption in spectral lines., This has been explained through the so-called radiation line-driven CAK model \citep*{1975Castor} in which the wind is driven by absorption in spectral lines.
 Hot stars emit most of their radiation in the ultraviolet (UV) where their atmosphere has many absorption lines., Hot stars emit most of their radiation in the ultraviolet (UV) where their atmosphere has many absorption lines.
 Photons coming from the photosphere of the star with the same wavelength are absorbed and re-emitted to the expanding medium in a random direction with almost the same momentum. which results in acceleration of the wind.," Photons coming from the photosphere of the star with the same wavelength are absorbed and re-emitted to the expanding medium in a random direction with almost the same momentum, which results in acceleration of the wind."
 This process is very effective because the line spectrum of the scattering ions in the wind is Doppler-shifted compared to the stellar rest frame. so the scattering atoms are shifted with respect to their neighbours at lower velocities and can interact with an unaffected part of the stellar spectrum.," This process is very effective because the line spectrum of the scattering ions in the wind is Doppler-shifted compared to the stellar rest frame, so the scattering atoms are shifted with respect to their neighbours at lower velocities and can interact with an unaffected part of the stellar spectrum."
 IGR J16318-4848 was proven to belong to a particular class of Β1 supergiants. the B[e] supergiants or sgB[e] (2)..," IGR J16318-4848 was proven to belong to a particular class of B1 supergiants, the B[e] supergiants or sgB[e] \citep*{2004Filliatre}."
 A physical definition of B[e] stars can be found in ?.., A physical definition of B[e] stars can be found in \citet{1998Lamers}.
 We just recall two of the characteristics here: the presence of forbidden emission lines of [Feu] and i| in the NIR spectrum and of a strong MIR excess due to hot circumstellar dust that re-emits the absorbed stellar radiation through free-free emission., We just recall two of the characteristics here: the presence of forbidden emission lines of ] and ] in the NIR spectrum and of a strong MIR excess due to hot circumstellar dust that re-emits the absorbed stellar radiation through free-free emission.
 Án sgB[e] is defined by the Ble] phenomenon. the indication of mass-loss in the optical spectrum (P-cygni profiles). and a hybrid spectrum characterised by the simultaneous presence of narrow low-excitation lines anc broad absorption features of high-excitation lines.," An sgB[e] is defined by the B[e] phenomenon, the indication of mass-loss in the optical spectrum (P-cygni profiles), and a hybrid spectrum characterised by the simultaneous presence of narrow low-excitation lines and broad absorption features of high-excitation lines."
 This hybrid nature was empirically explained by the simultaneous presence of a normal supergiant hot polar wind (fast and sparse) and responsible for the broad lines and a cool equatorial outflowing disk-like wind (slow and dense) responsible for the narrow lines (???)..," This hybrid nature was empirically explained by the simultaneous presence of a normal supergiant hot polar wind (fast and sparse) and responsible for the broad lines and a cool equatorial outflowing disk-like wind (slow and dense) responsible for the narrow lines \citep{1983Shore,1985Zickgraf,1987Shore}."
 This empirical model has recetved some confirmation from polarimetry (?).., This empirical model has received some confirmation from polarimetry \citep*{1999Oudjmaier}.
 There are a few models that explain the creation of this outflowing disk. and all of them consider the star rotation to be an important parameter in the process.," There are a few models that explain the creation of this outflowing disk, and all of them consider the star rotation to be an important parameter in the process."
 In this paper. we present only the most consistent of them. the Rotation Induced Bi-stability mechanism (RIB). but a review can be found in ?..," In this paper, we present only the most consistent of them, the Rotation Induced Bi-stability mechanism (RIB), but a review can be found in \citet*{2006Kraus}."
 The lines responsible for the creation of the wind are dependent on the tonisation structure. and a change in this structure leads to a change in the radiative flux.," The lines responsible for the creation of the wind are dependent on the ionisation structure, and a change in this structure leads to a change in the radiative flux."
 This. is the bi-stability jump found by ?.. which appears for B stars with effective temperatures of about 23000 K. Above this temperature. the wind tends to be fast and sparse.," This is the bi-stability jump found by \citet*{1991Lamers}, which appears for B stars with effective temperatures of about 23000 K. Above this temperature, the wind tends to be fast and sparse."
 Below. the mass-loss rate if five times higher and the terminal velocity two times slower. which leads to a wind that is ten times denser.," Below, the mass-loss rate if five times higher and the terminal velocity two times slower, which leads to a wind that is ten times denser."
 ? propose that the same effect is important from polar to equatorial regions for rapidly rotating B stars., \citet*{1997Cassinelli} propose that the same effect is important from polar to equatorial regions for rapidly rotating B stars.
 Indeed. the rapid rotation leads to polar brightening that increases the poles temperature to the hot side of the jump.," Indeed, the rapid rotation leads to polar brightening that increases the poles temperature to the hot side of the jump."
 At the same time. the rotation leading to gravity darkening. the equatorial region may be on the cool side of the jump.," At the same time, the rotation leading to gravity darkening, the equatorial region may be on the cool side of the jump."
 Consequently. the wind in the equatorial region is denser than the wind in the polar region.," Consequently, the wind in the equatorial region is denser than the wind in the polar region."
 Nevertheless. ? show that the rotational velocity of the star should be very close to its critical value to allow the equatorial wind to reach the density needed to create the disk.," Nevertheless, \citet{2000Pelupessy}
 show that the rotational velocity of the star should be very close to its critical value to allow the equatorial wind to reach the density needed to create the disk."
 However. supergiant stars cannot be close to critical rotational velocity because of probable disruption.," However, supergiant stars cannot be close to critical rotational velocity because of probable disruption."
 Additional mechanisms are therefore needed to allow the supergiant star to reach its critical velocity (seee.g.?)..," Additional mechanisms are therefore needed to allow the supergiant star to reach its critical velocity \citep[see
e.g. ][]{2006Owocki}."
 In the particular case of an sgB[e] star in an X-ray binary system. the spin-up should occur during the supergiant phase of the companion. which indicates a different evolutionary stage from other HMXBs.," In the particular case of an sgB[e] star in an X-ray binary system, the spin-up should occur during the supergiant phase of the companion, which indicates a different evolutionary stage from other HMXBs."
 This disk itself cannot explain the strong MIR excess the sgB[e] stars exhibit., This disk itself cannot explain the strong MIR excess the sgB[e] stars exhibit.
 Nevertheless. ? have shown the existence of a zone in the disk (about 50-60 stellar radii from the star) in which the temperature is below the temperatureof sublimation of the dust (about 1500 K) and the density high enough to allow for its creation.," Nevertheless, \citet*{1993Bjorkman} have shown the existence of a zone in the disk (about 50-60 stellar radii from the star) in which the temperature is below the temperatureof sublimation of the dust (about 1500 K) and the density high enough to allow for its creation."
several authors already noted that the energy spectrum of the DC-accelerated electrons may be characterized as either power-law or exponential. depending on the value of D. or the trapping time of the electrons inside the acceleration volume (Anastasiadis.Georgoulis 1997).,"Several authors already noted that the energy spectrum of the DC-accelerated electrons may be characterized as either power-law or exponential, depending on the value of $B_z$ \citep{hami05}
 or the trapping time of the electrons inside the acceleration volume \citep{anas97}."
. The test particle simulations in this paper. with sell-consistent electric ancl magnetic fields obtained from MIID. simulations. indicate that the electrons accelerated by the DC electric field of magnetic reconnection present a spectrum with the form which is similar to those obtained in the diffusive shock acceleration when the power-law behavior is truncated by a variety of effects (seeEllison&Ramaty1935.forcliscussions)..," The test particle simulations in this paper, with self-consistent electric and magnetic fields obtained from MHD simulations, indicate that the electrons accelerated by the DC electric field of magnetic reconnection present a spectrum with the form which is similar to those obtained in the diffusive shock acceleration when the power-law behavior is truncated by a variety of effects \citep[see][for discussions]{elli85}."
 The same spectral profile was also obtained in the electron acceleration by random DC electric field (Anastasiaclisetal.2002)., The same spectral profile was also obtained in the electron acceleration by random DC electric field \citep{anas02}.
". It is. however. mentioned here that among all our simulated scenarios. only in one case with D,=1.0. L4—50 m. oj=0.01. and yy=0.005.Hr the energy spectrum does show a clear broken power-law shape."," It is, however, mentioned here that among all our simulated scenarios, only in one case with $B_{g}=1.0$, $L_0$ =50 m, $\beta_0=0.01$, and $\eta_0=0.005$, the energy spectrum does show a clear broken power-law shape."
 several parameters can alfect the energy spectral profile of the DC-acceleratedelectrons in our simulations. where the spectral profile is characterized by 9 ancl £j as indicated by equation (11)).," Several parameters can affect the energy spectral profile of the DC-acceleratedelectrons in our simulations, where the spectral profile is characterized by $\delta$ and $E_0$ as indicated by equation \ref{eqa}) )."
" Theου parameters include the longitudinal component of the magnetic field (D2,). the length scale (Ly). the resistivity (5). and the magnetic field strength. as represented by the plasma beta (25)."," Thefree parameters include the longitudinal component of the magnetic field $B_{g}$ ), the length scale $L_0$ ), the resistivity $\eta_0$ ), and the magnetic field strength, as represented by the plasma beta $\beta_0$ )."
 In the following subsections. the effect of varving each parameter is investigated individually with other parameters keeping fixed.," In the following subsections, the effect of varying each parameter is investigated individually with other parameters keeping fixed."
" Dv theoretical analvsis of electron acceleration in a reconnecting current sheet. propounded that a longitudinal component of magnetic field is necessary (ο explain the accelerated electrons will energv up to LOO keV. In our simulations. the longitudinal component (ie.. the guide component along the z-direction) of the magnetic field near the reconnection N-point is around D,."," By theoretical analysis of electron acceleration in a reconnecting current sheet, \citet{lit96} propounded that a longitudinal component of magnetic field is necessary to explain the accelerated electrons with energy up to 100 keV. In our simulations, the longitudinal component (i.e., the guide component along the $z$ -direction) of the magnetic field near the reconnection X-point is around $B_{g}$."
" Therelore. we caleulated six cases with D, increasing from 0 to 1.0. while the other parameters are L5—50 m. oy)= 0.01. and no= 0.02."," Therefore, we calculated six cases with $B_{g}$ increasing from 0 to 1.0, while the other parameters are $L_0$ =50 m, $\beta_0=0.01$ , and $\eta_0=0.02$ ."
 The energv spectra of the accelerated electrons in the six cases are depicted in the upper panel, The energy spectra of the accelerated electrons in the six cases are depicted in the upper panel
the backgrouud level (Sect. 5)).,the background level (Sect. \ref{struc}) ).
"Γ Thus. to meet these criteria. the photometry for cach target was extracted frou in a wide circular field of radius RostGU. 90"". varving according to each case."," Thus, to meet these criteria, the photometry for each target was extracted from in a wide circular field of radius $\rx=60-90\arcmin$ , varying according to each case."
 As a photometric quality coustraint. only stars withJ../7.. aud cerrors lower than πας are used.," As a photometric quality constraint, only stars with, and errors lower than mag are used."
 Reddeniig corrections are based on the absorption relations AyfAy= 0270. Ag/Ay= 0176. Ags.fely= 0.115. and Ay=2.76.£07IF) οἴνοι by Dutra.Santiago&Bica (2002).. with Ay=3.1. considering the extinction curve of Cardelli.Clavtou&Mathis(1989).," Reddening corrections are based on the absorption relations $A_J/A_V=0.276$ , $A_H/A_V=0.176$ , $A_{K_S}/A_V=0.118$ , and $A_J=2.76\times\ejh$ given by \citet{DSB2002}, with $R_V=3.1$, considering the extinction curve of \citet{Cardelli89}."
. The first step for correctly characterising the rotometric and structural properties of a star cluster is to fud its actual ceutre. 1.0; the maxims of the overdensity xoduced. by member stars.," The first step for correctly characterising the photometric and structural properties of a star cluster is to find its actual centre, i.e., the maximum of the overdensity produced by member stars."
 To do this. we download he photometry ceutred on the input coordinates (cols.," To do this, we download the photometry centred on the input coordinates (cols."
 1 ale 5 yOof Table 1)). build the RDP (Sect. 5))," 4 and 5 of Table \ref{tab1}) ), build the RDP (Sect. \ref{struc}) )"
" for deriving a first estimate of target size (R=Rapp) aud ocation of the comparison field (Res,SRS Ress). ȟld the decoutamunated (Sect. 3.1))"," for deriving a first estimate of target size $R=\rl$ ) and location of the comparison field $R_{FS1}\la 
R\la R_{FS2}$ ), build the decontaminated (Sect. \ref{DecontCMD}) )"
 CMD of the region RsRapp. ve-compiute the central.. now with the decoutaminated photometry. and repeat steps for the new ceutral coordinates.," CMD of the region $R\la\rl$, re-compute the central, now with the decontaminated photometry, and repeat steps for the new central coordinates."
 Usually. there are sinall cdiffercuces between our coordinates (cols.," Usually, there are small differences between our coordinates (cols."
 8 aud 9 of Table 1)) aud the input ones., 8 and 9 of Table \ref{tab1}) ) and the input ones.
 The cfitcicucy of this approach can be assessed by the shape of the resulting RDPs (Fie. 5.., The efficiency of this approach can be assessed by the shape of the resulting RDPs (Fig. \ref{fig5}.
 All cases present a rather hieh ceutral density dropping relatively smoothly outwards., All cases present a rather high central density dropping relatively smoothly outwards.
 CNIDs extracted from a region that contains most of the stars (see the respective RDP - Sect. 5)), CMDs extracted from a region that contains most of the stars (see the respective RDP - Sect. \ref{struc}) )
 of each target are shown in Figs, of each target are shown in Figs.
 1. to |. top panels)., \ref{fig1} to \ref{fig4} top panels).
 These CAIDs should be compared to those extracted from equal-area offset (1üiddle panels)., These CMDs should be compared to those extracted from equal-area offset (middle panels).
 Except for a few case:μα (e.g. 112. 111231. and 11) where a cluster sequence shows up. it is clear that the field contamuinatio- has to be taken iuto account for a proper characterisatio- of the target.," Except for a few cases (e.g. 12, 1434, and 1) where a cluster sequence shows up, it is clear that the field contamination has to be taken into account for a proper characterisation of the target."
 Our group las been developing a set of analytical tools for diseutaugliug cluster evolutionary sequences from field stars iu CAIDs., Our group has been developing a set of analytical tools for disentangling cluster evolutionary sequences from field stars in CMDs.
 Iu turni. decontaminated CAIDs have been used to investigate the nature of star cluster candidates and derive their astrophysical parameters.," In turn, decontaminated CMDs have been used to investigate the nature of star cluster candidates and derive their astrophysical parameters."
 Briefly put. field-star decontamination is used to uncover the intrinsic CNID. morphology (esseutial for a proper derivation of reddening. age. and distance from the Sun}. and colour-magnitude filters are applied for building intrinsic stellar RDPs.," Briefly put, field-star decontamination is used to uncover the intrinsic CMD morphology (essential for a proper derivation of reddening, age, and distance from the Sun), and colour-magnitude filters are applied for building intrinsic stellar RDPs."
 In particular. the use of field-star decontaiiination with 2MLASS photometry in the construction of CMDz has shown to coustrain age and distance significantly more than the observed photometry. especially for latitude aud/or bulee-projected OCs (e.g. Bica.Bonatto 2008.. aud references therein).," In particular, the use of field-star decontamination with 2MASS photometry in the construction of CMDs has shown to constrain age and distance significantly more than the observed photometry, especially for low-latitude and/or bulge-projected OCs (e.g. \citealt{ProbFSR}, and references therein)."
 We apply the decontamination algorithm developed iu Bonatto&Bica(2007) ., We apply the decontamination algorithm developed in \citet{BB07} .
. For clarity. we provide a brief description below.," For clarity, we provide a brief description below."
 Asstune tha the region to decoutaminate is located within R=Reapo., Assume that the region to decontaminate is located within $R=R_{CMD}$.
 The alegorithin starts by dividiug the full ranec of magnitude aud colours of aCMDinto a 3D exid of colls with axes along the uunaenitude aud the aaud colours., The algorithm starts by dividing the full range of magnitude and colours of aCMDinto a 3D grid of cells with axes along the magnitude and the and colours.
 Then. for each cell it computes the total | field)nuuber-deusitv of stars. gk; (for," Then, for each cell it computes the total $+$ field)number-density of stars, $\eta_{tot}$ (for"
certain stage but they obey negative sign.,certain stage but they obey negative sign.
 After that s also decreases from -Γοο to some negative value as r increases from negative label to positive label during evolution of the Universe., After that $s$ also decreases from $+\infty$ to some negative value as $r$ increases from negative label to positive label during evolution of the Universe.
" Here, it is interesting to find the possible relation between the DBl-essence and the modified Chaplygin gas (MCG) (Benaoum2002)."," Here, it is interesting to find the possible relation between the DBI-essence and the modified Chaplygin gas (MCG) \citep{ujjal}."
. The MCG best fits with the 3—year WMAP and the SDSS data with the choice of parameters A=—0.085 and a=1.724 (Lu2008) which are improved constraints than the previous ones —0.35<A0.025 (Dao-Jun&Zhou2005)., The MCG best fits with the $3-$ year WMAP and the SDSS data with the choice of parameters $A=-0.085$ and $\alpha=1.724$ \citep{lu} which are improved constraints than the previous ones $-0.35<A<0.025$ \citep{jun}.
". Recently it is shown that the dynamical attractor for the MCG exists at Wage=—1, hence MCG crosses this value from either side wae>—1 or wae«—1, independent to the choice of model parameters (Jingetal2008)."," Recently it is shown that the dynamical attractor for the MCG exists at $\omega_{de}=-1$, hence MCG crosses this value from either side $\omega_{de}>-1$ or $\omega_{de}<-1$, independent to the choice of model parameters \citep{jing}."
". A generalization of MCG is suggested in (Debnath2007) by considering B=Βία)B,a*, where k and DB, are constants."," A generalization of MCG is suggested in \citep{debnath} by considering $B\equiv
B(a)=B_oa^k$, where $k$ and $B_o$ are constants."
" The MCG is the generalization of generalized Chaplygin gas pae=—B/p%, (Barreiro&Sen2004;Carturan&Finelli2003) with the addition of a barotropic term."," The MCG is the generalization of generalized Chaplygin gas $p_{de}=-B/\rho_{de}^\alpha$ \citep{sen,carturan} with the addition of a barotropic term."
 This special form also appears to be consistent with the WMAP 5—year data and henceforth the support the unified model with dark energy and matter based on generalized Chaplygin gas (Barriero2008;Makleretal2003).," This special form also appears to be consistent with the WMAP $5-$ year data and henceforth the support the unified model with dark energy and matter based on generalized Chaplygin gas \citep{barriero,makler}."
". In the cosmological context, the Chaplygin gas was first suggested as an alternative to quintessence and demonstrated an increasing A behavior for the evolution of the Universe (Kamenshchiketal2001)."," In the cosmological context, the Chaplygin gas was first suggested as an alternative to quintessence and demonstrated an increasing $\Lambda$ behavior for the evolution of the Universe \citep{kamenshchik}."
. Recent supernovae data also favors the two-fluid cosmological model with Chaplygin gas and matter (Panotopoulos2008)., Recent supernovae data also favors the two-fluid cosmological model with Chaplygin gas and matter \citep{grigoris}.
". Recently, several works on Chaplygin gas (Setare2007,a,b) and other dark energy model like tachyonic field (Setare2007c,2009) have been discussed for interacting and interacting scenarios of the accelerating universe."," Recently, several works on Chaplygin gas \citep{Setare1,Setare2a,Setare3a} and other dark energy model like tachyonic field \citep{Setare2b,Setare3b} have been discussed for interacting and non-interacting scenarios of the accelerating universe."
" In this section, we will show that, by choosing a proper potential, the DBl-essence can be described by a modified Chaplygin gas atlate times."," In this section, we will show that, by choosing a proper potential, the DBI-essence can be described by a modified Chaplygin gas atlate times."
" To find the possible relation between the DBl-essence and the modified Chaplygin gas, we set From energy conservation equation, we have the solution of py in modified Chaplygin gas as where C is an arbitrary positive integration constant."," To find the possible relation between the DBI-essence and the modified Chaplygin gas, we set From energy conservation equation, we have the solution of $\rho_{\phi}$ in modified Chaplygin gas as where $C$ is an arbitrary positive integration constant."
" From equations (4) - (6), we have Now consider the following two cases: IL: 7= constant."," From equations (4) - (6), we have Now consider the following two cases: : $\gamma=$ constant."
" From equations (6) and (22), it is easy to seen that the expression of ¢? is"," From equations (6) and (22), it is easy to seen that the expression of $\dot{\phi}^{2}$ is"
to model this process. we need a model for the convolving function.,"to model this process, we need a model for the convolving function."
 This is simply deduced. because the classification scheme automatically returns an estimate of the rms redshift error for each galaxy (see Wolfetal. 2004)).," This is simply deduced, because the classification scheme automatically returns an estimate of the rms redshift error for each galaxy (see \citealp{COMBOMain04}) )."
" Thus. given a pair of galaxies 7. ;. with redshift errors 7,, and o, the rms pairwise error is σι(a?|0113."," Thus, given a pair of galaxies $i$, $j$, with redshift errors $\sigma_{z_i}$ and $\sigma_{z_j}$ the rms pairwise error is $\sigma_{{\rm pair}_{i,j}}=\smash{(\sigma_{z_i}^2+\sigma_{z_j}^2)^{1/2}}$."
 The signal from this pair i smeared by a Gaussian with this width. so the overall convolving function is a sum of the Gaussians corresponding to all pairs: where Vis the number of pairs (/.j).," The signal from this pair is smeared by a Gaussian with this width, so the overall convolving function is a sum of the Gaussians corresponding to all pairs: where $N$ is the number of pairs $(i,j)$."
" After having transferred the pairwise redshift error distribution into comoving distances we can convolve €(1,,.7) with Eq. (9))."," After having transferred the pairwise redshift error distribution into comoving distances we can convolve $\xi(r_p,\pi)$ with Eq. \ref{pairwiseerrors}) )."
 The effect of this convolution is shown in the second panel in Fig. 3., The effect of this convolution is shown in the second panel in Fig. \ref{model}.
 The redshift-space correlations are now heavily elongated in the radial direction. and some care is needed in extracting the projected correlation signal.," The redshift-space correlations are now heavily elongated in the radial direction, and some care is needed in extracting the projected correlation signal."
" The simplest strategy for carrying out the projection needed in order to deduce i(7,) would be to integrate €(1,,.7) over a very large radial range."," The simplest strategy for carrying out the projection needed in order to deduce $w(r_p)$ would be to integrate $\xi(r_p,\pi)$ over a very large radial range."
 Fig., Fig.
 3 suggests that à maximum 7 value of 150 to 2007.+Mpc would be required to capture all the signal., \ref{model} suggests that a maximum $\pi$ value of $150$ to $200 \mpcoh$ would be required to capture all the signal.
" The problem with this strategy 1s that the random noise in £(7,.77) 1s independent of 7 at a given +, (because the expected pair counts have a cylindrical dependence xr,diy dz)."," The problem with this strategy is that the random noise in $\xi(r_p,\pi)$ is independent of $\pi$ at a given $r_p$ (because the expected pair counts have a cylindrical dependence $\propto r_p\, dr_p\, d\pi$ )."
" Thus. integration to 7=2007!Mpe would yield arandom error in (7, that is V? times larger than integration to z=100753Mpc — but the lower limit systematically misses part of the signal."," Thus, integration to $\pi=200\mpcoh$ would yield a random error in $w(r_p)$ that is $\sqrt{2}$ times larger than integration to $\pi=100\mpcoh$ – but the lower limit systematically misses part of the signal."
 We have developed a strategyfor solving this problem. which depends weakly on some prior knowledge of the likely form of the true clustering signal (after error convolution).," We have developed a strategyfor solving this problem, which depends weakly on some prior knowledge of the likely form of the true clustering signal (after error convolution)."
" A model for £(r,.7) defines how the real-space signal «(r,) is spread out in πι we are only concerned with the shape of"," A model for $\xi(r_p,\pi)$ defines how the real-space signal $w(r_p)$ is spread out in $\pi$ ; we are only concerned with the shape of"
Investigations into the interactions of circumstellar dises and embedded protoplanets were first conducted by ?..,Investigations into the interactions of circumstellar discs and embedded protoplanets were first conducted by \cite{GolTre1980}.
 They found that the exchange of angular momentum between the two should lead to migration of the protoplanet (latterly known as Type I migration). but their work did not suggest in which direction this migration would be.," They found that the exchange of angular momentum between the two should lead to migration of the protoplanet (latterly known as Type I migration), but their work did not suggest in which direction this migration would be."
 The analysis of 2? for a non-self gravitating. two-dimensional disc. showed that if the disce had a negative temperature gradient (.e. temperature reduces with increasing heliocentric radius) then an embedded protoplanet should migrate inwards.," The analysis of \cite{War1986} for a non-self gravitating, two-dimensional disc, showed that if the disc had a negative temperature gradient (i.e. temperature reduces with increasing heliocentric radius) then an embedded protoplanet should migrate inwards."
 When Hot Jupiters were discovered (2) and the dithculties with their in situ formation became apparent. this inward migration seemed to be an ideal mechanism by which to reconcile existing formation scenarios with these planets’ small final orbital radii.," When Hot Jupiters were discovered \citep{MayQue1995} and the difficulties with their in situ formation became apparent, this inward migration seemed to be an ideal mechanism by which to reconcile existing formation scenarios with these planets' small final orbital radii."
 However. the timescales of growth and migration did not at first compare favourably.," However, the timescales of growth and migration did not at first compare favourably."
 Migration timescales were so short that protoplanets should. plummet into their stars before they were able to grow to any considerable mass., Migration timescales were so short that protoplanets should plummet into their stars before they were able to grow to any considerable mass.
 Only by reaching masses suthcient to open dise gaps can protoplanets move from fast Type I migration to slower Type II migration. which proceeds at the dise's viscous evolution timescale.," Only by reaching masses sufficient to open disc gaps can protoplanets move from fast Type I migration to slower Type II migration, which proceeds at the disc's viscous evolution timescale."
 Once slowed. the planets only have to survive until the dise gas dissipates. thought to occur at a stellar age of less than 6 Myrs (2).. at which point migration due to planet-gas interactions necessarily ceases.," Once slowed, the planets only have to survive until the disc gas dissipates, thought to occur at a stellar age of less than 6 Myrs \citep*{HaiLadLad2001}, at which point migration due to planet-gas interactions necessarily ceases."
 Since ? further analytical descriptions νο. 22)).. and numerical modelling (Qu 9. 9.4. 9... D2u9. 9.?u 9. Dee Du. ue ?)) of planet migration have continued to find fast inward rates in he Type I regime (« 100 Mj».," Since \cite{War1986} further analytical descriptions (i.e. \citealt*{War1997, TanTakWar2002}) ), and numerical modelling \citealt{KorPol1993}; ; \citealt{NelPapMasKle2000}; \citealt{Mas2002}; \citealt*{DAnHenKle2002}; \citealt{BatLubOgiMil2003}; \citealt*{DAnKleHen2003}; \citealt*{AliMorBen2004}; \citealt*{DAnBatLub2005}; \citealt{KlaKle2006}; \citealt{DAnLub2008}; \citealt{LiLubLiLin2009}) ) of planet migration have continued to find fast inward rates in the Type I regime $<$ 100 )."
 However. these works have generally considered locally-isothermal conditions.," However, these works have generally considered locally-isothermal conditions."
 A large number of works. both analytical and numerical. have now been devoted o exploring the impact of more complex thermodynamies upon jyanet migration.," A large number of works, both analytical and numerical, have now been devoted to exploring the impact of more complex thermodynamics upon planet migration."
 The first of such works was published by ο. who performed local calculations focussing on a low-mass planet's interaction with its parent dise.," The first of such works was published by \cite{MorTan2003}, who performed local calculations focussing on a low-mass planet's interaction with its parent disc."
 They found that radiative cooling ed to a non-axisymmetrie mass distribution about the planet., They found that radiative cooling led to a non-axisymmetric mass distribution about the planet.
 This resulted in an additional torque beyond the commonly considered ditferential Lindblad torques. and altered the migration rate relative ο a purely isothermal calculation.," This resulted in an additional torque beyond the commonly considered differential Lindblad torques, and altered the migration rate relative to a purely isothermal calculation."
 ? found that a planet's migration rate was sensitive to the temperature and opacity structure of he dise through which it travelled. and under certain conditions he migration rate could be very much slower than that achieved in an isothermal model.," \cite{MenGoo2004} found that a planet's migration rate was sensitive to the temperature and opacity structure of the disc through which it travelled, and under certain conditions the migration rate could be very much slower than that achieved in an isothermal model."
 This was closely followed by ?./— who also identified a slow down in Type I migration ratesupon the introduction of radiative transfer., This was closely followed by \cite{JanSas2005} who also identified a slow down in Type I migration ratesupon the introduction of radiative transfer.
2001).,.
. The new points of interest preseuted im lis work include: seltceonsisteut solutions for the ICM cluperature and ionization resulting purely from an NRB: he significant effects of secondary electrons: aud the use of amore accurate calculations of photoionization cross sections and recombination rate coefficients., The new points of interest presented in this work include: self-consistent solutions for the IGM temperature and ionization resulting purely from an XRB; the significant effects of secondary electrons; and the use of more accurate calculations of photoionization cross sections and recombination rate coefficients.
" We find that he pre-velonization universe iiav be described by a model in which the first hunuimmous sources and their mdividual EUY Strónuugreu spheres are οοσα ii a pre-heated. xwtiallv ionized ICAL rather than in a cold. completely reutral ΔΙ,"," We find that the pre-reionization universe may be described by a model in which the first luminous sources and their individual EUV Strömmgren spheres are embedded in a pre-heated, partially ionized IGM, rather than in a cold, completely neutral IGM."
 Towever. an early XRD does not create sjenificaut amouuts of new inolecular hydrogen iu the ICM. despite the increased population of free electrons.," However, an early XRB does not create significant amounts of new molecular hydrogen in the IGM, despite the increased population of free electrons."
 This is primarily due to the strong photo-destruction of aud H» by the near IR/optical Cheneeforth IR/O) aud the far-UV (UV photons in the Lyiman-Werner bauds: henceforth FUW) backerounds. in the respective energv ranges 0.75511.2 eV and 11.213.6 eV. associated with any XRD generated by QSOs.," This is primarily due to the strong photo-destruction of $^{-}$ and $_2$ by the near IR/optical (henceforth IR/O) and the far-UV (UV photons in the Lyman-Werner bands; henceforth FUV) backgrounds, in the respective energy ranges 0.755–11.2 eV and 11.2–13.6 eV, associated with any XRB generated by QSOs."
 We also find that the enhanced. electron. fraction in the ICAL arising from au ARD pror to reionization may cause an overestination of the reionization epoch as determined from the cosmic nücrowave backerouud (CMD)., We also find that the enhanced electron fraction in the IGM arising from an XRB prior to reionization may cause an overestimation of the reionization epoch as determined from the cosmic microwave background (CMB).
 The plan of this paper is as follows., The plan of this paper is as follows.
 Iu 82. we outline the ICM heating aud cooling processes that we consider. aud the models for high-: NRBs.," In 2, we outline the IGM heating and cooling processes that we consider, and the models for $z$ XRBs."
 Iu 83. we present our results and discuss their duplications for the cosmological Jeaus mass. the CMD. the catalysis of molecular hydrogen. and the inhibition of galactic outflows.," In 3, we present our results and discuss their implications for the cosmological Jeans mass, the CMB, the $^{-}$ catalysis of molecular hydrogen, and the inhibition of galactic outflows."
 We stuuimarize our results in &l., We summarize our results in 4.
 Iu this section. we detail our assunptious for the NRB and ionizing QSO spectra. and we describe the various processes used to determine selfconsisteut [IGA teiuperatures and ionization fractions of livdrogen ai helium.," In this section, we detail our assumptions for the XRB and ionizing QSO spectra, and we describe the various processes used to determine self-consistent IGM temperatures and ionization fractions of hydrogen and helium."
 We focus ou the heating aud ionizing effects of the N-ravs on the initially neutral backerouud IGAL. but we do uot explicitly follow the erowth of individual fully ionize regions around the first QSOs or star-forming ealaxies.," We focus on the heating and ionizing effects of the X-rays on the initially neutral background IGM, but we do not explicitly follow the growth of individual fully ionized regions around the first QSOs or star-forming galaxies."
 As rejionization begius. the volume filling factor of such lughly ionized regious is λα].," As reionization begins, the volume filling factor of such highly ionized regions is small."
 The remaining IGAL is col aud neutral. with only a smell residual electrou fraction (~ 10!) from the recombination epoch (Seageretal. 2000).," The remaining IGM is cold and neutral, with only a small residual electron fraction $\sim 10^{-4}$ ) from the recombination epoch \citep{seager}."
.. Thehly energetic photous emitted by these sources will propagate mich more quickly than their associated ionization fronts., Highly energetic photons emitted by these sources will propagate much more quickly than their associated ionization fronts.
 This nuplies that au epoch will exist when the theruodyiuiuuic properties of most of the ICM iav be determiued by these N-ravs., This implies that an epoch will exist when the thermodynamic properties of most of the IGM may be determined by these X-rays.
 We model the properties of this volume by solving for ionization and thermal evolution i a ταον prinordial medii., We model the properties of this volume by solving for ionization and thermal evolution in a uniform primordial medium.
 We cousider the following processes for ionization solutious: photoionization. collisional ionizatiou. case D radiative recombination. dielectronie recombination for Ie L aud the coupliug between ID aud Ie caused bv the radiation fields from the He I 21.6 eV recombination continuum aud from the bouud-bound transitions of Te T (photon enereies at 19.5 eV. 21.2 eV. aud the two-photon contimmun with anu euergv suni of 20.6 eV).," We consider the following processes for ionization solutions: photoionization, collisional ionization, case B radiative recombination, dielectronic recombination for He I, and the coupling between H and He caused by the radiation fields from the He I 24.6 eV recombination continuum and from the bound-bound transitions of He I (photon energies at 19.8 eV, 21.2 eV, and the two-photon continuum with an energy sum of 20.6 eV)."
 The last of these processes is incorporated following the method iu Osterbrock(1989)., The last of these processes is incorporated following the method in \citet{ost}.
. The exact form of the pliotoiouization cross sections for IT I and Te II are taken from Spitzer(1978): we use the fit from Verneretal.(1996). for Te I. We also account for the effects of the secondary lohizations aud excitations of II I aud Πο I due to the energetic phooclectrous liberated bv the N-ravs (Shull&vanStechbere(1985): henceforth SVS85)., The exact form of the photoionization cross sections for H I and He II are taken from \citet{spitzer}; we use the fit from \citet{verner} for He I. We also account for the effects of the secondary ionizations and excitations of H I and He I due to the energetic photoelectrons liberated by the X-rays \citet{svs85}; henceforth SVS85).
 These introduce a further coupling between the ionization equilibria of IT anc Ile., These introduce a further coupling between the ionization equilibria of H and He.
 Secondary. ionization dominates over direct photoicmization for II I iu the specialized circumstance where N-ravs are the sole source of photoionization., Secondary ionization dominates over direct photoionization for H I in the specialized circumstance where X-rays are the sole source of photoionization.
 A vpical X-ray photon is far more likely o be absorbed bv Ue I rather than IE L The ejected xXiotoelectrou. however. will ionize many more IT I atoms han We T. as IL Tis uore abundant.," A typical X-ray photon is far more likely to be absorbed by He I rather than H I. The ejected photoelectron, however, will ionize many more H I atoms than He I, as H I is more abundant."
 As a result. secoudary ionizations from Ile I photoclectrous aud the radiation associated with Πο I recombination and excitation are he primary sources of I I ionization.," As a result, secondary ionizations from He I photoelectrons and the radiation associated with He I recombination and excitation are the primary sources of H I ionization."
" As pointed out bv SVSs85. the partitioniug of a prunary electrons energy. jetween heating the eas and secondary jonizatious aud excitations of II T aud Ie I. is itself à function of the gas ionization fraction. οὐ,"," As pointed out by SVS85, the partitioning of a primary electron's energy, between heating the gas and secondary ionizations and excitations of H I and He I, is itself a function of the gas ionization fraction, $x$."
 As ue decreases. aud iu particular ore SL. the photoclectrou deposits more of its energy in collisional iouizations/excitations and less in leat.," As $x$ decreases, and in particular for $x \la 0.1$, the photoelectron deposits more of its energy in collisional ionizations/excitations and less in heat."
 This a-cdependence is therefore niportaut to track iu the pre-reionization IGAL. so that the role of secondary ionizatious for II I is uot unclerestimated.," This $x$ -dependence is therefore important to track in the pre-reionization IGM, so that the role of secondary ionizations for H I is not underestimated."
 In order to be consisteut with SVSs5. who assiuned that the ionization fractious of lydrogen aud ouce-ionized helium were equal. appropriate for the interstellar cuviromuent they were considering.J we have recast the dependence in their results on μι to a direct. depeudence on the electron. fraction. Joc Dof(ng|ged. where the ummber deusitv of clectrous Πο=nundpar|221r ," In order to be consistent with SVS85, who assumed that the ionization fractions of hydrogen and once-ionized helium were equal, appropriate for the interstellar environment they were considering, we have recast the dependence in their results on $x_{\rm H^+}$ to a direct dependence on the electron fraction, $x_{\rm
e}$ = $n_{\rm e}/(n_{\rm H} + n_{\rm He})$, where the number density of electrons $n_{\rm e} = n_{\rm H II} + n_{\rm He II} + 2 n_{\rm He
III}$."
We compute the thermal evolution of the ICAL includiug the following processes: photoclectric heating from the secondary electrous of IT aud Te. as prescribed by SVS85 (the SVS85 solution. generates less heating relative to a prescription where of the photoclectron's excess energv goes iuto heating the ICM). aud heating from the ID I photoelectrous liberated bv the bouud-bound transitions or the 216 eV recombination continui of Ile I (here the loss of excess energev to heat is taken to be as further ionizations of II I or Te I ae not possible).," We compute the thermal evolution of the IGM including the following processes: photoelectric heating from the secondary electrons of H and He, as prescribed by SVS85 (the SVS85 solution generates less heating relative to a prescription where of the photoelectron's excess energy goes into heating the IGM), and heating from the H I photoelectrons liberated by the bound-bound transitions or the 24.6 eV recombination continuum of He I (here the loss of excess energy to heat is taken to be as further ionizations of H I or He I are not possible)."
 Cooling terius include radiative and cdielectronie recombination. thermal breimisstraliluug. Compton scattering off the CAB. collisional ionization and excitation. aud the adiabatic expansion of the ICM.," Cooling terms include radiative and dielectronic recombination, thermal bremsstrahlung, Compton scattering off the CMB, collisional ionization and excitation, and the adiabatic expansion of the IGM."
 The values of the recombination and cooling cocticicuts for temperatures < 10! I were taken from ΠΙΟ(19913. and IIunuuer&Storey(1998).. aud. the heating contribution frou the ο I two-photon process was calculated using the photon frequency distribution giveu in Drakeetal.(1969).," The values of the recombination and cooling coefficients for temperatures $\la$ $^4$ K were taken from \citet{hum94} and \citet{humst98}, and the heating contribution from the He I two-photon process was calculated using the photon frequency distribution given in \citet{drake69}."
. For the purposes of comparison. we will also consier cases that do not inchide adiabatic cooling. which is mimicked by artificially holding the ICAL density constant a its value at 2=10. so that there is no expansion cooling for 2«10.," For the purposes of comparison, we will also consider cases that do not include adiabatic cooling, which is mimicked by artificially holding the IGM density constant at its value at $z = 10$, so that there is no expansion cooling for $z < 10$."
 This would correspond to regions of the ICA that have ceased to participate in the IIubble expansion. but that have not vet begun to collapse.," This would correspond to regions of the IGM that have ceased to participate in the Hubble expansion, but that have not yet begun to collapse."
 The magnitude and spectral shape of the NRB at lüeh redshitt is uushown. aud a completely selt£-conusisteut model of its formation aud evolution is bevoud the scope," The magnitude and spectral shape of the XRB at high redshift is unknown, and a completely self-consistent model of its formation and evolution is beyond the scope"
of the sound. speed. profile. i is necessary (o use gravity modes. which have not vet been unequivocally detected (Vurk-Chiezze 2002).,"of the sound speed profile, it is necessary to use gravity modes, which have not yet been unequivocally detected (Turk-Chièzze 2002)."
 Obviously. another reason for the density cüllerence could. come from the physics of the solar standard. mocel. and not onlv from the density. profile inversion.," Obviously, another reason for the density difference could come from the physics of the solar standard model, and not only from the density profile inversion."
 However. this is more unlikely because the sound: speed. dillerence is very. small. reenforcing the view that the physics in the solar nuclear region is already described with the necessary ACCULPACV.," However, this is more unlikely because the sound speed difference is very small, reenforcing the view that the physics in the solar nuclear region is already described with the necessary accuracy."
" Even if the answers to some questions about the inversion are still unclear. it seems very likely that there exists a class of annihilating WIMPs with annihilation cross-section. £o,0$ of⋅ the order of⋅ 102Tτσ)em’3/see and relatively. small masses that are excluded by the present seismic results."," Even if the answers to some questions about the inversion are still unclear, it seems very likely that there exists a class of annihilating WIMPs with annihilation cross-section $\langle
\sigma_a v \rangle$ of the order of $10^{-27}\; \rm cm^{3}/sec$ and relatively small masses that are excluded by the present seismic results."
 \WHIAIPs with masses smaller than 60. Ge and scattering cross-sections between LO77cm? and 101i)Cni2 seem to significantly modify the profile of the sound. speed near the core., WIMPs with masses smaller than 60 GeV and scattering cross-sections between $10^{-38} \rm cm^2$ and $10^{-40}\rm cm^2$ seem to significantly modify the profile of the sound speed near the core.
 This result. is also reenforced. by the density profile inversion., This result is also reenforced by the density profile inversion.
 Hf we accept these results. both inverted quantities reject the existence of WIMPS with masses smaller than 30GeV in the proposed. scattering cross-section range.," If we accept these results, both inverted quantities reject the existence of WIMPs with masses smaller than $30 \; \rm GeV$ in the proposed scattering cross-section range."
 | follows that the acoustic spectrum of the previous WIMP-»accreting solar models is incompatible with the observec solar spectrum measured by the SOLLO seismic experiments., It follows that the acoustic spectrum of the previous WIMP-accreting solar models is incompatible with the observed solar spectrum measured by the SOHO seismic experiments.
 Usually. the solar model of the present Sun which bes reproduces the observed acoustic spectrum is referred as the solar seismic model.," Usually, the solar model of the present Sun which best reproduces the observed acoustic spectrum is referred as the solar seismic model."
 In particular the solar standard: moce leads to the best representation of the solar seismic moce but it is not the only solution., In particular the solar standard model leads to the best representation of the solar seismic model but it is not the only solution.
 Alodel-independent: predictions can be mace for neutrinos from the centre of the Sun. where neutralinos may. have been eravitationally trapped: ancl therefore. their. density enhanced.," Model-independent predictions can be made for neutrinos from the centre of the Sun, where neutralinos may have been gravitationally trapped and therefore their density enhanced."
 “Today. the rate of change of the number of neutralinos between capture and annihilation in the Sun is in equilibrium.," Today, the rate of change of the number of neutralinos between capture and annihilation in the Sun is in equilibrium."
 As they annihilate. many of the possible final states produce. after decays anc hadronization. energetic neutrinos which propagate out from the interior of the Sun.," As they annihilate, many of the possible final states produce, after decays and hadronization, energetic neutrinos which propagate out from the interior of the Sun."
 In particular. the muon neutrinos are useful for indirect detection of neutralino annihilation processes. since muons lave quite a long range in a suitable detector medium like ice or water.," In particular, the muon neutrinos are useful for indirect detection of neutralino annihilation processes, since muons have quite a long range in a suitable detector medium like ice or water."
 They can be detected through their Cherenkov raciation after having been produced at or near the detector., They can be detected through their Cherenkov radiation after having been produced at or near the detector.
 Detection of neutralino annihilation into neutrinos is one of he most promising indirect detection methods. and it will ος subject to extensive experimental investigations in view of the new neutrino telescopes such as AALANDA. ICeCube. Baikal. BAKSAN. AIACRO. NESTOR anc ANTALIS slannecl or under construction (Llalzen 1997).," Detection of neutralino annihilation into neutrinos is one of the most promising indirect detection methods, and it will be subject to extensive experimental investigations in view of the new neutrino telescopes such as AMANDA, ICeCube, Baikal, BAKSAN, MACRO, NESTOR and ANTARES planned or under construction (Halzen 1997)."
 The neutrino-induced muon flux may be detected in a neutrino telescope ον measuring the muons that come from the direction of the centre of the Sun or Earth., The neutrino-induced muon flux may be detected in a neutrino telescope by measuring the muons that come from the direction of the centre of the Sun or Earth.
 Phe energy of these muons will typically be between 1/2 and. 1/3 of the neutralino mass. so they will be much more energetic than ordinary solar neutrinos.," The energy of these muons will typically be between 1/2 and 1/3 of the neutralino mass, so they will be much more energetic than ordinary solar neutrinos."
 These neutrinos have energies of the order of a GeV. well above the energy of solar neutrinos which is of the order of MeV. To investigate this question. we concentrate our attention on supersvmmetrie dark matter and evaluate the expected: flux of neutrinos (ancl consequent muon [uxes in detectors) from annihilating neutralinos in the solar core.," These neutrinos have energies of the order of a GeV, well above the energy of solar neutrinos which is of the order of MeV. To investigate this question, we concentrate our attention on supersymmetric dark matter and evaluate the expected flux of neutrinos (and consequent muon fluxes in detectors) from annihilating neutralinos in the solar core."
" ""The numerical results discussed. in this work are obtained in the [framework of the Minimal Supersynimetric Standard: Model as implemented in the. DarkSUSY code (DAISSAL: Gondolo et al.", The numerical results discussed in this work are obtained in the framework of the Minimal Supersymmetric Standard Model as implemented in the DarkSUSY code (DMSSM; Gondolo et al.
 2000). which takes into account the most recent. particle physies constraints. such as the LEP lower bounds on the lightest Higgs and chareino masses.," 2000), which takes into account the most recent particle physics constraints, such as the LEP lower bounds on the lightest Higgs and chargino masses."
 We extended our analysis to some benchmark points of a different supersvnumetric scenario. the Constrained Minimal Supersununetric Standard. Model (CSSAL: Ellis et al.," We extended our analysis to some benchmark points of a different supersymmetric scenario, the Constrained Minimal Supersummetric Standard Model (CSSM; Ellis et al."
 2000)., 2000).
 In this work we are mainly concerned with WIMP candidates. such as the neutralinos capable of producing changes in the structure of the solar core which can be tested. against the solar seismic model.," In this work we are mainly concerned with WIMP candidates, such as the neutralinos capable of producing changes in the structure of the solar core which can be tested against the solar seismic model."
 Indeed. even after all the particle accelerator and relic abundance constraints are taken into account. there are large numbers of SUSY models which can produce neutralino dark matter.," Indeed, even after all the particle accelerator and relic abundance constraints are taken into account, there are large numbers of SUSY models which can produce neutralino dark matter."
 Lt is in js large parameter space of candidates proposed. by the ferent extensions of the standard model of particle physics jut the Sun can provide another independent diagnostic of we SUSY parameter space., It is in this large parameter space of candidates proposed by the different extensions of the standard model of particle physics that the Sun can provide another independent diagnostic of the SUSY parameter space.
 One should be aware that the choice of nuclear orm factors needed to compute neutralino-nucleus. elastic scattering. as well as other specific quantities related. to jwlronic physics which relate quarks/eluons with nucleons ancl also the quantities related with the step from nucleons o nuclei. are at. best. approximate.," One should be aware that the choice of nuclear form factors needed to compute neutralino-nucleus elastic scattering, as well as other specific quantities related to hadronic physics which relate quarks/gluons with nucleons and also the quantities related with the step from nucleons to nuclei, are at best approximate."
" ""This is the reason why detailed. processes such as scattering cross-sections are difficult to obtain with any generalityv.", This is the reason why detailed processes such as scattering cross-sections are difficult to obtain with any generality.
 A more sophisticated reatment would. however. change the values by much ess than the spread. due to the unknown super-symmoetric xwameters.," A more sophisticated treatment would, however, change the values by much less than the spread due to the unknown super-symmetric parameters."
 Indeed. our. understanding of SUSY models is still developing. so predictions of annihilation rates in he early Universe. and thus relic neutralino densities may require modification.," Indeed, our understanding of SUSY models is still developing, so predictions of annihilation rates in the early Universe, and thus relic neutralino densities may require modification."
 More significantly. another source of incertitude in modeling the incoming Lux of annihilating neutrinos is related with the poor description of the solar core usually assumed in the computations.," More significantly, another source of incertitude in modeling the incoming flux of annihilating neutrinos is related with the poor description of the solar core usually assumed in the computations."
 Llowever. the present and future capability of solar seismoloev will provide the means to reduce this source of error.," However, the present and future capability of solar seismology will provide the means to reduce this source of error."
" Future solar seismic experiments will be able to detec deviations of order 10"" [rom the luminosity. precictec in the solar standard. model.", Future solar seismic experiments will be able to detect deviations of order $10^{-5}$ from the luminosity predicted in the solar standard model.
 Lo the. microphvsies of the solar standard. model is. understood. with the necessary precision. then at this level of accuracy a large portion of the supersvmmetrie parameter space would be ruled out by means of the seismic diagnostics.," If the microphysics of the solar standard model is understood with the necessary precision, then at this level of accuracy a large portion of the supersymmetric parameter space would be ruled out by means of the seismic diagnostics."
 We show in Fig., We show in Fig.
 2 how this analysis would alfect the expected. muon Lux. induce," 2 how this analysis would affect the expected muon flux, induced"
to a wavelength range where spectral libraries are the most accurate.,to a wavelength range where spectral libraries are the most accurate.
" Adding the K band improves mass estimates in the non-stochastic regime of high total masses, but it has an observational cost as it requires the use of a different instrument."," Adding the K band improves mass estimates in the non-stochastic regime of high total masses, but it has an observational cost as it requires the use of a different instrument."
 Testing the UBVIK combination in the stochastic regime provides useful information for the design of future surveys., Testing the UBVIK combination in the stochastic regime provides useful information for the design of future surveys.
" In Sect. |,"," In Sect. \ref{sec:noKband},"
 we presented some effects of the presence of K band data in addition to UBVI photometry., we presented some effects of the presence of K band data in addition to UBVI photometry.
 The K band does not improve significantly the situation when models are being used (right panel on Fig. [TO))., The K band does not improve significantly the situation when models are being used (right panel on Fig. \ref{fig:UBVIK_distribs}) ).
" In particular, we mentioned that including the K band in the analysis of populations with AGB stars (100—500 Myr) may lead to even worse estimates (again with continuous models)."," In particular, we mentioned that including the K band in the analysis of populations with AGB stars $100-500$ Myr) may lead to even worse estimates (again with continuous models)."
 This effect is also visible on the left-hand side panels of Fig. [I2]., This effect is also visible on the left-hand side panels of Fig. \ref{fig:Age_Lum_Distribs}.
" On the other hand, we found only mild improvements when including K band data in the analysis: the presence of K band information translates into weaker artefacts in the derived age distributions (artefacts which disappear when reddening is not a free parameter)."," On the other hand, we found only mild improvements when including K band data in the analysis: the presence of K band information translates into weaker artefacts in the derived age distributions (artefacts which disappear when reddening is not a free parameter)."
 The left panel of Fig., The left panel of Fig.
"[[0] presents recovered age-mass distributions for UBVI and UBVIK datasets using the Bayesian approach, with free extinction."," \ref{fig:UBVIK_distribs} presents recovered age-mass distributions for UBVI and UBVIK datasets using the Bayesian approach, with free extinction."
 Old populations (>1 Gyr) age-mass estimates reflect the original distribution better when K band constraints are included., Old populations $> 1$ Gyr) age-mass estimates reflect the original distribution better when K band constraints are included.
" This is also visible on the right panels of Fig. [[2],"," This is also visible on the right panels of Fig. \ref{fig:Age_Lum_Distribs},"
 where the resulting distributions are significantly improved., where the resulting distributions are significantly improved.
" At young ages, both our test sample and our main MC catalog are underpopulated."," At young ages, both our test sample and our main MC catalog are underpopulated."
 Most small and young clusters have HR diagrams that resemble a truncated main sequence., Most small and young clusters have HR diagrams that resemble a truncated main sequence.
" Even if the stellar mass function from which their stars are drawn randomly extends to MMo, a small zero age cluster will in general contain zero ionizing stars, and a small cluster aged MMyr will contain zero red supergiants: two such objects are basically indistinguishable, be it with or without K band data."," Even if the stellar mass function from which their stars are drawn randomly extends to $_{\odot}$, a small zero age cluster will in general contain zero ionizing stars, and a small cluster aged Myr will contain zero red supergiants: two such objects are basically indistinguishable, be it with or without K band data."
" This problem shows up clearly when we run the Bayesian analysis at young ages, but quantifying this effect requires that we add more young clusters to our reference catalog."," This problem shows up clearly when we run the Bayesian analysis at young ages, but quantifying this effect requires that we add more young clusters to our reference catalog."
 The UV spectral range raises questions similar to the near-infrared., The UV spectral range raises questions similar to the near-infrared.
" We repeated some of the above experiments with UBVI and the F218W filter, centered around 220 nnm (WFPC2 instrument on-board the Hubble Space Telescope)."," We repeated some of the above experiments with UBVI and the F218W filter, centered around $220$ nm (WFPC2 instrument on-board the Hubble Space Telescope)."
" A brief summary is that the effects of adding this UV band have amplitudes similar to those obtained when adding K. The dispersions in the results are comparable to those without UV, both for Bayesian or standard estimates."," A brief summary is that the effects of adding this UV band have amplitudes similar to those obtained when adding K. The dispersions in the results are comparable to those without UV, both for Bayesian or standard estimates."
 Artefacts are also qualitatively similar., Artefacts are also qualitatively similar.
 Age estimates below 20 Myr are improved only slightly., Age estimates below $20$ Myr are improved only slightly.
" If one however wants to include UV bands, the choice of an extinction law becomes more of an issue."," If one however wants to include UV bands, the choice of an extinction law becomes more of an issue."
 Extinction laws indeed express a range of behaviours in the UV bands Fitzpatrick|Calzettiet& Mathis[1989;al.|2000).," Extinction laws indeed express a range of behaviours in the UV bands \citep[e.g][]{Allen1976, Fitzpatrick1986, Cardelli1989,
Calzetti2000}."
. The decision of which filters to use rests on considerations of the astrophysical problem to tackle., The decision of which filters to use rests on considerations of the astrophysical problem to tackle.
 Using either UV or K photometry does not deeply affect the resulting estimates ages and masses of small clusters., Using either UV or K photometry does not deeply affect the resulting estimates ages and masses of small clusters.
 One may first want to consider using discrete population models instead of continuous ones., One may first want to consider using discrete population models instead of continuous ones.
" Studies of star cluster populations in galaxies have been based until now on population synthesis models, that provide a very poor approximation of the integrated light of clusters of small and intermediate masses because this light is determined by a very small number of luminous stars."," Studies of star cluster populations in galaxies have been based until now on population synthesis models, that provide a very poor approximation of the integrated light of clusters of small and intermediate masses because this light is determined by a very small number of luminous stars."
" Based on large collections of Monte-Carlo simulations of star clusters that each contain a finite number of stars, this paper explores systematic errors that occur when the integrated fluxes of realistic clusters of small masses are analysed in terms of mass and age."," Based on large collections of Monte-Carlo simulations of star clusters that each contain a finite number of stars, this paper explores systematic errors that occur when the integrated fluxes of realistic clusters of small masses are analysed in terms of mass and age."
" Our main collection is built with the cluster age and mass distributions of |Fall,Chandar,&Whit-(2009)., extrapolated to masses lower than those observed [more]in the Antennae galaxies."," Our main collection is built with the cluster age and mass distributions of \citet{Fall2009}, extrapolated to masses lower than those observed in the Antennae galaxies."
" With the standard methods (continuous models), large systematic errors affect estimated ages and large random errors affect masses."," With the standard methods (continuous models), large systematic errors affect estimated ages and large random errors affect masses."
" If observational uncertainties on cluster fluxes are large and, as a consequence, quality-of-fit criteria fail to reject the numerous poor fits, systematic errors (of a few tenths of a dex) are also present in the estimated masses."," If observational uncertainties on cluster fluxes are large and, as a consequence, quality-of-fit criteria fail to reject the numerous poor fits, systematic errors (of a few tenths of a dex) are also present in the estimated masses."
 Derived age-mass or age-luminosity distributions for samples in which actual ages and masses are distributed as in our main collection display clustered patterns that very closely resemble those found in empirical samples in the current literature., Derived age-mass or age-luminosity distributions for samples in which actual ages and masses are distributed as in our main collection display clustered patterns that very closely resemble those found in empirical samples in the current literature.
" We find no immediately obvious reason to reject the age and mass distributions of our main collection, but clearly this essential point requires detailed study with real observations."," We find no immediately obvious reason to reject the age and mass distributions of our main collection, but clearly this essential point requires detailed study with real observations."
" A Bayesian method has been described and implemented, in order to account explicitly for the finite nature of clusters in the analysis."," A Bayesian method has been described and implemented, in order to account explicitly for the finite nature of clusters in the analysis."
 It is shown that their age and mass can be recovered with error bars that will be small enough for many purposes., It is shown that their age and mass can be recovered with error bars that will be small enough for many purposes.
 Young small mass clusters will remain difficult to age-date because HR-diagrams of many of them identically look like truncated main sequences with no ionizing or post-main sequence stars., Young small mass clusters will remain difficult to age-date because HR-diagrams of many of them identically look like truncated main sequences with no ionizing or post-main sequence stars.
" At intermediate ages, the variability of luminous AGB stars is expected to cause difficulties that we have not yet solved."," At intermediate ages, the variability of luminous AGB stars is expected to cause difficulties that we have not yet solved."
" The comparison between the results obtained with UBVI and UBVIK data sets shows that, in the stochastic context, the benefits of adding the K band to optical observations are rather small, except for the mass determination of clusters older than GGyr."," The comparison between the results obtained with UBVI and UBVIK data sets shows that, in the stochastic context, the benefits of adding the K band to optical observations are rather small, except for the mass determination of clusters older than Gyr."
" Clearly, adding near-IR or UV information is secondary, compared to the need to move from continuous to stochastic cluster models."," Clearly, adding near-IR or UV information is secondary, compared to the need to move from continuous to stochastic cluster models."
 The Bayesian analysis method can now be applied to existing data on cluster samples in nearby galaxies with the aim of constraining the actual age and mass distributions of these clusters., The Bayesian analysis method can now be applied to existing data on cluster samples in nearby galaxies with the aim of constraining the actual age and mass distributions of these clusters.
 We will also extend the study of systematic errors to the case where metallicity is an unknown parameter., We will also extend the study of systematic errors to the case where metallicity is an unknown parameter.
Accretion of material onto a supermassive black hole has lone been believed to be the fundamental power source active galactic nuclei (AGN: eg. see Rees 1984. for review).,Accretion of material onto a supermassive black hole has long been believed to be the fundamental power source of active galactic nuclei (AGN; e.g. see Rees 1984 for a review).
 However. the physical processes by which the eravitational potential energy of the accretion [ow energizes 16 observed. spectrum are still far from certain.," However, the physical processes by which the gravitational potential energy of the accretion flow energizes the observed spectrum are still far from certain."
 Recent spectroscopic studies in the N-rayv waveband have shown jut. in the innermost regions (ie. rZ10Hp: where Ion is the Sehwarzschild. radius of the central black hole) of at cast some AGN. there is a &eometricallv-thin. raciatively-ellicient. accretion disk. CIanaka et al.," Recent spectroscopic studies in the X-ray waveband have shown that, in the innermost regions (i.e. $r\approxlt
10\,{\rm R}_{\rm Sch}$; where ${\rm R}_{\rm Sch}$ is the Schwarzschild radius of the central black hole) of at least some AGN, there is a geometrically-thin, radiatively-efficient accretion disk (Tanaka et al."
 1995: Fabian et al., 1995; Fabian et al.
 1995)., 1995).
 X significant [raction of the accretion energy appears o be liberated in a hot. opticallv-thin. cisk-corona which is a prolific radiator of N-ravs ancl 5-ravs. (probably via he Comptonization of optical/UV. photons from the cold accretion disk: Llaardt Alaraschi 1991: Field Rogers 1993: Zelziarski et al.," A significant fraction of the accretion energy appears to be liberated in a hot, optically-thin, disk-corona which is a prolific radiator of X-rays and $\gamma$ -rays (probably via the Comptonization of optical/UV photons from the cold accretion disk: Haardt Maraschi 1991; Field Rogers 1993; Zdziarski et al."
 1994)., 1994).
 Although most of the primary radiation is produced in the inner regions of the accretion How. a significant fraction of this radiation is reprocessed at ercator distances from the black hole into UV. optical and IR wavelengths.," Although most of the primary radiation is produced in the inner regions of the accretion flow, a significant fraction of this radiation is reprocessed at greater distances from the black hole into UV, optical and IR wavelengths."
 Studying these reprocessing mechanisms allows the structures surrounding the accreting black hole to be probed and are necessary if we are to disentangle the primary emission [rom the reprocessed. emission., Studying these reprocessing mechanisms allows the structures surrounding the accreting black hole to be probed and are necessary if we are to disentangle the primary emission from the reprocessed emission.
 In recent wears. much has been learnt about the various reprocessing mechanisms.," In recent years, much has been learnt about the various reprocessing mechanisms."
" It has been realized that approximately half of the N-rav. photons emitted from the corona will strike the cold accretion disk. thereby. producing ""rellection! features in the X-ray spectrum (Cuilbert Rees 1988: Lightman White 1988: Pounds οἱ al."," It has been realized that approximately half of the X-ray photons emitted from the corona will strike the cold accretion disk, thereby producing `reflection' features in the X-ray spectrum (Guilbert Rees 1988; Lightman White 1988; Pounds et al."
 1990)., 1990).
 Phe emission that emerges from these central regions can also be intercepted by more distant. structures: these include the broad-line region (BLE). the putative molecular torus of the unified Sevfert schemes and the warm absorber.," The emission that emerges from these central regions can also be intercepted by more distant structures: these include the broad-line region (BLR), the putative molecular torus of the unified Seyfert schemes and the warm absorber."
 The scattering of primary radiation into our line-ol-sight is also known to be important in at [east some ACN., The scattering of primary radiation into our line-of-sight is also known to be important in at least some AGN.
matrices with different coverage rates.,matrices with different coverage rates.
 They apply compressive sampling for deconvolution by assuming the target signal is sparse., They apply compressive sampling for deconvolution by assuming the target signal is sparse.
 ? proposed a new spread spectrum technique for radio interferometry by using the non-negligible and constant component of the antenna separation in the pointing direction., \cite{Wiaux:2009p1697} proposed a new spread spectrum technique for radio interferometry by using the non-negligible and constant component of the antenna separation in the pointing direction.
" Recently, a new CS-based image deconvolution method was introduced in ? in which an isotropic undecimated wavelet transform is adopted as a dictionary for sparse representation for sky images."," Recently, a new CS-based image deconvolution method was introduced in \cite{deconvolution2011application} in which an isotropic undecimated wavelet transform is adopted as a dictionary for sparse representation for sky images."
" In this paper, we propose three new CS-based RM synthesis methods."," In this paper, we propose three new CS-based RM synthesis methods."
" In Section D], the three CS-based RM synthesis methods are proposed."," In Section \ref{sec:csrm}, the three CS-based RM synthesis methods are proposed."
 The implementation details of the general experiment layout is given in Section B]., The implementation details of the general experiment layout is given in Section \ref{sec:implementation}.
 Simulation results from the traditional methods are compared with those from CS-based methods in Section 4]., Simulation results from the traditional methods are compared with those from CS-based methods in Section \ref{sec:experiments}.
 The final conclusions are given in Section]. , The final conclusions are given in Section \ref{sec:conclusion}. .
CS is primarily a sampling theory for sparse signals.,	 CS is primarily a sampling theory for sparse signals.
 A sensing matrix (?) is used to sample a signal with sparsity (few non-zero terms) or a sparse representation with respect to a given basis function dictionary., A sensing matrix \citep{candes2006stable} is used to sample a signal with sparsity (few non-zero terms) or a sparse representation with respect to a given basis function dictionary.
" Given a limited number of measurements, generally less than the number of unknowns in the target signal, the target signal can be reconstructed by optimisation of an L1 norm."," Given a limited number of measurements, generally less than the number of unknowns in the target signal, the target signal can be reconstructed by optimisation of an L1 norm."
" More information on the key concepts (such as sparsity, incoherence, the restricted isometry property, and the L1 norm reconstruction) and results can be found in ????.."," More information on the key concepts (such as sparsity, incoherence, the restricted isometry property, and the L1 norm reconstruction) and results can be found in \cite{Candes:2007p2815,Candes:2004p2832,Candes:2008p14,Candes:2006p23}."
 CS includes two steps: sensing/sampling and reconstruction., CS includes two steps: sensing/sampling and reconstruction.
 This is in contrast to Nyquist-Shannon theory which measures the target signal directly without the reconstruction step., This is in contrast to Nyquist-Shannon theory which measures the target signal directly without the reconstruction step.
" In this paper, we will focus on the reconstruction step (calculating the Faraday dispersion function given an observing window) rather than the sensing step (the selection of the observing window), because the observing frequency range and the bandwidth for each channel are usually fixed for a given telescope array."," In this paper, we will focus on the reconstruction step (calculating the Faraday dispersion function given an observing window) rather than the sensing step (the selection of the observing window), because the observing frequency range and the bandwidth for each channel are usually fixed for a given telescope array."
" To proceed with the CS approach, we rewrite the Fourier relationship as a matrix equation."," To proceed with the CS approach, we rewrite the Fourier relationship as a matrix equation."
 The projection of the Faraday dispersion function to the polarized emission can be described as a matrix Y of size mxN The inverse of the projection is the conjugate transpose of Y where * denotes the conjugate transpose., The projection of the Faraday dispersion function to the polarized emission can be described as a matrix $Y$ of size $m\times N$ The inverse of the projection is the conjugate transpose of $Y$ where $\ast$ denotes the conjugate transpose.
" Suppose f denotes the original Faraday dispersion function F(@) in a vector format of length N, then the relationship between the Faraday dispersion function and the observed radio emission is: where p denotes the observed polarized emission in a vector format of length m."," Suppose $f$ denotes the original Faraday dispersion function $F(\phi)$ in a vector format of length $N$, then the relationship between the Faraday dispersion function and the observed radio emission is: where $\widetilde{p}$ denotes the observed polarized emission in a vector format of length $m$."
" Because we can only measure a limited number of observations with the limited number of channels, i.e. m<< N, there are many different potential Faraday dispersion functions consistent with the measurements."," Because we can only measure a limited number of observations with the limited number of channels, i.e. $m<<N$ , there are many different potential Faraday dispersion functions consistent with the measurements."
" To resolve these ambiguities, the usual approach is to use some prior information to select a solution."," To resolve these ambiguities, the usual approach is to use some prior information to select a solution."
" The prior information can be: the Faraday dispersion function is real; the Faraday dispersion function has only point like signals which are sparse in the Faraday depth domain or the Faraday dispersion function has a sparse presentation with respect to a dictionary of basis functions, to name just a few."," The prior information can be: the Faraday dispersion function is real; the Faraday dispersion function has only point like signals which are sparse in the Faraday depth domain or the Faraday dispersion function has a sparse presentation with respect to a dictionary of basis functions, to name just a few."
 Our three synthesis methods are based upon the last two structural assumptions., Our three synthesis methods are based upon the last two structural assumptions.
" Before introducing our new RM synthesis methods, we need to review two technical terms: Faraday thin and Faraday thick."," Before introducing our new RM synthesis methods, we need to review two technical terms: Faraday thin and Faraday thick."
" A source can be either Faraday thin if VA@«l,or Faraday thick if A?Ad>>1, where Aó is the extent of the source along the axis of Faraday depth $."," A source can be either Faraday thin if $\lambda^2\bigtriangleup \phi\ll 1$, or Faraday thick if $\lambda^2\bigtriangleup \phi\gg1$, where $\bigtriangleup \phi$ is the extent of the source along the axis of Faraday depth $\phi$."
" Faraday thin sources can be well described by Dirac 6 function of ¢, while Faraday thick sources have extensive support on the Faraday depth axis (?).."," Faraday thin sources can be well described by Dirac $\delta$ function of $\phi$, while Faraday thick sources have extensive support on the Faraday depth axis \citep{Brentjens:2005p3385}."
 Note that the definition of Faraday thin or thick is wavelength dependent., Note that the definition of Faraday thin or thick is wavelength dependent.
" The relationship between the Faraday dispersion function and the observed polarized radio emission is a Fourier pair if mu, where u is a wavelength related parameter."," The relationship between the Faraday dispersion function and the observed polarized radio emission is a Fourier pair if $\lambda^2=\pi u$ , where $u$ is a wavelength related parameter."
" Since the space and Fourier domain are perfectly incoherent (?),, we can apply CS for RM synthesis in a straightforward manner provided there are Faraday thin sources along the line of sight since the screen is necessarily sparse."," Since the space and Fourier domain are perfectly incoherent \citep{Candes:2007p2815}, we can apply CS for RM synthesis in a straightforward manner provided there are Faraday thin sources along the line of sight since the screen is necessarily sparse."
" In this context, CS recommends solving for the Faraday dispersion function by minimising the L1 norm (summed absolute value) of the dispersion function as inimising the L1 norm optimises the sparsity of the reconstruction."," In this context, CS recommends solving for the Faraday dispersion function by minimising the L1 norm (summed absolute value) of the dispersion function as inimising the L1 norm optimises the sparsity of the reconstruction."
 There remains one further obstacle - the dispersion function is complex., There remains one further obstacle - the dispersion function is complex.
" We handle this by summing the L1 norm of the real and imaginary parts: where Re(e) and Im(e) denote| the real and the imaginary parts, respectively."," We handle this by summing the L1 norm of the real and imaginary parts: where $(\bullet)$ and $(\bullet)$ denote the real and the imaginary parts, respectively."
" By forming a real-valued vector of double length (comprising of the real part and the imaginary part) of the complex-valued vector, almost all L1 norm optimization solvers can be used for Eq. 9}."," By forming a real-valued vector of double length (comprising of the real part and the imaginary part) of the complex-valued vector, almost all L1 norm optimization solvers can be used for Eq. \ref{e:faraday_thin}."
 This CS-based rotation measure synthesis for Faraday thin sources is abbreviated as CS-RM-Thin., This CS-based rotation measure synthesis for Faraday thin sources is abbreviated as CS-RM-Thin.
 This is similar in concept to RM-CLEAN because the assumption for RM-CLEAN is that the Faraday dispersion function comprising of spike like signals., This is similar in concept to RM-CLEAN because the assumption for RM-CLEAN is that the Faraday dispersion function comprising of spike like signals.
" However, results in SectionH] show that CS-RM-Thin can provides superior results to RM-CLEAN."," However, results in Section \ref{sec:experiments} show that CS-RM-Thin can provides superior results to RM-CLEAN."
 CS-RM-Thin can work effectively when the Faraday dispersion function includes Faraday thin sources along the line of sight., CS-RM-Thin can work effectively when the Faraday dispersion function includes Faraday thin sources along the line of sight.
 This limits its application for the case when there are some Faraday thick sources along the line of sight., This limits its application for the case when there are some Faraday thick sources along the line of sight.
" However, CS can still reconstruct the Faraday dispersion function efficiently provided that we can find a suitable dictionary of basis functions that can decompose the extended sources into a"," However, CS can still reconstruct the Faraday dispersion function efficiently provided that we can find a suitable dictionary of basis functions that can decompose the extended sources into a"
If the total far-infrared-derived SFR of. the clusters is normalised by total Cuminous+dark}) mass. we have a simple method to compare the activity in different environments. and the evolution of the cluster SFR budget over time (e.g. Geachetal. 2006).,"If the total far-infrared-derived SFR of the clusters is normalised by total (luminous+dark) mass, we have a simple method to compare the activity in different environments, and the evolution of the cluster SFR budget over time (e.g. \citealt{Geach06}) )."
 The mass estimates for these clusters are indirectly inferred from their optical richnesses (see Section ?2)). which gives the range ~1.5-16. 10 MM. — however. the conversion between optical richness and mass is highly uncertain. and the true masses are likely to be at the lower end of this range.," The mass estimates for these clusters are indirectly inferred from their optical richnesses (see Section \ref{cluster}) ), which gives the range $\sim$ $\times10^{14}$ $_\odot$ – however, the conversion between optical richness and mass is highly uncertain, and the true masses are likely to be at the lower end of this range."
 Even this might be an over-estimate of the total eluster mass., Even this might be an over-estimate of the total cluster mass.
 For example. to achieve a similar surface density of clusters in the Millennium Simulation (Springeletal.2005).. requires us to be probing to a mass limit of logMyaAl.)I13.5.," For example, to achieve a similar surface density of clusters in the Millennium Simulation \citep{Springel05}, requires us to be probing to a mass limit of $\log(M_{\rm
halo}/\mathrm{M}_\odot)\gtrsim 13.5$."
 Fig., Fig.
 + shows the average total SFR in our clusters compared to other infrared-derived rates in other clusters over 0<20.6. although we note that given the large uncertainties on the H-ATLAS cluster masses and the cool SED we have adopted. we consider our point to be a lower limit.," \ref{fig3} shows the average total SFR in our clusters compared to other infrared-derived rates in other clusters over $0<z<0.6$, although we note that given the large uncertainties on the H-ATLAS cluster masses and the cool SED we have adopted, we consider our point to be a lower limit."
 We note that if other infrared studies at similar redshifts and depths assume M82- or 2220-like templates for their cluster member galaxies when cooler H-ATLAS-type SEDs are more appropriate. then they may well be overestimating the level of star formation activity in those clusters.," We note that if other infrared studies at similar redshifts and depths assume M82- or 220-like templates for their cluster member galaxies when cooler H-ATLAS-type SEDs are more appropriate, then they may well be overestimating the level of star formation activity in those clusters."
 Although there is significant cluster-to-cluster scatter. in general there has been strong evolution of the cluster SFR (see 2006)).," Although there is significant cluster-to-cluster scatter, in general there has been strong evolution of the cluster SFR (see )."
 This is consistent with the scenario that there has been a sharper drop-off in the star formation activity of clusters since >| than occurs in the field. probably related to the build up of virialised structures hostile to on-going activity and gas cooling over this period.," This is consistent with the scenario that there has been a sharper drop-off in the star formation activity of clusters since $z\sim1$ than occurs in the field, probably related to the build up of virialised structures hostile to on-going activity and gas cooling over this period."
 Although the optically unidentified sources within 5' of the clusters do not contribute significantly to the excess signal seen in Section 2? and appear to lie at typically higher redshifts (2~ 1) onaverage than the optically identified H-ATLAS sources (Section 3.2)) — these results suggest that strong gravitational lensing by the cluster potential is not a major contributor to, Although the optically unidentified sources within $5'$ of the clusters do not contribute significantly to the excess signal seen in Section \ref{sec1} and appear to lie at typically higher redshifts $z\sim1$ ) on average than the optically identified H-ATLAS sources (Section \ref{excess}) ) – these results suggest that strong gravitational lensing by the cluster potential is not a major contributor to
age distributions demonstrate that. within the imner disk. the age of the majority of the stars decreases with increasing distance from the ealactic center.,"age distributions demonstrate that, within the inner disk, the age of the majority of the stars decreases with increasing distance from the galactic center."
 Iu addition. most of the disk stars outside of ~3 kpe formed since 2=dl. later than what is seen dn moro massive spiral ealaxies both in stellar populations studies aud iu redshift surveys.," In addition, most of the disk stars outside of $\sim$ 3 kpc formed since $z=1$, later than what is seen in more massive spiral galaxies both in stellar populations studies and in redshift surveys."
 Couparisous of the stellar population properties iu these fields with those of the outer NE33 disk as measured by Barkeretal.(20075). show an inversion of the radial dependence of stellar age. providing suppor for some current simulation results.," Comparisons of the stellar population properties in these fields with those of the outer M33 disk as measured by \citet{barker2007} show an inversion of the radial dependence of stellar age, providing support for some current simulation results."
 Toecther. these results provide stroug observational support to insicle-out erowth of low-mass spiral stellar disks. down-siziug. and the significance of disk breaks in formation models of galaxy disks.," Together, these results provide strong observational support to inside-out growth of low-mass spiral stellar disks, down-sizing, and the significance of disk breaks in formation models of galaxy disks."
 Support for this work was provided bv NASA through erants CO-10190 aud CGO-10915 from the Space Telescope Science. Tustitute. which is operated by the Association of Universities for Researcli in Astrouoniv. Iucorporated. under NASA contract NÀS5-26555.," Support for this work was provided by NASA through grants GO-10190 and GO-10915 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555."
»tween the models and the actual data.,between the models and the actual data.
 The mid-eclipse in our models is always centered at. phase zero. while the data seem to shift. during the outburst. especially during he second night of observations.," The mid-eclipse in our models is always centered at phase zero, while the data seem to shift during the outburst, especially during the second night of observations."
 Regardless of the drift the eclipse profiles retain their high level of symmetry., Regardless of the drift the eclipse profiles retain their high level of symmetry.
 Despite his peculiarity the model is able to reproduce the overall eclipse profile quite accurately., Despite this peculiarity the model is able to reproduce the overall eclipse profile quite accurately.
 Undoubtedlv. though. these models constitute only an upper limit on the disce radius and [are because the model uses a symmetric accretion disc and therefore any change of the eclipse ingress profile will similarly allect the egress profile.," Undoubtedly, though, these models constitute only an upper limit on the disc radius and flare because the model uses a symmetric accretion disc and therefore any change of the eclipse ingress profile will similarly affect the egress profile."
 Indeed. when we manually shift the data to our calculated phase zero. the model eclipse profiles are in very good agreement with the observed data.," Indeed, when we manually shift the data to our calculated phase zero, the model eclipse profiles are in very good agreement with the observed data."
 The x7 of the fi drops by a factor of 4 for the case of the early decline anc also goes down by a factor of 2 for the mocleled eclipse lduring the late stages of the decline., The ${\chi}^2$ of the fits drops by a factor of 4 for the case of the early decline and also goes down by a factor of 2 for the modeled eclipse during the late stages of the decline.
 Although the values derived here for the semi-opening angle and the dise radius only constitute upper limits. they do show that the aceretion disc is decreasing in size during the late stages of the decline.," Although the values derived here for the semi-opening angle and the disc radius only constitute upper limits, they do show that the accretion disc is decreasing in size during the late stages of the decline."
" Investigation of the results presented in section 5 show clearly that the November 1995 outburst of LWP Cas was of the ""outside - in type.", Investigation of the results presented in section \ref{mted} show clearly that the November 1995 outburst of HT Cas was of the “outside - in” type.
" We believe that the models show a relatively large luminous disc 2,=0412) during the tise to outburst. which then shrinks to (2)<0.324,)) in he later stages of the decline."," We believe that the models show a relatively large luminous disc $R_{d}=0.41R_{L1}$ during the rise to outburst, which then shrinks to $(R_{d}<0.32R_{L1})$ in the later stages of the decline."
" It might be that the dise was smaller than 2,=0.4172;, at the early stages of the rise but unfortunately our coverage does not include observations at hese outburst phases.", It might be that the disc was smaller than $R_{d}=0.41R_{L1}$ at the early stages of the rise but unfortunately our coverage does not include observations at these outburst phases.
 Although our results seem to be in general agreement with the predictions of the models of Mineshige&Osalsi(1985).. a discrepancy is noted.," Although our results seem to be in general agreement with the predictions of the models of \scite{Mineshige85}, a discrepancy is noted."
 The quiescent. disc radius or ILE Cas was measured by Horne (1991) and. was ound to be Rafa=0.23 where à is the binary separation., The quiescent disc radius for HT Cas was measured by Horne (1991) and was found to be $R_{d}/{a}=0.23$ where a is the binary separation.
 This translates to ει=0.33 using a mass ratio of q=0.15., This translates to $R_{d}/R_{L1}=0.33$ using a mass ratio of q=0.15.
" This value for 24 is considerably less than our value of Rifle,=OAL during the rise of the outburst.", This value for $R_{d}$ is considerably less than our value of $R_{d}/R_{L1}=0.41$ during the rise of the outburst.
 Also. investigation of the SU UAla system Z Cha by O'Donoghue(1986) shows that there is a decrease in radius of the accretion disc in the time between outbursts.," Also, investigation of the SU UMa system Z Cha by \scite{O'Donoghue86} shows that there is a decrease in radius of the accretion disc in the time between outbursts."
 Assuming that IUE Cas behaves in a similar manner this would mean that 10 pre-outburst disc was even smaller than that quoted by llorne (1991)., Assuming that HT Cas behaves in a similar manner this would mean that the pre-outburst disc was even smaller than that quoted by Horne (1991).
 Thus the luminous radius of the disc on the rise to outburst is larger than the physical radius in ulescence., Thus the luminous radius of the disc on the rise to outburst is larger than the physical radius in quiescence.
 This contrasts with the predictions of the models by Mineshige&Osaki(1985)., This contrasts with the predictions of the models by \scite{Mineshige85}.
. Γον show that a heating wave is initiated by a disc instability in the outer parts of the disc which travels inwards. with the luminous part never reaching the quiescent radius.," They show that a heating wave is initiated by a disc instability in the outer parts of the disc which travels inwards, with the luminous part never reaching the quiescent radius."
 This would suggest that during an outburst the disc would have a luminous size roughly the same as that of the quiescent disc. with cool material on the outward side of the hot front expanding slightly in order to preserve angular momentum.," This would suggest that during an outburst the disc would have a luminous size roughly the same as that of the quiescent disc, with cool material on the outward side of the hot front expanding slightly in order to preserve angular momentum."
" The dise never reaches the tidal radius. which for this system (q=0.18) is at ἐξ0.764,44."," The disc never reaches the tidal radius, which for this system $(q=0.18)$ is at $R_{tl}=0.76R_{L1}$."
 Phos. no superhump is observed during the eruption.," Thus, no superhump is observed during the eruption."
 Effects inthe O—C' diagram though are difficult to explain., Effects in the $O-C$ diagram though are difficult to explain.
 During eruption. and in particular during the second night of observations the OC values begin to drift and reach up to à maximum delay of 79 seconds.," During eruption, and in particular during the second night of observations the $O-C$ values begin to drift and reach up to a maximum delay of 79 seconds."
 “Phe dillieulty in explaining this feature as a simple islocation of the Dux centre comes from the fact that the eclipses retain their symmetry., The difficulty in explaining this feature as a simple dislocation of the flux centre comes from the fact that the eclipses retain their symmetry.
 Thus any dislocation of the —ux centre must be accompanied by another effect. such as disc asymmetry. in order to counteract the change of flux entre ancl keep the overall eclipse shape symmetric.," Thus any dislocation of the flux centre must be accompanied by another effect, such as disc asymmetry, in order to counteract the change of flux centre and keep the overall eclipse shape symmetric."
 The mass transfer rate through the disc. which is ependent on the distance. is found to be relatively high uring the rise (AI==9.3«10.MALgre +).," The mass transfer rate through the disc, which is dependent on the distance, is found to be relatively high during the rise $9.3\times10^{-10}{\Mdot}$ )."
 At the peak of the outburst the model results show a lower value of Me-6.10ΟΝΕ.gre+., At the peak of the outburst the model results show a lower value of $6.9\times10^{-10}{\Mdot}$.
 Ες is surprising but it can be explained if we consider that when the systeni is at the peak of outburst the inner disc. unlike before. is now very hot and uminous.," This is surprising but it can be explained if we consider that when the system is at the peak of outburst the inner disc, unlike before, is now very hot and luminous."
 Therefore in order to match the flux level of the system we do not need high mass transfer rates., Therefore in order to match the flux level of the system we do not need high mass transfer rates.
" The NE value. quoted. by Zhang.Robinson&Nather(1986) for the January 1985. superouthurst is 3.8""XLI.gre. T.", The Ṁ value quoted by \scite{Zhang86} for the January 1985 superoutburst is $3.8\times10^{-10}{\Mdot}$ .
 μις is about a factor of 2.5 times lower han our AL estimate for the rise to outburst., This is about a factor of 2.5 times lower than our Ṁ estimate for the rise to outburst.
 Our slightly ugher M valuesare easily explained by the fact that our disc models include an outer clise rim wall of semi-opening angle, Our slightly higher Ṁ valuesare easily explained by the fact that our disc models include an outer disc rim wall of semi-opening angle
to other spins.,to other spins.
 Thus this predicts that any of the deuse disk stress prescriptions will eive disk spectra at high spin with f; Iucreasing «Πο with / iu a way which is uot significantly: cdiffercut to that for low spin., Thus this predicts that any of the dense disk stress prescriptions will give disk spectra at high spin with $f_{\rm col}$ increasing slightly with $l$ in a way which is not significantly different to that for low spin.
 Thus extreme spins should simply manitest themselves as higher temperature disks at a eiven Iuninositv. eivine a clear signature of a maximal err black hole.," Thus extreme spins should simply manifest themselves as higher temperature disks at a given luminosity, giving a clear signature of a maximal Kerr black hole."
 However. none of the high mass N-rav binaries (ee. (νο N-1) show any sigus of this. so we conclude that accretion las not vet had time to significantly spin up the black holes iu these systems.," However, none of the high mass X-ray binaries (e.g. Cyg X-1) show any signs of this, so we conclude that accretion has not yet had time to significantly spin up the black holes in these systems."
 The ULAs are also poteutially lieh spin objects2008).. but these have spectra which are often more complex than a simple disk model2008).. iu which case they do not eive a straightforward diagnostic of black hole mass and spin2006).," The ULXs are also potentially high spin objects, but these have spectra which are often more complex than a simple disk model, in which case they do not give a straightforward diagnostic of black hole mass and spin."
. The observation that stable disk spectra are seen spamming /~0.050.5 shows that disks are not subject to the lait eveles predicted by the radiation pressure instability iu this range.," The observation that stable disk spectra are seen spanning $l\sim
0.05-0.5$ shows that disks are not subject to the limit cycles predicted by the radiation pressure instability in this range."
 This rules out au alpha type stress. aud instead that the surface density imereases (or remadus constant m the Dit of mareinal stability) as a function of / at cach radius. and this in itself implies that the accretion disk should remain effectively optically thick at high huninosities.," This rules out an alpha type stress, and instead that the surface density increases (or remains constant in the limit of marginal stability) as a function of $l$ at each radius, and this in itself implies that the accretion disk should remain effectively optically thick at high luminosities."
 Therefore the color-tempecrature corrections will be relatively coustaut. so predicting approximate LxT! relation for the disk dominated spectra.," Therefore the color-temperature corrections will be relatively constant, so the approximate $L\propto T^4$ relation for the disk dominated spectra."
the The observation that most binaries show au approximate LxT1 is strong confirmation of this conclusion., The observation that most binaries show an approximate $L\propto T^4$ is strong confirmation of this conclusion.
 Sadly. this also rules out the radiation pressure instability as being the plysical miechanisgi for any observed behavior for /«(0.5.," Sadly, this also rules out the radiation pressure instability as being the physical mechanism for any observed behavior for $l<0.5$."
 This is otherwise au attractive possibilitv for the origin of the ναν high state. the other spectral state seen m binaries at biel mass accretion rates.," This is otherwise an attractive possibility for the origin of the very high state, the other spectral state seen in binaries at high mass accretion rates."
 Although this does not show the predicted limit eveles; there is the possibility that the," Although this does not show the predicted limit cycles, there is the possibility that the"
As can be seen in Fig.,As can be seen in Fig.
 4 (lower panel) the evolution of Τι up to time about 0.5 Gyr is slightly too slow in comparison to N-body results. (, \ref{fig:tf_alfa_comparison} (lower panel) the evolution of $r_h$ up to time about 0.5 Gyr is slightly too slow in comparison to $N$ -body results. (
"This effect is even more pronounced for smaller N: see Fig.2, top panel.)","This effect is even more pronounced for smaller $N$: see \ref{fig:rh_tc_comparison}, top panel.)"
 This behaviour is connected with the way in which the effect of stellar mass loss is fed in to the cluster., This behaviour is connected with the way in which the effect of stellar mass loss is fed in to the cluster.
" In the Monte Carlo model the stellar evolution mass loss is postponed until the end of the overall time step, usually several Myr."," In the Monte Carlo model the stellar evolution mass loss is postponed until the end of the overall time step, usually several Myr."
" So, for the most massive stars the stellar evolution can be substantially delayed and the cluster expands slower."," So, for the most massive stars the stellar evolution can be substantially delayed and the cluster expands slower."
 In Fig., In Fig.
" 6 the evolution of r; is presented for different models in which the overall time step was reduced by factor of two up to a certain time, s."," \ref{fig:tf_iseed_s_comparison} the evolution of $r_h$ is presented for different models in which the overall time step was reduced by factor of two up to a certain time, $s$."
 It is clear that reduction of the overall time step in the phases of cluster evolution in which the most massive stars end their evolution helps to bring the Monte Carlo results close to the N-body ones., It is clear that reduction of the overall time step in the phases of cluster evolution in which the most massive stars end their evolution helps to bring the Monte Carlo results close to the $N$ -body ones.
" In later phases of cluster evolution, in which the time-scale of stellar evolution becomes larger than the half-mass relaxation time, the evolution does not depend systematically on the chosen overall time step. ("," In later phases of cluster evolution, in which the time-scale of stellar evolution becomes larger than the half-mass relaxation time, the evolution does not depend systematically on the chosen overall time step. ("
In the simulations used in the determination of the free code parameters the adopted overall time step was a compromise between accuracy and speed.),In the simulations used in the determination of the free code parameters the adopted overall time step was a compromise between accuracy and speed.)
" As can be seen in Figs. 7,, 8,,"," As can be seen in Figs. \ref{fig:tf_binen_comparison}, \ref{fig:tf_binfrac_comparison},"
" 9 the Monte Carlo code can reproduce N-body simulations not only in respect of the global parameters of the system, but also in respect of properties connected with binary activity."," \ref{fig:tf_binnum_comparison} the Monte Carlo code can reproduce $N$ -body simulations not only in respect of the global parameters of the system, but also in respect of properties connected with binary activity."
" Despite the fact that the total number of binaries in the system and the binary fraction agree quite well with N-body simulations, the total binding energy is substantially too high for the Monte Carlo simulations."," Despite the fact that the total number of binaries in the system and the binary fraction agree quite well with $N$ -body simulations, the total binding energy is substantially too high for the Monte Carlo simulations."
 T'his is connected with the fact that the present Monte Carlo simulations cannot follow 3- and 4-body interactions directly as the N-body code does., This is connected with the fact that the present Monte Carlo simulations cannot follow 3- and 4-body interactions directly as the $N$ -body code does.
 Binaries can only harden or dissolve., Binaries can only harden or dissolve.
 Therefore much of the, Therefore much of the
A number of white dwarfs with strong magnetic fields have been discovered (Kempetal. 1970:: Putney 1995;; Schmidt&Smith 1995; Reimersetal. 1996)) and extensively studied (Jordan1992:; Angel 1978:; Chanmugam1992 and references therein).,A number of white dwarfs with strong magnetic fields have been discovered \cite{kemp}; ; \cite{putney}; ; \cite{schmidt95}; \cite{reimers}) ) and extensively studied \cite{jordan92}; \cite{angle}; \cite{chanmugam} and references therein).
 Surface magnetic fields ranging from about 10? G to 10° G have been detected in about 50 (2%) of the z2100 known white dwarfs (Jordan1997 and references therein)., Surface magnetic fields ranging from about $10^5$ G to $10^9$ G have been detected in about 50 $\%$ ) of the $\approx 2100$ known white dwarfs \cite{jordan97} and references therein).
 As relies of stellar interiors. the study of the magnetic fields in and around degenerate stars should give important information on the role such fields play in star formation and stellar evolution.," As relics of stellar interiors, the study of the magnetic fields in and around degenerate stars should give important information on the role such fields play in star formation and stellar evolution."
 However. the origin and evolution of stellar magnetic fields remains obscure.," However, the origin and evolution of stellar magnetic fields remains obscure."
 As early as Ginzburg (1964) and Woltjer (1964) it was proposed that the magnetic flux (Py~ BR) of a star is conserved during its evolution and subsequent collapse to form a remnant white dwarf or neutron star., As early as Ginzburg (1964) and Woltjer (1964) it was proposed that the magnetic flux $\Phi_B \sim BR^2$ ) of a star is conserved during its evolution and subsequent collapse to form a remnant white dwarf or neutron star.
" A main sequence star with radius on the order of R~10!! em and surface magnetic field B—10—10* G [magnetic A-type stars have typical surface fields <10+ G (Shapiro&Teukolsky 1983))] would thus collapse to form a white dwarf with R~10° cm and B~10?—105 G. or a neutron star with R~10° em and B—10!10"" G. Indeed. shortly after their discovery (Hewish et al."," A main sequence star with radius on the order of $R \sim 10^{11}$ cm and surface magnetic field $B \sim 10 - 10^4$ G [magnetic A-type stars have typical surface fields $\lsim 10^4$ G \cite{ST}) )] would thus collapse to form a white dwarf with $R \sim 10^9$ cm and $B \sim 10^5 - 10^8$ G, or a neutron star with $R \sim 10^6$ cm and $B \sim 10^{11} - 10^{14}$ G. Indeed, shortly after their discovery (Hewish et al."
 1968) pulsars were identified as rotating neutron stars (Gold 1968)) with magnetic fields B—10!!10 G consistent with magnetic field amplification by flux conservation., 1968) pulsars were identified as rotating neutron stars \cite{gold}) ) with magnetic fields $B \sim 10^{11} - 10^{13}$ G consistent with magnetic field amplification by flux conservation.
 In addition. neutron stars with surface magnetic fields exceeding 107 G [so called magnetars] have been recently suggested as the source of soft gamma-ray repeaters (Duncan&Thompson1992:; Thompson&Duncan 1995)).," In addition, neutron stars with surface magnetic fields exceeding $10^{14}$ G [so called magnetars] have been recently suggested as the source of soft gamma-ray repeaters \cite{duncan}; \cite{thompson}) )."
 Moreover. the surface magnetic field of a star does not necessarily reflect the internal field (Ruderman 1980)).," Moreover, the surface magnetic field of a star does not necessarily reflect the internal field \cite{ruderman}) )."
 For example. the toroidal fields below the surface of the Sun are at least on the order of ~107 to ~10+ times stronger than the average surface dipole field strength of ~| G (Galloway.Proctor.&Weiss 1977)).," For example, the toroidal fields below the surface of the Sun are at least on the order of $\sim 10^2$ to $\sim 10^4$ times stronger than the average surface dipole field strength of $\sim 1$ G \cite{galloway}) )."
" Furthermore. at the region of the convective zone. the strength of small scale magnetic fields could reach a value as high as 7«10* G (Chauhan.Pandey&Pandey1999,Pulido 19985)."," Furthermore, at the region of the convective zone, the strength of small scale magnetic fields could reach a value as high as $7 \times 10^{4}$ G \cite{chauhan,pulido}) )."
" This would correspond to an interior field strength on the order of ~I0"" to ~I0? G in à white dwarf. or ~10° to ~10'* G in a neutron star. ["," This would correspond to an interior field strength on the order of $\sim 10^{9}$ to $\sim 10^{13}$ G in a white dwarf, or $\sim 10^{15}$ to $\sim 10^{18}$ G in a neutron star. ["
Condensed objects of size R and mass M have an upper limit to their field strengths of B—MR(8xG)7.,Condensed objects of size $R$ and mass $M$ have an upper limit to their field strengths of $B \lsim M R^2 (8 \pi G)^{1/2}$.
 For neutron stars with R=10 km and Mz... the limit is B:z—10/5 G (LercheSchramm1977)).]," For neutron stars with $R \approx 10$ km and $M \approx M_{\odot}$, the limit is $B \lsim \sim 10^{18}$ G \cite{lerche}) ).]"
 Indeed. the existence of white dwarfs with interior magnetic fields as strong as 4«10? G is not ruled out with the present uncertainties in the mass-radius relation (Shapiro&Teukolsky1983)).," Indeed, the existence of white dwarfs with interior magnetic fields as strong as $\sim 4 \times 10^{13}$ G is not ruled out with the present uncertainties in the mass-radius relation \cite{ST}) )."
 The present high upper limit on the strength of internal fields in white dwarfs is obtained by simply setting the magnetic pressure equal to the internal pressure of the star., The present high upper limit on the strength of internal fields in white dwarfs is obtained by simply setting the magnetic pressure equal to the internal pressure of the star.
 However. white dwarfs with internal fields at or around this strength could be constrained (Mestel 1965)) by a perceptibly different mass-radius relation.," However, white dwarfs with internal fields at or around this strength could be constrained \cite{mestel}) ) by a perceptibly different mass-radius relation."
 Although white dwarfs in binaries with well determinec masses do not appear to have surface magnetic fields larger than ~10° G. internal fields of order 10/7 G could be well hidden below the surface (Angel 1978)).," Although white dwarfs in binaries with well determined masses do not appear to have surface magnetic fields larger than $\sim 10^5$ G, internal fields of order $10^{12}$ G could be well hidden below the surface \cite{angle}) )."
 Newly discovered magnetic degenerate stars. especially those with surface fielc strengths near the range of B~10° G. always show strong circularly and/or linearly polarized spectral energy distributions (Schmidtetal. 1999)).," Newly discovered magnetic degenerate stars, especially those with surface field strengths near the range of $B \sim 10^9$ G, always show strong circularly and/or linearly polarized spectral energy distributions \cite{schmidt99}) )."
 Moreover. these stars reveal unique spectral features (Engelhardt&Bues 1994)) due to quasi-Landau resonances in extremely high magnetic fields of >10? G. In this work. we explicitly compute the mass-radius relation of white dwarfs with internal magnetic fields.," Moreover, these stars reveal unique spectral features \cite{engelhardt}) ) due to quasi-Landau resonances in extremely high magnetic fields of $> 10^9$ G. In this work, we explicitly compute the mass-radius relation of white dwarfs with internal magnetic fields."
 Previously. Ostriker Hartwick (1968) have estimated effects of interior magnetic fields by considering a correction in terms of the ratio of magnetic to gravitational energy.," Previously, Ostriker Hartwick (1968) have estimated effects of interior magnetic fields by considering a correction in terms of the ratio of magnetic to gravitational energy."
 They showed that a relatively small ratio of magnetic to gravitational energy would be sufficient to explain an observational discrepancy in the classical mass-radius relation for Sirius B. However. if white dwarfs could indeed have central magnetic fields as strong as 4.4«10!αν G. the revised mass-radius relation must be explicitly determined by taking the magnetic field into account in the equation of state.," They showed that a relatively small ratio of magnetic to gravitational energy would be sufficient to explain an observational discrepancy in the classical mass-radius relation for Sirius B. However, if white dwarfs could indeed have central magnetic fields as strong as $4.4 \times 10^{11} - 4.4 \times 10^{13}$ G, the revised mass-radius relation must be explicitly determined by taking the magnetic field into account in the equation of state."
 The present work thus expands upon that earlier study by explicitly computing the equation of state for a completely degenerate. noninteracting electron gas m a magnetic field.," The present work thus expands upon that earlier study by explicitly computing the equation of state for a completely degenerate, noninteracting electron gas in a magnetic field."
 This equation of state is then applied to the Tolmam-Oppenheimer-Volkoff (TOV) equation of stellarhydrostaticequilibrium., This equation of state is then applied to the Tolmam-Oppenheimer-Volkoff (TOV) equation of stellarhydrostaticequilibrium.
 The equation of state in à magnetic field should reduce to a normal equation of state in the absence of à magnetic field., The equation of state in a magnetic field should reduce to a normal equation of state in the absence of a magnetic field.
 Therefore. we use an Euwler-MacLaurin expansion," Therefore, we use an Euler-MacLaurin expansion"
"Detailed analyses of four distant galaxies of the IMAGES study have been performed by Puechetal.(2007a, 2009a),, Hammeretal.(2009b) and Peiranietal.(2008),, and four other studies of individual galaxies are in progress (Yang et al.,","Detailed analyses of four distant galaxies of the IMAGES study have been performed by \citet{Puech07,Puech09a}, , \citet{Hammer09b} and \citet{2008arXiv0812.1593P}, and four other studies of individual galaxies are in progress (Yang et al.,"
 2009; Fuentes et al., 2009; Fuentes et al.
 and Peirani et al., and Peirani et al.
 in preparation)., in preparation).
" By modelling gas motions as well as morphologies, these studies have shown their ability in reproducing the properties of distant galaxies with a similar accuracy to what is done for nearby galaxies."," By modelling gas motions as well as morphologies, these studies have shown their ability in reproducing the properties of distant galaxies with a similar accuracy to what is done for nearby galaxies."
 Puechetal.(2007a) have demonstrated that spatially resolved kinematics is sufficiently sensitive to detect the infall of a 1:18 satellite in a z=0.667 galaxy., \citet{Puech07} have demonstrated that spatially resolved kinematics is sufficiently sensitive to detect the infall of a 1:18 satellite in a z=0.667 galaxy.
" Peiranietal.(2008) identified a giant and starbursting bar induced by a 3:1 merger, and simulated both morphologies and the off-centre dynamical axis."," \citet{2008arXiv0812.1593P} identified a giant and starbursting bar induced by a 3:1 merger, and simulated both morphologies and the off-centre dynamical axis."
" In this case, the gas pressured in the tidally formed bar has condensed into young and blue stars."," In this case, the gas pressured in the tidally formed bar has condensed into young and blue stars."
" Hammeretal.(2009b) identified a compact LIRG dominated by a dust-enshrouded compact disk that surrounds a blue, centred helix (so-called a ""two arms-plus-bar"" structure)."," \citet{Hammer09b} identified a compact LIRG dominated by a dust-enshrouded compact disk that surrounds a blue, centred helix (so-called a ""two arms-plus-bar"" structure)."
 They interpret (see their Fig., They interpret (see their Fig.
 7) this structure as regulating the exchanges of the angular momentum and possibly stabilising the new disk (Hopkinsetal. 2009a)., 7) this structure as regulating the exchanges of the angular momentum and possibly stabilising the new disk \citep{Hopkins09a}.
". Indeed gas inflows along an helix are usual in simulations of mergers, especially in inclined and polar orbits."," Indeed gas inflows along an helix are usual in simulations of mergers, especially in inclined and polar orbits."
 This gaseous-rich galaxy appears to be an archetype of a disk rebuilding after a 1:1 or a 3:1 merger with an inclined orbit., This gaseous-rich galaxy appears to be an archetype of a disk rebuilding after a 1:1 or a 3:1 merger with an inclined orbit.
 Puech et al. (, Puech et al. (
20098) demonstrated that the presence of ionised gas without stars near a highly asymmetric disk can be only reproduced by a remnant of a merger.,2009a) demonstrated that the presence of ionised gas without stars near a highly asymmetric disk can be only reproduced by a remnant of a merger.
 These studies have been successful because they compared simulations of the gas phases to observations of both the morphology and the ionised gas motions., These studies have been successful because they compared simulations of the gas phases to observations of both the morphology and the ionised gas motions.
 Morphologies of starbursts -especially the numerous blue or dusty regions- are mostly relics of gas phases recently transformed into young stars that ionise the gas., Morphologies of starbursts -especially the numerous blue or dusty regions- are mostly relics of gas phases recently transformed into young stars that ionise the gas.
 Thus a common physical mechanism should reproduce them together with the observed large-scale motions of the ionised gas., Thus a common physical mechanism should reproduce them together with the observed large-scale motions of the ionised gas.
" Within most starbursts, the light is indeed dominated by < 100Myrs-old stars and at large distances, spatially-resolved kinematics only detect large-scale motions, with typical scales of ~3kpc."," Within most starbursts, the light is indeed dominated by $\le$ 100Myrs-old stars and at large distances, spatially-resolved kinematics only detect large-scale motions, with typical scales of $\sim$ 3kpc."
 A typical motion of 100km/s would cross such a length scale during ~ 50Myrs (32 Myrs for motions parallel to the sky plane)., A typical motion of 100km/s would cross such a length scale during $\sim$ 50Myrs (32 Myrs for motions parallel to the sky plane).
" Thus many morphological features with blue colors (bars,ringsandhe-lixes,seePeiranietal.2008;Hammer2009b) should be imprints of the gas hydrodynamics and they can be compared to the gas kinematics."," Thus many morphological features with blue colors \citep[bars, rings and
 helixes, see ][]{2008arXiv0812.1593P,Hammer09b} should be imprints of the gas hydrodynamics and they can be compared to the gas kinematics."
" For reasons of homogeneity, we study here the sub-sample of 33 IMAGES starbursts (see IMAGES-I) observed in the CDFS-GOODS."," For reasons of homogeneity, we study here the sub-sample of 33 IMAGES starbursts (see IMAGES-I) observed in the CDFS-GOODS."
 This sub-sample is representative of M;(AB)x -20.3 starbursts (see IMAGES-I)., This sub-sample is representative of $M_J$ $\le$ -20.3 starbursts (see IMAGES-I).
" Two galaxies have been rejected from the original sample of IMAGES-I, one (J033210.76-274234.6) because it turns out not to be a starburst (Yangetal.2009) and another one (J033250.24-274538.9) because the HST/ACS images are corrupted."," Two galaxies have been rejected from the original sample of IMAGES-I, one (J033210.76--274234.6) because it turns out not to be a starburst \citep{Yang09} and another one (J033250.24-274538.9) because the HST/ACS images are corrupted."
" We have verified that this sub-sample is representative of the stellar-mass and star formation densities at Znedian=0.65 (seee.g.Ravikumaretal.,2007).", We have verified that this sub-sample is representative of the stellar-mass and star formation densities at $z_{median}$ =0.65 \citep[see e.g.][]{Ravi07}.
. In this sample we do find only 6 rotating spiral disks to which we add one giant spiral (J033226.23-274222.8 that is also rotating while it likely experiences a satellite infall causing a small shift in the observed dispersion map (Puechetal.2007b)., In this sample we do find only 6 rotating spiral disks to which we add one giant spiral (J033226.23-274222.8 that is also rotating while it likely experiences a satellite infall causing a small shift in the observed dispersion map \citep{Puech07b}.
. Note also that one of the rotating spiral galaxy (see Fig., Note also that one of the rotating spiral galaxy (see Fig.
" 1, right) is within a confirmed interaction with an elliptical galaxy."," 1, right) is within a confirmed interaction with an elliptical galaxy."
 The 26 other galaxies all show peculiar morphologies and/or anomalous kinematics and are classified as such as non or relaxed systems., The 26 other galaxies all show peculiar morphologies and/or anomalous kinematics and are classified as such as non or semi-relaxed systems.
" It is an Herculean task to analyse in details all the considerable amount of data for each of these galaxies, as it has been described for few galaxies in section 2.1."," It is an Herculean task to analyse in details all the considerable amount of data for each of these galaxies, as it has been described for few galaxies in section 2.1."
" The accurate modelling of both morphology and kinematics takes several months, from two to six months for a well-experimented user."," The accurate modelling of both morphology and kinematics takes several months, from two to six months for a well-experimented user."
" This is due to the wide complexity of the morphologies and kinematics in these non-relaxed galaxies as well as the large parameter space offered by the simulations (mass ratio, orbit, temporal phase, peri-centre radius and parameters of the encounters, viewing angles)."," This is due to the wide complexity of the morphologies and kinematics in these non-relaxed galaxies as well as the large parameter space offered by the simulations (mass ratio, orbit, temporal phase, peri-centre radius and parameters of the encounters, viewing angles)."
" Our goal here is restricted to the following question: Recently, Barnes&Hibbard(2009) have defined a modelling tool to identify merger orbital parameters."," Our goal here is restricted to the following question: Recently, \citet{2009AJ....137.3071B} have defined a modelling tool to identify merger orbital parameters."
 It allows to change many parameters including the viewing angle., It allows to change many parameters including the viewing angle.
 However at high-z we cannot identify low surface brightness tidal features., However at high-z we cannot identify low surface brightness tidal features.
" We propose here toadapt a similar modelling tool for high-z observations, also allowing changes of the viewing angle."," We propose here toadapt a similar modelling tool for high-z observations, also allowing changes of the viewing angle."
" We then used the models from Barnes (2002).,"," We then used the models from \citet{Barnes02}, ,"
T'USS that makes dillicult to cisentangle the contribution from the photoionizecl accretion How ancl the inner disc from a theoretically hypothesised hot stellar wind.,TTSs that makes difficult to disentangle the contribution from the photoionized accretion flow and the inner disc from a theoretically hypothesised hot stellar wind.
 In 2005. Dupréee et al. claimed to have detected. for the first time. this hot wind.," In 2005, Dupréee et al, claimed to have detected, for the first time, this hot wind."
 These authors interpreted the absence. of blueshifted emission in the O VI resonance lines in TW να and E Tau. as an indication of the existence of a hot wind with temperatures as high as 300.000 Ix. and. mass-Ioss rates o[2.10.LM. vr. 1 that absorbs the blue wing of the prolile.," These authors interpreted the absence of blueshifted emission in the O VI resonance lines in TW Hya and T Tau, as an indication of the existence of a hot wind with temperatures as high as 300,000 K and mass-loss rates of $2\times 10^{-11}$ $_{\odot}$ $^{-1}$ that absorbs the blue wing of the profile."
 As pointed out by Johns-Ixrull Llerezee (2007). the lack of a blueshifted component could just be an indication of the ine being formed in the accretion Uow.," As pointed out by Johns-Krull Herczeg (2007), the lack of a blueshifted component could just be an indication of the line being formed in the accretion flow."
 Matter infall onto he stellar surface is channelled by the magnetic field driving o the formation of shocks at the impact. points where the kinetic energy. of the infalling gas is finally. released., Matter infall onto the stellar surface is channelled by the magnetic field driving to the formation of shocks at the impact points where the kinetic energy of the infalling gas is finally released.
 The emperature reached at the shocks can be as high as some 1091 and the photoionizing X-ray radiation preionizes the infalline eas column that radiates over a wide range of emperatures and tracers (Lamzin 1998)., The temperature reached at the shocks can be as high as some $^6$ K and the photoionizing X-ray radiation preionizes the infalling gas column that radiates over a wide range of temperatures and tracers (Lamzin 1998).
 An independent line of research. the one addressed. in his series. was to investigate whether the base of the jet could be hot enough to radiate at. temperatures as high as 50.000. Ix-S0.000. Ix. well below the temperature. range of the hot stellar wind but above the fiducial temperatures of optical jets: 10.000 Ix-20.000 Ix. “Phe motivation for this research came from the discovery of C IH] and $i LL] semiforbidden emission in the UV spectrum of RY Tau and UU Lup at the same velocity of the optical jet: this emission races gas at logd;~4.648 (Gommez de Castro Verdugo 2001).," An independent line of research, the one addressed in this series, was to investigate whether the base of the jet could be hot enough to radiate at temperatures as high as 50,000 K-80,000 K, well below the temperature range of the hot stellar wind but above the fiducial temperatures of optical jets: 10,000 K-20,000 K. The motivation for this research came from the discovery of C III] and Si III] semiforbidden emission in the UV spectrum of RY Tau and RU Lup at the same velocity of the optical jet; this emission traces gas at $\log T_e \sim 4.6-4.8$ (Gómmez de Castro Verdugo 2001)."
 Centrifugally driven IHows from maegnetised acecretion disces are submitted. to. pinching stresses 7B rccause the toroidal magnetic Ποια (B) collimates the current of eas along the disc axis GB., Centrifugally driven flows from magnetised accretion discs are submitted to pinching stresses $\vec j \times \vec B$ because the toroidal magnetic field $\vec B$ ) collimates the current of gas along the disc axis $\vec j$ ).
 Recollimation can drive o the formation of focal surfaces or shocks on the jet axis hat are able to heat the gas to the some 10.000 Ix traced w the optical forbidden lines of S H] (Gómmoez de Castro Pudritz 1993).," Recollimation can drive to the formation of focal surfaces or shocks on the jet axis that are able to heat the gas to the some 10,000 K traced by the optical forbidden lines of S II] (Gómmez de Castro Pudritz 1993)."
 However. temperatures as high as 50.000 Ix cannot be produced in cool disc winds.," However, temperatures as high as 80,000 K cannot be produced in cool disc winds."
 In the first article of this series. we examined whether the photoionisation of cool disc winds by the stellar corona could cause the observed: emission. (Ferro-Fontánn. Commez de Castro 2003. hereafter. Paper D).," In the first article of this series, we examined whether the photoionisation of cool disc winds by the stellar corona could cause the observed emission (Ferro-Fontánn Gómmez de Castro 2003, hereafter Paper I)."
 We found that the propagation of the stellar radiation generates a cocoon of photoionized gas around the star., We found that the propagation of the stellar radiation generates a cocoon of photoionized gas around the star.
 The extent of the photoionized region is small (tenths of au) in dense outflows and close to the dise. plane: however. it may. cover the whole wind extent in dilfuse winds. e.g. disc winds generated by small accretion rates (=190 Al.ve 1j ," The extent of the photoionized region is small (tenths of au) in dense outflows and close to the disc plane; however, it may cover the whole wind extent in diffuse winds, e.g. disc winds generated by small accretion rates $\leq 10^{-9}$ $_{\odot}$ $^{-1}$ )."
Photoionisation also modifies the electron density in the plasma., Photoionisation also modifies the electron density in the plasma.
 The interplay between ambipolar diffusion and the radiation field controls the electron temperature of the wind that is kept. around 10.000. Ix. well below the temperatures traced. by the UV semiforbidden Lines.," The interplay between ambipolar diffusion and the radiation field controls the electron temperature of the wind that is kept around 10,000 K, well below the temperatures traced by the UV semiforbidden lines."
 Dise winds are a fundamental mechanism for angular momentum transport in protostellar discs. contributing to the regulation of the accretion rate onto the star.," Disc winds are a fundamental mechanism for angular momentum transport in protostellar discs, contributing to the regulation of the accretion rate onto the star."
 Llowever. most of the transport occurs in the cise itself through the maenetorotational instability (Balbus Llawley 1991): weak fieles provide a tension force that allows two orbiting ILuid elements to exchange angular momentum on larger scales than the hvdrodynamical viscosity scales.," However, most of the transport occurs in the disc itself through the magnetorotational instability (Balbus Hawley 1991): weak fields provide a tension force that allows two orbiting fluid elements to exchange angular momentum on larger scales than the hydrodynamical viscosity scales."
 The. magneto rotational instability acts like a dynamo. amplifying the field which is lost due to buovancy. leading to a magnetised corona.," The magneto rotational instability acts like a dynamo, amplifying the field which is lost due to buoyancy, leading to a magnetised corona."
 Flares associated with reconnection events would naturally be produced: leading to the formation of a hot ise corona., Flares associated with reconnection events would naturally be produced leading to the formation of a hot disc corona.
 Warmer disc winds. centrifugallv launched from 10 disc corona. were shown to be able to reproduce the observed Line fluxes and line ratios provided that the winds we clumpy (with filling factors about 14)) in. Gommez e Castro Ferro-Fontánn 2005 (hereafter Paper 11). the second article of this series.," Warmer disc winds, centrifugally launched from the disc corona, were shown to be able to reproduce the observed line fluxes and line ratios provided that the winds are clumpy (with filling factors about ) in Gómmez de Castro Ferro-Fontánn 2005 (hereafter Paper II), the second article of this series."
 Warm clise winds have also been ga10wn to be able to reproduce larger scale jet observations (sce Le. Vlahakis Tsinganos 1999. Ferreira 2004).," Warm disc winds have also been shown to be able to reproduce larger scale jet observations (see i.e. Vlahakis Tsinganos 1999, Ferreira 2004)."
 Warm ise winds provide an elegant ancl simple solution to the ugh jet temperatures observed. in the UV. however. they are not adequate to reproduce in full detail the observed γηνσίος of the line formation region.," Warm disc winds provide an elegant and simple solution to the high jet temperatures observed in the UV however, they are not adequate to reproduce in full detail the observed physics of the line formation region."
 Long tails of blucwarcls shifted emission are detected in the Si HL] and € HI] plasma racers. suggesting that the outllow launching mechanism is more Cllicient and. at the same time. the outflow 1s ess collimated than predicted. by. the simple. self-similar warn disc wind theory.," Long tails of bluewards shifted emission are detected in the Si III] and C III] plasma tracers, suggesting that the outflow launching mechanism is more efficient and, at the same time, the outflow is less collimated than predicted by the simple self-similar warm disc wind theory."
 As shown in Paper HL. the sellsimilar solutions that are able to reproduce the observed jet properties (velocity and mass How) require that the ratio oween the sound speed. and. the escape velocity is 0.43 at the Alfvénn radius.," As shown in Paper II, the self-similar solutions that are able to reproduce the observed jet properties (velocity and mass flow) require that the ratio between the sound speed and the escape velocity is 0.43 at the Alfvénn radius."
 As a result. the radial expansion of he outflow - the main source of line broadening - is shifted o distances of about LO AU from the star. where plasma cannot contribute to the Si HI] and € EI] emission because he densities ancl temperatures are very low and. radiative cooling is dominated. by singly ionized. species (see Fig.," As a result, the radial expansion of the outflow - the main source of line broadening - is shifted to distances of about 10 AU from the star, where plasma cannot contribute to the Si III] and C III] emission because the densities and temperatures are very low and radiative cooling is dominated by singly ionized species (see Fig."
 3 in Gommez de Castro Verdugo 2007. hereafter CidCVO|.," 3 in Gómmez de Castro Verdugo 2007, hereafter GdCV07)."
 Thus. self-similar models produce winds too collimated at the base to reproduce the observed broadening of the Si L1) and. € ILI] profiles.," Thus, self-similar models produce winds too collimated at the base to reproduce the observed broadening of the Si III] and C III] profiles."
 The high. densities revealed. by the Si HH]. € II] and C IV] line ratios indicate that this line radiation is produced very close to the star.," The high densities revealed by the Si III], C III] and C IV] line ratios indicate that this line radiation is produced very close to the star."
 Henceforth the radiating plasma must be strongly allected by the disc-star interaction., Henceforth the radiating plasma must be strongly affected by the disc-star interaction.
 In fact. there is evidence that Si HI] and. C LI] radiation can be produced in structures very. close to the star such as the ionized plasma torus around RAW Aur (Gómmoez de Castro Verdugo 2003) or the accreting shell in RY Tau (οςV07).," In fact, there is evidence that Si III] and C III] radiation can be produced in structures very close to the star such as the ionized plasma torus around RW Aur (Gómmez de Castro Verdugo 2003) or the accreting shell in RY Tau (GdCV07)."
 The physies of the interaction between the stellar magnetic ielel and the accretion disc is very rich. and it has been shown extensively. that jet. launching can be produced roni this interaction region with physical temperatures and densities similar to those of stellar chromospheres (Goodson et al.," The physics of the interaction between the stellar magnetic field and the accretion disc is very rich, and it has been shown extensively that jet launching can be produced from this interaction region with physical temperatures and densities similar to those of stellar chromospheres (Goodson et al."
 1997. von Rekowski Brandenburg 2004. 2006).," 1997, von Rekowski Brandenburg 2004, 2006)."
 Jet aunching from the interface between the magnetic rotor he star) and the disc is much more cllicient than a pure disc wind. firstlv because the centrifugal gear is higher closer to the star and secondly because of the heavy. mass ρα] onto the field lines at this point.," Jet launching from the interface between the magnetic rotor (the star) and the disc is much more efficient than a pure disc wind, firstly because the centrifugal gear is higher closer to the star and secondly because of the heavy mass load onto the field lines at this point."
 Thus. to conclude us series. we have computed the radiative output. from numerical simulations of outllow launching from star- clise interaction.," Thus, to conclude this series, we have computed the radiative output from numerical simulations of outflow launching from star- disc interaction."
 Ht will be shown that the radial Dow expansion. i.c. the outflow from the cdisc-star interaction region. is able to reproduce the observed. broadenings for magnetospheric fields of about 1-2 kG. In Section 2. the characteristics of the simulations [rom von Itekowski Brandenburg (2004. 2006. hereafter. vRBO4 and viRBOG. respectively). that are used in this work. are summarised.," It will be shown that the radial flow expansion, i.e. the outflow from the disc-star interaction region, is able to reproduce the observed broadenings for magnetospheric fields of about 1-2 kG. In Section 2, the characteristics of the simulations from von Rekowski Brandenburg (2004, 2006, hereafter vRB04 and vRB06, respectively), that are used in this work, are summarised."
 In Section 3. the procedure to derive line fluxes and profiles from the simulations is," In Section 3, the procedure to derive line fluxes and profiles from the simulations is"
 One of he inost dnuportaut clues concerning the early evolution of dynamically hot ealaxics (DI[Cs: ellipticals. dwarf splieroidals. and bulges of spirals) iu the fundamental plane of galaxies is the existence of a welldefined relationship between metallicity aud mass (6.8.. Beucder et al. 19021).," One of the most important clues concerning the early evolution of dynamically hot galaxies (DHGs: ellipticals, dwarf spheroidals, and bulges of spirals) in the fundamental plane of galaxies is the existence of a well-defined relationship between metallicity and mass (e.g., Bender et al. \cite{Benderetal1993}) )."
 The fundamental lessou taught bv this relation is that star formation in DITGs stopped because of eas loss. with less massive systems losing ereater fractions of their eas.," The fundamental lesson taught by this relation is that star formation in DHGs stopped because of gas loss, with less massive systems losing greater fractions of their gas."
 Outflow probably beeius when supernovac have raised the internal cucrey of the eas enough to allow it to escape the potential well (c¢.e.. Brocato et al. L990)).," Outflow probably begins when supernovae have raised the internal energy of the gas enough to allow it to escape the potential well (e.g., Brocato et al. \cite{Brocatoetal1990}) )."
 Most conmuouly. the metallicity in DIICGs is measured via the Mg» iudex.," Most commonly, the metallicity in DHGs is measured via the $_2$ index."
 While the Me» iudex is an excellent means of raukiug galaxy imoetallicities. itf does not vield an abundance directly. ie... the nuuber deusity of a particular clement relative to hydrogen. aud calibrations of the Me» index (modeldepeudoeut) are usually in terms of the iron abundance. au clement whose production is notoriouslv difiicul to model.," While the $_2$ index is an excellent means of ranking galaxy metallicities, it does not yield an abundance directly, i.e., the number density of a particular element relative to hydrogen, and calibrations of the $_2$ index (model-dependent) are usually in terms of the iron abundance, an element whose production is notoriously difficult to model."
 Though this may be best for some o»rposes. e.g.o studies of stear populations. it is nof sutiicicut for all purposes.," Though this may be best for some purposes, e.g., studies of stellar populations, it is not sufficient for all purposes."
 To study the chemical evolution of DITGs requires the abundance of an element whose xoduction is wel uderstood., To study the chemical evolution of DHGs requires the abundance of an element whose production is well understood.
 Were such abundances available. there would be some hope of quautifving the gas yaction at which DIICis of ciffereut masses begin to lose nass.," Were such abundances available, there would be some hope of quantifying the gas fraction at which DHGs of different masses begin to lose mass."
 Knowledge ofthe abundances would adimit studving he vield of heavy clements. and hence the slope of the stellar initial mass function during the star formation epoch.," Knowledge of the abundances would admit studying the yield of heavy elements, and hence the slope of the stellar initial mass function during the star formation epoch."
 Given the known photometric and dynamical xoperties of DICs odav. abundances would also allow us to study the eloba energetics involved curving their star ornation phase.," Given the known photometric and dynamical properties of DHGs today, abundances would also allow us to study the global energetics involved during their star formation phase."
 This paper is one of a sequence investigating the oxygen abundances of DIICis., This paper is one of a sequence investigating the oxygen abundances of DHGs.
 Tere. we preseut oxvecu abuudances for samples of planetary nebulae in and in the bulge ofM31.," Here, we present oxygen abundances for samples of planetary nebulae in and in the bulge of."
. These two nearby systems are good representativos of typical DIICGs., These two nearby systems are good representatives of typical DHGs.
 Though Αμ light profile may be truncated compared to isolated ellipticals. its structural. dnaendeal auc spectral properties are pertectly typical for an elliptical of its luuinositv (INormendy 1985: Deuder et al. 1993)).," Though 's light profile may be truncated compared to isolated ellipticals, its structural, dynamical, and spectral properties are perfectly typical for an elliptical of its luminosity (Kormendy \cite{Kormendy1985}; Bender et al. \cite{Benderetal1993}) )."
 Simularly. receut work on the DIG fundamental plane has shown that the photometric. dvnamical. aud stellar population properties of bulges follow those of pure cllipticals (Beuder ct al. 1992.. 1993)).," Similarly, recent work on the DHG fundamental plane has shown that the photometric, dynamical, and stellar population properties of bulges follow those of pure ellipticals (Bender et al. \cite{Benderetal1992}, \cite{Benderetal1993}) )."
 Oxveen is an excellent clement with which to study the evolution of galaxies., Oxygen is an excellent element with which to study the evolution of galaxies.
 Oxvecn is a primary clement whose sole significant production site is type IT superunovae (Wheeler et al. 1989)).," Oxygen is a primary element whose sole significant production site is type II supernovae (Wheeler et al. \cite{Wheeleretal1989}) ),"
 so its abundance is tied directly to the history of massive star formation. aud the euriclineut time scale is short compared to the ooOgas consumption time," so its abundance is tied directly to the history of massive star formation, and the enrichment time scale is short compared to the gas consumption time"
coming inside the Earth's orbit.,coming inside the Earth's orbit.
 The increase of ice abundance lowers AZ with which the snow line migration levels off at the minimum distance or starts to move outwardly., The increase of ice abundance lowers $\dot{M}$ with which the snow line migration levels off at the minimum distance or starts to move outwardly.
 For example. if the water ice mass ratio to the disk gas Gee is increased by a factor of 107. it is expected that the snow line would not come inside the Earth's orbit even in the case in which a=0.01. the dust grain size is 1 min. and ο=0.0043 (the solar abundance).," For example, if the water ice mass ratio to the disk gas $\zeta_{\mathrm{ice}}$ is increased by a factor of $10^{4}$, it is expected that the snow line would not come inside the Earth's orbit even in the case in which $\alpha = 0.01$, the dust grain size is 1 mm, and $\zeta_{\mathrm{sil}} = 0.0043$ (the solar abundance)."
 When (he dominant dust grain size or (α6) is small. a more increase of the ice abundance is neecec.," When the dominant dust grain size or $(\alpha / \zeta_{d})$ is small, a more increase of the ice abundance is needed."
 In our solar svstem. the water distribution shows a drastic change at the asteroid belt: this may be a clue of the snow line.," In our solar system, the water distribution shows a drastic change at the asteroid belt; this may be a clue of the snow line."
 Terrestrial planets are thought to form from planetesinmals which have formed inside the snow line. otherwise a large amount of water is inevitably accumulated into planets.," Terrestrial planets are thought to form from planetesimals which have formed inside the snow line, otherwise a large amount of water is inevitably accumulated into planets."
 Then. the timing of planetesimal formation nav be restricted by the snow line evolution.," Then, the timing of planetesimal formation may be restricted by the snow line evolution."
 First. we consider (he possibility (hat planetesimals form alter the snow line leaves oulwardly Che terrestrial planet region.," First, we consider the possibility that planetesimals form after the snow line leaves outwardly the terrestrial planet region."
 When we look at the solid mass. the planetesimal formation with a large sized dust grains is favorable. because the gas surface clensity with which the snow line (urns its direction of motion and moves outwardly increases as the clust erain size increases (Figure 6)).," When we look at the solid mass, the planetesimal formation with a large sized dust grains is favorable, because the gas surface density with which the snow line turns its direction of motion and moves outwardly increases as the dust grain size increases (Figure \ref{solar_parameter_snowline}) )."
 As the most favorable case. we see the munerical result ol the 1 mm-sized dust. case.," As the most favorable case, we see the numerical result of the 1 mm-sized dust case."
 Our numerical simulation shows that the surface density of solid material at the heliocentric distance of | AU is L1xLO7 gem? when the outwarelly moving snow line reaches | AU., Our numerical simulation shows that the surface density of solid material at the heliocentric distance of 1 AU is $1.1\times 10^{-2}$ $\mathrm{g\ cm^{-2}}$ when the outwardly moving snow line reaches 1 AU.
 This is much smaller than that of the mininnun mass solar nebula model (about LO gem 7)., This is much smaller than that of the minimum mass solar nebula model (about $10$ $\mathrm{ g\ cm^{-2}}$ ).
 To match the minimum mass solar nebula model.," To match the minimum mass solar nebula model,"
will thus be detected.,will thus be detected.
 In return. this will give us a unique view of the cosmic web at the mass scale traced by this population.," In return, this will give us a unique view of the cosmic web at the mass scale traced by this population."
 This is the approach of the XMM Large-Scale Structure Survey (XMM-LSS. Pierre et al. 2001a.. 2001b)).," This is the approach of the XMM Large-Scale Structure Survey (XMM-LSS, Pierre et al. \cite{msngr}, , \cite{estec}) )."
 The final objective is to map a contiguous region of the sky and to study the large-scale distribution and the clustering properties of the matter traced by the galaxy clusters and the QSO/AGN population., The final objective is to map a contiguous region of the sky and to study the large-scale distribution and the clustering properties of the matter traced by the galaxy clusters and the QSO/AGN population.
 XMM-LSS ts based on XMM observations and a subsequent multi-wavelength follow-up programme., XMM-LSS is based on XMM observations and a subsequent multi-wavelength follow-up programme.
 The target XMM-LSS survey geometry and depth were chosen such that to have a statistically significant number of clusters so that the two-point correlation function of clusters at 0<z«0.5 and 0.5«zI can be calculated with a precision reaching that of the ROSAT-ESO Flux Limited X-ray Survey (REFLEX. Collins et al. 2000))," The target XMM-LSS survey geometry and depth were chosen such that to have a statistically significant number of clusters so that the two-point correlation function of clusters at $0<z<0.5$ and $0.5<z<1$ can be calculated with a precision reaching that of the ROSAT-ESO Flux Limited X-ray Survey (REFLEX, Collins et al. \cite{col00}) )"
 which covers a much larger area but only goes out to z«0.2., which covers a much larger area but only goes out to $z<0.2$.
 To achieve this goal we need a good X-ray cluster detection procedure., To achieve this goal we need a good X-ray cluster detection procedure.
 Using extensive XMM image simulations we have developed an efficient pipeline procedure that uses the full XMM instrument sensitivity and indeed allows us to detect extended sources down to flux levels of 5x107% ffor 10 ks exposures (Valtchanov et al. 2001..," Using extensive XMM image simulations we have developed an efficient pipeline procedure that uses the full XMM instrument sensitivity and indeed allows us to detect extended sources down to flux levels of $5\times 10^{-15}$ for 10 ks exposures (Valtchanov et al. \cite{val01},"
 Refregier et al. 2002))., Refregier et al. \cite{ref02}) ).
 The successful detection 1s quite crucial because even the mere counting of clusters at different redshifts can be usedto constrain cosmological parameters (e.g. Mathiesen Evrard 1998.. Henry 2000.. Borgani et al. 2001..," The successful detection is quite crucial because even the mere counting of clusters at different redshifts can be usedto constrain cosmological parameters (e.g. Mathiesen Evrard \cite{mat98}, , Henry \cite{hen00}, Borgani et al. \cite{bor01},"
 Refregieret al. 2002)., Refregier et al. \cite{ref02}) ).
 These cosmoslogical constraints that come from cluster abundance evolution are complementary and independent to those from cosmic microwave background and supernovae studies., These cosmoslogical constraints that come from cluster abundance evolution are complementary and independent to those from cosmic microwave background and supernovae studies.
 Each detected candidate cluster from the pipeline. depending on its estimated redshift by photometric redshifts. is programmed to a spectroscopic follow-up (z< 1) or NIR observations (z> 1).," Each detected candidate cluster from the pipeline, depending on its estimated redshift by photometric redshifts, is programmed to a spectroscopic follow-up $z<1$ ) or NIR observations $z>1$ )."
 The spectroscopic follow-up of the first sample of candidate clusters in the XMM-LSS at z«] was programmed for observations on Las Campanas/Magellan and on the ESO/VLT telescopes., The spectroscopic follow-up of the first sample of candidate clusters in the XMM-LSS at $z<1$ was programmed for observations on Las Campanas/Magellan and on the ESO/VLT telescopes.
 The subject of this paper is to present the first results for a sample of 5 clusters at z>0.6 while the low redshift sample is presented elsewhere (Willis et al..," The subject of this paper is to present the first results for a sample of 5 clusters at $z>0.6$ while the low redshift sample is presented elsewhere (Willis et al.,"
 in preparation)., in preparation).
 The paper is organised as follows: first we present the X- data reduction and source detection (Sect. 2)).," The paper is organised as follows: first we present the X-ray data reduction and source detection (Sect. \ref{sec:x}) ),"
 then we describe in Sect., then we describe in Sect.
 3. the optical identification. spectroscopic target selection procedure and the observations.," \ref{sec:opt} the optical identification, spectroscopic target selection procedure and the observations."
 In Sect. 4..," In Sect. \ref{sec:results},"
 we present the data analysis results from the spectroscopic. and X-ray observations., we present the data analysis results from the spectroscopic and X-ray observations.
 Next we discuss each individual object (Sect. 5)), Next we discuss each individual object (Sect. \ref{sec:obj}) )
 and we end up with the conclusions (Sect. 6))., and we end up with the conclusions (Sect. \ref{sec:end}) ).
" Except where is mentioned. we use ACDM cosmology (Ho.=70 km s! Mpe!. Q,,=0.3.O4 0.7) for all cosmologically dependent parameters."," Except where is mentioned, we use $\Lambda$ CDM cosmology $H_0=70$ km $^{-1}$ $^{-1}$, $\Omega_m=0.3,\
\Omega_{\Lambda}=0.7$ ) for all cosmologically dependent parameters."
 All X-ray luminosities are bolometric., All X-ray luminosities are bolometric.
 The candidate clusters for the first spectroscopic run. were chosen from all XMM-LSS pointings received. by August 2002., The candidate clusters for the first spectroscopic run were chosen from all XMM-LSS pointings received by August 2002.
 This includes 15 AO-1 pointings of 10 ks exposure and another 15 exposures of 20 ks from the Guaranteed Time XMM Medium Deep Survey (XMDS)., This includes 15 AO-1 pointings of 10 ks exposure and another 15 exposures of 20 ks from the Guaranteed Time XMM Medium Deep Survey (XMDS).
 All observations were of good quality. except two fields that suffered from high background contamination affecting more than of the exposure time.," All observations were of good quality, except two fields that suffered from high background contamination affecting more than of the exposure time."
 A detailed description of the pipeline used in the XMM-LSS data reduction will be presented elsewhere (Pacaud et al..," A detailed description of the pipeline used in the XMM-LSS data reduction will be presented elsewhere (Pacaud et al.,"
 in preparation)., in preparation).
 Here we just briefly mention the main steps., Here we just briefly mention the main steps.
 The raw X-ray observations (ODFs) are reduced by the standard XMM Science Analysis System (XMM-SAS) tasks and for MOS and PN detectors respectively., The raw X-ray observations (ODFs) are reduced by the standard XMM Science Analysis System (XMM-SAS) tasks and for MOS and PN detectors respectively.
" High background periods. related to soft protons. are excluded from the event lists and raw photon images with a given pixel scale (2.5""fpixel in this case) in different energy bands are then created."," High background periods, related to soft protons, are excluded from the event lists and raw photon images with a given pixel scale $2.5\arcsec$ /pixel in this case) in different energy bands are then created."
" Subsequently the raw images for each instrument are filtered using ""à trous"" (with holes) iterative wavelet technique with a Poisson noise model and a threshold of 1077 (equivalent to 3.7 in the Gaussian case) for the significant wavelet coefficients (Starck Pierre 1998.. Starck et al. 1998))."," Subsequently the raw images for each instrument are filtered using “à trous” (with holes) iterative wavelet technique with a Poisson noise model and a threshold of $10^{-4}$ (equivalent to $3.7\sigma$ in the Gaussian case) for the significant wavelet coefficients (Starck Pierre \cite{sta98}, Starck et al. \cite{mr1}) )."
 Each filtered image is then exposure corrected and à mask map that includes bad pixels. CCD gaps and non-exposed CCD regions (generally parts outside the field-of-view of the telescope) are created.," Each filtered image is then exposure corrected and a mask map that includes bad pixels, CCD gaps and non-exposed CCD regions (generally parts outside the field-of-view of the telescope) are created."
 Wavelet-filtered. exposure-corrected images for each instrument in a given energy band are added together to form à compound (MOSI-MOS2-«PN) single band image to be used in the first stage of the detection procedure.," Wavelet-filtered, exposure-corrected images for each instrument in a given energy band are added together to form a compound (MOS1+MOS2+PN) single band image to be used in the first stage of the detection procedure."
 Clusters of galaxies are extended sources in. X-ray images., Clusters of galaxies are extended sources in X-ray images.
 Their detection and correct classification is not trivial because of various peculiarities of the X-ray observations: Poisson noise regime. varying PSF as a function of the off-axis angle and the energy. the vignetting effect. and the geometry of the detector (CCD gaps).," Their detection and correct classification is not trivial because of various peculiarities of the X-ray observations: Poisson noise regime, varying PSF as a function of the off-axis angle and the energy, the vignetting effect, and the geometry of the detector (CCD gaps)."
 We use images in the [0.5-2] keV energy band which is well suited for clusters and groups (Scharf 2002))., We use images in the [0.5-2] keV energy band which is well suited for clusters and groups (Scharf \cite{sch02}) ).
 The detection procedure is based on the preseription of Valtchanov et al. (2001)), The detection procedure is based on the prescription of Valtchanov et al. \cite{val01}) )
 and has three stages: wavelet filtering (see the previous section). detection and measurements.," and has three stages: wavelet filtering (see the previous section), detection and measurements."
 The wavelet filtered image is fed to (Bertin Arnouts 1996)) for detection and characterisation., The wavelet filtered image is fed to (Bertin Arnouts \cite{sex}) ) for detection and characterisation.
 The classification to extended (clusters) and point-like sources (AGNs or QSOs) is done by using three parameters: the half-light radius. the FWHM from a Gaussian fit to the source and stellarity index adapted for the X-ray observations.," The classification to extended (clusters) and point-like sources (AGNs or QSOs) is done by using three parameters: the half-light radius, the FWHM from a Gaussian fit to the source and stellarity index adapted for the X-ray observations."
 The classification task is complicated by the fact that distant and faint clusters are not too different from a PSF., The classification task is complicated by the fact that distant and faint clusters are not too different from a PSF.
 Moreover. at greater off-axis angles the PSF shape can be quite distorted. although the half-energy width does not change significantly in the [0.5—2] keV energy band.," Moreover, at greater off-axis angles the PSF shape can be quite distorted, although the half-energy width does not change significantly in the $[0.5-2]$ keV energy band."
 This shape distortion can lead to a wrong classification and that iswhy we have constrained the cluster detection up to off-axis distancesnot greater than 12’., This shape distortion can lead to a wrong classification and that iswhy we have constrained the cluster detection up to off-axis distancesnot greater than $12\arcmin$ .
 This strategygives very good results using simulated XMM, This strategygives very good results using simulated XMM
A complementary approach for isobaric combustion evolution was recently formulated by ?..,A complementary approach for isobaric combustion evolution was recently formulated by \citet{2004ApJS..151..345C}.
 Although their approach is tied to the first-order Euler integration method. they demonstrated satisfactory accuracy and cousisteney of the thermocdwuamic and abundance evolutions.," Although their approach is tied to the first-order Euler integration method, they demonstrated satisfactory accuracy and consistency of the thermodynamic and abundance evolutions."
 A direct comparison of the two methods should be examined in future investigations., A direct comparison of the two methods should be examined in future investigations.
 Tere we describe our method. which is alinost completely as deseribed iu. 2.. for calculating the steady state velocities for unsupported detouations under curvature.," Here we describe our method, which is almost completely as described in \citet{sharpecurved}, for calculating the steady state velocities for unsupported detonations under curvature."
 The starting point is to consider the quasi-steady equations of hydrodvuauuies iu shock attached frame. assumndue curvature is constant through structure.," The starting point is to consider the quasi-steady equations of hydrodynamics in shock attached frame, assuming curvature is constant through structure."
" This gives us Sharpe's equs (6)(9): where s d: the coordinate normal to the shock. «,, aud D,, are the fluid velocities relative to the shock and D, is the normal detonation velocity. X; is the mass abuudauce of the ΠΕspecies. Ry is net production rate of the 7 species. p is the easdvuamic pressure. and ¢ is total specific energy of the fluid."," This gives us Sharpe's eqns (6)–(9): where $n$ is the coordinate normal to the shock, $u_n$ and $D_n$ are the fluid velocities relative to the shock and $D_n$ is the normal detonation velocity, $X_i$ is the mass abundance of the $i^{\mathrm{th}}$species, $R_i$ is net production rate of the $i^{\mathrm{th}}$ species, $p$ is the gasdynamic pressure, and $e$ is total specific energy of the fluid."
 Using arguments similar to those described in the previous appendix. oue can construct ODEs for the post-shock deusity aud temperature structure in the detonation: where ay. the frozen sound speed. is given by and o. the thermicity. is given by," Using arguments similar to those described in the previous appendix, one can construct ODEs for the post-shock density and temperature structure in the detonation: where $a_f$, the frozen sound speed, is given by and $\phi$ , the thermicity, is given by"
"We adopted :| princije tha the difference equations should be consistent wih the global properties. Le.. the Crauss'"" theorem and Stoke's theorem.","We adopted a principle that the difference equations should be consistent with the global properties, i.e., the Gauss's theorem and Stoke's theorem."
 We were satisfied with the first order accuracy at the erid level »ouucda‘ies., We were satisfied with the first order accuracy at the grid level boundaries.
 In other words we gave priority to tlie global p‘operties over the hieher order ac'CUuracy al a elyren point., In other words we gave priority to the global properties over the higher order accuracy at a given point.
 As a result we succeeded in computing tte eravily of a close ary aucl i reprodicing tle quacdraple moment., As a result we succeeded in computing the gravity of a close binary and in reproducing the quadraple moment.
 This success is analogous to tiat of a Total Varla1 Dimiuisune (TVD) sclele for wave equations aud that of symplectic inegrator for a Haijan systen (Yoslida1990)., This success is analogous to that of a Total Variation Diminishing (TVD) scheme for wave equations and that of symplectic integrator for a Hamiltonian system \citep{yoshida90}.
. TVD scheije gives priority to monotonuicity Oo“the solution Over 1 local acerracy (see.e.g.Hirsch1990).," TVD scheme gives priority to monotonicity of the solution over the local accuracy \citep[see, e.g.][]{hirsch90}."
. The solution is free from nume‘ical oscillations., The solution is free from numerical oscillations.
 A sylnp licillegraOr glves a solution which satisfies the conservation of the volume in phase space., A symplectic integrator gives a solution which satisfies the conservation of the volume in phase space.
 Asa ‘esult here is no secular change in the tota| energy. even though it is not couserved at each time ste» di elotie. limitecl accuracy.," As a result there is no secular change in the total energy, even though it is not conserved at each time step due to the limited accuracy."
 These exariples coufiri that the οobal properties are more importaul lian the higher order accuracy., These examples confirm that the global properties are more important than the higher order accuracy.
 An alte‘native method was proposed by Trueloveetal.(1998)., An alternative method was proposed by \citet{truelove98}.
. Their 1umerical scheme is based on that of Almerenetal.(1998) wlo solved the cyuamics of au i1colMp'essible fluid with ANR.," Their numerical scheme is based on that of \citet{almgren98}
 who solved the dynamics of an incompressible fluid with AMR."
 They evaluated the gravitational potejal. ©. not οι Ihe cell centers bu οithe vertexes.," They evaluated the gravitational potential, $ \phi $, not on the cell centers but on the vertexes."
 WIile they applied the cell ceutered ¢ifference to the lLvdrodsnamically equatious. tlev applied the verex centered difference to the Poisson equation.," While they applied the cell centered difference to the hydrodynamical equations, they applied the vertex centered difference to the Poisson equation."
 This met10d bas an acvantage that the different level cells share the same gravitational potential automatically., This method has an advantage that the different level cells share the same gravitational potential automatically.
1 Iu other words. this inetliod ensures he continuity of the gravitational potenial )etweenu ilthe grids of differeit levels.," In other words, this method ensures the continuity of the gravitational potential between the grids of different levels."
 This method. Loweyer. does not satisfies the Cat ssseorein aud aecordiugly does not eusure the coitinuity of the e'avity. g.," This method, however, does not satisfies the Gauss's theorem and accordingly does not ensure the continuity of the gravity, $ \mbox{\boldmath$ $} $."
 The method o ['Trueloveetal.(1998) has ai[9]her disadvantage that it underestimates οvl, The method of \citet{truelove98} has another disadvantage that it underestimates gravity.
 us clisadvautage is di elo averaging used to evaliate the vertex centered deusity., This disadvantage is due to averaging used to evaluate the vertex centered density.
 They evaun ecensity at a verlex siuce the Poisson ecation is evaluated on the vertex center., They evaluated the density at a vertex since the Poisson equation is evaluated on the vertex center.
 Averaging OW e peak deusity and b|oadens the deusity distribution., Averaging lowers the peak density and broadens the density distribution.
 Thus the gravitational potential evaπα ile vertex is shallowe ‘than that evaltvated at the cell center., Thus the gravitational potential evaluated at the vertex is shallower than that evaluated at the cell center.
 This clifference is seriously lare {οι the gas is coucentrated in a few ceS., This difference is seriously large when the gas is concentrated in a few cells.
 We have applied our Poiss¢i equatiol1 solver to numerical simulations of binary star formation., We have applied our Poisson equation solver to numerical simulations of binary star formation.
 le results will be publishecl iu near futye., The results will be published in near future.
 We thank an:VOLVINOUS 'eferee or his/her comnents o tlie earlier version of this manuscript., We thank an anonymous referee for his/her comments to the earlier version of this manuscript.
 They helped us for ip‘ovine this mauscript greatly., They helped us for improving this manuscript greatly.
 We thank the Astronomical Data Analysis Center of t1ο National Astronomica Society of Jayan for allowing us to use Fugitsu VPP5000., We thank the Astronomical Data Analysis Center of the National Astronomical Society of Japan for allowing us to use Fujitsu VPP5000.
 This study is financially. supported in part by the Crart-in-Aid for Encouragement of Young Scientists (12710123. 11710131) and hat for Scieutic Research (C) (13610237) of Japan Society of Promotion of Science (JSPS).," This study is financially supported in part by the Grant-in-Aid for Encouragement of Young Scientists (12740123, 14740134) and that for Scientific Research (C) (13640237) of Japan Society of Promotion of Science (JSPS)."
 It is also supported in part by the Cuannt-in-Aicl for Scientific Research oi Priority Areas (A) (13011201) of the Aiuistry of Exlucation. Culture. Sports. Science and Technoogy (NKLENT).," It is also supported in part by the Grant-in-Aid for Scientific Research on Priority Areas (A) (13011204) of the Ministry of Education, Culture, Sports, Science and Technology (MEXT)."
width at half maxima. but the more plavsical timescale is the Eiusteiu time.,"width at half maximum, but the more physical timescale is the Einstein time."
 Iuowiug the Eiusteiu times allows a much more accurate measurement of the lous mass. thus it is worth the extra trouble to try to measure the Eiisteim times of the detected events.," Knowing the Einstein times allows a much more accurate measurement of the lens mass, thus it is worth the extra trouble to try to measure the Einstein times of the detected events."
 We have shown that a iicrolensing halo in MD should be clearly distinguishable frou self lensingC» if an appreciable event rate away from the MD bulee is measured., We have shown that a microlensing halo in M31 should be clearly distinguishable from self lensing if an appreciable event rate away from the M31 bulge is measured.
 We have explored the use of cuts in eveut timescale to separate the self leusing component from the halo lensing component of the eveut rate. aud found that this helps near the bulee. but not further away.," We have explored the use of cuts in event timescale to separate the self lensing component from the halo lensing component of the event rate, and found that this helps near the bulge, but not further away."
 We lave quantified the level of halo that is detectable. aud fouud that a mareinal detection of a microlensiue halo would be possible in three seasons of groundbased observations.," We have quantified the level of halo that is detectable, and found that a marginal detection of a microlensing halo would be possible in three seasons of ground–based observations."
 Ileher halo fractions can be detected more convincinely of course., Higher halo fractions can be detected more convincingly of course.
 We wish to thank David Alves. Nezvsztof Stauck aud Lairy Widrow for useful conversations.," We wish to thank David Alves, Krzysztof Stanek and Larry Widrow for useful conversations."
 E.D. ackuowledges support from the Coluubia University. Academic Quality Fund., E.B. acknowledges support from the Columbia University Academic Quality Fund.
 CC. wishes to acknowledge facial support frou the Brinson Foundation., G.G. wishes to acknowledge financial support from the Brinson Foundation.
 A.C. was supported by erauts from NSF (AST 00-70882 and 98-02981) and(GO-7376).., A.C. was supported by grants from NSF (AST 00-70882 and 98-02984) and.
Deep optical surveys of the Milly Way ancl other Local-Group galaxies have uncovered numerous stellar streanis (Odenkirchenctal.2001:Majewskiet2004:etal.2006:[bata 2007).,"Deep optical surveys of the Milky Way and other Local-Group galaxies have uncovered numerous stellar streams \citep{Odenkirchen,Majewski04,fostreams,Ibata}."
. The Leiden-Argentine-Bonn survey of the Galaxy in the 216m line of hydrogen (Ixalberlaetal.2005). contains many similar streams.," The Leiden-Argentine-Bonn survey of the Galaxy in the $21\,$ cm line of hydrogen \citep{LAB} contains many similar streams."
 In all probability both stellar and gaseous streams have been idally torn from orbiting bodies. ancl as such delineate the orbits of those bodies around the Galaxy (Johnstonetal.1996:Odenkirchenetal.2003:Choi 2007).," In all probability both stellar and gaseous streams have been tidally torn from orbiting bodies, and as such delineate the orbits of those bodies around the Galaxy \citep{JohnstonHB,Odenkirchen03,Choi}."
. Newton's avs of motion severely constrain the readily observable «quantities along an orbit in the sky. namely the sequence of »ositions on the sky ai).bfu)] and the corresponding line- velocities. ος where η is a parameter that varies monotonically along the stream (Jin&Lynden-Bell2007:Binney2008.hereafterPaper D.," Newton's laws of motion severely constrain the readily observable quantities along an orbit in the sky, namely the sequence of positions on the sky $[l(u),b(u)]$ and the corresponding line-of-sight velocities, $v_\parallel(u)$, where $u$ is a parameter that varies monotonically along the stream \citep[][hereafter Paper
I]{complexA,paper1}."
.. In fact. if the observables are known to reasonable accuracy. data for a single stream can strongly constrain the Galaxy's gravitational potential. and once the potential is known. the distance and. proper motion at cach point on the stream can be predicted. with an accuracy that far exceeds anything likely to be possible by conventional astrometry (Paper 1).," In fact, if the observables are known to reasonable accuracy, data for a single stream can strongly constrain the Galaxy's gravitational potential, and once the potential is known, the distance and proper motion at each point on the stream can be predicted with an accuracy that far exceeds anything likely to be possible by conventional astrometry (Paper I)."
 From the work of Paper Lit emerges that the major limitation on the diagnostic power of streams is that streams do precisely delineate. individual orbits (Choiet.al. 2007)., From the work of Paper I it emerges that the major limitation on the diagnostic power of streams is that streams do precisely delineate individual orbits \citep{Choi}.
. This paper is devoted to exploring the extent to which this limitation can be overcome., This paper is devoted to exploring the extent to which this limitation can be overcome.
 In Section 77. we illustrate the extent of the problem. in Section. ?? we introduce significant improvements to the methodology. of Paper Land use these to identify orbits that are consisten with a given body of data.," In Section \ref{sec:norbit}
 we illustrate the extent of the problem, in Section \ref{sec:identify} we introduce significant improvements to the methodology of Paper I and use these to identify orbits that are consistent with a given body of data."
 ln Section ?? we test. this approach., In Section \ref{sec:test} we test this approach.
 In Section ??. we examine our ability to correctly diagnose the Galactic potential., In Section \ref{sec:potential} we examine our ability to correctly diagnose the Galactic potential.
 Section. 77. sums up ane discusses directions for future work.," Section \ref{sec:conclusions}
 sums up and discusses directions for future work."
 Except where stateck otherwise. orbits aux reconstructions— are caleulated— using the Galactic— potentia— of Model LE in Binney&“Premaine(2008).. which is à slighthy modified version of a halo-clominatecl potentia described. by Dehnen&Binney(1998a).," Except where stated otherwise, orbits and reconstructions are calculated using the Galactic potential of Model II in \cite{gd2}, which is a slightly modified version of a halo-dominated potential described by \cite{dehnenbinney}."
. We take the distance to the Galactic centre to be Skpe and from &Drunthaler(2005). (for V and VW) and Dehnen&Binney(LOOSb) we take the velocity of the Sun in the Galactic res frame to be (CVM)=(10.0.241.0.7.6)kms," We take the distance to the Galactic centre to be $8\kpc$ and from \cite{ReidB} (for $V$ and $W$ ) and \cite{Hipp} we take the velocity of the Sun in the Galactic rest frame to be $(U,V,W)=(10.0,241.0,7.6)\kms$."
 The full curves in show an orbit. superficially similar to that underlving the Orphan Stream (Belokuroyetal.2007) from two viewing locations — the position of the Sun and a position 120 further round the solar circle., The full curves in show an orbit superficially similar to that underlying the Orphan Stream \citep{orphan} from two viewing locations – the position of the Sun and a position $120^\circ$ further round the solar circle.
 Also shown in each projection are the locations of particles tically stripped. from a sell-gravitating N-body model of a cluster, Also shown in each projection are the locations of particles tidally stripped from a self-gravitating N-body model of a cluster
Because we have the relations. and substituting Equation (23)) into Equations (16)) aud (18)) vields The outer boundary couditiou for JjHiucr is then Aa70 atf spatial infinity.,"Because we have the relations, and substituting Equation \ref{eq:shift_decomp}) ) into Equations \ref{eq:beta}) ) and \ref{eq:taij}) ) yields The outer boundary condition for $\beta_{\rm iner}^i$ is then $\beta_{\rm iner}^i=0$ at spatial infinity."
 We actually solve for llicr Ho , We actually solve for $\beta_{\rm iner}^i$ .
The lyvdrostatic equations governing the quasi-equilibrium state are the Euler and continuitv equations., The hydrostatic equations governing the quasi-equilibrium state are the Euler and continuity equations.
 For both irrotational aud sxuchrouized motions. the Euler equation can be iutegrated once to eive where f=(p|pePyfp is the fluid specific cuthalpy. 59 is the Loreutz factor between the co-orbiting aud Eulerian observers. and 5 is the Loreutz factor between the fluid and co-orbiting observers.," For both irrotational and synchronized motions, the Euler equation can be integrated once to give where $h=(\rho +\rho \epsilon +P)/\rho$ is the fluid specific enthalpy, $\gamma_0$ is the Lorentz factor between the co-orbiting and Eulerian observers, and $\gamma$ is the Lorentz factor between the fluid and co-orbiting observers."
 If we define the Lvelocity of the co-orbiting observer by (7. the Loreutz factors are wirittcu as where Cj is the orbital 3-velocity with respect to the Eulerian observer. and (7 denotes the fluid 3-velocity with respect to the Eulerian observer. for rotational binary systems.," If we define the 4-velocity of the co-orbiting observer by $v^{\mu}$, the Lorentz factors are written as where $U_0^i$ is the orbital 3-velocity with respect to the Eulerian observer, and $U^i$ denotes the fluid 3-velocity with respect to the Eulerian observer, for irrotational binary systems."
" Here a? is the time component of the fluid. l-velocity and © is the velocity potential which is calculated by solving the equation of continuity written as where V, is the covariant derivative with respect to Gun.", Here $u^t$ is the time component of the fluid 4-velocity and $\Psi$ is the velocity potential which is calculated by solving the equation of continuity written as where $\nabla_{\mu}$ is the covariant derivative with respect to $g_{\mu \nu}$.
 Note that the fid 3-velocity UH corresponds to the orbital 3-velocity US for svuchrouized binary svstenis., Note that the fluid 3-velocity $U^i$ corresponds to the orbital 3-velocity $U_0^i$ for synchronized binary systems.
 For the determunation of the coustaut on the right-hand side of Equation (29)). we use the ceutral value of the quautities on its left-hand side.," For the determination of the constant on the right-hand side of Equation \ref{eq:euler}) ), we use the central value of the quantities on its left-hand side."
 The ceuter of à neutron star is defined as the location ofthe παπα baryou rest-1iass density in the preseut paper., The center of a neutron star is defined as the location of the maximum baryon rest-mass density in the present paper.
 Equation (29)) imcludes one more constant which should be determined for cach quasi-equilibrium figure: the constant is the orbital angular velocity as we find from Equations (32)). (23)). and (22)).," Equation \ref{eq:euler}) ) includes one more constant which should be determined for each quasi-equilibrium figure; the constant is the orbital angular velocity as we find from Equations \ref{eq:u0}) ), \ref{eq:shift_decomp}) ), and \ref{eq:shift_rot}) )."
 The method for calculating it will be explained in the next section., The method for calculating it will be explained in the next section.
 The method for determining the orbital angular velocity is as follows: we first set the rotation axis of the binary svsteii to be the Z-axis. aud the line connecting the centers of mass of cach neutron star to be the .X-axis.," The method for determining the orbital angular velocity is as follows: we first set the rotation axis of the binary system to be the $Z$ -axis, and the line connecting the centers of mass of each neutron star to be the $X$ -axis."
 Requiring a force balance along the X-axis. we impose a coucition of quasi-circular orbit for the binary svstem.," Requiring a force balance along the $X$ -axis, we impose a condition of quasi-circular orbit for the binary system."
" The force balance equation is obtained by setting the central values of the eradicut of euthalpy to be zero for cach star. where Q, (o= 1.2) denotes the ceuter of cach neutron star."," The force balance equation is obtained by setting the central values of the gradient of enthalpy to be zero for each star, where ${\cal O}_a$ $a=1,2$ ) denotes the center of each neutron star."
 Because Equation (29)) includes ϱ through Equation (22)). the force balance Equation (35)) may be regarded as the equation for determining the orbital aneular velocity.," Because Equation \ref{eq:euler}) ) includes $\Omega$ through Equation \ref{eq:shift_rot}) ), the force balance Equation \ref{eq:forcebalance}) ) may be regarded as the equation for determining the orbital angular velocity."
 Equation (35)) also depends on the location of the center of mass. because Equation (22)) includes R which is the radial coordinate measured from the center of mass of the binary system.," Equation \ref{eq:forcebalance}) ) also depends on the location of the center of mass, because Equation \ref{eq:shift_rot}) ) includes ${\bm R}$ which is the radial coordinate measured from the center of mass of the binary system."
 For equal- binaries. the force balance equations for cach star degenerate and the location of the center of amass becomes trivial ie.we can set it to," For equal-mass binaries, the force balance equations for each star degenerate and the location of the center of mass becomes trivial, i.e.,we can set it to"
As already done for the optical data. the stars have been divided into groups. using the same isophotal contours of the WEPC2 FSLIW iosaic image.,"As already done for the optical data, the stars have been divided into groups, using the same isophotal contours of the WFPC2 F814W mosaic image."
 Due to the smaller size of NIC2. these eroups contain stars only [rom Regions 5. 6 aud 7.," Due to the smaller size of NIC2, these groups contain stars only from Regions 4-5, 6 and 7."
 Region 7 iucludes the most luminous SSC and most of the brightest stars., Region 7 includes the most luminous SSC and most of the brightest stars.
 We have also cross-ideutified the stars appearing in both the PC auc NIC2 field of view by cousidering a matching radius of 2 pixels (about half of the PSF FWHAL in all the four filters)., We have also cross-identified the stars appearing in both the PC and NIC2 field of view by considering a matching radius of 2 pixels (about half of the PSF FWHM in all the four filters).
 Our final sample includes 1831 stars aud 11 cauclicate clusters with measurecl magnitudes iu all the four F555W. FSLIW. FLIOW aud F160W frames.," Our final sample includes 1834 stars and 11 candidate clusters with measured magnitudes in all the four F555W, F814W, F110W and F160W frames."
 Fig., Fig.
 LT shows the0s CMDs of all the stars measured iu tle seven Regions described in the previous section., \ref{cm_vi} shows the CMDs of all the stars measured in the seven Regions described in the previous section.
 The number of objects in each panel is labelled in its lower right corner., The number of objects in each panel is labelled in its lower right corner.
 As mentioned above. Regions 1 aud 2 are plotted together because both their populations aud their crowcdiug conditions are very similar.," As mentioned above, Regions 1 and 2 are plotted together because both their populations and their crowding conditions are very similar."
 The same occurs for Regious 3 aud I., The same occurs for Regions 3 and 4.
 The spatial cistributious of the stellar populations in the various Regions are clearly different [rom one another., The spatial distributions of the stellar populations in the various Regions are clearly different from one another.
 Bright stars are mostly coucentratecd toward the galactic center aud ouly a few oL them are present iu the outer regions., Bright stars are mostly concentrated toward the galactic center and only a few of them are present in the outer regions.
 Iusteacd. [aint stars are probably everywhere but are more easily resolvable iu the external regiis. thanks to the less crowded. coucditious.," Instead, faint stars are probably everywhere but are more easily resolvable in the external regions, thanks to the less crowded conditions."
 The two innermost Regious present a well defiued blue and red plume., The two innermost Regions present a well defined blue and red plume.
 The blue plume is located al c 00.1. with the brightest stars at ipw220.3. aud corresponds to the ualn-sequenunce (MS) evolutionary phase aud to the hot edge of the core helium burning phase.," The blue plume is located at $\,\simeq\,$ 0.1, with the brightest stars at 20.3, and corresponds to the main-sequence (MS) evolutionary phase and to the hot edge of the core helium burning phase."
 The red plume is at cl. aud extends up to 119.5., The red plume is at $\simeq$ 1.7 and extends up to 19.5.
 It is populated by red supergiants (RSCs) at the brighter magnitudes and asymptotic giant branch (ACB) stars al fainter luminosities., It is populated by red supergiants (RSGs) at the brighter magnitudes and asymptotic giant branch (AGB) stars at fainter luminosities.
 The brightest stars. of whatever color. are all located in Region 7. aud correspond to the pearl necklace visible in Fig.," The brightest stars, of whatever color, are all located in Region 7, and correspond to the pearl necklace visible in Fig."
 15 and described in the previous Section.," \ref{pc_nicmos_bw2}
 and described in the previous Section."
 The severe crowding of Region T prevents a reliable detection of objects fainter that about 25.5 in eitler the F5532W or the FSLIW. baud., The severe crowding of Region 7 prevents a reliable detection of objects fainter that about 25.5 in either the F555W or the F814W band.
 Region 6 is sufficiently less crowded to allow for the detection of much faiuter objects. aud already shows the concentration of stars with 1X X L5 aud € 36. which is much better delineated from Region 5 outwards aud correspouds to low-mass. old. stars in the red giant. branel (ROB) evolutionary. phase.," Region 6 is sufficiently less crowded to allow for the detection of much fainter objects, and already shows the concentration of stars with $\,\leq\,$ $\,\leq\,$ 1.8 and $\,\leq\,$ $\,\leq\,$ 26, which is much better delineated from Region 5 outwards and corresponds to low–mass, old, stars in the red giant branch (RGB) evolutionary phase."
 Regious [rom 3 to 0 contaiu very few. if any. stars outside the RGB.," Regions from 3 to 0 contain very few, if any, stars outside the RGB."
 Fig., Fig.
 18. shows iu the upper panels the infrared CMDs of the galaxy field covered by NIC2 (Regions 1-5. 6 aud 7).," \ref{cm_vjh} shows in the upper panels the infrared CMDs of the galaxy field covered by NIC2 (Regions 4–5, 6 and 7)."
 Iu this case. only a few stars are found iu the bluest part of the diagram.," In this case, only a few stars are found in the bluest part of the diagram."
 This is not due to a real lack of young stars (as we kuow from their couspicuous preseuce iu the optical CMD). but to the intrinsic faintuess of hot stars in the infrared bands.," This is not due to a real lack of young stars (as we know from their conspicuous presence in the optical CMD), but to the intrinsic faintness of hot stars in the infrared bands."
 The red plume at b ds instead very well sampled aud shows a tight vertical linger with from Ls to 20, The red plume at 1 is instead very well sampled and shows a tight vertical finger with from 18 to 20
lobe to mass transfer.,lobe to mass transfer.
 In the sinipest models of τιass traister. m which svstemic mass and orbital angular luoucΜπι loss rates are proportional to the iuass traisfer rae. Gr depends oulv ou the MALY Wass ratio.," In the simplest models of mass transfer, in which systemic mass and orbital angular momentum loss rates are proportional to the mass transfer rate, $\zeta_L$ depends only on the binary mass ratio."
 Qur stellu :labatic mass loss models therefore allow Us Qteteriine the critical mass ratio (douor/accretor) above whic binary will be unstable to dvizuuical tinue scale lass Leisfer., Our stellar adiabatic mass loss models therefore allow us to determine the critical mass ratio (donor/accretor) above which a binary will be unstable to dynamical time scale mass transfer.
 This is an esseutial consideration uu luaypig out üuarv population svuthesis models., This is an essential consideration in mapping out binary population synthesis models.
 We are currentv building a library of stellar adiabatic ταιass loss wnodels (Ceetal.2010).. covering the full range of evolutionary sages from ZAMS to the tip of the ROB or ACB. as appropriate.," We are currently building a library of stellar adiabatic mass loss models \citep{ge10}, covering the full range of evolutionary stages from ZAMS to the tip of the RGB or AGB, as appropriate."
 Fig., Fig.
 5 shows the model οil of our project., \ref{fig5} shows the model grid of our project.
 RLOF process aud CE evolution are very miportaut 11 he formalon of hot subdwuf stars aud other ynary systems., RLOF process and CE evolution are very important in the formation of hot subdwarf stars and other binary systems.
" Earlier published studies of Hjelliiiug&ANVebbink©OST.audreferencestherein)| proviled se""ul qualitative insights in RLOF aud CE evolution. ut left consicrable room for improvement. especiallv witji reed to the range of evolved phases that reed to be addressed."," Earlier published studies of \citet[and references therein]{hjel87} provided useful qualitative insights in RLOF and CE evolution, but left considerable room for improvement, especially with regard to the range of evolved phases that need to be addressed."
 These deficiencies were iu aL redressec oei later work (IEjelhuius19895).. ]out oulv a fragneut of that work was ever publislred (Ποπιο195940)..," These deficiencies were in part redressed in later work \citep{hjel89b}, but only a fragment of that work was ever published \citep{hjel89a}."
 The stellar adiabatic ass 1OSS nodels describe in this paper considerably exteud the scope of Ποιάres work., The stellar adiabatic mass loss models described in this paper considerably extend the scope of Hjellming's work.
 They allow us uot only to study the incrior structure of donor stars undoergoinusg clynamiical timescale mass transfer. |mt also to evaluate the stabiitv criteria for dvnauulcal mass fransfer iu binary population svuthesis.," They allow us not only to study the interior structure of donor stars undergoing dynamical timescale mass transfer, but also to evaluate the stability criteria for dynamical mass transfer in binary population synthesis."
 An iniial application of our models to 1.AL. and 10AM. stars has been described i this paper., An initial application of our models to $1~M_\odot$ and $10~M_\odot$ stars has been described in this paper.
 The reader shouα beware that the these models have lanitations to their usefulness. as they depeud ou being adle to searate the process of dvuawical relaxation to hydrostatic equilibrium from that of thermal relaxation to therma equilibrium.," The reader should beware that the these models have limitations to their usefulness, as they depend on being able to separate the process of dynamical relaxation to hydrostatic equilibrium from that of thermal relaxation to thermal equilibrium."
 On the main sequence. for cxalple. 1e dwnaiical time scale of the Suu is rougeily 10 that of its thermal time scale. making he adiabatic uass loss model an excellent description of he asviuptotic behavior of a solar-type star to very rapid mass oss.," On the main sequence, for example, the dynamical time scale of the Sun is roughly $10^{-10}$ that of its thermal time scale, making the adiabatic mass loss model an excellent description of the asymptotic behavior of a solar-type star to very rapid mass loss."
 However. at the opposite extreme m he IIR cliagrane stars near the tip of the RGB or ACB have hermal tiue scales approaching their dvuamical tilue scales. ancl he cutive mass transfer process may reqire ull-blown time-dependent modeling.," However, at the opposite extreme in the HR diagram, stars near the tip of the RGB or AGB have thermal time scales approaching their dynamical time scales, and the entire mass transfer process may require full-blown time-dependent modeling."
 This couvereeice of thermal aud dvuamical time scales is broadly relaed o the aliipt expansion seen m our models of 1AL. aud 10A. stars at the tip of the eiut brauch (TOB). when their outermost superaclabatic lavers are stripped away.," This convergence of thermal and dynamical time scales is broadly related to the abrupt expansion seen in our models of $1~M_\odot$ and $10~M_\odot$ stars at the tip of the giant branch (TGB), when their outermost superadiabatic layers are stripped away."
 In reality. Roche lobe overflow is far frol spherically-svuuuetric. as treated here (by necessity). but that superadiabatic expunusiou uav nevertheless reflect a real physical phenomenon.," In reality, Roche lobe overflow is far from spherically-symmetric, as treated here (by necessity), but that superadiabatic expansion may nevertheless reflect a real physical phenomenon."
 Convection itself is not spherically svuuuetre. and with couvective volocities iu the superaliabatic zone apmoaching sound speed. it mav be possible for ising flows near the lnuer Lagrangian ponr to xilee the votential to the companions Roche lobe while the donor stil lics well witlirits own Roche liuit.," Convection itself is not spherically symmetric, and with convective velocities in the superadiabatic zone approaching sound speed, it may be possible for rising flows near the inner Lagrangian point to bridge the potential to the companion's Roche lobe while the donor still lies well within its own Roche limit."
 We are not now able to pass judgement on that possibiliY., We are not now able to pass judgement on that possibility.
 Wwjen dynamical lustahility occurs. conmnioneuve ο. evoluion aliuost certainly follows. as tje thermal time scale of the accreting star is invariably onecr than that of the donor. which itself is ecuerally much longer than its clvuamical time scale.," When dynamical instability occurs, common envelope evolution almost certainly follows, as the thermal time scale of the accreting star is invariably longer than that of the donor, which itself is generally much longer than its dynamical time scale."
 This ordering of time scales eusures that the envelope caunot cool cficicutly on he rauster time scale. but remains extended aud eugulfs )oth stellar cores.," This ordering of time scales ensures that the envelope cannot cool efficiently on the transfer time scale, but remains extended and engulfs both stellar cores."
 It mav happen that thermal time scale mass loss frou the donor is still rapid cnouel Oo fori a conimion envelope. but this case cau ouly arise if the svstem is stable against dyvuzuical mass raster. while unsable to thermal time scale mass ransfer.," It may happen that thermal time scale mass loss from the donor is still rapid enough to form a common envelope, but this case can only arise if the system is stable against dynamical mass transfer, while unstable to thermal time scale mass transfer."
 Since the sellar dvuaimical time scales of both donor and accretor are shorter han their thermal time scales. tle prospec arises of a quasistatic como euvelope. that is. of formatioi of a contact binary.," Since the stellar dynamical time scales of both donor and accretor are shorter than their thermal time scales, the prospect arises of a quasistatic common envelope, that is, of formation of a contact binary."
 Such large nunbers of such objecs are known (the W OUMa systems. as examples) that they iust be very oue-lived. evolving in a very difforeit fashion from CE evolution as we lave used that term above.," Such large numbers of such objects are known (the W UMa systems, as examples) that they must be very long-lived, evolving in a very different fashion from CE evolution as we have used that term above."
 We believe that stellar acliabatic mass loss moclels xovile the iuost useful approach to date toward defining the luüts of dvuamical staylity in interacting ünariess essential mput to the construction of binary opulatiou svuthesis models.," We believe that stellar adiabatic mass loss models provide the most useful approach to date toward defining the limits of dynamical stability in interacting binaries, essential input to the construction of binary population synthesis models."
 This work is supported by the National Natural Science. Foundation of China (erant Nos., This work is supported by the National Natural Science Foundation of China (grant Nos.
 10821061. 10973036 aud 2007€D815106). the U.S. National Scicuccl Foundation (grant AST 0106726). the Chinese Academy of Sciences under Crant No.," 10821061, 10973036 and 2007CB815406), the U.S. National Science Foundation (grant AST 0406726), the Chinese Academy of Sciences under Grant No."
 KJCN2-YW-T21. aud the Yunnan Natural Science Foundation (ται No.," KJCX2-YW-T24, and the Yunnan Natural Science Foundation (Grant No."
 OSY10001)., 08YJ041001).
 We thank Philipp Podsiadlowski for insightful conunueuts., We thank Philipp Podsiadlowski for insightful comments.
 We also thank the anomvious referee for his valuable comments that helped us to inprove the paper., We also thank the anonymous referee for his valuable comments that helped us to improve the paper.
excited state are followed by the emission of gamma rays in the range from 1 to 20MeV through de-excitation processes.,"excited state are followed by the emission of gamma rays in the range from 1 to $20\,
\mathrm{MeV}$ through de-excitation processes."
 The spectral structure of these gamma rays is determined both by the composition and the energy spectrum of the energetic particles and by the respective properties of the ambient medium., The spectral structure of these gamma rays is determined both by the composition and the energy spectrum of the energetic particles and by the respective properties of the ambient medium.
" Especially cosmic rays with energies less than 100MeV are suited well to be studied in gamma rays, because for cosmic rays with greater energies the gamma fluxes owing to and collisions followed by πὸ desintegration are expected to be higher than the gamma fluxes resulting from nuclear de-excitations (?).."," Especially cosmic rays with energies less than $100\, \mathrm{MeV}$ are suited well to be studied in gamma rays, because for cosmic rays with greater energies the gamma fluxes owing to and collisions followed by $\pi^0$ desintegration are expected to be higher than the gamma fluxes resulting from nuclear de-excitations \citep{Meneguzzi1975}."
 That is why the observation of gamma-ray lines below 100MeV offers the opportunity of studying astrophysical processes in great detail and of revealing the origin of hadronic cosmic rays in SNRs.," That is why the observation of gamma-ray lines below $100\, \mathrm{MeV}$ offers the opportunity of studying astrophysical processes in great detail and of revealing the origin of hadronic cosmic rays in SNRs."
" The basic ingredients in determining the profile of a gamma-ray line from energetic particle interactions can be summarized as follows: According to ?,, the probability of photon emission per second into solid angle d(cos69)dóo can be written as (the z-axis is chosen in the direction of the incident particle) In the center-of-mass frame, the interaction produces an excited nucleus with recoil velocity in d(cos07)αφ,."," The basic ingredients in determining the profile of a gamma-ray line from energetic particle interactions can be summarized as follows: According to \citet{Ramaty1979}, the probability of photon emission per second into solid angle $d(\cos\theta_0)\:d\phi_0$ can be written as (the $z$ -axis is chosen in the direction of the incident particle) 	 In the center-of-mass frame, the interaction produces an excited nucleus with recoil velocity in $d(\cos\theta_r^*)\:d\phi_r$."
" E represents the energy of the incident particle before the interaction, n; the number density of the target particles."," $E$ represents the energy of the incident particle before the interaction, $n_i$ the number density of the target particles."
" v is the incident particle's velocity, do-/d€?* is the center-of-mass differential cross section, and g is the angular distribution of the resulting gamma rays."," $v$ is the incident particle's velocity, $d\sigma/d\Omega^*$ is the center-of-mass differential cross section, and $g$ is the angular distribution of the resulting gamma rays."
" ¢, and ¢o are azimuth angles measured in the (x, y)-plane, 67 and 6 are polar angles given with respect to the z-axis."," $\phi_r$ and $\phi_0$ are azimuth angles measured in the $(x,y)$ -plane, $\theta_r^*$ and $\theta_0$ are polar angles given with respect to the z-axis."
" To finally determine the gamma-ray spectrum, Eq. (IJ) "," To finally determine the gamma-ray spectrum, Eq. \ref{eq:1}) )"
"can be integrated over cos4"", ¢,, cos) and E by using the MonteCarlo simulation technique."," can be integrated over $\cos\theta_r^*$, $\phi_r$, $\cos\theta_0$ and $E$ by using the MonteCarlo simulation technique."
" Choosing random numbers (uniformly distributed from 0 to 1), the integrations can be carried out by solving for cos67, ¢,, cos05 and E from the equations Here N,(£) is the number of incident particles per unit energy, C is a normalization constant."," Choosing random numbers (uniformly distributed from 0 to 1), the integrations can be carried out by solving for $\cos\theta_r^*$, $\phi_r$, $\cos\theta_0$ and $E$ from the equations Here $N_p(E)$ is the number of incident particles per unit energy, $C$ is a normalization constant."
" The probability of observing gamma rays of energies between E, and Ey+AE, is then proportional to the sum of all angular distributions g for which Εγ is in range.", The probability of observing gamma rays of energies between $E_\gamma$ and $E_\gamma+\Delta E_\gamma$ is then proportional to the sum of all angular distributions $g$ for which $E_\gamma$ is in range.
" For a detailed description of the outlined methods above and a deeper insight into the different reaction types as well as the derivation of line production cross sections, we refer the reader to ? and ? and references therein."," For a detailed description of the outlined methods above and a deeper insight into the different reaction types as well as the derivation of line production cross sections, we refer the reader to \citet{Ramaty1979} and \citet{Kozlovsky2002}
 and references therein."
" To validate the chances for success of the introduced approach concerning Cas A, we first study the exemplary case of the carbon line at 4.4MeV."," To validate the chances for success of the introduced approach concerning Cas A, we first study the exemplary case of the carbon line at $4.4\,
\mathrm{MeV}$."
" Considering a scenario in which the gamma-ray emission of Cas A is modeled by a hadronic fit based on the 2°-decay of accelerated hadrons, the best-fit proton acceleration spectrum is given by Q,(p)«p??."," Considering a scenario in which the gamma-ray emission of Cas A is modeled by a hadronic fit based on the $\pi^0$ -decay of accelerated hadrons, the best-fit proton acceleration spectrum is given by $Q_p(p)\propto p^{-2.3}$."
" The resulting proton energy content of W,=JiowevIeQppdp4x10”erg corresponds to ~2% of the estimated SNR kinetic energy (?).."," The resulting proton energy content of $W_p=\int_{10\,
\mathrm{MeV}/c}Q_pp\,dp=4~\times~10^{49}\, \mathrm{erg}$ corresponds to $\sim2\,
\%$ of the estimated SNR kinetic energy \citep{Abdo2010}."
" By extrapolating the high-energy proton spectrum down to the MeV-range, the gamma-ray flux emitted in the 4.4MeV nuclear de-excitation line can be approximately calculated from where nc~10cm? is the adopted mean density of carbon atoms in the interaction region (cf.?),, v the velocity of the accelerated protons and o the cross section for the inelastic scattering processes."," By extrapolating the high-energy proton spectrum down to the MeV-range, the gamma-ray flux emitted in the $4.4\, \mathrm{MeV}$ nuclear de-excitation line can be approximately calculated from where $n_C\sim 10\, \mathrm{cm^{-3}}$ is the adopted mean density of carbon atoms in the interaction region \citep[cf.][]{Laming2003}, $v$ the velocity of the accelerated protons and $\sigma$ the cross section for the inelastic scattering processes."
" At first glance, line-broadening effects or additional contributions from unresolved gamma-ray lines in heavy nuclei and lines from long-term radioactive nuclei are neglected here."," At first glance, line-broadening effects or additional contributions from unresolved gamma-ray lines in heavy nuclei and lines from long-term radioactive nuclei are neglected here."
" Using d=3.4kpc (see above) and the cross section for the reaction ?C(p,p')?C* given by ? yields a flux of ~1079cm?s! at 4.4MeV."," Using $d=3.4\, \mathrm{kpc}$ (see above) and the cross section for the reaction $^{12}\mathrm{C}(p,p')^{12}\mathrm{C}^*$ given by \citet{Ramaty1979} yields a flux of $\sim 10^{-6}\, \mathrm{cm^{-2}s^{-1}}$ at $4.4\,\mathrm{MeV}$."
" This flux value is close to the sensitivity limit of the COMPTEL experiment: Following the analysis of ? concerning the MeV continuum emission from Cas A, only an upper limit of 1.4x10?cms! was obtained in the 3—10MeV energy range."," This flux value is close to the sensitivity limit of the COMPTEL experiment: Following the analysis of \citet{Strong2000} concerning the MeV continuum emission from Cas A, only an upper limit of $1.4\times 10^{-5}\, \mathrm{cm^{-2}s^{-1}}$ was obtained in the $3-10\, \mathrm{MeV}$ energy range."
" According to ?,, the COMPTEL line sensitivity is indicated with ~10?cm?s!."," According to \citet{Iyudin1995}, the COMPTEL line sensitivity is indicated with $\sim
10^{-5}\,\mathrm{cm^{-2}s^{-1}}$."
" So only a future gamma-ray mission with enhanced sensitivity in the MeV range will be able to obtain final results concerning the detection of de-excitation lines in Cas A. To compute the whole nuclear de-excitation spectrum for the specific case of Cas A, we used the Monte-Carlo code developed by ? jramaty/code(see also Sect. [2))."," So only a future gamma-ray mission with enhanced sensitivity in the MeV range will be able to obtain final results concerning the detection of de-excitation lines in Cas A. To compute the whole nuclear de-excitation spectrum for the specific case of Cas A, we used the Monte-Carlo code developed by \citet{Ramaty1979} (see also Sect. \ref{sec:2}) )."
" Besides the ingredients already mentioned.htm in the previous paragraph, the calculations take into account the following assumptions: The acceleration scenario for cosmic rays is assigned to the reverse-shock side and the chemical composition of the accelerated cosmic rays is inferred from ?.."," Besides the ingredients already mentioned in the previous paragraph, the calculations take into account the following assumptions: The acceleration scenario for cosmic rays is assigned to the reverse-shock side and the chemical composition of the accelerated cosmic rays is inferred from \citet{Engelmann1990}."
" The composition of the ambient gas, in fact a mixture of both massive Wolf-Rayet winds and subsequent supernova ejecta (cf.?),, is described by the use of results from X-ray spectroscopy (cf."," The composition of the ambient gas, in fact a mixture of both massive Wolf-Rayet winds and subsequent supernova ejecta \citep[cf.][]{Lingenfelter2007}, is described by the use of results from X-ray spectroscopy (cf."
 Table[I))., Table \ref{tab:1}) ).
 The abundances of H and He are deduced from optical measurements by ?.., The abundances of H and He are deduced from optical measurements by \citet{Chevalier1979}. .
" The resulting total mass is in line with the Wolf-Rayet-supernova scenario, i.e. there is no room for additional amounts of hydrogen that would enhance the pion vs. the nuclear de-excitation yields."," The resulting total mass is in line with the Wolf-Rayet-supernova scenario, i.e. there is no room for additional amounts of hydrogen that would enhance the pion vs. the nuclear de-excitation yields."
 Unresolved gamma-rays from heavy nuclei and lines from, Unresolved gamma-rays from heavy nuclei and lines from
!oower law BMare comparableI| to the errors iu the observed flux deusitics (Fig.,power law are comparable to the errors in the observed flux densities (Fig.
. 2). a spectral iudex. of 3.2.0.61 has been adopted for the whole frequency range between SO MIIZ/— aud 10.7 GIIz.," 2), a spectral index of 0.64 has been adopted for the whole frequency range between 80 MHz and 10.7 GHz."
 Our polurized iuteussitv map has an ruis., Our rized sity map has an r.m.s.
 noise of 0.18 ινναι shows two asviunietrie lobes with, noise of 0.18 mJy/b.a.. It shows two asymmetric lobes with
with a period of 0.24821 d) are shown in the bottom panels of Fig.,with a period of 0.24821 d) are shown in the bottom panels of Fig.
 3. 4 and 5.," 3, 4 and 5."
 We also observed the svstem in the 2 band. brielly on August 14 and 18. (only 6 images taken).," We also observed the system in the $B$ band briefly on August 14 and 18, (only 6 images taken)."
 The 2 brightness (not shown) varied between 18.5 anc 20.0 mae during our observations., The $B$ brightness (not shown) varied between 18.5 and 20.0 mag during our observations.
 The photometric data in dilferent bands were not taken simultaneously. therefore. we cannot calculate the colour excess without interpolations: however. the rapid decline in brightness and the sparse sampling during our observations do not permit a reliable interpolation.," The photometric data in different bands were not taken simultaneously, therefore we cannot calculate the colour excess without interpolations; however, the rapid decline in brightness and the sparse sampling during our observations do not permit a reliable interpolation."
 The detection of Tvpe-E: N-rav bursts. implies that the compact star in RATE 058 is à neutron star., The detection of Type-I X-ray bursts implies that the compact star in RXTE $-$ 058 is a neutron star.
 The distance determined. by assuming an Edclington Lux during the A-ray burst. is about. Lt kpe (oman 11999)., The distance determined by assuming an Eddington flux during the X-ray burst is about 14 kpc (Homan 1999).
 Llowever. the peak flux. during the burst. might not be at the Ecldineton limit.," However, the peak flux during the burst might not be at the Eddington limit."
 More often X-ray bursts are weaker. Le. the peak [uminosities are sub-ISddington (sce LLewin. van Paradijs Taam 1995).," More often X-ray bursts are weaker, i.e. the peak luminosities are sub-Eddington (see Lewin, van Paradijs Taam 1995)."
" When the persistent. Hux is high (which. indicates a high accretion rate). the hvdrogen-helium rich matter on the surface of the neutron star might be heated to the ignition temperature for the thermonuclear reaction such that. ""premature"" bursts"," When the persistent flux is high (which indicates a high accretion rate), the hydrogen-helium rich matter on the surface of the neutron star might be heated to the ignition temperature for the thermonuclear reaction such that “premature” bursts"
 , 
 p!) 0!) ο p! pl e! ~25 , $^-$$^+$ $^-$ $^+$ $\sim162.5$ $\beta = v/c = 0.26$ $^-$ $^+$ $^-$ $^+$ $^-$ $^+$ $\sim25$ 
"In the nonrotating case, we find three peaks at lower frequency than the f-mode in the frequency spectrum; we identify these as magnetically-restored modes.","In the nonrotating case, we find three peaks at lower frequency than the $f$ -mode in the frequency spectrum; we identify these as magnetically-restored modes."
" We label these modes ai,a2 and a3 based on the amplitude of their peaks, from strongest to weakest."," We label these modes $a_1,a_2$ and $a_3$ based on the amplitude of their peaks, from strongest to weakest."
" We expect a-mode frequencies to be proportional to the Alfvénn speed ca=B/./4rp and hence scale roughly linearly with B; this is borne out in our results, shown in figure 7.."," We expect $a$ -mode frequencies to be proportional to the Alfvénn speed $c_A=B/\sqrt{4\pi\rho}$ and hence scale roughly linearly with $\Bav$; this is borne out in our results, shown in figure \ref{amodes_B}."
 We can gain some understanding about the eigenfunction structure of these a-modes by comparison with the behaviour of the code for inertial modes (in unmagnetised stars)., We can gain some understanding about the eigenfunction structure of these $a$ -modes by comparison with the behaviour of the code for inertial modes (in unmagnetised stars).
" In this case we find that the lowest-lo modes have the highest-amplitude peaks in frequency space — these modes are excited more strongly because of the finite resolution of the numerical grid, combined with the low-l initial data we use."," In this case we find that the $l_0$ modes have the highest-amplitude peaks in frequency space — these modes are excited more strongly because of the finite resolution of the numerical grid, combined with the $l$ initial data we use."
" This provides us with a useful rough diagnostic to identify a-modes: we suggest thatthe eigenfunction of the strong peak αι contains lower Yj, contributions than the a2 or a3 modes.", This provides us with a useful rough diagnostic to identify $a$ -modes: we suggest thatthe eigenfunction of the strong peak $a_1$ contains lower $Y_{lm}$ contributions than the $a_2$ or $a_3$ modes.
" In a perfectly conducting medium, like the model NS considered in this paper, magnetically-restored oscillations can occur in a continuous band of frequencies rather than being discrete global modes."," In a perfectly conducting medium, like the model NS considered in this paper, magnetically-restored oscillations can occur in a continuous band of frequencies rather than being discrete global modes."
" This result was established by analytic work for an incompressible medium (see, e.g., Goossensetal. (1985))) and more recent numerical work has suggested that the axisymmetric oscillations of compressible stars may form a continuum too (SotaniColaiudaetal. 2009).."," This result was established by analytic work for an incompressible medium (see, e.g., \citet{goos_cont}) ) and more recent numerical work has suggested that the axisymmetric oscillations of compressible stars may form a continuum too \citep{sotani_ax,cerda,colaiuda}."
" It is known, however, that dissipative effects like viscosity and resistivity can act to remove the continuum (e.g. Irelandetal. (1992)))."," It is known, however, that dissipative effects like viscosity and resistivity can act to remove the continuum (e.g. \citet{ireland}) )."
" 'To test for a mode continuum, we look at the oscillation frequencies of perturbed quantities at different points within the star."," To test for a mode continuum, we look at the oscillation frequencies of perturbed quantities at different points within the star."
 If our system has discrete global modes we expect all these local oscillation frequencies to be equal; if there is a continuous mode spectrum then oscillation frequencies will be position-dependent., If our system has discrete global modes we expect all these local oscillation frequencies to be equal; if there is a continuous mode spectrum then oscillation frequencies will be position-dependent.
" From our evolutions we find the former: mode frequencies at different points within the star are equal, within the resolution dictated by the length of our evolutions (of the order 1%))."," From our evolutions we find the former: mode frequencies at different points within the star are equal, within the resolution dictated by the length of our evolutions (of the order )."
" Whilst this appears to contradict recent studies on magnetar QPOs that found evidence for a mode continuum (among them Sotanietal.(2008),, Colaiudaetal.(2009) and Cerdá-Duránetal. (2009))), it should be emphasised that these studies are not quite comparable."," Whilst this appears to contradict recent studies on magnetar QPOs that found evidence for a mode continuum (among them \citet{sotani_ax}, \citet{colaiuda} and \citet{cerda}) ), it should be emphasised that these studies are not quite comparable."
" For one, we study non-axisymmetric oscillations, rather than the m=0 modes in these earlier studies; in addition we have only looked at polar-led modes, in contrast with the axial oscillations of the other papers."," For one, we study non-axisymmetric oscillations, rather than the $m=0$ modes in these earlier studies; in addition we have only looked at polar-led modes, in contrast with the axial oscillations of the other papers."
" Our work is, however, in agreement with the study of polar Alfvénn modes by Sotani&Kokkotas(2009),, who also found a discrete oscillation spectrum."," Our work is, however, in agreement with the study of polar Alfvénn modes by \citet{sotani_pol}, who also found a discrete oscillation spectrum."
" Next we consider the mode spectrum of a rotating star with a poloidal magnetic field, but let us first recall our results on toroidal-field oscillation modes from Lander,Jones&Passamonti(2010)."," Next we consider the mode spectrum of a rotating star with a poloidal magnetic field, but let us first recall our results on toroidal-field oscillation modes from \citet{tor_mode}."
". In this earlier work we found hybrid modes, whose character was Alfvénn-like for slow rotation and inertial-like in more rapidly-rotating stars 2010),, so that their character depended on the ratio of magnetic to kinetic energy M/T' — we expect"," In this earlier work we found hybrid magneto-inertial modes, whose character was Alfvénn-like for slow rotation and inertial-like in more rapidly-rotating stars \citep{tor_mode}, , so that their character depended on the ratio of magnetic to kinetic energy $M/T$ — we expect"
"Following ?).. the radio spectral Inmiinositv in the opticallv-thin regime is given by where 2,—ce is the shock-wave radius. D is the strength of the magnetic field: and the constants 1οι. 56s. andοςi can be found in ?)..","Following \citet{chevalier98}, the radio spectral luminosity in the optically-thin regime is given by and the synchrotron-self-absorbed luminosity iswhere $R_{s}=v_s t$ is the shock-wave radius, $B$ is the strength of the magnetic field; and the constants $c_1$, $c_5$, and$c_6$ can be found in \cite{pacholczyk70}. ."
" Ng0 can be straightforwardly5 shown to be c,/(SxegMP(p—κο)7.", $N_0$ can be straightforwardly shown to be $\epsilon_e/(8\pi\epsilon_B)B^2(p-2)(\gamma_{\rm min}m_ec^2)^{p-2}$.
 Equation 2. can be simplified to vield Given (hat (the earliest observation(s) were undertaken only a day. after the explosion it is prudent to check if thereis significant [ree-Iree absorption., Equation \ref{eq:Lthin1} can be simplified to yield Given that the earliest observation(s) were undertaken only a day after the explosion it is prudent to check if thereis significant free-free absorption.
" The free-Iree optical depth is where T=10'T, is the electron temperature (in degreesKelvin). ipii is the frequency in GIIz and EM is the emission measure. the integral of n? along the line of sight. and in units of ""ppc."," The free-free optical depth is where $T=10^4T_4$ is the electron temperature (in degrees, $\nu_{\rm GHz}$ is the frequency in GHz and EM is the emission measure, the integral of $n_e^2$ along the line of sight, and in units of $^{-6}$ pc."
" The emission measure from a radius. sav. 7, ἰς infinity is where n, is (he density of electrons at radius r,."," The emission measure from a radius, say, $r_*$ to infinity is where $n_*$ is the density of electrons at radius $r_*$."
 Putting these equations together the Iree-Iree optical depth is For PTFILIkly. the photospheric velocity is e=2xLO’cmss '.," Putting these equations together the free-free optical depth is For PTF11kly, the photospheric velocity is $v=2\times 10^9\,$ $^{-1}$ ."
 The blast wave will at least have (his velocity ancl likely twice this value (???)..," The blast wave will at least have this velocity and likely twice this value \citep{chevalier+fransson06, fryer+07, soderberg+10}. ."
 For representative values ο... we=Ll. 09= d) we lind the following optical depth atthe first epoch of our observations:," For representative values $\dot M=3\times
10^{-7}\,M_\odot\,{\rm yr}^{-1}$ , $w_7=1$, $v_9=4$ ) we find the following optical depth atthe first epoch of our observations:"
Low surface brightness (LSB) galaxies are usually defined: as galaxies with D-band central surface brightness fry>23.5 mag arcsec7.,"Low surface brightness (LSB) galaxies are usually defined as galaxies with B-band central surface brightness $\mu_{0,B} > 23.5$ mag $\hbox{ arcsec}^{-2}$."
 The lower central surface brightness ol LSB galaxies makes them difficult to detect against the noise of the night sky., The lower central surface brightness of LSB galaxies makes them difficult to detect against the noise of the night sky.
 Therefore. thev are svstematically absent in many optical galactic surveys.," Therefore, they are systematically absent in many optical galactic surveys."
 Ii recent. vears. improved techniques to detect LSBs have been developed. and the bulk properties of LSBs are now," In recent years, improved techniques to detect LSBs have been developed, and the bulk properties of LSBs are now"
higher rate than the rate of its orbital motion.,higher rate than the rate of its orbital motion.
 In the course of millions to billions of vears. (he secular terms of the tidal torque cause the planet to spin down.," In the course of millions to billions of years, the secular terms of the tidal torque cause the planet to spin down."
 The tidal bulges moving across (he planet at different Irequencies result in a gradual loss of kinetic energy. (hrough friction ancl heating., The tidal bulges moving across the planet at different frequencies result in a gradual loss of kinetic energy through friction and heating.
 The energy dissipation rate is normally so slow. (hat most of the major planets in the Solar svstem still rotate faster (han thev revolve around the Sun. with the exception of Venus with its slow retrograde rotation and Mercury. which is in the 3:2 spin- resonance (Pettenegill&Dyce1965).," The energy dissipation rate is normally so slow, that most of the major planets in the Solar system still rotate faster than they revolve around the Sun, with the exception of Venus with its slow retrograde rotation and Mercury, which is in the 3:2 spin-orbit resonance \citep{pett}."
. Presumably. the planet. traversed a number of higher-order resonances before it reached this state.," Presumably, the planet traversed a number of higher-order resonances before it reached this state."
 The ultimate. and the most stable. state for a rotating planet subject to tidal forces is the 111 resonance. when the rotation rate is equal to the orbital rate. and (he planet is always pointing with its most elongated dimension toward the star.," The ultimate, and the most stable, state for a rotating planet subject to tidal forces is the 1:1 resonance, when the rotation rate is equal to the orbital rate, and the planet is always pointing with its most elongated dimension toward the star."
 The dissipation of the energv of rotation also diminishes the obliquity of the planets equator. eradually aligning (he axes of rotation and of the orbit.," The dissipation of the energy of rotation also diminishes the obliquity of the planets equator, gradually aligning the axes of rotation and of the orbit."
 Mercurys dynamical evolution has been much faster than Chat of other solar planets. because 1) it is closer to the Sun; 2) its orbital eccentricity varied in a relatively wide range and has been higher than the eccentricity of the other close-in planets.," Mercury's dynamical evolution has been much faster than that of other solar planets, because 1) it is closer to the Sun; 2) its orbital eccentricity varied in a relatively wide range and has been higher than the eccentricity of the other close-in planets."
 The importance of eccentricity for Mercurys chaotic evolution was emphasized by Correia&Laskar(2004.2009).. who revised upward the original estimate of the probability of capture to the present 3:2 resonance at 1966)..," The importance of eccentricity for Mercury's chaotic evolution was emphasized by \citet{corla04,corla09}, who revised upward the original estimate of the probability of capture to the present 3:2 resonance at \citep{gold}."
 Mercury can serve as a good model for smaller mass. rocky exoplanets. especially those orbiting M cdwarfs in their habitable zones.," Mercury can serve as a good model for smaller mass, rocky exoplanets, especially those orbiting M dwarfs in their habitable zones."
 Although the exact rheology of exoplanets will remain a matter of speculation for the foreseeable future. it seems reasonable to adopt the parameters and models obtained for the Earth and the Moon.," Although the exact rheology of exoplanets will remain a matter of speculation for the foreseeable future, it seems reasonable to adopt the parameters and models obtained for the Earth and the Moon."
 The objective of this paper is to investigate (he circumstances of the transition of a Mercury-like planet with an rheologv through a hieh order spin orbit resonance., The objective of this paper is to investigate the circumstances of the transition of a Mercury-like planet with an Earth-like rheology through a high order spin orbit resonance.
 In (his case. the widely accepted approximations for the value of dal torque in the vicinity of a resonance are not applicable.," In this case, the widely accepted approximations for the value of tidal torque in the vicinity of a resonance are not applicable."
 Furthermore. the oscillatory terms of the force can not be neglected.," Furthermore, the oscillatory terms of the force can not be neglected."
 We emplov high-order expansions of the torque in harmonics of (dal frequency. ancl powers of eccentricity. and a relation for the Love number as a function of tidal Irequency in terms of real and imagimary compliances(82).," We employ high-order expansions of the torque in harmonics of tidal frequency and powers of eccentricity, and a relation for the Love number as a function of tidal frequency in terms of real and imaginary 2)."
 The resulting differential equation of second order. which includes both the tidal ancl (axial torque components. is integrated will a step much smaller than the period of rotation. with the current best estimates lor Mercury (83).," The resulting differential equation of second order, which includes both the tidal and triaxial torque components, is integrated with a step much smaller than the period of rotation, with the current best estimates for Mercury 3)."
 With the current. value of eccentricitv (e= 0.20563). (he planet traverses the 2:1 resonance wilh an estimated probability of 0.77. and is always captured in (he 3:2 resonance.," With the current value of eccentricity $e=0.20563$ ), the planet traverses the 2:1 resonance with an estimated probability of 0.77, and is always captured in the 3:2 resonance."
 The (ransiGion is very last. acconpanied by a significant step-down in the average rotation rate.," The transition is very fast, accompanied by a significant step-down in the average rotation rate."
 In 84.. more integrations are performed with (he initial rate set to exactly the 2:1 resonance and with various initial phase angles.," In \ref{con.sec}, more integrations are performed with the initial rate set to exactly the 2:1 resonance and with various initial phase angles."
 It is revealed (hat such a planet inserted in resonance almost always stavs in it., It is revealed that such a planet inserted in resonance almost always stays in it.
 The actual passage through the resonance can only occur through a (ny area of the phase, The actual passage through the resonance can only occur through a tiny area of the phase
broad. diffuse jet o the north (PA ~57).,"broad, diffuse jet to the north (PA $\approx
-5$ )."
 The oClue auele of the jet is wide (“55° )., The opening angle of the jet is wide $\sim$ ).
 The core is uuxsolved iu a deep VLA map (Figure 18)): however. very faint extended fiux is dotected to tre north (PA =57 ) and south (PA z|175 ) of the core.," The core is unresolved in a deep VLA map (Figure \ref{fig-20}) ); however, very faint extended flux is detected to the north (PA $\approx -5$ ) and south (PA $\approx +175$ ) of the core."
 Thus the VLBA jet appears to be well alieued wih the northern lobe., Thus the VLBA jet appears to be well aligned with the northern lobe.
" LES 2311)511: The VLBA map (Figure 19)) sLOWS a jet extending to he southeas (PA = |115): it appears to be well-collimated for abou 10 parsecs before bending 25""to the south aud broadeniie iuto a cone with a ~35 oopening angle.", 1ES 2344+514: The VLBA map (Figure \ref{fig-21}) ) shows a jet extending to the southeast (PA = +145); it appears to be well-collimated for about 10 parsecs before bending to the south and broadening into a cone with a $\sim$ opening angle.
 A deep VLA map (Fieure 20)) detects chussion exteudiie to the cas (PA = LO5°)) in a ccone., A deep VLA map (Figure \ref{fig-22}) ) detects emission extending to the east (PA = ) in a cone.
 The ffor this source is at least[07., The for this source is at least.
. Previous studies of the VLBI structure of DL Lac objects. nearly all of which were of LBLs. have shown that luge nsaiennmenut angles are common im these objects (Ixolleiucdetal.1992:Appl1996:Cassioetal. 2002).," Previous studies of the VLBI structure of BL Lac objects, nearly all of which were of LBLs, have shown that large misalignment angles are common in these objects \citep{kol92,app96,cas02}."
. This is to be expected in sources that are seen close to fie line of sight. as projection effects will maenity the aparent distortion from iutriusic ends aud complex structure within these jets.," This is to be expected in sources that are seen close to the line of sight, as projection effects will magnify the apparent distortion from intrinsic bends and complex structure within these jets."
 Measuring the pirsec-cale jet PAs in BL Lacs is very difficult or several reasons., Measuring the parsec-scale jet PAs in BL Lacs is very difficult for several reasons.
 May. of these objects show jets whic1i bene within several parsecs from the core: aud lh niulv cases he cussion where the beudiug οςcurs Is very faint., Many of these objects show jets which bend within several parsecs from the core; and in many cases the emission where the bending occurs is very faint.
 Thus the neasured PA is very sensiive to the linear resolution aud the sensitivity of the observations. which of course depeud ou the observed waveleneth. the distance to the objec. the (αν 0) coverage aud he overall quality ο the observations.," Thus the measured PA is very sensitive to the linear resolution and the sensitivity of the observations, which of course depend on the observed wavelength, the distance to the object, the $u,v$ ) coverage and the overall quality of the observations."
 The parsec-scale jcts secu 1u Alku 501 and 1Jw 1jlr215 are goo exanrples of this xoblei (Conway&Wrobel1995:Canmzdaoeal.1990:C'assaroetal.2002).," The parsec-scale jets seen in Mkn 501 and 1Jy 1147+245 are good examples of this problem \citep{con95,gab99,cas02}."
 . Adding anotler dimesion to the xoblem. there is evicence that the jet trajectorv for some of these objects cau claice on short tiLLescaes: e.g.. 1Jv 95/35|178 (Comeetal.2001).," Adding another dimension to the problem, there is evidence that the jet trajectory for some of these objects can change on short timescales; e.g., 1Jy 0735+178 \citep{gom01}."
. Like the VLBI iua])5. he measured jet PAs in the VLA naps are also dependeif on sensitivity iux 1050lution: e.g.àY the measured PAs can differ by as nuc ras ybased upon the resolution of the maps for LJv 08711125 aud τν 2131021 (Cassaroetal.2002:Rector&Stocke 2002).," Like the VLBI maps, the measured jet PAs in the VLA maps are also dependent on sensitivity and resolution; e.g., the measured PAs can differ by as much as based upon the resolution of the maps for 1Jy 0814+425 and 1Jy 2131–021 \citep{cas02,rec02}."
. Additionallv. tje kpe-scale structire of these sources are usually highly distorted. often with a ~πα. that surounds the core with uo clear PA.," Additionally, the kpc-scale structure of these sources are usually highly distorted, often with a “halo"" that surrounds the core with no clear PA."
 Tjus. d is not surrising that we see such a range of vvalues. evel without considering the οιις1111159 ΠΠ i physical scales between the VLA iux VLDI mms aud the physical envirouments through which a jet propagates frou the core to kiloparsec scales.," Thus, it is not surprising that we see such a range of values, even without considering the enormous difference in physical scales between the VLA and VLBI maps and the physical environments through which a jet propagates from the core to kiloparsec scales."
 Despite he uncertaimties iuhereut iu such 1uneasurenments. we have measured parsec- ando kpc-SCe jet posiion augles for our IIBE sample.," Despite the uncertainties inherent in such measurements, we have measured parsec- and kpc-scale jet position angles for our HBL sample."
 We imclude the four IIBLs observed by INolleaardetal.(1996) iuto our IIBL sample., We include the four HBLs observed by \citet{kol96} into our HBL sample.
 For comparison. we cousicer all of the LBLs in the ¢‘ommplete 1Jy sample (Stickeletal.1991). for which lieh «vuaic-range VLA maps exist (Rector&Stocke2001.2002.andreferencestherein). aud that have been studied in detail with VEDI techniques1998).," For comparison, we consider all of the LBLs in the complete 1Jy sample \citep{sti91} for which high dynamic-range VLA maps exist \citep[and references
therein]{rec01,rec02} and that have been studied in detail with VLBI techniques."
. For cosistency. woe measure jet position angles frou these ma5 using the methodology described below rather than use published values.," For consistency, we measure jet position angles from these maps using the methodology described below rather than use published values."
 There are ouly a QW cases WUrere the jet PA is Πο., There are only a few cases where the jet PA is unambiguous.
 Thus t16 parsec- aud spe-scale jet posllon angles were measured with the folowing moethodokSN., Thus the parsec- and kpc-scale jet position angles were measured with the following methodology.
 For both the VLA iux VLBI maps the PA is iieastred from the core through contiguous jet components that are more than 30 etectious., For both the VLA and VLBI maps the PA is measured from the core through contiguous jet components that are more than $\sigma$ detections.
 Iu some cases the PA on VLBI scales is 1ncertaiu Όσσαse the jet is diffuse with a broad openiis angle (6.9. LES 08061521 aud LES 1959|650).," In some cases the PA on VLBI scales is uncertain because the jet is diffuse with a broad opening angle (e.g., 1ES 0806+524 and 1ES 1959+650)."
 In tjese cases the PA is measured ceiher down the ceuer of the jet or along t1¢ brightest cotours within the jet., In these cases the PA is measured either down the center of the jet or along the brightest contours within the jet.
" Also. there are four objects in our ΠΡΙ, saluple (LES 00:331595. LES 0111009. LES 17111196 and LES 2311511) that have bright. wellcollimated arsec-scale jets close to the core ae show evidence of vending furtier from the core."," Also, there are four objects in our HBL sample (1ES 0033+595, 1ES 0414+009, 1ES 1741+196 and 1ES 2344+514) that have bright, well-collimated parsec-scale jets close to the core and show evidence of bending further from the core."
 However. the cussion where the bending may be occurie is faint: and it is rot clear whether the jet is actually vending or simply xoadenime.," However, the emission where the bending may be occuring is faint; and it is not clear whether the jet is actually bending or simply broadening."
 For this reason the jet PA is nieasurec from he bright jet components ucar the core., For this reason the jet PA is measured from the bright jet components near the core.
 In three «ot the our objects the kpe-scale structure is well aligned with hese measurements: the exception is LES 23111511. for which no measurement of the PA. will alien it with he VLÀ Αι.," In three of the four objects the kpc-scale structure is well aligned with these measurements; the exception is 1ES 2344+514, for which no measurement of the $_{\rm pc}$ will align it with the VLA $_{\rm kpc}$."
 Thus it is possible that the jets iu hese objects are bending aud may not as well aieued as Dueasured., Thus it is possible that the jets in these objects are bending and may not as well aligned as measured.
 The better aliguiment of the parsec-scale jet near the core with the kpc-scale jets in these sources may be the result of collisious with clense clouds of eas near the core., The better alignment of the parsec-scale jet near the core with the kpc-scale jets in these sources may be the result of collisions with dense clouds of gas near the core.
 For a powerfu jet. such collisions are uot effective at deflecting the jet im a coherent manner: however they may result iu |eniporary distortions of the jets ou timescales of <10! vr (DeYoung1991:Wane.Witta&Πουαα 2000).," For a powerful jet, such collisions are not effective at deflecting the jet in a coherent manner; however they may result in temporary distortions of the jets on timescales of $< 10^7$ yr \citep{dey91,wan00}."
. Tius. df is possible that the observed VLDI inorphologies could be explained by an oftf-ceuter collision with a dense eas cloud LO20 parsecs from the core which distorts he observed PA at this distance but doesn't affect the loie-tera propagation of the jet to kpe distances.," Thus, it is possible that the observed VLBI morphologies could be explained by an off-center collision with a dense gas cloud 10–20 parsecs from the core which distorts the observed PA at this distance but doesn't affect the long-term propagation of the jet to kpc distances."
 It is worth noting that IIoehetal.(2002) fiud significant PA differenees between inner avl outer VLBI jet components in a siuuple of oboe-donmirated quasars. wherein the outer VLDI jet conmpouents are better aligned with the kilo]xursec-scale jets.," It is worth noting that \citet{hou02} find significant PA differences between inner and outer VLBI jet components in a sample of lobe-dominated quasars, wherein the outer VLBI jet components are better aligned with the kiloparsec-scale jets."
 This suggests that. in quasars at least. jcTS nav odisort or bexd close to the core before becomο welblcollinated further from the core.," This suggests that, in quasars at least, jets may distort or bend close to the core before becoming well-collimated further from the core."
 The comparison is Inuited ]OCATISE Casar jets are of much higher power: :ad due to the much lugher redshift of their quasar sani αν ltic VLBI naps in Houghetal.(2002) are studvine larger plysical scales by a factor of 10.," The comparison is limited because quasar jets are of much higher power; and due to the much higher redshift of their quasar sample $z>1$ ), the VLBI maps in \citet{hou02} are studying larger physical scales by a factor of $\sim$ 10."
 Also. obe-domnated quasar jets are seeu at large angeles to the line of sight. aud herefore do not suffer from projectio1 effects to neailv the degree as BL Lac objects.," Also, lobe-dominated quasar jets are seen at large angles to the line of sight, and therefore do not suffer from projection effects to nearly the degree as BL Lac objects."
" Tn all of the resolved VLBI maps jet structure is apparent: however fιο VLA uaps reveal that many of these sources have a “halo” uorphologw. Ίνοι, extended Cluission that surrounds the core with no clear jet."," In all of the resolved VLBI maps jet structure is apparent; however the VLA maps reveal that many of these sources have a “halo"" morphology, i.e., extended emission that surrounds the core with no clear jet."
 For these objects thο PA is measured to the brightest “hotspot” within the lobe: aid for objects which have two distinct lobes and no clear jet. the PA is measured to the lobe most likely associated with the parsec-scale," For these objects the PA is measured to the brightest “hotspot"" within the lobe; and for objects which have two distinct lobes and no clear jet, the PA is measured to the lobe most likely associated with the parsec-scale"
version of MOOG (?) and Kurucz model atmospheres which include overshooting (?)..,version of MOOG \citep{sneden1973} and Kurucz model atmospheres which include overshooting \citep{castelli1997}.
 These authors estimated the error on logg to be 0.22 dex from the scatter found in a comparison with literature values., These authors estimated the error on $\log g$ to be 0.22 dex from the scatter found in a comparison with literature values.
 A detailed description of the stellar parameters for individual stars and a comparison with literature values are available in ? and is therefore omitted here., A detailed description of the stellar parameters for individual stars and a comparison with literature values are available in \citet{hekker2007} and is therefore omitted here.
" In Fig. 3,,"," In Fig. \ref{klogg},"
 we show half of the peak-to-peak value of the observed radial velocity variations as a function of logg for K giants in our sample., we show half of the peak-to-peak value of the observed radial velocity variations as a function of $\log g$ for K giants in our sample.
" A clear trend is visible between increasing radial velocity variations in single stars, and decreasing logg, which provides a strong indication that, at least for a large fraction of stars in our sample, the observed radial velocity variations are induced by a mechanism intrinsic to the star."," A clear trend is visible between increasing radial velocity variations in single stars, and decreasing $\log g$, which provides a strong indication that, at least for a large fraction of stars in our sample, the observed radial velocity variations are induced by a mechanism intrinsic to the star."
 This trend is present for stars with random as well as stars with periodic radial velocity variations., This trend is present for stars with random as well as stars with periodic radial velocity variations.
" Also, nearly all stars with periodic radial velocity variations and logg>1.6 are located above the fit in Fig. 3.."," Also, nearly all stars with periodic radial velocity variations and $\log g \geq 1.6$ are located above the fit in Fig. \ref{klogg}."
" Seven single stars have a higher radial velocity variation than expected based on their logg value, tthey are situated more than 3.5c above the best fit for the relation obtained for single stars."," Seven single stars have a higher radial velocity variation than expected based on their $\log g$ value, they are situated more than $3.5\sigma$ above the best fit for the relation obtained for single stars."
 These stars are indicated with arrows in Fig. 3.., These stars are indicated with arrows in Fig. \ref{klogg}.
" The radial velocity variation observed for HIP53229 may be due to a stellar companion in a wide orbit, with a period much longer than the observation time span."," The radial velocity variation observed for HIP53229 may be due to a stellar companion in a wide orbit, with a period much longer than the observation time span."
" Due to this long period the companion mass, and, therefore, the (sub-)stellar nature, is still very uncertain."," Due to this long period the companion mass, and, therefore, the (sub-)stellar nature, is still very uncertain."
 HIP33152 is classified as a supergiant., HIP33152 is classified as a supergiant.
" The observed radial velocity variations for HIP80693, HIP36616, and HIP88048 can be fitted with two Keplerian orbits, while HIP75458 can be explained by an eccentric sub-stellar companion (?) and an additional linear trend, indicating a companion in a wide orbit."," The observed radial velocity variations for HIP80693, HIP36616, and HIP88048 can be fitted with two Keplerian orbits, while HIP75458 can be explained by an eccentric sub-stellar companion \citep{frink2002} and an additional linear trend, indicating a companion in a wide orbit."
 HIP34693 can be fitted very accurately with a Keplerian orbit of a single nearly sinusoidal sub-stellar companion., HIP34693 can be fitted very accurately with a Keplerian orbit of a single nearly sinusoidal sub-stellar companion.
" In order to investigate the simultaneous occurrence of sub- companions and oscillations in giants, the best Keplerian"," In order to investigate the simultaneous occurrence of sub-stellar companions and oscillations in giants, the best Keplerian"
density of the galaxies (7%).,density of the galaxies $7\%$ ).
 The quoted errors are at the le level., The quoted errors are at the $1\sigma$ level.
 The two most notable features of our derived. LEs are he svstematic variation of the faint end slope (a) and the characteristic magnitude (A5) with spectral type., The two most notable features of our derived LFs are the systematic variation of the faint end slope $\alpha$ ) and the characteristic magnitude $M^*$ ) with spectral type.
 The faint end slope steepens significantly [rom à=0.54 for the most owsive star-forming galaxies CEvpe 1) to a=1.50 for he most active galaxies (Type 4)., The faint end slope steepens significantly from $\alpha=-0.54$ for the most passive star-forming galaxies (Type 1) to $\alpha=-1.50$ for the most active galaxies (Type 4).
" On the other hand the characteristic magnitude becomes svstematically fainter as we σο [rom the most passive CA5log,,(h)— 19.58) ο active CAL?Slog)(fr)=— 19.15) star-lorming galaxies.", On the other hand the characteristic magnitude becomes systematically fainter as we go from the most passive $M^*-5\log_{10}(h)= -19.58$ ) to active $M^*-5\log_{10}(h) = -19.15$ ) star-forming galaxies.
 These results agree with previous measurements in that the ate-type galaxies are systematically fainter than their ype counterparts., These results agree with previous measurements in that the late-type galaxies are systematically fainter than their early-type counterparts.
" Note that our results do not change much if we exclude our correction for the errors in our 6, magnitudes 1.05 0.06. Ae—0.02. 0.05)."," Note that our results do not change much if we exclude our correction for the errors in our $\bj$ magnitudes $\Delta M^*= 0.05-0.06$ , $\Delta \alpha= 0.02-0.05$ )."
" The fact that the Schechter function is not a good fit to he data over the entire Ad), magnitude range is mostly due oan over- CEvpe 1) or under- CIEvpe 4) abundance of faint objects relative to bright objects.", The fact that the Schechter function is not a good fit to the data over the entire $M_{\bj}$ magnitude range is mostly due to an over- (Type 1) or under- (Type 4) abundance of faint objects relative to bright objects.
 his is particularly. true of the passive (Lype 1) sample of galaxies for which there is avery significant increase in the predicted number density of faint galaxies., This is particularly true of the passive (Type 1) sample of galaxies for which there is a very significant increase in the predicted number density of faint galaxies.
 Ες feature has been present in. previous analyses (c.g. F99) however the small sample size has meant hat only a statistically insignificant number of galaxies have contributed., This feature has been present in previous analyses (e.g. F99) however the small sample size has meant that only a statistically insignificant number of galaxies have contributed.
 Lence previous studies could not determine if his feature was real or à consequence of the small volume ing samiplec at these magnitudes., Hence previous studies could not determine if this feature was real or a consequence of the small volume being sampled at these magnitudes.
" For the first time here we show significant evidence for the presence ofa substantial dwarf (passive star-forming) population with 142 galaxies iwing M,ος) magnitude fainter than — 16.0 027).", For the first time here we show significant evidence for the presence of a substantial dwarf (passive star-forming) population with 142 galaxies having $M_{\bj}-5\log_{10}(h)$ magnitude fainter than $-$ 16.0 $\bar{z} = 0.027$ ).
 Of course these objects will tend to have low signal-o-nolse ratio spectra so some degree of contamination in his sample should. be present. particularly from. erroneous redshift determinations.," Of course these objects will tend to have low signal-to-noise ratio spectra so some degree of contamination in this sample should be present, particularly from erroneous redshift determinations."
 However. these preliminary. results ook promising and we expect more detailed analyses to be ortheoming in the near future.," However, these preliminary results look promising and we expect more detailed analyses to be forthcoming in the near future."
 1799 has performed similar calculations of the LE per spectral type using a subset of the data presented here., F99 has performed similar calculations of the LF per spectral type using a subset of the data presented here.
 In Fig., In Fig.
 Ll we compare their results with those presented here., \ref{cpsf} we compare their results with those presented here.
 Note that in order to make this comparison we have recalculated the LES assuming (for consistencv) an Einstein cle-Sitter Universe (ο— 1..X— 0). and we have reduced the 5 classes of E99 to our 4 types by taking linear combinations of their LES which give the same fractions of galaxies per type as our own.," Note that in order to make this comparison we have recalculated the LFs assuming (for consistency) an Einstein de-Sitter Universe $\Omega=1$, $\Lambda=0$ ), and we have reduced the 5 classes of F99 to our 4 types by taking linear combinations of their LFs which give the same fractions of galaxies per type as our own."
 Lt can be seen from the figure that our results are in good agreement with those of FOO except for some small systematic shifts., It can be seen from the figure that our results are in good agreement with those of F99 except for some small systematic shifts.
 These cillerences are due to four factors which we believe have significantly improved the accuracy of our analysis., These differences are due to four factors which we believe have significantly improved the accuracy of our analysis.
 The most similar independent analysis of the LE per spectral type has been conducted by Bromley et al. (, The most similar independent analysis of the LF per spectral type has been conducted by Bromley et al. (
1998). using the Las Campanas Recshift Survey.,"1998), using the Las Campanas Redshift Survey."
 We also compare hese results with our own in Fig. 11.., We also compare these results with our own in Fig. \ref{cpsf}.
 Again. in order to compare the 6 clans with our + types we have had to combine heir LE determinations in a wav which vields the same ractions of galaxies per type as our own.," Again, in order to compare the 6 clans with our 4 types we have had to combine their LF determinations in a way which yields the same fractions of galaxies per type as our own."
" In addition we jwe applied the transformation Moi,=M.|1.1 (Lin et al.", In addition we have applied the transformation $M_{\bj} = M_{\rm r}+1.1$ (Lin et al.
 1996) to convert the LORS CGunn-r Magnitudes to 5j., 1996) to convert the LCRS $r$ Magnitudes to $\bj$.
 The trend. of the galaxy. LES to become progressively inter as one moves [rom passive to active star-forming ealaxies is clear for both sets of results., The trend of the galaxy LFs to become progressively fainter as one moves from passive to active star-forming galaxies is clear for both sets of results.
 However there appears to be some significant disagreement particularly in he faint end slope between the two LE determinations., However there appears to be some significant disagreement particularly in the faint end slope between the two LF determinations.
 Given the poor fit of the Schechter function to the faint end of the LE we would not expect these two sets of results o necessarily agree within their stated. errors., Given the poor fit of the Schechter function to the faint end of the LF we would not expect these two sets of results to necessarily agree within their stated errors.
" The large dillerences observed are most. probably due to the different selection. elfects (ο. surface. brightness and b, versus r selection) which can be particularly prominent for fainter ealaxies. hence adding more uncertainty to a than can be estimated from a standard error analysis."," The large differences observed are most probably due to the different selection effects (e.g. surface brightness and $\bj$ versus $r$ selection) which can be particularly prominent for fainter galaxies, hence adding more uncertainty to $\alpha$ than can be estimated from a standard error analysis."
 Our total luminosity density (again assuming an Einstein cle-Sitter Universe). is within of the figure obtained in E99 and is lower than the figure quoted by Blanton et al. (, Our total luminosity density (again assuming an Einstein de-Sitter Universe) is within of the figure obtained in F99 and is lower than the figure quoted by Blanton et al. (
2001) for the Sloan Digital Sky Survey early data release.,2001) for the Sloan Digital Sky Survey early data release.
 The reasons for this discrepancy are ciscussed in Norberg et al. (, The reasons for this discrepancy are discussed in Norberg et al. (
2001). but in summary we believe that the Blanton et al.,"2001), but in summary we believe that the Blanton et al."
 figure is too high. partlv owing to large-scale structure in their small initial sample. ancl also through the use of an inappropriate colour equation to predict 2dbC1 magnituces.," figure is too high, partly owing to large-scale structure in their small initial sample, and also through the use of an inappropriate colour equation to predict 2dFGRS magnitudes."
" The spectra observed. as part of the 2dECGIUS are acquired through optical fibres with a diameter of 120/42. corresponding to between 2 and 2.16"" on the sky (depending on plate-position. sce Lewis et al."," The spectra observed as part of the 2dFGRS are acquired through optical fibres with a diameter of $\mu$ m, corresponding to between $2''$ and $2.16''$ on the sky (depending on plate-position, see Lewis et al.,"
 2001)., 2001).
" In our assumed cosmology (£3,,20.3. O4—0.7) this translates to an aperture width of approximately 2.85.| kpe at the survey median redshift of z=0.1."," In our assumed cosmology $\Omega_{\rm{m}}$ =0.3, $\Omega_\Lambda$ =0.7) this translates to an aperture width of approximately $2.8h^{-1}$ kpc at the survey median redshift of $z=0.1$."
 The fact that fitted galaxy brightness profiles have scale. lengths. of the order of 3-4 kpe (Binney Merrifield. 1998) raises the question of how representative the observed spectra are of the galaxics as à whole., The fact that fitted galaxy brightness profiles have scale lengths of the order of 3-4 kpc (Binney Merrifield 1998) raises the question of how representative the observed spectra are of the galaxies as a whole.
" However. with. typical. seeing. (1.5""H"" 1.57) and"," However, with typical seeing $1.5''-1.8''$ ) and"
(2) through (5) give the elemental abundances and their uncertainties. derived as explained above. where IIle/Il is given in linear form. while the other abundances are given in the usual form A(X)=loe(X/IL)-2-12.,"(2) through (5) give the elemental abundances and their uncertainties, derived as explained above, where He/H is given in linear form, while the other abundances are given in the usual form A(X)=log(X/H)+12."
 The 1143 PNe in Acker's catalog belong to the thin disk. thick disk. halo. and bulge populations.," The 1143 PNe in Acker's catalog belong to the thin disk, thick disk, halo, and bulge populations."
 In some of the applications below (i.e.. disk metallicity gradients) we select a pure disk population.," In some of the applications below (i.e., disk metallicity gradients) we select a pure disk population."
" We use the standard criteria to select bulge population PNe within angular distances less than 10 degrees [rom the Galactic center. angular radii smaller than 10 arcsec. and 5 Gllz fIuxes smaller (han 0.1 Jv (e. ο,. Chiappini et al."," We use the standard criteria to select bulge population PNe within angular distances less than 10 degrees from the Galactic center, angular radii smaller than 10 arcsec, and 5 GHz fluxes smaller than 0.1 Jy (e. g., Chiappini et al."
 2009)., 2009).
 There are 147 PNe in ow sample that satisfy all these conditions., There are 147 PNe in our sample that satisfy all these conditions.
" Next we classify (he PNe with determined abundances as Type I (with logCN/O)2-0.3 and IHe/II7.125). Tvpe IL (non-Tvpe I PNe with peculiar radial velocity V,«60 kins ly and Type HIE (non-Type I PNe with V, 260 km !) as defined in POS."," Next we classify the PNe with determined abundances as Type I (with $>$ -0.3 and $\ge$ .125), Type II (non-Type I PNe with peculiar radial velocity $_{\rm p}<$ 60 km $^{-1}$ ), and Type III (non-Type I PNe with $_{\rm p}>$ 60 km $^{-1}$ ) as defined in P04."
 Peculiar velocities have been derived from measured radial velocities by Durand et al. (, Peculiar velocities have been derived from measured radial velocities by Durand et al. (
1998) ancl Galactic rotation model therein. assuming a constant rotation for PNe with B;> 9Η...,"1998) and Galactic rotation model therein, assuming a constant rotation for PNe with $_{\rm G} > 2$ $_{\odot}$."
 The Tvpe III PNe with altitude on the Galactic plane larger (han 800 pe are likely to be halo PNe., The Type III PNe with altitude on the Galactic plane larger than 800 pc are likely to be halo PNe.
 In Table 2. column (6). we eive the disk population designation (Ivpe I. II. or III) for the PNe. where possible. based on the abundances ancl kinematics.," In Table 2, column (6), we give the disk population designation (Type I, II, or III) for the PNe, where possible, based on the abundances and kinematics."
 For non-disk PNe we indicate whether thev belong to the bulge or to the halo., For non-disk PNe we indicate whether they belong to the bulge or to the halo.
 In Figure 1 we show the sample of PNe with known distances in the Hc; z plane.," In Figure 1 we show the sample of PNe with known distances in the $_{\rm G}$ –z plane,"
direction.,direction.
" The injection rate of electrons was calculated by convolving the pair production kernel with proton svnchrotron spectrum multipliel by Che factor (1—exp(—7;,)).", The injection rate of electrons was calculated by convolving the pair production kernel with proton synchrotron spectrum multiplied by the factor $\left(1-\exp(-\tau_{\rm in})\right)$.
 The enerev distribution of electrons was calculated using the approximation of continuous losses accounting for dominant svnchrotron losses only., The energy distribution of electrons was calculated using the approximation of continuous losses accounting for dominant synchrotron losses only.
 The secondary svichlirotron emission was calculated. using the obtained distribution of electrons., The secondary synchrotron emission was calculated using the obtained distribution of electrons.
 The variability properties of this radiation component are related to the variability of (he intrinsic 5-ravs as well as to the to the change of their absorption rate., The variability properties of this radiation component are related to the variability of the intrinsic $\gamma$ -rays as well as to the to the change of their absorption rate.
 To demonstrate the potential of the proposed model for the explanation of very hard intrinsic 5-rav spectra. we focused on (wo distant objects. namely LES 02294-200 (2= 0.1396) and ος GGA (2=0.444.thoughthisvalueisdebated. 2011).. ," To demonstrate the potential of the proposed model for the explanation of very hard intrinsic $\gamma$ -ray spectra, we focused on two distant objects, namely 1ES 0229+200 $z=0.1396$ ) and 3C 66A \citep[$z=0.444$, though this value is debated, see e.g.][]{lat66a}. ."
These two BLLacs have different 5-ray. properties., These two BLLacs have different $\gamma$ -ray properties.
 In particular. LES 02294200 shows VIIE 5-rav emission without significant flux or spectral changes between (wo HESS measurements separated bv one vear (Aharonianetal.2007).," In particular, 1ES 0229+200 shows VHE $\gamma$ -ray emission without significant flux or spectral changes between two HESS measurements separated by one year \citep{aharonian07}."
. Moreover. Fermi LAT was nol able to detect GeV emission [rom the direction of LES 02294200.," Moreover, Fermi LAT was not able to detect GeV emission from the direction of 1ES 0229+200."
 In the SED plot. the upper limit of the GeV flix appears below the TeV flux corrected [ον intergalactic absorption.," In the SED plot, the upper limit of the GeV flux appears below the TeV flux corrected for intergalactic absorption."
 The blazar 3C 66À shows a variable VILE signal. as seen with VERITAS 2011).. with a 676 Crab flux flaring episode.," The blazar 3C 66A shows a variable VHE signal, as seen with VERITAS \citep{acciari09*c,lat66a}, with a $6\%$ Crab flux flaring episode."
 Fermi LAT collaboration reported a sienilicant GeV 5-rayv. excess [rom the source., Fermi LAT collaboration reported a significant GeV $\gamma$ -ray excess from the source.
 Moreover. an increase of the GeV flux simultaneously with the VIIE flare was observed (Abdoetal.2011).," Moreover, an increase of the GeV flux simultaneously with the VHE flare was observed \citep{lat66a}."
. Importantly. the GeV flix level exceedssignificantly the de-absorbed VIE flux. thus a smooth connection," Importantly, the GeV flux level exceedssignificantly the de-absorbed VHE flux, thus a smooth connection"
LAINBs indicates that the slope of the optical spectrmi alone does not seem to be a reliable iudicator of N-rav heating.,LMXBs indicates that the slope of the optical spectrum alone does not seem to be a reliable indicator of X-ray heating.
 Ou the other haud. the observation of ΠΡΟος in NTE J11ls]|[80 aud other black hole NRNe curing outburst (O'Donoghue&Charles1996) does not in itself exclude X-ray heating as the dominant source of optical uumositv (aswelletal.2001).," On the other hand, the observation of superhumps in XTE J1118+480 and other black hole XRNe during outburst \citep{odo96} does not in itself exclude X-ray heating as the dominant source of optical luminosity \citep{has01}."
. Another wav to estimate the contribution from N-rav radiation is to use the relation between the absolute uaenitude and the orbital pertod/X-ray huninosity for LAINBs found bv vanParadis& MeCliutock.(1991)., Another way to estimate the contribution from X-ray irradiation is to use the relation between the absolute magnitude and the orbital period/X-ray luminosity for LMXBs found by \citet{van94}.
. Waeueretal.(2001) derive a distance of d—1.9-40.1 kpc or NTE JI1118150., \citet{wag01} derive a distance of $\pm$ 0.4 kpc for XTE J1118+480.
 This implies au absolute magiuitude of ML μη in disagreement with the expected value or an mradiatiou-domiuated disk of Mq29 3.00.5 (vanParadijs&McClintock.1991.Fig. 2)., This implies an absolute magnitude of ${_V}$ $^{+0.5}_{-0.4}$ in disagreement with the expected value for an irradiation-dominated disk of ${_V}\approx$ $\pm$ 0.5 \citep[Fig. 2]{van94}.
 Here we have corrected the resultaut absolute maguitude by - 0.7 mag o take iuto account that the visual huninosity due to N-ray reprocessing in the disk scales with the compact object mass as ~ ALY3., Here we have corrected the resultant absolute magnitude by - 0.7 mag to take into account that the visual luminosity due to X-ray reprocessing in the disk scales with the compact object mass as $\sim$ ${_{1}}^{1/3}$.
 A 7 AL. black hole was asstuued., A 7 $_\odot$ black hole was assumed.
 Furthermore. it is clear from Fig.," Furthermore, it is clear from Fig."
 2 of Uemura(20000) that on at least two occasions. the source of the optical flux was other than X-rav irracliation.," 2 of \citet{uem00C} that on at least two occasions, the source of the optical flux was other than X-ray irradiation."
 The first. before the eud of the January outburst. was an optical flare (of amplitude 2 1.5 mag) without aay accompauving X-ray flare.," The first, before the end of the January outburst, was an optical flare (of amplitude $\gtrsim$ 1.5 mag) without any accompanying X-ray flare."
 In the second event. at the begiuniug of the March outburst. the steep rise iu the optical fix was accompanied by a much slower increase in the N-vav flux.," In the second event, at the beginning of the March outburst, the steep rise in the optical flux was accompanied by a much slower increase in the X-ray flux."
 Heuce we think it unlikely that X-ray reprocessing dominates the outhurst optical flux., Hence we think it unlikely that X-ray reprocessing dominates the outburst optical flux.
 Viscous dissipation iu the disk is an alternative explanation of the optical fis., Viscous dissipation in the disk is an alternative explanation of the optical flux.
 Using the ΑΕ Τε relation for DNe in outburst (Warner1987).. we have estimated AL =L7 for a DN with an orbital period of L1 hr.," Using the $_V$ $_{orb}$ relation for DNe in outburst \citep{war87}, we have estimated ${_V}$ =4.7 for a DN with an orbital period of 4.1 hr."
 But since the area of the disk scales with the primary mass as AQ? for a fixed orbital period (Caunizzo1995) and the euergv released at a given distance from the xunary scales with the primary mass as M4 (Frank.Nine&Raine 1985). we expect the optical dux generated wea disk in a black hole NRN to be ~ AQ? higher han that enmütted by a disk surrounding the —1 M. mumary i a DN.," But since the area of the disk scales with the primary mass as ${_{1}}^{2/3}$ for a fixed orbital period \citep{can98} and the energy released at a given distance from the primary scales with the primary mass as $_1$ \citep{fra85}, we expect the optical flux generated by a disk in a black hole XRN to be $\sim$ ${_{1}}^{5/3}$ higher than that emitted by a disk surrounding the $\sim$ 1 $_\odot$ primary in a DN."
 This correction προς Aly~1.2 if NTE 115150 contains a 7 AL. black hole., This correction implies ${_V}\sim1.2$ if XTE J1118+480 contains a 7 $_\odot$ black hole.
 Note hat we have assumed a immoderate inclination for the duarv system., Note that we have assumed a moderate inclination for the binary system.
" For au inclination ;/=τοῦ, the outburst isolute magnitude of the viscously heated disk corrected using the prescription of Warner(1987). is MV~1.9. close to the observed absolute magnitude."," For an inclination $i=70^{\circ}$, the outburst absolute magnitude of the viscously heated disk corrected using the prescription of \citet{war87} is $^{corr}_{V}\sim1.9$, close to the observed absolute magnitude."
 For /zNO. the inclination favoured when fitting the near quiesceuce optical liebt. curve with au ellipsoidal model (MeCliutocketal20012:Waeneral. 20013.. the above correction vives Mi~2.8.," For $i\simeq80^{\circ}$, the inclination favoured when fitting the near quiescence optical light curve with an ellipsoidal model \citep{mcc01A,wag01}, the above correction gives $^{corr}_{V}\sim2.8$."
 Although this maguitude is £üuter thui the observed absolute magnitude. DNe superoutbursts are 0.5-1 maguitudes brighter than normal outbursts aud even 2 magnitudes brighter (or iore) in the case of the TOAD superoutbursts (IlowellSzkodwv&Cauuizzo1995:Iaulkers.Πονο&vanParadis 1996).," Although this magnitude is fainter than the observed absolute magnitude, DNe superoutbursts are 0.5-1 magnitudes brighter than normal outbursts and even 2 magnitudes brighter (or more) in the case of the TOAD superoutbursts \citep{how95,kuu96}."
". If the outburst in NTE J1118][8O is similar to a DN superoutburst then Mi""~Ls.", If the outburst in XTE J1118+480 is similar to a DN superoutburst then $^{corr}_{V}\sim1.8$.
" The presence of a bright. viscously heated disk is supported by the detection of a siguificaut Bahuer juup in the ultraviolet spectra (Haswell.Ines&Wing2000:McClintocketal. 200110), which suggestsOO an appreciable thermal disk contribution to the emission."," The presence of a bright, viscously heated disk is supported by the detection of a significant Balmer jump in the ultraviolet spectrum \citep{has00,mcc01B}, which suggests an appreciable thermal disk contribution to the emission."
 Teuce the viscously heated disk is likely to be a siguificaut contributor to the optical flux during the outburst of NTE J1118][80 as in the SU UMXa systems., Hence the viscously heated disk is likely to be a significant contributor to the optical flux during the outburst of XTE J1118+480 as in the SU UMa systems.
 AlultiÁeopoch optical spectroscopic observatious of NTE J1118]|[80 wield valuable tuformation about the properties and evolution. of the accretion disk during outburst., Multi-epoch optical spectroscopic observations of XTE J1118+480 yield valuable information about the properties and evolution of the accretion disk during outburst.
 The data reveal strong double-peaked Io. ITJj. and A £686 enissiou lines whose double-peak iuteusitv varies on time scales longer than the L1 hr orbital cvele.," The data reveal strong double-peaked $\alpha$, $\beta$, and $\lambda$ 4686 emission lines whose double-peak intensity varies on time scales longer than the 4.1 hr orbital cycle."
 These changes in the line profiles can be interpreted as resulting from a precessiug ccceutric disk around the compact primary., These changes in the line profiles can be interpreted as resulting from a precessing eccentric disk around the compact primary.
" Ποπονο, a search for periodic variability iu the A 1686 ciission line failed to fiud a modulation within the estimated precession period rauge."," However, a search for periodic variability in the $\lambda$ 4686 emission line failed to find a modulation within the estimated precession period range."
 Therefore conclusive evidence for a precessing disk in the system is still required., Therefore conclusive evidence for a precessing disk in the system is still required.
 Doppler tomograms display a bright bow-shaped cussion in the -Vy. Vy: quadrant which we interpret as cuuission from the accretion gas stream. the hotspot or both.," Doppler tomograms display a bright bow-shaped emission in the $_X$, $_Y$ quadrant which we interpret as emission from the accretion gas stream, the hotspot or both."
 A more accurate ephemeris is needed to properly constrain the location of the chussion within the binary svstem., A more accurate ephemeris is needed to properly constrain the location of the emission within the binary system.
 A comparison with DNe in superoutburst shows that viscous dissipation iu the disk may make a significant contribution to the optical Iuuinosity duriug outburst., A comparison with DNe in superoutburst shows that viscous dissipation in the disk may make a significant contribution to the optical luminosity during outburst.
 Use of MOLLY. DOPPLER aud TRAILER routines developed. hugelv bx T. BR. Alarsh ds acknowledged.," Use of MOLLY, DOPPLER and TRAILER routines developed largely by T. R. Marsh is acknowledged."
 We thauk Aun Esin for helpful comments and Makoto Uecunra for providing the VSNET light curve., We thank Ann Esin for helpful comments and Makoto Uemura for providing the VSNET light curve.
 We are erateful to the anonymous referee for useful commicuts which improved the quality of the manuscript., We are grateful to the anonymous referee for useful comments which improved the quality of the manuscript.
 MBRG was supported by NASA coutract NASS-39073., MRG was supported by NASA contract NAS8-39073.
The propagation of CR electrons and positrons in case of the diffusion coefficient  being spatially constant. is described by a S=hAN NN. where \V is the differential number density. 5 the source term. A the Lapace operator. and 6 the rate of energy losses.,"The propagation of CR electrons and positrons in case of the diffusion coefficient $k$ being spatially constant, is described by -S = N ), where $N$ is the differential number density, $S$ the source term, $\Delta$ the Lapace operator, and $b$ the rate of energy losses."
 For a funetional form of the diffusion coefficient A=yl’. wilh a=3/5 and the energy losses 6=byE? ssvnchrotron and inverse Compton losses) one canfind a Green's function solving in the literature (Derezinskiietal.1990)..," For a functional form of the diffusion coefficient $k=k_0E^{\alpha}$ , with $\alpha\,=\,3/5$ and the energy losses $b=b_0E^2$ synchrotron and inverse Compton losses) one canfind a Green's function solving in the literature \citep{1990acr..book.....B}."
" It is given by (2, cU) with N= Thus. the solution of is given by."," It is given by ,E,E_0,t,t_0) = ( ) with = Thus, the solution of is given by,"
from the fitting of X-ray data.,from the fitting of X-ray data.
 Combination of the results from lensing and SZ data with those from an analysis of X-ray data will thus break the degeneracy between the gas fraction and the Hubble parameter: this combination may be done cquivalenthy by simultaneously fitting all three data sets simultaneously. or by applying the joint. posterior pdf from the N-ray analysis as a prior for the SZ/lensing analvsis. OF vico versa.," Combination of the results from lensing and SZ data with those from an analysis of X-ray data will thus break the degeneracy between the gas fraction and the Hubble parameter; this combination may be done equivalently by simultaneously fitting all three data sets simultaneously, or by applying the joint posterior pdf from the X-ray analysis as a prior for the SZ/lensing analysis, or vice versa."
" In this work. we leave the f-cependence of the gas fraction as it is. simply using the uniform: priors of Table 1 on Alaa, ancl Moos."," In this work, we leave the $h$ -dependence of the gas fraction as it is, simply using the uniform priors of Table \ref{tab:models} on $M_{\rm gas}$ and $M_{200}$."
 However. these apparently innocuous priors lead to an informative prior on the combination fax.," However, these apparently innocuous priors lead to an informative prior on the combination $f_{\rm gas} h$."
 This can be seen by sampling the joint prior with no data using the AICAIC algorithm (Slosar 2)). and computing μις/Moos for cach sample in the same way as would be done in the data analysis process.," This can be seen by sampling the joint prior with no data using the MCMC algorithm (Slosar \citeyear{COS/Slo++03}) ), and computing $M_{\rm gas}/M_{200}$ for each sample in the same way as would be done in the data analysis process."
 The resulting histogram is shown in Figure 3.., The resulting histogram is shown in Figure \ref{fig:fgasprior}.
 The clleet of the upper limit on the gas mass can be seen as the turnover point ad Adaauax/Moonasus=0.15.," The effect of the upper limit on the gas mass can be seen as the turnover point at $M_{\rm gas, max}/M_{200, max} = 0.15$."
" Below this value. the prior is uniform. whereas above it the larger values of fa, are increasingly clisfavoured. well rellecting our prior knowledge of cluster masses."," Below this value, the prior is uniform, whereas above it the larger values of $f_{\rm gas} h$ are increasingly disfavoured, well reflecting our prior knowledge of cluster masses."
 Example mocel parameter inferences are shown in Figure 4.. where in each panel the posterior density has been marginalised over all but two of the parameter dimensions.," Example model parameter inferences are shown in Figure \ref{fig:VSA-pars}, where in each panel the posterior density has been marginalised over all but two of the parameter dimensions."
 The clleet of the Gaussian prior on the gas temperature can be seen in the right-hand. panel., The effect of the Gaussian prior on the gas temperature can be seen in the right-hand panel.
" The estimated. precision on each of the three parameters Afeoo. c. and Mai, are 25. 25 and 50 percent respectively."," The estimated precision on each of the three parameters $M_{200}$, $c$ , and $M_{\rm gas}$ are 25, 25 and 50 percent respectively."
 The left-hand panel of Figure 5. shows the cosmological results from the joint analysis of the current generation low redshift SZ and lensing data., The left-hand panel of Figure \ref{fig:VSA-fgas} shows the cosmological results from the joint analysis of the current generation low redshift SZ and lensing data.
 This plot shows the answer to question (iii) as posed in Section 2.., This plot shows the answer to question (iii) as posed in Section \ref{sect:infer}.
 The joint. evidences calculated for cach model. for either. given dataset; were equal within the numerical errors: this indicates that the model averaging equation has two terms to be considered. leading to the (quasi) mocdel-independent statement about fF given in the left panel of the figure.," The joint evidences calculated for each model, for either given dataset, were equal within the numerical errors; this indicates that the model averaging equation has two terms to be considered, leading to the (quasi) model-independent statement about $f_{\rm gas}$ given in the left panel of the figure."
 Llowever. the right-hand. panel shows the sensitivity of the VSA SZ data to the contaminant primorclial CAB fluctuations: the miocdel-averaged fax. probability distributions show significant variation with CAIB realisation.," However, the right-hand panel shows the sensitivity of the VSA SZ data to the contaminant primordial CMB fluctuations: the model-averaged $f_{\rm gas}$ probability distributions show significant variation with CMB realisation."
 ltealisations 1. 2 and 3 correspond το the situations where the cluster lies approximately in front of a primordial CALB saddle point. a shallow trough and a peak respectively.," Realisations 1, 2 and 3 correspond to the situations where the cluster lies approximately in front of a primordial CMB saddle point, a shallow trough and a peak respectively."
 La the latter case the gas mass (and so gas fraction) is then underestimatect., In the latter case the gas mass (and so gas fraction) is then underestimated.
 The evidence analysis of CAIB realisations 2 ancl 3 show neither model being preferred by more than a small factor in probability. (<<3) regardless of the truce cluster mocel., The evidence analysis of CMB realisations 2 and 3 show neither model being preferred by more than a small factor in probability $<3$ ) regardless of the true cluster model.
 In some cases the primordial CALB is being fitted (by the more I[lexible Beta model) as well as the cluster. and in others the noise is high. enough for the Occam [factor in the evidence to dominate anc the simpler WISE model is preferred.," In some cases the primordial CMB is being fitted (by the more flexible Beta model) as well as the cluster, and in others the noise is high enough for the Occam factor in the evidence to dominate and the simpler iHSE model is preferred."
 However. the extent to which the evidence favours either model is never greater than the belief. threshold sugeested in Section 2..," However, the extent to which the evidence favours either model is never greater than the belief threshold suggested in Section \ref{sect:infer}."
 This indicates that the presence of the primordial CMD. Ductuations has been dealt. with correctly — the inconclusivencss of the evidence ratios ensure hat the conclusions drawn about the structure of the cluster are not systematically incorrect., This indicates that the presence of the primordial CMB fluctuations has been dealt with correctly – the inconclusiveness of the evidence ratios ensure that the conclusions drawn about the structure of the cluster are not systematically incorrect.
 However the implication of this result is that in order o investigate the astrophiysies of low redshilt clusters via SZ and gravitational lensing (questions (i) ancl (ii)). more information is required.," However the implication of this result is that in order to investigate the astrophysics of low redshift clusters via SZ and gravitational lensing (questions (i) and (ii)), more information is required."
 This could take the form of multi-pequencey SZ observations. to allow better separation of the cluster ancl primordial CMD components (Lancaster 2003. in preparation). or stronger priors on the cluster xwameters.," This could take the form of multi-frequency SZ observations, to allow better separation of the cluster and primordial CMB components (Lancaster 2003, in preparation), or stronger priors on the cluster parameters."
 Reducing the freedom. of the Beta model to it the CMD fluctuations will indeed. produce more precise eas fraction estimates. but to be confident of the accuracy of these numbers the applied. priors should be strongly ohvsically motivated.," Reducing the freedom of the Beta model to fit the CMB fluctuations will indeed produce more precise gas fraction estimates, but to be confident of the accuracy of these numbers the applied priors should be strongly physically motivated."
 A good first. step in this direction would be to derive joint. priors on any models parameters rom a Large sample of hyvedrodsnamicallv-simulated clusters., A good first step in this direction would be to derive joint priors on any model's parameters from a large sample of hydrodynamically-simulated clusters.
 We now move on to consider the kind of observations we can expect from upcoming SZ telescopes such as AME (?).. the SZA (7?) and AMHBA (?).. in combination with matched lensing observations from wide field optical cameras.," We now move on to consider the kind of observations we can expect from upcoming SZ telescopes such as AMI \citep{SZ/Kne++01}, the SZA \citep{SZ/Moh++02} and AMiBA \citep{SZ/Lo++00}, in combination with matched lensing observations from wide field optical cameras."
 Rather than compare the dilferent experiments. we note that they are qualitatively similar instruments ancl proceed: to use ΑΔΗ. and for the mock lensing observations the ESO Wide Field. Imager. as specific examples in this work.," Rather than compare the different experiments, we note that they are qualitatively similar instruments and proceed to use AMI, and for the mock lensing observations the ESO Wide Field Imager, as specific examples in this work."
 ΑΔΗ will consist of (a) ten close-packed 3.7-m. dishes operating at 15Gllz and (b) the eight. 132m cishes of the current. Rate ‘Telescope (which are separated. by longer baselines)., AMI will consist of (a) ten close-packed 3.7-m dishes operating at 15GHz and (b) the eight 13-m dishes of the current Ryle Telescope (which are separated by longer baselines).
 The two parts of this array will have cillerent correlators and therefore provide two independent measurements of the sky. allowing the two datasets to be combined by a simple sum of the individual log-likelihoods.," The two parts of this array will have different correlators and therefore provide two independent measurements of the sky, allowing the two datasets to be combined by a simple sum of the individual log-likelihoods."
 An important question is that of the strength. of the primordial CAIB on the angular scales to which ANIL is sensitive., An important question is that of the strength of the primordial CMB on the angular scales to which AMI is sensitive.
 These correspond to a maximum /-range of 1000 to 6600 for MES small dishes. and 00060 to 20000 Lor the large Rwle Telescope dishes: note that in practice the minimum £ values used in observations willbe significantly ereater.," These correspond to a maximum $l$ -range of 1000 to 6600 for AMI's small dishes, and 6000 to 36000 for the large Ryle Telescope dishes; note that in practice the minimum $\ell$ values used in observations willbe significantly greater."
 The primordial CAIB power spectrum is relatively, The primordial CMB power spectrum is relatively
emission model created with as detailed in Section 2.4..,emission model created with as detailed in Section \ref{sec:taking-acco-nebul}.
 Inclusion of nebular continuum emission leads to only a slight decrease in the maximum EW allowed by up to 10 percent., Inclusion of nebular continuum emission leads to only a slight decrease in the maximum EW allowed by up to 10 percent.
" Here we calculate predicted values for the strength (equivalent width; EW) of Wolf Rayet features as defined by Brinchmann et al, removing the contribution of nebular lines to allow fair comparison with the data."," Here we calculate predicted values for the strength (equivalent width; EW) of Wolf Rayet features as defined by Brinchmann et al, removing the contribution of nebular lines to allow fair comparison with the data."
 As illustrated by Figures 2 and 3 in general our models reproduce the range of observed equivalent widths of both features with the exception of a few extreme cases., As illustrated by Figures \ref{final1} and \ref{final2} in general our models reproduce the range of observed equivalent widths of both features with the exception of a few extreme cases.
" For a simple check of our nebula model, Figure 4 shows a comparison between the equivalent widths of the Blue WR bump to a nearby nebula emission line, H-f."," For a simple check of our nebula model, Figure \ref{final3} shows a comparison between the equivalent widths of the Blue WR bump to a nearby nebula emission line, $\beta$."
 Comparing the ratio of these EWs will indicate whether we are estimating the strength of the nebula emission lines correctly relative to the stellar spectrum., Comparing the ratio of these EWs will indicate whether we are estimating the strength of the nebula emission lines correctly relative to the stellar spectrum.
 We see that our model predictions of this ratio agree with the range of ratios from observed galaxies and previous estimates from the binary models of(2003).., We see that our model predictions of this ratio agree with the range of ratios from observed galaxies and previous estimates from the binary models of.
 Binary populations at metallicities below solar metallicity produce the highest ratio we discuss why this is below., Binary populations at metallicities below solar metallicity produce the highest ratio we discuss why this is below.
" We note our predicted ratios are a lower limit as the ratio we predict can be varied by changing the details of our model, especially the covering factor."," We note our predicted ratios are a lower limit as the ratio we predict can be varied by changing the details of our model, especially the covering factor."
 Decreasing this lets more ionising photons to escape and therefore decreases the nebula emission features such as the H-@ line luminosity without significantly affecting the blue WR bump EW which is determined by the stellar population., Decreasing this lets more ionising photons to escape and therefore decreases the nebula emission features such as the $\beta$ line luminosity without significantly affecting the blue WR bump EW which is determined by the stellar population.
 Thus the vertical spread has degeneracy between age and covering factor., Thus the vertical spread has degeneracy between age and covering factor.
 In Figure 5 we show the strength of the key Wolf-Rayet emission features in our model spectra as a function of the age of the stellar population and its metallicity., In Figure \ref{final7b} we show the strength of the key Wolf-Rayet emission features in our model spectra as a function of the age of the stellar population and its metallicity.
" We see that the spread of values in Figures 2,, 3 and 4 is due to a range of ages in the stellar population."," We see that the spread of values in Figures \ref{final1}, \ref{final2} and \ref{final3} is due to a range of ages in the stellar population."
" Emission features peak at ages of a few million years for single stars and can be extended to much later times, up to 10 million years, by the inclusion of binaries."," Emission features peak at ages of a few million years for single stars and can be extended to much later times, up to 10 million years, by the inclusion of binaries."
 We note that similar diagrams with a nebula continuum component would reduce these observed EWs by a small amount., We note that similar diagrams with a nebula continuum component would reduce these observed EWs by a small amount.
 In Figure 6 we show how the strength of H-8 varies with age., In Figure \ref{final5} we show how the strength of $\beta$ varies with age.
 We see that binary models exhibit H-8 to later ages., We see that binary models exhibit $\beta$ to later ages.
" This is why at solar metallicity in Figure 4 at Solar metallicity single stars have a greater maximum ratio than binary stars, a smaller H-3 EW gives a larger ratio rather than great blue WR bump EW."," This is why at solar metallicity in Figure \ref{final3} at Solar metallicity single stars have a greater maximum ratio than binary stars, a smaller $\beta$ EW gives a larger ratio rather than great blue WR bump EW."
 In Figure 5 there are large peaks in the strength of Hell and the blue WR bump at around 10 million years., In Figure \ref{final7b} there are large peaks in the strength of HeII and the blue WR bump at around 10 million years.
 These peaks are due to WNL stars formed from binary, These peaks are due to WNL stars formed from binary
Finally we note that although vastly more technically challenging. if the could be detected by (the same instruments (e.g.. for giant planets in the HR). a similar constraint could be mace for the antipodal orbital velocity which. together with the primary eclipse data. and the relative timing of both primary and secondary eclipses. would enable the orbital parameters to be filly determined.,"Finally we note that although vastly more technically challenging, if the could be detected by the same instruments (e.g., for giant planets in the IR), a similar constraint could be made for the antipodal orbital velocity which, together with the primary eclipse data, and the relative timing of both primary and secondary eclipses, would enable the orbital parameters to be fully determined."
 For low-mass planets at ~LAU (his is something that might otherwise remain bevond (he capabilities of Doppler-based measurements., For low-mass planets at $\sim 1AU$ this is something that might otherwise remain beyond the capabilities of Doppler-based measurements.
 Obviously. if transit (imine perturbations due to the presence of unseen planets or objects are present thev can confuse Chis scheme.," Obviously, if transit timing perturbations due to the presence of unseen planets or objects are present they can confuse this scheme."
 llowever. as described previously. the parallax effects can in principle be well understood ancl (his simultanenous observation will separate the phenomena.," However, as described previously, the parallax effects can in principle be well understood and this simultanenous observation will separate the phenomena."
 In addition to providing strong confirmation of planet transits and constraints on orbital parameters. the use of simultaneous long-baseline observations might in principle also provide inlormation on the transit light curve shape.," In addition to providing strong confirmation of planet transits and constraints on orbital parameters, the use of simultaneous long-baseline observations might in principle also provide information on the transit light curve shape."
 In the case illustrated in Figure Ib the transit occurs al different inclinations for (wo observers and hence at different stellar. latitudes., In the case illustrated in Figure 1b the transit occurs at different inclinations for two observers and hence at different stellar latitudes.
 The stellar limb darkening is the dominant factor in determining the shape of the transit light curve., The stellar limb darkening is the dominant factor in determining the shape of the transit light curve.
 Realistically however the physical range of the stellar photosphere sampled with long-baseline observations is likely to be small., Realistically however the physical range of the stellar photosphere sampled with long-baseline observations is likely to be small.
 At LO pe with a 2 AU total baseline the actual difference in sampled photosphere for a solar radius star is only some ~0.7 kin., At 10 pc with a 2 AU total baseline the actual difference in sampled photosphere for a solar radius star is only some $\sim 0.7$ km.
 Thus. although there is an effect. it is verv unlikelv to be measurable.," Thus, although there is an effect, it is very unlikely to be measurable."
 The ellect of parallax on exoplanet transit observations is both a potential source of svstematic error in quantifvine (ransil events. and a possible means bv which more inlormation ean be extracted. from a transit.," The effect of parallax on exoplanet transit observations is both a potential source of systematic error in quantifying transit events, and a possible means by which more information can be extracted from a transit."
 Although the magnitude of the effect for an Earth-bound observer is. in most [orseeable cases. quite small it may nonetheless enters the reeime of future hieh precision (ransil measurements.," Although the magnitude of the effect for an Earth-bound observer is, in most forseeable cases, quite small it may nonetheless enters the regime of future high precision transit measurements."
 In particular. the secular changes in transit (iming and duration due to relative stellar motion should be taken into account [or hieh-precision. long timeline transit observations.," In particular, the secular changes in transit timing and duration due to relative stellar motion should be taken into account for high-precision, long timeline transit observations."
 This amounts to an additional svstematic that might confuse efforts to measure orbital precessions and the presence of other planets in a svslem., This amounts to an additional systematic that might confuse efforts to measure orbital precessions and the presence of other planets in a system.
 An observational scheme with simultaneous measurements of (ransits made across a long baseline (e.g.. 2 AU) could provide unique constraints on the orbital parameters of," An observational scheme with simultaneous measurements of transits made across a long baseline (e.g., 2 AU) could provide unique constraints on the orbital parameters of"
Ay=0.7. aud the formation epoch of τε—5.,"$\lambda_0=0.7$, and the formation epoch of $z_{\rm f}=5$."
 Figure 1 shows the cosmic supernova rates in cluster galaxies., Figure 1 shows the cosmic supernova rates in cluster galaxies.
 The SN Ia rate iu spirals drops at 2~1.9 because of the low-metallicitv inhibition of SNe Ia. We can precisely test the metallicity effect by &iudiug this drop of the SN Ta in spirals. if high-redshift SNe Ta at z>1.5 and their host galaxies are observed with the Next Generation Space Telescope.," The SN Ia rate in spirals drops at $z \sim 1.9$ because of the low-metallicity inhibition of SNe Ia. We can precisely test the metallicity effect by finding this drop of the SN Ia in spirals, if high-redshift SNe Ia at $z \gtsim 1.5$ and their host galaxies are observed with the Next Generation Space Telescope."
 In ellipticals. the clemical enrichment taxes place so early that the metallicity is large chough to produce SNe In at 2>2.," In ellipticals, the chemical enrichment takes place so early that the metallicity is large enough to produce SNe Ia at $z \gtsim 2$."
 The two peaks of SN Ta rates at z~2.6 aud 2~1.6 conie from the MS|WD aud the RG|WD systems. respectively.," The two peaks of SN Ia rates at $z \sim 2.6$ and $z \sim 1.6$ come from the MS+WD and the RG+WD systems, respectively."
 Tle SN Ia rate iu ellipticals decreases at z—2.6. which is determined from the shortest lifetime of SNe Ia of ~0.5 Cor.," The SN Ia rate in ellipticals decreases at $z \sim 2.6$, which is determined from the shortest lifetime of SNe Ia of $\sim 0.5$ Gyr."
 Thus. the total SN Ta rate decrease at the same redshift as ellipticals. 1.6... 52.6.," Thus, the total SN Ia rate decrease at the same redshift as ellipticals, i.e., $z \sim 2.6$."
 We also predict the cosmic supernova rates assuming that the formation of cllipticals in field took place for over the wide range of redshifts. which is inpriuted iu the observed spectra of ellipticals in the Wabble Deep Field.," We also predict the cosmic supernova rates assuming that the formation of ellipticals in field took place for over the wide range of redshifts, which is imprinted in the observed spectra of ellipticals in the Hubble Deep Field."
 The adopted SFR» are the same as the case of cluster galaxies. but for tle formation epochs τε of ellipticals distribute iu the range of 0x;x5.," The adopted SFRs are the same as the case of cluster galaxies, but for the formation epochs $z_{\rm f}$ of ellipticals distribute in the range of $0 \le z \le 5$."
 Figure 2 shows the cosmic supernova rates in field galaxies., Figure 2 shows the cosmic supernova rates in field galaxies.
 As in Figure 1. the SN In rate in spirals drops at 2~1.9.," As in Figure 1, the SN Ia rate in spirals drops at $z \sim 1.9$."
" The averaged SN Ia rate in ellipticals decreases at ~2,2 as a result of ~0.5 Cyr delay of the decrease in the SER at 2>9, ", The averaged SN Ia rate in ellipticals decreases at $z \sim 2.2$ as a result of $\sim 0.5$ Gyr delay of the decrease in the SFR at $z \gtsim 3$.
Then. the total SN Ia rate decreases gradually from +~2 to. ~3.," Then, the total SN Ia rate decreases gradually from $z \sim 2$ to $z \sim 3$."
 Although the error bars are huge. there is a hint that the observed SN Ta rate decreases from 2~0.14 to the present.," Although the error bars are large, there is a hint that the observed SN Ia rate decreases from $z \sim 0.4$ to the present."
 If this is confirmed. it could oeuply that the rate of SNe Ia from loue-lived (OAL. companions is lower than that assumed in our model.," If this is confirmed, it could imply that the rate of SNe Ia from long-lived $0.9 M_\odot$ companions is lower than that assumed in our model."
 From τ~0.L. the observed SN Ia rate secus to VAightly decrease toward higher redshifts.," From $z \sim 0.4$, the observed SN Ia rate seems to slightly decrease toward higher redshifts."
 To discuss their implications iu ferius of the progenitors’ evolution. we should exclude the πιοαν uncertaimties iu the unit of supernova rates aud introduce more detail galaxy models inchiding internal structure of a ealaxy aud galaxy uuniber evolution.," To discuss their implications in terms of the progenitors' evolution, we should exclude the luminosity uncertainties in the unit of supernova rates and introduce more detail galaxy models including internal structure of a galaxy and galaxy number evolution."
 The rate of SNe II in ellipticals evolves following the SFR without time delay., The rate of SNe II in ellipticals evolves following the SFR without time delay.
 Then. it is possible to observe SNe IT in ellipticals around +—1.," Then, it is possible to observe SNe II in ellipticals around $z \sim 1$."
 The iffereuce in the SN IT aud Ia rates between cluster aud field ellipticals reflects the difference in the galaxy formation histories iu the different euviromuenuts., The difference in the SN II and Ia rates between cluster and field ellipticals reflects the difference in the galaxy formation histories in the different environments.
orbits based on the closest approach to the boundary ODo for increasing eccentricity values.,orbits based on the closest approach to the boundary $\partial \mathcal{D}_0$ for increasing eccentricity values.
" For each shown eccentricity value, we select 100000 uniformly distributed initial conditions in the region defined by to€(7,27) and Eo€(ODo+2bsin(to),ODo)."," For each shown eccentricity value, we select 100000 uniformly distributed initial conditions in the region defined by $t_0\in(\pi,2\pi)$ and $E_0\in(\partial \mathcal{D}_0 + 2 b\sin(t_0), \partial
\mathcal{D}_0)$."
 These boundaries describe a band of initial conditions bounded above by the escape boundary., These boundaries describe a band of initial conditions bounded above by the escape boundary.
 This band also encompasses the capture region Bo., This band also encompasses the capture region $\mathcal{B}_0$.
 The drop in the density to the right of each curve occurs at the distance between the lower boundary curve and the escape boundary., The drop in the density to the right of each curve occurs at the distance between the lower boundary curve and the escape boundary.
 Note that the density drops off as initial conditions approach the escape boundary., Note that the density drops off as initial conditions approach the escape boundary.
 Data was fitted using a variable bandwidth kernel density function., Data was fitted using a variable bandwidth kernel density function.
 It was found above that as orbits approach the escape boundary the likelihood of an orbit being shadowed decreases., It was found above that as orbits approach the escape boundary the likelihood of an orbit being shadowed decreases.
 This has an impact on the shadow-ability of orbitsin the capture region Bo., This has an impact on the shadow-ability of orbitsin the capture region $\mathcal{B}_0$.
 The capture region area is directly proportional to the eccentricity of the binary., The capture region area is directly proportional to the eccentricity of the binary.
" As ο--0, the initial conditions in By become pushed up against the boundary OD."," As $e\rightarrow 0$, the initial conditions in $\mathcal{B}_0$ become pushed up against the boundary $\partial\mathcal{D}_0$."
" It is expected then that for small eccentricities, orbits would be less likely to be shadow-able."," It is expected then that for small eccentricities, orbits would be less likely to be shadow-able."
" To test this hypothesis, 10? uniformly distributed initial conditions are selected in Bo and iterated forwards until each orbit escapes."," To test this hypothesis, $10^5$ uniformly distributed initial conditions are selected in $\mathcal{B}_0$ and iterated forwards until each orbit escapes."
 This is performed for a variety of eccentricity values and the fraction of shadow-able orbits in each case is determined., This is performed for a variety of eccentricity values and the fraction of shadow-able orbits in each case is determined.
 The results are shown in Figure 11.., The results are shown in Figure \ref{fig:ECCvsPERCENT}.
 The fraction of shadow-able orbits increases as the eccentricity of the binary increases., The fraction of shadow-able orbits increases as the eccentricity of the binary increases.
 This is because the area of the capture region increases proportionally to e., This is because the area of the capture region increases proportionally to $e$.
" As the area increases, initial conditions can be selected at a much further distance from the escape boundary making them more likely shadow-able."," As the area increases, initial conditions can be selected at a much further distance from the escape boundary making them more likely shadow-able."
 The failure of the refinement procedure can happen at any point along the orbit and not necessarily at a close approach to the escape boundary., The failure of the refinement procedure can happen at any point along the orbit and not necessarily at a close approach to the escape boundary.
 The shadow duration is defined as the number of iterations for which a given orbit can be shadowed., The shadow duration is defined as the number of iterations for which a given orbit can be shadowed.
" For an orbit [(t;,E;)4o the shadow duration, T, can take on positive integer values T'«M."," For an orbit $\{(t_i,E_i)\}_{i=0}^{M}$ the shadow duration, $T$ , can take on positive integer values $T<M$."
 Consider the initial conditions for e—0.61 shown in Figure 9.., Consider the initial conditions for $e=0.61$ shown in Figure \ref{fig:shadowing}.
" For each resulting orbit, it is determined how long the orbit is shadow-able."," For each resulting orbit, it is determined how long the orbit is shadow-able."
 Figure 12 provides some information on the distribution of shadow lengths., Figure \ref{fig:probden} provides some information on the distribution of shadow lengths.
 Initial conditions are chosen in Do and iteratedforwards in time using (20))., Initial conditions are chosen in $\mathcal{D}_0$ and iteratedforwards in time using \ref{eq:map}) ).
" Each orbit is iterated for 50,000 iterations or until the solution escapes."," Each orbit is iterated for $50,000$ iterations or until the solution escapes."
 The solid line in Figure 12 represents the density of the numerical experiments.," The solid line in Figure \ref{fig:probden}
 represents the density of the numerical experiments."
" 'The spike at 50,000 iterations is mostly due to quasi-periodic orbits which remain bounded for all time."," The spike at 50,000 iterations is mostly due to quasi-periodic orbits which remain bounded for all time."
" As shown in Figure 12, the density can be approximated, for small iterations, by an exponential density function given by £exp(—£x)for £= 0.0019."," As shown in Figure \ref{fig:probden}, , the density can be approximated, for small iterations, by an exponential density function given by $\xi \exp(-\xi x)$for $\xi=0.0019$ ."
 The inset graph is a, The inset graph is a
The catalogue of groups/clusters contains the following information (the column numbers are given in square brackets):,The catalogue of groups/clusters contains the following information (the column numbers are given in square brackets):
The XMM-Newton Science Archive (XSA) contains three observations of the X-ray sky in the direction ofErt.,The XMM-Newton Science Archive (XSA) contains three observations of the X-ray sky in the direction of.
.. They are listed with their nominal exposure times in Tab. .., They are listed with their nominal exposure times in Tab. \ref{t:log}.
" We refer to individual observations by an ""E followed by the last three digits of the OBSID. i.e. E201 for the observation on 28"" of April. 2002."," We refer to individual observations by an 'E' followed by the last three digits of the OBSID, i.e. E201 for the observation on $^{\rm th}$ of April, 2002."
 All X-ray observations were obtainec in full frame mode., All X-ray observations were obtained in full frame mode.
 The RGS did not reveal useful data due to low count rate and will not considered further., The RGS did not reveal useful data due to low count rate and will not considered further.
 Data processing was performed with the latest version of the XMM-Newtor SAS (version 7.0). a spectral analysis of the X-ray data was performed with XSPEC.," Data processing was performed with the latest version of the XMM-Newton SAS (version 7.0), a spectral analysis of the X-ray data was performed with XSPEC."
 Despite the relatively short exposure times. almost full phase coverage of the Po.= 8lmmu binary was achieved at two occasions (E401 and E501).," Despite the relatively short exposure times, almost full phase coverage of the $\porb = 81$ min binary was achieved at two occasions (E401 and E501)."
 The accumulated phase uncertainty of the period derived by Piirola et al. (, The accumulated phase uncertainty of the period derived by Piirola et al. (
1987) at the epoch of the last XMM-Newton X-ray observation. re. after ~ 155000 binary cycles. is 0.014 phase units only and thus negligible.,"1987) at the epoch of the last XMM-Newton X-ray observation, i.e. after $\sim$ 155000 binary cycles, is 0.014 phase units only and thus negligible."
" EPIC-MOS and EPIC-PN show a faint apparent companion to at a(2000)=0314140 and 6(2000)=—22*36/04"".", EPIC-MOS and EPIC-PN show a faint apparent companion to at $\alpha(2000) = 03^h 14^m 14\fs0$ and $\delta(2000) = -22\degr 36' 04''$.
 The source has no counterpart on DSS? images., The source has no counterpart on DSS2 images.
 It contributes at a level of Fy=1.5x107 iin the 0.1 — 10 keV band., It contributes at a level of $F_X \simeq 1.5 \times 10^{-14}$ in the 0.1 – 10 keV band.
 This source could not be resolved in all previous X-ray observations with other satellites., This source could not be resolved in all previous X-ray observations with other satellites.
 [ts faint flux was just a small contamination of all previous X- observations and thus irrelevant., Its faint flux was just a small contamination of all previous X-ray observations and thus irrelevant.
 It represents. however. a ~20% contamination of the flux of dduring XMM-Newton observations.," It represents, however, a $\sim$ contamination of the flux of during XMM-Newton observations."
 We thus chose source and background regions for the extraction of light curves and spectra avoiding the region around this source., We thus chose source and background regions for the extraction of light curves and spectra avoiding the region around this source.
 The net exposure time of observation E20] was just ss. The source was detected with EPIC-PN at a mean count rate ofcrat., The net exposure time of observation E201 was just s. The source was detected with EPIC-PN at a mean count rate of.
. The spectrum contains no photons above 5 keV. it could be successfully fitted (reduced y=0.93 for 9 degrees of freedom) with a cooling plasma model (MEKAL in XSPEC terms) with a temperature of AT=2.8€1.7kkeV_ only very little affected by interstellar absorption.," The spectrum contains no photons above 5 keV, it could be successfully fitted (reduced $\chi^2 = 0.93$ for 9 degrees of freedom) with a cooling plasma model (MEKAL in XSPEC terms) with a temperature of $kT = 2.8\pm1.7$ keV only very little affected by interstellar absorption."
 In general. all X-ray spectral fits based on XMM-Newton observations are compatible with zero interstellar absorption. in accord with the low column density inferred from ROSAT and EXOSAT. Na=107? cem. (Beuermann et al.," In general, all X-ray spectral fits based on XMM-Newton observations are compatible with zero interstellar absorption, in accord with the low column density inferred from ROSAT and EXOSAT, $N_{\rm H} = 10^{19}$ $^{^2}$ (Beuermann et al."
 199]: Watson. King Williams 1987). and from EINSTEIN. Ny<|x10 cen (BSP87).," 1991; Watson, King Williams 1987), and from EINSTEIN, $N_{\rm H} < 1 \times 10^{20}$ $^{^2}$ (BSP87)."
 The integrated flux in this component was Fy=107 ((0.] — 10 keV)., The integrated flux in this component was $F_X = 7 \times 10^{-14}$ (0.1 – 10 keV).
 Observation E401 was performed with EPIC-MOS only and resulted in the detection of 26/20 photons in ss with MOS1/2. respectively.," Observation E401 was performed with EPIC-MOS only and resulted in the detection of 26/20 photons in s with MOS1/2, respectively."
 The spectrum was found to be very soft again. an unconstrained fit yielded AT=0.5+I kkeV. but the spectral parameters remained highly uncertain due to the small number of photons.," The spectrum was found to be very soft again, an unconstrained fit yielded $kT = 0.5 \pm 1$ keV, but the spectral parameters remained highly uncertain due to the small number of photons."
 A fit using the same parameters as for E501. see below. yielded a flux of Fy=4x1077 ((0.1 — 10 keV). slightly indicative of a lower X-ray flux at that epoch.," A fit using the same parameters as for E501, see below, yielded a flux of $F_X \simeq 4 \times 10^{-14}$ (0.1 – 10 keV), slightly indicative of a lower X-ray flux at that epoch."
 Observation E501 was performed with all three X-ray cameras onboard and revealed 140. 43. and 40 source photons with EPIC-PN. MOSI. and MOS2. respectively.," Observation E501 was performed with all three X-ray cameras onboard and revealed 140, 43, and 40 source photons with EPIC-PN, MOS1, and MOS2, respectively."
 The mean spectrum. which is à good approximation to the orbital mean spectrum also. is shown in Fig. 1..," The mean spectrum, which is a good approximation to the orbital mean spectrum also, is shown in Fig. \ref{f:spec501}."
 Again. it is a soft spectrum which could be fitted with just one emission component (reduced y=0.81 for 33 doof).," Again, it is a soft spectrum which could be fitted with just one emission component (reduced $\chi^2 = 0.81$ for 33 d.o.f.)."
 The best-fit: plasma temperature of the MEKAL model is KT.=1.7+0.2 kkeV. and the integrated flux Fy=6x1077 ((0.1 — 10 keV).," The best-fit plasma temperature of the MEKAL model is $kT = 1.7 \pm 0.2$ keV, and the integrated flux $F_X = 6 \times 10^{-14}$ (0.1 – 10 keV)."
 The ο—C residuals of such a fit (see Fig. 1)), The $O-C$ residuals of such a fit (see Fig. \ref{f:spec501}) )
 give the slight impression of a systematic trend with an excess of photons between kkeV. However. the parameters of any additional spectral component cannot be constrained significantly and we thus stick to à oe component X-ray spectrum.," give the slight impression of a systematic trend with an excess of photons between keV. However, the parameters of any additional spectral component cannot be constrained significantly and we thus stick to a one component X-ray spectrum."
 We found no significant X-ray variability of the total X-ray flux between the three XMM-Newton observations., We found no significant X-ray variability of the total X-ray flux between the three XMM-Newton observations.
 X-ray variability in E501. the longest of the three observations. was almost insignificant.," X-ray variability in E501, the longest of the three observations, was almost insignificant."
 A binned light curve with bin size 243 s (20 phase bins per orbital cycle) shows oe bin with no source photon., A binned light curve with bin size 243 s (20 phase bins per orbital cycle) shows one bin with no source photon.
 It occurs at phase 0.7. 1.e. 1t cannot be associated with the high state absorption dip (1f the accuracy of Prirola/s period is as high as the formal uncertainties given in their suggest).," It occurs at phase 0.7, i.e. it cannot be associated with the high state absorption dip (if the accuracy of Piirola's period is as high as the formal uncertainties given in their suggest)."
 Given the small number of X-ray photons a secure claim on the existence of a dip cannot be made., Given the small number of X-ray photons a secure claim on the existence of a dip cannot be made.
 The optical monitor OM was used in observations E201 and E501 with the V and UVWI] filters. respectively (see Tab.," The optical monitor OM was used in observations E201 and E501 with the $V$ and $UVW1$ filters, respectively (see Tab."
 | for details)., \ref{t:log} for details).
 In E201 full phase coverage was achieved. in E501 only parts of the orbital cycle were covered with the two filters.," In E201 full phase coverage was achieved, in E501 only parts of the orbital cycle were covered with the two filters."
galaxies divided in 5 clumps with mean separation 2.7Ph Alpe.,"galaxies divided in 5 clumps with mean separation $2.7 \, h^{-1}$ Mpc."
 As one can see [from Table 2.. the recovery docs not depend on the distance from the observer.," As one can see from Table \ref{tab2}, the recovery does not depend on the distance from the observer."
 However at small distances the Hubble flow and the peculiar velocities of the ealaxies becomes comparable. and we must take into account this effect.," However at small distances the Hubble flow and the peculiar velocities of the galaxies becomes comparable, and we must take into account this effect."
 We have repeated the analysis on each out. of 20 realizations of the four clusters obtained by randomly “reshullline” the original simulated catalogues with two different method: 1., We have repeated the analysis on each out of 20 realizations of the four clusters obtained by randomly ”reshuffling” the original simulated catalogues with two different method: 1.
 the first 10 reshulllings were mace by redistributing randomly the redshifts among the galaxies while keeping the angular coordinates fixed (see Table 7)): 2., the first 10 reshufflings were made by redistributing randomly the redshifts among the galaxies while keeping the angular coordinates fixed (see Table \ref{resh1}) ); 2.
 the remaining 10 reshulllings were made varving the redshilts (namely the value of ον) of a typical value. of the galaxies peculiar velocities in a random clirection. while keeping the angular coordinates fixed (see Table 8)).," the remaining 10 reshufflings were made varying the redshifts (namely the value of $cz$ ) of a typical value of the galaxies peculiar velocities in a random direction, while keeping the angular coordinates fixed (see Table \ref{resh2}) )."
 1n the first case. the average values of the number of structures found is always smaller than the one found in the original simulated clusters.," In the first case, the average values of the number of structures found is always smaller than the one found in the original simulated clusters."
 Εις test. already performed. in GPAB on a catalogue of clusters from the Coma cluster with the same result. strenethens our confidence on the physical significance of the structures detected in Coma.," This test, already performed in GPAB on a catalogue of clusters from the Coma cluster with the same result, strengthens our confidence on the physical significance of the structures detected in Coma."
 In the second case the number of structures is nearly the same as in the original catalogues., In the second case the number of structures is nearly the same as in the original catalogues.
 We “followed” some galaxies labelling them in the reshulllines and we have seen that the ealaxies labelled are always inside the same substructure for the clusters C1. C2. C3 and. reshullled. samples. but. may change substructure for the case of the cluster C4.," We ”followed” some galaxies labelling them in the reshufflings and we have seen that the galaxies labelled are always inside the same substructure for the clusters C1, C2, C3 and reshuffled samples, but may change substructure for the case of the cluster C4."
 This happens because in this latter case the peculiar velocities and the Hubble [low become comparable., This happens because in this latter case the peculiar velocities and the Hubble flow become comparable.
 However Ἡ is worth noticing that. although the galaxies may “leap” from. one substructure to another. the number of these is always nearly the same.," However it is worth noticing that, although the galaxies may ”leap” from one substructure to another, the number of these is always nearly the same."
 We simulate six clusters of galaxies made of an increasing number of data points (galaxies) ranging from a minimum of 118 to a maximum of 14712., We simulate six clusters of galaxies made of an increasing number of data points (galaxies) ranging from a minimum of 118 to a maximum of 14712.
 Clusters are identified. by the names €5 (mace of 1128 galaxies). €6 (330 galaxies). C7 (528 galaxies). C1(1512 galaxies). CS (7032 galaxies) and CO (14712 ealaxies).," Clusters are identified by the names C5 (made of 118 galaxies), C6 (330 galaxies), C7 (528 galaxies), C1 (1512 galaxies), C8 (7032 galaxies) and C9 (14712 galaxies)."
 MI these clusters are composed of 5 ebumps with mean separation διτῇ Alpe.," All these clusters are composed of 5 clumps with mean separation $2..7 \, h^{-1}$ Mpc."
 Lt is clear [from our results that a minimum number of at least 200 data points is required to ensure a correct. substructure recovery and that an increasing number of points improves the confidence of the analysis., It is clear from our results that a minimum number of at least 200 data points is required to ensure a correct substructure recovery and that an increasing number of points improves the confidence of the analysis.
 Clusters are identified by the names CLO (mean separation L5h* Alpe). CI (2.7h* Alpe). CLL G7h Alpe) and μμ... Alpe).," Clusters are identified by the names C10 (mean separation $1.5 \, h^{-1}$ Mpc), C1 $2.7 \, h^{-1}$ Mpc), C11 $3.7 \, h^{-1}$ Mpc) and C12 $4.7 \, h^{-1}$ Mpc)."
 We note no significant variations in the number of substructures detected as the mean interebunps separation vary. as one can see from. Table 4.. if the mean separation. is. greater than 1.5fL Alpe.," We note no significant variations in the number of substructures detected as the mean interclumps separation vary, as one can see from Table \ref{tab4}, if the mean separation is greater than $1.5 \, h^{-1}$ Mpc."
 Clusters are. identified by the names C17 (LOO completeness at mg= 22). CIS (mg= 20). CI9 (mg= 18) and C20 (mg= 16).," Clusters are identified by the names C17 (100 completeness at $m_B=22$ ), C18 $m_B=20$ ), C19 $m_B=18$ ) and C20 $m_B=16$ )."
 We note a progressive decrease in the number of structures found. as the magnitude. of completeness decrease.," We note a progressive decrease in the number of structures found, as the magnitude of completeness decrease."
 However. it is worth noticing that. till the value mig.=16 included. this decrease i9. not clramatic and the number of structures detected is very close to the elective number of structures composing the clusters.," However, it is worth noticing that, till the value $m_B=16$ included, this decrease is not dramatic and the number of structures detected is very close to the effective number of structures composing the clusters."
of our data is too low to measure line ratio gradients for individual galaxies; instead we stack the 2D spectroscopy to study line ratio gradients.,of our data is too low to measure line ratio gradients for individual galaxies; instead we stack the 2D spectroscopy to study line ratio gradients.
" We stack the 2D images for each galaxy, weighting each galaxy by normalizing its total (Hj+[O11]44959+ [O1u]A5007) line emission."," We stack the 2D images for each galaxy, equal-weighting each galaxy by normalizing its total $\Hb+\OIII\lambda4959+\OIII\lambda5007$ ) line emission."
 Images are aligned by the peak of the emission (dominated by the line)., Images are aligned by the peak of the emission (dominated by the $\lambda$ 5007 line).
 This stacked spectrum allows us to study the [O11]A5007spatial extent of the aand eemission lines., This stacked spectrum allows us to study the spatial extent of the and emission lines.
 One-dimensional spatial profiles can be constructed by extracting each emission line along the cross-dispersion direction., One-dimensional spatial profiles can be constructed by extracting each emission line along the cross-dispersion direction.
" Figure 5 shows the spatial profiles for the H8A4861 and [Orn]A5007 emission lines, along with the collapsed cross-dispersion profile of the entire 2D spectrum."," Figure \ref{fig:linespatial} shows the spatial profiles for the $\lambda4861$ and $\lambda5007$ emission lines, along with the collapsed cross-dispersion profile of the entire 2D spectrum."
 Each emission line is extracted from the central three pixels (140À)) about the line center., Each emission line is extracted from the central three pixels ) about the line center.
" The line has a cross-dispersion full-width half-maximum (FWHM) of 7.2 pixels (0794, ~8 kpc), while the line is narrower with a FWHM of 4.9 pixels (0:64, ~5 We kpc)."," The line has a cross-dispersion full-width half-maximum (FWHM) of 7.2 pixels $0\farcs94$, $\sim$ 8 kpc), while the line is narrower with a FWHM of 4.9 pixels $0\farcs64$, $\sim$ 5 kpc)."
test the significance of the lline being more spatially compact[O thanr1] the line by bootstrapping 100 000 resampled profiles., We test the significance of the line being more spatially compact than the line by bootstrapping 100 000 resampled profiles.
" We construct each bootstrapped profile by adding a normally-distributed random error (with o given by the propagated error of the stacked profile) to the original data, and then measure FWHM([Ori])) and FWHM(H5))."," We construct each bootstrapped profile by adding a normally-distributed random error (with $\sigma$ given by the propagated error of the stacked profile) to the original data, and then measure ) and )."
 The fraction of bootstrapped profiles with FWHM([Or1))FWHM(H)) gives the significance of bbeing more compact thanΗβ., The fraction of bootstrapped profiles with ) gives the significance of being more compact than.
". This occurs in of the resampled data sets, and so the lline is more compact than the lline with confidence."," This occurs in of the resampled data sets, and so the line is more compact than the line with confidence."
 We also measure the spatially resolved /(|O11])/f(H8) ratio and (U—B) in the inner and outer regions of the stacked spectrum., We also measure the spatially resolved $f(\OIII)/f(\Hb)$ ratio and $(U-B)$ in the inner and outer regions of the stacked spectrum.
" We designate the ""inner region"" as the central 3x pixel box (0739x0739, or 3.2x kpc at z— 1.86) in the cross-dispersion direction, and the “outer region"" as the two boxes 3 pixels wide from pixel numbers 4 through 6 (0739— 0""78) above and below the center in the cross-dispersion direction."," We designate the “inner region” as the central $3 \times 3$ pixel box $0\farcs39 \times 0\farcs39$, or $3.2 \times 3.2$ kpc at $z=1.86$ ) in the cross-dispersion direction, and the “outer region” as the two boxes 3 pixels wide from pixel numbers 4 through 6 $0\farcs39-0\farcs78$ ) above and below the center in the cross-dispersion direction."
" Line ratios are calculated for both the inner and outer regions, using the same method of continuum subtraction and Gaussian fitting described above."," Line ratios are calculated for both the inner and outer regions, using the same method of continuum subtraction and Gaussian fitting described above."
" Color gradients were calculated using the CANDELS WFC3 Y, J, and H imaging2011)."," Color gradients were calculated using the CANDELS WFC3 $Y$, $J$ , and $H$ imaging."
". The WFC3 images are drizzled to a finer resolution (07006) than the WFC3 spectroscopy, and so we adopt 0756 (6 pixel circular diameter) as the inner region and 0736—0""72 (circular annulus from 6 to 12 pixels) as the outer region."," The WFC3 images are drizzled to a finer resolution 06) than the WFC3 spectroscopy, and so we adopt $0\farcs36$ (6 pixel circular diameter) as the inner region and $0\farcs36-0\farcs72$ (circular annulus from 6 to 12 pixels) as the outer region."
" Rather than stacking, we measure aperture Y, J, and H for each individual galaxy."," Rather than stacking, we measure aperture $Y$ , $J$, and $H$ for each individual galaxy."
 We then treat the median Y—J (for low redshift z« 1.8) or J—H z> 1.8) difference from the inner to outer (for(0736— aperture as the change in («(U0736)—B)yest over the same 0772)aperture., We then treat the median $Y-J$ (for low redshift $z<1.8$ ) or $J-H$ (for $z>1.8$ ) difference from the inner $<0\farcs36$ ) to outer $0\farcs36-0\farcs72$ ) aperture as the change in $(U-B)_{\rm rest}$ over the same aperture.
" As Figure 4 shows, the stacked inner region has marginally redder colors and slightly higher line ratios than the outer region."," As Figure \ref{fig:bpt} shows, the stacked inner region has marginally redder colors and slightly higher line ratios than the outer region."
" In other words, the inner region is more like an AGN than the outer region."," In other words, the inner region is more like an AGN than the outer region."
 However the large errors (particularly on the outer ratio) mean that this is significant only at the 1.00 level , However the large errors (particularly on the outer ratio) mean that this is significant only at the $1.0\sigma$ level ).
"This is probably because the 039 size of the inner (67%)).region corresponds to the inner 3.2 kpc of the galaxy (at the median redshift z— and so includes much more than the typical ~1 kpc 1.86),narrow line region(NLR) of an AGN."," This is probably because the $0\farcs39$ size of the inner region corresponds to the inner 3.2 kpc of the galaxy (at the median redshift $z=1.86$ ), and so includes much more than the typical $\sim$ 1 kpc narrow line region(NLR) of an AGN."
" The marginal difference between inner andouter line ratios is merely suggestive, but is reinforced by the"," The marginal difference between inner andouter line ratios is merely suggestive, but is reinforced by the"
"We can abbreviate (13)) as Here 77,ui. produces motionless geodesics. Hey gives the IKkeplerian phenomenology. Hee Is the weak-field Schwarzschild contribution that produces pericenter precession. while the angular-temporal terim Hyy produces the Lens-Thirrine effect or frame drageing.","We can abbreviate \ref{timelikeMetric}) ) as Here $\H_\static$ produces motionless geodesics, $\H_\kep$ gives the Keplerian phenomenology, $\H_\schw$ is the weak-field Schwarzschild contribution that produces pericenter precession, while the angular-temporal term $\H_\fd$ produces the Lens-Thirring effect or frame dragging."
 Continuing now io photon trajectories. we remark (hat by the equivalence principle. the full Wamil(onian is exactly (he same for photons aud stars.," Continuing now to photon trajectories, we remark that by the equivalence principle, the full Hamiltonian is exactly the same for photons and stars."
 Lowever. the same terms can have different orders in (he (wo regimes. prompling approximation He!," However, the same terms can have different orders in the two regimes, prompting approximation $\H^\photon$."
" dn particular. the approximation (11)) obviously does not hold for photons. which have ο=1. implving the scalings with p,1 beinge O(1)."," In particular, the approximation \ref{velocity}) ) obviously does not hold for photons, which have $v^2=1$, implying the scalings with $p_r$ being $\O(1)$."
 Expandinge as before. we obtain - a different selection of terms compared to the post-Newtoniancase.," Expanding as before, we obtain - a different selection of terms compared to the post-Newtoniancase."
 There is no term at O(e?)., There is no term at $\O(\epsilon^5)$.
 We may abbreviate (16)) as At zeroth order we have special relativistic or Minkowski photons., We may abbreviate \ref{nullmetric}) ) as At zeroth order we have special relativistic or Minkowski photons.
 The leadinge order Schwarzschild effect HL° gives the gravitational deflection of light., The leading order Schwarzschild effect $\H^\slo$ gives the gravitational deflection of light.
 At ο(e+). however. there are three distinet effects: first 2275-0. oOeives a next-to-leaclinge order correction to the Schwarzschild effect. (he off-diagonal term H!'P gives frame dragging again but [or photon trajectories. while 27! provides a torque proportional to ο”.," At $\O\left(\epsilon^4\right)$, however, there are three distinct effects: first $\H^\snlo$ gives a next-to-leading order correction to the Schwarzschild effect, the off-diagonal term $\H^\fd$ gives frame dragging again but for photon trajectories, while $\H^\torq$ provides a torque proportional to $s^2$ ."
"momentum of the star owing to the wind is where €? is the angular velocity of the star and Ra is the Alfvénn radius at which outflow speed equals the local magnetic Alfvénn speed where pa is the density of wind material, B4 is the magnetic field strength at the Alfvénn surface and M,,«0 is the mass-loss rate.","momentum of the star owing to the wind is where $\Omega$ is the angular velocity of the star and $R_{\rm
 A}$ is the Alfvénn radius at which outflow speed equals the local magnetic Alfvénn speed where $\rho _{\rm A}$ is the density of wind material, $B_{\rm A}$ is the magnetic field strength at the Alfvénn surface and $\dot{M}_{\rm
 w} < 0$ is the mass-loss rate."
 For a spherical outflow The angular momentum loss rate depends on the field structure and flow velocity which are not easily determined a priori for the wind., For a spherical outflow The angular momentum loss rate depends on the field structure and flow velocity which are not easily determined a priori for the wind.
 We need to make assumptions about both., We need to make assumptions about both.
" To model the magnetic field structure in a simple manner, we assume that field strength follows a single power law of the form where n describes the geometry of the stellar field and n=3 corresponds to a dipole field (Weber&Davis|1967;|MestelSpruit}|1987)) while B; and B4 are the magnetic flux densities at the stellar surface and at the Alfvénn radius, respectively."," To model the magnetic field structure in a simple manner, we assume that field strength follows a single power law of the form where $n$ describes the geometry of the stellar field and $n=3$ corresponds to a dipole field \citep{weber1967,mestel1987} while $
B_{\rm s} $ and $ B_{\rm A} $ are the magnetic flux densities at the stellar surface and at the Alfvénn radius, respectively."
 It is usually assumed that the thermal wind velocity is of the order of the escape velocity, It is usually assumed that the thermal wind velocity is of the order of the escape velocity
The determination of accurate current star orluation rates (SFRs) is of fundamental importance or the understanding and investigation of the orocesses relevant for star formation and ealaxy evolution.,The determination of accurate current star formation rates (SFRs) is of fundamental importance for the understanding and investigation of the processes relevant for star formation and galaxy evolution.
 A commonly used tracer to calculate he current SER of ealaxies is he measurement of the Πα chussion line which is Luked to the oxesence of short-lived. πο.ars., A commonly used tracer to calculate the current SFR of galaxies is the measurement of the $\alpha$ emission line which is linked to the presence of short-lived massive stars.
 The standard way to construct relatious hetween he total Πα hunuinositv aud the total SER of a galaxv ix to apply ou galaxyv-wide scales an invariant stellar initial mass function (IME) which is determined in star clusters (eg.7?77?77)..," The standard way to construct relations between the total $\alpha$ luminosity and the total SFR of a galaxy is to apply on galaxy-wide scales an invariant stellar initial mass function (IMF) which is determined in star clusters \citep[eg.][]{kennicutt1983a,gallagher1984a,kennicutt1994a,kennicutt1998b,kennicutt1998a}."
" This iethod provides a linear SER-Zj,, relation as long as the assinned: galaxyv-wide IMPE is treated to be constant aud independent of the SER.", This method provides a linear $L_\mathrm{H\alpha}$ relation as long as the assumed galaxy-wide IMF is treated to be constant and independent of the SFR.
" A basic result of SFR studies is that 9ER/M,. decreases with decreasing total neutral eas mass. Maas."," A basic result of SFR studies is that $SFR/M_\mathrm{gas}$ decreases with decreasing total neutral gas mass, $M_\mathrm{gas}$."
 Low-gasanass (dwirf nregular) galaxies wb their gas iuto stars over much lonecr time scales than hieh-sgas-niass (large disk) galaxies (ec.777).," Low-gas-mass (dwarf irregular) galaxies turn their gas into stars over much longer time scales than high-gas-mass (large disk) galaxies \citep[eg.][]{skillman2003a,karachentsev2007a,kaisin2008a}."
" That dwiuf galaxies have lower star-ormation efficiencies, defined as 7,4IBSPR/ALA han niassive galaxies has been a generally accepted act at he base of most theoretical work ou galaxy evolution."," That dwarf galaxies have lower star-formation efficiencies, defined as $\tau_\mathrm{gas}^{-1}=SFR/M_\mathrm{gas}$, than massive galaxies has been a generally accepted fact at the base of most theoretical work on galaxy evolution."
 But iu the last vears it has heen shown that he application of the IMIF in star clusters to ealaxv-wide scales is doubful οον. Tusteacl.," But in the last years it has been shown that the application of the IMF in star clusters to galaxy-wide scales is doubtful \citep{weidner2003a,weidner2005a,weidner2006a,hoversten2008a,meurer2009a,lee2009a}."
" he galaxwv-wide IME has to be calculated by adding all IMEs of all vouug star clusters leading o an iutegrated ealactic stellar initial nias ""unction. (IGINE)."," Instead, the galaxy-wide IMF has to be calculated by adding all IMFs of all young star clusters leading to an integrated galactic stellar initial mass function (IGIMF)."
 The fundamental property of the IGIME-theorv is hat for massive stars, The fundamental property of the IGIMF-theory is that for massive stars
"given above, so the model could be in even bigger trouble.","given above, so the model could be in even bigger trouble."
 The alternative claims (??) of light DM annihilations in our Galaxy will also be stringently tested.," The alternative claims \citep{2009arXiv0910.2998G,2011PhLB..697..412H} of light DM annihilations in our Galaxy will also be stringently tested."
" Finally, it would be interesting to compare the bounds given in ?,, which are based on the results obtained by ?,, with our values."," Finally, it would be interesting to compare the bounds given in \citet{2009PhRvD..80d3526S}, which are based on the results obtained by \citet{2009PhRvD..80b3505G}, with our values."
" However, since ? used ‘on the spot’ approximation for the energy deposition, the comparison can only be approximate."," However, since \citet{2009PhRvD..80b3505G} used `on the spot' approximation for the energy deposition, the comparison can only be approximate."
 The WMAP5 sigma bound as given by Eq. (, The WMAP5 2-sigma bound as given by Eq. (
6) of? can be cast in the form (cav)[3x10-26em?s71]/mpm[GeV]«0.12/f.,"6) of\citet{2009PhRvD..80d3526S} can be cast in the form $\cs\,\left[3\times10^{-26}\,{\rm cm}^3{\rm s}^{-1}\right]/m_{{\rm DM}}\,\left[{\rm GeV}\right]<0.12/f$."
" To compare this with our WMAP7 results, we have to set f,—0 in Eq. (i) "," To compare this with our WMAP7 results, we have to set $f_{\nu}=0$ in Eq. \ref{eq1}) )"
"and, in the above relation, use a typical value for the f-parameterat z~1000, which from Fig."," and, in the above relation, use a typical value for the $f$ -parameterat $z\sim 1000$, which from Fig."
 is f~0.85., \ref{fig4} is $f\sim 0.85$.
" Thus, the value for r that should be directly comparable to the 2-sigma WMAP value given in Table [l| is 0.12/0.85~0.14."," Thus, the value for $r$ that should be directly comparable to the 2-sigma WMAP value given in Table \ref{tab1} is $0.12/0.85\sim 0.14$."
" Considering the differences in the treatment for the energy deposition, this value agrees reasonably well with our result."," Considering the differences in the treatment for the energy deposition, this value agrees reasonably well with our result."
" However, there are significantly greater differences if one compares the forecasts for the Planck and CVL experiments."," However, there are significantly greater differences if one compares the forecasts for the Planck and CVL experiments."
" In our case Planck and CVL would tighten the 2-sigma bound of WMAP by a factor of —6 and -14, respectively."," In our case Planck and CVL would tighten the 2-sigma bound of WMAP by a factor of $\sim 6$ and $\sim 14$, respectively."
" The corresponding numbers (~13 and ~40, respectively) from ? are certainly more optimistic."," The corresponding numbers $\sim 13$ and $\sim 40$, respectively) from \citet{2009PhRvD..80b3505G} are certainly more optimistic."
" For CVL, some of this discrepancy is surely due to the higher £44; value assumed in ?:: €max=2500 compared to our fmax= 2000."," For CVL, some of this discrepancy is surely due to the higher $\ell_{\max}$ value assumed in \citet{2009PhRvD..80b3505G}: $\ell_{\max}=2500$ compared to our $\ell_{\max}=2000$ ."
" Even though we are comparing here the results derived from WMAP5 and WMAP7, the difference is expected to be negligible because the accuracy of the cosmological parameters with an additional two years of WMAP data improves only very moderately (typically somewhere between 5— 15%), and thus cannot be the cause of the above discrepancy."," Even though we are comparing here the results derived from WMAP5 and WMAP7, the difference is expected to be negligible because the accuracy of the cosmological parameters with an additional two years of WMAP data improves only very moderately (typically somewhere between $5-15\%$ ), and thus cannot be the cause of the above discrepancy."
" NOTE: After the first version of this work was submitted, a new paper by ? appeared where the authors have performed a similar analysis (now also using WMAP7 data), this time finding results that agree with ours more closely: typical deviations are now within factors 1.2—2, with their bounds on annihilation cross section being somewhat stronger."," NOTE: After the first version of this work was submitted, a new paper by \citet{2011PhRvD..84b7302G} appeared where the authors have performed a similar analysis (now also using WMAP7 data), this time finding results that agree with ours more closely: typical deviations are now within factors $1.2-2$, with their bounds on annihilation cross section being somewhat stronger."
 These relatively small deviations are actually quite negligible keeping in mind several approximations used in both analyses., These relatively small deviations are actually quite negligible keeping in mind several approximations used in both analyses.
" To see how much the omission of the additional excitations of atoms could change our results, we also performed several calculations where the exciting Ly-a photons are treated along the lines presented in ?.."," To see how much the omission of the additional excitations of atoms could change our results, we also performed several calculations where the exciting $\alpha$ photons are treated along the lines presented in \citet{2004PhRvD..70d3502C}."
" In agreement with the claim in ?,, we find that the bounds on annihilation cross section are getting tighter only up to ~10%; 1.ο., the excitations seem to have only a relatively weak effect with the current prescription."," In agreement with the claim in \citet{2011PhRvD..84b7302G}, we find that the bounds on annihilation cross section are getting tighter only up to $\sim 10\%$; i.e., the excitations seem to have only a relatively weak effect with the current prescription."
" Although for most of the channels and, in particular, for the lower end of the considered DM particle mass range, the number of protons produced is completely negligible, for quark and gluon channels the contribution can reach ~15% of the total energy input if one has masses at the higher end of the considered range."," Although for most of the channels and, in particular, for the lower end of the considered DM particle mass range, the number of protons produced is completely negligible, for quark and gluon channels the contribution can reach $\sim 15\%$ of the total energy input if one has masses at the higher end of the considered range."
" As this is still only a relatively mild contribution, we did not attempt any detailed modeling for the proton component and simply assumed that all of this energy is absorbed as heat by the cosmic medium."," As this is still only a relatively mild contribution, we did not attempt any detailed modeling for the proton component and simply assumed that all of this energy is absorbed as heat by the cosmic medium."
 A simple justification is the following., A simple justification is the following.
 The energy loss rate for protons with the energies of interest in this paper is dominated by proton-proton scattering., The energy loss rate for protons with the energies of interest in this paper is dominated by proton-proton scattering.
" Thus the loss rate Τ=—45:7npcoppKpp, where np is the number density of target protons, opp the scattering cross section, and K,, the inelasticity parameter."," Thus the loss rate $\Gamma\equiv -\frac{1}{E}\frac{{\rm d}E}{{\rm d}t}\simeq n_{\rm p}c\sigma_{\rm pp}K_{\rm pp}$, where $n_{\rm p}$ is the number density of target protons, $\sigma_{\rm pp}$ the scattering cross section, and $K_{\rm pp}$ the inelasticity parameter."
" The cross section opp depends only weakly on proton energy with typical values of 30—40 mbarn and inelasticity parameter Ky,~0.5 for the energies of interest in this work (see e.g. ?)).", The cross section $\sigma_{\rm pp}$ depends only weakly on proton energy with typical values of $30-40$ mbarn and inelasticity parameter $K_{\rm pp}\simeq 0.5$ for the energies of interest in this work (see e.g. \citealt{2008MNRAS.387..987W}) ).
 At redshifts z~1000 we therefore get [10-1? s-! for the energy loss rate., At redshifts $z\sim 1000$ we therefore get $\Gamma\simeq 10^{-13}$ $^{-1}$ for the energy loss rate.
" Comparing this to the expansion rate H at the same redshift, H~0.4x107? s-!, we see that I'>H, so one might expect a significant fraction of the proton energy to be absorbed."," Comparing this to the expansion rate $H$ at the same redshift, $H\simeq 0.4\times 10^{-13}$ $^{-1}$ , we see that $\Gamma \gtrsim H$ , so one might expect a significant fraction of the proton energy to be absorbed."
 In this paper we have calculated the existing and future CMB constraints on annihilating DM assuming the S-wave annihilation mode to be dominant., In this paper we have calculated the existing and future CMB constraints on annihilating DM assuming the S-wave annihilation mode to be dominant.
 Our results can be summarized as follows., Our results can be summarized as follows.
ratios should come out the same as long as the selection criteria are the same.,ratios should come out the same as long as the selection criteria are the same.
 However. the small number of observed stars that actually fall within our selection box make it hard to draw any firm conclusions from this comparison.," However, the small number of observed stars that actually fall within our selection box make it hard to draw any firm conclusions from this comparison."
 We present new evolution calculations for stellar collision products. where we have allowed the progenitor stars to have a different helium abundance.," We present new evolution calculations for stellar collision products, where we have allowed the progenitor stars to have a different helium abundance."
 Our collision models do a reasonable job of reproducing the observed blue straggler luminosity function and colour distribution., Our collision models do a reasonable job of reproducing the observed blue straggler luminosity function and colour distribution.
 We predict. perhaps. too few blue stragglers at the red edge of the observed distribution.," We predict, perhaps, too few blue stragglers at the red edge of the observed distribution."
" For NGC 1851. the best agreement is obtained for a single yopulation of helium normal stars οὐ= 0.24) while for NGC 2808 the best fit is obtained with a population of mixed Y,=0.24 and Y,=0.32 stars."," For NGC 1851, the best agreement is obtained for a single population of helium normal stars $Y_0 = 0.24$ ) while for NGC 2808 the best fit is obtained with a population of mixed $Y_0 = 0.24$ and $Y_0 = 0.32$ stars."
 Tjese results are what we would expect in ight of observations of multiple populations in these clusters., These results are what we would expect in light of observations of multiple populations in these clusters.
" A ower metallicity set o"" models agrees with NGC 6093 and NGC 5634 in the sense that t1e best fitting models are those without a jelium. enhanced popuation.", A lower metallicity set of models agrees with NGC 6093 and NGC 5634 in the sense that the best fitting models are those without a helium enhanced population.
 The observed population ratios of blue stragglers to evolved blue stragglers is larger than is seen in the observations. but the number of observed evolved blue straggler candidates is small.," The observed population ratios of blue stragglers to evolved blue stragglers is larger than is seen in the observations, but the number of observed evolved blue straggler candidates is small."
 Recently. reported the presence of two distinct populations in NGC 1851. one helium normal and one helium enhanced (Y= 0.28).," Recently, reported the presence of two distinct populations in NGC 1851, one helium normal and one helium enhanced $Y =
0.28$ )."
 However. they also report that the helium-rich population has a higher metallicity. which offsets the colour changes due to helium enhancement. at least in V—/ colours.," However, they also report that the helium-rich population has a higher metallicity, which offsets the colour changes due to helium enhancement, at least in $V - I$ colours."
 Since all our models have the same metallicity. there is no corresponding compensation for the shift in colour due to helium enhancement.," Since all our models have the same metallicity, there is no corresponding compensation for the shift in colour due to helium enhancement."
 To compare our models more directly we would need to allow for a similar shift in metallicity., To compare our models more directly we would need to allow for a similar shift in metallicity.
 Although the agreement between our models and the observations is reasonable. the agreement is not perfect and the models presented here are not complete.," Although the agreement between our models and the observations is reasonable, the agreement is not perfect and the models presented here are not complete."
 There are two obvious improvements that can be made., There are two obvious improvements that can be made.
 The tirst of these has to do with he blue straggler formation rate. which we have effectively taken o be constant and independent of the helium abundances of the two colliding stars.," The first of these has to do with the blue straggler formation rate, which we have effectively taken to be constant and independent of the helium abundances of the two colliding stars."
 By allowing the collision rate V. in ¢?2)) to vary with feo) We have more freedom in shaping the colour and luminosity 'unctions — in fact. if we want to use blue stragglers (and possibly evolved blue stragglers) to learn about the dynamical history of heir host cluster. then it is essential that we allow this factor to vary.," By allowing the collision rate $\Psi$ in \ref{eqn:weight}) ) to vary with $t_\mathrm{coll}$ we have more freedom in shaping the colour and luminosity functions – in fact, if we want to use blue stragglers (and possibly evolved blue stragglers) to learn about the dynamical history of their host cluster, then it is essential that we allow this factor to vary."
 Simulations of clusters hosting multiple populations. like those of may serve as a guide for how this should be done.," Simulations of clusters hosting multiple populations, like those of may serve as a guide for how this should be done."
 Ideally. he collision rate should be directly determined from dynamical simulations of cluster evolution.," Ideally, the collision rate should be directly determined from dynamical simulations of cluster evolution."
 A software environment that might be especially suited for this task is the MUSE software package. which is in active development(?)}.," A software environment that might be especially suited for this task is the MUSE software package, which is in active development."
. The second improvement that can (and should) be made is that we should consider binaries in addition to single star models., The second improvement that can (and should) be made is that we should consider binaries in addition to single star models.
 For the blue stragglers. this is an obvious addition because binary mass transfer is an alternative scenario for blue straggler productionmainBodyCitationEnd6073][]ChenHan2009.," For the blue stragglers, this is an obvious addition because binary mass transfer is an alternative scenario for blue straggler production."
 However. binaries are also important in another respect: observationally. it is not possible to distinguish the light of the two stars in a binary system. which may place the system in an unusual point in the colour magnitude diagram that is hard to reproduce with single star evolution tracks.," However, binaries are also important in another respect: observationally, it is not possible to distinguish the light of the two stars in a binary system, which may place the system in an unusual point in the colour magnitude diagram that is hard to reproduce with single star evolution tracks."
 This becomes especially important when we look for evolved blue stragglers because a blend of a horizontal branch star and a red giant may appear in the same region of the colour-magnitude diagram as the evolved blue stragglers., This becomes especially important when we look for evolved blue stragglers because a blend of a horizontal branch star and a red giant may appear in the same region of the colour-magnitude diagram as the evolved blue stragglers.
 Such unresolved binaries can be recognised by multi-wavelength photometry because the colour of the unresolved binary will not change in the same way as that of a single star. and the binary will move to a different region of the colour-magnitude diagram: a normal star will stay close to other stars of a similar spectral type. but an unresolved binary wil move closer to the position of one of its unresolved components.," Such unresolved binaries can be recognised by multi-wavelength photometry because the colour of the unresolved binary will not change in the same way as that of a single star, and the binary will move to a different region of the colour-magnitude diagram: a normal star will stay close to other stars of a similar spectral type, but an unresolved binary will move closer to the position of one of its unresolved components."
 Evolved blue stragglers offer an interesting possibility to test our understanding of blue straggler evolution. but because the number of observed post-blue straggler candidates is small it is especially important to understand how this region of the colour magnitude diagram may be influenced by the presence of binaries.," Evolved blue stragglers offer an interesting possibility to test our understanding of blue straggler evolution, but because the number of observed post-blue straggler candidates is small it is especially important to understand how this region of the colour magnitude diagram may be influenced by the presence of binaries."
 Both normal binary interaction and collisions can increase the actual number of stars in the evolved blue straggler region without increasing the number of blue stragglers., Both normal binary interaction and collisions can increase the actual number of stars in the evolved blue straggler region without increasing the number of blue stragglers.
 Unstable binary mass transfer from a red giant to an unevolved main sequence star companion can lead to a spiral in and merger of the two stars if the envelope is not ejected., Unstable binary mass transfer from a red giant to an unevolved main sequence star companion can lead to a spiral in and merger of the two stars if the envelope is not ejected.
 A collision with a red giant will have a similar result., A collision with a red giant will have a similar result.
 The red giant core is likely to remain intact during the merger so the merger product will still have a degenerate helium core and evolve like a more massive red giant., The red giant core is likely to remain intact during the merger so the merger product will still have a degenerate helium core and evolve like a more massive red giant.
" Such a merger would show up as an ""evolved blue straggler"" despite never having been a blue straggler itself.", Such a merger would show up as an “evolved blue straggler” despite never having been a blue straggler itself.
 Our population models are consistent with observations of multiple populations in the sense that helium enhanced model sets fit best with clusters tin particular. NGC 2808) where helium enhancement has been inferred from the observations.," Our population models are consistent with observations of multiple populations in the sense that helium enhanced model sets fit best with clusters (in particular, NGC 2808) where helium enhancement has been inferred from the observations."
 We hope that with the inclusion of a population of binaries. population models such as we have presented in this paper could be used not only to test our understanding of cluster dynamics but also to get a better handle on the nature of the multiple populations that are now observed in star clusters.," We hope that with the inclusion of a population of binaries, population models such as we have presented in this paper could be used not only to test our understanding of cluster dynamics but also to get a better handle on the nature of the multiple populations that are now observed in star clusters."
 Future cluster simulations that include an accurate treatment of the evolution of stellar collision products as well as multiple populations will be an important diagnostic tool and we plan to make our models available for such a study., Future cluster simulations that include an accurate treatment of the evolution of stellar collision products as well as multiple populations will be an important diagnostic tool and we plan to make our models available for such a study.
by a Bayesian analysis.,by a Bayesian analysis.
" The average dust attenuation curve we obtain can be written: where ,t=5500 Α. ΚΑ) is given in Calzettietal.(2000) (Eq.4) and Strictly speaking this average attenuation curve applies to the young stellar component only (as explained i sectioαυ] 3). the dust attenuation. applied to the old component beingο reduced by a factor 2."," The average dust attenuation curve we obtain can be written: where $\lambda_V = 5500$ $\AA$, $k'(\lambda)$ is given in \citet{calzetti00} (Eq.4) and Strictly speaking this average attenuation curve applies to the young stellar component only (as explained in section 3), the dust attenuation applied to the old component being reduced by a factor 2."
 In practice. the SEDs of our galaxies appear to be dominated by the young stellar component (modeled as a constant star formation rate over ~105 years). especially in UV.," In practice, the SEDs of our galaxies appear to be dominated by the young stellar component (modeled as a constant star formation rate over $\sim 10^8$ years), especially in UV."
 As a result the global attenuation curve is found to be quite similar to that of the young stellar component The uncertainty on the average value of o implies quite a large dispersion of the attenuation curve at 2«2500A (Fig. 7)), As a result the global attenuation curve is found to be quite similar to that of the young stellar component The uncertainty on the average value of $\delta$ implies quite a large dispersion of the attenuation curve at $\lambda < 2500~ \AA$ (Fig. \ref{att}) )
 and of the determination of dust attenuation at UV wavelengths., and of the determination of dust attenuation at UV wavelengths.
 For a visual attenuation Ay=| mag the difference between the dust attenuation at 1500 A obtained by using Eq., For a visual attenuation $A_{\rm V} = 1$ mag the difference between the dust attenuation at 1500 $\AA$ obtained by using Eq.
 3 (0= -0.13) or a Calzetti et al., 3 $\delta=-0.13$ ) or a Calzetti et al.
 law (6= 0) reaches 0.5 mag., law $\delta=0$ ) reaches 0.5 mag.
 A value of 0# also implies a change in the value of the effective total obscuration Ry=Αν/Εν. Calz, A value of $\delta \not= 0$ also implies a change in the value of the effective total obscuration ${\rm R_V= A_{\rm V}/E_{B-V}}$.
ettietal.(2000) obtain Ry=4.05£0.80 by comparing. the predicted and observed absorbed emission (1.8. by performing an energetic budget)., \citet{calzetti00} obtain $\rm {R_V=4.05\pm 0.80}$ by comparing the predicted and observed absorbed emission (i.e. by performing an energetic budget).
 Adopting a value of 06=—0.13 leads to Ry=Ay/Ep-y3.7. still consistent with the value found by Calzettietal.(2000).," Adopting a value of $\delta=-0.13$ leads to $\rm {R_V= A_V/E_{B-V}=3.7}$, still consistent with the value found by \citet{calzetti00}."
 The introduction of a bump of moderate amplitude i the dust attenuation curve (Eq., The introduction of a bump of moderate amplitude in the dust attenuation curve (Eq.
" 3) leads to an increase of AGDO/Av at =2000A of =0.35 mag as compared to the same curve with Dy.5,G0=0."," 3) leads to an increase of $A(\lambda)/A_{\rm V}$ at $\simeq 2000~ \AA$ of $\simeq 0.35$ mag as compared to the same curve with $D_{\lambda_0,\gamma,E_{\rm b}}(\lambda) = 0$."
 We can compare our average dust attenuation curve to other attenuation curves in the literature., We can compare our average dust attenuation curve to other attenuation curves in the literature.
" Charlot&Fall(2000) propose a recipe consisting in attenuating the stellar emission by a factor proportional to 27"" and in reducing the normalization of the attenuation for stars older than 10’ years; the resulting effective absorption curve they obtain for a constant star formation rate over 310? years (their Fig."," \citet{charlot00} propose a recipe consisting in attenuating the stellar emission by a factor proportional to $\lambda^{-0.7}$, and in reducing the normalization of the attenuation for stars older than $10^7$ years; the resulting effective absorption curve they obtain for a constant star formation rate over $3~10^8$ years (their Fig."
 5) is reported in Fig. 7.., 5) is reported in Fig. \ref{att}.
 A period of 310° years is close to the mean duration of the burst of star formation we obtain for the young stellar population (10? years. cf.," A period of $3~10^8$ years is close to the mean duration of the burst of star formation we obtain for the young stellar population $10^8$ years, cf."
 section 3)., section 3).
 Apart from the presence of the bump. not considered by (2000).. our mean attenuation curve and that of Charlot&Fall(2000) exhibit similar shapes and steepening for decreasing Although we are dealing with attenuation and. not extinction. we also compare our resulting curve with the extinction curves found in the Milky Way and the Magellanie Clouds.," Apart from the presence of the bump, not considered by \citet{charlot00}, our mean attenuation curve and that of \citet{charlot00} exhibit similar shapes and steepening for decreasing Although we are dealing with attenuation and not extinction, we also compare our resulting curve with the extinction curves found in the Milky Way and the Magellanic Clouds."
 The relative extinctions are compared in Fig. 8.., The relative extinctions are compared in Fig. \ref{att1}.
 The general shape of the extinction curve of the LMC2 supershell is consistent with our attenuation curve. whereas the MW and SMC extinction curve show flatter and steeper variation. respectively. at short The exact shape of the extinction curve (slope in the UV range and amplitude of the bump) cannot be constrained with the present data since the attenuation curve we derive strongly depends on the distribution of both stars and dust.," The general shape of the extinction curve of the LMC2 supershell is consistent with our attenuation curve, whereas the MW and SMC extinction curve show flatter and steeper variation, respectively, at short The exact shape of the extinction curve (slope in the UV range and amplitude of the bump) cannot be constrained with the present data since the attenuation curve we derive strongly depends on the distribution of both stars and dust."
 Witt&Gor-don(2000) show that the shape of the attenuation functio also depends on the total amount of dust attenuation., \citet{witt00} show that the shape of the attenuation function also depends on the total amount of dust attenuation.
 We do not observe any variation of Ej and 0 with Au: it can be explained by the homogeneity of our sample in terms of dust attenuatio associated to the large uncertainties on the determination of these parameters., We do not observe any variation of $E_{\rm b}$ and $\delta$ with $A_{\rm UV}$: it can be explained by the homogeneity of our sample in terms of dust attenuation associated to the large uncertainties on the determination of these parameters.
 Radiative transfer models in opaque diskan with various configurations of stars and dust (especially 1 a clumpy medium) are able to reduce the amplitude of the UV bump in the effective attenuation with a dust compositio similar to that of the MW or the average LMC. the attenuatio curve becoming grayer when the opacity increases (e.g.WittPanuzzoetal.. 2007).," Radiative transfer models in opaque disks with various configurations of stars and dust (especially in a clumpy medium) are able to reduce the amplitude of the UV bump in the effective attenuation with a dust composition similar to that of the MW or the average LMC, the attenuation curve becoming grayer when the opacity increases \citep[e.g.][]{witt00,pierini04,inoue06,panuzzo07}."
. These models also predict a flattening of the attenuation curve in UV (as an effect of the gray attenuation) as compared to the original extinction curve., These models also predict a flattening of the attenuation curve in UV (as an effect of the gray attenuation) as compared to the original extinction curve.
 The average attenuation curve we deduce increases steeply at short wavelengths: it seems to favour the scenario of a deficiency of bump carriers with respect to the case of MW or average LMC., The average attenuation curve we deduce increases steeply at short wavelengths: it seems to favour the scenario of a deficiency of bump carriers with respect to the case of MW or average LMC.
 We will see in section 5.2 that our sources roughly follow the Avy-P relation found by Meureretal.(1999). for local starbursts which is well explained by à clumpy shell geometry (Witt&Gordon(2000);Calzetti (2001))).," We will see in section 5.2 that our sources roughly follow the $A_{UV}$ $\beta$ relation found by \citet{Meurer99} for local starbursts which is well explained by a clumpy shell geometry \citet{witt00,calzetti01}) )."
 Such a dust/star configuration favours the interpretation of a moderate UV bump in the extinction curve itself in agreement with our conclusion (e.g.Witt&Gordon.2000:Nolletal.. 20092)..," Such a dust/star configuration favours the interpretation of a moderate UV bump in the extinction curve itself in agreement with our conclusion \citep[e.g.][]{witt00,noll09a}. ."
the extinction contributed by each cloud on the basis of its integrated CO brightness temperature. Corbel Eikenberry obtained a total visual extinction A.~13 mag for the set of foreground clouds listed above.,"the extinction contributed by each cloud on the basis of its integrated CO brightness temperature, Corbel Eikenberry obtained a total visual extinction $A_v \sim 13$ mag for the set of foreground clouds listed above."
 Although obtained along two different sight-lines. both of which are offset from the one that we have observed. we adopt these extinction estimates for G10.6-0.4.," Although obtained along two different sight-lines, both of which are offset from the one that we have observed, we adopt these extinction estimates for G10.6–0.4."
 Given an Nj;/Av ratio of 1.9x10°!em? (Bohlin. Savage Drake 1978). this extinction estimate implies à value ~2.7x107em? for the total column density of H nuclei. Ny=N(H)+2N(H2). along the sight-line to G10.6-0.4.," Given an $N_H / A_V$ ratio of $1.9 \times 10^{21} \rm \, cm^{-2}$ (Bohlin, Savage Drake 1978), this extinction estimate implies a value $\sim 2.7 \times 10^{22}\, \rm \, cm^{-2}$ for the total column density of H nuclei, $N_H = N({\rm H}) + 2N({\rm H_2})$, along the sight-line to G10.6–0.4."
" This estimate 1s a factor ~4 larger than that adopted by Falgarone et iin their recent study of ""CH- absorption toward G10.6-0.4.", This estimate is a factor $\sim 4$ larger than that adopted by Falgarone et in their recent study of $^{13}$ $^+$ absorption toward G10.6–0.4.
" The reason for this discrepaney ts that Falgarone et wwere concerned with the column density of material possessing a molecular to atomic hydrogen ratio <0.5: in the present analysis. we seek to determine HF and para-—H,O abundances averaged over all the material along the line-of-sight."," The reason for this discrepancy is that Falgarone et were concerned with the column density of material possessing a molecular to atomic hydrogen ratio $\le 0.5$; in the present analysis, we seek to determine HF and $_2$ O abundances averaged over all the material along the line-of-sight."
" Our estimate of Nj, is more than twice the atomic hydrogen column density inferred by Godard et (2010) from the 21 em absorption observations of Fish et al.."," Our estimate of $N_H$ is more than twice the atomic hydrogen column density inferred by Godard et (2010) from the 21 cm absorption observations of Fish et al.,"
 implying that the absorbing material is predominantly molecular., implying that the absorbing material is predominantly molecular.
 Given the estimate Nj=2.7x10em for the total column density of H nuclei. we obtain a conservative lower limit N(HE)/N;>6x 1077.," Given the estimate $N_H = 2.7 \times 10^{22}\, \rm \, cm^{-2}$ for the total column density of H nuclei, we obtain a conservative lower limit $N({\rm HF})/N_H \ge 6 \times 10^{-9}$ ."
" By comparison. the solar and meteoritic elemental abundances for fluorme are Np/N;,=3.6712x10 and 2.63031x1075. respectively (Asplund et 22009). whilst the average gas-phase interstellar abundance in diffuse atomic gas clouds is Ne/Ny=1.8x107? (Snow. Destree Jensen. 22007)."," By comparison, the solar and meteoritic elemental abundances for fluorine are $N_F/N_H = 3.6^{+3.6}_{-1.8} \times 10^{-8}$ and $2.63^{+0.39}_{-0.34} \times 10^{-8}$, respectively (Asplund et 2009), whilst the average gas-phase interstellar abundance in diffuse atomic gas clouds is $N_F/N_H = 1.8 \times 10^{-8}$ (Snow, Destree Jensen 2007)."
 Thus. our observations suggest that HF accounts for at least one-third of fluorine in the gas phase along the sight-line to G10.6-0.4.," Thus, our observations suggest that HF accounts for at least one-third of fluorine in the gas phase along the sight-line to G10.6–0.4."
 Our detection of optically-thick absorption in the HF /=1-0 transition over a broad range of LSR velocities corroborates the theoretical prediction that HF is the dominant reservoir of gas-phase fluorine under à wide variety of interstellar conditions., Our detection of optically-thick absorption in the HF $J=1-0$ transition over a broad range of LSR velocities corroborates the theoretical prediction that HF is the dominant reservoir of gas-phase fluorine under a wide variety of interstellar conditions.
 This conclusion suggests that HIFI observations of HF will provide a useful probe of diffuse molecular gas throughout the Galaxy. and — if its high abundance is confirmed along other similar sight-lines for which upcoming HIFI observations are planned — a potentially valuable surrogate for molecular hydrogen.," This conclusion suggests that HIFI observations of HF will provide a useful probe of diffuse molecular gas throughout the Galaxy, and – if its high abundance is confirmed along other similar sight-lines for which upcoming HIFI observations are planned – a potentially valuable surrogate for molecular hydrogen."
 Along sight-lines where absorbing material covers a substantial range of LSR velocities. HF absorption should be detectable (although spectrally unresolved) even at the resolution of Herschel’s SPIRE instrument (Griffin. et. 22010): this opens up the possibility of detecting hydrogen fluoridetoward suitable extragalactic sources as well.," Along sight-lines where absorbing material covers a substantial range of LSR velocities, HF absorption should be detectable (although spectrally unresolved) even at the resolution of Herschel's SPIRE instrument (Griffin et 2010); this opens up the possibility of detecting hydrogen fluoridetoward suitable extragalactic sources as well."
degenerate area in Fig. 4)).,degenerate area in Fig. \ref{fig:GJ436b}) ).
 Even for constant outer envelope metallicity there are also models that have a larger ko. indicating a rather homogeneous planet. but nevertheless a more massive core.," Even for constant outer envelope metallicity there are also models that have a larger $k_2$, indicating a rather homogeneous planet, but nevertheless a more massive core."
 This behavior is caused by the outer density discontinuity at the water-H/He layer boundary as discussed in Sect., This behavior is caused by the outer density discontinuity at the water-H/He layer boundary as discussed in Sect.
 3 and predicted by Fig. 2.., \ref{sec:3L-model} and predicted by Fig. \ref{fig:3L-degeneracy}.
 In this paper we investigated the effect of the density distribution of a planet on its tidal Love number κ. in order to find out what conclusions can be drawn from a measured A> on the internal structure of a planet., In this paper we investigated the effect of the density distribution of a planet on its tidal Love number $k_2$ in order to find out what conclusions can be drawn from a measured $k_2$ on the internal structure of a planet.
 We confirmed that the Love number A> is a measure of the level of central condensation of a planet., We confirmed that the Love number $k_2$ is a measure of the level of central condensation of a planet.
However. in a three layer model approach κ. 1s nora unique function of the core mass.,"However, in a three layer model approach $k_2$ is a unique function of the core mass."
 There is a degeneracy of ko with respect to a density discontinuity 11 the envelope of the planet., There is a degeneracy of $k_2$ with respect to a density discontinuity in the envelope of the planet.
 It is possible to have several acceptable models for a given A> value. which can differ significantly in core mass.," It is possible to have several acceptable models for a given $k_2$ value, which can differ significantly in core mass."
 The effect of the outer density discontinuity on A> is compensating the etfect of the core., The effect of the outer density discontinuity on $k_2$ is compensating the effect of the core.
 Furthermore. we showed that the Radau-Darwin relation is a too crude approxomation to describe the moment of inertia of gas giant planets.," Furthermore, we showed that the Radau-Darwin relation is a too crude approxomation to describe the moment of inertia of gas giant planets."
 We verified our results on A> with models of existing planets., We verified our results on $k_2$ with models of existing planets.
 For Saturn the freedom to place the layer boundary in the envelope leads to a high uncertainty in the core mass., For Saturn the freedom to place the layer boundary in the envelope leads to a high uncertainty in the core mass.
 Regardless of the core mass all Saturn models have the same ks. demonstrating the degeneracy caused by the outer layer boundary.," Regardless of the core mass all Saturn models have the same $k_2$, demonstrating the degeneracy caused by the outer layer boundary."
 For extrasolar planets the Love number &» can be an equivalent constraint to J. for the solar system planets., For extrasolar planets the Love number $k_2$ can be an equivalent constraint to $J_2$ for the solar system planets.
 However. one has to be careful with estimates about the core mass derived from K» as degeneracy may also occur in extrasolar planets.," However, one has to be careful with estimates about the core mass derived from $k_2$ as degeneracy may also occur in extrasolar planets."
 For GJ4436b we find a highly degenerate area of kx<0.24 where a measurement of &» would barely help to further constrain the interior models., For 436b we find a highly degenerate area of $k_2<0.24$ where a measurement of $k_2$ would barely help to further constrain the interior models.
 Only a core mass and for kx>0.24 a large metallicity can be inferred., Only a core mass and for $k_2>0.24$ a large metallicity can be inferred.
 With additional knowledge about the atmospheric metal abundance the uncertainty about the core mass could be significantly narrowed., With additional knowledge about the atmospheric metal abundance the uncertainty about the core mass could be significantly narrowed.
 Tabulating 42 values of various planetary models can prove to be very useful once κ. is actually measured for extrasolar transiting planets., Tabulating $k_2$ values of various planetary models can prove to be very useful once $k_2$ is actually measured for extrasolar transiting planets.
 For instance. for the Super-Earth ? demonstrated that H/He or water envelopes result in significantly different values of 42.," For instance, for the Super-Earth \citet{Nettelmannetal10b} demonstrated that H/He or water envelopes result in significantly different values of $k_2$."
 Furthermore. we have shown in this paper that even though the Love number K» is a degenerate quantity it can help constraining the core mass of a planet.," Furthermore, we have shown in this paper that even though the Love number $k_2$ is a degenerate quantity it can help constraining the core mass of a planet."
 Knowledge about the core masses of planets 1s highly desired because it is thought to help to distinguish between the possible planet formation scenarios of core accretion (seee.g.?) and gravitational instability (seee.g.2).., Knowledge about the core masses of planets is highly desired because it is thought to help to distinguish between the possible planet formation scenarios of core accretion \citep[see e.g.][]{Pollacketal96} and gravitational instability \citep[see e.g.][]{Boss97}.
 However. one has to keep in mind that core accretion models can also result in very small cores of or in the case of grain-free or even metal-free envelopes. respectively (?)..," However, one has to keep in mind that core accretion models can also result in very small cores of or in the case of grain-free or even metal-free envelopes, respectively \citep{HoriIkoma10}."
 On the other hand. gravitational instability models allow the formation of a massive core as well if the protoplanet is cold enough for grain settling to take place (?)..," On the other hand, gravitational instability models allow the formation of a massive core as well if the protoplanet is cold enough for grain settling to take place \citep{HelledSchubert08}."
 A clear distinction between the two formation models can only be made for massive extra-solar giant planets > MJ.. ? showed that such massive protoplanets formed by disk instability cannot build up a core at all due to their high internal temperatures and evaporation of the grains., A clear distinction between the two formation models can only be made for massive extra-solar giant planets $\geq$ \citet{HelledSchubert08} showed that such massive protoplanets formed by disk instability cannot build up a core at all due to their high internal temperatures and evaporation of the grains.
curve.,curve.
 During the maximum phase there is about 0.4 mag difference between both light curves., During the maximum phase there is about 0.4 mag difference between both light curves.
 We have to point out that for our NLTE models. the energy is not conserved because the radiation does not thermalize within the envelope.," We have to point out that for our NLTE models, the energy is not conserved because the radiation does not thermalize within the envelope."
 After maximum the NLTE model light curve approaches the LTE light curve and agrees with the observed light curves as well as the LTE light curve., After maximum the NLTE model light curve approaches the LTE light curve and agrees with the observed light curves as well as the LTE light curve.
 However. the NLTE model light curve in the V band does not agree with the observed light curves very accurately.," However, the NLTE model light curve in the V band does not agree with the observed light curves very accurately."
 With the assumption of an atmosphere in LTE. a better fit is obtained. although NLTE is more accurate.," With the assumption of an atmosphere in LTE, a better fit is obtained, although NLTE is more accurate."
 The NLTE model light curve of the U band is shown in Fig. 22.., The NLTE model light curve of the U band is shown in Fig. \ref{fig:lc_nltefixu}.
 The NLTE light curve shows almost no deviations from the LTE light curve., The NLTE light curve shows almost no deviations from the LTE light curve.
 During the later phase the steep decline is also present in the NLTE model light curves., During the later phase the steep decline is also present in the NLTE model light curves.
 In Fig. 23..," In Fig. \ref{fig:lc_nltefixb},"
 the NLTE model light curve in the B band ts presented., the NLTE model light curve in the B band is presented.
 The NLTE model light curve ts slightly fainter than the LTE light curve., The NLTE model light curve is slightly fainter than the LTE light curve.
 The shape of the NLTE light curve seems to be the same as for the LTE light curve., The shape of the NLTE light curve seems to be the same as for the LTE light curve.
 The NLTE model light curve ts also an accurate fit to the observed light curves., The NLTE model light curve is also an accurate fit to the observed light curves.
Our understanding of how objects in (he early solar svstem coagulated to form planetsesimals ol the kilometer size scale is mostly limited to theory (Bottke et al.,Our understanding of how objects in the early solar system coagulated to form planetsesimals of the kilometer size scale is mostly limited to theory (Bottke et al.
 2005: Johansen οἱ al., 2005; Johansen et al.
 2007: Bhim Wurm 20083: Cuzzi et al., 2007; Blum Wurm 2008; Cuzzi et al.
 2008: Morbidelli et al., 2008; Morbidelli et al.
 2009)., 2009).
 Though we can detect some eas and dust disks as well as large planets around stars. we will not be able to detect planetesimals on the kilometer to thousands of kilometer size scale in the foreseeable future.," Though we can detect some gas and dust disks as well as large planets around stars, we will not be able to detect extra-solar planetesimals on the kilometer to thousands of kilometer size scale in the foreseeable future."
 Currently. (he only way to directly study such a population is through the stable reservoirs in our solar svstem (Jewitt et al.," Currently, the only way to directly study such a population is through the stable reservoirs in our solar system (Jewitt et al."
 2000: IXenvon Bromley 2004: Pan Sari 2005: Bottke οἱ al., 2000; Kenyon Bromley 2004; Pan Sari 2005; Bottke et al.
 2005: Fraser Navelaars 2008: Fuentes Holman 2008: Fraser et al., 2005; Fraser Kavelaars 2008; Fuentes Holman 2008; Fraser et al.
 2008: Fuentes et al., 2008; Fuentes et al.
 2009: Fraser 2009: Morbidelli et al., 2009; Fraser 2009; Morbidelli et al.
 2009)., 2009).
 The orbits of objects in the main asteroid belt. Kuiper belt aud Trojan regions have been highly influenced by (he migration and evolution of the Solar System.," The orbits of objects in the main asteroid belt, Kuiper belt and Trojan regions have been highly influenced by the migration and evolution of the Solar System."
 Since Trojan asteroids share (heir planets orbital period and semi-najor axis (μον are especially useful in constraining (he formation and mieration of their planet (Morbidelli et al., Since Trojan asteroids share their planet's orbital period and semi-major axis they are especially useful in constraining the formation and migration of their planet (Morbidelli et al.
 2005: Tsiganis et al., 2005; Tsiganis et al.
 2005)., 2005).
 Trojan asteroids lead (L4) or trail (L5) a planet by about sixty degrees near the two triangular Lagrangian points οἱ eravitational stability., Trojan asteroids lead (L4) or trail (L5) a planet by about sixty degrees near the two triangular Lagrangian points of gravitational stability.
 The Jupiter Trojans have been known since Max Wolf discovered 538 Achilles in 1906., The Jupiter Trojans have been known since Max Wolf discovered 588 Achilles in 1906.
 There are currently about 3000 known Trojans in the L4 and L5 regions of Jupiter., There are currently about 3000 known Trojans in the L4 and L5 regions of Jupiter.
 Neptune's first Trojan was discovered within the L4 reeion in 2001 while several more Neptune Trojans have been discovered in recent vears (Chiang οἱ al., Neptune's first Trojan was discovered within the L4 region in 2001 while several more Neptune Trojans have been discovered in recent years (Chiang et al.
 2003: Sheppard Trujillo 2006. 2010: Decker et al.," 2003; Sheppard Trujillo 2006, 2010; Becker et al."
 2003)., 2008).
 The other giant planets Saturn and Uranus are nol expected to have a significant number of Trojans since their Lagrangian reglons are more dvnamically unstable over the age of the solar svstem (Nesvorny Dones 2002)., The other giant planets Saturn and Uranus are not expected to have a significant number of Trojans since their Lagrangian regions are more dynamically unstable over the age of the solar system (Nesvorny Dones 2002).
 The dynamics of Kuiper Bell objects in outer mean-mnotion resonances wilh Neptune. such as the 3:2 and 2:1 resonances. suggest that Neptune likely migrated several AU outwards during its lifetime (Hahn Malhotra 2005: Chiang Lithwick 2005: Levison οἱ al.," The dynamics of Kuiper Belt objects in outer mean-motion resonances with Neptune, such as the 3:2 and 2:1 resonances, suggest that Neptune likely migrated several AU outwards during its lifetime (Hahn Malhotra 2005; Chiang Lithwick 2005; Levison et al."
 2008)., 2008).
 Similarly. (the IHildas in (he main asteroid belt are in the 2:3 mean-motion resonance wilh Jupiter and their orbital distribution suggests Jupiter migrated inward by a few tenths of AU (Franklin et al.," Similarly, the Hildas in the main asteroid belt are in the 2:3 mean-motion resonance with Jupiter and their orbital distribution suggests Jupiter migrated inward by a few tenths of AU (Franklin et al."
 2004)., 2004).
 Unlike these inner and outer resonance objects. the Trojans. which are in à 1:1 resonance with (heir respective planet. would likely have been depleted during any large. irregular planetary migration.," Unlike these inner and outer resonance objects, the Trojans, which are in a 1:1 resonance with their respective planet, would likely have been depleted during any large, irregular planetary migration."
 The capture of Trojans in the current Solar System is not an effective process ancl (hus capture happened when the Solar System clvnamics were significantly different (han now (Ilorner Evans 2006)., The capture of Trojans in the current Solar System is not an effective process and thus capture happened when the Solar System dynamics were significantly different than now (Horner Evans 2006).
 Thus the Trojans were likely captured during either a slow smooth planetary migration process or more likely after anv significant planetary mieration through a Neptune [reeze-àn circularization process (Ixortenkanmp et al., Thus the Trojans were likely captured during either a slow smooth planetary migration process or more likely after any significant planetary migration through a Neptune freeze-in circularization process (Kortenkamp et al.
 2004: Morbidelli et al., 2004; Morbidelli et al.
 2005: Sheppard Trujillo 2006: Li et al., 2005; Sheppard Trujillo 2006; Li et al.
 2007: Nesvorny, 2007; Nesvorny
The Sombrero galaxy (NGC 4594. or M. 104). is a local. massive disc galaxy.,"The Sombrero galaxy (NGC 4594, or M 104) is a local, massive disc galaxy."
 Classified as an unbarred Sa (2)... it is at a distance of 9.1Mpoc [uctuations).. and has a stellar mass of ~2.3«104 M.2).," Classified as an unbarred Sa , it is at a distance of 9.1Mpc , and has a stellar mass of $\sim2.3\times10^{11}$ $_\odot$."
 At this distance. 1 corresponds to about 44pc.," At this distance, 1"" corresponds to about 44pc."
 It is seen almost. perfectly. edegc-on. with an inclination angle of =SA(2)...," It is seen almost perfectly edge-on, with an inclination angle of $\approx84^\circ$."
 Ht exhibits a remarkable spheroidal structure which extends to distances much larger than usually seen in other inclined disc galaxies., It exhibits a remarkable spheroidal structure which extends to distances much larger than usually seen in other inclined disc galaxies.
 Figure 1. shows an archive Spitzer URAC image of this ealaxv at 3.6520.?).. where there is very. little dust absorption or emission. as well as little contamination from hot. voung stars2).," Figure \ref{fig:irac} shows an archive Spitzer IRAC image of this galaxy at $\mu m$, where there is very little dust absorption or emission, as well as little contamination from hot, young stars."
 It is thus a superb source to study the bulk structural properties of the galaxy., It is thus a superb source to study the bulk structural properties of the galaxy.
 This deep image shows that the extended: stellar. halo seems rouncer than the more compact central bulge. closer to the disc plane.," This deep image shows that the extended stellar halo seems rounder than the more compact central bulge, closer to the disc plane."
 In. carly studies based. on shallower or optical images the full extent of the halo is not evident. and thus Sombrero has been traditionally considered. a bulge|disc system only. with a very high bulge-to-total ratioI89]kenss.," In early studies based on shallower or optical images the full extent of the halo is not evident, and thus Sombrero has been traditionally considered a bulge+disc system only, with a very high bulge-to-total ratio."
 This difference between. 7???)the shape of the extended: halo and the central bulge might suggest. different formation oocesses for both components., This difference between the shape of the extended halo and the central bulge might suggest different formation processes for both components.
 Alternatively. if halo and xilee form as a single entity. then they could have followed different evolutionary. paths.," Alternatively, if halo and bulge form as a single entity, then they could have followed different evolutionary paths."
 A further alternative is that he variation in cllipticity is a projection elfect ona single spheroidal component., A further alternative is that the variation in ellipticity is a projection effect on a single spheroidal component.
 Since most previous works did not distinguish. the ido from the bulge. the whole spheroid. was well fitted woa Sérrsic law with high Sérrsic index. Le. mcd. although then the disc had to be fitted using complicated non-standard functions2).," Since most previous works did not distinguish the halo from the bulge, the whole spheroid was well fitted by a Sérrsic law with high Sérrsic index, i.e. $n\sim4$, although then the disc had to be fitted using complicated non-standard functions."
. The spheroid is obviously rounder ancl vertically more extended than the disc. and it," The spheroid is obviously rounder and vertically more extended than the disc, and it"
"frequency-dependent core shifts from the time lags and the validity of our assumptions, we calculated time lags from the total flux-density light curves for the AGN 3C 345, whose core shift has been measured at the same frequencies used to construct the light curves.","frequency-dependent core shifts from the time lags and the validity of our assumptions, we calculated time lags from the total flux-density light curves for the AGN 3C 345, whose core shift has been measured at the same frequencies used to construct the light curves."
" The frequency-dependent time delays were calculated by fitting Gaussian functions to the total flux-density light curves from the University of Michigan (Alleretal.1999;Aller,&Hughes2003) and Metsáhhovi Radio Observatory (Terasrantaetal.1992,1998,2004,2005) monitoring databases at 4.8 GHz, 8 GHz, 14.5 GHz, 22 GHz, and 37 GHz."," The frequency-dependent time delays were calculated by fitting Gaussian functions to the total flux-density light curves from the University of Michigan \citep{Aller_1999,Aller_2003} and Metsähhovi Radio Observatory \citep{terasranta_1992,terasranta_1998,terasranta_2004, terasranta_2005} monitoring databases at 4.8 GHz, 8 GHz, 14.5 GHz, 22 GHz, and 37 GHz."
 The total flux-density light curves were decomposed into Gaussian components following the procedure discussed in Pyatuninaetal.(2006) and Pyatuninaetal.(2007).," The total flux-density light curves were decomposed into Gaussian components following the procedure discussed in \citet{Pyatunina_2006}
 and \citet{Pyatunina_2007}."
. Long-term trends in the total flux-density variations were calculated as polynomial approximations for the deepest minima in the light curves and subtracted before the fitting., Long-term trends in the total flux-density variations were calculated as polynomial approximations for the deepest minima in the light curves and subtracted before the fitting.
" The Gaussian decomposition was performed such that it first removed the trend, then found the highest peak in the light curve and fitted a Gaussian to the peak, based on a X? minimization."," The Gaussian decomposition was performed such that it first removed the trend, then found the highest peak in the light curve and fitted a Gaussian to the peak, based on a $\chi^2$ minimization."
 The fitted component was then removed from the light curve and the procedure was repeated until all significant peaks were fitted with Gaussians., The fitted component was then removed from the light curve and the procedure was repeated until all significant peaks were fitted with Gaussians.
" During the fitting, we applied the general criterion that the smallest number of individual flares (Gaussian components) providing a complete description of the light curve was used."," During the fitting, we applied the general criterion that the smallest number of individual flares (Gaussian components) providing a complete description of the light curve was used."
 The number of fitted Gaussians depended on the time interval covered by the light curve and the characteristic time scale of the source variability., The number of fitted Gaussians depended on the time interval covered by the light curve and the characteristic time scale of the source variability.
" The quasar 3C 345 (z — 0.5928, Marzianietal. (1996))) is one of the best studied AGN on VLBI scales."," The quasar 3C 345 (z = 0.5928, \citet{Marziani_1996}) ) is one of the best studied AGN on VLBI scales."
" Several jet components with apparent velocities of 2—20c have been observed, moving along strongly curved trajectories (e.g.Zensus,&Lobanov 2000)."," Several jet components with apparent velocities of $2-20c$ have been observed, moving along strongly curved trajectories \citep*[e.g.][]{Unwin_1983,Zensus_1995,Lobanov_1999,
Rantakyro_1995,Ros_2000}."
. ? found evidence for periodic changes in the parsec-scale jet with a 9-year period., \citet{Klare_2005} found evidence for periodic changes in the parsec-scale jet with a 9-year period.
" 'The total flux-density light curves at 4.8 GHz, 8 GHz, 14.5 GHz, 22 GHz and 37 GHz are shown in Fig. 2.."," The total flux-density light curves at 4.8 GHz, 8 GHz, 14.5 GHz, 22 GHz and 37 GHz are shown in Fig. \ref{3c345_lcurve}."
 The best x? values were reached with a fit of 9 Gaussians to the light curve; the Gaussians fitted are shown together with the light curve at 14.5 GHz in Fig. 3.., The best $\chi^2$ values were reached with a fit of 9 Gaussians to the light curve; the Gaussians fitted are shown together with the light curve at 14.5 GHz in Fig. \ref{3c345_decomp}.
 The long- curves show the Gaussians and the solid curve the final sum of all 9 fitted Gaussians., The long-dashed curves show the Gaussians and the solid curve the final sum of all 9 fitted Gaussians.
 It is clear that the sum of the Gaussians fits well all the main features in, It is clear that the sum of the Gaussians fits well all the main features in
orbital phase in the same manner.,orbital phase in the same manner.
 We recognize that à two-component deblending is simplistic: however. it does. allow us to quantify the asymmetric lines.," We recognize that a two-component deblending is simplistic; however, it does allow us to quantify the asymmetric lines."
 This line was chosen as representative of the sample of ines and met the criteria listed in the previous paragraph., This line was chosen as representative of the sample of lines and met the criteria listed in the previous paragraph.
 Since the lines are asymmetric during most of the orbit. this ms the effect of damping the RV amplitude at. maximum and minimum RY.," Since the lines are asymmetric during most of the orbit, this has the effect of damping the RV amplitude at maximum and minimum RV."
 This explains the dillerence between MI UN and RV measured by vanWinckel.Waelkens.&Waters(1995) at maximum and minimum RW. as shown in Fig. 9..," This explains the difference between M1 RV and RV measured by \citet{vanwinckel1995} at maximum and minimum RV, as shown in Fig. \ref{fig9}."
 The FWIIAL of the Gaussian for both profile components was assumed to be the same. assuming the primary star is he dominant source of light in the central cavity.," The FWHM of the Gaussian for both profile components was assumed to be the same, assuming the primary star is the dominant source of light in the central cavity."
 The width of the symmetric profile spectrum .113.. which occurs at inferior conjunction (ὁ= 0.21). was used as the intrinsic width of the underlying line profile.," The width of the symmetric profile spectrum 13, which occurs at inferior conjunction $\phi = 0.21$ ), was used as the intrinsic width of the underlying line profile."
 From our observations. we measure a nearly constant total equivalent width having no dependence on the orbital motion of the star.," From our observations, we measure a nearly constant total equivalent width having no dependence on the orbital motion of the star."
 Therefore. we also constrained. the equivalent width of the line to be constant.," Therefore, we also constrained the equivalent width of the line to be constant."
 We associate the strong component with the true RY of the primary star., We associate the strong component with the true RV of the primary star.
 The resulting strong ων). and weak uu) components are tabulated in Table 1.., The resulting strong $_{strong}$ ) and weak $_{weak}$ ) components are tabulated in Table \ref{table1}.
 Ehe spony values are plotted in Fig., The $_{strong}$ values are plotted in Fig.
 9 (fillecl trianels), \ref{fig9} (filled triangles).
 The maximum RY values of M2 are in agreement with the data of vanWinckel. (1995).. while the minimum RV values of ALL (στον euxJes) match the vanWinckel.Waelkens.&Waters(1995) data better.," The maximum RV values of M2 are in agreement with the data of \citet{vanwinckel1995}, while the minimum RV values of M1 (grey circles) match the \citet{vanwinckel1995} data better."
 This indicates that M2. is at least reasonable or determining the RV of the primary star., This indicates that M2 is at least reasonable for determining the RV of the primary star.
 'The results of à2 for the strong component are equivalent to measuring tx BN at the deepest part of the absorption line., The results of M2 for the strong component are equivalent to measuring the RV at the deepest part of the absorption line.
" Phe velocity ""of the RVuud with respect to the uisus ", The velocity of the $_{weak}$ with respect to the $_{strong}$ 
"of 4 x 300 s exposures, that used dithering along the slit to improve the removal of the sky background during the reduction stage.","of 4 $\times$ 300 s exposures, that used dithering along the slit to improve the removal of the sky background during the reduction stage."
 The total exposure time was 1 hour through each filter., The total exposure time was 1 hour through each filter.
 The slit was put at a position angle of 226.7° to cover the two strong infrared components from the lensed source., The slit was put at a position angle of $\degr$ to cover the two strong infrared components from the lensed source.
 The standard star HD162208 was also observed four times each in N6 and N7 for calibration., The standard star HD162208 was also observed four times each in N6 and N7 for calibration.
" We reduce the data with a Python-based pipeline that removes cosmic rays, subtracts the sky, wavelength calibrates using the atmospheric sky-lines and extracts a one-dimensional spectrum."," We reduce the data with a Python-based pipeline that removes cosmic rays, subtracts the sky, wavelength calibrates using the atmospheric sky-lines and extracts a one-dimensional spectrum."
" Furthermore, we use the standard star HD162208 to correct for the response of the spectrograph."," Furthermore, we use the standard star HD162208 to correct for the response of the spectrograph."
" The reduced spectra for both filters are presented in the bottom panel of Figure 4,, and the atmospheric transmission is shown in the top panel."," The reduced spectra for both filters are presented in the bottom panel of Figure \ref{fig:spec:zs}, and the atmospheric transmission is shown in the top panel."
 The spectra are smoothed using a 7-pixel moving average with each point being weighted by the inverse variance associated with it., The spectra are smoothed using a 7-pixel moving average with each point being weighted by the inverse variance associated with it.
" We identify a strong emission line in the N6 spectrum (bottom panel, left), but do not see any spectral features in the N7 spectrum (bottom panel, right)."," We identify a strong emission line in the N6 spectrum (bottom panel, left), but do not see any spectral features in the N7 spectrum (bottom panel, right)."
" Therefore, we believe that the detected emission line is likely Ha blended with two τῇ] emission lines, corresponding to a source redshift of[N zs=1.71+0.01."," Therefore, we believe that the detected emission line is likely $\alpha$ blended with two ] emission lines, corresponding to a source redshift of $z_{\rm s} = 1.71 \pm 0.01$."
 The uncertainty in the redshift is conservative and accounts for the blending of the lines and also the contamination by atmospheric lines on both sides of the emission line., The uncertainty in the redshift is conservative and accounts for the blending of the lines and also the contamination by atmospheric lines on both sides of the emission line.
" We note that the strong emission line detected here has been previously reported by ?,, based on an unpublished spectrum that was taken with the United Kingdom Infrared Telescope (UKIRT)."," We note that the strong emission line detected here has been previously reported by \citet{Biggs++00}, based on an unpublished spectrum that was taken with the United Kingdom Infrared Telescope (UKIRT)."
" Then the line was interpreted to be HG at redshift 2.62, due to a second spectral feature that was believed to be Ha in the K-band."," Then the line was interpreted to be $\beta$ at redshift 2.62, due to a second spectral feature that was believed to be $\alpha$ in the K-band."
" Our much better spectral resolution and higher sensitivity data do not detect the second emission line in N7, which would certainly have been detected if it were Ha given the relative flux of the supposed Hf line in N6 and the noise level."," Our much better spectral resolution and higher sensitivity data do not detect the second emission line in N7, which would certainly have been detected if it were $\alpha$ given the relative flux of the supposed $\beta$ line in N6 and the noise level."
 We therefore rule out a redshift of 2.62 for the lensed source., We therefore rule out a redshift of 2.62 for the lensed source.
 Archival iimages of iin the F160W filter with the Near Infrared Camera and Multi-Object Spectrometer (NICMOS; Proposal ID: 9744; PI: Kochanek) and the F555W and F814W filters with the Wide Field and Planetary Camera 2 (WFPC2; Proposal ID: 9133; PI: Falco) are available., Archival images of in the F160W filter with the Near Infrared Camera and Multi-Object Spectrometer (NICMOS; Proposal ID: 9744; PI: Kochanek) and the F555W and F814W filters with the Wide Field and Planetary Camera 2 (WFPC2; Proposal ID: 9133; PI: Falco) are available.
 We used to combine the exposures in each filter and correct for geometric distortion., We used to combine the exposures in each filter and correct for geometric distortion.
 The F555W data were discarded due to the low signal-to-noise ratio (SNR)., The F555W data were discarded due to the low signal-to-noise ratio (SNR).
" We oversampled the F814W and F160W images with to the same pixel scale as the NIRC2 image, and show the color image composed of the three filters in Figure 5.."," We oversampled the F814W and F160W images with to the same pixel scale as the NIRC2 image, and show the color image composed of the three filters in Figure \ref{fig:colour}."
 The images of the lensed source in the plane of the lens galaxy (corresponding to radio components 3 and 6) suffer from dust extinction., The images of the lensed source in the plane of the lens galaxy (corresponding to radio components 3 and 6) suffer from dust extinction.
 We use the stars in the WFPC2 F814W images to obtain the pixel scale of the NIRC2 image in Section 2.2 and the alignment of radio and NIRC2 images in Section 3.., We use the stars in the WFPC2 F814W images to obtain the pixel scale of the NIRC2 image in Section \ref{sec:obs:AO} and the alignment of radio and NIRC2 images in Section \ref{sec:align}.
" Furthermore, we use the F814W and F160W photometries in Section 4.3 to estimate the stellar mass of the lens galaxy (that incorporates the effects of dust) in Section 9.4.."," Furthermore, we use the F814W and F160W photometries in Section \ref{sec:lenslight:phot} to estimate the stellar mass of the lens galaxy (that incorporates the effects of dust) in Section \ref{sec:IMF}."
" In order to use both the radio image positions of the source and the NIRC2 image of the lens galaxy to constrain the lens mass distribution, we need to align the radio and the NIRC2 images."," In order to use both the radio image positions of the source and the NIRC2 image of the lens galaxy to constrain the lens mass distribution, we need to align the radio and the NIRC2 images."
 We assume that the two coordinate systems differ by a rotation and a translation., We assume that the two coordinate systems differ by a rotation and a translation.
" By aligning the stars in the NIRC2 images to the corresponding stars in the WFPC2 images with WCS information, we determine the north direction"," By aligning the stars in the NIRC2 images to the corresponding stars in the WFPC2 images with WCS information, we determine the north direction"
axis consistent with zero (flux olfset C=—5zE38 count 1 errors are confidence),"axis consistent with zero (flux offset $C=-5\pm38$ count $^{-1}$, errors are confidence)."
 The linear rms-Iux. relation shown by the pulse confirms hat aperiodic ancl periodic variations are coupled. and herefore at. least. some component of the aperiocic N-rav variability must originate at or close to the magnetic caps of he neutron star.," The linear rms-flux relation shown by the pulse confirms that aperiodic and periodic variations are coupled, and therefore at least some component of the aperiodic X-ray variability must originate at or close to the magnetic caps of the neutron star."
 However. this does not necessarily imply hat the component of aperiodic X-ray variability showing a incar rms-Iux relation also originates at the same location.," However, this does not necessarily imply that the component of aperiodic X-ray variability showing a linear rms-flux relation also originates at the same location."
 For example. if à component with a linear rms-Iux relation. which is not coupled to the pulse. contributes a similar [Lux o à component with constant rms which is coupled to the suse. both the pulse ancl aperiocic rms-ux relations can ος preserved.," For example, if a component with a linear rms-flux relation, which is not coupled to the pulse, contributes a similar flux to a component with constant rms which is coupled to the pulse, both the pulse and aperiodic rms-flux relations can be preserved."
 This is because the highest and lowest total observed. [uxes correspond to the times when the fluxes ofbolh aperiodic components are high and low respectively., This is because the highest and lowest total observed fluxes correspond to the times when the fluxes of aperiodic components are high and low respectively.
 llence. when the total flux is high both the pulse rms and the aperiodic rms will be high. and the rms of the pulse and aperiodic variability will both be low when the total Dux is low.," Hence, when the total flux is high both the pulse rms and the aperiodic rms will be high, and the rms of the pulse and aperiodic variability will both be low when the total flux is low."
 Llowever. in the case where the aperiodic rms-Iux relation is produced in a separate component to the pulsed component ol aperiodic variability. we expect that the amplitude of the aperiodic variability and the rms of the pulse will not he correlated.," However, in the case where the aperiodic rms-flux relation is produced in a separate component to the pulsed component of aperiodic variability, we expect that the amplitude of the aperiodic variability and the rms of the pulse will not be correlated."
 To demonstrate this fact. we use simulated light curves.," To demonstrate this fact, we use simulated light curves."
 As shown in Uttley.M'Hardy&Vaughan:(2003) and Uttlev. M'LHardy Vaughan (in prep.).," As shown in \citet{utt03} and Uttley, $^{\rm c}$ Hardy Vaughan (in prep.),"
 aperiodic light curves with a linear rnis-Hux relation on all time-scales may. be simply. &enerated bv replacing each data point in a linear light curve (e.g. eencrated using the algorithm of Timmer&Ixónig 1995)) with its exponential., aperiodic light curves with a linear rms-flux relation on all time-scales may be simply generated by replacing each data point in a linear light curve (e.g. generated using the algorithm of \citealt{tim95}) ) with its exponential.
 We examined two cases: In both cases. the simulated aperiodie variability. assumed a broken power-law power spectrum with power-law slope 0 below 0.3 Lz and -1 at higher frequencies (up to the Nyquist. frequeney). to approximate the observed: power spectrum (Wijnands&vanderWlis.1998b).," We examined two cases: In both cases, the simulated aperiodic variability assumed a broken power-law power spectrum with power-law slope 0 below 0.3 Hz and -1 at higher frequencies (up to the Nyquist frequency), to approximate the observed power spectrum \citep{wij98b}."
. Phe simulated amplitudes of variability (combined. amplitude in case (ii)) were chosen to match that of the source. and Poisson noise corresponding to the observed source plus background count rates was also inclucecd.," The simulated amplitudes of variability (combined amplitude in case (ii)) were chosen to match that of the source, and Poisson noise corresponding to the observed source plus background count rates was also included."
 Jo examine the correlation between the amplitude of aperiodic variability and the pulse amplitude. we averaged ogether the 1 s measurements of the power spectrum (discussed. in Section 2.1)) according to their noise-subtracted variance (i.e. integrated power) measured in the 1-10 Uz band. to obtain the pulse rms as a function. of rw aperiodic 1-10 Lz variance.," To examine the correlation between the amplitude of aperiodic variability and the pulse amplitude, we averaged together the 1 s measurements of the power spectrum (discussed in Section \ref{pulsermssec}) ) according to their noise-subtracted variance (i.e. integrated power) measured in the 1-10 Hz band, to obtain the pulse rms as a function of the aperiodic 1-10 Hz variance."
 We bin the pulse rms as a function of 1-10. Lz variance rather than rms. because in individual | s segments the true noise level may exceed re estimated value. which can lead to negative noise- variance. so that rms cannot be determined (e.g. see discussion in Uttlev&AlTardy2001... Gleissner 2003))," We bin the pulse rms as a function of 1-10 Hz variance rather than rms, because in individual 1 s segments the true noise level may exceed the estimated value, which can lead to negative noise-subtracted variance, so that rms cannot be determined (e.g. see discussion in \citealt{utt01}, \citealt{gle03}) )."
 Fig., Fig.
 2 shows the pulse rms versus aperiodic variance for the case (1) and case (i) simulations described above., \ref{simrmsvar} shows the pulse rms versus aperiodic variance for the case (i) and case (ii) simulations described above.
 Case (1). where the pulsed aperiodic variability contains a linear rnis-us relation. shows a clear correlation between pulse ros ancl aperiodic. variance.. with. a linear. plus constant model 472 fit vielding a positive gradient (23404).104 for 42=L3 [or 2 degrees of freedom. (errors are confidence limits).," Case (i), where the pulsed aperiodic variability contains a linear rms-flux relation, shows a clear correlation between pulse rms and aperiodic variance, with a linear plus constant model $\chi^{2}$ fit yielding a positive gradient $(2.3\pm0.4)\times10^{-4}$ for $\chi^{2}=1.3$ for 2 degrees of freedom (errors are confidence limits)."
 Note that the inerease in pulse. rms with aperiodic variance is relatively small. because. the aperiodic variance contains a large amount of intrinsic scatter. unrelated. to the. rms-Hux. relation. due to the stochastic nature of the variabilitv and the ellects of noise.," Note that the increase in pulse rms with aperiodic variance is relatively small, because the aperiodic variance contains a large amount of intrinsic scatter, unrelated to the rms-flux relation, due to the stochastic nature of the variability and the effects of noise."
 Nonetheless. a significant correlation between pulse rms ancl periodic variance is easily seen.," Nonetheless, a significant correlation between pulse rms and aperiodic variance is easily seen."
 Case (ii). on the other hand. shows no such correlation. (gradient. (0.1-E0.5)10 Dyfor yo=5.9. for 2 degrees of freedom) due to the fact that 10. pulsed aperiodic component does not contain the linear rmis-Iux relation.," Case (ii), on the other hand, shows no such correlation (gradient $(0.4\pm0.5)\times10^{-4}$ for $\chi^{2}=5.9$, for 2 degrees of freedom), due to the fact that the pulsed aperiodic component does not contain the linear rms-flux relation."
 Note that the spread in 1-10 Lz variance is larger in case (i) than in case (ii) because of the stronger, Note that the spread in 1-10 Hz variance is larger in case (i) than in case (ii) because of the stronger
"To investigate the X-ray variability ofCoRoT-2A,, we constructed background-subtracted light curves with various binnings.","To investigate the X-ray variability of, we constructed background-subtracted light curves with various binnings."
" A barycentric time-correction was applied to all light curves to obtain time stamps, which can be easily reconciled with planetary ephemerides given in the literature."," A barycentric time-correction was applied to all light curves to obtain time stamps, which can be easily reconciled with planetary ephemerides given in the literature."
" Figure 9 presents the light curve ofCoRoT-2A,, which shows no indications of strong short-term variability like flares, and, therefore, we argue in favor of quiescent emission."," Figure \ref{fig:CoRoT2lc} presents the light curve of, which shows no indications of strong short-term variability like flares, and, therefore, we argue in favor of quiescent emission."
 The ephemerides of wwere derived by ? using the CoRoT data., The ephemerides of were derived by \citet{Alonso2008} using the CoRoT data.
" The transit duration is 8208 s, during which the relative flux deficit in the optical reaches 3 Our oobservation completely covers one planetary transit (epoch651withrespecttotheephemeridesfrom?).."," The transit duration is $8208$ s, during which the relative flux deficit in the optical reaches $3$ Our observation completely covers one planetary transit \citep[epoch 651 with respect to the ephemerides from][]{Alonso2008}."
" The ingress begins 6538 s after the start of the observation and the egress is finished shortly before the observation ends (cf.,"," The ingress begins $6538$ s after the start of the observation and the egress is finished shortly before the observation ends (cf.,"
 Fig. 9))., Fig. \ref{fig:CoRoT2lc}) ).
" Our analysis showed that the source count rate, if anything, increased by 17 Similarly, the hardness ratio HR=(H-S)/(H+S) with S=0.3—1 keV and H=1—4 keV (lower panel in Fig. 9))"," Our analysis showed that the source count rate, if anything, increased by $17$ Similarly, the hardness ratio $HR = (H - S )/(H + S )$ with $S = 0.3-1$ keV and $H = 1-4$ keV (lower panel in Fig. \ref{fig:CoRoT2lc}) )"
 remains unaffected., remains unaffected.
" On the one hand, given 82 source counts in 15 ks, detecting a3 On the other hand, the sources of X-ray emission are believed to be distributed much more inhomogeneously across the stellar surface than those of optical light."," On the one hand, given $82$ source counts in 15 ks, detecting a $3$ On the other hand, the sources of X-ray emission are believed to be distributed much more inhomogeneously across the stellar surface than those of optical light."
" We conclude that either the planet did not eclipse a strong concentration of X-ray emitting material in this particular case, the emission is distributed homogeneously, or concentrated at higher latitudes avoided by the planetary disk."," We conclude that either the planet did not eclipse a strong concentration of X-ray emitting material in this particular case, the emission is distributed homogeneously, or concentrated at higher latitudes avoided by the planetary disk."
" To check whether CoRoT-2A’ss potentially physical companion,J19270636+0122577,, is an X-ray source, we collected the photons within a circle of 1"" radius centered on the star's 2MASS position."," To check whether s potentially physical companion, is an X-ray source, we collected the photons within a circle of $1\arcsec$ radius centered on the star's 2MASS position."
" According to our modeling, this region contains 93 A single photon with an energy of 1.1 keV was detected in this region."," According to our modeling, this region contains $93$ A single photon with an energy of $1.1$ keV was detected in this region."
" Because 99 of 4"" and less fromCoRoT-2A,, the detected photon is unlikely to stem from that source."," Because $99$ of $4\arcsec$ and less from, the detected photon is unlikely to stem from that source."
" From nearby source-free regions, we estimated the rate of background-counts with energies of 1.10.1 keV, where the 0.1 keV range accounts for Chandra’ss eenergy resolution, to be 2x107* ctsss~! within the encircled region centered on the companion."," From nearby source-free regions, we estimated the rate of background-counts with energies of $1.1 \pm 0.1$ keV, where the $0.1$ keV range accounts for s energy resolution, to be $2\times 10^{-4}$ $^{-1}$ within the encircled region centered on the companion."
" The detected photon may, consequently, be associated with an X-ray source at the companion's position."," The detected photon may, consequently, be associated with an X-ray source at the companion's position."
" To derive an upper limit on the X-ray flux of the companion, we determined the count rate yielding one or less detected photons with a probability of 95 Assuming that the source has a 1 keV thermal spectrum, a distance of 270 pc (cf."," To derive an upper limit on the X-ray flux of the companion, we determined the count rate yielding one or less detected photons with a probability of $95$ Assuming that the source has a $1$ keV thermal spectrum, a distance of $270$ pc (cf."
" Sect. 2.8)),"," Sect. \ref{sec:interstAbsDist}) ),"
" and neglecting absorption, we used to convert the count rate into an upper limit of Lx«9x1076 ergs-!for the companion's X-ray luminosity."," and neglecting absorption, we used to convert the count rate into an upper limit of $L_\mathrm{X}<9\times10^{26}$ for the companion's X-ray luminosity."
 We presented new X-ray and optical data of the active planet host-starCoRoT-2A., We presented new X-ray and optical data of the active planet host-star.
". Below, we discuss the impact of our findings on our understanding of the ssystem."," Below, we discuss the impact of our findings on our understanding of the system."
" We studied the photosphere of aapplying different techniques of spectroscopic analysis to determine the stellar effective temperature, surface gravity, metallicity, and microturbulence velocity."," We studied the photosphere of applying different techniques of spectroscopic analysis to determine the stellar effective temperature, surface gravity, metallicity, and microturbulence velocity."
" First, we measured the EW of 238 and lines and determined the entire set of parameters by imposing excitation and ionization balance."," First, we measured the EW of 238 and lines and determined the entire set of parameters by imposing excitation and ionization balance."
" Second, we redetermined the parameters by directly fitting several sensitive spectral lines and found consistent results, which are, moreover, in line with previously published values (??).."," Second, we redetermined the parameters by directly fitting several sensitive spectral lines and found consistent results, which are, moreover, in line with previously published values \citep{AmmlervonEiff2009, Bouchy2008}."
" With an effective temperature of 5598+34 K and a surface gravity of logg=4.47+0,14, iis a star of spectral type G6-G7 (2,p.151,Table7.5) with slightly increased metallicity compared to the Sun."," With an effective temperature of $5598\pm34$ K and a surface gravity of $\log{g}=4.47\pm0,14$, is a star of spectral type G6--G7 \citep[][p. 151, Table 7.5]{AllenEd4} with slightly increased metallicity compared to the Sun."
 We compared the stellar parameters to those predicted by theoretical isochrone calculations for main and main-sequence stars (?).., We compared the stellar parameters to those predicted by theoretical isochrone calculations for pre-main and main-sequence stars \citep{Siess2000}.
" Assuming that iis close to the zero-age main sequence, these models favor a spectral type of G7 given the observed values of effective temperature and metallicity."," Assuming that is close to the zero-age main sequence, these models favor a spectral type of G7 given the observed values of effective temperature and metallicity."
 The fact that iis a highly active star became first obvious in the photometry observed by the CoRoT observatory., The fact that is a highly active star became first obvious in the photometry observed by the CoRoT observatory.
 The light curve shows pronounced rotational variability caused, The light curve shows pronounced rotational variability caused
The demand for loug-«istance lieh-baudwidth data trausfer iu the field of optical telecommmumications has lead to research about the use οfoptica euvelope solitons as information carriers.,The demand for long-distance high-bandwidth data transfer in the field of optical telecommunications has lead to research about the use of optical envelope solitons as information carriers.
 Solitous are ideal for optical teleconuunnicatious because the dispersion of the optical fiber is exactly couiterbalaiced. by the nonlinearity., Solitons are ideal for optical telecommunications because the dispersion of the optical fiber is exactly counterbalanced by the nonlinearity.
 As a result of this. the information carrier cau naintal Lits pulsc-sliape over long distances.," As a result of this, the information carrier can maintain its pulse-shape over long distances."
 Tn au ideal optical fiber. the nonlinear Schródcdiuger equation describes the cJectromaeguetie field euvelope iu a sinele poarization case.," In an ideal optical fiber, the nonlinear Schröddinger equation describes the electromagnetic field envelope in a single polarization case."
 Actual optical fibers however. have the property that there is a difference iu the propagatioi velocity for the two diiffereut polarization states of the electromagnetic field.," Actual optical fibers however, have the property that there is a difference in the propagation velocity for the two different polarization states of the electromagnetic field."
 Tus property is called birefringence., This property is called birefringence.
 The effecs of birefrinecuce are almost never scady. but they vary randomly. in both magnitude and oricutation.," The effects of birefringence are almost never steady, but they vary randomly, in both magnitude and orientation."
 The racloi hireYingence will cusure that an initially localized pulse will eventually disintegrate., The random birefringence will ensure that an initially localized pulse will eventually disintegrate.
 This effect is called Polarizatio1 Mode Dispersion (PAID)., This effect is called Polarization Mode Dispersion (PMD).
 PMD is importaif in situations where lieh-hit-rate optical signals have to be transporteL over kong distances such as παπαπο iutercontiuecutal optical connections., PMD is important in situations where high-bit-rate optical signals have to be transported over long distances such as sub-marine intercontinental optical connections.
 This is the reason that the topic has :uready rack considerable attention iu both theoretical aud experimental research iu the field of optical teleconimnuicatious [1--|13}.. ), This is the reason that the topic has already had considerable attention in both theoretical and experimental research in the field of optical telecommunications \cite{Fontaine}- \cite{Gisin}.
 The dynamics of nonlinear waves iu birefringeut optical fibers is described in the literature by the ‘ollowing set of coupled noulimear ditffereutial equations. which were originuly introduced by Berkhoer aud Zakharov |12]: A detailed derivation of Eq.{1}). which are from uow on called the birefringcuce equations. can be found iu the book by Tasceawa [1..," The dynamics of nonlinear waves in birefringent optical fibers is described in the literature by the following set of coupled nonlinear differential equations, which were originally introduced by Berkhoer and Zakharov \cite{Berkhoer}: A detailed derivation of \ref{eq: manakov}) ), which are from now on called the birefringence equations, can be found in the book by Hasegawa \cite{Hasegawa}."
" Iu Eq.(1)). the (scaled) electromagnetic field euvelopes of the ditfereut polarization states (αποος) aredescribed by wy, and πω respectively."," In \ref{eq: manakov}) ), the (scaled) electromagnetic field envelopes of the different polarization states (modes) aredescribed by $u_{1}$ and $u_{2}$ respectively."
 The parameter > describes the streugth of the cross-phase modulation., The parameter $\gamma$ describes the strength of the cross-phase modulation.
 For sinele mode optical fibers we cau use 5=Dαν, For single mode optical fibers we can use $\gamma = \frac{2}{3}$.
 TheJd pariety Ó describes the eroup velocity birefringence., The parameter $\delta$ describes the group velocity birefringence.
 Ii the limit Ó»0. the well known Manakovy equation is retained.," In the limit $\delta \rightarrow 0$, the well known Manakov equation is retained."
 Ued: vand Kath have argued that the parameter ó is actually a randon parameter with zero mean |!)sr: As a result of this. Eq.(1)) is a stochastic differcutial equation.," Ueda and Kath have argued that the parameter $\delta$ is actually a random parameter with zero mean \cite{Ueda}: As a result of this, \ref{eq: manakov}) ) is a stochastic differential equation."
 In the following. we treat the parziueter à as the hal£cüfference of the eroup velocity between the local xincipal birefringcuce axes.," In the following, we treat the parameter $\delta$ as the half-difference of the group velocity between the local principal birefringence axes."
 If we are able to solve Eq.(1)) analytically however. we can obtain analytical expressions fex the propagation properties of au initially localized soliton in a birefringent mediun.," If we are able to solve \ref{eq: manakov}) ) analytically however, we can obtain analytical expressions for the propagation properties of an initially localized soliton in a birefringent medium."
 The set of coupled equations (1)) have also been invesigated by others., The set of coupled equations \ref{eq: manakov}) ) have also been investigated by others.
 In BRe£.|15]. the behavior of solutious of Eq.(O) is investigatedS muuaericallv., In \cite{Menyuk} the behavior of solutions of \ref{eq: manakov}) ) is investigated numerically.
 One of the conclusions of Ref.|15) is that for solitonic initial conditions the two ↻⋜∐⋅↑↕⋜↧∩∏∏↴∖↴↸∖↴∖↴⋖⋯∪≼∐∖↴∖↴⋟⋜↧↕↖↖⇁⋜↧⋅↖↽↴∖↴⋯, One of the conclusions of \cite{Menyuk} is that for solitonic initial conditions the two partial pulses (modes) always move together.
∪↖↽↸∖↑∪∶↴∙⊾↸∖↑∐↸∖↥⋅∙⋎↸⊳∪↕⊔↻∐↸⊳⋜↧↑↸∖≼↧↻⋜↧↑↑↸∖↥⋅∐∪↕≯↴∖↴∪∐↑∪∐≓↴∖↴∪∐↑∪∐↕∐↑↸∖↥⋯⊳↑↕∪∐↴∖↴↴⋝↸∖, A complicated pattern of soliton-soliton interactions between the modes is presented.
↑∖↖↽↸∖↸∖∐↑∐↸∖⋯∪≺∐∖↴∖↴ ↕↴∖↴↻↥⋅↸∖↴∖↴↸∖∐↑↸∖≼↧∙⋎∐∪↑∐↸∖↥⋅↕∐∏⋯↥⋅↑⋜⋯↑↥⋅↸∖↴∖↴∏↕↑↕↴∖↴↻↥⋅↸∖↴∖↴↸∖∐↑↸∖≼↧↕∐↕⊰↸∖⊔↽ 6|., Another important result is presented in \cite{Kath}. .
. Firstly. it is shown in this publication that by applying the transformation: the set of equations Eq.(1)) transform iuto:," Firstly, it is shown in this publication that by applying the transformation: the set of equations \ref{eq: manakov}) ) transform into:"
"P. van der M. W. Sterrewacht Leiden. Leiden University. PO Box 9513. 2300 RA ST The Sunyaev-Zel'dovich (SZ) effect is a distortion of the spectral shape of the cosmic microwave background (CMB) due to inverse Compton scattering in the ubiquitous. hot (T,~ 107K) intracluster medium (ICM) of galaxy clusters (?)..","P. van der M. W. Sterrewacht Leiden, Leiden University, PO Box 9513, 2300 RA Leiden, the The Sunyaev-Zel'dovich (SZ) effect is a distortion of the spectral shape of the cosmic microwave background (CMB) due to inverse Compton scattering in the ubiquitous, hot $T_{\mathrm{e}} \sim 10^{7} \,$ K) intracluster medium (ICM) of galaxy clusters \citep{Sunyaev1972}."
 The canonical thermal SZ spectrum ts a decrement in the brightness of the CMB as measured through galaxy clusters at mm wavelengths and an increment at sub-mm wavelengths which passes though a null at 20= 13mm.," The canonical thermal SZ spectrum is a decrement in the brightness of the CMB as measured through galaxy clusters at mm wavelengths and an increment at sub-mm wavelengths which passes though a null at $\lambda
\approx 1.3 \,$ mm."
 To correctly describe the SZ spectral distortion when relativistic electrons are present or the cluster is moving with respect to the CMB additional correction terms. usually termed “relativistic” (or “finite temperature”) corrections and “kinetic” SZ effect. are required.," To correctly describe the SZ spectral distortion when relativistic electrons are present or the cluster is moving with respect to the CMB additional correction terms, usually termed “relativistic” (or “finite temperature”) corrections and “kinetic” SZ effect, are required."
 Measurement of these corrections ts only possible using observations at multiple wavelengths. and ts expedited by measurement at wavelengths where the expected modifications to the thermal SZ effect are largest.," Measurement of these corrections is only possible using observations at multiple wavelengths, and is expedited by measurement at wavelengths where the expected modifications to the thermal SZ effect are largest."
 In the case of the finite temperature corrections. the largest changes expected in the SZ increment are at wavelengths shorter than | jam. Decrements in emission are rare astrophysically and can be ascribed to the SZ effect with little ambiguity: this has lead to measurements of the SZ effect at 2.> 2mm becoming almost routine.," In the case of the finite temperature corrections, the largest changes expected in the SZ increment are at wavelengths shorter than $1 \, \mu$ m. Decrements in emission are rare astrophysically and can be ascribed to the SZ effect with little ambiguity; this has lead to measurements of the SZ effect at $\lambda \gtrsim 2 \,$ mm becoming almost routine."
 In comparison. measurements of the SZ effect increment are complicated by the presence of the dusty. high redshift galaxies which constitute the sub-mm cosmic background.," In comparison, measurements of the SZ effect increment are complicated by the presence of the dusty, high redshift galaxies which constitute the sub-mm cosmic background."
 Additionally. the individual sources comprising the sub-mm background are gravitationally lensed by galaxy clusters. the effect of which is to preferentially correlate increases in sub-mm emission with clustering.," Additionally, the individual sources comprising the sub-mm background are gravitationally lensed by galaxy clusters, the effect of which is to preferentially correlate increases in sub-mm emission with clustering."
" This correlation makes unambiguous detection of the SZ increment difficult. though successful measurements do exist (2.. 2.. ?., ?.. ?))."," This correlation makes unambiguous detection of the SZ increment difficult, though successful measurements do exist \citealt{Lamarre1998}, \citealt{Komatsu1999}, \citealt{Zemcov2003}, \citealt{Zemcov2007}, \citealt{Nord2009}) )."
 Moreover. the presence of the sub-mm background may contaminate measurements of the SZ effect for ο»1 mm in less massive galaxy clusters (?)..," Moreover, the presence of the sub-mm background may contaminate measurements of the SZ effect for $\lambda > 1 \,$ mm in less massive galaxy clusters \citep{Aghanim2005}."
 A better understanding of the sub-mm emission associated with galaxy clusters is required., A better understanding of the sub-mm emission associated with galaxy clusters is required.
 Heretofore. systematic far infrared (FIR) surveys of many galaxy clusters to large radii have been technically challenging so à complete census of sub-mm emission from clusters has lteeidlehiffibe Νεα: hi," Heretofore, systematic far infrared (FIR) surveys of many galaxy clusters to large radii have been technically challenging so a complete census of sub-mm emission from clusters has been difficult to obtain."
benSvetaef-SPRRdEoC Tehos (?) has. for the first time. provided the capability to make deep maps of clusters to large angles on the sky and to use colour information to separate the different sources of sub-mm emission present in. galaxy clusters.," The advent of SPIRE \citep{Griffin2010} on \citep{Pilbratt2010} has, for the first time, provided the capability to make deep maps of clusters to large angles on the sky and to use colour information to separate the different sources of sub-mm emission present in galaxy clusters."
 In addition to gravitationally lensed background sources (2).. emission in clusters above the confused sub-mm background may also comprise emission from galaxies in the cluster itself (2)... as well as truly diffuse emission from the SZ effect and possibly even cold dust in the ICM.," In addition to gravitationally lensed background sources \citep{Rex2010}, emission in clusters above the confused sub-mm background may also comprise emission from galaxies in the cluster itself \citep{Rawle2010}, as well as truly diffuse emission from the SZ effect and possibly even cold dust in the ICM."
 SPIRE's ability to separate sources of emission based both on spatial and spectral information allows the demographics of the sub-mm emission to. be measured., SPIRE's ability to separate sources of emission based both on spatial and spectral information allows the demographics of the sub-mm emission to be measured.
 In this paper. we use deep SPIRE maps of the z=0.3 Bullet cluster (1E0657—56)) taken as part of the Lensing Survey (HLS. P.I. Egami) at 250. 350. and 500um with 18. 25 and 36 aresec resolution to measure the SZ effect and constrain other diffuse emission associated with the cluster.," In this paper, we use deep SPIRE maps of the $z=0.3$ Bullet cluster ) taken as part of the Lensing Survey (HLS, P.I. Egami) at $250$, $350$, and $500 \, \mu$ m with $18$, $25$ and $36$ arcsec resolution to measure the SZ effect and constrain other diffuse emission associated with the cluster."
" The HLS ts a programme to observe 40 massive clusters in the range 0.1<z« 1.0: during ""s science demonstration phase wwas observed to full depth.", The HLS is a programme to observe 40 massive clusters in the range $0.1 < z < 1.0$ ; during 's science demonstration phase was observed to full depth.
 The specific observation strategy. low level data reduction and map making processes are summarized in ?:: here we begin with the calibrated flux and noise maps at 250.350 and 500 jm (Fig.," The specific observation strategy, low level data reduction and map making processes are summarized in \citet{Egami2010}; here we begin with the calibrated flux and noise maps at $250, 350$ and $500 \, \mu$ m (Fig."
 2 of ?))., 2 of \citealt{Egami2010}) ).
 Measurement of dim. extended emission is complicated by the presence of background sub-mm galaxies the confusion noise from which. at SPIRE's resolution. is measured to be ~ 6mly in all three bands for blank fields (?)..," Measurement of dim, extended emission is complicated by the presence of background sub-mm galaxies the confusion noise from which, at SPIRE's resolution, is measured to be $\sim 6 \,$ mJy in all three bands for blank fields \citep{Nguyen2010}."
 Indeed. in these naps we measure an RMS notse of (6.0.6.0.7.5] mJy/beam at 250.350.500 umm. consistent with the combination of confusion hoise and instrument noise expected. from the integration time.," Indeed, in these maps we measure an RMS noise of $\{6.0,6.0,7.5\} \,$ mJy/beam at $250, 350, 500
\, \mu$ m, consistent with the combination of confusion noise and instrument noise expected from the integration time."
 Obviously. care must be taken to disentangle extended emission from confused sources.," Obviously, care must be taken to disentangle extended emission from confused sources."
 To do this. we employ the approach discussed below. the fundamental tenet of which ts to account for and remove all 250 jm emission from thetwo longer wavelength channels.," To do this, we employ the approach discussed below, the fundamental tenet of which is to account for and remove all $250 \, \mu$ m emission from thetwo longer wavelength channels."
short lifetimes of massive stars and VAIOs. several generations of these stars would form during our adopted evolution time (10 vr).,"short lifetimes of massive stars and VMOs, several generations of these stars would form during our adopted evolution time $10^8$ yr)."
 Because of the progressive pollution of the IGML. the subsequent. generations of stars would form with a non strictly zero metallicity.," Because of the progressive pollution of the IGM, the subsequent generations of stars would form with a non strictly zero metallicity."
 Although we also have vields for massive stars computed with the FRANEC code for different metallicities. as far as we know there is no mention in the literature of (his kind of computation for VMOs [setting aside the possibility that these objects may form with a non-zero metallicity (see however Figer et al.," Although we also have yields for massive stars computed with the FRANEC code for different metallicities, as far as we know there is no mention in the literature of this kind of computation for VMOs [setting aside the possibility that these objects may form with a non-zero metallicity (see however Figer et al."
 1993)., 1998)].
 Therefore. for the sake of homogeneity in our conmutations. we did not consider this effect. ie. (he metallicity dependent vields.," Therefore, for the sake of homogeneity in our computations, we did not consider this effect, i.e. the metallicity dependent yields."
 We believe nevertheless. that this inconsistency in the model would only have a minimal elect due to the very short time interval considered.," We believe nevertheless, that this inconsistency in the model would only have a minimal effect due to the very short time interval considered."
 In Table 2 we show the total metallicity reached in the IGM for the different. ΙΔΙΕΣ al several values of (he cosmic Gime., In Table 2 we show the total metallicity reached in the IGM for the different IMFs at several values of the cosmic time.
 We consider this metallicity as (wpical mean values since al very early epochs the pollution of the IGAL was very inhomogeneous. probably occurring through the mixing of cloud patches already. contaminated with metals 2000).," We consider this metallicity as typical mean values since at very early epochs the pollution of the IGM was very inhomogeneous, probably occurring through the mixing of cloud patches already contaminated with metals \citep{arg00}."
. We emphasize (hat the metallicitw values in Table 2 are extremely dependent on the star lormation rate history assumed., We emphasize that the metallicity values in Table 2 are extremely dependent on the star formation rate history assumed.
 What is important in Table 2 is (he comparison between the results obtained with different IMFEs at a given cosmic time., What is important in Table 2 is the comparison between the results obtained with different IMFs at a given cosmic time.
 As expected from Figure 1. the evolution of the metallicity obtained in the Salpeter case is between that of the YSa and. YSb cases.," As expected from Figure 1, the evolution of the metallicity obtained in the Salpeter case is between that of the YSa and YSb cases."
 Note the very low value of Z/Z. in the YSb case at log (= 6.5., Note the very low value of $Z/Z_\odot$ in the YSb case at log t= 6.5.
 This is due to the steeper slope of this IME for the high stellar mass range., This is due to the steeper slope of this IMF for the high stellar mass range.
 In contrast. al log (8 the Ysa IME. presents an important degree of metal enrichment due to the smoother (han conventional slope of this IMF lor the massive stars (see Figure 1).," In contrast, at log $\sim 8$ the YSa IMF presents an important degree of metal enrichment due to the smoother than conventional slope of this IMF for the massive stars (see Figure 1)."
 The hieh metallicity value reached Z73x107? Z. ([Fe/Il]o —1.7) at log /e8 in the YSa case is similar to that of the low metallicity tail in the metal distribution of thick disk stars in our ealaxv (Norris&Ryan1991)., The high metallicity value reached $Z\sim 3\times 10^{-2}$ $_\odot$ $\sim -1.7$ ) at log $t\sim 8$ in the YSa case is similar to that of the low metallicity tail in the metal distribution of thick disk stars in our galaxy \citep{nor91}.
. For the Nakamura Umenmura IME cases. the metallicity in the IGM increases rapidly at verv early times due to the contamination from massive," For the Nakamura Umemura IMF cases, the metallicity in the IGM increases rapidly at very early times due to the contamination from massive"
"What is a single spin asymmetry Consider the collision of a proton of momentum 7, carrying a transverse spin 57 and producing an outgoing hadron with transverse momentum ky.","What is a single spin asymmetry Consider the collision of a proton of momentum $\overrightarrow{p}$, carrying a transverse spin $\overrightarrow{s_T}$ and producing an outgoing hadron with transverse momentum $\overrightarrow{k_T}$."
" The SSA defined as is zero, unless the cross section contains a term 57-CExkr)."," The SSA defined as is zero, unless the cross section contains a term $\overrightarrow{s_T}\cdot(\overrightarrow{p}\times \overrightarrow{k_T})$."
" It can be shown that this requires the existence of anflip andinteractions, which generate a phase difference between the flip and the non-flip amplitudes, to avoid violation of time reversal invariance."," It can be shown that this requires the existence of an and, which generate a phase difference between the flip and the non-flip amplitudes, to avoid violation of time reversal invariance."
" In the naive parton model one expects very small SSA, becauseof the double suppression a,m,/Q, where m, is the quark mass and Q the energy scale of the Actually a large SSA has been discovered 30 years ago at FNAL with a 300 GeV/c unpolarized proton beam in pBe—AtX [17] and many more SSA have been observed later, in particular large SSA in p'p—7X and p!p—7X at FNAL by E704 [18] and more recently by STAR at BNL-RHIC [19].."," In the naive parton model one expects very small SSA, becauseof the double suppression $\alpha_s m_q/Q$, where $m_q$ is the quark mass and $Q$ the energy scale of the Actually a large SSA has been discovered 30 years ago at FNAL with a 300 GeV/c unpolarized proton beam in $pBe \to \Lambda^{\uparrow} X$ \cite{bunce} and many more SSA have been observed later, in particular large SSA in $p^{\uparrow}p \to \pi X$ and $\bar {p}^{\uparrow}p \to \pi X$ at FNAL by E704 \cite{E704} and more recently by STAR at BNL-RHIC \cite{STAR}. ."
" These data have the same trend, as shown"," These data have the same trend, as shown"
 1 3% 5% ," $\sim
3.4$ $3^{\prime}$ $5^{\prime}$ "
AGNs have the same plivsical eugiue as a Type l1 or Type 2 ACN. but with additional obscuration within a few parsecs completely blocking the ionizing coutimuun radiation from exciting even the narrow cuiission lines.,"AGNs have the same physical engine as a Type 1 or Type 2 AGN, but with additional obscuration within a few parsecs completely blocking the ionizing continuum radiation from exciting even the narrow emission lines."
 Rigbyetal.(2006) instead sugecst that optically dull AGNs are obscured by extrauuclear (7100 pe) eas and dust in the host galaxy. blocking the narrow/ ines along the observer's line of sight.," \citet{rig06} instead suggest that optically dull AGNs are obscured by extranuclear $>$ 100 pc) gas and dust in the host galaxy, blocking the narrow lines along the observer's line of sight."
 No matter the physical location of the obscurime material. it ust xefereutiallv absorb the optical enission. since optically dull AGNs remain N-rvay bright.," No matter the physical location of the obscuring material, it must preferentially absorb the optical emission, since optically dull AGNs remain X-ray bright."
 Indeed. more thaw iuf of optically dull ACNs are relatively unobscured (Nyx107 7) in the Nerayvs (Severeninictal.2003:Pageet 2003).," Indeed, more than half of optically dull AGNs are relatively unobscured $N_H<10^{22}$ $^{-2}$ ) in the X-rays \citep{sev03,pag03}."
. Prefercutially obscuring he optical emission while remaining X-ray unabsorbed would require extreme gas-to-dust ratios not observed iu other ACNs (Maiolinoetal.2001)., Preferentially obscuring the optical emission while remaining X-ray unabsorbed would require extreme gas-to-dust ratios not observed in other AGNs \citep{mai01}.
. Optically dull ACNs could also be Type 2 AGNs with narrow chussion lines diluted bv a bright host galaxy., Optically dull AGNs could also be Type 2 AGNs with narrow emission lines diluted by a bright host galaxy.
 Tudeed. Moran.Filippeuko&Chornock(2002) showed that many 2~0 ACNs would appear optically dull if observed at 2~1. since the host ealaxy would occupy more of the spectroscopic slit or fiber aud consequently overwhlelin the ACN emission lines.," Indeed, \citet{mor02} showed that many $z \sim 0$ AGNs would appear optically dull if observed at $z \sim 1$, since the host galaxy would occupy more of the spectroscopic slit or fiber and consequently overwhelm the AGN emission lines."
 HST/ACS images additionally show that may optically dull AGN hosts at DocL are edge-on (Rigbyetal.2006) or have a secoud ealaxy falling within the spectroscopic aperture (Trapetal. 2009h)., HST/ACS images additionally show that many optically dull AGN hosts at $z<1$ are edge-on \citep{rig06} or have a second galaxy falling within the spectroscopic aperture \citep{tru09c}.
. However of local (undiluted) ACNs are optically dull (LaFrancactal.2002:Horuschemeier 2005).," However of local (undiluted) AGNs are optically dull \citep{laf02,hor05}."
. Aud even after removing the host ealaxy helt by decomposing the spectral energy. distribution. ~1/3 of optically dull ACNs have anomalously high rav to optical flux ratios (Timmpetal.200010).," And even after removing the host galaxy light by decomposing the spectral energy distribution, $\sim$ 1/3 of optically dull AGNs have anomalously high X-ray to optical flux ratios \citep{tru09c}."
 Another possibility is that optically dull ACNs have different accretion physics due to low accretion rates (Yuan&Naravan2001)., Another possibility is that optically dull AGNs have different accretion physics due to low accretion rates \citep{yuan04}.
. Models have long predicted that an AGN with a low accretion rate 0=LuofLeaa= 0.0L) will have a radiatively inefficient accretion flow CREATE) within some truucation radius A. with Ay defined as where the collisional cooling time is comparable to the accretion time (Beechuan.Blandford&Rees198E:Navavanctal. 1995).," Models have long predicted that an AGN with a low accretion rate $\dot{m}
\equiv L_{\rm bol}/L_{\rm Edd} \lesssim 0.01$ ) will have a radiatively inefficient accretion flow (RIAF) within some truncation radius $R_t$, with $R_t$ defined as where the collisional cooling time is comparable to the accretion time \citep{beg84,nar95}."
. Devoud B. accretion willremain ina standard ecometrically thin aud optically thick disk with a thermal blackbody spectrum (c.e..Shakura&Suuvaev 1973).," Beyond $R_t$, accretion will remain in a standard geometrically thin and optically thick disk with a thermal blackbody spectrum \citep[e.g.,][]{sha73}."
" However within 7,"" there are too few collisions to couple the ious aud electrons and the gas becomes a two-tempcrature plasima.", However within $R_t$ there are too few collisions to couple the ions and electrons and the gas becomes a two-temperature plasma.
 The electrons are cooled by bremsstraliluue. svuchrotron. aud Compton up-scattering. while the ions remain at the virial temperature.," The electrons are cooled by bremsstrahlung, synchrotron, and Compton up-scattering, while the ions remain at the virial temperature."
 This mcanus the flow is ecometrically thick and optically thin., This means the flow is geometrically thick and optically thin.
 A RIAFthen lacks much of the optical/UV blackbody emission of an optically thick accretion disk. and consequently caunot jonize aud/or excite the broad or narrow optical e1uission les secu in other AGNs (Yuan&Naravan2001:Trumpctal. 2011).," A RIAFthen lacks much of the optical/UV blackbody emission of an optically thick accretion disk, and consequently cannot ionize and/or excite the broad or narrow optical emission lines seen in other AGNs \citep{yuan04,tru11}."
. Because the ions iu the RIAF are only marginally bound. such ACNs should also have strong; outflows aud be consequently radio luninous.," Because the ions in the RIAF are only marginally bound, such AGNs should also have strong outflows and be consequently radio luminous."
 Optically dull ACiNs. especially those with high N-ray to optical flux ratios. are indeed observed to be have higher ratios of radio to optical/UV luminosity than Type 1 AGNs (Trpetal.2009b. 2011).," Optically dull AGNs, especially those with high X-ray to optical flux ratios, are indeed observed to be have higher ratios of radio to optical/UV luminosity than Type 1 AGNs \citep{tru09c,tru11}."
. Much of the optical aud iufrared light in RIAF AGNs iav be svuchrotron radiation associated with the radio jet (IIo2009)., Much of the optical and infrared light in RIAF AGNs may be synchrotron radiation associated with the radio jet \citep{ho09}.
. Each of these three paradiguis has a different signature iu spectropolarimetry., Each of these three paradigms has a different signature in spectropolarimetry.
 Anisotropic obscuration of the narrow cluission lines would leave telltale reflected cluission lines iu the polarized spectra (Nagaoet20010)., Anisotropic obscuration of the narrow emission lines would leave telltale reflected emission lines in the polarized spectrum \citep{nag04}.
 On the other haud. if au optically dull AGN is a Type 2 AGN diluted by a host galaxy. its polarized flux would be equally. diluted. (," On the other hand, if an optically dull AGN is a Type 2 AGN diluted by a host galaxy, its polarized flux would be equally diluted. ("
A diluted optically dull ACN Πο exhibit polarized broad. e1iission lines like those secu in Type 2 AGNs. but the host ealaxy would probably overwhehu them to a nou-detectable level.),"A diluted optically dull AGN might exhibit polarized broad emission lines like those seen in Type 2 AGNs, but the host galaxy would probably overwhelm them to a non-detectable level.)"
" Aud if optically dull AGNs have RIAFs we iielt observe a featureless polarized coutimmun. either frou the svuchrotron cussion associated with the stronger radio jet (οιοι,Jannuzictal.1901:Cohen1999) or because we are viewing the naked. lineless ΟΕΙΙ (from the disk bevoud the RIAF) reflected by a scattering surface in the host galaxy CAutouucci&Miller1985:Oc5etal.1999:Iishimoto 2001)."," And if optically dull AGNs have RIAFs we might observe a featureless polarized continuum, either from the synchrotron emission associated with the stronger radio jet \citep[e.g.,][]{jan94,coh99} or because we are viewing the naked, lineless continuum (from the disk beyond the RIAF) reflected by a scattering surface in the host galaxy \citep{ant85,ogl99,kis01}."
. We sunuuarize the polarization signatures of cach paracienm in Table 1.., We summarize the polarization signatures of each paradigm in Table \ref{tbl:paradigm}.
" We used SubarufFOCAS to observe the two brightest optically dull AGNs of Trumpetal.90000). 0905819|013220. and 100036|02929,"," We used Subaru/FOCAS to observe the two brightest optically dull AGNs of \citet{tru09c}, 095849+013220 and 100036+024929."
 The objects have multiwavelength observatious frouthe Cosmic Evolution Survey (COSAIOS.Scovilleetal.2007).. a survey based oua 1.7 deg? HST/ACS treasury srograinn (Ixoekemocretal. 2007).," The objects have multiwavelength observations from the Cosmic Evolution Survey \citep[COSMOS,][]{sco07}, a survey based ona 1.7 $^2$ HST/ACS treasury program \citep{koe07}."
. Both targets have idewications aud redshifts from the NMIALCOSAMOS AGN spectroscopic eiuupaieu with Magellan/INLACS. (Timpetal.2009a)., Both targets have identifications and redshifts from the XMM-COSMOS AGN spectroscopic campaign with Magellan/IMACS \citep{tru09a}.
. Despite their absorption Lue optical specra. they are confirmed as bona-fide ACN using their NMM. data (Cappollutietal.2009:Drusa 2010): each has an Nav luminosity of Lystygv038LOY eres. requiing au AGN (Iloruscheineieretal.2001).," Despite their absorption line optical spectra, they are confirmed as bona-fide AGN using their XMM data \citep{cap09,bru10}: each has an X-ray luminosity of $L_{\rm
0.5-10~keV}>3 \times 10^{42}$ erg/s, requiring an AGN \citep{hor01}."
.. We show properties of 095819|013220 and 100036|021929 in Table 2.. Trumpetal., We show properties of 095849+013220 and 100036+024929 in Table \ref{tbl:odagns}.
(20091) used. ACN plus galaxy fits to the 6otical photometry to sugeest that both of these targets are roughly ACN and host galaxy in the / baud., \citet{tru09c} used AGN plus galaxy fits to the optical photometry to suggest that both of these targets are roughly AGN and host galaxy in the $i$ band.
 Table 2. also gives the X-ray. to optical flux ratios. given by X/O=logfy/foους»gv)l/xn/2.515.352.," Table \ref{tbl:odagns} also gives the X-ray to optical flux ratios, given by $X/O = \log{f_X/f_O} =
\log(f_{0.5-2~{\rm keV}}) + i_{\rm AB}/2.5 + 5.352$."
" The second target. 100036|021929. is a good candidate to be a normal AGN diluted by a host galaxy because of its V/O(ACN)=0.6. fitting nicely in the traditional ""N-arav ACN locus” of 1<X/O (Maccacarootal. 1988)."," The second target, 100036+024929, is a good candidate to be a normal AGN diluted by a host galaxy because of its $X/O{\rm (AGN)}=-0.6$, fitting nicely in the traditional “X-ray AGN locus” of $-1<X/O<1$ \citep{mac88}."
. ILoxvever the first target. 095819|013220. is anomalously X-ray bright auc optically dull. with V/O= and VN/OCAGN)= LL.," However the first target, 095849+013220, is anomalously X-ray bright and optically dull, with $X/O=1.1$ and $X/O{\rm (AGN)}=1.4$ ."
 Since starlight dilution would increase the optical emission and decrease the V/O ratio. the high X/O ratio for the first target means it cannot be explained by starlight dilution.," Since starlight dilution would increase the optical emission and decrease the $X/O$ ratio, the high $X/O$ ratio for the first target means it cannot be explained by starlight dilution."
 TIustead 095819|013220 is a good candidate to host a RIAF (Trumpetal. 20095).., Instead 095849+013220 is a good candidate to host a RIAF \citep{tru09c}. .
 Spectropolarimetric observations of both targets were undertaken using the Faint Object Camera and, Spectropolarimetric observations of both targets were undertaken using the Faint Object Camera and
Udalski (2003) obtained from deep Ix band imaging of red chunp stars (rue distance moduli of 20.165 4 0.015 mag and 20.353 + 0.013 mag for Carina aud Fornax. respectively.,"Udalski (2003) obtained from deep K band imaging of red clump stars true distance moduli of 20.165 $\pm$ 0.015 mag and 20.858 $\pm$ 0.013 mag for Carina and Fornax, respectively."
 Similar results were obtained for the Carina distance from an analysis of its RR Lyrae stars ( 20.10 + 0.12 mae: DallOra οἱ al. (, Similar results were obtained for the Carina distance from an analysis of its RR Lyrae stars ( 20.10 $\pm$ 0.12 mag; Dall'Ora et al. (
2003)). [rom its optical TRGB and horizontal branch (119) luminosities (20.05 + 0.06 mag and 20.12 + 0.08 mag: Smecker-IIlane et al.,"2003)), from its optical TRGB and horizontal branch (HB) luminosities (20.05 $\pm$ 0.06 mag and 20.12 $\pm$ 0.08 mag; Smecker-Hane et al."
 1994). and from dwarf. Cepheids (20.069 + 0.12 mag: Mateo οἱ al.," 1994), and from dwarf Cepheids (20.06 $\pm$ 0.12 mag; Mateo et al."
" 1905),", 1998).
 A shorter distance to Carina of 19.94 mag was calculated by Udalski (2000) from I band photometry of red clamp stars aud the TRGB. and from V. band photometry of RR Lyrae stus.," A shorter distance to Carina of 19.94 mag was calculated by Udalski (2000) from I band photometry of red clump stars and the TRGB, and from V band photometry of RR Lyrae stars."
 However. Udalski's distance estimation lor Carina was tied to a short assumed. LAIC distance of 18.24 mag. which is probably an underestimation of (he (vue LAIC distance modulus (e.g. Schaefer 2008. Fouque el al.," However, Udalski's distance estimation for Carina was tied to a short assumed LMC distance of 18.24 mag, which is probably an underestimation of the true LMC distance modulus (e.g. Schaefer 2008, Fouqué et al."
 2007)., 2007).
 Correcting the LAIC distance to a more likely value near 18.5 would bring Udalski's result for the Carina distance in close agreement wilh the present work. aud the other results cited above.," Correcting the LMC distance to a more likely value near 18.5 would bring Udalski's result for the Carina distance in close agreement with the present work, and the other results cited above."
 Dtegmirding the Fornax dsph galaxy. optical photometry of (he TRGB and HB has vielded the following distance moduli: 20.76 + 0.02 (Buonanno et al. (," Regarding the Fornax dSph galaxy, optical photometry of the TRGB and HB has yielded the following distance moduli: 20.76 $\pm$ 0.02 (Buonanno et al. ("
1999). 20.70 - 0.12 (Saviane et al. (,"1999), 20.70 $\pm$ 0.12 (Saviane et al. ("
2000). 20.65 + 0.11 (Bersier (2000). and 20.71 4 0.07 (Rizzi et al.,"2000), 20.65 $\pm$ 0.11 (Bersier (2000), and 20.71 $\pm$ 0.07 (Rizzi et al."
 2007)., 2007).
 Greco et al. (, Greco et al. (
2005) measured (51—A/)y — 20.72 d 0.10 for this galaxy [rom RR Lyrae stars.,2005) measured $(m-M)_{0}$ = 20.72 $\pm$ 0.10 for this galaxy from RR Lyrae stars.
 A slightly shorter distance modulus (20.66 mag) was obtained by Bersier from I band. photometry of red chump stus., A slightly shorter distance modulus (20.66 mag) was obtained by Bersier from I band photometry of red clump stars.
 Recently Gullieuszik et al. (, Recently Gullieuszik et al. (
2007) derived the distance modulus for Fornax from near-inlrared photometry of the TRGB (20.75 + 0.19) and red clump stars (20.74 — 0.11) applving population corrections derived [rom models.,2007) derived the distance modulus for Fornax from near-infrared photometry of the TRGB (20.75 $\pm$ 0.19) and red clump stars (20.74 $\pm$ 0.11) applying population corrections derived from models.
 Our current distance result. [or Fornax is al the upper limit of the distribution of these earlier measurements. but. within iis uncertainty clearly consistent with these.," Our current distance result for Fornax is at the upper limit of the distribution of these earlier measurements, but within its uncertainty clearly consistent with these."
 It is likely Chat (he quality of the distance determinations to galaxies from their TRGB in the optical I band ancl in (the near-I8R. JIx bands is quite similar as to (he correction of the effect of the varving metallicities of different red giant populations: however. a decisive advantage of (he infrared TRGB method is its basic insensilivily to reddening corrections.," It is likely that the quality of the distance determinations to galaxies from their TRGB in the optical I band and in the near-IR JK bands is quite similar as to the correction of the effect of the varying metallicities of different red giant populations; however, a decisive advantage of the infrared TRGB method is its basic insensitivity to reddening corrections."
 While (his has no strong consequences in the case of the Carina and Fornax dwarf galaxies due (o their low foreground reddenings. aud (assumed) negligible internal redcdenings. things might be very different when highly reddened galaxies are under stud.," While this has no strong consequences in the case of the Carina and Fornax dwarf galaxies due to their low foreground reddenings, and (assumed) negligible internal reddenings, things might be very different when highly reddened galaxies are under study."
 (Frou nearnfared photometry of (he Carina and Fornax dSph galaxies we have derived the distances to these galaxies using the calibration of the TRGB absolute magnitudes in the J and IX bands given by Valenti. Ferraro and Olivia (2004).," >From near-infared photometry of the Carina and Fornax dSph galaxies we have derived the distances to these galaxies using the calibration of the TRGB absolute magnitudes in the J and K bands given by Valenti, Ferraro and Olivia (2004)."
 We have obtained the following, We have obtained the following
sale signature as cond cloucs on the dusty atmosphere (see rofvarb])).,same signature as cond clouds on the dusty atmosphere (see \\ref{var5}) ).
 Cool spots. ou the other haud. have a weaker signature and could cover up o about of the surface before being detected.," Cool spots, on the other hand, have a weaker signature and could cover up to about of the surface before being detected."
 If 2M1115 is warler (with a dusty atinosphiere). then clouds could be larger: At TTS. a cloud coverage of up to would be possible| before it is cetected by the ucasuremenuts of this sensitivity.," If 2M1145 is warmer (with a dusty atmosphere), then clouds could be larger: At K, a cloud coverage of up to would be possible before it is detected by the measurements of this sensitivity."
 The lits on cool spots are not chauged at this teuerature (see refvar3))., The limits on cool spots are not changed at this temperature (see \\ref{var3}) ).
 If 2M1I115 is cooler IIs). then clouds are inied to bei18o much smaller: a coverage of just wotld inve elven rise ο a detectable signature rofvarl))h," If 2M1145 is cooler K), then clouds are limited to being much smaller: a coverage of just would have given rise to a detectable signature \\ref{var4}) )."
 Large cool spots. on the other haud. coveri18o up o o [the surface. ave permitted.," Large cool spots, on the other hand, covering up to of the surface, are permitted."
 At this lower enr)oratiure the dusty iiolels inav not be valid (due ο 1icreased. dust precipitation). so cond models shotld ρα considered.," At this lower temperature the dusty models may not be valid (due to increased dust precipitation), so cond models should be considered."
 For a coud atinosphere at KI. cool spots can still cover a large fraction of the surface. 3) before eiviug a detectable signature in these bands. mt note tha rese bands were nof designed with such a situation in uid.," For a cond atmosphere at K, cool spots can still cover a large fraction of the surface ) before giving a detectable signature in these bands, but note that these bands were not designed with such a situation in mind."
 Dusty clouds ire restricted to a coverage of no more than20%., Dusty clouds are restricted to a coverage of no more than.
. Tn all cases. these limits apphv to a suelesi clouds]vot or several clouds/spots raving «οσοitv.," In all cases, these limits apply to a single cloud/spot or several clouds/spots behaving coherently."
 Clearly. ΠΙΑ sinall features evolving ---»peudenutly ο Peach other will have no net effect on he ht curve ofthe unresolved clisk.," Clearly, many small features evolving independently of each other will have no net effect on the light curve of the unresolved disk."
 These πιάτς can be conixmwed with the feature sizes crivable from he detectiois of variability iu 2MIT15 N BJAL. specifically the derived. amplitudes aud: noises eiven iu their Table 2.," These limits can be compared with the feature sizes derivable from the detections of variability in 2M1145 by BJM, specifically the derived amplitudes and noises given in their Table 2."
 Usine he 1olse subtraction method in section 6 οἳ the preseut paper. the 99-01 and 00-2 data from BJA correspond to peak-to-peak signal uplitudes of 0.025 ancl unmaes respectively.," Using the noise subtraction method in section \ref{analysis} of the present paper, the 99-01 and 00-02 data from BJM correspond to peak-to-peak signal amplitudes of 0.025 and mags respectively."
" For dusty atmosphere at Kk. these translate to clear cloud coverages of alu respectively, aud about re same for KIS cooler spots."," For a dusty atmosphere at K, these translate to clear cloud coverages of and respectively, and about the same for K cooler spots."
 These are well below 1e upper Bits iniposed by he present infrared data aud rerefore eutirelv. consistent wit1 them., These are well below the upper limits imposed by the present infrared data and therefore entirely consistent with them.
 All of these limits are biwed on the assumptions (1) iat the liuifiug cases o the AMES-dustv aud AMES-cond atniospreves of Allard et ((2001) are appropriate. (2) that 2M]115 was no olserved durus au abnormal ohase of atinosphieric or magnetic inactivitv. aud (3) that he timescale for the evolttio Lot surface features iu UCDs is much less hau the 51 LOUr observing period.," All of these limits are based on the assumptions (1) that the limiting cases of the AMES-dusty and AMES-cond atmospheres of Allard et (2001) are appropriate, (2) that 2M1145 was not observed during an abnormal phase of atmospheric or magnetic inactivity, and (3) that the timescale for the evolution of surface features in UCDs is much less than the 54 hour observing period."
 The case or the latter was argued bv DJM., The case for the latter was argued by BJM.
 Clearly. the preseut worς can be improved upon iu a nuniber of wavs. nof least through having a more stable iustruiieut to avoid slit losses.," Clearly, the present work can be improved upon in a number of ways, not least through having a more stable instrument to avoid slit losses."
" A wider slit may nonetheless be required to achieve pure relative spectroplotometry in order to acconiunodate brightuess changes due to seciug flucuations,", A wider slit may nonetheless be required to achieve pure relative spectrophotometry in order to accommodate brightness changes due to seeing fluctuations.
 This iav require observing iu the optical where the sky background is reduced aud there are still sienificaut features (see and section 3.5))., This may require observing in the optical where the sky background is reduced and there are still significant features (see and section \ref{optical}) ).
 While L chwarts are wich fainter here refscdl)). this may still be a amore effective nethod if the data quality is limited ]wosvstcluatic errors and not photon noise.," While L dwarfs are much fainter here \\ref{sed1}) ), this may still be a more effective method if the data quality is limited by systematic errors and not photon noise."
 Alteruatively. J aud I& band has a senificaut signature. and has the advantage flat ΑΝ. reference stars can be usecL to calibrate sky. variations (sco Bailer-Jones Lamu 2002)).," Alternatively, J and K band has a significant signature, and has the advantage that many reference stars can be used to calibrate sky variations (see Bailer-Jones Lamm \cite{bjl}) )."
 Ultimately. Doppler nuaging of the brightest. most rapidly rotatiae UCDs provides the possibility to monitor surface features in a Πο cürect laaaer.," Ultimately, Doppler imaging of the brightest, most rapidly rotating UCDs provides the possibility to monitor surface features in a more direct manner."
 Nonu-seriodic photometric variability iu late M and L dwiufs has been indicated wea few observing progranus to date., Non-periodic photometric variability in late M and L dwarfs has been indicated by a few observing programs to date.
" In this paper. I have presented the results of a prejan to spectrophionietrically iuouitor the known variadle L1.5 field cdwart 251115 iu the near infrared n)). in an attempt to identify the Case of its variaημίν,"," In this paper, I have presented the results of a program to spectrophometrically monitor the known variable L1.5 field dwarf 2M1145 in the near infrared ), in an attempt to identify the cause of its variability."
 Primary caudidaes are the teuporal evolution of cool iiaenueticalls-iuduced spots and. dust-relatec photospheric clouds., Primary candidates are the temporal evolution of cool magnetically-induced spots and dust-related photospheric clouds.
 Usiug he spectral nodels of Alliux et ((2001)). I have clenonstrated he photometric signatures of these two typcs of variability in various bands across the near mfrared spectrum.," Using the spectral models of Allard et \cite{allard01}) ), I have demonstrated the photometric signatures of these two types of variability in various bands across the near infrared spectrum."
 For the evolution of either a clear. dust-precipiated cloud against a dusty atmosphere or a dustv ¢oud against a dust-cleare atinosphere. there is au auicorrelated variability in the J aud K bands.," For the evolution of either a clear, dust-precipitated cloud against a dusty atmosphere or a dusty cloud against a dust-cleared atmosphere, there is an anticorrelated variability in the J and K bands."
 At au effecive temperature of TIT. the peak-to-peak amplitucles are 0.07 and 0.03 magnitudes respectively for a cloud covering of the surface. both decreasing by a factor of about three at TIS. aud the J baud signature increasing by a factor of over five at τς]. A cool spot. on the other haud. shows a correlated JAN signature at all temperatures.," At an effective temperature of K, the peak-to-peak amplitudes are 0.07 and 0.03 magnitudes respectively for a cloud covering of the surface, both decreasing by a factor of about three at K, and the J band signature increasing by a factor of over five at K. A cool spot, on the other hand, shows a correlated J,K signature at all temperatures."
" The observational data. which cover several hours ou three consecutive nights. slic""v no evidence for variability in any of four inclividual οςdour indices."," The observational data, which cover several hours on three consecutive nights, show no evidence for variability in any of four individual colour indices."
 However. there is evidence for m the coours which cannot be attributed to moise or artifacts of the observi18o ucthod.," However, there is evidence for in the colours which cannot be attributed to noise or artifacts of the observing method."
 These changes are I1uore consisten with t1C xeseuce of a cdust-cleared ¢loud ou a dusty atinosphere han a cool dusty spot on πιch an atinosphliere., These changes are more consistent with the presence of a dust-cleared cloud on a dusty atmosphere than a cool dusty spot on such an atmosphere.
 T ron-detectious iu the iudividual bands permit upper iuits to be place on the size of anv clots Or spots., The non-detections in the individual bands permit upper limits to be placed on the size of any clouds or spots.
 Adopting a dusty atinospLCLe for 2NIT11ID wi han effective eniperature of IK. the caa restrict clear clouds cover less than “the μιrface. or a KI coo spot (or spots) fo cover less tiu of the surface.," Adopting a dusty atmosphere for 2M1145 with an effective temperature of K, the data restrict clear clouds to cover less than of the surface, or a K cooler spot (or spots) to cover less than of the surface."
 If 2M1115 is as cool as IKIN. anc stil has a clus atmosphere. then cCar οouds are restrictcc to cover less than of the surface.," If 2M1145 is as cool as K and still has a dusty atmosphere, then clear clouds are restricted to cover less than of the surface."
 However. if a cust-cleared model is riore appropriate at IK. the upper nuit on cloud coverage is more like 2054..," However, if a dust-cleared model is more appropriate at K, the upper limit on cloud coverage is more like ."
Iu general. it seems plausible that some fraction of the total feedback euergv will be processed into each one of these forms. aud we consider models which inclide a conibination of these processes ou an equal footing with models that iuclude ouly one.,"In general, it seems plausible that some fraction of the total feedback energy will be processed into each one of these forms, and we consider models which include a combination of these processes on an equal footing with models that include only one."
" The hot gascous courponeut in dark matter halos is asstuned initially to lave a density profile. pot). given by the o-model. ie. at radius r d the halo (whose dark matter deusity profile is assmmed to have the NEW profile. Navarro.Freaks&White1996. 19973). where py is the density at the centre of the halo. à, is the radius of the “core” aud ds a parameter which sets the slope of the profile on scales larger than r7."," The hot gaseous component in dark matter halos is assumed initially to have a density profile, $\rho_{\rm g}(r)$, given by the $\beta$ -model, ie, at radius $r$ in the halo (whose dark matter density profile is assumed to have the NFW profile, \citealt{nfw96,nfw97}) ), where $\rho_0$ is the density at the centre of the halo, $r_{\rm c}$ is the radius of the “core” and $\beta$ is a parameter which sets the slope of the profile on scales larger than $r_{\rm c}$."
 Departing from the prescription of Coleetal.(2000). we adopt a gas density profile in the abseuce of energy injection with fixed ο=Ομων (and — 2/3) in all halos.," Departing from the prescription of \citet{cole00}, we adopt a gas density profile in the absence of energy injection with fixed $r_{\rm c}=0.07 r_{\rm vir}$ (and $\beta=2/3$ ) in all halos."
 This provides a reasonable match to egas- smiulatious of nou-radiative eas in clusters (e.g. Eke.Navarro&Frenk 1998)) and to the observed N-rav profiles of relaxed clusters (e... Allenetal. 906011)., This provides a reasonable match to gas-dynamic simulations of non-radiative gas in clusters (e.g. \citealt{eke98}) ) and to the observed X-ray profiles of relaxed clusters (e.g. \citealt{allen01}) ).
 The normalization of the profile is deterimuned by the otal diffuse eas mass remaining in the halo. aud the cluperature of the eas d8 sot assunüug lvdrostatic equilibrium.," The normalization of the profile is determined by the total diffuse gas mass remaining in the halo, and the temperature of the gas is set assuming hydrostatic equilibrium."
 As ai boundary condition. we set the cluperature at the virial radius equal to the virial cluperature (eqn.," As a boundary condition, we set the temperature at the virial radius equal to the virial temperature (eqn."
 Ll in Coleetal. 2000))., 4.1 in \citealt{cole00}) ).
" This ""default? xofile is modified if the diffuse eas gaius further energy (""excess enerev) as a result of enerev injection (process 2 in Section 2.1).", This “default” profile is modified if the diffuse gas gains further energy (“excess energy”) as a result of energy injection (process 2 in Section 2.1).
" We use the prescription described iu Boweretal.(2001).. in which the excess energv first causes the slope of the eas profile to decrease down to a inimuuni value of A44,=0.2. after which it increases the )undary temperature of the eas halo."," We use the prescription described in \citet{bower01}, in which the excess energy first causes the slope of the gas profile to decrease down to a minimum value of $\beta_{\rm min}= 0.2$, after which it increases the boundary temperature of the gas halo."
 The effect of the excess cherey is to decrease the central density of the gas. chethenine its cooling time.," The effect of the excess energy is to decrease the central density of the gas, lengthening its cooling time."
 Mass is conserved by pushing some of the diffuse gas outside the halo: however. this gas can be recaptured as the total halo mass (and thus the eravitational binding euergv) increases.," Mass is conserved by pushing some of the diffuse gas outside the halo; however, this gas can be recaptured as the total halo mass (and thus the gravitational binding energy) increases."
 We assimune that the excess energy is conserved diving mergers between halos. although the results are uot qualitatively affected by a sinall dilution or amplification of energy diving halo luergers.," We assume that the excess energy is conserved during mergers between halos, although the results are not qualitatively affected by a small dilution or amplification of energy during halo mergers."
" We define the effective cooling time at radius r. £7,407). as the maxiunn true cooling time G.c. that defined by Coleetal.20003) occuring at smaller radii. plus the frec-fall time from r to the halo ceutre."," We define the effective cooling time at radius $r$ , $t_{\rm
cool}^\prime(r)$, as the maximum true cooling time (i.e. that defined by \citealt{cole00}) ) occurring at smaller radii, plus the free-fall time from $r$ to the halo centre."
 This eusures that dtfdr>0. so the cooling radius is always a inoothly increasing fuuction of radius.," This ensures that $\d t_{\rm
cool}^\prime/\d r > 0$, so the cooling radius is always a smoothly increasing function of radius."
 Experiunecuts with cliffercut approaches show that the results we present here are not sensitive to the details of this prescription., Experiments with different approaches show that the results we present here are not sensitive to the details of this prescription.
 Conduction iu the ionized gas can transport energv mto theinner regious of the halo. effectively increasing the cooling time of the eas there.," Conduction in the ionized gas can transport energy into theinner regions of the halo, effectively increasing the cooling time of the gas there."
 The rate at which cucrey is deposited into the shell between radi kr aud r|dr is eiven by: where the conductivity. αι may depend on radius through its temperature dependence.," The rate at which energy is deposited into the shell between radii $r$ and $r+\d r$ is given by: where the conductivity, $\kappa$, may depend on radius through its temperature dependence."
 We approximate X as where «is the Spitzer conductivity (Spitzer1962).. aud Qeond IS a parameter that absorbs the dependence on the shape of the temperature profile as well as any difference between the actual conductivity aud the Spitzer rate.," We approximate $\Sigma$ as where $\kappa_{\rm s}$ is the Spitzer conductivity \citep{spitzer}, and $\alpha_{\rm cond}$ is a parameter that absorbs the dependence on the shape of the temperature profile as well as any difference between the actual conductivity and the Spitzer rate."
" For a power-law temperature profile. Txr. aud conductivity of the Spitzer form. KXT, OcondFo|70/2) where fy, is the ratio of the conductivity to the Spitzer value."," For a power-law temperature profile, $T\propto r^a$, and conductivity of the Spitzer form, $\kappa_{\rm s}\propto T^{5/2}$, $\alpha_{\rm cond}=f_{\rm sp} a
(1+7a/2)$ where $f_{\rm sp}$ is the ratio of the conductivity to the Spitzer value."
" Adopting a temperature profile with &=0.1 as sugeested by recent ταν observations (Voietetal.2002) CIVOS Ocgnd0.96£.,."," Adopting a temperature profile with $a=0.4$ as suggested by recent X-ray observations \citep{voight} gives $\alpha_{\rm
cond}=0.96 f_{\rm sp}$."
 Adopting a linear teiiperature eradieut gives oca=LOfay , Adopting a linear temperature gradient gives $\alpha_{\rm cond}=4.5 f_{\rm sp}$.
The heating rate due to conduction is subtracted from the radiative cooling rate to give a net cooling rate for the gas., The heating rate due to conduction is subtracted from the radiative cooling rate to give a net cooling rate for the gas.
 This net cooling rate isused to compute the cooling tine., This net cooling rate isused to compute the cooling time.
 Conduction causes the cooling radius to become smaller than in the standard model., Conduction causes the cooling radius to become smaller than in the standard model.
 The result Is a suppression of cooling im hot halos. aud the mass at which this effect becomes inportaut is determined by the ραΛΟΓΟΣ ocu.," The result is a suppression of cooling in hot halos, and the mass at which this effect becomes important is determined by the parameter $\alpha_{\rm cond}$."
 While we ciplov the detailed model of galaxy mereiug developed by Bensonetal.(2002)... we choose to use a muuch simpler model of the effects of reiouization than used in that paper. in order to incorporate thoi easily iuto our caleulation of the galaxy huniuositv function.," While we employ the detailed model of galaxy merging developed by \citet{benson02}, we choose to use a much simpler model of the effects of reionization than used in that paper, in order to incorporate them easily into our calculation of the galaxy luminosity function."
 We simply assune that galaxy formation is completely suppressed by relonizationin dark matter halos with circular velocities below Vig after redshift tego..., We simply assume that galaxy formation is completely suppressed by reionizationin dark matter halos with circular velocities below $V_{\rm reion}$ after redshift $z_{\rm reion}$.
" Uuless otherwise stated. we adopt Va44,=50lnis5 and ναι=6."," Unless otherwise stated, we adopt $V_{\rm reion}=50\kms$ and $z_{\rm reion}=6$."
 With this choice. this simple model matches the results of the full caleulatiouof Bensonetal.(2002) quite well.," With this choice, this simple model matches the results of the full calculationof \citet{benson02} quite well."
" Throughout this paper. we use the same parameter values adoptedby Deusonetal. (2002).. with the exception of a larger barvon fraction corresponding to Q),= 0.015. consistent with constraints from Dig Bane uucleosvutliesis (O'\earaetal. 2001)."," Throughout this paper, we use the same parameter values adoptedby \citet{benson02}, , with the exception of a larger baryon fraction corresponding to $\Omega_{\rm b}=0.045$ , consistent with constraints from Big Bang nucleosynthesis \citep{omeara}. ."
". We assume a ACDM universe with mean inatter densitv Oy= 0.3. cosmological coustaut toii O4= (0,7. Hubble Wy= τα ! "," We assume a $\Lambda$ CDM universe with mean matter density $\Omega_0=0.3$ , cosmological constant term $\Omega_\Lambda=0.7$ , Hubble $H_0=70$ km $^{-1}$ "
where The flexion measurement errors then result in an additive colored Gaussian noise whose power is a function of 1/7.,where The flexion measurement errors then result in an additive colored Gaussian noise whose power is a function of $1/k$.
 The right panel of the Fig., The right panel of the Fig.
" 1. shows a convergence map recovered [rom simulated flexion measurements F;,,."," \ref{convergence} shows a convergence map recovered from simulated flexion measurements ${\mathcal{F}_{i,n}}$."
 As expected. the convergence map appears contaninatecd bv a colored Gaussian noise whose power is inversely proportional to the Irequencey. fk.," As expected, the convergence map appears contaminated by a colored Gaussian noise whose power is inversely proportional to the frequency $k$."
 No cluster is detected despite the fact that the map has been smoothed by a Gaussian In this paper. we compare the ability of flexion and shear to reconstruct the dark matter distribution.," No cluster is detected despite the fact that the map has been smoothed by a Gaussian In this paper, we compare the ability of flexion and shear to reconstruct the dark matter distribution."
 Since flexion. dominates on small scales. we calculate here the scale at which flexion becomes dominant over shear.," Since flexion dominates on small scales, we calculate here the scale at which flexion becomes dominant over shear."
 To do this. in Fig. 2..," To do this, in Fig. \ref{crossing},"
 we compare the noise power spectrum on convergence map obtaimed from shear measurements (solid black line) to the one obtained from flexion measurements (solid red. line)., we compare the noise power spectrum on convergence map obtained from shear measurements (solid black line) to the one obtained from flexion measurements (solid red line).
 The two solid lines have been obtained with realistic values of dispersion for space-based observations., The two solid lines have been obtained with realistic values of dispersion for space-based observations.
 The crossing of these {wo curves gives us the seale al which flexion becomes dominant over shear., The crossing of these two curves gives us the scale at which flexion becomes dominant over shear.
 As expected. the shear noise power spectrum is flat and the flexion noise power spectrum is inversely proportional to the frequency fh.," As expected, the shear noise power spectrum is flat and the flexion noise power spectrum is inversely proportional to the frequency $k$."
" The relations 14 ancl 160 can be used to derive the analviie shear and [lexion noise power spectrum: If the average number of galaxies in a pixel (V,) is kept the same between shear and flexion measurements. the intersection of the (wo noise power spectra A7 is given by ht=e"," The relations \ref{eq:shear3} and \ref{eq:flex5} can be used to derive the analytic shear and flexion noise power spectrum: If the average number of galaxies in a pixel $N_g$ ) is kept the same between shear and flexion measurements, the intersection of the two noise power spectra $k^T$ is given by $k^T=\frac{\sigma_\epsilon^\mathcal{F}}{\sigma_\epsilon^\gamma}$."
 If the standard values are used for shear and [flexion dispersion (0;=0.3 and o?=0.04 Lope=0.1333 1) this corresponds to a scale of 7.5 arcsec.," If the standard values are used for shear and flexion dispersion $\sigma^\gamma_\epsilon = 0.3$ and $\sigma^\mathcal{F}_\epsilon = 0.04$ $^{-1}$, $k^T=0.1333$ $^{-1}$ ) this corresponds to a scale of 7.5 arcsec."
 Thus. the flexion becomes interestinge for scales smaller than 7.5 arcsec.," Thus, the flexion becomes interesting for scales smaller than 7.5 arcsec."
 To have at least a mean of 1 egalaxy per pixel (with a pixel size of 7.5 aresec). (he galaxy. density. should be significantly larger," To have at least a mean of 1 galaxy per pixel (with a pixel size of 7.5 arcsec), the galaxy density should be significantly larger"
Using helioseismology. it has recently been shown that the solar internal differential rotation is in a non-Tavlor-Proudiman state (seereviewbyThompsonetal.2003).. meaning the iso-rolalion surfaces arenof parallel to the axis.,"Using helioseismology, it has recently been shown that the solar internal differential rotation is in a non-Taylor-Proudman state \citep[see review by][]{2003ARA&A..41..599T}, meaning the iso-rotation surfaces are parallel to the axis."
 Dased on solar observations. it is known that Ca II-Ix [hixes can be a signature of stellar chromospheric activity. and such chromospheric signatures are in correlation. wilh magnetic activitv.," Based on solar observations, it is known that Ca H-K fluxes can be a signature of stellar chromospheric activity, and such chromospheric signatures are in correlation with magnetic activity."
 Wilson(1968.1978) and Daliunasetal.(1995). discuss a class of stars that shows a periodic variation in Ca I-Ex fluxes. which suggests that thev have a magnetic evele similar (o our sun.," \cite{1968ApJ...153..221W,1978ApJ...226..379W} and \cite{1995ApJ...438..269B} discuss a class of stars that shows a periodic variation in Ca H-K fluxes, which suggests that they have a magnetic cycle similar to our sun."
 It is natural to conjecture that such magnetic activity is maintained bv dynamo action., It is natural to conjecture that such magnetic activity is maintained by dynamo action.
 Various studies have been conducted to investigate the relationship between stellar angular velocity QO) and its Ilatitudinal difference AO i.e. AQxOF. where the suggested range of 7 is 0<n«I (Donalmeetal.1996:Reiners&Schmittetal. 2005)..," Various studies have been conducted to investigate the relationship between stellar angular velocity $\Omega_0$ and its latitudinal difference $\Delta\Omega$ i.e., $\Delta\Omega\propto\Omega_0^n$ , where the suggested range of $n$ is $0 <n < 1$ \citep{1996ApJ...466..384D,2003A&A...398..647R,2005MNRAS.357L...1B}."
 This means that the angular velocitv difference AQ increases and the relative dillerence AQ/Ωμ decreases with increases in the stellar rotation rate Qo. In (his paper. we investigate differential rotation in rapidly rotating stars using a mean field framework.," This means that the angular velocity difference $\Delta\Omega$ increases and the relative difference $\Delta\Omega/\Omega_0$ decreases with increases in the stellar rotation rate $\Omega_0$ In this paper, we investigate differential rotation in rapidly rotating stars using a mean field framework."
 Our study is based on the work of Rempel(2005b).. in which he suggests (he importance of the role of the subadiabatic laver below (he convection zone in order to maintain a non-Tavlor-Proudinan state in (he Sun.," Our study is based on the work of \cite{2005ApJ...622.1320R}, in which he suggests the importance of the role of the subadiabatic layer below the convection zone in order to maintain a non-Taylor-Proudman state in the Sun."
 The aim of this paper is (o use a mean fieldl model to analvze firstly the dependence of the morphology. of differential rotation on stellar angular velocity. aud secondly (he physical process which determines the observable angular velocity difference AQ.," The aim of this paper is to use a mean field model to analyze firstly the dependence of the morphology of differential rotation on stellar angular velocity, and secondly the physical process which determines the observable angular velocity difference $\Delta \Omega$."
 According to our knowledge. this is the first work which svstematicallv discusses the application of Rempels (2005b) solar model to stars.," According to our knowledge, this is the first work which systematically discusses the application of Rempel's (2005b) solar model to stars."
 Other research adopts another approach to the use of mean field models for the analysis of differential rotation in rapidlv-rotating stars (Ixitchatinov&huüdiger1995:Sx 2001)..," Other research adopts another approach to the use of mean field models for the analysis of differential rotation in rapidly-rotating stars \citep{1995A&A...299..446K,2001A&A...366..668K}."
 Ii these studies. the non-Tavlor-Proudiman state is sustained by anisotropy. ofturbulent thermal conduction.," In these studies, the non-Taylor-Proudman state is sustained by anisotropy ofturbulent thermal conduction."
 This anisotropy is generated by the effects of stellar rotation, This anisotropy is generated by the effects of stellar rotation
"where & is Boltzmann's constant. and jim, is the mean mass per particle.","where $k$ is Boltzmann's constant, and $\mu m_p$ is the mean mass per particle."
 The only free parameter in this expression is M. which can be estimated from the density distribution inferred from the X-ray image of the cluster core.," The only free parameter in this expression is $\dot{M}$, which can be estimated from the density distribution inferred from the X-ray image of the cluster core."
 The resulting spectrum can be calculated using a collisional equilibrium spectral synthesis model with an assumed set of elemental abundances. and normalizing the contribution in each temperature interval as given in Equation (1).," The resulting spectrum can be calculated using a collisional equilibrium spectral synthesis model with an assumed set of elemental abundances, and normalizing the contribution in each temperature interval as given in Equation (1)."
 To a good approximation. a cluster spectrum should consist of two components: 1) the cooling-flow spectrum. as described above. and£o 2) an isothermal spectrum evaluated at the temperature of the background cluster gas.," To a good approximation, a cluster spectrum should consist of two components: 1) the cooling-flow spectrum, as described above, and 2) an isothermal spectrum evaluated at the temperature of the background cluster gas."
 Data acquired by the Reflection Grating Spectrometer (RGS) on XMM-Newton enable this robust spectral prediction. to be quantitatively. tested. for the first time., Data acquired by the Reflection Grating Spectrometer (RGS) on XMM-Newton enable this robust spectral prediction to be quantitatively tested for the first time.
 Surprisingly. the observed spectra reveal a remarkable systematic deficit of emission at the lowest temperatures. as compared to the multi- model (Petersonetal.2001.. Tamuraetal. 2001a.. Kaastraetal. 2001.. Tamuraetal. 2001b.. Xuetal. 2002.. Sakelliouetal. 2002)).," Surprisingly, the observed spectra reveal a remarkable systematic deficit of emission at the lowest temperatures, as compared to the multi-phase model \citealt{peterson1}, \citealt{tamura}, \citealt{kaastra}, \citealt{tamura2}, \citealt{xu}, \citealt{sakelliou}) )."
 This result has been confirmed through medium resolution spatially-resolved spectroscopy using the XMM-Newton European Photon Imaging Cameras (EPIC) and Chandra ACIS observations. where spectral fits have yielded significantly smaller Ms than expected (Davidetal.2001.. Bohringeretal. 2001.. Molendi&Pizzolato 2001.. Allen.&Fabian 2001.. Ettorietal. 2002.. Johnstoneet 2002).," This result has been confirmed through medium resolution spatially-resolved spectroscopy using the XMM-Newton European Photon Imaging Cameras (EPIC) and Chandra ACIS observations, where spectral fits have yielded significantly smaller $\dot{M}$ 's than expected \citealt{david}, \citealt{boehringer}, \citealt{molendi}, \citealt{schmidt}, \citealt{ettori}, \citealt{johnstone2}) )."
 We refer to the observed deficit of the predicted soft X-ray emission as thep, We refer to the observed deficit of the predicted soft X-ray emission as the.
"roblem, As we discuss in this paper. the soft X-ray cooling-flow problem may or may not be related to the classic cooling-flow problem."," As we discuss in this paper, the soft X-ray cooling-flow problem may or may not be related to the classic cooling-flow problem."
 Here we present a systematic study of I4 clusters with the RGS to quantify in detail the soft X-ray cooling-flow problem., Here we present a systematic study of 14 clusters with the RGS to quantify in detail the soft X-ray cooling-flow problem.
 We present four basic results: 1) We find no evidence for X-ray absorption by cold material. which had been inferred from lower spectral and angular resolution data (Whiteetal.199]).," We present four basic results: 1) We find no evidence for X-ray absorption by cold material, which had been inferred from lower spectral and angular resolution data \citep{white}."
. 2) We find a severe lack of emission from lower temperature tons expected in the standard cooling-flow model., 2) We find a severe lack of emission from lower temperature ions expected in the standard cooling-flow model.
" 3) We demonstrate the ubiquity of significant plasma just below the ambient gas temperature. 7). down to 1,/2 in roughly the predicted amount."," 3) We demonstrate the ubiquity of significant plasma just below the ambient gas temperature, $T_0$, down to $T_0/2$ in roughly the predicted amount."
 This last result is the most perplexing and is difficult to reconeile with. proposed explanations for the cooling-flow problems., This last result is the most perplexing and is difficult to reconcile with proposed explanations for the cooling-flow problems.
 4) We offer an empirical parameterization of the temperature distribution which is consistent with the entire sample., 4) We offer an empirical parameterization of the temperature distribution which is consistent with the entire sample.
 The paper is organized as follows., The paper is organized as follows.
 In $22 we discuss the expected spectrum of the isobarie radiative multi-phase model and various associated temperature diagnostics., In 2 we discuss the expected spectrum of the isobaric radiative multi-phase model and various associated temperature diagnostics.
 In $33. we discuss the spectral capabilities of the RGS for sources of moderate extent., In 3 we discuss the spectral capabilities of the RGS for sources of moderate extent.
 In $44 we deseribe our analysis methods and present the high resolution spectra., In 4 we describe our analysis methods and present the high resolution spectra.
 In $55 we discuss several qualitative aspects of the spectra., In 5 we discuss several qualitative aspects of the spectra.
 In $66 we describe the model used to set cooling luminosity limits., In 6 we describe the model used to set cooling luminosity limits.
 In $77 we present the results., In 7 we present the results.
 In $88 we discuss the results with respect to potential modifications of the cooling-flow scenario., In 8 we discuss the results with respect to potential modifications of the cooling-flow scenario.
 It has been argued that the intracluster medium (ICM) should remain in collisional ionization equilibrium. even as it cools.," It has been argued that the intracluster medium (ICM) should remain in collisional ionization equilibrium, even as it cools."
 Both the recombination time scale and electron equilibriation time scale through Coulomb collisions. are much less than the cooling time seale. evaluated at characteristic ray temperatures and densities in the ICM (Edgar&Chevalier1986.. Hicks&Canizares200100).," Both the recombination time scale and electron equilibriation time scale through Coulomb collisions, are much less than the cooling time scale, evaluated at characteristic X-ray temperatures and densities in the ICM \citealt{edgar}, \citealt{hicks}) )."
 At high temperatures. the X-ray spectrum is produced through bremsstrahlung and line emission from abundant elemeits.," At high temperatures, the X-ray spectrum is produced through bremsstrahlung and line emission from abundant elements."
 The spectra are dominated by lines from hydrogen-like ad helium-like tons. and iron L shell emission.," The spectra are dominated by lines from hydrogen-like and helium-like ions, and iron L shell emission."
 In principle. the temperature distribution can be determined by three different nethods: I) through the shape of the exponential cut-off of the bremsstrahlung spectrum. 2) the ratios of hydrogen-like to helium-like lines. and 3) through the distribution of line emission from iron. L-shell ions.," In principle, the temperature distribution can be determined by three different methods: 1) through the shape of the exponential cut-off of the bremsstrahlung spectrum, 2) the ratios of hydrogen-like to helium-like lines, and 3) through the distribution of line emission from iron L-shell ions."
 However. the bremsstrahlung spectrum constrains only the highest temperatures present in the spectrum. and the ratio of hydrogen-like to helium-like lines ts relatively unconstraming since both charge states are present over a very broad range of temperatures.," However, the bremsstrahlung spectrum constrains only the highest temperatures present in the spectrum, and the ratio of hydrogen-like to helium-like lines is relatively unconstraining since both charge states are present over a very broad range of temperatures."
 Therefore. Fe L emission is the most useful diagnostic. and provides the primary method for determining the temperature distribution presented in this paper.," Therefore, Fe L emission is the most useful diagnostic, and provides the primary method for determining the temperature distribution presented in this paper."
 The isobaric multi-phase model yields a unique spectral signature given an isothermal outer cluster temperature and a set of assumed abundances., The isobaric multi-phase model yields a unique spectral signature given an isothermal outer cluster temperature and a set of assumed abundances.
 This is shown in Figure | for a maximum temperature of 8 keV and for 1/3 solar abundances., This is shown in Figure 1 for a maximum temperature of 8 keV and for 1/3 solar abundances.
 In Figure 2. we divide the temperature distribution below 6 keV into four bands.," In Figure 2, we divide the temperature distribution below 6 keV into four bands."
 The curves are the spectra produced by emission from the multi-phase model in bins of 3 to 6. 1.5 to 3. 0.75 to 1.5. and 0.375 to 0.75 keV. Important line blends are compiled in Table 1.," The curves are the spectra produced by emission from the multi-phase model in bins of 3 to 6, 1.5 to 3, 0.75 to 1.5, and 0.375 to 0.75 keV. Important line blends are compiled in Table 1."
 Several important diagnostics and aspects of the model can be noted., Several important diagnostics and aspects of the model can be noted.
 The first is that line emission from ions between Fe XXIV and Fe XVII provide tight constraints on the temperature distribution., The first is that line emission from ions between Fe XXIV and Fe XVII provide tight constraints on the temperature distribution.
 There 1s roughly comparable emission in the emission line blends from each Fe L ion., There is roughly comparable emission in the emission line blends from each Fe L ion.
 Also note that Fe XVII line emission ts predicted to be three times as strong as Fe XVIII, Also note that Fe XVII line emission is predicted to be three times as strong as Fe XVIII.
 ο VIII and other hydrogen-like ions are produced at a range of temperatures. and thus do not provide strong constraints on the temperature distribution.," O VIII and other hydrogen-like ions are produced at a range of temperatures, and thus do not provide strong constraints on the temperature distribution."
 The overall normalization is proportional to the mass deposition rate. and the spectrum should be a strict superposition of all the individual temperatures up to the ambient temperature.," The overall normalization is proportional to the mass deposition rate, and the spectrum should be a strict superposition of all the individual temperatures up to the ambient temperature."
 In order to test aspects of this model in detail. the Fe L spectrum needs to be resolved for a spatially-extended object.," In order to test aspects of this model in detail, the Fe L spectrum needs to be resolved for a spatially-extended object."
 This could not be accomplished with previous instrumentation: however. the launch of the XMM-Newton RGS experiment now makes it possible.," This could not be accomplished with previous instrumentation; however, the launch of the XMM-Newton RGS experiment now makes it possible."
 For a full description of the RGS experment see denHerderetal.(2001)., For a full description of the RGS experment see \cite{denherder}.
. The two RGS spectrometers have 160 em? of combined collecting area and with a spectral resolution given roughly by: for an extended source larger than 10 areseconds., The two RGS spectrometers have 160 $\mbox{cm}^2$ of combined collecting area and with a spectral resolution given roughly by: for an extended source larger than 10 arcseconds.
 The wavelength band extends from 5 to 38 A. which samples Si K shell transitions to C. K transitions.," The wavelength band extends from 5 to 38 ${\mbox{\AA}}$, which samples Si K shell transitions to C K transitions."
 The field of view is effectively 5 areminutes by | degree. which is large enough to capture the entire cooling-flow region.," The field of view is effectively 5 arcminutes by 1 degree, which is large enough to capture the entire cooling-flow region."
 The former is set by the width of the CCD array in the cross-dispersion direction. and the latter is set by self-vignetting of the telescope shells.," The former is set by the width of the CCD array in the cross-dispersion direction, and the latter is set by self-vignetting of the telescope shells."
 For the cooling-flow clusters. data selection cuts are tailored to include," For the cooling-flow clusters, data selection cuts are tailored to include"
on relatively short timescales (months-years).,on relatively short timescales (months-years).
 Relativistic transient lines could be a cause for the difference in variability of the iron line region between multiple observations especially if they are strongly variable., Relativistic transient lines could be a cause for the difference in variability of the iron line region between multiple observations especially if they are strongly variable.
 Mrk 766(2) was found by Turner et al. (, Mrk 766(2) was found by Turner et al. (
2004) to have such a spectral component between 3.6 - 5.75 keV but this bin shows no excess rms variability.,2004) to have such a spectral component between 5.6 - 5.75 keV but this bin shows no excess rms variability.
 NGC 3516(2) was also found to have narrow transient iron lines at 5.6 KeV and 6.2 keV (Turner et al., NGC 3516(2) was also found to have narrow transient iron lines at 5.6 keV and 6.2 keV (Turner et al.
 2002) and these bins are are variable in the rms spectra though it is likely that this is mainly due to the variable broad iron line., 2002) and these bins are are variable in the rms spectra though it is likely that this is mainly due to the variable broad iron line.
 Furthermore. the lines are narrower than the 0.4 keV energy bins of the rms spectra so the variability of the transient line might be washed out.," Furthermore, the lines are narrower than the 0.4 keV energy bins of the rms spectra so the variability of the transient line might be washed out."
 Longer observations with high signal-to-noise ratio are needed to investigate the variability of transient iron lines., Longer observations with high signal-to-noise ratio are needed to investigate the variability of transient iron lines.
 There are alternatives to. gravitational light bending in explaining a flat rms spectrum., There are alternatives to gravitational light bending in explaining a flat rms spectrum.
 The reduced variability of the line could also be due to the inner disk being absent or suppressed so the ine is unable to form close to the black hole where it would be more variable., The reduced variability of the line could also be due to the inner disk being absent or suppressed so the line is unable to form close to the black hole where it would be more variable.
 This could be because the inner disk is highly ionized. radiatively inefficient or truncated.," This could be because the inner disk is highly ionized, radiatively inefficient or truncated."
 The bulk of the observed line flux would then arise from the outer region of the disk., The bulk of the observed line flux would then arise from the outer region of the disk.
 However. many ofthe observations with flat rms spectra have very broad iron ines. with a profile indicating that the emission is concentrated close to the black hole. so non-variability of the line should not ον]ο due to the inner disk emission being missing.," However, many of the observations with flat rms spectra have very broad iron lines, with a profile indicating that the emission is concentrated close to the black hole, so non-variability of the line should not be due to the inner disk emission being missing."
 The origin of the narrower variability excesses. typically seen o]ueward of the line core. are also difficult to explain.," The origin of the narrower variability excesses, typically seen blueward of the line core, are also difficult to explain."
" When they are seen there is generally no variability at the red wing. so if the blue emission is the high energy wing of the diskline. it is hard o understand why the red part is not also variable: the red wing ( ""the line should originate closer to the black hole where strong gravitational redshifting effects are present."," When they are seen there is generally no variability at the red wing, so if the blue emission is the high energy wing of the diskline, it is hard to understand why the red part is not also variable: the red wing of the line should originate closer to the black hole where strong gravitational redshifting effects are present."
 An alternative is that ye blue variability is due to absorption or emission by ionized iron close to the central source. but not too close so as to be broadened.," An alternative is that the blue variability is due to absorption or emission by ionized iron close to the central source, but not too close so as to be broadened."
 This has been suggested for Mrk 766(3) by Miller et al (2006)., This has been suggested for Mrk 766(3) by Miller et al (2006).
 They split the iron K band into high and low ionisation bands and find only the former is variable., They split the iron K band into high and low ionisation bands and find only the former is variable.
 This agrees with the rms spectrum showing an excess in the 6.6-7.0 keV bin that is as large as the time-averaged component., This agrees with the rms spectrum showing an excess in the 6.6-7.0 keV bin that is as large as the time-averaged component.
 Mrk 766(2) does not show such a strong excess at a similar energy and Pounds et al (2003) do not find any complexity around 7keV in the spectrum., Mrk 766(2) does not show such a strong excess at a similar energy and Pounds et al (2003) do not find any complexity around 7keV in the spectrum.
" In addition there are also observations with clear evidence for relatively narrow. ionized lines in their time-averaged spectra (e.g. NGC 3783. NGC 4593) which show no evidence for variability, indicating a more distant origin for these lines."," In addition there are also observations with clear evidence for relatively narrow, ionized lines in their time-averaged spectra (e.g. NGC 3783, NGC 4593) which show no evidence for variability, indicating a more distant origin for these lines."
 Perhaps most puzzling of all are cases like NGC S5506¢1) tor NGC 5548(2)) which show strong blue tor red) wing variability without any obvious associated features in the time averaged spectrum., Perhaps most puzzling of all are cases like NGC 5506(1) (or NGC 5548(2)) which show strong blue (or red) wing variability without any obvious associated features in the time averaged spectrum.
 Even if absorption or emission by photoionised gases does contribute. simple models would find it difficult to explain the varying strengths of the excesses.," Even if absorption or emission by photoionised gases does contribute, simple models would find it difficult to explain the varying strengths of the excesses."
 NGC 4151(2) is unusual in that it shows a narrow excess redward of the line core., NGC 4151(2) is unusual in that it shows a narrow excess redward of the line core.
" The evidence for a red wing the time-averaged spectrum during this observation is not compelling. but if the red variability excess is real it may be indicative of emission from a relatively isolated “hot spot"" from a narrow range of radii in the relativistic region of the disk."," The evidence for a red wing the time-averaged spectrum during this observation is not compelling, but if the red variability excess is real it may be indicative of emission from a relatively isolated ""hot spot"" from a narrow range of radii in the relativistic region of the disk."
 It is interesting to compare our work to that of De Marco et al. (, It is interesting to compare our work to that of De Marco et al. (
2009: DMO9). who have studied the iron Ka line variability of a sample of nearby radio-quiet AGN by searching for excess emission in the time-energy plane.,"2009; DM09), who have studied the iron $\alpha$ line variability of a sample of nearby radio-quiet AGN by searching for excess emission in the time-energy plane."
" Twelve of their observations overlap with rms spectra from our work: MCG-5-23-16(2). NGC 3516(2). NGC 3783. NGC 405101). Mrk 766(2). NGC 4593. MCG-6-30-15¢1.2). NGC 55482), NGC 75140. Ark 564 and NGC 7469(2)."," Twelve of their observations overlap with rms spectra from our work: MCG-5-23-16(2), NGC 3516(2), NGC 3783, NGC 4051(1), Mrk 766(2), NGC 4593, MCG-6-30-15(1,2), NGC 5548(2), NGC 7314(1), Ark 564 and NGC 7469(2)."
 Their method differs from ours in that it is optimised to search for narrow. transient features in the excess maps. whereas ours will characterize any variability. or lack thereof.," Their method differs from ours in that it is optimised to search for narrow, transient features in the excess maps, whereas ours will characterize any variability, or lack thereof."
 Comparing the overlapping sample. eight out of the twelve showed no significant variability across the iron K band due to narrow transient lines in the excess maps.," Comparing the overlapping sample, eight out of the twelve showed no significant variability across the iron K band due to narrow transient lines in the excess maps."
 This includes MCG-5-23-16(2). NGC 351603 and NGC 405161} in which we found variability across the iron line region that must then be due to a variable broad line. rather than narrow transient lines.," This includes MCG-5-23-16(2), NGC 3516(2) and NGC 4051(1) in which we found variability across the iron line region that must then be due to a variable broad line, rather than narrow transient lines."
 DMO09 found significant variability in four observations for which we also have rms spectra., DM09 found significant variability in four observations for which we also have rms spectra.
 NGC 731461) showed significant variations in the 5.4-6.]1. keV band., NGC 7314(1) showed significant variations in the 5.4-6.1 keV band.
 Our rms spectrum of this observation was difficult to classify although there is a signiticant variability excess in the 5.4-5.8 keV bin that could be a redshifted Fe Ka component as found in a 2002 Chandra observation CYaqoob et al., Our rms spectrum of this observation was difficult to classify although there is a significant variability excess in the 5.4-5.8 keV bin that could be a redshifted Fe $\alpha$ component as found in a 2002 Chandra observation (Yaqoob et al.
 2003)., 2003).
 Both observations of MCG-6-30-15 were found to exhibit Fe K band variability in the excess maps of DMO9., Both observations of MCG-6-30-15 were found to exhibit Fe K band variability in the excess maps of DM09.
 This agrees broadly with our result for MCG-6-30-15¢1). although we note that the variability aeross the iron line region in this observation is unlikely to be due solely to narrow line components as the excess extends down to 4.6 keV and it overlaps well with the time-averaged line profile.," This agrees broadly with our result for MCG-6-30-15(1), although we note that the variability across the iron line region in this observation is unlikely to be due solely to narrow line components as the excess extends down to 4.6 keV and it overlaps well with the time-averaged line profile."
 The rms spectrum of the second MCG-6-30-15 observation shows narrow variability to the blue side., The rms spectrum of the second MCG-6-30-15 observation shows narrow variability to the blue side.
 Comparison with the excess maps is more difficult in this case. as DMO09 considered each of the three rrevolutions separately. whereas we have combined them.," Comparison with the excess maps is more difficult in this case, as DM09 considered each of the three revolutions separately, whereas we have combined them."
 However. we note that at least one of these does show blue variability. consistent with our result.," However, we note that at least one of these does show blue variability, consistent with our result."
 Finally NGC 3783(2) has a variability excess in the rms spectrum that corresponds to the weak broad and redshifted iron line., Finally NGC 3783(2) has a variability excess in the rms spectrum that corresponds to the weak broad and redshifted iron line.
 DMO09 also tind significant variability between 5.4-6.1 keV in this source. in agreement with the rms spectrum.," DM09 also find significant variability between 5.4-6.1 keV in this source, in agreement with the rms spectrum."
 Overall our results confirm the work of DMO9 in the sense that both studies show that. contrary to some previous reports. variations in the iron Ka ," Overall our results confirm the work of DM09 in the sense that both studies show that, contrary to some previous reports, variations in the iron $\alpha$ "
as where @ is the spin-weight of the field X.,as where $\sigma$ is the spin-weight of the field $\chi$.
 As the names imply. the spin-raising and lowering operators increase or decrease the spin-weight of a field by one unit.," As the names imply, the spin-raising and lowering operators increase or decrease the spin-weight of a field by one unit."
 See. e.g... ? [or some details concerning these operators and the spherical harmonics used to expand a field of arbitrary spin-weight.," See, e.g., \citet{Goldberg:1966uu} for some details concerning these operators and the spherical harmonics used to expand a field of arbitrary spin-weight."
" Using fyb!""=2B?PEP. the Maxwell action in terms of the Debye potentials is Lt is evident from the action that the physical degrees of [reedonm are carried. by the helicitv-one. representations QU. and OV."," Using $F_{\mu\nu} F^{\mu\nu} = 2 \mathbf{B}^2 - 2 \mathbf{E}^2$, the Maxwell action in terms of the Debye potentials is It is evident from the action that the physical degrees of freedom are carried by the helicity-one representations $\eth U$ and $\eth V$."
 This is in agreement with the well-known properties of a photon., This is in agreement with the well-known properties of a photon.
 Furthermore. it is not surprising that the two helicity degrees of freedom decouple in a spherically symmetric background.," Furthermore, it is not surprising that the two helicity degrees of freedom decouple in a spherically symmetric background."
 The equations of motion and the same for V., The equations of motion and the same for $V$.
 Since C and V have. identical properties. we will from now on only focus on C.," Since $U$ and $V$ have identical properties, we will from now on only focus on $U$."
 All results apply to V in exactly the same way., All results apply to $V$ in exactly the same way.
 In the above expression. we have introduced. the spatial Laplace operator A for a scalar field. defined as The operator LJ in (6)) is precisely. the dAlembertian for a Lorentz scalar.," In the above expression, we have introduced the spatial Laplace operator $\Delta$ for a scalar field defined as The operator $\Box$ in \ref{eq:eom}) ) is precisely the d'Alembertian for a Lorentz scalar."
 However. since C is not itself a Lorentz scalar. it also acquires an elfective mass mir which is precisely the one that corresponds to a conformal coupling lo curvature.," However, since $U$ is not itself a Lorentz scalar, it also acquires an effective mass $m_{\mathrm{eff}}$ which is precisely the one that corresponds to a conformal coupling to curvature."
 In the case of spatial [atness. a complete set. of eigenfunctions to A is given by where we have chosen the spherical Bessel functions Jj; which are regular at the origin.," In the case of spatial flatness, a complete set of eigenfunctions to $\Delta$ is given by where we have chosen the spherical Bessel functions $j_\ell$ which are regular at the origin."
 The eigenvalue equation on the flat three-dimensional surface is and the eigenfunctions are normalized as In the case of an open geometry where s=sinhr. the cigenfunetions are the harmonics on the three-hyperboloid.," The eigenvalue equation on the flat three-dimensional surface is and the eigenfunctions are normalized as In the case of an open geometry where $s = \sinh r$, the eigenfunctions are the harmonics on the three-hyperboloid."
" The eigenvalue equation reads where the eigenfunctions Y, which are regular at are given by sec. e.g. ὃν,"," The eigenvalue equation reads where the eigenfunctions $Y_{p \ell m}$ which are regular at $r = 0$ are given by see, e.g., \citet{Sasaki:1994yt}."
 Phe normalization is again such that this time on the three-hyperboloid., The normalization is again such that this time on the three-hyperboloid.
 The Debye potentials are conformally coupled to gravity. meaning that any. conformal factor can be absorbed into a redetinition of the fields.," The Debye potentials are conformally coupled to gravity, meaning that any conformal factor can be absorbed into a redefinition of the fields."
 En particular this means that the equation of motion (6)) is invariant under a time-dependent conformal rescaling ο⋅we(uy (with the corresponding redefinition of time) and a simple rescaling of the Ποιά as (⇁nUm(1i., In particular this means that the equation of motion \ref{eq:eom}) ) is invariant under a time-dependent conformal rescaling $g_{\mu\nu} \rightarrow \omega^2(t) g_{\mu\nu}$ (with the corresponding redefinition of time) and a simple rescaling of the field as $U \rightarrow \omega^{-1}(t) U$.
 A special situation is given in the open universe models cause the three-hyperboloids used in the foliation do not usually represent. global Cauchy surfaces., A special situation is given in the open universe models because the three-hyperboloids used in the foliation do not usually represent global Cauchy surfaces.
 Therefore. the adlure of modes to be normalizable on the hyperboloids docs not necessarily imply that they should be excluded from the ohvsical spectrum.," Therefore, the failure of modes to be normalizable on the hyperboloids does not necessarily imply that they should be excluded from the physical spectrum."
 What really matters is the question of whether or not a mode is normalizable on a Cauchy surface., What really matters is the question of whether or not a mode is normalizable on a Cauchy surface.
 ]t is well-known that in certain scalar field models this leacks o the occurrence of modes with discrete imaginary. values ofp in the spectrum which are usually referred to àsmodes., It is well-known that in certain scalar field models this leads to the occurrence of modes with discrete imaginary values of $p$ in the spectrum which are usually referred to as.
 1n the case of the magnetic field. it was found in ? see also references therein to earlier work. citetBarrow:2008)p.Vsagas:2005nn that supercurvature modes. if they exist. give rise to superadiabatie evolution aud can therefore help to solve the problem of magnetogenesis.," In the case of the magnetic field, it was found in \citet{Barrow:2011ic} – see also references therein to earlier work, \\citet{Barrow:2008jp,Tsagas:2005nn} – that supercurvature modes, if they exist, give rise to superadiabatic evolution and can therefore help to solve the problem of magnetogenesis."
 It is therefore of relevance whether or not the electromagnetic field can support supereurvature modes., It is therefore of relevance whether or not the electromagnetic field can support supercurvature modes.
 With the formalism of the Debye potentials. we can now easily address this question.," With the formalism of the Debye potentials, we can now easily address this question."
 In order to study. whether such supercurvature moces are relevant. we have to check if there are some modes with imaginary p which are normalizable on a Cauchy surface.," In order to study whether such supercurvature modes are relevant, we have to check if there are some modes with imaginary $p$ which are normalizable on a Cauchy surface."
 As mentioned. before. such a surface can usually not be found. within the patch covered by the open coordinate," As mentioned before, such a surface can usually not be found within the patch covered by the open coordinate"
packages.,packages.
 The reduction. process. included: overscan. bias. clark. [at and badpixel corrections.," The reduction process included overscan, bias, dark, flat and badpixel corrections."
 The primary goal of the CCD observations was to extend the time base for period-change studies. therefore. aperture photometry for variables with long enough historical record was obtained. in comparison with the mean ensemble magnitudes: of 23 standard stars from the [ist of Stetson(2000).," The primary goal of the CCD observations was to extend the time base for period-change studies, therefore, aperture photometry for variables with long enough historical record was obtained, in comparison with the mean ensemble magnitudes of 23 standard stars from the list of \citet{st00}."
.. The measurements were transformed to the standard JohnsonCousins Vc system., The measurements were transformed to the standard Johnson--Cousins $VI_C$ system.
 The tvpical error of the data of single variables is ~0.02 mag., The typical error of the data of single variables is $\sim0.02$ mag.
 The photometry provides the most densely covered. ~100 days long. accurate observations for these objects. but it is seriously biased. in. amplitude and mean magnitude for crowded stars.," The photometry provides the most densely covered $\sim100$ days long, accurate observations for these objects, but it is seriously biased in amplitude and mean magnitude for crowded stars."
 The above listed. photographic and CCD time series of the variables are available from the electronic edition of this article., The above listed photographic and CCD time series of the variables are available from the electronic edition of this article.
 Table 3. gives a sample of the data regarding its form and content., Table \ref{data} gives a sample of the data regarding its form and content.
 The method used. for the analysis of period changes is the same as emploved by Juresiketal.(2001) and Szeidlοἱal.(2011) to study the period changes of RR Lyrac stars in o Con and ALS. respectively.," The method used for the analysis of period changes is the same as employed by \citet{ocen} and \citet{m5} to study the period changes of RR Lyrae stars in $\omega$ Cen and M5, respectively."
 The original lisht-curve data (time series) were used for the analysis., The original light-curve data (time series) were used for the analysis.
 Photographic. CCD D (9). and CCD V data if," Photographic, CCD $B$ $g$ ), and CCD $V$ data if"
roughly their respective orbit speeds.,roughly their respective orbit speeds.
 Three distinct. mechanisms may be involved in releasing gas from the gravitational potential well., Three distinct mechanisms may be involved in releasing gas from the gravitational potential well.
 First. the disruption and ejection of the outer-parts of circinstellar. disks during the final dvnamic encounter leading the binary formation.," First, the disruption and ejection of the outer-parts of circumstellar disks during the final dynamic encounter leading the binary formation."
 Second. recoil of the pre-existing circunme-cluster envelope following stellar ejection.," Second, recoil of the pre-existing circum-cluster envelope following stellar ejection."
 Finally. the release of stored magnetic stress.," Finally, the release of stored magnetic stress."
 Each process is a consequence of (he removal of gravitational attraction on a lime-scale given by the relevant crossing time., Each process is a consequence of the removal of gravitational attraction on a time-scale given by the relevant crossing time.
 Disk disruption occurs within a lime-scale lassP/V<< d vear ab r= 1 AU for V~ 100 kms !. the Kepler speed around a LO M. star.," Disk disruption occurs within a time-scale $t_{cross} \approx r / V << $ 1 year at $r$ = 1 AU for $V \sim$ 100 km $^{-1}$, the Kepler speed around a 10 $_{\odot}$ star."
 Abr = LOO AU. stellar ejection with a mean speed of V = 20 km ! implies that the envelope gas would be unbound several decades.," At $r$ = 100 AU, stellar ejection with a mean speed of $V$ = 20 km $^{-1}$ implies that the envelope gas would be unbound several decades."
 In both cases. (he expulsion velocity. would be comparable to the Kepler speed prior to ejection. or about 20 km ! for an envelope initially orbiting 40 M. of stars at r = 100 AU to over 100 km ! for parts of disks ejected from within 1 AU of à 10 AL. star.," In both cases, the expulsion velocity would be comparable to the Kepler speed prior to ejection, or about 20 km $^{-1}$ for an envelope initially orbiting 40 $_{\odot}$ of stars at $r$ = 100 AU to over 100 km $^{-1}$ for parts of disks ejected from within 1 AU of a 10 $_{\odot}$ star."
 These mechanisms are explored in more detail below., These mechanisms are explored in more detail below.
 OAC spawned at least 20 to over 40 ML. of stars., OMC1 spawned at least 20 to over 40 $_{\odot}$ of stars.
" Assuming a typical star-formation efficiency of to typical of massive cluster forming chimps. the OMCH proto-cluster clump must have initially contained at least Mu,  100 M. of gas."," Assuming a typical star-formation efficiency of to typical of massive cluster forming clumps, the OMC1 proto-cluster clump must have initially contained at least $M_{clump}$ $\sim$ 100 $_{\odot}$ of gas."
 As a fiducial example. consider a clump with an ‘isothermal’ density distribution p(r)=po(r/ry)? Lov radius r less than the clump outer radius 2.," As a fiducial example, consider a clump with an `isothermal' density distribution $\rho (r) = \rho_0 (r/r_0)^{-2}$ for radius r less than the clump outer radius $R$ ."
" A champ with mass M,""=LOO M. inside H — 0.1 pe implies mean orbital velocity. (which is independent of r). Vzm(ορpj)?=2.1 kms | where pyz5.0x10! e& * would be the density al ry = 1 cem if the power-law distribution were extended (to (his radius."," A clump with mass $M_{clump} = 100$ $_{\odot}$ inside $R$ = 0.1 pc implies mean orbital velocity (which is independent of $r$ ), $V \approx (GM_{clump}/R)^{1/2} = (4 \pi G \rho_0)^{1/2} = 2.1$ km $^{-1}$ where $\rho_0 \approx 5.0 \times 10^{16}$ g $^{-3}$ would be the density at $r_0$ = 1 cm if the power-law distribution were extended to this radius."
" Ii this example. the density at à — 5.000 AU [rom the center is (1/2)&2x105  and the crossing-lime is fuu,~R/V«5x10! vears."," In this example, the density at $r$ = 5,000 AU from the center is $n(H_2) \approx 2 \times 10^6$ $^{-3}$ and the crossing-time is $t_{cross} \sim R / V < 5 \times 10^4$ years."
 The most massive protostellar objects are likely to either form in the center where (he densitv and pressure are the greatest. or if they form away [rom the center. (o rapidly migrate to the center of the potential due (o orbit decay (Zinnecker 1982: Donnell οἱ al.," The most massive protostellar objects are likely to either form in the center where the density and pressure are the greatest, or if they form away from the center, to rapidly migrate to the center of the potential due to orbit decay (Zinnecker 1982; Bonnell et al."
 2001)., 2001).
 Orbits can decay due to Dondi-Hoyle (BIL) accretion as they move though clump gas and dvenamic-Iriction caused by the gravitational pull of the wake produced by converging streamlines behind the YSO., Orbits can decay due to Bondi-Hoyle (BH) accretion as they move though clump gas and dynamic-friction caused by the gravitational pull of the wake produced by converging streamlines behind the YSO.
 The DII accretion rate is roughly MjC2J*? where Cy is the effective sound speed (which includes the effects of turbulent motion and magnetic support) in the gas (usually <1 kms ο).," The BH accretion rate is roughly $
\dot M_{BH} = \pi G^2 M_{YSO}^2 \rho(r) / (V_*^2 + C_s^2)^{3/2}
$ where $C_s$ is the effective sound speed (which includes the effects of turbulent motion and magnetic support) in the gas (usually $< 1$ km $^{-1}$ )."
 A star moving with a speed V—2.1 km 5.000 AU from the center of theabove gas distribution would accrete at a rate May29x107 M. for a l M. YSO and May2x10/7 M. fora 5 M. ," A star moving with a speed $V = 2.1$ km $^{-1}$ 5,000 AU from the center of theabove gas distribution would accrete at a rate $\dot M_{BH} \approx 9 \times 10^{-7}$ $_{\odot}$ $^{-1}$ for a 1 $_{\odot}$ YSO and $\dot M_{BH} \approx 2 \times 10^{-5}$ $_{\odot}$ $^{-1}$ for a 5 $_{\odot}$ "
Based on the results of our analysis. we feel (hat any determination of the space density ol white cdwarls in the halo or even in the thick disk based solely on a kinematic analvsis is basically flawecl. ancl one must combine such analyses with a precise determination of total stellar ages. which implies in turn that distance estimates nist also be obtaimed 2005).,"Based on the results of our analysis, we feel that any determination of the space density of white dwarfs in the halo or even in the thick disk based solely on a kinematic analysis is basically flawed, and one must combine such analyses with a precise determination of total stellar ages, which implies in turn that distance estimates must also be obtained \citep[see, e.g.][]{pauli05}."
. Similarly. analyses based on reduced proper motion diagrams are likely {ο reveal more of (hese voung high-velocity white dwarls rather than the long sought old white cwarf halo population.," Similarly, analyses based on reduced proper motion diagrams are likely to reveal more of these young high-velocity white dwarfs rather than the long sought old white dwarf halo population."
 We thank D. R. Oppenheimer for providing us with his spectroscopic observations., We thank B. R. Oppenheimer for providing us with his spectroscopic observations.
 This work was supported in part bv the NSERC Canada and by the Fund FORNT. (Québbec)., This work was supported in part by the NSERC Canada and by the Fund FQRNT (Québbec).
 MTR. received partial support from Fondecevt (1010404) and FONDAP (15010003)., MTR received partial support from Fondecyt (1010404) and FONDAP (15010003).
 Support for this work was also provided to MII by NASA through Hubble Fellowship grant. awarded bt the Space Telescope Science Institute. which is operated bv the Association of Universities for Research in Astvonomy. Inc.. for NASA. under contract NAS 5-26555.," Support for this work was also provided to MH by NASA through Hubble Fellowship grant HST-HF-01139.01A awarded bt the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555."
 The United Ixingdom Infrared Telescope is operated by the Joint Astronomy Centre on behalf of the U.Ix. Particle Physies ancl Astronomy Research Council., The United Kingdom Infrared Telescope is operated by the Joint Astronomy Centre on behalf of the U.K. Particle Physics and Astronomy Research Council.
eiven the lighteurves currently available (Vaughan Uttley 2005).,given the lightcurves currently available (Vaughan Uttley 2005).
 Thus the single significant AGN QDPO. seen in the Narrow Line Sevlert | galaxy. RE 1034|396. (Cierlifsski et al.," Thus the single significant AGN QPO, seen in the Narrow Line Seyfert 1 galaxy RE J1034+396 (Gierlińsski et al."
 2008: confirmed. using even more robust. techniques by Vaughan 2010) is most likely associated. instead. with the higher frequeney QPOs seen. in DIIDs., 2008; confirmed using even more robust techniques by Vaughan 2010) is most likely associated instead with the higher frequency QPOs seen in BHBs.
 These are associated only with very specific spectral states. (very high/intermediate). so are much less. frequently observed (e.g. Remillard et al.," These are associated only with very specific spectral states (very high/intermediate), so are much less frequently observed (e.g. Remillard et al."
 2002: Remillard McClintock 2006)., 2002; Remillard McClintock 2006).
 While there is currently no reliable mass estimate for this AGN (though recent work is converging on 1-4. I0M.. e.g. Bian Lluang 2010: Jin et al., While there is currently no reliable mass estimate for this AGN (though recent work is converging on $\sim$ $\times$ $^{6}$ $_{\odot}$: e.g. Bian Huang 2010; Jin et al.
 in press). the best match in terms of mass scaled. frequency. (and Ενω). appears to be the 67 Lz QPO seen in the probably super-Eddington BUBGRS 1915|105 (ος. Middleton Done 2010: Morgan. Remillard Greiner LOOT: Veda. Yamaoka. Remillare 2009: Cui 1999: Belloni οἱ al.," in press), the best match in terms of mass scaled frequency (and $_{Edd}$ ) appears to be the 67 Hz QPO seen in the probably super-Eddington BHB GRS 1915+105 (e.g. Middleton Done 2010; Morgan, Remillard Greiner 1997; Ueda, Yamaoka, Remillard 2009; Cui 1999; Belloni et al."
 2006)., 2006).
 The much longer timescale of the AGN ΟΡΟ presents an opportunity to examine this feature on the level of individual evcles., The much longer timescale of the AGN QPO presents an opportunity to examine this feature on the level of individual cycles.
 This contrasts with the high. frequency BUB QPOs which can currently only be studied. in à statistical sense by averaging the behaviour over very many eveles. due to the small number of photons detected: per evele.," This contrasts with the high frequency BHB QPOs which can currently only be studied in a statistical sense by averaging the behaviour over very many cycles, due to the small number of photons detected per cycle."
 Thus the AGN QPO may give more stringent tests of the origin of this oscillation than the corresponding DIL data., Thus the AGN QPO may give more stringent tests of the origin of this oscillation than the corresponding BHB data.
 3oth the spectrum ane variability of these data can be well modellecl using (wo components. namely an extremely large πο X-ray excess (SX) which remains relatively constant on the timescale of the QPO. together with a weak power law tail to higher energies which is strongly modulated on the QPO timescale (Middleton et al.," Both the spectrum and variability of these data can be well modelled using two components, namely an extremely large soft X-ray excess (SX) which remains relatively constant on the timescale of the QPO, together with a weak power law tail to higher energies which is strongly modulated on the QPO timescale (Middleton et al."
 2009)., 2009).
 Models of the complete spectral energy. distribution (SED) of this object show that the SX is the dominant component of the total bolometric Luminosity of ~5. 10 τας s4 (Puchnarewicez et al., Models of the complete spectral energy distribution (SED) of this object show that the SX is the dominant component of the total bolometric luminosity of $\sim$ $\times$ $^{44}$ erg $^{-1}$ (Puchnarewicz et al.
 1998: Wane Netzer 2003: C'asebeer ct al., 1998; Wang Netzer 2003; Casebeer et al.
 2006: Middleton ct al., 2006; Middleton et al.
 2007: Jin et al., 2007; Jin et al.
" in press). giving LfLewe ~ d-l for the black hole mass range of 10""M. discussed: above."," in press), giving $_{Edd}$ $\sim$ 4-1 for the black hole mass range of $\times$ $^6$ $_{\odot}$ discussed above."
 Thus the equivalent sources in terms of veh Edcinegton fraction are GRS 1915|105 (see above). which has been acercting at or above Eclelington for more han 20 vears (e.g. Truss Done 2006) and probably also the Ultra-Iuminous N-rav Sources (ULXs: see Fabbiano 1989: Miller Colbert 2004: Roberts 2007).," Thus the equivalent sources in terms of high Eddington fraction are GRS 1915+105 (see above), which has been accreting at or above Eddington for more than 20 years (e.g. Truss Done 2006) and probably also the Ultra-luminous X-ray Sources (ULXs; see Fabbiano 1989; Miller Colbert 2004; Roberts 2007)."
" Both of these can show an SED dominated w a similarly distorted ""hot disc component to that which", Both of these can show an SED dominated by a similarly distorted `hot disc' component to that which
ümespan.,timespan.
" The combination of Fig.s 1,,2 and 3 suggests that the instability is evolving in two phases."," The combination of Fig.s \ref{B_vergleich}, , \ref{9_slices_5} and \ref{9_slices_100} suggests that the instability is evolving in two phases."
 In the first phase light particles are accelerated and in the second phase the heavier parücles are also involved in the instability., In the first phase light particles are accelerated and in the second phase the heavier particles are also involved in the instability.
" For mass-ratios of 715/m,x20.0 the instabilities and therefore particle acceleration of the two species cannot be separated.", For mass-ratios of $m_p/m_e \lesssim 20.0$ the instabilities and therefore particle acceleration of the two species cannot be separated.
 There are (wo possible reasons for this: Either the coupling of the two species is still strong enough to co-accelerate the heavier parucles or the time scales of the two instabiliies are still matching rather well., There are two possible reasons for this: Either the coupling of the two species is still strong enough to co-accelerate the heavier particles or the time scales of the two instabilities are still matching rather well.
 A strong argument for the second option 15 the fact that the instability time scale for the heavy species increases less than linear with the mass-ratio for a certain size of the computational domain., A strong argument for the second option is the fact that the instability time scale for the heavy species increases less than linear with the mass-ratio for a certain size of the computational domain.
 Considering only mass-ratos ny/n.>20.0 the instabilities are clearly separated which is also apparent in the double-hump structure in the energy-diagrams of Fig., Considering only mass-ratios $m_p/m_e > 20.0$ the instabilities are clearly separated which is also apparent in the double-hump structure in the energy-diagrams of Fig.
 1 and in Fig., \ref{B_vergleich} and in Fig.
 3 illustrating the development of the flux tubes in two phases., \ref{9_slices_100} illustrating the development of the flux tubes in two phases.
 In the larger simulation (twice the size in the perpendicular directions) it takes even longer for the proton instability to develop because the flux tubes have more space to develop and therefore it takes longer for them to merge until only two are left., In the larger simulation (twice the size in the perpendicular directions) it takes even longer for the proton instability to develop because the flux tubes have more space to develop and therefore it takes longer for them to merge until only two are left.
 This is also the reason for the slightly diflerent slopes in the two simulations with mass-ratio 100., This is also the reason for the slightly different slopes in the two simulations with mass-ratio 100.
" The maxima and minima of the magnetic energy occur around the point in lime, when the current density in the direction of streaming averaged over the whole computational domain changes its sign."," The maxima and minima of the magnetic energy occur around the point in time, when the current density in the direction of streaming averaged over the whole computational domain changes its sign."
 When (in the larger simulation) the proton instability kicks in (at around 65c) the flux tubes are not yet fully merged down to two and therefore the proton instability does not grow with the same rate as in the smaller simulation.," When (in the larger simulation) the proton instability kicks in (at around $65\, \omega_p^{-1}$ ) the flux tubes are not yet fully merged down to two and therefore the proton instability does not grow with the same rate as in the smaller simulation."
 The resulting flux tubes around the maximum of the second instability still resemble the two flux tube regime as seen in the smaller simulations., The resulting flux tubes around the maximum of the second instability still resemble the two flux tube regime as seen in the smaller simulations.
" As described in chapter 3. all simulations were initialized with thermal particle distributions (width of the thermal distribution 0.1c and 0.1c-περιο)! for electrons and protons, respecüvely) which are then boosted with a Lorentz factor of y=10 in either direction."," As described in chapter \ref{setup} all simulations were initialized with thermal particle distributions (width of the thermal distribution $0.1 c$ and $0.1 c \cdot (m_p/m_e)^{-1}$ for electrons and protons, respectively) which are then boosted with a Lorentz factor of $\gamma = 10$ in either direction."
" While some parücles gain a lot of energy during the simulation in total, the shape of the particle distribution is also changing."," While some particles gain a lot of energy during the simulation in total, the shape of the particle distribution is also changing."
" To analyze and quantify the change of the particle energy distributions we utilize two distinct types of graphs: (1) a two-dimensional plot in the lab frame relating the absolute value of the momentum parallel (vj/cΥ/ with vq=|v-)) ) and (v,⋅ ywith ⋅v, ⊔↥⋯⊓≳⊔⊔≼↔⊺⊔↕∟↜⋯∣∙↿⋝∟↜↥∖⊽∖⇁≳∐∟∖−≳∐Qitντ)1) avd,to the initial ⋅⋅⋅streaming direction,⋅ perpendicularrespectively⋅ and⋅ (2) an↕∣⊔∟↜∐≳∐∖↿⋅⊏⊾⋅↰∕∖↖⇁↕↿⋅∶∖↿⋅−↿⋅−⋅≓∪ one-dimensional plot of the distribution of the parucles speed in the lab frame."," To analyze and quantify the change of the particle energy distributions we utilize two distinct types of graphs: (1) a two-dimensional plot in the lab frame relating the absolute value of the momentum parallel $v_{||}/c \cdot \gamma$ with $v_{||} = \left| v_z \right|$ ) and perpendicular $v_{\perp}/c \cdot \gamma$ with $v_{\perp} = (v_x^2 + v_y^2)^{\frac{1}{2} }$ ) to the initial streaming direction, respectively and (2) an one-dimensional plot of the distribution of the particles speed in the lab frame."
 In Fig., In Fig.
 4. we show the tme evolution of the electron and positron distribution (all electrons and positrons in both streams are plotted in a 2D histogram for the mass-ratios 5 (upper panels) and 100 (lower panels)., \ref{2Dhist_elec_pos} we show the time evolution of the electron and positron distribution (all electrons and positrons in both streams are plotted in a 2D histogram for the mass-ratios 5 (upper panels) and 100 (lower panels).
 The same conjuncture is illustrated in Fig., The same conjuncture is illustrated in Fig.
" 5 for the protons, but the axis are diflerent."," \ref{2Dhist_prot} for the protons, but the axis are different."
" As expected, the parücle distribution in the early stage of the simulation (before the onset of the first instability hump) is centered at the iniual Lorentz boost y=10 with a thermal width of 0.1c for the electrons/positrons and 0.1c-npm,| for the protons."," As expected, the particle distribution in the early stage of the simulation (before the onset of the first instability hump) is centered at the initial Lorentz boost $\gamma = 10$ with a thermal width of $0.1 c$ for the electrons/positrons and $0.1 c \cdot (m_p/m_e)^{-1}$ for the protons."
Several electrons have already been accelerated,Several electrons have already been accelerated
A thorough understanding of star formation is medicated on a knowledge of the physical conditions hat surround the process at cach of its stages.,A thorough understanding of star formation is predicated on a knowledge of the physical conditions that surround the process at each of its stages.
 The determination of these properties has proven to i a challenging eudeavour for the carly plases of star formation because molecular lydrogen (IL;)). the wimary coustitucut of developing stars. cannot be ueasured directly.," The determination of these properties has proven to be a challenging endeavour for the early phases of star formation because molecular hydrogen ), the primary constituent of developing stars, cannot be measured directly."
 Iustead. the excitation properties of race niolecules iuust be used to infer the conditions within the ereater cloud.," Instead, the excitation properties of trace molecules must be used to infer the conditions within the greater cloud."
 Thus. all measurements of density iu molecular clouds are subject to the biascs of the chosen tracer.," Thus, all measurements of density in molecular clouds are subject to the biases of the chosen tracer."
 Even more problematic are viria density estimates determined via inferred) mass anc source size due to the uncertainties inherent iu both quantities., Even more problematic are virial density estimates determined via inferred mass and source size due to the uncertainties inherent in both 	quantities.
 Formaldehyde is uniquely scusitive to spatial density aud au ideal probe of molecular clou cores for a nunuboer of reasons that are discussed in reth2coProhe.., Formaldehyde ) is uniquely sensitive to spatial density and an ideal probe of molecular cloud cores for a number of reasons that are discussed in \\ref{h2coProbe}.
 The (5. GIIZ) and (11 CIIz) ARdoublet transitions of have previously been used to measure densitv iu a munber of studies of galactic (c.c. Henkeletal.1980:Dickel&Coss1987:Turnerctal.1989:Zvlkact 1992)) aud extragalactic (Mauguiaetal.2008) star formation regious.," The (5 GHz) and (14 GHz) -doublet transitions of have previously been used to measure density in a number of studies of galactic (e.g. \citealt{Hen80,DG87,Tur89,Zyl92}) ) and extragalactic \citep{Man08} star formation regions."
 Our work ocniplovs an essentially identical strategv using the (29 (1) aud CIS. GIIZ) transitions. which offer a few advantages over their lower excitation counterparts.," Our work employs an essentially identical strategy using the (29 GHz) and (48 GHz) transitions, which offer a few advantages over their lower excitation counterparts."
" Principally. the higher frequencies translate to smaller sinele-dish beam sizes (GBT beam sizes of 26"" and 16” for the J=3 aud J=| trausitions. respectively as opposed to 153” and 51” for J=1 and J=2 -doublets)."," Principally, the higher frequencies translate to smaller single-dish beam sizes (GBT beam sizes of $\arcsec$ and $\arcsec$ for the $J=3$ and $J=4$ transitions, respectively, as opposed to $\arcsec$ and $\arcsec$ for $J=1$ and $J=2$ -doublets)."
 The added spatial resolution is important when considering that stars formi in spatially compact regions within molecular clouds aud thus laree beau sizes nav serve to dilute the areas of interest., The added spatial resolution is important when considering that stars form in spatially compact regions within molecular clouds and thus large beam sizes may serve to dilute the areas of interest.
 This point is compounded by the fact that the lower excitation ransitions are bv their nature often more sensitive to spatial densitics aud kinetic temperatures lower than hose of interest in studies of star-formuue molecular cores., This point is compounded by the fact that the lower excitation transitions are by their nature often more sensitive to spatial densities and kinetic temperatures lower than those of interest in studies of star-forming molecular cores.
 The aud transitions are therefore nore efficient probes of spatial deusity iu this context., The and transitions are therefore more efficient probes of spatial density in this context.
 Few studies of the J—3 and 1 A--doublet trausitious wave heen made due partially to their relatively low intensitics aud lieh ceutimeteravave frequencies., Few studies of the $J=3$ and 4 -doublet transitions have been made due partially to their relatively low intensities and high centimeter-wave frequencies.
 The J=3 transition was first detected by Welch(1970) in absorption toward the radio coutimmiun source Ser D2., The $J=3$ transition was first detected by \citet{Wel70} in absorption toward the radio continuum source Sgr B2.
 Subsequent experiments were conducted toward the xiehtest source in our sample. Orioun-kL (Wilsonetal.1980:Myers&BustonBastienet 1985). after which exploration of this transition seeniuelv ος».," Subsequent experiments were conducted toward the brightest source in our sample, Orion-KL \citep{Wil80,MB80,Bas85}, after which exploration of this transition seemingly ends."
 We could find no previous measurements of the transition. whose vet higher frequency aud. weaker intensity pose additional observational difficulties.," We could find no previous measurements of the transition, whose yet higher frequency and weaker intensity pose additional observational difficulties."
 Since our abilitv to detect these transitions aud the reliability of deriving deusitv measurements from them was uncertain. a sample of very bright and well-studied objects were chosen (Table 1)).," Since our ability to detect these transitions and the reliability of deriving density measurements from them was uncertain, a sample of very bright and well-studied objects were chosen (Table \ref{tab:sources}) )."
 Strong detections of both transitions proved to be fairly casy to obtain. requiring an average of l7 min of iuteeration time. aud the resulting spatial density iieasireimenuts ceur?)) are cousisteut with what is known for molecular— cores.," Strong detections of both transitions proved to be fairly easy to obtain, requiring an average of 17 min of integration time, and the resulting spatial density measurements ) are consistent with what is known for molecular cores."
 These results are encouragiug for the prospect of future experiments., These results are encouraging for the prospect of future experiments.
 Details on the utility of as a high-density probe are elven i O reth2coProhe.., Details on the utility of as a high-density probe are given in \\ref{h2coProbe}. .
 Iu our observational and calibration procedures are presented with a brief discussion of the, In \\ref{observations} our observational and calibration procedures are presented with a brief discussion of the
intrinsically faint (e.g. SNI987A. Αλί~ 5.5) or because of high host extinction.,"intrinsically faint (e.g. SN1987A, $\Delta M_{570}\sim 5.5$ ) or because of high host extinction."
 SNLS obviously cannot say anything about mtrinsically faint supernovae., SNLS obviously cannot say anything about intrinsically faint supernovae.
 However. by adopting a host galaxy extinction model. we can estimate the number of SNee that have intrinsic luminosities within our range of sensitivity but that are lost because of high host extinction.," However, by adopting a host galaxy extinction model, we can estimate the number of SNcc that have intrinsic luminosities within our range of sensitivity but that are lost because of high host extinction."
 We have used the results of Hatanoetal.(1998) who give (their table | and Figure |) the distribution of Ag as a function of host inclination angle., We have used the results of \citet{dustext} who give (their table 1 and Figure 1) the distribution of $A_B$ as a function of host inclination angle.
 This can be converted to a distribution of absorption at 570nm and convoluted with the pre-absorption distribution of Ms;o.," This can be converted to a distribution of absorption at $570\,{\rm nm}$ and convoluted with the pre-absorption distribution of $M_{570}$."
 For example. if we model the intrinsic SNee magnitude distribution shown as the dashed line in Fig. 12..," For example, if we model the intrinsic SNcc magnitude distribution shown as the dashed line in Fig. \ref{absratefig},"
 then the SNec host extinction model of Hatanoetal.(1998) predicts the distribution shown by the solid line in the Figure., then the SNcc host extinction model of \citet{dustext} predicts the distribution shown by the solid line in the Figure.
 With this model. of SNee have ήτο> 4.5.," With this model, of SNcc have $\Delta M_{570}>4.5$ ."
 Our estimated total rate is then increased to Αι=1.63x107yrig Mper?., Our estimated total rate is then increased to $R_{cc}=1.63 \times10^{-4}\yr^{-1}(h_{70}^{-1}\Mpc)^{-3}$ .
 In our model. most of the events with Αλάτι>4.5 are highly absorbed so our estimate should be considered a lower limit on the SNee rate that ignores supernovae that are intrinsically fainter than AMs;o=4.5.," In our model, most of the events with $\Delta M_{570}>4.5$ are highly absorbed so our estimate should be considered a lower limit on the SNcc rate that ignores supernovae that are intrinsically fainter than $\Delta M_{570}=4.5$."
 Figure 13 summarizes the published measurement of the SNee rate., Figure \ref{ratesumfig} summarizes the published measurement of the SNcc rate.
 All data is consistent with a rate that increases with redshift like the SER o(1+2)°°., All data is consistent with a rate that increases with redshift like the SFR $\propto(1+z)^{3.6}$.
 It should be emphasized that the previous measurements use quite different detection and analysis procedures., It should be emphasized that the previous measurements use quite different detection and analysis procedures.
 We therefore refrain from drawing any quantitative conclusions about the redshift dependence of the SNee rate., We therefore refrain from drawing any quantitative conclusions about the redshift dependence of the SNcc rate.
 Our results will be improved in the future with the addition of two more years of SNLS data. and with the use of host spectroscopic redshifts that we are in theprocess of obtaining.," Our results will be improved in the future with the addition of two more years of SNLS data, and with the use of host spectroscopic redshifts that we are in theprocess of obtaining."
asymptotically follows a Gaussian distribution and so a bootstrap or Monte-Carlo method is required to derive the correct p-value from the test distribution.,asymptotically follows a Gaussian distribution and so a bootstrap or Monte-Carlo method is required to derive the correct $p$ -value from the test distribution.
" Our optimal strategy (summarised by Figure 2)) for ISW detection is the following: As we have chosen to work with the fields, the very first step is to deal with the missing data."," Our optimal strategy (summarised by Figure \ref{fig:saclaymethod}) ) for ISW detection is the following: As we have chosen to work with the fields, the very first step is to deal with the missing data."
" This is an ill-posed problem, which can be solved using sparse inpainting (see Appendix AppendixA: for more details)."," This is an ill-posed problem, which can be solved using sparse inpainting (see Appendix \ref{app:inpainting} for more details)."
" This approach reconstructs the entirety of the field, including along the Galactic plane and bulge."," This approach reconstructs the entirety of the field, including along the Galactic plane and bulge."
 We show in Section 5 that the use of sparse inpainting does not introduce a bias in the detection of the ISW effect., We show in Section \ref{sec:validation} that the use of sparse inpainting does not introduce a bias in the detection of the ISW effect.
 We then perform a correlation detection on the reconstructed fields data using a double bootstrap (see Appendix B.1.))., We then perform a correlation detection on the reconstructed fields data using a double bootstrap (see Appendix \ref{app:bootstrap:correlation}) ).
" Experiments show that the bootstrap tends to over-estimate the confidence interval, especially when the p-values are small."," Experiments show that the bootstrap tends to over-estimate the confidence interval, especially when the $p$ -values are small."
" This is why the obtained detection must be used as a indicator when near a significant value (for high p-values, the bootstrap remains accurate)."," This is why the obtained detection must be used as a indicator when near a significant value (for high $p$ -values, the bootstrap remains accurate)."
" The second test evaluates the signal amplitude, which validates both the presence of a signal and the chosen model."," The second test evaluates the signal amplitude, which validates both the presence of a signal and the chosen model."
 Bootstrapping test can also be used here as it has no assumption on the underlying cosmology., Bootstrapping test can also be used here as it has no assumption on the underlying cosmology.
" However, since the accuracy of bootstrap depends on the quantity of observed elements, it may become inaccurate for low p-value, 1.6. when there is detection."," However, since the accuracy of bootstrap depends on the quantity of observed elements, it may become inaccurate for low $p$ -value, i.e. when there is detection."
" In such case, Monte-Carlo (MC) will provide more accurate p-values and, for example, with 10° MC simulations, we have an accuracy of about 1/1000."," In such case, Monte-Carlo (MC) will provide more accurate $p$ -values and, for example, with $10^6$ MC simulations, we have an accuracy of about $1/1000$."
" This second test compares the ISW signal with a fiducial model, but does not consider the possibility that the measured signal could in fact be consistent with the ‘null hypothesis’."," This second test compares the ISW signal with a fiducial model, but does not consider the possibility that the measured signal could in fact be consistent with the `null hypothesis'."
" So even with a significant signal, a third test is necessary."," So even with a significant signal, a third test is necessary."
" This more pertinent question is addressed by using the ‘Model Comparison’ method (defined in Section 4.2.2)), for the first time using the fields approach."," This more pertinent question is addressed by using the `Model Comparison' method (defined in Section \ref{sec:fields-models-comp}) ), for the first time using the fields approach."
" In conclusion, our method consists of a series of complementary tests which together answer several questions."," In conclusion, our method consists of a series of complementary tests which together answer several questions."
" The first test seeks the presence of a correlation between two fields, without any referring cosmology."," The first test seeks the presence of a correlation between two fields, without any referring cosmology."
 The second model-dependent test searches a given signal and tests its nullity., The second model-dependent test searches a given signal and tests its nullity.
 The third test asks whether the data prefers a fiducial ISW signal over the null hypothesis., The third test asks whether the data prefers a fiducial ISW signal over the null hypothesis.
viscosity tensor (here we use the uusplit finite volume version of the scalar viscosity from (Amuinosetal.2005) with hy=2.0 aud Aj=0.1). P is the fluid pressure. Be is the coutravariant magnetic field vector. Pp=BiD;/sz is the maguetic pressure.,"viscosity tensor (here we use the unsplit finite volume version of the scalar viscosity from \citep{anninos05} with $k_q=2.0$ and $k_l=0.1$ ), $P$ is the fluid pressure, $B^k$ is the contravariant magnetic field vector, $P_B = B^iB_i/8\pi$ is the magnetic pressure."
 ® is the eravitatioual potential. which is found by solving equation (5)) with multipole boundary conditious that iuclude up to 15 spherical-polar hiriuonies aud all correspondiug azinmthal moments.," $\Phi$ is the gravitational potential, which is found by solving equation \ref{eqn:grav}) ) with multipole boundary conditions that include up to 15 spherical-polar harmonics and all corresponding azimuthal moments."
 Iu this work. we assiuue au ideal gas equation of state in the form P=(P.1)e.," In this work, we assume an ideal gas equation of state in the form $P=(\Gamma-1)e$."
 The MIID equations are derived with the standard assuniptions relevant for many astrophysical problems: the svsteni is nourelativistic and fully ionized. the displacement currents in Maxwell's equations are ucelected. the net electric charge is s)all and the characteristic leneth scales are large compared toparticle evxroracdii scales.," The MHD equations are derived with the standard assumptions relevant for many astrophysical problems: the system is nonrelativistic and fully ionized, the displacement currents in Maxwell's equations are neglected, the net electric charge is small, and the characteristic length scales are large compared toparticle gyroradii scales."
 The scalar potential c iu the magnetic induction equation (1)) is introduced. as a divergence cleanser to inaiutain a divergence-free inaguetie feld (OgBij= 0)., The scalar potential $\psi$ in the magnetic induction equation \ref{eqn:mag}) ) is introduced as a divergence cleanser to maintain a divergence-free magnetic field $\partial_i(\sqrt{g}~B^i) = 0$ ).
 Options are included in Cosmos to solve any one of the following constraint equations for c (Deducrctal. 2002): which correspond. respectively. to clliptic. parabolic. and mixed hyperbolic aud parabolic coustraiuts.," Options are included in Cosmos to solve any one of the following constraint equations for $\psi$ \citep{dedner02}: which correspond, respectively, to elliptic, parabolic, and mixed hyperbolic and parabolic constraints."
 Tere ον and ορ are user-specified constants used to regulate the filtering process and weight the relative siguificance of the hyperbolic and parabolic coumoncnuts., Here $c_p$ and $c_h$ are user-specified constants used to regulate the filtering process and weight the relative significance of the hyperbolic and parabolic components.
 Also the tine derivative in equation (6)) is approximated as a finite difference with zero divergence at the initialtime., Also the time derivative in equation \ref{eqn:psi_ell}) ) is approximated as a finite difference with zero divergence at the initialtime.
 For all of the calculations presented in this paper. we use the mixed Lyperbolic and parabolic form withparameters ey—026092)vu(AF ancl e= 02ο. where eg= 0.118 the Courant cocficieut. Ac is the mua covariant zone leneth. and Af is the evolution time step.," For all of the calculations presented in this paper, we use the mixed hyperbolic and parabolic form withparameters $c_h = 0.2 c_\mathrm{cfl} \Delta x_\mathrm{min}/\Delta t$ and $c_p^2 = 0.3 c_h$ , where $c_\mathrm{cfl}=0.4$ is the Courant coefficient, $\Delta x_\mathrm{min}$ is the minimum covariant zone length, and $\Delta t$ is the evolution time step."
" Equatious (1)) (5)) ancl (8)) are solved in a modified evlindrical coordinate svstem £9Gy.το), where jj= is a logarithmic radial coordinate used to lu(zcconcentrate resolution toward the interior of the star. with z=rsind beime the usual cvliudical radius."," Equations \ref{eqn:dens}) ) – \ref{eqn:grav}) ) and \ref{eqn:psi}) ) are solved in a modified cylindrical coordinate system $\xi^i = (\eta,z,\phi)$, where $\eta=\ln (\varpi+1)$ is a logarithmic radial coordinate used to concentrate resolution toward the interior of the star, with $\varpi=r\sin \theta$ being the usual cylindrical radius."
 With this coordinate choice. tho liue element for the metric g;; becomes and νο=eMet1).," With this coordinate choice, the line element for the metric $g_{ij}$ becomes and $\sqrt{g} = e^\eta(e^\eta - 1)$."
 We consider two different mesh resolutions. 61 and 967. to address the robustuess aud relative convergence of our results.," We consider two different mesh resolutions, $64^3$ and $96^3$, to address the robustness and relative convergence of our results."
 These are about optimal resolutions for threc-dinensional simulations where a huge umber of parameters are to be explored. particularly with active maeuetic fields which increase substantially the computational workload ancl suffer ercater wave speed restrictions on the time step.," These are about optimal resolutions for three-dimensional simulations where a large number of parameters are to be explored, particularly with active magnetic fields which increase substantially the computational workload and suffer greater wave speed restrictions on the time step."
 We begin bv coustructing equilibriun models ofrapidly rotating polvtropic stars using Hachisus selbconsistent Ποια technique (Jachisu 1986)., We begin by constructing equilibrium models ofrapidly rotating polytropic stars using Hachisu's self-consistent field technique \citep{hachisu86}.
. For an initially axisvnunetric configuration with aneular velocity Q=O(a) that depends only on the distauce of the fluid from the rotation axis (==επι). the equilibrium configuration satisfies where fig and Cy are constants. Π=fpLWP is the fiuid euthalpy. 9 is the eravitational potential obtained by solving the Poisson equation (5)). and describes the rotational profile of the star.," For an initially axisymmetric configuration with angular velocity $\Omega =\Omega (\varpi)$ that depends only on the distance of the fluid from the rotation axis $\varpi=r \sin\theta$ ), the equilibrium configuration satisfies where $h_0$ and $C_0$ are constants, $H=\int \rho^{-1} dP$ is the fluid enthalpy, $\Phi$ is the gravitational potential obtained by solving the Poisson equation \ref{eqn:grav}) ), and describes the rotational profile of the star."
 For a polvtropic gas with P=αρ;sp(LILES) we have where pass is the initial maxima deusity.," For a polytropic gas with $P=\kappa \rho^\Gamma = \kappa \rho^{(1+1/N)}$, we have where $\rho_\mathrm{max,0}$ is the initial maximum density."
 A varicty of rotation profiles can be considered. such as rigid rotation (Q=coust.). constant linear velocity (Q=Vofa). or coustaut specific angular moment (QO=fy/z7. where { is the specific angular momentum of the finid).," A variety of rotation profiles can be considered, such as rigid rotation $\Omega = \mathrm{const.}$), constant linear velocity $\Omega = V_0/\varpi$ ), or constant specific angular momentum $\Omega = j_0/\varpi^2$, where $j$ is the specific angular momentum of the fluid)."
 In our case. we choose a Maclaurin splieroid profile to compare with the earlier work of uumnagnetized neutron stars (Newetal.2000) where AL equals the total mass of the star (splieroicl). mice) as the mass interior to ze. and can now be specified in terms of the total angular momentum J of the star.," In our case, we choose a Maclaurin spheroid profile to compare with the earlier work of unmagnetized neutron stars \citep{new00}
 where $M$ equals the total mass of the star (spheroid), $m(\varpi)$ is the mass interior to $\varpi$, and can now be specified in terms of the total angular momentum $J$ of the star."
 The constants Jy and Cy in equation (10)) are set by an appropriate choice of boundary conditions., The constants $h_0$ and $C_0$ in equation \ref{eqn:equilib}) ) are set by an appropriate choice of boundary conditions.
 Specifically. we require that p. P. and J£ vanish at the surface of the star.," Specifically, we require that $\rho$, $P$, and $H$ vanish at the surface of the star."
 Auv two points on the surface of the star can then be used to specify a solution: we choose a poiut on the equator (point 44) aud one of the poles (point D) by specifving the equatorial surface radius ape and axis ratio tpfae. where zp is the polar radius.," Any two points on the surface of the star can then be used to specify a solution; we choose a point on the equator (point $A$ ) and one of the poles (point $B$ ) by specifying the equatorial surface radius $\varpi_E$ and axis ratio $z_P/\varpi_E$, where $z_P$ is the polar radius."
 The coustauts are then eivenu as aud Finally we unst specify P. (or [IN) and & (or pias.) to close the svstem of equatious.," The constants are then given as and Finally we must specify $\Gamma$ (or $N$ ) and $\kappa$ (or $\rho_\mathrm{max,0}$ ) to close the system of equations."
 The solution proceeds by euessiug an initial distribution for js solving equations (5)) aud (11)) for ® and W. respectively: usine equation (10)) to set FF aud JL: and then using equation (12)) to determine a new density distribution.," The solution proceeds by guessing an initial distribution for $\rho$ ; solving equations \ref{eqn:grav}) ) and \ref{eqn:rotate}) ) for $\Phi$ and $\Psi$ , respectively; using equation \ref{eqn:equilib}) ) to set $H$ and $H_\mathrm{max}$ ; and then using equation \ref{eq:enthalpy}) ) to determine a new density distribution."
 This procedure is repeated iteratively until the solution converges sufficiently (for us. once Afig/hy. ACy/Cy. aud AJI/IDare all <10 i).," This procedure is repeated iteratively until the solution converges sufficiently (for us, once $\Delta h_0/h_0$ , $\Delta C_0/C_0$ , and $\Delta H/H$are all $\le 10^{-4}$ )."
 The initial data are solved in two-dimensional logarithmic cvlndrical coordinates using the same polar, The initial data are solved in two-dimensional logarithmic cylindrical coordinates using the same polar
The first subject of cosmology is the overall motion of the universe.,The first subject of cosmology is the overall motion of the universe.
" In terms of the current understanding. (his means figuring oul whether it is open or closed. flat or curved. dense or rarified: and determining a few numbers (//,. 2) which describe it."," In terms of the current understanding, this means figuring out whether it is open or closed, flat or curved, dense or rarified; and determining a few numbers $H_0, \Omega$ ) which describe it."
 In the past few νους (his task seems to have been carried almost to completion., In the past few years this task seems to have been carried almost to completion.
 The next task is to study the details of the universe. (hat is. the departures [rom smoothness and overall motion.," The next task is to study the details of the universe, that is, the departures from smoothness and overall motion."
 These take the form of the visible features (galaxies. as well as collections of them in groups. clusters. superclusters. aud so forth) ancl their peculiar motions.," These take the form of the visible features (galaxies, as well as collections of them in groups, clusters, superclusters, and so forth) and their peculiar motions."
 On the largest scales this may be approached by using perturbations of the background cosmology. where linearity makes (he calculations easier (or possible at all).," On the largest scales this may be approached by using perturbations of the background cosmology, where linearity makes the calculations easier (or possible at all)."
 Llere. the picture ol structure growing bv gravitational instability from small initial fluctuations in a smooth distribution of dark ancl Dhuninous matter seems to work well (see Courteau.Strauss.&(2000) [or a review: more recent work includes Dranchinietal.(2000) and," Here, the picture of structure growing by gravitational instability from small initial fluctuations in a smooth distribution of dark and luminous matter seems to work well (see \citet{CSW00} for a review; more recent work includes \citet{BZP00} and"
galaxies.,galaxies.
 In order to more precisely disentangle the lens and background components we represent the flux from the lensed SMGs with Sérrsic profiles., In order to more precisely disentangle the lens and background components we represent the flux from the lensed SMGs with Sérrsic profiles.
" Peaks were identified in the IRAC single profile fit residual images, by fitting Gaussian profiles."," Peaks were identified in the IRAC single profile fit residual images, by fitting Gaussian profiles."
" We add three profiles for SDP.81 and two for SDP130, which all correspond to significant sub-mm contour peaks in the SMA data, within 0.8”."," We add three profiles for SDP.81 and two for SDP130, which all correspond to significant sub-mm contour peaks in the SMA data, within $''$."
" N10 modeled the Keck{ band with a Sérrsic profile plus an exponential disk, as this combination gave a marginally improved x? over single profile models, and found that the exponential component significantly contributes to the total profile for SDP.130."," N10 modeled the Keck band with a Sérrsic profile plus an exponential disk, as this combination gave a marginally improved $\chi^2$ over single profile models, and found that the exponential component significantly contributes to the total profile for SDP.130."
" Therefore, a Sérrsic plus exponential disk profile is adopted for the SDP.130 lens and a single Sérrsic profile for the SDP.81 lens."," Therefore, a Sérrsic plus exponential disk profile is adopted for the SDP.130 lens and a single Sérrsic profile for the SDP.81 lens."
" To produce the final models for the lens and background galaxies, we refit the profile representing the lens galaxy and the additional Sérrsic profiles simultaneously for each system with GALFIT."," To produce the final models for the lens and background galaxies, we refit the profile representing the lens galaxy and the additional Sérrsic profiles simultaneously for each system with GALFIT."
 These final model fits for the background component of SDP.81 show a partial “Kinstein ring”-like morphological structure for the lensed source [3))., These final model fits for the background component of SDP.81 show a partial “Einstein ring”-like morphological structure for the lensed source (Figure. \ref{id81multi}) ).
" For SDP.130, the lensed component is more (Figure.compact and in close proximity to the lens profile."," For SDP.130, the lensed component is more compact and in close proximity to the lens profile."
" The resulting best fit profiles for the background galaxies agree well with the SMA contours, and the combined models subtract cleanly, suggesting successful lens/source decoupling."," The resulting best fit profiles for the background galaxies agree well with the SMA contours, and the combined models subtract cleanly, suggesting successful lens/source decoupling."
" The GALFIT-integrated magnitudes for each component of the final SDP.81 and SDP.130 models were converted to flux density to extend the existing multi-waveband photometry table and N10, and references therein) into the near-IR."," The GALFIT-integrated magnitudes for each component of the final SDP.81 and SDP.130 models were converted to flux density to extend the existing multi-waveband photometry (see table \ref{tab:results} and N10, and references therein) into the near-IR."
"(see We [1]assign σ errors to the photometry obtained from the final GALFIT model profiles, using the magnitude distributions for all the GALFIT trials that converged."," We assign $\,\sigma$ errors to the photometry obtained from the final GALFIT model profiles, using the magnitude distributions for all the GALFIT trials that converged."
 PACS re-imaging of the lensed H-ATLAS sources provides new photometry at and upper limits at Valtchanov et al.," PACS re-imaging of the lensed H-ATLAS sources provides new photometry at $\,\mu$ m and upper limits at $\,\mu$ m (I. Valtchanov et al."
 in μπιpreparation; Ibar et al., in preparation; Ibar et al.
 70m2010)., 2010).
" (I.For the goal of the IRAC photometry adds derivingparticularly physicalimportant properties,constraints to the SMG which consisted of just upper limits at wavelengthsSEDs, below previously 250m for SDP.130 and um for SDP.81."," For the goal of deriving physical properties, the IRAC photometry adds particularly important constraints to the SMG SEDs, which previously consisted of just upper limits at wavelengths below $\,\mu$ m for SDP.130 and $\,\mu$ m for SDP.81."
 The SEDs of the SMGs are fitted using the models of da Cunha et al. (, The SEDs of the SMGs are fitted using the models of da Cunha et al. (
"2008), calibrated to reproduce the ultraviolet-to-infrared SEDs of local, purely star-forming Ultra Luminous Infrared Galaxies (ULIRGs; 1013< LyrR/Lo«1019: da Cunha et al.","2008), calibrated to reproduce the ultraviolet-to-infrared SEDs of local, purely star-forming Ultra Luminous Infrared Galaxies (ULIRGs; $^{12} \leq$ $L_{\rm IR}/L_{\odot} < 10^{13}$; da Cunha et al."
 2010)., 2010).
 The SED models assume a Chabrier (2003) initial mass function (IMF) that is cutoff below 0.1 and above 100 Mo; using a Salpeter IMF instead gives stellar masses that are a factor of ~1.5 larger., The SED models assume a Chabrier (2003) initial mass function (IMF) that is cutoff below 0.1 and above 100 $M_{\odot}$; using a Salpeter IMF instead gives stellar masses that are a factor of $\sim1.5$ larger.
" We find that a significant attenuation by dust (Ay ~4-5) is required to be consistent with the IRAC photometry and optical/near-IR, upper limits (Figure 4)), which is consistent with other ULIRGs and SMGs (e.g. Geach et al."," We find that a significant attenuation by dust $A_{\rm V} \sim $ 4-5) is required to be consistent with the IRAC photometry and optical/near-IR upper limits (Figure \ref{seds}) ), which is consistent with other ULIRGs and SMGs (e.g. Geach et al."
 2007; Hainline et al., 2007; Hainline et al.
 2010; Michalowski et al., 2010; owski et al.
 2010; Wardlow et al., 2010; Wardlow et al.
 , 2010).
"Using the Chabrier2010). IMF, with parameters derived from the SED (2003)we find that SDP.81 and SDP.130 have stellar massesfits, (M,) of"," Using the Chabrier (2003) IMF, with parameters derived from the SED fits, we find that SDP.81 and SDP.130 have stellar masses $M_\star$ ) of"
In principle. even if one bases the model of the telescope on simple assumptions. it is possible that the final model contains too many free parameters that cannot be constrained by the observations.,"In principle, even if one bases the model of the telescope on simple assumptions, it is possible that the final model contains too many free parameters that cannot be constrained by the observations."
 In such a case. when one fits the model parameters to a set of calibration observations. the model might not be representative of the general behavior of the telescope.," In such a case, when one fits the model parameters to a set of calibration observations, the model might not be representative of the general behavior of the telescope."
 Obviously. this is produced by the overfitting ability of a model with too many free parameters.," Obviously, this is produced by the overfitting ability of a model with too many free parameters."
 This is particularly relevant when several parameters are degenerated. meaning that the variation of one parameter can be compensated to a great extent with variations in one or more of the other parameters.," This is particularly relevant when several parameters are degenerated, meaning that the variation of one parameter can be compensated to a great extent with variations in one or more of the other parameters."
 Consequently. we analyze the intrinsic dimensionality of the model using the maximum-likelihood estimation developed by ? and applied with success by ? to estimate the intrinsic dimensionality of spectro-polarimetric data.," Consequently, we analyze the intrinsic dimensionality of the model using the maximum-likelihood estimation developed by \cite{levina_bickel05} and applied with success by \cite{asensio_dimension07} to estimate the intrinsic dimensionality of spectro-polarimetric data."
 By intrinsic dimensionality we mean the number of free parameters that the T-matrix really depends on. taking into account that degeneracies introduce correlations between the parameters and reduce the dimensionality.," By intrinsic dimensionality we mean the number of free parameters that the $\tens{T}$ -matrix really depends on, taking into account that degeneracies introduce correlations between the parameters and reduce the dimensionality."
 Given N vectors of dimension M represented as x;. the dimensionality is estimated by using the expression: where 7;(x;) represents the Euclidean distance between point x; and its &-th nearest neighbor.," Given $N$ vectors of dimension $M$ represented as $\vec{x}_i$, the dimensionality is estimated by using the expression: where $T_k(\mathbf{x}_i)$ represents the Euclidean distance between point $\mathbf{x}_i$ and its $k$ -th nearest neighbor."
 The previous equation is only valid for &>2 and it depends on the number of neighbors that we select., The previous equation is only valid for $k>2$ and it depends on the number of neighbors that we select.
 In principle. this can be used to analyze variations of the intrinsic dimensionality at different scales. but our results are relatively constant with k.," In principle, this can be used to analyze variations of the intrinsic dimensionality at different scales, but our results are relatively constant with $k$."
 The computational cost of this method is mainly dominated by the calculation of the & nearest neighbors for every point x;., The computational cost of this method is mainly dominated by the calculation of the $k$ nearest neighbors for every point $\mathbf{x}_i$.
 As an illustrative example. we have considered data generated with a polynomial function: This function may be viewed as a non-linear model with 77 free parameters (the c; coefficients).," As an illustrative example, we have considered data generated with a polynomial function: This function may be viewed as a non-linear model with $n$ free parameters (the $c_i$ coefficients)."
 Our aim is to estimate the order of the polynomial just from the samples., Our aim is to estimate the order of the polynomial just from the samples.
 Since we have generated the data for this experimient. we can then verifyposteriori that the results accurately yield the correct number.," Since we have generated the data for this experimient, we can then verify that the results accurately yield the correct number."
 Three different experiments were carried out for polynomials of order 1. 2 and 3. respectively.," Three different experiments were carried out for polynomials of order 1, 2 and 3, respectively."
 For each value of n. we generate N=10 vectors composed of samples of the polynomial at M=10 different positions Cv).," For each value of $n$, we generate $N=10^4$ vectors composed of samples of the polynomial at $M=10$ different positions $x$ )."
 The estimation of the dimensionality is shown in Fig | where 7 indicates the number of coefficientes of the polynomial (1.e.. the polynomial order is 1— 1).," The estimation of the dimensionality is shown in Fig \ref{fig:polynomial} where $n$ indicates the number of coefficientes of the polynomial (i.e., the polynomial order is $n-1$ )."
 Note that the results converge towards the correct dimensionality for small number of neighbors (for large values. the results are sensitive to the finite and discrete nature of the grid).," Note that the results converge towards the correct dimensionality for small number of neighbors (for large values, the results are sensitive to the finite and discrete nature of the grid)."
 Further details of this procedure and more exhaustive tests can be found in ?.., Further details of this procedure and more exhaustive tests can be found in \cite{asensio_dimension07}.
 Here we simply intend to use this example to illustrate the application to the telescope model presented below. where instead of a simple polynomial we have the T-matrix constructed as indicated in Eq 2 above from its 8 free parameters.," Here we simply intend to use this example to illustrate the application to the telescope model presented below, where instead of a simple polynomial we have the $\tens{T}$ -matrix constructed as indicated in Eq \ref{eq:T} above from its 8 free parameters."
 If we had correlations or degeneracies among these parameters. then the dimensionality of the data produced with the model would be less than the number of free parameters.," If we had correlations or degeneracies among these parameters, then the dimensionality of the data produced with the model would be less than the number of free parameters."
 For the analysis of the telescope model we consider each Stokes parameter Q. U and V separately. and the N vectors are built as follows.," For the analysis of the telescope model we consider each Stokes parameter $Q$, $U$ and $V$ separately, and the $N$ vectors are built as follows."
 Let Νροι be the number of angles of the axis of our EW polarizers., Let $N_\mathrm{pol}$ be the number of angles of the axis of our EW polarizers.
 Let N44. be the number of combinations of azimuth. elevation and table angles that characterize the telescope configuration.," Let $N_\mathrm{ang}$ be the number of combinations of azimuth, elevation and table angles that characterize the telescope configuration."
 For each combination of polarizer angle. azimuth. elevation and table angle. we propagate a Stokes vector representing unpolarized light through the telescope (with its EW polarizers) by multiplying (1.0.0.0)+ by the full telescope Muller matrix T (the symbol * represents the matrix transposition operation).," For each combination of polarizer angle, azimuth, elevation and table angle, we propagate a Stokes vector representing unpolarized light through the telescope (with its EW polarizers) by multiplying $(1,0,0,0)\dagger$ by the full telescope Muller matrix $\tens{T}$ (the symbol $\dagger$ represents the matrix transposition operation)."
 Keeping the parameters of the matrix fixed. we construct the vector of length M=NpotVang=100 by stacking the emergent Stokes parameter (Q. U or V) for all the possible combinations.," Keeping the parameters of the matrix fixed, we construct the vector of length $M=N_\mathrm{pol}
N_\mathrm{ang}=100$ by stacking the emergent Stokes parameter $Q$, $U$ or $V$ ) for all the possible combinations."
 Each such vector then represents a realization of the observable that can be used to characterize the Mueller matrix of the telescope., Each such vector then represents a realization of the observable that can be used to characterize the Mueller matrix of the telescope.
 This procedure is repeated N times until the entire database ts filled., This procedure is repeated $N$ times until the entire database is filled.
 Due to computational limitations in the & nearest neighbors calculation. we limit ourselves to N=107 different values of the parameters.," Due to computational limitations in the $k$ nearest neighbors calculation, we limit ourselves to $N=10^4$ different values of the parameters."
 These values have beer generated by means of a latin hypercube sampling (?).. which produces a better sampling of the parameter space.," These values have been generated by means of a latin hypercube sampling \citep{MKBC79}, which produces a better sampling of the parameter space."
 We have applied the dimension analysis on these data and obtained the results plotted in Fig 2.., We have applied the dimension analysis on these data and obtained the results plotted in Fig \ref{fig:dimensionality8}.
 AM of the Stokes parameters exhibit the same behavior and converge to approximately 7.5. which is very close to the number of free parameters (8. see Section 2)) in our model.," All of the Stokes parameters exhibit the same behavior and converge to approximately 7.5, which is very close to the number of free parameters (8, see Section \ref{sec:telescopemodel}) ) in our model."
 From this we can conclude that no significant degeneracies exist among the various free parameters and that a variation on each one of them produces an independent. measureable result on the observables.," From this we can conclude that no significant degeneracies exist among the various free parameters and that a variation on each one of them produces an independent, measureable result on the observables."
 In other words. we can be confident," In other words, we can be confident"
"It .is well-known that the luminosity""M £ of. luminous. spiral. galaxies. correlates tightly: with. their. rotation. velocity. -ην as called the .Tully-Fisher) relation. thereafter.TFR.Tully&opeFisher1977).","It is well-known that the luminosity $L$ of luminous spiral galaxies correlates tightly with their rotation velocity $V_{\rm rot}$, as called the Tully-Fisher relation \citep[hereafter TFR,][]{tf77}."
. The arpΤΕΕ is usually described. as a power-law scaling- relation. £x|Biet and the rms scatter of. the TFR .is smaller for. optical. passbands of longer wavelengths.," The TFR is usually described as a power-law scaling relation $L\propto V_{\rm rot}^{\gamma}$, and the rms scatter of the TFR is smaller for optical passbands of longer wavelengths."
 In particular. the I-band TFR is signiticantly tight. and .its scatter .is approximately. as small as 0.4 mag CWillickual1007:>KKannappan.|Fabricant&ΕFranx2002). 2002)... withwill a |power- ;index ?23.∙3.5 (e.g.Pierce.&;Tully1988:ΓΡ...," In particular, the I-band TFR is significantly tight and its scatter is approximately as small as 0.4 mag \citep{w97, kff02}, with a power-law index $\gamma\simeq 3-3.5$ \citep[e.g.][]{pt88, s00}."
Sakaietal.2000).. longer27 wavelengths from galaxies tracesscaling oldrelation late-type stars. n » formation. of young -stars.constant andAZ represents the : a ore matter.," Light at longer wavelengths from galaxies traces old late-type stars, unaffected by sporadic formation of young stars, and represents the mass of luminous matter."
 Thus. vthe tightness of the galaxiesI-band TFR(e.g. suggests the Faberexistence of some driving mechanism that depends on mass of galaxies in processes of their formation.," Thus, the tightness of the I-band TFR suggests the existence of some driving mechanism that depends on mass of galaxies in processes of their formation."
 The current standard model of cosmology is the cold dark matter (CDM) model., The current standard model of cosmology is the cold dark matter (CDM) model.
" Since the initial spectrum of density fluctuations has larger amplitudes for smaller scales in this model. the scenario of structure formation is hierarchical clustering. in the sense that smaller dark haloes cluster to form larger dark haloes hierarchically. thereby creating a scaling relation between mass A7 and circular velocity Vou. of dark haloes (Faber.1982:Blumen-thaletal., 1984)."," Since the initial spectrum of density fluctuations has larger amplitudes for smaller scales in this model, the scenario of structure formation is hierarchical clustering, in the sense that smaller dark haloes cluster to form larger dark haloes hierarchically, thereby creating a scaling relation between mass $M$ and circular velocity $V_{\rm circ}$ of dark haloes \citep{f82, bfpr84}."
". High-resolution⊽ s N-body ∡∙simulations.[ based on a power spectrum P(&)x&"" with an index n=—2.5 appropriate for. galaxy scales or reciprocal: of. wavenumber 4)17. have provided. AMxumMg. reminiscent2o. of. the TFR »if a constant mass-to-light. AL/L ratioao csis assumedQus (e.g.Navarro.NFrenk0L&ogWhiteunoc1997)."," High-resolution $N$ -body simulations, based on a power spectrum $P(k)\propto k^{n}$ with an index $n=-2.5$ appropriate for galaxy scales or reciprocal of wavenumber $k^{-1}$, have provided $M\propto V_{\rm cir}^3$, reminiscent of the TFR if a constant mass-to-light $M/L$ ratio is assumed \citep[e.g.][]{nfw}."
 Consequently.. the CDM. model naturally :involves a TFR-like. as ∙∙↜observed for ⊲↜luminous spiralul galaxies.∡∙ .because a. Light. at is indeedknown to Lobe a good approximation to such unaffected. by sporadic &MN Gallagher1979).," Consequently, the CDM model naturally involves a TFR-like scaling relation as observed for luminous spiral galaxies, because a constant $M/L$ is indeed known to be a good approximation to such galaxies \citep[e.g.][]{fg79}."
massanof.luminous When studying the formation of galaxies originated from the growth of density fluctuations in the early universe. hnowever. it is also necessary to take into account the effects of star formation and supernova (SN) explosions in individual galaxies.," When studying the formation of galaxies originated from the growth of density fluctuations in the early universe, however, it is also necessary to take into account the effects of star formation and supernova (SN) explosions in individual galaxies."
 In particular. dwarf galaxies have shallow gravitational potential wells. so that energy feedback from SN explosions significantly affects their evolution and hence scaling relations that follow.," In particular, dwarf galaxies have shallow gravitational potential wells, so that energy feedback from SN explosions significantly affects their evolution and hence scaling relations that follow."
 In a framework of monolithie collapse scenario of galaxy formation. several authors," In a framework of monolithic collapse scenario of galaxy formation, several authors"
are real and not due fo.e.g... systematic errors in the spectrophotometzy due to telluric water Figure 1. provides a comparison of IEA 0230-Z1 with local T dafs found in the SDSS aud classified by Coballeetal.(2002).,"are real and not due to, systematic errors in the spectrophotometry due to telluric water Figure \ref{fig-spectra} provides a comparison of IfA 0230-Z1 with local T dwarfs found in the SDSS and classified by \citet{geb01}."
. Based ou this. we estimate a spectral type of T3Τι for HA 0230-Z1. which agrees with the typing οι the broad-band colors alone.," Based on this, we estimate a spectral type of T3–T4 for IfA 0230-Z1, which agrees with the typing from the broad-band colors alone."
 Since the shape of the IT-biaud continue is chaneie rapidly with spectral type. the uncertainty in the spectral typing is no more than L spectral subclass.," Since the shape of the $H$ -band continuum is changing rapidly with spectral type, the uncertainty in the spectral typing is no more than 1 spectral subclass."
 Ouly three T dwirfs have kuowu distances. all of them colpanious to main sequence stars.," Only three T dwarfs have known distances, all of them companions to main sequence stars."
 Two ofthem. CL 229B and GL 570D. are mach cooler objects than IfA 0230-Z1. with stronecr aabsorption (Oppenheimeretal.1995:Bureasser 2000b)..," Two of them, GL 229B and GL 570D, are much cooler objects than IfA 0230-Z1, with stronger absorption \citep{1995Sci...270.1478O, 2000ApJ...531L..57B}."
 The third. GL s6B. appears to have modest uethane absorption like THA 0230-Z1. but its maguitudes and colors are poorly known (Elsctal.2001).," The third, GL 86B, appears to have modest methane absorption like IfA 0230-Z1, but its magnitudes and colors are poorly known \citep{els01}."
. Also. at fixed effective temperature/spectral type. vounecr (less nassivo) brown dwarfs will be more dluninuous than older (amore massive) ones.," Also, at fixed effective temperature/spectral type, younger (less massive) brown dwarfs will be more luminuous than older (more massive) ones."
 Hence. even if there were T3 dwarts with kuown distances. their ages aud heuce their nuinosities mieht be different than ILA 0230-Z1.," Hence, even if there were T3 dwarfs with known distances, their ages and hence their luminosities might be different than IfA 0230-Z1."
 We estimate the distance as follows., We estimate the distance as follows.
 For ages older han ~0.1 Cr. the radius of a brown chwart is hugely indepeudent of its mass. to within about (Burrowsetal. 2001).," For ages older than $\sim$ 0.1 Gyr, the radius of a brown dwarf is largely independent of its mass, to within about \citep{bur01}."
. Hence. £~Tig," Hence, $L\sim\Teff^4$."
 The bolometric correction at J-haucl is observed to be nearly coustaut for late-L aud T dwarts (Legecttotal.2002). so the absolute J-band naenitude ALy will scale directly with Zi!, The bolometric correction at $J$ -band is observed to be nearly constant for late-L and T dwarfs \citep{leg01} so the absolute $J$ -band magnitude $M_J$ will scale directly with $^4$.
 The difference in effective. temperature between the late-L dwiufs aud he late-T dwarf GL 229D is estimated to be quite simall. haps only 1300 to 1000 In (INirkpatrieketal.2000:Bureasseretal. 2002).," The difference in effective temperature between the late-L dwarfs and the late-T dwarf GL 229B is estimated to be quite small, perhaps only 1300 to 1000 K \citep{2000AJ....120..447K,
burg01}."
. Adopting Tig~1150 EK for TfA ΕΙ its J-baud absolute magnitude will be 0.6 mag brighter than for GL 229B. which has M;=15.51£0.09 mae (Leeeettetal.1999).. (," Adopting $\Teff\approx1150$ K for IfA 0230-Z1 means its $J$ -band absolute magnitude will be $\approx$ 0.6 mag brighter than for GL 229B, which has $M_J = 15.51\pm0.09$ mag \citep{1999ApJ...517L.139L}. ("
Note that this is a differential comparison and does not depend on the absolute sscale adopted.),Note that this is a differential comparison and does not depend on the absolute scale adopted.)
 Παισο. we estimate M;z1L9 mag for ILA 0230-Z1.," Hence, we estimate $M_J\approx14.9$ mag for IfA 0230-Z1."
 This compares favorably to the two Ls dwarfs with known distances. which have an average M;zzLI8D mag (Iirkpatricketal.2000)...," This compares favorably to the two L8 dwarfs with known distances, which have an average $M_J\approx14.85$ mag \citep{2000AJ....120..447K}."
 The resulting distance estimate for ΠΑ 0230-Z1 is 15 pe. with an eror of ~20% (£9 pe} based ou the uucertainties in the radius and absolute J-baud maenitucle.," The resulting distance estimate for IfA 0230-Z1 is 45 pc, with an error of $\sim$ $\pm$ 9 pc) based on the uncertainties in the radius and absolute $J$ -band magnitude."
 The 0230 field of the ΗΠΑΏου) survey is contained with the SDSS Early Data Release (Stoughtonetal.2002).. but TEA 0230-Z1 is —0.6 mags too fait in tto be detected by SDSS.," The 0230 field of the IfA-Deep survey is contained with the SDSS Early Data Release \citep{sdss-edr}, but IfA 0230-Z1 is $\sim$ 0.6 mags too faint in to be detected by SDSS."
 With the detection of ouly a single object. any discussion of the T dwarf number counts at magnitudes fainter than SDSS is muwarrauted.," With the detection of only a single object, any discussion of the T dwarf number counts at magnitudes fainter than SDSS is unwarranted."
 However. we cau do a simple comparison.," However, we can do a simple comparison."
 The first five T dwarfs from SDSS were found iu an area of 355 square degrees. with an effective. limiting magnitude of z/zm19.5 mags (Vega).," The first five T dwarfs from SDSS were found in an area of 355 square degrees, with an effective limiting magnitude of $\zp\approx19.5$ mags (Vega)."
 This means a surface density of about 1 per TO square degrees., This means a surface density of about 1 per 70 square degrees.
 Our :'—baud naagius of the 0230 Seld used in this paper reaches ~l mags deeper., Our -band imaging of the 0230 field used in this paper reaches $\sim$ 4 mags deeper.
 Assuming a uniform volume density of T dwarfs. the expected surface deusitv would be 1l per 0.3 square degrees. consistent with our discovery of a single object.," Assuming a uniform volume density of T dwarfs, the expected surface density would be 1 per 0.3 square degrees, consistent with our discovery of a single object."
 The final IEA survey will eo a factor of 3 deeper in flux and cover 5 times more area. sugecsting a total vield of ~ 10 T dwarf.," The final IfA survey will go a factor of 3 deeper in flux and cover 5 times more area, suggesting a total yield of $\sim$ 40 T dwarfs."
 In comparison. 13 T dwarts lave heen found from the ~ of the 2\LASS data searched to date (Bureasser2001)..," In comparison, 13 T dwarfs have been found from the $\sim$ of the 2MASS data searched to date \citep{burg01b}."
 This suggests the IfA survey will find a comparable umuber of T dwarfs as the cutire 2\LASS survey. albeit at a 1uuch larger average distance.," This suggests the IfA survey will find a comparable number of T dwarfs as the entire 2MASS survey, albeit at a much larger average distance."
 However. these nuubers should be taken with caution since they are based ou the sinall sample of objects found to date by SDSS.," However, these numbers should be taken with caution since they are based on the small sample of objects found to date by SDSS."
 The completed IfA-Deep srvey will be scusitive to T chwarts out to ~300 pe aud LE dwarfs out to ~2 kpc., The completed IfA-Deep survey will be sensitive to T dwarfs out to $\sim$ 300 pc and L dwarfs out to $\sim$ 2 kpc.
 By probing several lines of sight. the survey should provide the first iusights into the vertical scale height of ultracoo dwarts.," By probing several lines of sight, the survey should provide the first insights into the vertical scale height of ultracool dwarfs."
" To examine this aspect quautiatively, we consider a siniple model of an exponential disk based on Waiuscoaetal(1992).. with a radial scale leneth of 3.5 kpc ame different vertical scale heights."," To examine this aspect quantiatively, we consider a simple model of an exponential disk based on \citet{1992ApJS...83..111W}, with a radial scale length of 3.5 kpc and different vertical scale heights."
 For the L dwarfs. we adop a local vole deusity of 0.01 aand assuimne an equal nuniber of objects per spectra subclass (LO to LS). consistent with the analyses of Reidetal.(1999). aud Chabrier(2001).," For the L dwarfs, we adopt a local volume density of 0.01 and assume an equal number of objects per spectral subclass (L0 to L8), consistent with the analyses of \citet{1999ApJ...521..613R} and \citet{chab01}."
. We adopt a οσα] voluue density for T dwarfs of 0.006 using 1ο Durgasser(2001) results for T5 to Τὸ dwarfs anc ren doubling it to account for carly T dwarfs exclude roni their 2\TASS-selected sample.," We adopt a local volume density for T dwarfs of 0.006, using the \citet{burg01b} results for T5 to T8 dwarfs and then doubling it to account for early T dwarfs excluded from their 2MASS-selected sample."
 For the T dafs. we assume half the population is in carly T dwufs with je rest equally divided iuto T6. T7. aud Ts dwarts.," For the T dwarfs, we assume half the population is in early T dwarfs, with the rest equally divided into T6, T7, and T8 dwarfs."
 These inputs are very approximate. but consistent with 1ο limuted current observations.," These inputs are very approximate, but consistent with the limited current observations."
" Finally. we compute ας, absolute maguitudes using data from Kirkpatrickal. (2000).. Bureasseretal. (2000b).. Elsetal. (2001).. id Leeeettetal.(2002)."," Finally, we compute -band absolute magnitudes using data from \citet{2000AJ....120..447K}, \citet{2000ApJ...531L..57B}, \citet{els01}, and \citet{leg01}."
. The differences in the observed couuts of L and T chwarts between our low aud high galactic latitude fields will be very sensitive to the objects! vertical scale height., The differences in the observed counts of L and T dwarfs between our low and high galactic latitude fields will be very sensitive to the objects' vertical scale height.
 The 0230 field lies at very. high galactic latitude (b=— 537). while other fields in the HA-Deep Survey cover lower latitucles. down to the 0719 field at 6=187.," The 0230 field lies at very high galactic latitude $b=-53\degs$ ), while other fields in the IfA-Deep Survey cover lower latitudes, down to the 0749 field at $b=18\degs$."
 For a canonical scale height of 325 pe. we predict the counts of E dwarfs iu our lugh aud low latitude felds will differ by a factor of 3.," For a canonical scale height of 325 pc, we predict the counts of L dwarfs in our high and low latitude fields will differ by a factor of 3."
 Iu contrast. if the scale height for ultracool objects is LOO pc. akin to the Population I coustituteuts of the Galactic disk (Cox2000).. the difference between high aud low latitude counts will be much larger. about a factor of 9.," In contrast, if the scale height for ultracool objects is 100 pc, akin to the Population I constitutents of the Galactic disk \citep{2000asqu.book.....C}, the difference between high and low latitude counts will be much larger, about a factor of 9."
 For the Todwurfs. the depeudeuce ou scale height has a different behavior. since our survey is onlv seusitive to mitch closer objects.," For the T dwarfs, the dependence on scale height has a different behavior, since our survey is only sensitive to much closer objects."
 For a 325 pe scale height. the low latitude field is predicted to have about 1.5 times as many T dwarfs as the lüeh latitude field.," For a 325 pc scale height, the low latitude field is predicted to have about 1.5 times as many T dwarfs as the high latitude field."
 However. iu the case of a LOO pc scale height. there should be 3 times as many T dwiufs in the," However, in the case of a 100 pc scale height, there should be 3 times as many T dwarfs in the"
"the ""cloud"" and ""exterior"" regions.","the “cloud"" and “exterior"" regions."
 Also shown are the model curves for the COND and DUSTY models (age 1 Myr) and main sequence stars for an assumed distance of 124 pc., Also shown are the model curves for the COND and DUSTY models (age 1 Myr) and main sequence stars for an assumed distance of 124 pc.
 Comparison of the two plots in Figure 4. shows that the number of points which fall on or close to the COND/DUSTY model curves is much greater on the 7cloud plot than on the “exterior” plot. consistent. with the presence of brown dwarls in the cloud core region.," Comparison of the two plots in Figure \ref{fig4} shows that the number of points which fall on or close to the COND/DUSTY model curves is much greater on the “cloud"" plot than on the “exterior"" plot, consistent with the presence of brown dwarfs in the cloud core region."
" It is also apparent (hat the majority of points in the ""exterior"" plot correspond to TurZ2800 Ix and are below the main sequence line for a distance of 124 pe."," It is also apparent that the majority of points in the “exterior"" plot correspond to $T_{\rm eff}\stackrel{>}{_\sim}2800$ K and are below the main sequence line for a distance of 124 pc."
 They are therefore consistent with normal stars al distances larger than 124 pe., They are therefore consistent with normal stars at distances larger than 124 pc.
" The same population is evident in the ""cloud plot. and hence the points which fall below (he main sequence line on that plot can conficlently be identified as background sts."," The same population is evident in the “cloud"" plot, and hence the points which fall below the main sequence line on that plot can confidently be identified as background stars."
" They number 882 and 666 in the ""cloud"" ancl ""exterior"" regions. respectively,"," They number 882 and 666 in the “cloud"" and “exterior"" regions, respectively."
" Alter exelusion of those objects we are left with Nau=139 cluster member candidates in the “cloud” region aud AN...=18 in the ""exterior"" region."," After exclusion of those objects we are left with $N_{\rm cloud}=139$ cluster member candidates in the “cloud"" region and $N_{\rm ext}=18$ in the “exterior"" region."
 This set of candidates may still. however. contain non-cluster contaminants.," This set of candidates may still, however, contain non-cluster contaminants."
" Possibilities include: The likelihood of foreground contamination bv L and T dwarls can be assessed from available number density statistics given that the volume of space in the cone capped by our ""cloud"" region is 54 pc."," Possibilities include: The likelihood of foreground contamination by L and T dwarfs can be assessed from available number density statistics given that the volume of space in the cone capped by our “cloud"" region is 54 $^3$."
 Since the estimated space densities of L and T dwarls in the solar, Since the estimated space densities of L and T dwarfs in the solar
other hand. show (wo prominent svmmetric arms within of Ds; (tvpically on the scale of a few kiloparsecs): these arms do not necessarily extend (o the center of the galaxy.,"other hand, show two prominent symmetric arms within of $D_{25}$ (typically on the scale of a few kiloparsecs); these arms do not necessarily extend to the center of the galaxy."
 In fact. these two (vpes of eran design structure are nearly disjoint: (he nuclear spiral arms in only two of the twenty LGD galaxies in our sample extend into the unresolved center of the galaxy. (1.e.. also displaved SGD structure).," In fact, these two types of grand design structure are nearly disjoint: the nuclear spiral arms in only two of the twenty LGD galaxies in our sample extend into the unresolved center of the galaxy (i.e., also displayed SGD structure)."
 The LGD spirals are found in svstematically more stronglv barred host galaxies., The LGD spirals are found in systematically more strongly barred host galaxies.
 This strongly confirms previous indications from much smaller samples and demonstrates that the dust lanes along the leading edges of large-scale spirals do not generally extend all the wav into the nuclear region. but instead lose coherence al the scale of several huidred. parsecs.," This strongly confirms previous indications from much smaller samples and demonstrates that the dust lanes along the leading edges of large-scale spirals do not generally extend all the way into the nuclear region, but instead lose coherence at the scale of several hundred parsecs."
 While SGD spirals are not found in galaxies with a signilicantlv different barstreneth than (vpical galaxies. (μον are found in galaxies with significantly less dust structure in the central regions than LGD galaxies.," While SGD spirals are not found in galaxies with a significantly different barstrength than typical galaxies, they are found in galaxies with significantly less dust structure in the central regions than LGD galaxies."
 The reduced dust structure mav reflect. a requirement for the formation of SGD morphology. or simply a requirement for ils detection.," The reduced dust structure may reflect a requirement for the formation of SGD morphology, or simply a requirement for its detection."
 The LGD spiral arms max not maintain colierence to the nucleus because mass inflow due to the presence of a large-scale bar prompts star formation. which can disrupt a nuclear erand design spiral.," The LGD spiral arms may not maintain coherence to the nucleus because mass inflow due to the presence of a large-scale bar prompts star formation, which can disrupt a nuclear grand design spiral."
 In acldition. fortv. percent of the LGD spirals do not extend into the nuclear region because (here is à circumuuclear starburst ring.," In addition, forty percent of the LGD spirals do not extend into the nuclear region because there is a circumnuclear starburst ring."
 We find that all of the galaxies with cireiumnuclear starburst rings have LGD structure and are more strongly barred. than other galaxies., We find that all of the galaxies with circumnuclear starburst rings have LGD structure and are more strongly barred than other galaxies.
" Within the rings. three fourths of the galaxies with cireumnmuclear rings have coherent loosely wound spirals within the ring. while the others have less coherent. chaotic spirals,"," Within the rings, three fourths of the galaxies with circumnuclear rings have coherent loosely wound spirals within the ring, while the others have less coherent chaotic spirals."
 We also find that among SB galaxies. SB(s) galaxies have more dust structure and are more strongly barred than 5D(r) galaxies.," We also find that among SB galaxies, SB(s) galaxies have more dust structure and are more strongly barred than SB(r) galaxies."
 This is partially at odds with the prevailing view in (he literature. which is that SBir) galaxies should be more strongly barred. although there is consensus (hat SD(r) galaxies have less central dust (e.g.Normencdy&Ix," This is partially at odds with the prevailing view in the literature, which is that SB(r) galaxies should be more strongly barred, although there is consensus that SB(r) galaxies have less central dust \citep[e.g.][]{kormendy04}."
ennieutt 2004).. Sanders&Tubbs(1980). suggest that differences in the bar pattern speed mar also explain (he large-scale morphological differences between SB(s) aud SD(r) galaxies: as our results indicate that SD(s) galaxies are more strongly barred. pattern speed may be the more relevant parameter.," \citet{sanders80} suggest that differences in the bar pattern speed may also explain the large-scale morphological differences between SB(s) and SB(r) galaxies; as our results indicate that SB(s) galaxies are more strongly barred, pattern speed may be the more relevant parameter."
 Overall. (here is agreement in the literature that more strongly barred galaxies should dohave more clust and gas in their centers (INormendy&Ixennieutt2004).," Overall, there is agreement in the literature that more strongly barred galaxies should---and do—have more dust and gas in their centers \citep{kormendy04}."
.. We find that for the most strongly. barred. &alaxies. (here are several possible morphologies the jrcummnuclear dust can take.," We find that for the most strongly barred galaxies, there are several possible morphologies the circumnuclear dust can take."
" This mav indicate (hat not all bars of a given strength Qy; funnel malerial toward the centers of galaxies with equal efficiency. potentially due to the effects ""pattern speed on bar efficiency. or simply the fact (hat Qy; is a one-parameter description “the bar."," This may indicate that not all bars of a given strength $Q_b$ funnel material toward the centers of galaxies with equal efficiency, potentially due to the effects of pattern speed on bar efficiency, or simply the fact that $Q_b$ is a one-parameter description of the bar."
 In the most strongly. barred. galaxies. there can be an LGD spiral whose aruis," In the most strongly barred galaxies, there can be an LGD spiral whose arms"
"The 21 em transition has long proved to be an extremely useful to probe the neutral hydrogen (H 1) in sourceboth the local and the , universe.",The 21 cm transition has long proved to be an extremely useful tool to probe the neutral hydrogen (H ) in both the local and the distant universe.
". In. particular, thena H 1 em emission hasthe been . to study. in detail. properties of the interstellar medium (ISM) Recently. the nearby galaxies in the local universe (Briggs 1990:Zwaan>al.1997.3005.andreferencestherein)..."," In particular, the H 21 cm emission has been used to study, in detail, properties of the interstellar medium (ISM) of the nearby galaxies in the local universe \citep[][and references therein]{br90,zw97,zw05}."
 Particularly for gas rich Large galaxies (at low and moderate distances) where the H I (ALFALFA) significantly bigger than the stellar disk. H 1 provide the not only on the dynamics of the particular galaxy Environment interest but also on the galaxy environment and on possible only of neighbouring galaxies (e.g.. Howard&Byrd1990:al.Sengupta.Dwarakanath&Saikia2009).," Particularly for gas rich spiral galaxies (at low and moderate distances) where the H disk is significantly bigger than the stellar disk, H observations provide information not only on the dynamics of the particular galaxy of interest but also on the galaxy environment and on possible interactions of neighbouring galaxies \citep[e.g.,][]{ho90,ro90,ka05,ho07,se09}."
. Cosmic evolution using the properties of neutral gas in galaxies also have important resulted on our understanding of star formation and. galaxy a, Cosmic evolution of the properties of neutral gas in galaxies also have important implications on our understanding of star formation and galaxy evolution.
 Verheijen it should be noted here that. due to weakness of 19 emission signal. detecting H 1 from galaxies even 219? moderate redshift ἐς =0.05) is a challenging task.," However, it should be noted here that, due to weakness of the emission signal, detecting H emission from galaxies even at moderate redshift $z 
> 0.05$ ) is a challenging task."
 Instead. galaxies 1 has been extensively used to probe ISM at high at (e.g.. but only in the intervening gas along a narrow line of sight towards the background andEN therefore can eo.not be as informative ∙∡⊲↜∡⊽∙as H T in↼ tool Kinematies andD. the dynamics ofm ∙∡∡the eas -within ∡∙ealaxies.," Instead, H absorption has been extensively used to probe ISM at high redshift but only in the intervening gas along a narrow line of sight towards the background source and therefore can not be as informative as H emission in the kinematics and the dynamics of the gas within galaxies."
 useddistant↝ however. attempts to detect H 1 at high of have been made with upgraded or new powerful receivers.," Recently, however, attempts to detect H emission at high $z$ have been made with upgraded or new powerful receivers."
 et H 1 like the ongoing Arecibo Legacy Fast ALFA spiral Survey. the H 1 All-Sky Survey (HIPASS). is H 1 All-Sky Survey CHIJASS) and the Arecibo Galaxy information Survey (AGES) are targeting detailed study of H I in nearby galaxies at 2. Z50.06(Barnes etal.2001:Langinteractions2003:Giovanellietal.2005a.b:Auld2006).," Large H surveys like the ongoing Arecibo Legacy Fast ALFA (ALFALFA) Survey, the H Parkes All-Sky Survey (HIPASS), the H Jodrell All-Sky Survey (HIJASS) and the Arecibo Galaxy Environment Survey (AGES) are targeting detailed study of H only in nearby galaxies at $z \lesssim 0.06$ \citep{ba01,la03,gi05a,gi05b,au06}."
. In the last Rots years. sensitive observations with very long integration times 2007: radio telescopes like Arecibo. GMRT. VLA and WSRT have of in a few detection ofHI from galaxies at 2<0.1:implications single galaxy in Abell 2218 at z =0.18(Zwaan. vanDokkum&evolution.2001).. one in Abell 2192 at + =0.19(Verheijen2004).However. galaxies in Abell 963 at > =0.21and 23 galaxies in Abell the at 2 =0.19(Verheijen etal.2007)and 20 optically selected at from the Sloan Digital Sky Survey (Catinella etal.2008)H redshifts between > =0.17—0.25.," In the last ten years, sensitive observations with very long integration times using radio telescopes like Arecibo, GMRT, VLA and WSRT have resulted in a few detection of H emission from galaxies at $z \gtrsim 0.1$: a single galaxy in Abell 2218 at $z = 0.18$ \citep{zw01}, , one in Abell 2192 at $z = 0.19$\citep{ve04}, 19 galaxies in Abell 963 at $z= 0.21$ and 23 galaxies in Abell 2192 at $z = 
0.19$ \citep{ve07} and 20 optically selected galaxies from the Sloan Digital Sky Survey \citep{ca08} at redshifts between $z = 0.17 - 0.25$."
Additionally. there have redshift measurements of neutral atomic hydrogen gas content from multiple galaxies using co-adding techniquefor galaxy clusters Abell 3128 at 2 =0.06.Abell 2218 at — 0.15. a sample of star- E-mail: at + =0.24and Abell370 at 2 =0.37(Zwaan 2009).," Additionally, there have been measurements of neutral atomic hydrogen gas content from multiple galaxies using co-addingtechnique for galaxy clusters Abell 3128 at $z = 0.06$, Abell 2218 at $z = 0.18$ , a sample of star-forming galaxies at $z= 0.24$ andAbell 370 at $z = 0.37$ \citep{zw00,ch01,la07,la09}. ."
discuss later. both the overall N-ray to optical spectra aud variability are very simular to those observed in the SAN JIsOS.L3658 system (Campanaetal.2002.200L).,"discuss later, both the overall X-ray to optical spectrum and variability are very similar to those observed in the SAX J1808.4–3658 system \citep{Camp02,Camp04}."
. The combined N-vay and optical data permit us to determine the origi of the energv supplied to the secoudary star., The combined X-ray and optical data permit us to determine the origin of the energy supplied to the secondary star.
 Ta particular. we fud that the total X-rav aud UV flux from the iutrabinary shock is insufficient to heat the face of the companion star to the observed temperature (Tjj~5100GSO0O IN).," In particular, we find that the total X-ray and UV flux from the intrabinary shock is insufficient to heat the face of the companion star to the observed temperature $T_{H}\sim5400-6800$ K)."
 Therefore. we conchide that the heating of the secondary. nimmst instead be due to the relativistic particle wind of the AISP. eoncrated at the expense of the rotational euergv of the uuderlving NS.," Therefore, we conclude that the heating of the secondary must instead be due to the relativistic particle wind of the MSP, generated at the expense of the rotational energy of the underlying NS."
" The rate of this energy loss is given by E—πο[ο where fis the NS moment of inertia. typically. assumed to be ,10 ο cme."," The rate of this energy loss is given by $\dot{E}=4\pi^2I\dot{P}/P^3$, where $I$ is the NS moment of inertia, typically assumed to be $10^{45}$ g $^2$."
2 Unfortunately.~¢ Li= Tuc W is rarely detected at radio frequencies which does uot allow a determination of the pulsar spindown rate 7.," Unfortunately, 47 Tuc W is rarely detected at radio frequencies which does not allow a determination of the pulsar spindown rate $\dot{P}$."
 Hence. we have no direct 1rieasure of £.Nonetheless. we cau use the correlation between the observed thermal rav huuinositv (Lxp) and £ found for the 17 Tuc MSP. to obtain a crude estimate of this paramcter.," Hence, we have no direct measure of $\dot{E}$.Nonetheless, we can use the correlation between the observed thermal X-ray luminosity $L_{\rm X,T}$ ) and $\dot{E}$ found for the 47 Tuc MSPs, to obtain a crude estimate of this parameter."
 Using Exp~(0.5Ls cress + aud the empirical relation logL£y.¢=0.59oeE|10.0 (Caiudlayetal.2002).. we obtain E~1«10 eres ft.," Using $L_{\rm X,T}\sim(0.5-1)\times10^{31}$ ergs $^{-1}$ and the empirical relation $\log L_{\rm
X,T}=0.59\log\dot{E}+10.0$ \citep{Grind02}, we obtain $\dot{E}\sim1\times 10^{35}$ ergs $^{-1}$."
" Asstumine an isotropic pulsar wind. we find that the total incident power ou the secondary star is Lg,dos1075 eres 1."," Assuming an isotropic pulsar wind, we find that the total incident power on the secondary star is $L_{\rm irr}\sim1\times10^{33}$ ergs $^{-1}$."
 This value is sufficient to heat the face of the companion star to the observed huuiuositv (Ly1«107? eyes +). if we allow or are-radiation efficiency of order 0.1.," This value is sufficient to heat the face of the companion star to the observed luminosity $L_{H}\sim1\times10^{32}$ ergs $^{-1}$ ), if we allow for a re-radiation efficiency of order 0.1."
 Furthermore. the flux from the MSP wind at the surface of the secondary (1077 ores 7s 4) is conducive to bloating of the star to a significantly larger radius (sceFig.LinPodsiad-owsld 1991).. provided that the particles coustituting the wind deposit their energy below the stellar photosphere.," Furthermore, the flux from the MSP wind at the surface of the secondary $\sim$$10^{12}$ ergs $^{-2}$ $^{-1}$ ) is conducive to bloating of the star to a significantly larger radius \citep[see Fig. 1 in][]{Pod91}, provided that the particles constituting the wind deposit their energy below the stellar photosphere."
 Given that the pulsar wind is probably composed of üuehlv relativistic electrons. positrous. and ions. which are able to penetrate deep iuto the stellar interior. this condition for expansion of the star can be satisfied. inplviug that the secondary star is iiost likely RL filliue.," Given that the pulsar wind is probably composed of highly relativistic electrons, positrons, and ions, which are able to penetrate deep into the stellar interior, this condition for expansion of the star can be satisfied, implying that the secondary star is most likely RL filling."
" Finally. the flux from the pulsar wind at L4 is cousisteut with the observed value of Exvp2ον1075 exgs s.+. if we take iuto account the particle acceleration efficiency €,c0.2 (Arons&Tavani1993).. as well as the fraction of the wind interacting with matter from the companion (~ 10%)."," Finally, the flux from the pulsar wind at $L_1$ is consistent with the observed value of $L_{\rm
X,NT}\approx3\times10^{31}$ ergs $^{-1}$, if we take into account the particle acceleration efficiency $\epsilon_{a}\simeq0.2$ \citep{Arons93}, as well as the fraction of the wind interacting with matter from the companion $\sim10^{-3}$ )."
 The compact nature of the LF Tuc W binary eusures that the iutrabinary shock is located im a relatively strong pulsar maguetic field., The compact nature of the 47 Tuc W binary ensures that the intrabinary shock is located in a relatively strong pulsar magnetic field.
 Therefore. we expect svuchrotrou cluission to be the principal enerev loss imechanisin in the shock.," Therefore, we expect synchrotron emission to be the principal energy loss mechanism in the shock."
" However. the proximity of the shock. wave to the secondary star miplies that the relativistic electrons in the shock are inunuersed ia a ""sea of optical photons enmauatiug from the secondary star."," However, the proximity of the shock wave to the secondary star implies that the relativistic electrons in the shock are immersed in a “sea” of optical photons emanating from the secondary star."
 Thus. inverse Compton scattering (ICS) may also be an nmuportaut production imechanisni for ligh-cucrey photons.," Thus, inverse Compton scattering (ICS) may also be an important production mechanism for high-energy photons."
" The magnetic field strength iuunuedciatelv upstream of the shock is given by By=|o/(τσ]τςcfPy2| where σ is the ratio of the maenetic energy flux to the kinetic enerev flux. f, is a geometric factor that defines he fraction of the skv iuto which the pulsar wind is enütted. and d is the distance between the MSP ain he shock (Arvons&Tavani1993)."," The magnetic field strength immediately upstream of the shock is given by $B_1=[\sigma/(1+\sigma)]^{1/2}(\dot{E}/cf_{p}d^2)^{1/2}$, where $\sigma$ is the ratio of the magnetic energy flux to the kinetic energy flux, $f_p$ is a geometric factor that defines the fraction of the sky into which the pulsar wind is emitted, and $d$ is the distance between the MSP and the shock \citep{Arons93}."
. For simplicity. we wil ake d=6.1«1079 cii. correspouding approximately to he distance from the MSP to Ly assumniug Msyjapb=1. AD. and ¢=60°.," For simplicity, we will take $d\approx6.4\times10^{10}$ cm, corresponding approximately to the distance from the MSP to $_1$ assuming $M_{\rm MSP}=1.4$ $_{\odot}$ and $i=60^{\circ}$."
" For au isotropic pulsar wind (f,=1). we obtain Byz2 € aud Byz30 € corresponding o the two possible cases of a kinetic energy. douinatec (c=0.003 as in the case of the Crab nebula) and a nagnctically dominated (0291) wind. respectively."," For an isotropic pulsar wind $f_{p}=1$ ), we obtain $B_1\approx 2$ G and $B_1\approx 30$ G corresponding to the two possible cases of a kinetic energy dominated $\sigma=0.003$ as in the case of the Crab nebula) and a magnetically dominated $\sigma\gg 1$ ) wind, respectively."
" This iuples a maeuetic field strength bevoud the shock of By—MB6G or By~90 C. respectively,"," This implies a magnetic field strength beyond the shock of $B_2=3B_1\sim 6$ G or $B_2\sim90$ G, respectively."
 Production of the observed £—0.3.8 keV pliotous via svuchrotron. therefore. requires relativistic electrons witli Loreutz factors ;=2.1.10οDS)?—1410!510.," Production of the observed $\varepsilon=0.3-8$ keV photons via synchrotron, therefore, requires relativistic electrons with Lorentz factors $\gamma=2.4\times10^5(\varepsilon/B_2)^{1/2}\sim1\times10^4-5\times10^5$."
 From these values. we obtain a radiative loss time of fau5dAO(5BS)Pod 60s (Rybicki&Lightman1979).," From these values, we obtain a radiative loss time of $t_{\rm
synch}=5.1\times10^8(\gamma B_2^2)^{-1}\sim1-60$ s \citep{Ryb79}."
". If we consider a power-law distribution of electron enereiesio.n4(5) xw5Pl"". where pis related to the photon index bv p=20|1 (Rvbicki&Lieltinan1979).. iuxl assune a roughly cylindrical shocked enmission regio1 with length /~2<1019 ci and radius ~2&10? cu. we find that the required electron density is à,~LO! or p,~105 7. corresponding to c=0.003 and σ> l. respectively."," If we consider a power-law distribution of electron energies i.e. $n_{e}(\gamma)\propto\gamma^{-p}$, where $p$ is related to the photon index by $p=2\Gamma+1$ \citep{Ryb79}, and assume a roughly cylindrical shocked emission region with length $l\sim2\times10^{10}$ cm and radius $\sim$$2\times10^{9}$ cm, we find that the required electron density is $n_e\sim10^7$ or $n_e\sim10^4$ $^{-3}$, corresponding to $\sigma=0.003$ and $\sigma\gg 1$ , respectively."
" These values imply energy deusities in electronso£, ~102οςολο ~105.109 Cres cii>.", These values imply energy densities in electronsof $U_e\sim10^2-5\times10^3$ or $U_{e}\sim10^5-5\times10^6$ ergs $^{-3}$.
 The value for ¢>Lis comparable to the inaguetic energy density Up=D$3/sz—d.300 erg 7., The value for $\sigma\gg 1$ is comparable to the magnetic energy density $U_{B}=B_2^2/8\pi\sim1-300$ ergs $^{-3}$.
 Thus. based ou equipartition of enerev arguments. the wind is most Likely magnetically douinated.," Thus, based on equipartition of energy arguments, the wind is most likely magnetically dominated."
" We note that if ICS were to dominate the N-ray enission. the raciating electrous need to be oulv weakly accelerated to +~100. implying radiative loss times of trey=(UpfUpi)faua~10100 hours where ται=RHcopli/(R.c)~d eres cin? ds the seed photon energev density. while Πρι Tj. aud AR. are the radius. temperature, aud distance from the surface of the secondary star. respectively."," We note that if ICS were to dominate the X-ray emission, the radiating electrons need to be only weakly accelerated to $\gamma\sim100$, implying radiative loss times of $t_{\rm ICS}=(U_{B}/U_{\rm ph})t_{\rm
synch}\sim10-100$ hours, where $U_{\rm ph}=R_c \sigma_B
T_c^4/(R_{*}c)\sim 1$ ergs $^{-3}$ is the seed photon energy density, while $R_{c}$, $T_{H}$, and $R_{*}$ are the radius, temperature, and distance from the surface of the secondary star, respectively."
" The implied C,~10* eres 7. however. greatly exceeds the values of Up aud Uy."," The implied $U_{e}\sim10^7$ ergs $^{-3}$, however, greatly exceeds the values of $U_{B}$ and $U_{\rm ph}$."
 Therefore. ICS is an uulikelv soft. X-ray production mechanisin in dr Tuc W. Future detailed. multinvaveleneth observatious of the lí Tue WO system may reveal amore information concerning the nature of the shock ciission. which. in tin. may provide insight ito the little uuderstood properties of AISP winds. collisionless relativistic shocks. and particle acceleration mechauisius.," Therefore, ICS is an unlikely soft X-ray production mechanism in 47 Tuc W. Future detailed multi-wavelength observations of the 47 Tuc W system may reveal more information concerning the nature of the shock emission, which, in turn, may provide insight into the little understood properties of MSP winds, collisionless relativistic shocks, and particle acceleration mechanisms."
 The existence of a reeularly eclipsed shock makes 17 Tuc W well suited for studies of these phenomena., The existence of a regularly eclipsed shock makes 47 Tuc W well suited for studies of these phenomena.
 The data presented here have revealed that 17 Tuc W exhibits N-ray variability that is unique among the ISPs (as evident in Fig., The data presented here have revealed that 47 Tuc W exhibits X-ray variability that is unique among the MSPs (as evident in Fig.
 1)., 1).
 These variations can be most casily explained by the presence of a relativistic shock within the binary that is regularly eclipsed by the secondary star., These variations can be most easily explained by the presence of a relativistic shock within the binary that is regularly eclipsed by the secondary star.
 An intrabinary shock is also believed to be present in PSR D1957|20. the so-called “black widow” eclipsingpulsar (Fruchter.Stinebring.&Taylor 1988)..," An intrabinary shock is also believed to be present in PSR B1957+20, the so-called ""black widow"" eclipsingpulsar \citep{Fru88}. ."
 This MSP has a nou-thermal spectrum with P—1.940.5 aud Ly=2.7<10°! ores 1 (0.5-7.0 keV) (Stappers 2003).. for an assumed distance of 2.5 kpe," This MSP has a non-thermal spectrum with $\Gamma =
1.9\pm0.5$ and $L_{X} = 2.7\times 10^{31}$ ergs $^{-1}$ (0.5-7.0 keV) \citep{Stap03}, , for an assumed distance of 2.5 kpc"
where £67) is 2pCE of the whole matter. £(7) is 2pCF of quasars and 6 is the bias parameter.,"where $\xi_{m}(r)$ is 2pCF of the whole matter, $\xi(r)$ is 2pCF of quasars and $b$ is the bias parameter."
" The second problem: of the 3-dimensional analysis of the matter distribution is due to the fact that the observed redshifts of extragalactic objects are ""contaminated! by measurement errors and non-lLlubble motions.", The second problem of the 3-dimensional analysis of the matter distribution is due to the fact that the observed redshifts of extragalactic objects are `contaminated' by measurement errors and non-Hubble motions.
 The distances calculated from these redshifts without taking into account the unknown peculiar velocities are. called. distances in redshift-space (in contrast to the real space)., The distances calculated from these redshifts without taking into account the unknown peculiar velocities are called distances in redshift-space (in contrast to the real space).
 As our Universe is isotropic. the correlation function. must. be spherically symmetric in the real-space.," As our Universe is isotropic, the correlation function must be spherically symmetric in the real-space."
 But in the redshift-space it appears to be distorted., But in the redshift-space it appears to be distorted.
 On smaller. scales. the profile of galaxies 2pCTE is stretched along the line of sight (‘Finger of Cod! elfect) due to virial velocities of objects inside the galaxy clusters (this can be neglected for quasars if we consider +7 1). weir random: velocities ancl redshift errors.," On smaller scales the profile of galaxies 2pCF is stretched along the line of sight (`Finger of God' effect) due to virial velocities of objects inside the galaxy clusters (this can be neglected for quasars if we consider $z>1$ ), their random velocities and redshift errors."
 This cllect is especially. noticeable for quasar pairs with the projected. linear separations =2 Alpe. where the SDSS data are expected to be incomplete (Hennawictal. 2006).," This effect is especially noticeable for quasar pairs with the projected linear separations $\lesssim2$ Mpc, where the SDSS data are expected to be incomplete \citep{hennawi_06}."
. On larger scales the 2pCb profile is IHlattened along the line of sight (The Bull’s eve’ or Ixaiser(LOST) effect) due to the gravitational infall to density. inhomogeneities: this kind of redshift-space. distortion. dominates on. the linear scales., On larger scales the 2pCF profile is flattened along the line of sight (`The Bull's eye' or \citet{kaiser_1987} effect) due to the gravitational infall to density inhomogeneities; this kind of redshift-space distortion dominates on the linear scales.
 These cllects are parameterized by line-of-sight pairwise velocity. dispersion (we2 and infall. parameter lt, These effects are parameterized by line-of-sight pairwise velocity dispersion $\langle w^{2}\rangle^{1/2}$ and infall parameter $\beta$.
 is worth to note that the non-Llubble motions and redshift errors are not the only sources of redshift-space distortions., It is worth to note that the non-Hubble motions and redshift errors are not the only sources of redshift-space distortions.
 One more elfect of geometric Uattening that can lead to distortion of 2pCE can be due to a wrong choice of cosmological parameters Oy. Qa: this provides an acelitional tool for estimation of these parameters by means of a geometrical test of Aleock&Paczynski(1979).," One more effect of geometric flattening that can lead to distortion of 2pCF can be due to a wrong choice of cosmological parameters $\Omega_{M}$, $\Omega_{\Lambda}$; this provides an additional tool for estimation of these parameters by means of a geometrical test of \citet{alcock_paczynski_1979}."
.. Phe redshift-space 2pCT of quasars can be in principle used for estimation of all parameters (23. (uw7 ancl cosmological ones) simultaneously.," The redshift-space 2pCF of quasars can be in principle used for estimation of all parameters $\beta$, $\langle w^{2}\rangle^{1/2}$ and cosmological ones) simultaneously."
 But clue to a degencracy between the geometric distortions and the redshift-space distortions (sec. e.g.. Hovleetal. (2002))) this problem is complicated.," But due to a degeneracy between the geometric distortions and the redshift-space distortions (see, e.g., \citet{hoyle_2002}) ) this problem is complicated."
 Hovleetal.(2002). and daAngelaetal.(2005) proposed. a method that allows to break this degeneracy by means of combination of the Aleock&Paczvnski(1979). test with that based on evolution of the quasar clustering amplitude. which has a different dependence on 2(2) ancl ο)(01.," \citet{hoyle_2002} and \citet{daAngela_2005} proposed a method that allows to break this degeneracy by means of combination of the \citet{alcock_paczynski_1979} test with that based on evolution of the quasar clustering amplitude, which has a different dependence on $\beta(\bar{z})$ and $\Omega_{M}(0)$."
 As we cannot estimate the non-lLlubble motion of cach quasar independently. the effects of the redshift-space distortion are at present the only source. of. statistical information about proper velocities of quasars.," As we cannot estimate the non-Hubble motion of each quasar independently, the effects of the redshift-space distortion are at present the only source of statistical information about proper velocities of quasars."
 On the other hand. these ellects prevent direct determination of 3D 2pCE that involves line-of-sight distances between objects determined from z-measurements.," On the other hand, these effects prevent direct determination of 3D 2pCF that involves line-of-sight distances between objects determined from $z$ -measurements."
 This urges us to use only the projected. distances oa (ie. orthogonal to the line of sight. which may be considered. as independent of proper motions) to determine the projected. 2pCE and then to restore the real-space 2pCT.," This urges us to use only the projected distances $\sigma$ (i.e. orthogonal to the line of sight, which may be considered as independent of proper motions) to determine the projected 2pCF and then to restore the real-space 2pCF."
 Lt is well known that. such reconstruction of the real-space 2pCT from projected one is mathematically ill-posec problem., It is well known that such reconstruction of the real-space 2pCF from projected one is mathematically ill-posed problem.
 However. most. authors avoicl this cillieulty using a concrete functional. form of 2pCE.," However, most authors avoid this difficulty using a concrete functional form of 2pCF."
 Typically 2pCbk is represented in a power-law form £r)=QGufr) rough it is clear that 2pCT slope and correlation length may be dillerent on dillerent interval.," Typically 2pCF is represented in a power-law form $\xi(r)=\left(r_0/r\right)^{\gamma}$, though it is clear that 2pCF slope and correlation length may be different on different interval."
 For example. daAngelaetal.(2005). showed that double Ποοἱ gives à goodfit to 2pCT of quasars distribution with £(r)=(6.0re over scales of 1&r«10h 1 Alpe and £=(τος) over scales of 10«kr<40 fb+ Alpe or a quasar sample from 2QZ catalogue with recshilts within the range 0.3<z«2.2.," For example, \citet{daAngela_2005} showed that double model gives a goodfit to 2pCF of quasars distribution with $\xi(r)=\left(6.0/r\right)^{1.45}$ over scales of $1<r<10$ $h^{-1}$ Mpc and $\xi=\left(7.25/r\right)^{2.30}$ over scales of $10<r<40$ $h^{-1}$ Mpc for a quasar sample from 2QZ catalogue with redshifts within the range $0.3<z<2.2$."
 Using quasar catalogue of spectroscopically confirmed. quasars (Schneider.Hall&Richards2OOT) based. on the Sth data release of SDSS tossetal.(2009). obtained ry=5.45ο h| Mpeand ~=1.90Qo. over scales of 1<c0130 h+ Mpe for ow-redshift (0.8«z2.2) quasars. and for high-redshift (2.9«z5.4) quasars from the same catalogue Shenctal.(2007) obtained my=15τή 3 Alpe and 5=2.00.3 over scales 4«&6«150 5.+ Alpe.," Using quasar catalogue of spectroscopically confirmed quasars \citep{Schneider_2007} based on the 5th data release of SDSS \citet{ross_2009} obtained $r_{0}=5.45^{+0.35}_{-0.45}$ $h^{-1}$ Mpcand $\gamma=1.90^{+0.04}_{-0.03}$ over scales of $1<\sigma<130$ $h^{-1}$ Mpc for low-redshift $0.3<z<2.2$ ) quasars, and for high-redshift $2.9<z<5.4$ ) quasars from the same catalogue \citet{shen_2007} obtained $r_{0}=15.2\pm2.7$ $h^{-1}$ Mpc and $\gamma=2.0\pm0.3$ over scales $4<\sigma<150$ $h^{-1}$ Mpc."
 Note that similar large correlation length was obtained for racio-sources by Mauch&Sacer(2003) and for X-ray. sources by Plionisetal.(2004) ancl Dasilakosetal.(2004):: at least a part of both of these object types are considered to be AGNs., Note that similar large correlation length was obtained for radio-sources by \citet{blake_2003} and for X-ray sources by \citet{plionis_2004} and \citet{basilakos_2004}; at least a part of both of these object types are considered to be AGNs.
 In addition to redshift dependence of the quasar clustering confirmed by Croometal.(2005):Myers(2006.2007):Porciani.daAngelaetal. (2008).. some authors (Porciani&Norbere2006:daAngelaetal.2008:Mountrichas2009) argue that quasar clustering depends weakly on Luminosity.," In addition to redshift dependence of the quasar clustering confirmed by \citet{croom_2005,myers_2006,myers_2006_1,porciani_2004,porciani_2006,daAngela_2008}, some authors \citep{porciani_2006,daAngela_2008,Mountrichas_2009} argue that quasar clustering depends weakly on luminosity."
 Hence speaking about representation of 2pCbk in power-law form in the present paper we always mean that 2pCT is averaged over quasars with cdillerent luminosities and over certain redshift range and distance intervals described: below., Hence speaking about representation of 2pCF in power-law form in the present paper we always mean that 2pCF is averaged over quasars with different luminosities and over certain redshift range and distance intervals described below.
 La particular. when dealing with the bias estimates we confine ourselves to the intervals where our results may be compared with the linear theory of matter inhomogeneity.," In particular, when dealing with the bias estimates we confine ourselves to the intervals where our results may be compared with the linear theory of matter inhomogeneity."
 The most complete full investigation on non-ETubble motions of quasars together with cosmological parameters was done hy 2k team for 2dk QSO Survey (see Croomctrametal. (2004))).," The most complete full investigation on non-Hubble motions of quasars together with cosmological parameters was done by 2dF team for 2dF QSO Survey (see \citet{croom_2005,daAngela_2005,hoyle_2002,outram_2004}) )."
 Eg. dàAngelaetal.(2005). obtained Oy=035515 and 3=0.50512 (for the sample mean redshift 2=— 1.4)., E.g. \citet{daAngela_2005} obtained $\Omega_{M}=0.35^{+0.19}_{-0.13}$ and $\beta=0.50^{+0.13}_{-0.15}$ (for the sample mean redshift $\bar{z}=1.4$ ).
 In these studies the value of pairwise velocity. dispersion of quasars was usually treated. as fixed xweameter and its value was chosen either. from. Hubble volume simulations or following previous results on galaxy orwise velocity dispersion. assuming that this value does not evolve strongly with time., In these studies the value of pairwise velocity dispersion of quasars was usually treated as fixed parameter and its value was chosen either from Hubble volume simulations or following previous results on galaxy pairwise velocity dispersion assuming that this value does not evolve strongly with time.
 For galaxies. we have more definite results for the velocity clispersion obtained: from. he redshift-space distortions.," For galaxies, we have more definite results for the velocity dispersion obtained from the redshift-space distortions."
 The first estimate of Davis&Peebles (1983)... 340+40 κι. remained a canonica one almost a decade.," The first estimate of \citet{davis_peebles_1983}, $340\pm40$ km/s, remained a canonical one almost a decade."
 However. later Alo.Jing&Borner993) showed that the value of pairwise peculiar velocity dispersion depends strongly on the sample.," However, later \citet{mo_1993} showed that the value of pairwise peculiar velocity dispersion depends strongly on the sample."
 Later this resul was confirmed. by values 5404180 km/s. given by Marzk« for the Second Center for Astrophysics Galaxy {οκαί Survey (CEX2) and. the Southern Sky Reclshil Survey (SSRS2). and 416£36 km/s. given by Ratclillee for Durham/United Ixingdom Schmidt Telescope (UIxS'T) Galaxy Redshift Survey and others.," Later this result was confirmed by values $540\pm180$ km/s, given by \citet{marzke_1995} for the Second Center for Astrophysics Galaxy Redshift Survey (CfA2) and the Southern Sky Redshift Survey (SSRS2), and $416\pm36$ km/s, given by \citet{ratcliffe_IV_1998} for Durham/United Kingdom Schmidt Telescope (UKST) Galaxy Redshift Survey and others."
 Ratclillectal. also presented the value 7= 0.4840.11. which agrees well with later results. such as the results of Hawkinsetal. for 2dE Galaxy Hedshift Survey.," \citet{ratcliffe_IV_1998} also presented the value $\beta=0.48\pm0.11$ , which agrees well with later results, such as the results of \citet{hawkins_2003} for 2dF Galaxy Redshift Survey."
 A similar value. 330 kms. was obtained for luminous red galaxies (LAC) rom the 2dE-SDSS LAG and QSO (28LAQ) survey by )..," A similar value, 330 km/s, was obtained for luminous red galaxies (LRG) from the 2dF-SDSS LRG and QSO (2SLAQ) survey by \citet{ross_2008}. ."
 In this paper. we present new results on the 2pCTE slope and correlation length. infall parameter 2 using the last 7-th," In this paper, we present new results on the 2pCF slope and correlation length, infall parameter $\beta$ using the last 7-th"
with amplitude that increases with the relative inclination (in particular. coplanar orbits keep constant eccentricity. ey).,"with amplitude that increases with the relative inclination (in particular, coplanar orbits keep constant eccentricity, $e_1$ )."
" When 7?&Po40°. there are stationary solutions (7= consl. c,=/(5/3)cos?iconsi. wp,=£907). and lxozai eveles whereVel 7. e, and oscillate around the stationary solutions."," When $i>i_{c} \approx 40^{\circ}$, there are stationary solutions $i=const$ , $e_{1}=\sqrt{1-(5/3)\,\cos^2{i}}=const$, $\omega_{1}=\pm 90^{\circ}$ ), and Kozai cycles where $i$ , $e_1$ and oscillate around the stationary solutions."
" ? showed that the secular motion of the inner binary when 0x;90 (prograde orbits) is. in the general problem (mi,= 0). equivalent to the inner restricted problem (m,— 0). as long as Defining.X=Ls/L,. we can write Equation (21)) as The left-hand. side. of Eq. ) "," \citet{Farago&Laskar2010} showed that the secular motion of the inner binary when $0\le i\le 90^\circ$ (prograde orbits) is, in the general problem $m_1\ne 0$ ), equivalent to the inner restricted problem $m_1=0$ ), as long as Defining$X=L_2/L_1$, we can write Equation \ref{limit0}) ) as The left-hand side of Eq. \ref{limit}) )"
is a second degree polvnomial in No which is a convex function with two roots διςθ and 5/22Noo Ny., is a second degree polynomial in $X$ which is a convex function with two roots $X_1<0$ and $5/2\ge X_2>X_1$ .
 Pherefore. inequality (eq. 21))," Therefore, inequality (Eq. \ref{limit0}) )"
 is verified if Lí/Lo»<2/5 which is generally. true i£ 1l (hierarchical svstem) unless mu|mymo, is verified if $L_1/L_2<2/5$ which is generally true if $a_1/a_2\ll 1$ (hierarchical system) unless $m_0+m_1 \gg m_2$.
 Equations (17))and (18)) with j=2 describe the secular evolution of the outer. binary’s eccentricitv. and argument of pericentre., Equations \ref{gdot}) )and \ref{omdot}) ) with $j=2$ describe the secular evolution of the outer binary's eccentricity and argument of pericentre.
 We saw that the secular quackupole Hamiltonian (eq. 6)), We saw that the secular quadrupole Hamiltonian (Eq. \ref{hamiltonian}))
 does not depend on c». hence from Eq. (17))," does not depend on $\omega_2$, hence from Eq. \ref{gdot}) )"
 with j=2. the conjugate momentum. Go. and thus the cecentricity. es. are constant.," with $j=2$, the conjugate momentum, $G_2$ , and thus the eccentricity, $e_2$, are constant."
 From Iq. (18)), From Eq. \ref{omdot}) )
 with j —2weobtain the outer binary pericentres precession rate Lligher order secular octupole terms cause long-term small amplitude oscillations in e; and eo». which are more important for small to. moderate values of the relative inclination. 7 (??7)..," with $j=2$ we obtain the outer binary pericentre's precession rate Higher order secular octupole terms cause long-term small amplitude oscillations in $e_1$ and $e_2$, which are more important for small to moderate values of the relative inclination, $i$ \citep{Krymo&Mazeh1999MNRAS,Ford_etal2000ApJ,Lee&Peale2003ApJ}."
 The outer binary precession rate (Iq. 23)), The outer binary's precession rate (Eq. \ref{om2dotgen}) )
 depends on the secular motion of sthe inner binary., depends on the secular motion of the inner binary.
 Moreover. in the invariant reference Lrame (Fig.," Moreover, in the invariant reference frame (Fig."
 1) we have Since αιa» (hierarchical svstem) then. in ecneral. CC (unless mu|mia m») thus sinfol tthe outer binarys motion coincides approximately with the invariant plane.," 1) we have Since $a_1\ll a_2$ (hierarchical system) then, in general, $G_1\ll G_2$ (unless $m_0+m_1\gg m_2$ ) thus $\sin{I_2} \ll 1$ the outer binary's motion coincides approximately with the invariant plane."
 Therefore. we express the right hand. side of Eq. (23))," Therefore, we express the right hand side of Eq. \ref{om2dotgen}) )"
 using the reference plane of the outer hinary’s orbit. ssetting /»=0and ἐν=7 in Eqs. (8)). (9))," using the reference plane of the outer binary's orbit, setting $I_2=0$and $I_1=i$ in Eqs. \ref{ci}) ), \ref{sisom}) )"
 thus obtaining where ϐ=cosi., thus obtaining where $\theta=\cos{i}$.
 Equation (25)) is an approximation of the precession pale. we. because the outer binary’s orbit is notfixed. but exhibits small amplitude oscillations around the invariant plane.," Equation \ref{om2dotgen0}) ) is an approximation of the precession rate, $\dot{\omega}_2$, because the outer binary's orbit is notfixed but exhibits small amplitude oscillations around the invariant plane."
" The angle w, on the right hand. side of Ίσα. (26))", The angle $\omega_1$ on the right hand side of Eq. \ref{atheta}) )
 is measured. with respect to the outer binarys orbit. or. equivalentlv. with respect to the invariantplane?.," is measured with respect to the outer binary's orbit or, equivalently, with respect to the invariant."
. his formulation is necessary in order to describe the motion of the inner binary (???)..," This formulation is necessary in order to describe the motion of the inner binary \citep{Kozai1962AJ,Kinoshita&Nakai2007,Farago&Laskar2010}."
 However. the angle a. represents the location of the outer binarys periapse with respect to the intersection with the observer's plane (when dealing with radial velocity data. this is the plane orthogonal to the line of sight).," However, the angle $\omega_2$ represents the location of the outer binary's periapse with respect to the intersection with the observer's plane (when dealing with radial velocity data, this is the plane orthogonal to the line of sight)."
 The long-term evolution of Ixozai evles (which exist. if Poldo840°) was investigated. by 2?2..," The long-term evolution of Kozai cyles (which exist if $i>i_{c}\approx 40^\circ$ ) was investigated by \citet{Eggleton&Kiseleva2001ApJ,Fabrycky&Tremaine2007,Wu&Murray2007}."
 Typically. if ey becomes close to unity during a Ixozai ονο]ο. a combination of tidal evolution and relativistic ellects. will eventually disrupt the Ixozai evele and freeze the relative inclination. {ἐς," Typically, if $e_1$ becomes close to unity during a Kozai cycle, a combination of tidal evolution and relativistic effects will eventually disrupt the Kozai cycle and freeze the relative inclination, $i$."
 Phis will be followed by tical clamping of the semi-major axis. αι. and eccentricity. ey.," This will be followed by tidal damping of the semi-major axis, $a_1$, and eccentricity, $e_1$."
" Phe end state of a IxXozai evele hat reaches e,21 will be a tighter inner binary (smaller a=ayfas) on a circular orbit.", The end state of a Kozai cycle that reaches $e_1\approx 1$ will be a tighter inner binary (smaller $\alpha=a_1/a_2$ ) on a circular orbit.
 Obviously. ifa «1 then. as doexene. the precession of the outer binary’s orbit. will x slow thus clillicult to detect from observational data.," Obviously, if $\alpha\ll 1$ then, as $\dot{\omega}_2 \propto \alpha^2\,n_2$, the precession of the outer binary's orbit will be slow thus difficult to detect from observational data."
 On he other hand. orbits nearby 10 [xozai stationary solution are less prone to undergo tidal evolution ancl should. keep he original value of a.," On the other hand, orbits nearby the Kozai stationary solution are less prone to undergo tidal evolution and should keep the original value of $\alpha$."
 We will. therefore. assume three scenarios for the inner jnarv's motion in the invariant plane reference frame : In all scenarios above the precession rate. dg» is approximately constant.," We will, therefore, assume three scenarios for the inner binary's motion in the invariant plane reference frame : In all scenarios above the precession rate, $\dot{\omega}_2$ is approximately constant."
 In Fig., In Fig.
 2 we plot the normalized precession rate. οἱ given by Eq. (26)).," 2 we plot the normalized precession rate, $A$ given by Eq. \ref{atheta}) ),"
 when e;=0 and at the Wozai stationary solution., when $e_1=0$ and at the Kozai stationary solution.
 We see that when e;=0. precession is prograde when /«54.73 and retrograde when 754.737.," We see that when $e_1=0$, precession is prograde when $i<54.73^\circ$ and retrograde when $i>54.73^\circ$."
 At the ]xozai stationarysolution. which exists only when 40°. precession is retrogradewhen 7245°.," At the Kozai stationarysolution, which exists only when $i>i_{c}\approx 40^\circ$ , precession is retrogradewhen $i>45^\circ$."
 ligure 2 shows the normalized. precession rate. 2X. for OF«i90 (prograde orbits).," Figure 2 shows the normalized precession rate, $A$ , for $0^\circ<i<90^\circ$ (prograde orbits)."
 However. we saw previously that Eq. (10))," However, we saw previously that Eq. \ref{hamiltonian0}) )"
 is invariant with respect to the transformation PorLso' i| hencethe precession rate (eq. relatheta)," is invariant with respect to the transformation $i\rightarrow 180^\circ-i$ , hencethe precession rate (Eq. )"
 is the same for prograde (inclination 7) or retrograde (inclination Iso’ 7) orbits., is the same for prograde (inclination $i$ ) or retrograde (inclination $180^\circ-i$ ) orbits.
" We performed numerical integrations of the equations of motion of hierarchicaltriple star svstems with parameters mo= M.. ag=3.0 AU. ο= 0.2. and initial anglesfo— Qf,=Ὡς andw,=90°."," We performed numerical integrations of the equations of motion of hierarchicaltriple star systems with parameters $m_2=M_{\odot}$ , $a_2=3.0$ AU, $e_2=0.2$ , and initial angles$I_2=0^{\circ}$ , $\Omega_1=\Omega_2$ and$\omega_1=90^{\circ}$ ."
" The inner binary had my,=0.08M. and my=0.42 M.. semi-major axis ratioa= ayfas."," 	The inner binary had $m_1=0.08\,M_{\odot}$ and $m_0=0.42\,M_{\odot}$ , semi-major axis ratio$\alpha=a_1/a_2$ ."
 We chose two configurations: (1) 7=0 and, We chose two configurations: (i) $i=0$ and
and quasars are basically the same. aud differ oulv i it proportion of light coming from the active nucleus arc the hos ealaxy. so we do uot make a distinction between these oyects: the iuportaut feature is the broadening of IL.,"and quasars are basically the same, and differ only in the proportion of light coming from the active nucleus and the host galaxy, so we do not make a distinction between these objects; the important feature is the broadening of $H_\beta $."
 Fig., Fig.
 3 eives a zoon of Fie., 3 gives a zoom of Fig.
 2a for the object 2 aro IT; iux OIL lines which shows better the broadening of IL;, 2a for the object 2 around $H_\beta $ and OIII lines which shows better the broadening of $_\beta$.
 For t16 object the broadening is similar but the signal/ioise ratio is sinaller aud xxhaps uot conclusive.," For the object 3, the broadening is similar but the signal/noise ratio is smaller and perhaps not conclusive."
 A high contrast ὩςTween the widths of the LALTOW ale the wide ines cannot be expected because the aperti used n otr slit produce a large iistrunental broadoeni of the lues., A high contrast between the widths of the narrow and the wide lines cannot be expected because the aperture used in our slit produce a large instrumental broadening of the lines.
 These spectra are simular to otjer spec for quasars/Sevterts 1 iun other examples of anomalous redshits (Burbicdec 1995. 1997).," These spectra are similar to other spectra for quasars/Seyferts 1 in other examples of anomalous redshifts (Burbidge 1995, 1997)."
" NOrCcovor. hey are poiit-like olyjects (FWIIM equal to the secine: ~-- 1.07) which is αποher expected featurein this kind of οjects,"," Moreover, they are point-like objects (FWHM equal to the seeing: $\approx 1.0''$ ) which is another expected feature in this kind of objects."
 οher authors (Durbidee 1995. 1997: Arp et al.," Other authors (Burbidge 1995, 1997; Arp et al."
 20H) have aπο reported the detection of quasius/Sevferts l apparently ejected by a paren Sevtert galaxy., 2001) have also reported the detection of quasars/Seyferts 1 apparently ejected by a parent Seyfert galaxy.
 If we did LO trust either the argunueut of the broadenuiug of IL; nor the argument of heir being poi-[like objects. they would be narrow enission ine exteuded objects.," If we did not trust either the argument of the broadening of $_\beta $ nor the argument of their being point-like objects, they would be narrow emission line extended objects."
 They would be III galaxies or LINERS because Roy=ο... =1.2 aud 5.5 respectively for objects 2 ane 3. while Sevtert 2 should have this ratio larecr than 12.5 (Dessauges-Zavadsky ot al.," They would be HII galaxies or LINERs because $R_{23}\equiv \frac{[OII]+[OIIIa]+[OIIIb]}{H_\beta}=$ 4.2 and 5.5 respectively for objects 2 and 3, while Seyfert 2 should have this ratio larger than 12.5 (Dessauges-Zavadsky et al."
 2000)., 2000).
 They should uot be LINERs because η=2.1 aud 1.0 respectively for objects 2 and 3. lavecr than 0.5 (Filippenko Terevich 1992).," They should not be LINERs because $\frac{[OIIIb]}{H_\beta}=2.4$ and 1.0 respectively for objects 2 and 3, larger than 0.5 (Filippenko Terlevich 1992)."
 Hence. they would be TTI ealaxies.," Hence, they would be HII galaxies."
 NGC 7603D avd the filament present absorption lines. respectively with redshifts 0.058 and 0.030. (like NGC7603).," NGC 7603B and the filament present absorption lines, respectively with redshifts 0.058 and 0.030 (like NGC7603)."
 Tn Fig., In Fig.
 2b. it is shown a part of the spectra. where we can idenify IL; OI aud Mel. The filament zones were taken as a sun of ST coluunus (0.1588 arceseconds cach) in the zone l aud 173 columns in the zoue 2.," 2b, it is shown a part of the spectra, where we can identify $_\beta$, OIII and MgI. The filament zones were taken as a sum of 87 columns (0.188 arcseconds each) in the zone 1 and 173 columns in the zone 2."
 Although the idenication of Lines for the fibunent is not as clear as for the emission liue oljects (because the sjenal/uoise ratio is lower). we can tentatively attribute to it a redshift of 0.030 COUSINent wwith the δις7603 redshift.," Although the identification of lines for the filament is not as clear as for the emission line objects (because the signal/noise ratio is lower), we can tentatively attribute to it a redshift of 0.030 consistent with the NGC7603 redshift."
 This meaus that we do not sec a progressive change of the redshift between 0.029 aud 0.057. which would be expected if |oth galaxies were at the sane distance and the differeut redshit were due to a Doppler effect of peculiar motions.," This means that we do not see a progressive change of the redshift between 0.029 and 0.057, which would be expected if both galaxies were at the same distance and the different redshift were due to a Doppler effect of peculiar motions."
 This is. in some we. the least problematic of our measures.," This is, in some way, the least problematic of our measures."
" It would ]ο ideal to have longer exposures or a larger telescope to confi this meastrement. although im iu Case, the most remarkable fact here is the redshift of filament.objects J1(NCC 1T603D3-3 rather than the redshift of the "," It would be ideal to have longer exposures or a larger telescope to confirm this measurement, although in any case, the most remarkable fact here is the redshift of objects 1(NGC 7603B)-3 rather than the redshift of the filament."
NGC 7603B is a galaxy. with magutude mp=16.8 (Sharp 1986) and we have measured uaenitudes mj;= 2].8axd ing=21.LE respectively for oljects 2 and 3 (table 2)., NGC 7603B is a galaxy with magnitude $m_B=16.8$ (Sharp 1986) and we have measured magnitudes $m_R=21.8$ and $m_R=21.4$ respectively for objects 2 and 3 (table \ref{Tab:objetos}) ).
" Ttose two objects are more proniicut iu blue plates than i1 red plates (Sharp 1986): object 2 is even visible iu the blue POSSII plates Gvith limiting maenitude between 214 αid 21.5). so we cau be sure that he equivalent Hip, is not züuter than z21.9. even brighter if there were some extinction through the flament."," Those two objects are more prominent in blue plates than in red plates (Sharp 1986); object 2 is even visible in the blue POSSII plates (with limiting magnitude between 21.0 and 21.5), so we can be sure that the equivalent $m_{b_j}$ is not fainter than $\approx 21.9$, even brighter if there were some extinction through the filament."
 U) to these maguitudes. we have Ny~& ? (from complete galaxy counts: Aetealfe et al.," Up to these magnitudes, we have $N_1\sim 8$ $^{-2}$ (from complete galaxy counts: Metcalfe et al."
 1991): aud No~Ns-T0350 P depending ou the classification o the oljjects: το it they were quasars/Sevtert 1 (fromconplete quasar counts: Dovle et al.," 1991); and $N_2\sim N_3\sim 70-350$ $^{-2}$, depending on the classification of the objects: $\sim 70$ if they were quasars/Seyfert 1 (from complete quasar counts: Boyle et al."
 19913. or 5 tines more 1 they were IIT galaxies of tle emission li16 objects are quasars/Sevtert 1axd ave ΠΠ ealaxies: IIo et al.," 1991), or 5 times more if they were HII galaxies of the emission line objects are quasars/Seyfert 1 and are HII galaxies; Ho et al."
 1997. Alever et al.," 1997, Meyer et al."
 POOL)., 2001).
 That is. there should be one object like these per cach square of 3-7 arcuο size (20 arciuimute size for NOC 7603B): auch larecr tvan the area of the filament (~100 AYCSOCTP ).," That is, there should be one object like these per each square of 3-7 arcminute size (20 arcminute size for NGC 7603B); much larger than the area of the filament $\sim 100$ $^2$ )."
 We have clearly shown that two of the ο emission lues objects in the filament have redshifts very much, We have clearly shown that two of the compact emission lines objects in the filament have redshifts very much
(especially iu the Z baud) are probably not significant.,(especially in the $I$ band) are probably not significant.
 The helt curves will be analysed further in Sect.3., The light curves will be analysed further in Sect.3.
 Spectroscopic observatious were gathered with au objective. priun attached to the 60/90. cii. Scliniclt telescope at Piszkésstetó Station of Noulkoly Observatory. between 26th aud 2sth February. 2000 (JD 2151601 - 03). when SN 2000E was about 1 inouth past maxima.," Spectroscopic observations were gathered with an objective prism attached to the 60/90 cm Schmidt telescope at Piszkésstető Station of Konkoly Observatory, between 26th and 28th February, 2000 (JD 2451601 - 03), when SN 2000E was about 1 month past maximum."
 The images were exposed outo au electronically cooled Thomson 1536«1021 CCD-chip (readout noise about 16 έ V, The images were exposed onto an electronically cooled Thomson $1536 \times 1024$ CCD-chip (readout noise about 16 $e^-$ ).
 The dispersion axis was aligned in the ποτ direction. along the srorter side of the CCD-chip.," The dispersion axis was aligned in the north-south direction, along the shorter side of the CCD-chip."
 An objective prin spectrograph is certainly not au ideal tool for SN specroscopy., An objective prism spectrograph is certainly not an ideal tool for SN spectroscopy.
 However. this was the only spectroscovic dustriment available to us at that time.," However, this was the only spectroscopic instrument available to us at that time."
 A considerable unuuboer of image processing steps were necessary to extract the SN from the sieared spectra. of the host galaxy., A considerable number of image processing steps were necessary to extract the SN from the smeared spectrum of the host galaxy.
 The location of the SN. spectrm was determined from an intensity plot alone the line perpendicular to the dispersion axis., The location of the SN spectrum was determined from an intensity plot along the line perpendicular to the dispersion axis.
 At first. this was possible only in the blue region where the host galaxy showed neeheible contribution.," At first, this was possible only in the blue region where the host galaxy showed negligible contribution."
 The red side. however. was heavily contaminated by the smeared backeround spectrin of the host ealaxy.," The red side, however, was heavily contaminated by the smeared background spectrum of the host galaxy."
 Removal of this backeromud was essential to obtain reliable SN spectra., Removal of this background was essential to obtain reliable SN spectra.
 The easier way to correct for the galaxy backeromud would have been the usage of an objective priui picture of the host galaxy without the SN., The easier way to correct for the galaxy background would have been the usage of an objective prism picture of the host galaxy without the SN.
 Si1ος it was not possible for us. we had to choose another. more approximative approach.," Since it was not possible for us, we had to choose another, more approximative approach."
 First. the ceutral peak of the backeround galaxy spectrum was identified vistally.," First, the central peak of the background galaxy spectrum was identified visually."
 Tien. the galaxy naage was cut into two pieces at this οentral ridge. and the western part (includiugthe SN) was dropped.," Then, the galaxy image was cut into two pieces at this central ridge, and the western part (including the SN) was dropped."
 The easteru side was reflected aud adde back iuto the position of the western side. thus. ecucrating à sviunietrie picture of the ealaxy.," The eastern side was reflected and added back into the position of the western side, thus, generating a symmetric picture of the galaxy."
 This picture was hen subtracted from the original one. resulting in a much cleaner SN spectra," This picture was then subtracted from the original one, resulting in a much cleaner SN spectrum."
" While the removal of the galaxy Us""specrun was far from complete. its contribution at the position of the SN spectrum was considerably suppressed in this wax."," While the removal of the galaxy “spectrum” was far from complete, its contribution at the position of the SN spectrum was considerably suppressed in this way."
 The extraction of the cleaned SN. spectra was performed with the standard subroutines in, The extraction of the cleaned SN spectrum was performed with the standard subroutines in
Ligh multiplex multi-object spectrographs have been key to many core astronomical investigations since their routine operation began over three decades. ago.,High multiplex multi-object spectrographs have been key to many core astronomical investigations since their routine operation began over three decades ago.
" However. even with the great advances made in our understanding of the Universe via large scale spectroscopic surveys (such as those previously under taken at the ANP with the 2b instrument: 2dECGINS - Colless(1999).. 2QZ - Bovle.Shanks.Croom (2000).. WigeleZ - Drinkwaterefa£,(2000).. CLANLA - DriverelaL (2009))). or closer to home with stellar surveys (such as the URST RAVE project - Steinmetz.Zwitter.Siebertefad. (2006))). there remains an ever increasing desire Lor more powerful survey machines."," However, even with the great advances made in our understanding of the Universe via large scale spectroscopic surveys (such as those previously under taken at the AAT with the 2dF instrument: 2dFGRS - \citet{2dFGRS}, 2QZ - \citet{2QZ}, , WiggleZ - \citet{WiggleZ}, GAMA - \citet{GAMA}) ), or closer to home with stellar surveys (such as the UKST RAVE project - \citet{RAVE}) ), there remains an ever increasing desire for more powerful survey machines."
 As astronomy enters the cra of the Extremely Large Telescopes (ELT) it is appropriate to pause and assess the techniques and methodologies available to modern instrumentation in order to fully utilise the valuable photons gathered by these gargantuan machines., As astronomy enters the era of the Extremely Large Telescopes (ELT) it is appropriate to pause and assess the techniques and methodologies available to modern instrumentation in order to fully utilise the valuable photons gathered by these gargantuan machines.
 1n the same vein. older facilities strive to identifv new modes of operation.," In the same vein, older facilities strive to identify new modes of operation."
 These stalwarts ofthe past two decades of research must find the best modes of operation to support the ambitions of the new generation of facilities. whose availability will be restricted at best.," These stalwarts of the past two decades of research must find the best modes of operation to support the ambitions of the new generation of facilities, whose availability will be restricted at best."
 Lt is critical that we take time to review theoptions and identify the roles each, It is critical that we take time to review theoptions and identify the roles each
 , 
"refshape-as-shear)), so the minor axis width is 2.350».","), so the minor axis width is $2.35\sigma_b$."
" Figure 2((a) clearly shows that for a native fit to converge reliably, S/N must be >10 and its minor axis width be >2.8 pixels."," Figure \ref{fig:native-contour}( (a) clearly shows that for a native fit to converge reliably, $S/N$ must be $\geq10$ and its minor axis width be $\geq2.8$ pixels."
 The convergence contour for Gaussian radial profiles is found to be identical to the exponential-profile contour., The convergence contour for Gaussian radial profiles is found to be identical to the exponential-profile contour.
" The fact that the minor axis dimension is the limiting factor for convergence implies a shear-dependent selection, since o, does not remain constant under a shear operation."," The fact that the minor axis dimension is the limiting factor for convergence implies a shear-dependent selection, since $\sigma_b$ does not remain constant under a shear operation."
" 'The required sampling rate depends, however, on the orientation of the minor axis."," The required sampling rate depends, however, on the orientation of the minor axis."
" Figure 2((a) shows the convergence contour when the ellipse is elongated along the pixel axis, where Figure 2((b) shows the case when the elongation is along the pixel diagonal."," Figure \ref{fig:native-contour}( (a) shows the convergence contour when the ellipse is elongated along the pixel axis, where Figure \ref{fig:native-contour}( (b) shows the case when the elongation is along the pixel diagonal."
" In the second case, the required sampling rate appears to decrease with increasing e, until it settles at 2.0 pixel for e>0.6."," In the second case, the required sampling rate appears to decrease with increasing $e$, until it settles at 2.0 pixel for $e\geq0.6$."
" Figure 3 illustrates that for objects elongated along the pixel diagonal, the effective sampling rate along the minor axis becomes 1/2 of the pixel spacing."," Figure \ref{fig:diag-sampling} illustrates that for objects elongated along the pixel diagonal, the effective sampling rate along the minor axis becomes $1/\sqrt{2}$ of the pixel spacing."
 'The GL decomposition of the PSF is determined via a native fit., The GL decomposition of the PSF is determined via a native fit.
" Hence, the images must sample the PSF minor axis width by more than 2.8 pixels for the tto be applied successfully to individual stars."," Hence, the images must sample the PSF minor axis width by more than 2.8 pixels for the to be applied successfully to individual stars."
 Note that it is possible to increase the sampling rate by dithering for a CCD of any pixel size., Note that it is possible to increase the sampling rate by dithering for a CCD of any pixel size.
" For the deconvolution test, we convolve the model galaxies with a circular Airy-function PSF, whose characteristic width is opgr~0.21A/D."," For the deconvolution test, we convolve the model galaxies with a circular Airy-function PSF, whose characteristic width is $\sigma_{\rm PSF}\simeq 0.21\,\lambda/D$."
" The model galaxies in this test are symmetric elliptical objects of exponential radial profile with minor axis Gaussian width σι, before PSF convolution.", The model galaxies in this test are symmetric elliptical objects of exponential radial profile with minor axis Gaussian width $\sigma_b$ before PSF convolution.
" The pixel size is irrelevant to the convergence rate, as long as opgr>2.8 pixels refnativeconvergence))."," The pixel size is irrelevant to the convergence rate, as long as $\sigma_{\rm PSF} \ge\,2.8$ pixels \\ref{nativeconvergence}) )."
 We find that the convergence rate of iis independent of the orientation of the major axis under these conditions., We find that the convergence rate of is independent of the orientation of the major axis under these conditions.
 Figure 4 shows the convergence contour for deconvolution fits., Figure \ref{fig:deconv-contour} shows the convergence contour for deconvolution fits.
 The horizontal axis is the minor-axis resolution, The horizontal axis is the minor-axis resolution
represents. and the tvpe of object in the class.,"represents, and the type of object in the class."
 For our experiments. we treated one or (vo of the classes as being unknown. withholding from use during model learning the label for every data example from each of the unknown Classes.," For our experiments, we treated one or two of the classes as being unknown, withholding from use during model learning the label for every data example from each of the unknown classes."
 For data from all other classes. we retained the labels for a randomly selected subset (roughlv. of the points from these classes521 examples for the ESOLV. cata and 5400 exanples for the SDSS data).," For data from all other classes, we retained the labels for a randomly selected subset (roughly of the points from these classes–521 examples for the ESOLV data and 5400 examples for the SDSS data)."
" The random selection was performed in a stratified"" fashion. ensuring that the number of labeled examples [rom each known class is in proportion to the nass. or Irequency of occurrence. of the class."," The random selection was performed in a “stratified” fashion, ensuring that the number of labeled examples from each known class is in proportion to the mass, or frequency of occurrence, of the class."
 Ir (his way. we obtained a data set containing both labeled and unlabeled examples. and with all labels missing from one or two classes.," In this way, we obtained a data set containing both labeled and unlabeled examples, and with all labels missing from one or two classes."
 This is precisely the data scenario proposed ancl addressed in Miller&Browning(2003a) and Miller&Browning(2003b)., This is precisely the data scenario proposed and addressed in \citet{pami} and \citet{Browning}.
. We used two algorithms to classify the data and perform class discovery. a mixture moclel and a backpropagation algorithm.," We used two algorithms to classify the data and perform class discovery, a mixture model and a backpropagation algorithm."
 These approaches are described in detail below., These approaches are described in detail below.
 This subsection reviews the work in Miller&Browning(2003a).. (2003b).," This subsection reviews the work in \citet{pami}, \citet{Browning}."
. There are (three main contributions in these works: 1) the problem of new class discoverv in müxed labeled/unlabeled data was proposed: 2) a mixture model was proposed for this scenario. one (that incorporates a realistic labeling mechanism.," There are three main contributions in these works: 1) the problem of new class discovery in mixed labeled/unlabeled data was proposed; 2) a mixture model was proposed for this scenario, one that incorporates a realistic labeling mechanism."
 This model has built into it (he competing hvpotheses that a data sample may come from known or unknown/outlier groups., This model has built into it the competing hypotheses that a data sample may come from known or unknown/outlier groups.
 Thus. this model naturally vields probabilities for these hypotheses. as well as the standardposterior? probabilies on the known classes (now," Thus, this model naturally yields probabilities for these hypotheses, as well as the standard probabilities on the known classes (now"
Hillenbrand Lartmann (1998).. and in such a case the density evolution would not occur and the core encounter distribution predicted by Bonnell et shorteiteBon|** would be appropriate.,"Hillenbrand Hartmann \shortcite{HilHar98}, and in such a case the density evolution would not occur and the core encounter distribution predicted by Bonnell et \\shortcite{Bon+**} would be appropriate."
 Llowever. we point out that for initial conditions that are not so carefully constructed. we expect the core density to fall and for most of the closest. encounters in the ONC to have occurred. by ItsH present lt ds clear from the mass loss rate in (1)) that photoevaporation can remove a large amount of clisk material from systems in the core of the ONC over the ~5 Ave lifetime ofOri.," However, we point out that for initial conditions that are not so carefully constructed, we expect the core density to fall and for most of the closest encounters in the ONC to have occurred by its present It is clear from the mass loss rate in \ref{E:mdotFUV}) ) that photoevaporation can remove a large amount of disk material from systems in the core of the ONC over the $\sim 5$ Myr lifetime of."
. Our simulations. which keep track," Our simulations, which keep track"
turbulence in the tropopause.,turbulence in the tropopause.
 Nevertheless. the quadratic approximation (32.. 34)) is still valid and can be used.," Nevertheless, the quadratic approximation \ref{eq:corr_wind2}, , \ref{eq:cov_wind2}) ) is still valid and can be used."
 Authors are grateful to astroclimatic community for the interest to our research which reveal itself. at two Latest conferences ancl stimulated: completion of this work., Authors are grateful to astroclimatic community for the interest to our research which reveal itself at two latest conferences and stimulated completion of this work.
 We also would. like to thank our colleagues from. Sternberg Astronomical Institute which provided us with observational data obtained. with NLASS/DIMM device. on. Mount Shatdjatmaz., We also would like to thank our colleagues from Sternberg Astronomical Institute which provided us with observational data obtained with MASS/DIMM device on Mount Shatdjatmaz.
 Bos. acknowledges financial support from “Dynasty” foundation., B.S. acknowledges financial support from “Dynasty” foundation.
 Averaging of components of dillerential motion spectrum depending on angle © over this anele results in the expressions and Llere the integrals Zo and οι from Append., Averaging of components of differential motion spectrum depending on angle $\phi$ over this angle results in the expressions and Here the integrals $\mathcal J_0$ and $\mathcal J_1$ from Append.
 ο were usec., \ref{sec:integrals} were used.
 For c-motion o?=σ|a7. result of the averaging is equal to sum Vi(q)|Μις)or (26)) ms(29 Co X. (2):," For $c$ -motion $\sigma_c^2 = \sigma_l^2+\sigma_t^2$, result of the averaging is equal to sum $\Psi_l(q)+\Psi_t(q)$or \ref{eq:S1_series}) \ref{eq:C1_series}) \ref{sec:integrals} \ref{sec:a1} \citep{grad_en}:"
o a high deeree of confidence.,to a high degree of confidence.
 The orbits of the inary members can also be rturbed bv other bodies iu the svstems. either on shorter (planets or other πια. bodies iu close orbits) or longer timescales (a distant body).," The orbits of the binary members can also be perturbed by other bodies in the systems, either on shorter (planets or other small bodies in close orbits) or longer timescales (a distant body)."
 Iu both cases. oxturbations m trant timing may be visible (sce Agoletal.2005 for a detailed discussion).," In both cases, perturbations in transit timing may be visible (see \citealt{assc05}
 for a detailed discussion)."
 Caven the wide varicty iu possible situations it is out of the scope of us Letter to cousider. but anv perceived variation in rausit timing must be compared against the possible xesenuce of additional bodies.," Given the wide variety in possible situations it is out of the scope of this Letter to consider, but any perceived variation in transit timing must be compared against the possible presence of additional bodies."
 There could also be effects rat alter the perceived primary versus secondary eclipse nues without altering the orbit. such as hot spots duc o yradiation (I&uutsonetal.2007:Agol2010) or accretion.," There could also be effects that alter the perceived primary versus secondary eclipse times without altering the orbit, such as hot spots due to irradiation \citep{kcn+07,ack+10} or accretion."
" For the former. I note that the imcoming radiation iu the double WD systems is typically very sual, ~10 ?ofthe outgoing radiation."," For the former, I note that the incoming radiation in the double WD systems is typically very small, $\sim 10^{-3}$ of the outgoing radiation."
 As for accretion. both WDs are well inside their Roche lobes aud so none Is expected.," As for accretion, both WDs are well inside their Roche lobes and so none is expected."
 I fined the fortunate coiucideunce that18.. the one object known to be eclipsing. also has the binary piriuueters that lead to the highest value of aamong siuilar double WD binaries.," I find the fortunate coincidence that, the one object known to be eclipsing, also has the binary parameters that lead to the highest value of among similar double WD binaries."
 IHopofulh. with dedicated observing this effect will be detected and can constrain the ssvsteni even more than is possible today.," Hopefully, with dedicated observing this effect will be detected and can constrain the system even more than is possible today."
 I thank the anouvimous referee. as well as L. Dildsten. T. Marsh. J. Winn. E. Agol. D. Fabrvekw. S. Candi. AL van Adelsbere. aud R. Cooper for helpful discussious.," I thank the anonymous referee, as well as L. Bildsten, T. Marsh, J. Winn, E. Agol, D. Fabrycky, S. Gaudi, M. van Adelsberg, and R. Cooper for helpful discussions."
 DLK was supported by NASA through Hubble Fellowship Caant #001207.01-A awarded by the STScI which is operated bv AURA. Inc.. for NASA. uuder contract NAS 5-26555.," DLK was supported by NASA through Hubble Fellowship Grant 01207.01-A awarded by the STScI which is operated by AURA, Inc., for NASA, under contract NAS 5-26555."
 This work was supported by the NSF under erauts PITY 05-51161 and AST 07-07633, This work was supported by the NSF under grants PHY 05-51164 and AST 07-07633.
barvon and metal losses due to strong galactic winds driving much of the ICM out of them (Renzini et al.,baryon and metal losses due to strong galactic winds driving much of the ICM out of them (Renzini et al.
 1993: 197: Davis et al., 1993; R97: Davis et al.
 1998)., 1998).
 For the rest of this paper 1 will concentrate on clusters with AY223 keV. Fiews 1-3 show that both the iron abundance and the iin richclusters (AD23 keV) are independent. of cluster temperature. hence of cluster richness and optical luminosity.," For the rest of this paper I will concentrate on clusters with $kT\gsim 2-3$ keV. Fig.s 1-3 show that both the iron abundance and the in richclusters $kT\gsim 3$ keV) are independent of cluster temperature, hence of cluster richness and optical luminosity."
" For these clusters one has Zl,=0.3d0.1 solar. and ME“iL,=(0.02+£0.01) for 1Η.=50."," For these clusters one has $\zfecm =0.3\pm 0.1$ solar, and $\mfecm/\lb = (0.02\pm 0.01)$ for $\ho=50$."
 The most straightforward interpretation is that clusters did not lose iron (hence baryons). nor differentially acquired pristine barvonie material. and that the conversion of barvonic gas into stars ancl galaxics has proceeded with the same cllicieney and the stellar LME in all clusters (1597).," The most straightforward interpretation is that clusters did not lose iron (hence baryons), nor differentially acquired pristine baryonic material, and that the conversion of baryonic gas into stars and galaxies has proceeded with the same efficiency and the stellar IMF in all clusters (R97)."
 Otherwise. we should observe cluster to cluster variations of the iron abundance and of theFeAl/L.," Otherwise, we should observe cluster to cluster variations of the iron abundance and of the."
. The absence of such variations also argues for the iron now residing in the LOCAL having beenejected [rom galaxies by supernova- (or AGN-) driven galactic winds. rather than having been stripped by ram pressure (Itenzini et al.," The absence of such variations also argues for the iron now residing in the ICM having been from galaxies by supernova- (or AGN-) driven galactic winds, rather than having been stripped by ram pressure (Renzini et al."
 1993: Dupke White 1999)., 1993; Dupke White 1999).
 Indeed. raum pressure effects become much stronger with incereasing cluster richmess. hence galaxy velocity clispersion and ICM temperature.," Indeed, ram pressure effects become much stronger with incereasing cluster richmess, hence galaxy velocity dispersion and ICM temperature."
 Correspondingly. if ram pressure would. play a major role in getting iron out of galaxies one would. expect the ICM abundance and. tto increase with AY. which is not observed.," Correspondingly, if ram pressure would play a major role in getting iron out of galaxies one would expect the ICM abundance and to increase with $kT$ , which is not observed."
at aandAA.,at and.
". The observed component ratio varies from quasar to quasar but is normally in the range 0.8:1—0.9:1, leading to the effective wavelength of aadopted."," The observed component ratio varies from quasar to quasar but is normally in the range 0.8:1–0.9:1, leading to the effective wavelength of adopted."
 redshifts are available for a further 12289 quasars with redshifts z<1.10., redshifts are available for a further 12289 quasars with redshifts $z$$\le$ 1.10.
 The minimum rest-frame wavelength involved in the cross-correlation is aand systematic offsets relative to the emission line redshifts generated in the previous sub-Section are not predicted or detectable., The minimum rest-frame wavelength involved in the cross-correlation is and systematic offsets relative to the emission line redshifts generated in the previous sub-Section are not predicted or detectable.
" In the interval 1.1<z<2.1, the redshifts involve rest-frame wavelengths below aand the signal is increasingly dominated by the emission as redshift increases and the line shifts into the far red of the SDSS spectra."," In the interval $<$$z$$<$ 2.1, the redshifts involve rest-frame wavelengths below and the signal is increasingly dominated by the emission as redshift increases and the line shifts into the far red of the SDSS spectra."
" Additionally, there is also the luminosity-dependent variation in the location of the emission complex to take into account."," Additionally, there is also the luminosity-dependent variation in the location of the emission complex to take into account."
" The amplitude of the systematic redshift bias is small, only ~2x10~* too large at the highest redshift z=2.1."," The amplitude of the systematic redshift bias is small, only $\simeq$ $\times$ $^{-4}$ too large at the highest redshift $z$ =2.1."
 Taking the redshifts and the corresponding emission line centroid determinations from the SDSS pipeline allows the dependence of the cross-correlation bias on redshift and absolute magnitude to be quantified., Taking the redshifts and the corresponding emission line centroid determinations from the SDSS pipeline allows the dependence of the cross-correlation bias on redshift and absolute magnitude to be quantified.
" Treating the systematic as separable in redshift and luminosity, a sample of ~420000 quasars, in the redshift interval 1.1<z<2.1, shows that linear corrections to the raw cross-correlation redshifts, with slopes of 1.61x10~* per unit redshift and 7.2x10~° per unit magnitude (reducing the raw redshift estimates as redshift and luminosity increase), bring any residual systematic trends down to the ~1x10~° level."," Treating the systematic as separable in redshift and luminosity, a sample of $\simeq$ 000 quasars, in the redshift interval $<$$z$$<$ 2.1, shows that linear corrections to the raw cross-correlation redshifts, with slopes of $\times$ $^{-4}$ per unit redshift and $\times$ $^{-5}$ per unit magnitude (reducing the raw redshift estimates as redshift and luminosity increase), bring any residual systematic trends down to the $\simeq$ $\times$ $^{-5}$ level."
 Note that the sense and amplitude of the difference between the raw redshifts and the emission line centroids are entirely consistent with the existence of the luminosity-dependent emission line shifts and the way that the master quasar template spectrum is constructed (Section ??))., Note that the sense and amplitude of the difference between the raw redshifts and the emission line centroids are entirely consistent with the existence of the luminosity-dependent emission line shifts and the way that the master quasar template spectrum is constructed (Section \ref{sec:em_shifts}) ).
 Corrected redshifts are available for 7728 quasars in the interval 1.1<z<2.1., Corrected redshifts are available for 728 quasars in the interval $<$$z$$\le$ 2.1.
 At redshifts z>2.1 the line no longer contributes to the cross-correlation redshifts and the full effect of the systematic variation in the rest-frame locations of the and emission lines must be taken into account., At redshifts $z$$>$ 2.1 the line no longer contributes to the cross-correlation redshifts and the full effect of the systematic variation in the rest-frame locations of the and emission lines must be taken into account.
" Fortunately, an empirical determination of the systematic differences between the corrected, un-biased, redshifts derived above and cross-correlation redshifts using only the rest-wavelength region 1675«A «2650A,, termed redshifts, is straightforward to make."," Fortunately, an empirical determination of the systematic differences between the corrected, un-biased, redshifts derived above and cross-correlation redshifts using only the rest-wavelength region $<$$\lambda$$<$ 2650, termed redshifts, is straightforward to make."
" The differences between the corrected redshifts and raw redshifts, derived using a maximum rest-frame wavelength of A-2650AA,, i.e. excluding the emission line, are available for 35 0000 quasars with 1.1<z<2.0."," The differences between the corrected redshifts and raw redshifts, derived using a maximum rest-frame wavelength of $\lambda$, i.e. excluding the emission line, are available for $\simeq$ 000 quasars with $<$$z$$<$ 2.0."
" The difference as a function of quasar absolute magnitude is systematic and well represented by linear trend; a linear fit has slope 1.67x 10, increasing the araw redshifts for increasing bright quasars."," The difference as a function of quasar absolute magnitude is systematic and well represented by a linear trend; a linear fit has slope $\times$ $^{-4}$, increasing the raw redshifts for increasing bright quasars."
 Application of the correction removes any detectable systematic effects as a function of absolute magnitude (Fig. 7)), Application of the correction removes any detectable systematic effects as a function of absolute magnitude (Fig. \ref{hw_ciii_mabs}) )
 or redshift (Fig. 8))., or redshift (Fig. \ref{hw_ciii_z}) ).
 The same correction is then applied to redshifts for 13859 quasars with z>2.1., The same correction is then applied to redshifts for 13859 quasars with $z$$>$ 2.1.
" The intention throughout is to avoid the use of the rest- wavelength region including the emission line, which is known to show large asymmetric variations in shape, and hence"," The intention throughout is to avoid the use of the rest-frame wavelength region including the emission line, which is known to show large asymmetric variations in shape, and hence"
Support for this work was provided by NASA through grant number GO-10131. [rom the Space Telescope Science Institute and by NASA through grant NAG5-9377.,Support for this work was provided by NASA through grant number GO-10131 from the Space Telescope Science Institute and by NASA through grant NAG5-9377.
we might expect that any errors in the fitting would be Gaussian and caused entirely by noise. and so this component of the residual images would behave similarly to the noise component.,"we might expect that any errors in the fitting would be Gaussian and caused entirely by noise, and so this component of the residual images would behave similarly to the noise component."
 The fact hat the skewness in the fitting errors appears to come partly from arge scales suggests that bias in the fitting may allow some leakage hrough from the foregrounds themselves. which are correlated on arge scales.," The fact that the skewness in the fitting errors appears to come partly from large scales suggests that bias in the fitting may allow some leakage through from the foregrounds themselves, which are correlated on large scales."
 If the skewness of the foregrounds is larger than we dave assumed. therefore. we will need to fit them more accurately in addition to exploiting this scale dependence.," If the skewness of the foregrounds is larger than we have assumed, therefore, we will need to fit them more accurately in addition to exploiting this scale dependence."
" In the present case. yO"" is similar to [/22"" at the scale at which the latter is dwarfed by the| contribution from the| CS."," In the present case, $|\mu_3^\mathrm{FE}|$ is similar to $|\mu_3^\mathrm{noise}|$ at the scale at which the latter is dwarfed by the contribution from the CS."
 In practice. to extract the skewness as a function of frequency we make the natural choice of smoothing scale. using the same kernel as was used to degrade the signal and foregrounds to the resolution of the telescope.," In practice, to extract the skewness as a function of frequency we make the natural choice of smoothing scale, using the same kernel as was used to degrade the signal and foregrounds to the resolution of the telescope."
 We then compute the skewness in each slice as before., We then compute the skewness in each slice as before.
 The skewness as a function of frequency for each datacube. after following this procedure. is shown in Fig. 6..," The skewness as a function of frequency for each datacube, after following this procedure, is shown in Fig. \ref{fig:rskew3s}."
 To improve the clarity of the plot. each line is smoothed by aking a moving average with a span of nine points (a boxcar filter).," To improve the clarity of the plot, each line is smoothed by taking a moving average with a span of nine points (a boxcar filter)."
 To estimate the error. we generate. 100 datacubes containing the oregrounds and with different realizations of the noise. but with no CS present.," To estimate the error, we generate 100 datacubes containing the foregrounds and with different realizations of the noise, but with no CS present."
 We feed each cube through our fitting and smoothing orocedure. calculate the skewness as a function of redshift. and smooth this function with a moving average filter just as for the cubes containing a signal.," We feed each cube through our fitting and smoothing procedure, calculate the skewness as a function of redshift, and smooth this function with a moving average filter just as for the cubes containing a signal."
 The range between the l6th and 84th yercentile of the skewness for these realizations is shown as the ight grey shaded area in the figure., The range between the 16th and 84th percentile of the skewness for these realizations is shown as the light grey shaded area in the figure.
 One can see from Fig., One can see from Fig.
 6 that this smoothing procedure allows us to extract a significant signal. despite making only rather general assumptions about the scale at which features due to the signal. instrument and noise are important.," \ref{fig:rskew3s} that this smoothing procedure allows us to extract a significant signal, despite making only rather general assumptions about the scale at which features due to the signal, instrument and noise are important."
 The result for f250C (blue. solid line) is most striking. with rapid transitions in the skewness in he range +z 7.5-8.5.," The result for f250C (blue, solid line) is most striking, with rapid transitions in the skewness in the range $z\approx 7.5$ $8.5$."
 The position of the dip corresponds to the xosition of the dip in the uncorrupted simulation shown in Fig. 2.., The position of the dip corresponds to the position of the dip in the uncorrupted simulation shown in Fig. \ref{fig:skewo}.
 While the skewness continues to rise in the original simulation. 13owever. for the extracted signal it returns to zero at low redshift.," While the skewness continues to rise in the original simulation, however, for the extracted signal it returns to zero at low redshift."
 This is because the variance of the CS becomes very small at low redshift., This is because the variance of the CS becomes very small at low redshift.
 In the uncorrupted simulation. this allows the skewness ο grow very large.," In the uncorrupted simulation, this allows the skewness to grow very large."
 In the residual images. however. the variance of the noise and fitting residuals comes to dominate. even after smoothing. which drives the skewness towards zero.," In the residual images, however, the variance of the noise and fitting residuals comes to dominate, even after smoothing, which drives the skewness towards zero."
 We return o this point below when we consider alternative statistics., We return to this point below when we consider alternative statistics.
 The extracted signal for the other two simulations shows the behaviour one might expect: the T-QSO simulation (red. dashed line) shows only a weak dip in skewness. but a strong peak due to the rapid rise in skewness for the uncorrupted simulation at z8.5.," The extracted signal for the other two simulations shows the behaviour one might expect: the T-QSO simulation (red, dashed line) shows only a weak dip in skewness, but a strong peak due to the rapid rise in skewness for the uncorrupted simulation at $z\lesssim 8.5$."
 The T-star simulation. meanwhile. shows a gradual rise in skewness throughout the redshift range. with significant non-zero skewness detected Τουςο9.5 and 2:Z7.5.," The T-star simulation, meanwhile, shows a gradual rise in skewness throughout the redshift range, with significant non-zero skewness detected for $z\gtrsim 9.5$ and $z\lesssim 7.5$."
" We now move on to an analysis of the so-called ""dirty maps’.", We now move on to an analysis of the so-called `dirty maps'.
 To generate these. we first add together the unsmoothed foreground and signal cubes. where the latter have been tiled. as before. to produce maps of the right angular size.," To generate these, we first add together the unsmoothed foreground and signal cubes, where the latter have been tiled, as before, to produce maps of the right angular size."
 Each slice is then corrupted by the instrumental response., Each slice is then corrupted by the instrumental response.
 We achieve this in practice by Fourier transforming the image. multiplying by the sampling function (calculated on a grid with the same number of points as the image). and then applying the inverse Fourier transform.," We achieve this in practice by Fourier transforming the image, multiplying by the sampling function (calculated on a grid with the same number of points as the image), and then applying the inverse Fourier transform."
 This is equivalent to convolving each image with the point spread function (PSF) of the instrument., This is equivalent to convolving each image with the point spread function (PSF) of the instrument.
 We make the simplifying assumption that the sampling function does not change with frequency., We make the simplifying assumption that the sampling function does not change with frequency.
 If the plane, If the plane
Gravitational mucroleusiug as a imeaus το detect conrpact objects in the Galactic halo was first considered bv Paczyvisski (1986). but the basic idea is much older (Eiusteiu 1936).,"Gravitational microlensing as a means to detect compact objects in the Galactic halo was first considered by Paczyńsski (1986), but the basic idea is much older (Einstein 1936)."
 This suggestion was realized as results from two survevs of niücroleusiug eveuts towards the Large and Simall Magellanic Clouds (LAIC aud SMC) (Alcock et al., This suggestion was realized as results from two surveys of microlensing events towards the Large and Small Magellanic Clouds (LMC and SMC) (Alcock et al.
 2000: Ansari et al., 2000; Ansari et al.
 1996)., 1996).
 These were consistent with a significant. but subdominant. coutributiou of nücroleusiug masses to the Calactic dark matter halo.," These were consistent with a significant, but subdominant, contribution of microlensing masses to the Galactic dark matter halo."
 Nonetheless. these conclusious are still controversial. aud the identity aud location of the microleusing masses are still nivsterious.," Nonetheless, these conclusions are still controversial, and the identity and location of the microlensing masses are still mysterious."
 A decade ago. ΑΟ was suggested as a promising venue where galactic mücrolensing nüsht be explored iu wavs advantageous and distinctive from that in aud around the Galaxy (Crotts 1992).," A decade ago, M31 was suggested as a promising venue where galactic microlensing might be explored in ways advantageous and distinctive from that in and around the Galaxy (Crotts 1992)."
 Several papers (Jetzer 1991: Tan Could 1996: Baltz Silk 2000: I&erius et 22001) have confirmed that a substantial nücroleusing sigual cau be expected., Several papers (Jetzer 1994; Han Gould 1996; Baltz Silk 2000; Kerins et 2001) have confirmed that a substantial microlensing signal can be expected.
 Two collaborations. MEGA (preceded. by the VATT/Cohluubia survey) aud ACADPE have produced a ΠΟ of microlensing event caudidates iuvolviug stars m AIL (Crotts Tomanuer 1996. Ausari et al.," Two collaborations, MEGA (preceded by the VATT/Columbia survey) and AGAPE have produced a number of microlensing event candidates involving stars in M31 (Crotts Tomaney 1996, Ansari et al."
 1999. Aurierre et al.," 1999, Aurièrre et al."
 2001. Uelesichi 2001. Calchi Novati et al.," 2001, Uglesich 2001, Calchi Novati et al."
 2002)., 2002).
 Tere we show the potential for these aud future surveys to settle sole of the outstanding questions regarding microlensing in spiral galaxies., Here we show the potential for these and future surveys to settle some of the outstanding questions regarding microlensing in spiral galaxies.
 This is the second paper m a series., This is the second paper in a series.
 Paper I (Conk. Crotts 2000) provides optical depth maps for MO., Paper I (Gyuk Crotts 2000) provides optical depth maps for M31.
 While these are useful tools for certain purposes they are unfortunatelv not directlv measurable., While these are useful tools for certain purposes they are unfortunately not directly measurable.
 Event rates ou the other hand directly measurable and heuce their magnitude aud variation across the face of M31 are more meaniusgful iu planning and evaluating surveys of mucrolensing., Event rates on the other hand directly measurable and hence their magnitude and variation across the face of M31 are more meaningful in planning and evaluating surveys of microlensing.
 In this paper we extend Paper I to include eveut rate maps. both total and also differcutial rates with respect to the event timescale.," In this paper we extend Paper I to include event rate maps, both total and also differential rates with respect to the event timescale."
 This paper is organized as follows., This paper is organized as follows.
 Iu refinodel owe breflv discuss the A312 models we used. including disk. bulge aud halo components.," In \\ref{model} we briefly discuss the M31 models we used, including disk, bulge and halo components."
 Following this we present rate maps for various halo models. inchiding the self lensing contribution. iu refratemaps..," Following this we present rate maps for various halo models, including the self lensing contribution, in \\ref{ratemaps}."
 Iu roftiniescales. we provide differential rate distributions as a function of two different timescale measures. and we discuss how cuts im timescale can be used to separate solf lensing from a MACTIO halo contribution to the lensing rate.," In \\ref{timescales} we provide differential rate distributions as a function of two different timescale measures, and we discuss how cuts in timescale can be used to separate self lensing from a MACHO halo contribution to the lensing rate."
 We conclude with a cliscussion of measunus leus masses and halo properties iu rofdiscussion.., We conclude with a discussion of measuring lens masses and halo properties in \\ref{discussion}.
 The execution of a microlensing survey of MOL is qualitatively different from those towards the Magellauic Clouds or our own Galactic bulec., The execution of a microlensing survey of M31 is qualitatively different from those towards the Magellanic Clouds or our own Galactic bulge.
 For the latter. individual stars can often be resolved. aud their uuleused fluxes measured. acuuitting a direct measurement of the maemification during a wmicrolensing event.," For the latter, individual stars can often be resolved, and their unlensed fluxes measured, admitting a direct measurement of the magnification during a microlensing event."
 Iu contrast. AIB1 is more than ten times farther away. aud individual stars are rarely resolved from the erouncd.," In contrast, M31 is more than ten times farther away, and individual stars are rarely resolved from the ground."
 huages are almost always highly crowded. and individual sources are almost always lighly bleuded.," Images are almost always highly crowded, and individual sources are almost always highly blended."
 This is the ~pixcl lensine” τοσο (Crotts 1992: Baillou et al., This is the “pixel lensing” regime (Crotts 1992; Baillon et al.
 1993)., 1993).
 Tage subtraction. necessitated by the high ceeree of crowding. has been very successful.," Image subtraction, necessitated by the high degree of crowding, has been very successful."
" While this technique allows the detection of variable objects of amy kind. aud is plotou noise limited. the uuleused fuxes of leused sources are ""uxnown."," While this technique allows the detection of variable objects of any kind, and is photon noise limited, the unlensed fluxes of lensed sources are unknown."
 Thus ΑΟ mücroleusiug survevs must make do with a full width at half maxim timescale and a fiux Increase at inaxinmun as the useful fit parameters., Thus M31 microlensing surveys must make do with a full width at half maximum timescale and a flux increase at maximum as the useful fit parameters.
" The uulensed flux measured by classical iücroleusiug surveys is unavailable uuder most ονομασος,", The unlensed flux measured by classical microlensing surveys is unavailable under most circumstances.
 Sources are taken to reside in à Iuuiuous two-component model ofN31 cousistiug of a double exponential disk aud a bulge., Sources are taken to reside in a luminous two-component model of M31 consisting of a double exponential disk and a bulge.
 The disk model is inclined at an angle of 777 and Las a scale radius of 5.98 kpe. a scale height of LOO pc. a central surface brightness of gj=20. VR=0.67. and we ignore spiral arin effects (Walterbos Kennicutt 19858: Could 1991).," The disk model is inclined at an angle of $^\circ$ and has a scale radius of 5.98 kpc, a scale height of 400 pc, a central surface brightness of $\mu_R = 20$, $V-R=0.67$, and we ignore spiral arm effects (Walterbos Kennicutt 1988; Gould 1994)."
 We take an J baud surface briiehtuess profile from, We take an $I$ band surface brightness profile from
The DAN model is based on the occupation probability formalism introduced by IAI for caleulating (thermodynamical properlies of a non-ideal gas.,The DAM model is based on the occupation probability formalism introduced by HM for calculating thermodynamical properties of a non-ideal gas.
 ILM introduced the non-ideal effects on the equation of state by modilving the internal partition fictions of bound species., HM introduced the non-ideal effects on the equation of state by modifying the internal partition functions of bound species.
 The modified partition function of the hydrogen atom is given by where Aj is the Bolizmann constant. / indicates the atomic level. g; is the statistical weight. e; is the οποιον of hydrogen atom counted [rom the οποιον of the ground state G— 0). Tis the temperature. and c; is the occupation probability.," The modified partition function of the hydrogen atom is given by where $k_{B}$ is the Boltzmann constant, $i$ indicates the atomic level, $g_i$ is the statistical weight, $\epsilon_{i}$ is the energy of hydrogen atom counted from the energy of the ground state $i\rm =0$ ), $T$ is the temperature, and $\omega_i$ is the occupation probability."
 In. the HAL model. &; represents (he strength of non-ideal gas perturbations on an atomic level £.. Its value for the physical conditions found inside weakly ionized cool white dwarl atiospheres is given bv the excluded volume interactions model (Bergeronetal.1991) and decreases for higher principal «quantum number (IAI. Equation 3.4).," In the HM model, $\omega_{i}$ represents the strength of non-ideal gas perturbations on an atomic level i. Its value for the physical conditions found inside weakly ionized cool white dwarf atmospheres is given by the excluded volume interactions model \citep{BWF91}
 and decreases for higher principal quantum number (HM, Equation 3.4)."
"J) The number of hydrogen atoms in the excited state i is expressed as where n,,4 is the total number density of atomic hydrogen.", The number of hydrogen atoms in the excited state $i$ is expressed as where $n_{tot}$ is the total number density of atomic hydrogen.
 DAM extended this model for the ealeulation of the optical properties of hydrogen atoms in the partially ionized plasma., DAM extended this model for the calculation of the optical properties of hydrogen atoms in the partially ionized plasma.
" Thev interpreted (he [actor 1—5; as the Ilraction of hydrogen atoms wilh atomic level / being ""dissolved."" i.e. sufficiently perturbed to describe an unbound electron and ion."," They interpreted the factor $1-\omega_{i}$ as the fraction of hydrogen atoms with atomic level $i$ being “dissolved,"" i.e. sufficiently perturbed to describe an unbound electron and ion."
 Γον assigned (his value to the Iraction of free-electrons states available [or à bound-lree transition to level 7., They assigned this value to the fraction of free-electrons states available for a bound-free transition to level $i$.
" DAM used this interpretation to derive that for the absorption of a photon associated with (he transition from level 7 to level j. the probability that level j is bound. and the transition is ""bound-bound. is w/w,<I."," DAM used this interpretation to derive that for the absorption of a photon associated with the transition from level $i$ to level $j$, the probability that level $j$ is bound, and the transition is “bound-bound,"" is $\omega_j/\omega_i<1$."
" Therefore. the probability of having a ""bound-free transition is To describe the pseudo-continuum. absorption to the continuum energy levels localized between (wo discrete but. “dissolved” levels of the hydrogen atom. DANI introduced. the pseudo-level »* with occupation probability o."," Therefore, the probability of having a “bound-free"" transition is To describe the pseudo-continuum absorption to the continuum energy levels localized between two discrete but “dissolved"" levels of the hydrogen atom, DAM introduced the pseudo-level $n^{*}$ with occupation probability $\omega_{n^{*}}$."
 The latter is calculated by the interpolation between the «o; s. Therefore. the probability that. during the 7 to n* transition. the absorbing electron goes into the continuum is given by (Eq.," The latter is calculated by the interpolation between the $\omega_{i}$ 's. Therefore, the probability that, during the $i$ to $n^{*}$ transition, the absorbing electron goes into the continuum is given by (Eq."
 32 of DAM), 32 of DAM)
Another way to analyze the level of equipartition is to compute the energy density of the magnetic field relative to that of the accelerated particles.,Another way to analyze the level of equipartition is to compute the energy density of the magnetic field relative to that of the accelerated particles.
 In. this case. the ratio runs from - 3000 at early epochs to ~170 at late epochs.," In this case, the ratio runs from $\sim$ 3000 at early epochs to $\sim$ 170 at late epochs."
 Therefore. equipartition between magnetic field and relativistic particles is roughly obtained. again. provided that the efficieney in the acceleration of tons is similar to that of the electrons.," Therefore, equipartition between magnetic field and relativistic particles is roughly obtained, again, provided that the efficiency in the acceleration of ions is similar to that of the electrons."
 In Fig. 2..," In Fig. \ref{FFAvsSSA},"
 we show the SSA and FFA opacities computed with RAMSES in the optically-thick part of the light curves at 1.4. 8.4. and GGHz.," we show the SSA and FFA opacities computed with RAMSES in the optically-thick part of the light curves at 1.4, 8.4, and GHz."
 It can be seen in the figure that SSA dominates versus FFA for all frequencies and epochs., It can be seen in the figure that SSA dominates versus FFA for all frequencies and epochs.
 The FFA evolution changes its slope at ~80ddays. because of the radial gradient of unshocked electron temperatures used in the model of the CSM (see next section and Appendix A).," The FFA evolution changes its slope at $\sim$ days, because of the radial gradient of unshocked electron temperatures used in the model of the CSM (see next section and Appendix A)."
 It can also be seen in Fig., It can also be seen in Fig.
 2. that. for each frequency. the opacity of SSA is To| at roughly the same time as the light curve reaches its maximum (see also Fig. 1)).," \ref{FFAvsSSA} that, for each frequency, the opacity of SSA is $\tau \sim 1$ at roughly the same time as the light curve reaches its maximum (see also Fig. \ref{SIMULFIT}) ),"
 as expected for SSA-dominated light curves., as expected for SSA-dominated light curves.
 Chevalier (1998)) studied the case of SSA-dominated light curves 1n radio supernovae and reported a relationship between the maximum flux-density at a given frequency. the supernova age at the maximum. and the mean expansion velocity of the shock.," Chevalier \cite{Chevalier1998}) ) studied the case of SSA-dominated light curves in radio supernovae and reported a relationship between the maximum flux-density at a given frequency, the supernova age at the maximum, and the mean expansion velocity of the shock."
 The mean expansior velocity estimated in this way is a lower bound to the true shock velocity when FFA is not negligible relative to SSA., The mean expansion velocity estimated in this way is a lower bound to the true shock velocity when FFA is not negligible relative to SSA.
 The ratios of VLBI-inferred expansion velocities to those estimatec using the relationship of Chevalier (1998)) can be computec for several radio supernovae: this ratio is ~2.6 for 11986J and 11979C (from the results reported in Pérrez-Torres et al. 2002b..," The ratios of VLBI-inferred expansion velocities to those estimated using the relationship of Chevalier \cite{Chevalier1998}) ) can be computed for several radio supernovae: this ratio is $\sim$ 2.6 for 1986J and 1979C (from the results reported in Pérrez-Torres et al. \cite{PerezTorres2002b},"
 Bartel Bietenholz 2003.. and Marcaide et al. 2009b)).," Bartel Bietenholz \cite{Bartel2003}, and Marcaide et al. \cite{Marcaide2009b}) ),"
 2.3—3.6 for 22004et (Marti-Vidal et al. 2007).," $2.3-3.6$ for 2004et (Martí–Vidal et al. \cite{MartiVidal2007}) ),"
 and ~2.5 for 22008iz (Brunthaler et al. 2010)., and $\sim$ 2.5 for 2008iz (Brunthaler et al. \cite{Brunthaler2010}) ).
 However. for 11993J we find a much smaller ratio (~ 1.5). which ts indicative of a low FFA (or a high level of SSA compared to PPA). thus supporting the model here proposed for the 11993J radio emission.," However, for 1993J we find a much smaller ratio $\sim$ 1.5), which is indicative of a low FFA (or a high level of SSA compared to FFA), thus supporting the model here proposed for the 1993J radio emission."
" We note that the minimum energy in the population. of accelerated electrons (which we set to 7, c7) affects the SSA opacity and. therefore. plays a role in the estimate of the electron number density. ων."," We note that the minimum energy in the population of accelerated electrons (which we set to $m_e\,c^2$ ) affects the SSA opacity and, therefore, plays a role in the estimate of the electron number density, $n_{csm}$."
 If à low-energy cutoff is applied to the electron population. SSA decreases. although the etfects of this cutoff are only significant at very early epochs. when the magnetic field ts high and the electron energies corresponding to high critical frequencies are low.," If a low-energy cutoff is applied to the electron population, SSA decreases, although the effects of this cutoff are only significant at very early epochs, when the magnetic field is high and the electron energies corresponding to high critical frequencies are low."
" In the optically-thin part of the light curves. a low-energy cutoff does not change the emissivity. but when the source is optically thick a low-energy cutoff implies a larger source function (1.e.. 6./«,.) and therefore a larger fitted n..,, (to raise FFA in the optically-thick region and maintain the fit of the model to the observations)."," In the optically-thin part of the light curves, a low-energy cutoff does not change the emissivity, but when the source is optically thick a low-energy cutoff implies a larger source function (i.e., $\epsilon_\nu/\kappa_\nu$ ) and therefore a larger fitted $n_{csm}$ (to raise FFA in the optically-thick region and maintain the fit of the model to the observations)."
 This. in turn. slightly decreases the fitted magnetic field. to fit the model to the observations in the optically-thin part of the light curves.," This, in turn, slightly decreases the fitted magnetic field, to fit the model to the observations in the optically-thin part of the light curves."
" In short. the use of a low-energy cutoff increases the importance of FFA relative to SSA (for instance. by a factor ~2 if a cutoff of 107,c7 is applied). but the overall effects in the model light curves is very small."," In short, the use of a low-energy cutoff increases the importance of FFA relative to SSA (for instance, by a factor $\sim$ 2 if a cutoff of $10\,m_e\,c^2$ is applied), but the overall effects in the model light curves is very small."
 The flux-density evolution of a supernova in the optically-thick regime can provide detailed information on the radial density profile of the CSM., The flux-density evolution of a supernova in the optically-thick regime can provide detailed information on the radial density profile of the CSM.
 The opacity of the unshocked CSM to the radio emission is assumed to be produced by free-free interactior of the radiation with the thermal electrons that fill the ionized CSM., The opacity of the unshocked CSM to the radio emission is assumed to be produced by free-free interaction of the radiation with the thermal electrons that fill the ionized CSM.
 Therefore. a precise estimate of the CSM temperature 1s required to reliably model the CSM density profile using the radio light curves.," Therefore, a precise estimate of the CSM temperature is required to reliably model the CSM density profile using the radio light curves."
 By analysing the early X-ray and radio light curves of 11993J at several frequencies. Fransson. Lundqvist Chevalier (1996)) modelled a CSM radial density profile with an structure index s~1.7. which is Indicative of variable mass-loss rate for the precursor star.," By analysing the early X-ray and radio light curves of 1993J at several frequencies, Fransson, Lundqvist Chevalier \cite{Fransson1996}) ) modelled a CSM radial density profile with an structure index $s \sim 1.7$, which is indicative of variable mass-loss rate for the precursor star."
 Similar results were found from the analysis of the late X-ray emission (Immler. Aschenbach Wang 2001)).," Similar results were found from the analysis of the late X-ray emission (Immler, Aschenbach Wang \cite{Immler2001}) )."
 However. Fransson Bjórrnsson (1998)) were able to model the early radio light curves with s=2 by adding cooling effects to the electron population and assuming a dependence of the CSM temperature on distance from the explosion centre. which maps into a radial dependence of the FFA.," However, Fransson Björrnsson \cite{Fransson1998}) ) were able to model the early radio light curves with $s = 2$ by adding cooling effects to the electron population and assuming a dependence of the CSM temperature on distance from the explosion centre, which maps into a radial dependence of the FFA."
 The use of this extra degree of freedom im the model resulted in a satisfactory fit to the radio light curves without assumiig a variable mass- rate of the precursor star., The use of this extra degree of freedom in the model resulted in a satisfactory fit to the radio light curves without assuming a variable mass-loss rate of the precursor star.
 In our work. we adopted the," In our work, we adopted the"
The dust thermal enüssiou toward MWC 758 was observed on January 2009 using the Combined Array or Research in Millimeter-wave (CARMA) ocated at the altitude of 7200 feet in the πο mountains of eastern California.,The dust thermal emission toward MWC 758 was observed on January 2009 using the Combined Array for Research in Millimeter-wave (CARMA) located at the altitude of 7200 feet in the Inyo mountains of eastern California.
 The array was in the extended D coufiguratiou. which provides baselines between 80.9 and 916.3 a. The observatious were obtained at the ocal oscillator frequency of 97.5 GIIz (A~3.3 nua).," The array was in the extended B configuration, which provides baselines between 80.9 and 946.3 m. The observations were obtained at the local oscillator frequency of 97.5 GHz $\lambda \sim 3.3$ mm)."
 The CARMA correlator was coufigured with six bauds. cach of which was configured to £68 MITz baud-width to xovide ιαπαι continu seusitivitv.," The CARMA correlator was configured with six bands, each of which was configured to 468 MHz band-width to provide maximum continuum sensitivity."
 No molecular cussion line was observed with CARALA during this rack., No molecular emission line was observed with CARMA during this track.
 The passbaud shape was calibrated by observing BSCISLS and the flux calibration was set bv observing Uranus., The passband shape was calibrated by observing 3C454.3 and the flux calibration was set by observing Uranus.
 The quasar 0510|180 was observed every 15 uinutes to correct for atmospheric and iustrmucutal effects., The quasar J0510+180 was observed every 15 minutes to correct for atmospheric and instrumental effects.
 The data reduction aud the age reconstruction were obtained using the MIBIAD software package., The data reduction and the image reconstruction were obtained using the MIRIAD software package.
" Figure 1 shows the resulting map. which is characterized by a ruis noise of 0.25 1beam aud a svuthesized beam FWIIAL of 0,62"" when natural weighting is applied to the data."," Figure \ref{fig:cont} shows the resulting map, which is characterized by a rms noise of 0.25 mJy/beam and a synthesized beam FWHM of $\times$ when natural weighting is applied to the data."
 Figures 1.. 2.. and 3. show the dust and CO emission towards AWC 758 as observed by pointing the telescope at the ICRS coordinates of the star atthe epoch J2000. RA=05h 3010: 278.530 (412.89 mas) and ..08 (25.57 mas).," Figures \ref{fig:cont}, \ref{fig:CO}, and \ref{fig:CO_mom} show the dust and CO emission towards MWC 758 as observed by pointing the telescope at the ICRS coordinates of the star atthe epoch J2000, RA=05h 30m 27s.530 $\pm12.89$ mas) and .08 $\pm5.57$ mas)."
 The position of the star at the date of the observation is shown by the sviubol κ and is calculated by applying a proper motion of ó(R.À)25.2341.10 inas/vr aud 6(Dec)=-25.95+0.66 muas/vr to the J2000 coordinates (boththestellarcoordinatesandthepropermotionarefrom ?)..," The position of the star at the date of the observation is shown by the symbol $\star$ and is calculated by applying a proper motion of $\delta\textrm{(R.A)}$ $\pm$ 1.40 mas/yr and $\delta\textrm{(Dec)}$ $\pm$ 0.66 mas/yr to the J2000 coordinates \citep[both the stellar coordinates and 
the proper motion are from][]{Perryman97}."
 The unecitaintics on the stellar position resulting bot[uium from the Uspparcos astrometry aud proper iotio uncertainties are stualler than the size of svaubol itself., The uncertainties on the stellar position resulting both from the Hypparcos astrometry and proper motion uncertainties are smaller than the size of symbol itself.
 The dust cimission at both 0.87 and 23.9 nuu is characterized by two peaks which are sviuuetric with respect of the position of the star and are separated by about0.77.. or 110. AU at the distance of 200 pe.," The dust emission at both 0.87 and 3.3 mm is characterized by two peaks which are symmetric with respect of the position of the star and are separated by about, or 140 AU at the distance of 200 pc."
 At the wavelength of 0.87 mau. the northern aud southeru peaks have fluxes of 89 and 77 1iJvοσα respectively.," At the wavelength of 0.87 mm, the northern and southern peaks have fluxes of 89 and 77 mJy/beam respectively."
 A similay flux ratio between the two peaks is measured at 3.35 nun. sugeesting that the observed morphology correspouds to an asviunietrie dust cussion between the two sides of the disk.," A similar flux ratio between the two peaks is measured at 3.3 mm, suggesting that the observed morphology corresponds to an asymmetric dust emission between the two sides of the disk."
" By iutegratiug over a circle with a radius of ccentered at the position of the star. woe measure fluxes of 217240 παν and LOL mv at OAT and 23.3 nua respectively, where the errors account for both the thermal noise and absolute calibration uncertainties."," By integrating over a circle with a radius of centered at the position of the star, we measure fluxes of $\pm$ 40 mJy and $\pm$ 1.7 mJy at 0.87 and 3.3 mm respectively, where the errors account for both the thermal noise and absolute calibration uncertainties."
 The integrated fluxes are iu agreement with the values nmieasured at aaneular resolution bv 7? sugeesting that the dust Cluission is all coming from the spatial scales probed by our observations., The integrated fluxes are in agreement with the values measured at angular resolution by \citet{Chapillon08} suggesting that the dust emission is all coming from the spatial scales probed by our observations.
 Asstuuine that the disk millimeter cluission follow a power law Fv)xwvt. we derive a spectral ides. 0-3: =3.0.," Assuming that the disk millimeter emission follow a power law $F(\nu)\propto \nu^\alpha$, we derive a spectral index $\alpha_{\textrm{1-3mm}}$ =3.0."
 Fieue 2 shows the echannel maps in the velocity rauge between 2.91 and y93 Ikaun/sec., Figure \ref{fig:CO} shows the channel maps in the velocity range between 2.94 and 8.93 km/sec.
 The CO cinission is spatially resolved aud shows a velocity pattern typical of an inclined. rotating disk., The CO emission is spatially resolved and shows a velocity pattern typical of an inclined rotating disk.
 The first moment of the CO cinission. be. the velocity eradieuts across the disk. indicates that the western and eastern sides of the disk are respectively red- and blic-shitted with respect to the relative velocity of the star (sce the left paucl of Figure 3)).," The first moment of the CO emission, i.e., the velocity gradients across the disk, indicates that the western and eastern sides of the disk are respectively red- and blue-shifted with respect to the relative velocity of the star (see the left panel of Figure \ref{fig:CO_mom}) )."
 The velocity eracieut also sugeests a position angle of the disk major ands of about aas ineasured from north to east., The velocity gradient also suggests a position angle of the disk major axis of about as measured from north to east.
 The central panel of Figure 3. shows the spectrally integrated CO. enission., The central panel of Figure \ref{fig:CO_mom} shows the spectrally integrated CO emission.
 Iu coutrast to what is observed iu the dust contimmin. he CO cunission has a single peak coincident with the xosition of the stay.," In contrast to what is observed in the dust continuum, the CO emission has a single peak coincident with the position of the star."
 The CO emissiou is observed up to a distauce of in the red-shifted side of the disk. aud ouly to about Hn the other side.," The CO emission is observed up to a distance of in the red-shifted side of the disk, and only to about in the other side."
 The liue inteerated fix is 12.9 Jv uu/sec., The line integrated flux is 12.9 Jy km/sec.
 This value is about smaller than that ueasured in single dish observatious (7).. suggesting hat part of the CO einission is resolved out in the interferometric observations.," This value is about smaller than that measured in single dish observations \citep{Dent05}, suggesting that part of the CO emission is resolved out in the interferometric observations."
 As a consequence. the observed asvuuuetry iu the CO enmission/ might be due o the lack of short baselines in the SATA observations instead of to a real asvuuuetry in the gas teniperature or distribution.," As a consequence, the observed asymmetry in the CO emission might be due to the lack of short baselines in the SMA observations instead of to a real asymmetry in the gas temperature or distribution."
" Finally. the spatially inteerated CO spectrin (ight panel of Figure 3)) has a double peak profile ceutered at the velocity of (ji,=6.0 ki/sec."," Finally, the spatially integrated CO spectrum (right panel of Figure \ref{fig:CO_mom}) ) has a double peak profile centered at the velocity of $v_{lsr}=6.0$ km/sec."
 The line eiissiou is observed in the velocity range Ομ kan/sec with a brighter fux in the rec-shitted half of the disk., The line emission is observed in the velocity range $v_{lsr}\pm$ 4 km/sec with a brighter flux in the red-shifted half of the disk.
 To date. the different morphologies observed in the dust and eas cussion toward MNC 758 represcut a Tuque ease among the sample of circumstellar disks spatially resolved with millameterawave interferometers.," To date, the different morphologies observed in the dust and gas emission toward MWC 758 represent a unique case among the sample of circumstellar disks spatially resolved with millimeter-wave interferometers."
 Our observations suggest that the optical depth of the dust continua cussion decreases within a radius of 70-100 AU from the stay., Our observations suggest that the optical depth of the dust continuum emission decreases within a radius of 70-100 AU from the star.
 Despite that. the disk remains eas-ricli down to at least a distance of 30 AU to explain the centrally peaked CO emission.," Despite that, the disk remains gas-rich down to at least a distance of 30 AU to explain the centrally peaked CO emission."
 Iu addition. the SED of AIWC 758 shows a flux excess above the stellar plotosphere between uear- aud far-intrared wavelengths typical of optically thick flaring disk extending to few stellar radii (see Figure 5)).," In addition, the SED of MWC 758 shows a flux excess above the stellar photosphere between near- and far-infrared wavelengths typical of optically thick flaring disk extending to few stellar radii (see Figure \ref{fig:sed}) )."
" The next section is devoted to recouciling all these observations iu the framework of existing disk models, in order to coustrain the radial distribution of the circumstellar material around MIWC 758."," The next section is devoted to reconciling all these observations in the framework of existing disk models, in order to constrain the radial distribution of the circumstellar material around MWC 758."
 To analyze the data we adopt the disk model discussed in 77?..," To analyze the data we adopt the disk model discussed in \citet[][]{Isella07,Isella09}."
" In brief. we compute the radial dust teniperature profile following the ""two-lawer approximation of ?.. where the disk is characterized by a wari surface laver and a cooler interior."," In brief, we compute the radial dust temperature profile following the ""two-layer"" approximation of \citet{Chiang97}, , where the disk is characterized by a warm surface layer and a cooler interior."
 Both temperatures are calculated as a function of the orbital radius by iterating on the, Both temperatures are calculated as a function of the orbital radius by iterating on the
to ~LOM% at npoLO? ((ISaufiian et al.,to $\sim$ at $n_{\rm H} \sim 10^3$ (Kaufman et al.
 2006)., 2006).
 Because both. considered high-redshift ti] c1itters lone to the eiut molecular gas complexes with AL~LMPAL. (Omout et al., Because both considered high-redshift ] emitters belong to the giant molecular gas complexes with $M \sim 10^{10}M_\odot$ (Omont et al.
 1999: Walter et al., 1999; Walter et al.
 2001). the contribution to the inteerated observed intensity of the rr| emission from the regions is probably negligible.," 2004), the contribution to the integrated observed intensity of the ] emission from the regions is probably negligible."
 In particular. [ono et al. (," In particular, Iono et al. ("
2006) note au excelleut agreement between the r1] aud CO profiles at +=1.69.,2006) note an excellent agreement between the ] and CO profiles at $z = 4.69$.
 At ;— 6.12. Maiolino et al. (," At $z = 6.42$ , Maiolino et al. ("
"2005) favor ay~107 tto explain the observed luminosities in FIR. CO. aud [ο lines,","2005) favor $n_{\rm H} \sim 10^5$ to explain the observed luminosities in FIR, CO, and ] lines."
 Our estimate of the value of the Doppler noise for the CO and eniüsson lines at 2ον6 is based on typical parameters of the interstellar molecular clouds with similax eas densities: pj=10?1057. AL10 10!37.. ze L—220 pe (Table Lin Mac Low Ilesseun 2001).," Our estimate of the value of the Doppler noise for the CO and ] emission lines at $z \sim 6$ is based on typical parameters of the interstellar molecular clouds with similar gas densities: $n = 10^2-10^4$, $M = 10^2-10^4M_\odot$ , size $L = 2-20$ pc (Table 1 in Mac Low Klessen 2004)."
 Using the velocity dispersion aud region size relation. σκι lyy = 1.40£9PS (5c). enipiricallv derived. for molecular clouds by Lirsou (1981) aud. then studied in detail by Solomon ct al. (," Using the velocity dispersion and region size relation, $\sigma_v$ ) = $1.10 L^{0.38}$ (pc), empirically derived for molecular clouds by Larson (1981) and then studied in detail by Solomon et al. ("
"1987) aud by other eroups (00, Falearone ct al.","1987) and by other groups (e.g., Falgarone et al."
 1992: \Gesch Bally 199 Casclli λίπος 1995: Frieswijk et al., 1992; Miesch Bally 1994; Caselli Myers 1995; Frieswijk et al.
" 2007). we find S,3hinsL2 "," 2007), we find $\sigma_v \sim 1-3$."
Thus we may asmnue that if the 11] and CO lines arise co-spatiallv. then the velocity offset )etwoeen them does not exceed the velocity dispersion within the cloud which is of order of a few1.," Thus, we may assume that if the ] and CO lines arise co-spatially, then the velocity offset between them does not exceed the velocity dispersion within the cloud which is of order of a few."
 Ou the other haud. our derived limit [AF/F|«10.! correspouds Od—30 which is the eror of the line position neasurenient.," On the other hand, our derived limit $|\Delta F/F| < 10^{-4}$ corresponds to $\sigma_v = 30$ which is the error of the line position measurement."
 From these values. we are confident that he quotient F=a?io Yroniadns constan at the level of toa ook-back iue of 13 Cx.," From these values, we are confident that the quotient $F = \alpha^2/\mu$ remains constant at the level of to a look-back time of 13 Gyr."
 The reliabilitv of the result obtaimed can be conrpared with previous radio observations of molecules at intermediate redshifts., The reliability of the result obtained can be compared with previous radio observations of molecules at intermediate redshifts.
 Kanelkar oet al. (, Kanekar et al. (
2005) used observations of 21 cm and ΟΠ 15 ci lines from two absorbers at ;270.7 and found Af/f=(0.112:0.364:£lO)d0 7.,2005) used observations of 21 cm and OH 18 cm lines from two absorbers at $z \simeq 0.7$ and found $\Delta f/f = (0.44\pm0.36_{\rm stat}\pm1.0_{\rm syst})\times10^{-5}$ .
" Hee flarfhe, aud gy, is the proton evromaguetic ratio."," Here $f = g_{\rm p}(\alpha^2/\mu)^{1.57}$, and $g_{\rm p}$ is the proton gyromagnetic ratio."
 The systematic error was set from the assuniptiou that the Doppler noise is 3, The systematic error was set from the assumption that the Doppler noise is 3.
 llowever. this seen to be too optimistic taking into account observations of the nearby diffuse/transhicent gas clouds in our Galaxy.," However, this seems to be too optimistic taking into account observations of the nearby diffuse/translucent gas clouds in our Galaxy."
 For instance. absorption profiles of the OIL Ls cii and WCO! 3 nua lines studied at 110-210 rresolution towards extragalactic compact continui sources (Liszt Lucas 2000) exhibit. in general similar complex structures over the radial velocity interval of ~10-20 D. while showing small differences in details ou the scale of 1-2Ἐ," For instance, absorption profiles of the OH 18 cm and $^+$ 3 mm lines studied at 140-240 resolution towards extragalactic compact continuum sources (Liszt Lucas 2000) exhibit, in general, similar complex structures over the radial velocity interval of $\sim$ 10-20 , while showing small differences in details on the scale of 1-2."
"ν, Hosever. comparison of ICO! absorption with 21 cia absorption towards the same targets reveals significant discrepancies."," However, comparison of $^+$ absorption with 21 cm absorption towards the same targets reveals significant discrepancies."
 Figs., Figs.
 6 aud 7 from Liszt Lucas show that there are rather wide velocity iutervals (—20 5) where absorption is ποσα but ! is absent., 6 and 7 from Liszt Lucas show that there are rather wide velocity intervals $\sim$ 20 ) where absorption is seen but $^+$ is absent.
 It &eenis quite possible that the Doppler noise for a seanple of 21 emi aud molecular lines couk be as large as 10|., It seems quite possible that the Doppler noise for a sample of 21 cm and molecular lines could be as large as 10.
. Another set of observations of local warin gas clouds within 15 pc around the Sun (Redfield Liusky 2007) show that he distribution of cloud velocity difference has a width of ~10, Another set of observations of local warm gas clouds within 15 pc around the Sun (Redfield Linsky 2007) show that the distribution of cloud velocity difference has a width of $\sim$ 10.
 This mieaus that iu lower resolution observations of quasar intervening svstenis the line-of-sight velocity differences of order 10 ΗΠΙΑ occur on a rather short linear scale of ~1LO-LO0 pe., This means that in lower resolution observations of quasar intervening systems the line-of-sight velocity differences of order 10 may occur on a rather short linear scale of $\sim$ 10-100 pc.
 The limit on Αμίμς0.G-E1.9 ppm by ELlunubamna I&ozlov (2007) was estimated youn the NID; transitions rear A=1.26 «mn and nmniewave lines of CO. IICO!. and IICN detected. frou: one absorption-line svstem.," The limit on $\Delta\mu/\mu = -0.6\pm1.9$ ppm by Flambaum Kozlov (2007) was estimated from the $_3$ transitions near $\lambda = 1.26$ cm and mm-wave lines of CO, $^+$, and HCN detected from one absorption-line system."
 In his case Αμίμ=(.289Ac/e. which means that the uncertainty of 2 ppim corresponds to Ac25.," In this case $\Delta \mu/\mu = 0.289 \Delta v/c$, which means that the uncertainty of 2 ppm corresponds to $\Delta v \simeq 2$."
 As discussed. above. the systematic error from the Doppler roise can be of the sane order or even larger.," As discussed above, the systematic error from the Doppler noise can be of the same order or even larger."
 To avoid the influence of the Doppler noise on differcutial mecasurements of plivsical constants. lines of oulv one clement should be utilized.," To avoid the influence of the Doppler noise on differential measurements of physical constants, lines of only one element should be utilized."
 For instance. erouud state FIR fine-structure transitions of 1|] AA370.G09 jiu. [O1] AAG.LLG jan. [Ni] AM22.205 jn. [Ot AA52.88 μα. and |Fen| AA15.26 you can be used to directly constrain/a.," For instance, ground state FIR fine-structure transitions of ] $\lambda\lambda370, 609$ $\mu$ m, ] $\lambda\lambda63, 146$ $\mu$ m, ] $\lambda\lambda122, 205$ $\mu$ m, ] $\lambda\lambda52, 88$ $\mu$ m, and ] $\lambda\lambda15, 26$ $\mu$ m can be used to directly constrain."
. The sensitivity of this procedure to a- variation will be discussed in the following paper., The sensitivity of this procedure to $\alpha$ -variation will be discussed in the following paper.
 Up to now. [C1] was detected in five high-: objects where CO has been observed:117.. 7=1-0 line (Barvaiuis et al.," Up to now, ] was detected in five $z$ objects where CO has been observed:, $J$ =1-0 line (Barvainis et al."
 1997: cot al., 1997; et al.
 2005) and J—2-1 liue ect al., 2005) and $J$ =2-1 line et al.
 2003) at 2=2.557: IRAS aud SMAL0252... 7=1-0 line at 2=2.285 and 2.565. respectively ect al.," 2003) at $z = 2.557$; IRAS and SMM, $J$ =1-0 line at $z = 2.285$ and 2.565, respectively et al."
 2005):5255... 7=1-0 line at +=3.913 (Wageapi€ ct al.," 2005);, $J$ =1-0 line at $z = 3.913$ (Wagg et al."
 2006):19LL. 7=L0 line at :=1.120 (Pety et al.," 2006);, $J$ =1-0 line at $z = 4.120$ (Pety et al."
 2001)., 2004).
" Unfortunately. low signal-to-noise < 10) and large uncertainties of the positions of 1| and CO lines (~25 )) prevent us from coustrainiug relative changes im coustauts with au accuracy better than lot,"," Unfortunately, low signal-to-noise $\la 10$ ) and large uncertainties of the positions of ] and CO lines $\sim$ 25 ) prevent us from constraining relative changes in constants with an accuracy better than $10^{-4}$."
 Iu this letter we propose to use the FIR fine-structure lines of atoms aud ious in conjuction with low-Ixiug rotational lines of CO for probing the cosmic time evolution of the fundamental pliysical coustauts. namely the quotieut F=a? fp.," In this letter we propose to use the FIR fine-structure lines of atoms and ions in conjunction with low-lying rotational lines of CO for probing the cosmic time evolution of the fundamental physical constants, namely the quotient $F = \alpha^2/\mu$ ."
 The reported constraints on AF/F are obtained for two [Cu emitters recently discovered at 2=6.12 (Mioliuo et al., The reported constraints on ${\Delta F}/{F}$ are obtained for two ] emitters recently discovered at $z = 6.42$ (Maiolino et al.
 2005)and :=1.69 (lone et al., 2005)and $z = 4.69$ (Iono et al.
 2006)., 2006).
 We found no evideuce for thevariability of F at the level of 10.+ over a period of 13 Cyr., We found no evidence for thevariability of $F$ at the level of $10^{-4}$ over a period of 13 Gyr.
" The statistical reliability of this limit secs to be highenough since the expected value of the Doppler noise for the co-spatially distributed (Cu) and CO cinission lines σε~ a few +. is less that the error of the ue position measurement. s,=30 "," The statistical reliability of this limit seems to be highenough since the expected value of the Doppler noise for the co-spatially distributed ] and CO emission lines, $\sigma_v \sim$ a few , is less that the error of the line position measurement, $\sigma_v = 30$ "
For each planet the tables list the planet and parent star characteristics.,For each planet the tables list the planet and parent star characteristics.
 In addition there is an individual page for each planet and for each planetary system., In addition there is an individual page for each planet and for each planetary system.
 It is accessible by clicking on the planet name in the table (Fig 4.)., It is accessible by clicking on the planet name in the table (Fig 4.).
 The planet characteristics in the tables are given (when available) by Table 1., The planet characteristics in the tables are given (when available) by Table 1.
 The parent star characteristics given by individual tables are shown in Table 2 and Fig., The parent star characteristics given by individual tables are shown in Table 2 and Fig.
" 5 The individual pages for planets and planetary systems ""Notes for planet xx"" contain additional - they give the quantities listed in Table 1 plus data listed in Table 3 (when available) and their - molecules detected in the planet - specific - bibliography relevant for the planet (sorted by author or publication - links to professional websites associated with the planetary system."," 5 The individual pages for planets and planetary systems ""Notes for planet xx"" contain additional - they give the quantities listed in Table 1 plus data listed in Table 3 (when available) and their - molecules detected in the planet - specific - bibliography relevant for the planet (sorted by author or publication - links to professional websites associated with the planetary system."
 Data may be continuously refined on observers web pages: therefore we give a link to these - link to Simbad and ADS pages of the corresponding parent star., Data may be continuously refined on observers web pages: therefore we give a link to these - link to Simbad and ADS pages of the corresponding parent star.
 'The Fig 6 gives as an example the individual page for HD 189733 b. For multiplanet systems there is a synthetic page with all planets in the system and their characteristics (click on the star name in individual pages)., The Fig 6 gives as an example the individual page for HD 189733 b. For multiplanet systems there is a synthetic page with all planets in the system and their characteristics (click on the star name in individual pages).
 Links to individual planet pages of the Exoplanet Orbit Database at exoplanets.org are under development. -, Links to individual planet pages of the Exoplanet Orbit Database at exoplanets.org are under development. -
 Data are the latest known., Data are the latest known.
 They are updated daily., They are updated daily.
 As of February 2011 they are taken, As of February 2011 they are taken
terms of a sequential evolution of (he filamentary cloud.,terms of a sequential evolution of the filamentary cloud.
 If this is the case. the molecular ridge extending north from the L673-5MMMA would contract first at (he southern part of the cloud. and then the contraction would be propagating toward the northern part.," If this is the case, the molecular ridge extending north from the L673-SMM4 would contract first at the southern part of the cloud, and then the contraction would be propagating toward the northern part."
 We note that the observed line profiles toward the CCS peak in L673-9MMMA are svstematically broader than those in CD1230-3 and (vpical dense cores., We note that the observed line profiles toward the CCS peak in L673-SMM4 are systematically broader than those in CB130-3 and typical dense cores.
 This might reflect. possible effects of star formation such as infalline and/or outflow motions. alihough the infalling line asvimimetry has not been searched for L673-SMMA.," This might reflect possible effects of star formation such as infalling and/or outflow motions, although the infalling line asymmetry has not been searched for L673-SMM4."
 Previously. L673-SMMGA is reported to be a starless core (Visserelal.2002).. while a faint protostar candidate has been idenüfied toward the submillimeter dust continuum peak SMMA based on the mid-infrared observations with the Spitzer Space Telescope (Tsitaliοἱal.2010).," Previously, L673-SMM4 is reported to be a starless core \citep{visser2002}, while a faint protostar candidate has been identified toward the submillimeter dust continuum peak SMM4 based on the mid-infrared observations with the Spitzer Space Telescope \citep{tsitali2010}."
. The broader line widths in L613-5MMMA could be affected by the newly formed protostar in the vicinity of the submillimeter peak position., The broader line widths in L673-SMM4 could be affected by the newly formed protostar in the vicinity of the submillimeter peak position.
 If so. L612-SMMA is regarded as a chemically voung core with a signature of star forming aclivilies.," If so, L673-SMM4 is regarded as a chemically young core with a signature of star forming activities."
 We have carried out molecular line observations of newly found dark cloud cores. CD130- and L673-85MMA. showing remarkably intense spectra of the carbon-chain molecules such as CCS. IIC4N. and ICsN. We have also observed the NID; lines and other fundamental molecular lines toward these (wo cores.," We have carried out molecular line observations of newly found dark cloud cores, CB130-3 and L673-SMM4, showing remarkably intense spectra of the carbon-chain molecules such as CCS, $_{3}$ N, and $_{5}$ N. We have also observed the $_{3}$ lines and other fundamental molecular lines toward these two cores."
 Judeing from the NIL;/CCS ratios and DNC/IINE'C ratios. CD130-3 and L673-SMMA are analogous to the chemically voung dark cloud. cores called CCPRs named by Suzukietal.(1992). but. are slightly evolved (han those found in the Taurus region.," Judging from the $_{3}$ /CCS ratios and $^{13}$ C ratios, CB130-3 and L673-SMM4 are analogous to the chemically young dark cloud cores called CCPRs named by \citet{suzuki1992} but are slightly evolved than those found in the Taurus region."
 It should be noted that one of the newly found CCPR candidates. CDI30-3. is located close to other dense cores rich in carbon-chain molecules. L492 (IHirota&Yamamotollirotaetal.2009). and L483 (Ilirotaetal.2010).," It should be noted that one of the newly found CCPR candidates, CB130-3, is located close to other dense cores rich in carbon-chain molecules, L492 \citep{hirota2006, hirota2009} and L483 \citep{hirota2010}."
.. All of these cores belong to an optical dark cloud GE4 (Schneider&Elmeereen1979). as shown in Figure 1.., All of these cores belong to an optical dark cloud GF4 \citep{schneider1979} as shown in Figure \ref{fig-gf4}.
 We speculate (hat chemical properties in GF4 in the Aquila rift region are similar to those in the Taurus region., We speculate that chemical properties in GF4 in the Aquila rift region are similar to those in the Taurus region.
 According to the chemical model ealeulations (Suzukiοἱal.1992).. earbon-chain molecules are expected to be abundant in lower extinction and less dense regions where (he atomic carbon has not been locked into CO.," According to the chemical model calculations \citep{suzuki1992}, carbon-chain molecules are expected to be abundant in lower extinction and less dense regions where the atomic carbon has not been locked into CO."
 Thus. it is likely that the ΟΕ could be lower ex(ncetion ancl less dense molecular gas chuups formed in the regions in between translucent and dense molecular clouds.," Thus, it is likely that the CCPRs could be lower extinction and less dense molecular gas clumps formed in the regions in between translucent and dense molecular clouds."
 In fact. some of the CCPRs are identilied as relatively isolated small Bok globules (e.g. L492 and CB130-3 in the Aquila region) unlike the dense molecular cloud such as the Ophiuchus region.," In fact, some of the CCPRs are identified as relatively isolated small Bok globules (e.g., L492 and CB130-3 in the Aquila region) unlike the dense molecular cloud such as the Ophiuchus region."
 However. the CCPRs found in the Taurus and Aquila regions have almost similar ll» densities to other tvpical dark cloud cores according to the," However, the CCPRs found in the Taurus and Aquila regions have almost similar $_{2}$ densities to other typical dark cloud cores according to the"
nearly lareer than the N-rav scatter at 0.031250.007.,nearly larger than the X-ray scatter at $0.031 \pm 0.007$.
 A f-test of the means of the two samples rejects the null hypothesis that the two samples come from the same underlviug population at the level., A $t$ -test of the means of the two samples rejects the null hypothesis that the two samples come from the same underlying population at the level.
 The scatter is thought to reflect variations in ealaxy formation time (butseeMencietal.2008)., The scatter is thought to reflect variations in galaxy formation time \citep[but see][]{menci08}.
. It has thus been modeled using Bruzual-Charlot sinele-burst models (Druzual&Charlot2003).. which posit that all the stars in a given ealaxy are formed in a coeval burst at some redshift. τε. aud evolve passively thereafter.," It has thus been modeled using Bruzual-Charlot single-burst models \citep{bruzual03}, which posit that all the stars in a given galaxy are formed in a coeval burst at some redshift, $z_f$, and evolve passively thereafter."
 The scatter in the CM results from the variation iu formation times for the constituent ealaxies that have formed iu single bursts between relonization. τρ. and some lower redshift. ne," The scatter in the CMR results from the variation in formation times for the constituent galaxies that have formed in single bursts between reionization, $z_r$, and some lower redshift, $z_l$."
 Using the ACS fers iud κο respouse curves as described im Siriannietal. (2005).. we determine the expected observed scatter du /z75—ts5y using a sinele-burst spectrum. following the Monte Carlo method first described in vanDokkuimetal.(1998).," Using the ACS $i_{775}$ and $z_{850}$ response curves as described in \citet{sirianni05}, , we determine the expected observed scatter in $i_{775} - z_{850}$ using a single-burst spectrum, following the Monte Carlo method first described in \citet{vandokkum98}."
". Assumine a galaxy formed at some redshift. τε. we create 10.000 ""galaxies by drawine frou a vaucdom uniformi formation age distribution corresponding to a redshift range of uoXoig€oi "," Assuming a galaxy formed at some redshift, $z_f$, we create 10,000 “galaxies” by drawing from a random uniform formation age distribution corresponding to a redshift range of $z_l \le z_f \le z_r$."
For cach +). the last redshift at which ealaxies formed. the model predicts a scatteriu/zz5κου that would be observed at some redshift. τωρα.," For each $z_l$, the last redshift at which galaxies formed, the model predicts a scatter in $i_{775}-z_{850}$ that would be observed at some redshift, $z_{obs}$."
" For a eiven set of clusters. we then choose the best-fit model by uiuinizng : where the ""mniod aud ""obs superscripts refer to the predicted model aud observed data scatters. aud 06,44. 1s the error on cach observed a"","," For a given set of clusters, we then choose the best-fit model by minimizing $\chi^2$: where the “mod” and “obs” superscripts refer to the predicted model and observed data scatters, and $\sigma_{err}$ is the error on each observed $\sigma^{obs}$."
 Ti Figure L. we show the result of this process for both the optical (solid) aud. X-rav (dashed) samples.," In Figure 1, we show the result of this process for both the optical (solid) and X-ray (dashed) samples."
" The optical sample favors +,=1.6. and the N-rav seuple favors 4=2.1. suggestiug that the E/SO ealaxies ou the red-sequeuce in X-ray selected clusters euded their star formation some 0.9 Cyr earlier."," The optical sample favors $z_l= 1.6$, and the X-ray sample favors $z_l= 2.1$, suggesting that the E/S0 galaxies on the red-sequence in X-ray selected clusters ended their star formation some 0.9 Gyr earlier."
 The stall umuber of E/S0 galaxies. Neysy. n some of the less rich clusters lighlielts a possible concern.," The small number of E/S0 galaxies, $N_{E/S0}$, in some of the less rich clusters highlights a possible concern."
 Siuple Monte. Carlo simulations of random draws frou a normal distribution indicate that at No=10. even the bi-weight estimator of scale τοις a scatter that is biased high by1056: this is reduced to by N=20. and Z1 at N—10.," Simple Monte Carlo simulations of random draws from a normal distribution indicate that at $N=10$, even the bi-weight estimator of scale returns a scatter that is biased high by; this is reduced to by $N=20$ , and $ \lesssim 1\%$ at N=40."
 Contamination by non-cluster members also coutributes to scatter., Contamination by non-cluster members also contributes to scatter.
 Randomly adding a single galaxy that passes the red-sequence color cuts adds as much as an additional bias at No=10., Randomly adding a single galaxy that passes the red-sequence color cuts adds as much as an additional bias at $N=10$.
" Fortunately, our analysis of the fields indicate that the average backerounel or morphologicallv selected. galaxies passing our color aud Iuniuositv cuts) is X1 galaxy."," Fortunately, our analysis of the fields indicate that the average background (for morphologically selected galaxies passing our color and luminosity cuts) is $\lesssim 1$ galaxy."
 Another concern is line-ofsielt projection of large structures., Another concern is line-of-sight projection of large structures.
 RCS J0139.6-2901 is known to show two redshift peaks at 2=0.9135 and 2=0.9681 (Cilbaulsetal.2007:Cainct 2008).. for a separation of &7000 lan +.," RCS J0439.6-2904 is known to show two redshift peaks at $z=0.9435$ and $z=0.9681$ \citep{gilbank07,cain08}, , for a separation of $\simeq 7000$ km $^{-1}$."
 A cursory analvsis of the halo catalogs from the VIRGO simulations (Evrardetal.2002)— shows that halo-halo projections of this sort are expected iu about ~1020% of RCS clusters im this mass range at 2~l:oa similar value is found in spectroscopic data (Cülbauketal.2007)., A cursory analysis of the halo catalogs from the VIRGO simulations \citep{evrard02} shows that halo-halo projections of this sort are expected in about $\simeq 10-20\%$ of RCS clusters in this mass range at $z \sim 1$; a similar value is found in spectroscopic data \citep{gilbank07}.
". At such a separation. Monte Carlo simulations show that two projected halos cach with o,=1000 lau s.4 have a resultant measured scatter inflated by oulv 0.003 1nagnitudes. which has no siguificaut effect on our results."," At such a separation, Monte Carlo simulations show that two projected halos each with $\sigma_v = 1000$ km $^{-1}$ have a resultant measured scatter inflated by only $0.003$ magnitudes, which has no significant effect on our results."
 Spectroscopy does uot vet exist for RCS JO337.8-28LL and spectroscopic confirmation is pending., Spectroscopy does not yet exist for RCS J0337.8-2844 and spectroscopic confirmation is pending.
 Oulw limited spectroscopy exists for RCS J2156.7-01L8 (5 confined spectroscopic nmnienibers). auc its measured N-ray fiux is consistent with zero (Wicksctal.2008). although the stroug lensing in this svstem (Claddersetal.2003) indicates that its mass is cluster scale.," Only limited spectroscopy exists for RCS J2156.7-0448 (5 confirmed spectroscopic members), and its measured X-ray flux is consistent with zero \citep{hicks08}, although the strong lensing in this system \citep{gladders03}
 indicates that its mass is cluster scale."
 Regardless. we find that removing one or both of these clusters does not affect our couclusious.," Regardless, we find that removing one or both of these clusters does not affect our conclusions."
 The other seven clusters are robustly spectroscopically confirmed (Cilbaulsetal. 20049)., The other seven clusters are robustly spectroscopically confirmed \citep{gilbank09}.
. For three of the N-rayv clusters (all except WARP JL115.113612). Meietal.(2009) place coustraiuts on z With sinele-burst models. using a combination of TST data. manual morphological measurements. and spectroscopic confirmation where available.," For three of the X-ray clusters (all except WARP J1415.1+3612), \citet{mei09} place constraints on $z_l$ with single-burst models, using a combination of HST data, manual morphological measurements, and spectroscopic confirmation where available."
" They eeneralle find formation epochs of 7,&2.2. only slightly hieher than our own mcasurcients."," They generally find formation epochs of $z_l \simeq 2.2$, only slightly higher than our own measurements."
 As part of the validation process of our pipeline. we compare our measured CAITR parameters in these 3 X-ray clusters witli previous work. and find that they agree within crrors.," As part of the validation process of our pipeline, we compare our measured CMR parameters in these 3 X-ray clusters with previous work, and find that they agree within errors."
" Forthe [| optical clusters in this study that have velocity dispersion estimates, wefiud the distribution of velocity dispersions is simular to the X-ray sample. with"," Forthe 4 optical clusters in this study that have velocity dispersion estimates, wefind the distribution of velocity dispersions is similar to the X-ray sample, with"
particlesaremeter-size (Adachi1976;Weidenschilling1977)..SincegaspressuregradientWard1972).. dustsettlinginturbulentaccretiondiskswerecarriedoutby Cuzzietal.(1993).. Alivake&Nakagawa(1995)and Dubrulleetal.(199,"\defcitealias{kato08}{\tikzmark{mainBodyCitationEnd0}{Paper~I}\tikzmark{mainBodyStart1}}\tikzmark{mainBodyEnd1}


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\section{Introduction}


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5)..Thevpresentedthatlargeinstability.2005).. (Weidenschilling1977.1980:Ishitsu&Sekiva2003:GomezOstriker Johansenetal.(2006b)..h," \citet{cuzzi93},\tikzmark{mainBodyCitationEnd135}\tikzmark{mainBodyStart136},\tikzmark{mainBodyEnd136} \tikzmark{mainBodyCitationStart137}\citet{miyake95} \citet{miyake95} \tikzmark{mainBodyCitationEnd137} \tikzmark{mainBodyStart138}and\tikzmark{mainBodyEnd138} \tikzmark{mainBodyCitationStart139}\citet{dub95}. \citet{dub95}.\tikzmark{mainBodyCitationEnd139}\tikzmark{mainBodyStart140}.\tikzmark{mainBodyEnd140} \tikzmark{mainBodyStart141}They\tikzmark{mainBodyEnd141} \tikzmark{mainBodyStart142}presented\tikzmark{mainBodyEnd142} \tikzmark{mainBodyStart143}that\tikzmark{mainBodyEnd143} \tikzmark{mainBodyStart144}large\tikzmark{mainBodyEnd144} \tikzmark{mainBodyStart145}dust\tikzmark{mainBodyEnd145} \tikzmark{mainBodyStart146}particles\tikzmark{mainBodyEnd146} \tikzmark{mainBodyStart147}settle\tikzmark{mainBodyEnd147} \tikzmark{mainBodyStart148}down\tikzmark{mainBodyEnd148} \tikzmark{mainBodyStart149}toward\tikzmark{mainBodyEnd149} \tikzmark{mainBodyStart150}their\tikzmark{mainBodyEnd150} \tikzmark{mainBodyStart151}equilibrium\tikzmark{mainBodyEnd151} \tikzmark{mainBodyStart152}distribution\tikzmark{mainBodyEnd152} \tikzmark{mainBodyStart153}in\tikzmark{mainBodyEnd153} \tikzmark{mainBodyStart154}a\tikzmark{mainBodyEnd154} \tikzmark{mainBodyStart155}turbulent\tikzmark{mainBodyEnd155} \tikzmark{mainBodyStart156}diffusive\tikzmark{mainBodyEnd156} \tikzmark{mainBodyStart157}time\tikzmark{mainBodyEnd157} \tikzmark{mainBodyStart158}scale\tikzmark{mainBodyEnd158} \tikzmark{mainBodyStart159}while\tikzmark{mainBodyEnd159} \tikzmark{mainBodyStart160}small\tikzmark{mainBodyEnd160} \tikzmark{mainBodyStart161}ones\tikzmark{mainBodyEnd161} \tikzmark{mainBodyStart162}remain\tikzmark{mainBodyEnd162} \tikzmark{mainBodyStart163}mixed\tikzmark{mainBodyEnd163} \tikzmark{mainBodyStart164}throughout\tikzmark{mainBodyEnd164} \tikzmark{mainBodyStart165}the\tikzmark{mainBodyEnd165} \tikzmark{mainBodyStart166}whole\tikzmark{mainBodyEnd166} \tikzmark{mainBodyStart167}gas\tikzmark{mainBodyEnd167} \tikzmark{mainBodyStart168}disk.\tikzmark{mainBodyEnd168} \tikzmark{mainBodyStart169}If\tikzmark{mainBodyEnd169} \tikzmark{mainBodyStart170}dust\tikzmark{mainBodyEnd170} \tikzmark{mainBodyStart171}density\tikzmark{mainBodyEnd171} \tikzmark{mainBodyStart172}in\tikzmark{mainBodyEnd172} \tikzmark{mainBodyStart173}midplane\tikzmark{mainBodyEnd173} \tikzmark{mainBodyStart174}becomes\tikzmark{mainBodyEnd174} \tikzmark{mainBodyStart175}high\tikzmark{mainBodyEnd175} \tikzmark{mainBodyStart176}enough,\tikzmark{mainBodyEnd176} \tikzmark{mainBodyStart177}Kelvin-Helmholtz\tikzmark{mainBodyEnd177} \tikzmark{mainBodyStart178}instabilities\tikzmark{mainBodyEnd178} \tikzmark{mainBodyStart179}between\tikzmark{mainBodyEnd179} \tikzmark{mainBodyStart180}a\tikzmark{mainBodyEnd180} \tikzmark{mainBodyStart181}sediment\tikzmark{mainBodyEnd181} \tikzmark{mainBodyStart182}layer\tikzmark{mainBodyEnd182} \tikzmark{mainBodyStart183}of\tikzmark{mainBodyEnd183} \tikzmark{mainBodyStart184}dust\tikzmark{mainBodyEnd184} \tikzmark{mainBodyStart185}and\tikzmark{mainBodyEnd185} \tikzmark{mainBodyStart186}the\tikzmark{mainBodyEnd186} \tikzmark{mainBodyStart187}overlying\tikzmark{mainBodyEnd187} \tikzmark{mainBodyStart188}gas\tikzmark{mainBodyEnd188} \tikzmark{mainBodyStart189}can\tikzmark{mainBodyEnd189} \tikzmark{mainBodyStart190}drive\tikzmark{mainBodyEnd190} \tikzmark{mainBodyStart191}turbulence\tikzmark{mainBodyEnd191} \tikzmark{mainBodyStart192}and\tikzmark{mainBodyEnd192} \tikzmark{mainBodyStart193}mix\tikzmark{mainBodyEnd193} \tikzmark{mainBodyStart194}the\tikzmark{mainBodyEnd194} \tikzmark{mainBodyStart195}dust\tikzmark{mainBodyEnd195} \tikzmark{mainBodyStart196}layer\tikzmark{mainBodyEnd196} \tikzmark{mainBodyStart197}enough\tikzmark{mainBodyEnd197} \tikzmark{mainBodyStart198}to\tikzmark{mainBodyEnd198} \tikzmark{mainBodyStart199}prevent\tikzmark{mainBodyEnd199} \tikzmark{mainBodyStart200}gravitational\tikzmark{mainBodyEnd200} \tikzmark{mainBodyStart201}instability\tikzmark{mainBodyEnd201} \tikzmark{mainBodyCitationStart202}\citep{wei77, wei80, ishi03, gomez05}. \citep{wei77, wei80, ishi03, gomez05}.\tikzmark{mainBodyCitationEnd202}\tikzmark{mainBodyStart203}.\tikzmark{mainBodyEnd203} \tikzmark{mainBodyCitationStart204}\citet{joh06b},"
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LEM (Ho) > 5 A)) with nearly all having spectral twpes rom M3-Mb5.,$>$ $\alpha$ ) $>$ 5 ) with nearly all having spectral types from M3-M5.
. We note that variability plavs a role in (he identification of la emission (e.g.. Wilkine 1987: HLartigaa 1993).," We note that variability plays a role in the identification of $\alpha$ emission (e.g., Wilking 1987; Hartigan 1993)."
 Among the six Ho emitters with multiple observations. the equivalent width of Object 2-30 (field number-aperture from Table 2) dropped from 38 {to 8.5 iin only one dav.," Among the six $\alpha$ emitters with multiple observations, the equivalent width of Object 2-30 (field number-aperture from Table 2) dropped from 38 to 8.5 in only one day."
 The brown dwarf candidate GY 5 was observed to have an (IIa) = 15 wwhereas a similar spectrum obtained in 1998 showed no detectable emission (Wilking 1999)., The brown dwarf candidate GY 5 was observed to have an $\alpha$ ) = 15 whereas a similar spectrum obtained in 1998 showed no detectable emission (Wilking 1999).
 In addition. the shape of the emission profile also appeared to change in three cases (Chini 8. EL 24. and Object 2-30).," In addition, the shape of the emission profile also appeared to change in three cases (Chini 8, EL 24, and Object 2-30)."
 All of the strong Ilo. emission lines were well-resolved with typical EWIIMs of 250 km | compared to the 128 km ! velocity resolution of our data., All of the strong $\alpha$ emission lines were well-resolved with typical FWHMs of 250 km $^{-1}$ compared to the 128 km $^{-1}$ velocity resolution of our data.
 These broad Πα profiles. which can exceed 300 km + in our sample. have been successfully modeled. as arising in magnetospheric accretion columns. (Ilartinann.. Hewett. Calvet 1994: Muzerolle. Calvet. Ilartmann 2001).," These broad $\alpha$ profiles, which can exceed 300 km $^{-1}$ in our sample, have been successfully modeled as arising in magnetospheric accretion columns (Hartmann, Hewett, Calvet 1994; Muzerolle, Calvet, Hartmann 2001)."
 Thirteen of the Ila profiles were Clearly asvinnmetric or displaved non-gaussian wings., Thirteen of the $\alpha$ profiles were clearly asymmetric or displayed non-gaussian wings.
 The profile shapes are noted in Table 3 using the classification scheme of Reipurth. Pedrosa. Lago (1996).," The profile shapes are noted in Table 3 using the classification scheme of Reipurth, Pedrosa, Lago (1996)."
 The prevalence of wines or asvnunelries on the blue-side of the profile is (vpical among CTTS and suggests the presence of mass outflows., The prevalence of wings or asymmetries on the blue-side of the profile is typical among CTTS and suggests the presence of mass outflows.
 The Ca II triplet at 8660 wwas observed in emission in 14 of the Πα emitters and was strongest in the G or IX spectral ivpe objects., The Ca II triplet at 8660 was observed in emission in 14 of the $\alpha$ emitters and was strongest in the G or K spectral type objects.
 No attempt was mace to deblend them from the weaker Paschen emission lines Pa 13. Pa 15. and Pa 16.," No attempt was made to deblend them from the weaker Paschen emission lines Pa 13, Pa 15, and Pa 16."
 In general. the Ca HI lines were narrower than Ho and barely resolved in our data with typical FWILMs of 150 kins !.," In general, the Ca II lines were narrower than $\alpha$ and barely resolved in our data with typical FWHMs of 150 km $^{-1}$."
 Fig., Fig.
 5 shows an expanded view of the Ia emission and Ca II emission lines for a representative sample of 7 CTTS., 5 shows an expanded view of the $\alpha$ emission and Ca II emission lines for a representative sample of 7 CTTS.
 As in Fig., As in Fig.
 1L. the spectra have been smoothed to a resolution of 5.7À.," 1, the spectra have been smoothed to a resolution of 5.7."
. Ha profiles for objects 1-24 and 1-29 were symmetric while the rest of (he profiles in Fie., $\alpha$ profiles for objects 1-24 and 1-29 were symmetric while the rest of the profiles in Fig.
 5a exhibited a blueward asvaumetry., 5a exhibited a blueward asymmetry.
 Only the source Object 2-31/1-35 (bottom wo spectra in Fig., Only the source Object 2-31/1-35 (bottom two spectra in Fig.
 5a and 5b) displaved asymmetric profiles in both Ca II and Ia., 5a and 5b) displayed asymmetric profiles in both Ca II and $\alpha$ .
 Emission lines from both permitted and forbidden atomic (ransiGions were detected in the spectra of the strongest Ilo. emitters in Table 3 with EW(Ila) > 28A., Emission lines from both permitted and forbidden atomic transitions were detected in the spectra of the strongest $\alpha$ emitters in Table 3 with $\alpha$ ) $>$ 28.
. Both Pa 14 and O 1 (7773 À)) displaved broad profiles with FWHAIs similar to that of Ho. The other O I lines and the Ile I lines all appeared to be barely resolved. with FWIIMSs between 150-130 kms +.," Both Pa 14 and O I (7773 ) displayed broad profiles with FWHMs similar to that of $\alpha$ The other O I lines and the He I lines all appeared to be barely resolved, with FWHMs between 150-180 km $^{-1}$."
 The detection of forbidden line emission from [O I] was observed in 6 objects., The detection of forbidden line emission from [O I] was observed in 6 objects.
 Weak (5 HI] emission at 6731 wwas detected in only 2 objects (SR 22 and WSD 46)., Weak [S II] emission at 6731 was detected in only 2 objects (SR 22 and WSB 46).
 The detection of these lines is consistent with the presence of winds associatedwith CTTS (Edwards 1931)., The detection of these lines is consistent with the presence of winds associatedwith CTTS (Edwards 1987).
redshifts both for source and lens are unavailablet.,redshifts both for source and lens are unavailable.
. Moreover. the measured image separations ol 1359--154. 1608+656 and 21144022 are not used because the observed angular sizes are due to multiple galaxies within their critical The Sloan Dieital Sky Survey Quasar Lens Search (SQLS: Oguietal.(2006))) is a photometric and spectroscopic survey covering nearly a quarter of the entire skv 2000).," Moreover, the measured image separations of 1359+154, 1608+656 and 2114+022 are not used because the observed angular sizes are due to multiple galaxies within their critical The Sloan Digital Sky Survey Quasar Lens Search (SQLS; \citet{Ogu06}) ) is a photometric and spectroscopic survey covering nearly a quarter of the entire sky \citep{Yor00}."
. We (ry to [ind suitable lens samples [rom the optical quasar catalog of the Sloan Digital Sky Survev (SDSS: Yorketal. (2000)))., We try to find suitable lens samples from the optical quasar catalog of the Sloan Digital Sky Survey (SDSS; \citet{Yor00}) ).
 The first complete lens sample [rom Data Release 3 selected from 22.683 low-redshift (0.6<2« 2.2) is provided in Inadaetal.(2003).," The first complete lens sample from Data Release 3 selected from 22,683 low-redshift $0.6<z<2.2$ ) is provided in \citet{Inada08}."
". It consists of 11 lensed quasars satisfying the following well-defined selection criteria: 1)The image separation is between I"" and 20"" with quasars brighter than 7=19.1: 2) The flux ratio of faint to bright images is greater than 10. for double lenses.", It consists of 11 lensed quasars satisfying the following well-defined selection criteria: 1)The image separation is between $1''$ and $20''$ with quasars brighter than $i=19.1$; 2) The flux ratio of faint to bright images is greater than $10^{-0.5}$ for double lenses.
 In this paper. an additional cut is applied to select a appropriate subsaimple: (he lensing ealaxy should be fainter (han (he quasar components. because a too bright lens galaxy will strongly. allect the colors of the quasars (Richardsetal.2002).," In this paper, an additional cut is applied to select a appropriate subsample: the lensing galaxy should be fainter than the quasar components, because a too bright lens galaxy will strongly affect the colors of the quasars \citep{Richards02}."
. Four lensed quasars. Q09572-561. SDSS J10042-4112. SDSS J1332+0347 and SDSS J15244-4409 are removed with this eut.," Four lensed quasars, Q0957+561, SDSS J1004+4112, SDSS J1332+0347 and SDSS J1524+4409 are removed with this cut."
 Like the CLASS. due to the absence of lens redshifts. (wo more quasars. SDSS J100125027 and SDSS J102144913 are excluded.," Like the CLASS, due to the absence of lens redshifts, two more quasars, SDSS J1001+5027 and SDSS J1021+4913 are excluded."
 ILowever. we successfully add four lens redshift data including SDSS J1620+1203. one of the eight newly discovered ancl confined (wo-iage lensed quasars by SDSS Quasar Lens Search (Ixavoetal.2009).," However, we successfully add four lens redshift data including SDSS J1620+1203, one of the eight newly discovered and confirmed two-image lensed quasars by SDSS Quasar Lens Search \citep{Kayo09}."
. In table 1.. we summarize 29 Strongly-lensed Sources (redshifts both for sources ancl lenses. as well as the largest image separations ancl galaxy tvpes) [rom the CLASS (JVAS). ihe SDSS. the PANELS and the Snapshot. which formulate a well-defined combined statistical sample for model constraints.," In table \ref{tab:data}, we summarize 29 Strongly-lensed Sources (redshifts both for sources and lenses, as well as the largest image separations and galaxy types) from the CLASS (JVAS), the SDSS, the PANELS and the Snapshot, which formulate a well-defined combined statistical sample for model constraints."
 In what follows. we choose two popular dark enerey models ancl examine whether they are consistent with the lens redshift data listed above.," In what follows, we choose two popular dark energy models and examine whether they are consistent with the lens redshift data listed above."
mmagnelic flux cannot be dissipated.,magnetic flux cannot be dissipated.
 ILowever. even at b—0.95. the upper branch of the dispersion relation carries particles with a mean Lorentz factor one order of magnitude larger (han those of the incoming. striped wind solution.," However, even at $b=0.95$, the upper branch of the dispersion relation carries particles with a mean Lorentz factor one order of magnitude larger than those of the incoming, striped wind solution."
 According to the above figures. superhuninal waves cannot propagate in (he inner paris of a pulsar wind.," According to the above figures, superluminal waves cannot propagate in the inner parts of a pulsar wind."
 The radius al which propagation becomes possible is close to 4$=1 for vanishing phase-averaged magnetic field. aud rises with (his quantity.," The radius at which propagation becomes possible is close to $R=1$ for vanishing phase-averaged magnetic field, and rises with this quantity."
" However. in the striped wind model. (he luminosity of the wind. aud. hence. the parameter ej, is a function of latitude."," However, in the striped wind model, the luminosity of the wind, and, hence, the parameter $a_{\rm L}$ is a function of latitude."
 In particular. the energy flix carried by the fields is proportional to sin?&. where 9 is (he colatitude. (measured Grom the rotation axis).," In particular, the energy flux carried by the fields is proportional to $\sin^2\theta$, where $\theta$ is the colatitude, (measured from the rotation axis)."
 The flux carried by (he particles. on the other hand. is expected to be much smaller. but. its angular dependence is uncertain.," The flux carried by the particles, on the other hand, is expected to be much smaller, but its angular dependence is uncertain."
 Assuming. for simplicity. that the ratio σ of these fluxes is independent of colatitude. one has ⋅ Wo. − ∩∟⋡≺⋅≼↓∶∔⋅−≻⋗⋖↓∩↓∎∣∠⋮⊰⋉⋅↕⋟∖⊽⊔∐↲∖↽≀↧↴↥⋯↲∪↓∩∟∐↥⊔∐↲≼↲≺⇂∏≀↧↴↥∪↕⋅↕≀↕↴↥↕↽≻↥≀↧↴∐≼↲⋅ ↴∏∐↲≼⇂≼↲↕↽≻≼↲∐≼⇂≼," Assuming, for simplicity, that the ratio $\sigma$ of these fluxes is independent of colatitude, one has $a_{\rm L, eq}=4.2\times10^{10} L_{38}^{1/2}$, is the value of $a_{\rm L}$ in the equatorial plane."
↲∐≺∢≼↲∪↓⋟⊔∐↲≀↧↴∖↽≼↲↕⋅≀↧↴≸≟≼↲∐↓≀↧↴↖≺↽↔↴∐≼↲∐≺∢⇂∎∐↲↥≺⇂≺∢≀↧↴↕⋅↕⋅↕≼↲≼⊓↽≻⋡∖↽⊔∐↲⊳∖⇁↥∏↕↽≻≼↲≼⇂∖∖↽↥∐≼⇂∪∐↥≀↧↴⋯⋯⇂≼↲ depends on the inclination angle a between the magnetic aud rotation axes., The dependence of the average magnetic field carried by the striped wind on latitude depends on the inclination angle $\alpha$ between the magnetic and rotation axes.
 Two current sheets are present in the striped wind. located at phases where n is an integer (?)..," Two current sheets are present in the striped wind, located at phases where $n$ is an integer \citep{kirketal02}."
 Al @=atan(cota). the sheets merge. and vanish at higher latitudes (smaller colatitudes 9).," At $\theta=\textrm{atan}(\textrm{cot}\alpha)$, the sheets merge, and vanish at higher latitudes (smaller colatitudes $\theta$ )."
 At these sheets. the magnetic field reverses direction. so," At these sheets, the magnetic field reverses direction, so"
samples of Feltzing et ((2001) and Nordstrómm οἱ al. (,samples of Feltzing et (2001) and Nordströmm et al. (
2004) apply mainly. for stars less than 3 Gyr. whereas ages of our stars are generally greater than this limit.,"2004) apply mainly for stars less than 3 Gyr, whereas ages of our stars are generally greater than this limit."
 For ages larger than 3 Gyr the age-metallicity diagrams of Feltzing et al. (, For ages larger than 3 Gyr the age-metallicity diagrams of Feltzing et al. (
2001: their Fig.,2001; their Fig.
 10) and of Nordstrómm οἱ al. (, 10) and of Nordströmm et al. (
2004: their Fig.,2004; their Fig.
 27) appear very similar to our Fig., 27) appear very similar to our Fig.
 9a. almost no correlation between age anc metallicity.," 9a, almost no correlation between age and metallicity."
 In Fig., In Fig.
 9a the 22 thick-disk stars show a range of 7 Gyr in their ages but no obvious correlation between the ages and metallicities. in contrast with the results of Bensby. Feltzing Luncdstrómm (2004). who find a pronounced age-metallicity relation for the thick disk.," 9a the 22 thick-disk stars show a range of 7--8 Gyr in their ages but no obvious correlation between the ages and metallicities, in contrast with the results of Bensby, Feltzing Lundströmm (2004), who find a pronounced age-metallicity relation for the thick disk."
 However. Bensby et ((2004) work with a thick-clisk sample ten times larger than ours. separated from the thin disk more rigorously. and so their conclusions should be preferred.," However, Bensby et (2004) work with a thick-disk sample ten times larger than ours, separated from the thin disk more rigorously, and so their conclusions should be preferred."
 We do agree with them that the thick-clisk stars show a very significant range in ages. <5 Gye.," We do agree with them that the thick-disk stars show a very significant range in ages, $\ga 5$ Gyr."
 From Vig., From Fig.
 9a. it can be seen that there is lack of metal-poor voung stars in the left-bottom corner.," 9a, it can be seen that there is lack of metal-poor young stars in the left-bottom corner."
 However. there exists numerous old metal-rich stars in the right-upper corner. which leads to the substantial scatter and the Ilattening of the plot.," However, there exists numerous old metal-rich stars in the right-upper corner, which leads to the substantial scatter and the flattening of the plot."
 The existence of the old. metal-rich stars can also seen in the works of Feltzing et al... (, The existence of the old metal-rich stars can also seen in the works of Feltzing et al. (
(2001). Nordstrómam et al. (,"2001), Nordströmm et al. ("
2004). Roeha-Pinto et al. (,"2004), Rocha-Pinto et al. ("
2000). and Chen et al. (,"2000), and Chen et al. ("
2003).,2003).
 I'ig.9c shows the same age-metallicity plot for the main sequence stars from. Nidever et al. (, Fig.9c shows the same age-metallicity plot for the main sequence stars from Nidever et al. (
2002) for which extra-solar planets have been detected (Schneider 2005: Mayor et al.,2002) for which extra-solar planets have been detected (Schneider 2005; Mayor et al.
 2005)., 2005).
 Again. the relation between the metallicity and the age is very [lat as in Fig.," Again, the relation between the metallicity and the age is very flat as in Fig."
 9a. the main cdillerence being that the large majority of these stars have high metallicities. AL/LL]0.2 dex. as has been pointed out in many studies. such as Gonzalez (1997). Laughlin (2000). Santos. Israclian Mawvor (2001). Murray Chabover (2002). and. τος (2002).," 9a, the main difference being that the large majority of these stars have high metallicities, $[M/H] \ga -0.2$ dex, as has been pointed out in many studies, such as Gonzalez (1997), Laughlin (2000), Santos, Israelian Mayor (2001), Murray Chaboyer (2002), and Reid (2002)."
 However. two of these stars (IID 1143729 and. HD 114762) have lower metallicities. M1]~0.6 dex. and have been classified thick disk. with rather large ages. ~12 Cyr.," However, two of these stars (HD 114729 and HD 114762) have lower metallicities, $[M/H] \sim -0.6$ dex, and have been classified thick disk, with rather large ages, $\sim 12$ Gyr."
 Interestinglv. this entire sample of stars with extra-solar planetary systems has large ages and a large range in ages. 37. age S13 Cyr.," Interestingly, this entire sample of stars with extra-solar planetary systems has large ages and a large range in ages, $3 \la$ age $\la 13$ Gyr."
 In Fig.10 we plot the ages ancl moetallicities for our tota sample. for three bins of Ady.," In Fig.10 we plot the ages and metallicities for our total sample, for three bins of $M_{\rm V}$."
 A similar pattern as in bie. of Feltzing et al. (, A similar pattern as in Fig.14 of Feltzing et al. (
2001) appears.,2001) appears.
 As we allow stars with fain absolute magnitudes to enter our samples. the upper right-rand corner of the age-metallicity plot is progressively fillec in.," As we allow stars with faint absolute magnitudes to enter our samples, the upper right-hand corner of the age-metallicity plot is progressively filled in."
 In panel (c) of Fig., In panel (c) of Fig.
 10. stars with ΑΗ]0.1 dex aux ages larger than LO Cir become numerous in the upper right-1and corner.," 10, stars with $[M/H]>-0.1$ dex and ages larger than 10 Gyr become numerous in the upper right-hand corner."
 From panel (b) of Fig., From panel (b) of Fig.
 10. one might conclude a zürlv obvious and. pronounced age-metallicity relation. bu with the stars of panel (c) this has mostly disappeared.," 10, one might conclude a fairly obvious and pronounced age-metallicity relation, but with the stars of panel (c) this has mostly disappeared."
 Fig., Fig.
 106 reveals that old. metal-rich stars are dominant. a he faint absolute magnitudes.," 10c reveals that old, metal-rich stars are dominant at the faint absolute magnitudes."
 Chen et al. (, Chen et al. (
2003) investigate the nature of these ol metal-rich stars in the solar neighbourhood. ancl conclude hat most seem to have originated [rom the inner thin disk.,2003) investigate the nature of these old metal-rich stars in the solar neighbourhood and conclude that most seem to have originated from the inner thin disk.
 They note that LED. 190360 is an exception in their sample and suggest that it is a metal-rich thick-disk star., They note that HD 190360 is an exception in their sample and suggest that it is a metal-rich thick-disk star.
" A 15.8 Gyr age can be attributed to this star since its position in the VA. (boy), diagram of Fig."," A 15.8 Gyr age can be attributed to this star since its position in the $M_{\rm V}$, $(b-y)_{o}$ diagram of Fig."
 S places it slightly to the left of the 16 Gr isochrone., 8 places it slightly to the left of the 16 Gyr isochrone.
 Our photometric metal abundance CAL/H]=10.17 dex) and a 15.8 Gyr age show that this star is old and metal-rich. in accordance with the suggestion of Chen et al. (," Our photometric metal abundance $[M/H]=+ 0.17$ dex) and a 15.8 Gyr age show that this star is old and metal-rich, in accordance with the suggestion of Chen et al. ("
2003).,2003).
" For this star. our kinematics (3, —190 kmsto =56⋅ km n ) and. photometric. abundance CALM)=10.17 dex) are almost identical to the ones of Chen et al. ("," For this star, our kinematics $V_{\rm rot} = $ 190 km $^{-1}$, $W' = -56$ km $^{-1}$ ) and photometric abundance $[M/H]=+ 0.17$ dex) are almost identical to the ones of Chen et al. ("
2003).,2003).
 Whereas our Y=35 value indicates that it is a thin-disk star. the rather large absolute value for W would suggest thick disk. again in agreement with Chen et al. (," Whereas our $X=-35$ value indicates that it is a thin-disk star, the rather large absolute value for $W'$ would suggest thick disk, again in agreement with Chen et al. ("
2003).,2003).
 LD 190360 is another star which does not fit cleanly into all the criteria for a single stellar population. and shows again the risk in using only two variables. MALI] and Via. to define the population type of a single star.," HD 190360 is another star which does not fit cleanly into all the criteria for a single stellar population, and shows again the risk in using only two variables, [M/H] and $V_{\rm rot}$, to define the population type of a single star."
 The scatter observed in age-metallicity plot of Fig., The scatter observed in age-metallicity plot of Fig.
 9a can be interpreted. within the scope of models of Galactic chemical evolution of Pilvugin Eclmunes (1996). ane Raiteri. Villata Navarro (1996).," 9a can be interpreted within the scope of models of Galactic chemical evolution of Pilyugin Edmunds (1996) and Raiteri, Villata Navarro (1996)."
 These models consider the chemical enrichment with time. together with the dvnamica evolution.," These models consider the chemical enrichment with time, together with the dynamical evolution."
 The model of Pilvugin Edmunds (1996) specifically. takes into account. both the self-enrichment. of star forming regions with sequential star formation anc the effect of irregular rates of infall of un-processed. matter onto the stellar disk., The model of Pilyugin Edmunds (1996) specifically takes into account both the self-enrichment of star forming regions with sequential star formation and the effect of irregular rates of infall of un-processed matter onto the stellar disk.
 These Galactic: chemical-evolution models can generate a very conspicuous scatter. such as tha seen in the observational age-metallicity. plots. such as our Fig.," These Galactic chemical-evolution models can generate a very conspicuous scatter, such as that seen in the observational age-metallicity plots, such as our Fig."
 9a. Fig.," 9a, Fig."
 14a of Ecvardsson et al. (, 14a of Edvardsson et al. (
1993). Figs.,"1993), Figs."
 2728, 27–28
olfers an explanation for their formation.,offers an explanation for their formation.
 The scenario proposed here is in a preliminary stage., The scenario proposed here is in a preliminary stage.
 It has a big advantage in that the same basic mechanism can work to suppress star formation in newly formed galaxies (Paper 2) and in forming wide jets in cooling flow clusters aud planetary nebulae (Paper 1)., It has a big advantage in that the same basic mechanism can work to suppress star formation in newly formed galaxies (Paper 2) and in forming wide jets in cooling flow clusters and planetary nebulae (Paper 1).
 Namely. ] suggest that NSs (or DIIs) at the center of CCSNs shut off their own growth ancl expel the rest of the mass available for accretion bv the same mechanism that SAIBIT shut off their own growth. as well as that of their host bulge. in voung galaxies.," Namely, I suggest that NSs (or BHs) at the center of CCSNs shut off their own growth and expel the rest of the mass available for accretion by the same mechanism that SMBH shut off their own growth, as well as that of their host bulge, in young galaxies."
 IT thank Eli Livne and. Milos Milosavljevie. for useful comments. This research was supported by the Asher Fund for Space Research at the Technion. and by the Israel Science Foundation.," I thank Eli Livne and Milos Milosavljevic, for useful comments, This research was supported by the Asher Fund for Space Research at the Technion, and by the Israel Science Foundation."
we find no relation between P and 7 for GX 3394 or for any ο the field stars. within the errors of each measurement. ,"we find no relation between P and $\nu$ for GX 339–4 or for any of the field stars, within the errors of each measurement. :"
40:: ~DUC LP is detected in this source at the 30 level in Hf and dvs. when it was in a hard state at the end of its 2005 outburst.," $\sim 5$ LP is detected in this source at the $\sigma$ level in $H$ and $Ks$, when it was in a hard state at the end of its 2005 outburst."
 In the upper panel of Fig., In the upper panel of Fig.
 4 we plot the polarisation spectrum. including the optical measurements of CGliozzietal.(1998). during outburst in. 1997.," 4 we plot the polarisation spectrum, including the optical measurements of \cite{glioet98} during outburst in 1997."
 The optical polarisation. which varies as a function. of orbital phase (taken during a soft X-ray state). is caused by local scattering and should decrease at lower frequencies.," The optical polarisation, which varies as a function of orbital phase (taken during a soft X-ray state), is caused by local scattering and should decrease at lower frequencies."
 We see a statistical increase in LP in the NUR (shown by the fit to the opticalNIR data) which must therefore have a clilferent origin to the optical LP., We see a statistical increase in LP in the NIR (shown by the fit to the optical–NIR data) which must therefore have a different origin to the optical LP.
 Our A s-band LP of 5.83: is not consistent with the confidence upper limit of LP« in As seen during quiescence (Dubus&Chaty2006)., Our $Ks$ -band LP of $\pm$ is not consistent with the confidence upper limit of $<$ in $Ks$ seen during quiescence \citep{dubuch06}.
.. The NIIS LP we measure must be intrinsic and transient. and we interpret it as originating from the optically thin region of the jets(see Section 3.2).," The NIR LP we measure must be intrinsic and transient, and we interpret it as originating from the optically thin region of the jets (see Section 3.2)."
 The PA of the optical LP 1307) is also cilferent from that measured both in Jf (444187) and dvs (157187), The PA of the optical LP $^\circ$ ) is also different from that measured both in $H$ $\pm 18^\circ$ ) and $Ks$ $\pm18^\circ$ ).
 Rotation of PA with time is seen in some jets (c.g.Llan- indicating an overall rotation of the local. magnetic field.," Rotation of PA with time is seen in some jets \citep[e.g.][]{hannet00,fendet02,gallet04} indicating an overall rotation of the local magnetic field."
 The As LP detection is 14 days after the Z£. implving the magnetic field may be rotating during this time.," The $Ks$ LP detection is 14 days after the $H$, implying the magnetic field may be rotating during this time."
 The //-band DA is consistent with the direction of the jet on the plane of the skv: 47° (Hljellming&Rupen1995).. implying that the electrie feld. vector is parallel to thejets at this time and the magnetic fieldis perpendicular to the jets.," The $H$ -band PA is consistent with the direction of the jet on the plane of the sky; $^\circ$ \citep{hjelru95}, implying that the electric field vector is parallel to the jets at this time and the magnetic field is perpendicular to the jets."
 Two weeks later the field orientation had appeared to change by ~707., Two weeks later the field orientation had appeared to change by $\sim 70^\circ$.
" Interestinely, Hlannikainenetal.(2000). found. from. well-sampled. racio data that the field orientation changed only near the end of the 1994 outburst: here we see a change also at the end of its 2005 outburst."," Interestingly, \cite{hannet00} found from well-sampled radio data that the field orientation changed only near the end of the 1994 outburst; here we see a change also at the end of its 2005 outburst."
 The de-reddened ο){νο Uusx densities of GRO J1655 indicate a bluc spectrum. and are similar to those measured by Migliarietal.(2007) between two and Live weeks earlier.," The de-reddened $JHKs$ flux densities of GRO J1655--40 indicate a blue spectrum, and are similar to those measured by \cite{miglet07} between two and five weeks earlier."
 In their Fig., In their Fig.
 6. the broadband. SED shows 1c companion stardominating the optical anc NER. with 1c jet. dominatingη. only below voz510713 Iz.," 6, the broadband SED shows the companion stardominating the optical and NIR, with the jet dominating only below $\nu \approx 5\times 10^{13}$ Hz."
 Our Jilivs observations are therefore also dominated by the sta., Our $JHKs$ observations are therefore also dominated by the star.
 According to the model in Fig., According to the model in Fig.
 6 of Migliarictal. , 6 of \citeauthor{miglet07} 
"1ο histogram of concentration values for haloes in the 10""M. mass bin.",the histogram of concentration values for haloes in the $10^6 \Msun$ mass bin.
 We report little to no dependence. of C's on spin in these mass ranges., We report little to no dependence of $C_{178}$ on spin in these mass ranges.
 We also look at the relationship between halo mass and Cz., We also look at the relationship between halo mass and $C_{178}$.
" We find tha e fitting function in Bullocketal.(200A). extrapolatec down to these masses and up to these high redshifts. given we OvmOpe840|c) where pp=MM, and AL is 10 twpical collapsing mass at redshift z. is not à σοοι it. ancl precliets values for the concentration that are too small compared to our estimates from the simulation."," We find that the fitting function in \citet{Bullock01A} extrapolated down to these masses and up to these high redshifts, given by $C_{\rm{vir}} \approx 9 \mu^{-0.13}/(1+z)$, where $\mu = M/M_\star$ and $M_\star$ is the typical collapsing mass at redshift $z$, is not a good fit, and predicts values for the concentration that are too small compared to our estimates from the simulation."
 This disagreement is not surprising as Bullock ct al., This disagreement is not surprising as Bullock et al.
 stucdiec ueher mass haloes at lower redshifts (2<5) that have aad a significant amount of time to merge and virialize.," studied higher mass haloes at lower redshifts $z\,<\,5)$ that have had a significant amount of time to merge and virialize."
 Observed rotation curves are used to obtain mass estimates of galaxies anc clusters., Observed rotation curves are used to obtain mass estimates of galaxies and clusters.
 The measured velocity of stars and gas rellects the combined. gravitational potential of roth the barvons and dark matter in the galaxy., The measured velocity of stars and gas reflects the combined gravitational potential of both the baryons and dark matter in the galaxy.
 To infer he total mass from an observationally determined rotation curve requires understanding how both types of matter ave distributed spatially in galaxies., To infer the total mass from an observationally determined rotation curve requires understanding how both types of matter are distributed spatially in galaxies.
 Persic.Salucci.&Stel(1996) report that for Sb-Im spirals. rotation curves can »v represented by a universal function which is the sum in quadrature of two velocity curves: one [rom the disc and one rom the dark matter halo.," \citet{Persic96} report that for Sb-Im spirals, rotation curves can be represented by a universal function which is the sum in quadrature of two velocity curves: one from the disc and one from the dark matter halo."
 This mocel is developed further in Saluceietal.(2007)... where the dark matter velocity component is strictly. a function of the virial mass of the alo.," This model is developed further in \citet{Salucci07}, where the dark matter velocity component is strictly a function of the virial mass of the halo."
 1 however. the velocity curve of the dark matter halo is dependent on a second. parameter. such as A. we would expect to find a systematic error in a mass estimate for the ealaxy derived from the observed rotation curve.," If, however, the velocity curve of the dark matter halo is dependent on a second parameter, such as $\lambda$, we would expect to find a systematic error in a mass estimate for the galaxy derived from the observed rotation curve."
 A relationship between A and a characteristic circular velocity can be expected i£ we consider an alternative spin parameter given in Bullocketal. (2001B):: A=JJDOAIVη. where J is the angular momentum inside some radius. £2. AL is the mass inside Z? and V. is the circular velocity at Z2.," A relationship between $\lambda$ and a characteristic circular velocity can be expected if we consider an alternative spin parameter given in \citet{Bullock01B}: : $\lambda^\prime = J/\sqrt{2}MVR$, where $J$ is the angular momentum inside some radius, $R$, $M$ is the mass inside $R$ and $V$ is the circular velocity at $R$."
 For the case of a truncated. singular isothermal sphere. A= at the virial radius.," For the case of a truncated, singular isothermal sphere, $\lambda^\prime = \lambda$ at the virial radius."
 Thus it is expected that a relationship between the A used in our work and a characteristic circular velocity should. exist., Thus it is expected that a relationship between the $\lambda$ used in our work and a characteristic circular velocity should exist.
 We find that the peak velocity. Vin. in the measured circular velocity curve. defined as 1;=VCMG(v. systematically depends on spin.," We find that the peak velocity, $V_{\rm{max}}$, in the measured circular velocity curve, defined as $V_c = \sqrt{GM(<r)/r}$, systematically depends on spin."
 Fo measure this curve. we sort all particles in the halo by their distance to the halo centre.," To measure this curve, we sort all particles in the halo by their distance to the halo centre."
 From this. we can read olf the circular velocity curve at the radius of cach particle. ancl we define Vis as the maximum value of this curve.," From this, we can read off the circular velocity curve at the radius of each particle, and we define $V_{\rm{max}}$ as the maximum value of this curve."
 Figure 6. (right column) shows that for all mass bins. there is à svstematic offset in the peas velocity as a function of halo spin: high spin haloes have higher Vis than their low spin counterparts.," Figure \ref{Struct} (right column) shows that for all mass bins, there is a systematic offset in the peak velocity as a function of halo spin: high spin haloes have higher $V_{\rm{max}}$ than their low spin counterparts."
 The bottom panel shows two histograms of Vias. binned by. spin.," The bottom panel shows two histograms of $V_{\rm{max}}$, binned by spin."
" The peal of the high and. low spin curves is olfset by in the 10""M. mass bin. and in the 10AL. haloes (not plotted)."," The peak of the high and low spin curves is offset by in the $10^6 \Msun$ mass bin, and in the $10^7 \Msun$ haloes (not plotted)."
 From a given Vias one can infer a halo mass using the definition of cireular velocity such that A(«r)=Viar/C., From a given $V_{\rm{max}}$ one can infer a halo mass using the definition of circular velocity such that $M(<r) = V_{\rm{max}}^2 r / G$.
 Alternatively. one can use published relationships between Vias and Adve such as the power law VinsXALK where a=0.3140.08 from Shawetal.(2006).2001A).," Alternatively, one can use published relationships between $V_{\rm{max}}$ and $M_{\rm{vir}}$ such as the power law $V_{\rm{max}} \propto M^{1/\alpha}$ where $\alpha = 0.31 \pm 0.08$ from \citet{Shaw06} ."
. Either way. when two halos of the same (unknown) mass have dillerent spins. there is a bias in the resulting Vines. Which will leacl to a bias in the mass estimated from the circular velocity.," Either way, when two halos of the same (unknown) mass have different spins, there is a bias in the resulting $V_{\rm{max}}$, which will lead to a bias in the mass estimated from the circular velocity."
 We can estimate the extra uncertainty in the halo mass due to the bias induced by A., We can estimate the extra uncertainty in the halo mass due to the bias induced by $\lambda$.
 Using the circular velocity definition. we can translate a dillerence in velocity to a dillerence in. mass: DACey—INCMDAM.," Using the circular velocity definition, we can translate a difference in velocity to a difference in mass: $2 \Delta(v) / v = \Delta(M) / M$."
 Therefore the estimated total mass from an observationally measured. value of Vinay can be oll bv arising due to the unknown value of the spin parameter of the dark matter halo that hosts the galaxy., Therefore the estimated total mass from an observationally measured value of $V_{\rm{max}}$ can be off by arising due to the unknown value of the spin parameter of the dark matter halo that hosts the galaxy.
 Another well explored correlation at low recshift is between he shapes of dark matter haloes ancl the spin parameter., Another well explored correlation at low redshift is between the shapes of dark matter haloes and the spin parameter.
 lere. we investigate the corresponding correlations for these veh redshift haloes.," Here, we investigate the corresponding correlations for these high redshift haloes."
 Phe existence of a correlation between 1alo shape ancl spin is likely to have important consequences or the formation of pre-ealactic disks in these haloes., The existence of a correlation between halo shape and spin is likely to have important consequences for the formation of pre-galactic disks in these haloes.
 We calculate the sphericity. s=cfe. and triaxialitv. T=bD)wec7). from the eigenvalues (a6c6) of he normalized moment of inertia tensor. where οἱ is the distance to the halo center.," We calculate the sphericity, $s = c/a$, and triaxiality, $T=(a^2-b^2)/(a^2-c^2),$ from the eigenvalues $ a > b > c$ ) of the normalized moment of inertia tensor, where $\vec{x}$ is the distance to the halo center."
 The tensor is calculated using onlv the particles assigned to the halo. not from all particles within the Z?;z« as is often done.," The tensor is calculated using only the particles assigned to the halo, not from all particles within the $R_{178}$ as is often done."
 This allows for consistency with our measurements of A., This allows for consistency with our measurements of $\lambda$.
 We used the normalized. tensor so that we do not weight. particles on the outskirts of a halo stronger., We used the normalized tensor so that we do not weight particles on the outskirts of a halo stronger.
 This helps to prevent the halo shape being dominated: by residual tidal features from a recent merger or other irregularities found. only in the outer regions which are not present in the halo interior., This helps to prevent the halo shape being dominated by residual tidal features from a recent merger or other irregularities found only in the outer regions which are not present in the halo interior.
 We caution that both the normalized (e.g.Xvila-Iteese2005:Alleoodctal.2006) and unnormalized. (e.g.Jang- tensor are used in the literature. and so caution must be used when comparing shape distributions.," We caution that both the normalized \citep[e.g.][]{Avila05, Allgood06} and unnormalized \citep[e.g.][]{jch01,Shaw06, Maccio08, Faltenbacher09} tensor are used in the literature, and so caution must be used when comparing shape distributions."
 We show in Figure 7 histograms of s and 7 when calculated using both a normalized. and unnormalized. moment of inertia tensor., We show in Figure \ref{NormShape} histograms of $s$ and $T$ when calculated using both a normalized and unnormalized moment of inertia tensor.
 We find that many more halos are significantly. aspherical. ancl halos tend to be less prolate when the shape is found using the unnormalized tensor.," We find that many more halos are significantly aspherical, and halos tend to be less prolate when the shape is found using the unnormalized tensor."
 This is contrary to the study in (Allgoodetal.2006).. which reported no systematic offset in 5 between the two methods.," This is contrary to the study in \citep{Allgood06}, which reported no systematic offset in $s$ between the two methods."
 We note. however. that they onlyused. particles within 0.3744. rather than all particles assigned to the halo as we do.," We note, however, that they onlyused particles within $0.3 R_{\rm{vir}}$, rather than all particles assigned to the halo as we do."
 Fherefore. our unnormalized method will have a stronger bias because we include distant particles in the calculation of the halo shape.," Therefore, our unnormalized method will have a stronger bias because we include distant particles in the calculation of the halo shape."
In what follows. we use the normalized tensor to calculate the shape of the haloes.,"In what follows, we use the normalized tensor to calculate the shape of the haloes."
 We show in Figure 8 the relations between s (left column). 7 (right column). and A. as well as the histograms os and T binned by spin and mass.," We show in Figure \ref{shape} the relations between $s$ (left column), $T$ (right column), and $\lambda$ , as well as the histograms of $s$ and $T$ binned by spin and mass."
 For higher spin haloes.," For higher spin haloes,"
sources im halos of fixed mass or for the same source viewed along differcut directions (Figure 1)).,sources in halos of fixed mass or for the same source viewed along different directions (Figure \ref{fig:PSF}) ).
 The ouc-ido term in Equation (1)) should have dependence on environment in addition to halo mass., The one-halo term in Equation \ref{eqn:2halo}) ) should have dependence on environment in addition to halo mass.
" To obtain the nean one-halo teri for the stacked image and decompose he surface brightuess profile. we perform, radiative ranster calculations separately for cach source with halo uass in the Lott13£. inass bin."," To obtain the mean one-halo term for the stacked image and decompose the surface brightness profile, we perform radiative transfer calculations separately for each source with halo mass in the $10^{11}\hMsun$ mass bin."
 We then stack the individual ouc-hialo terms to obtain the mean., We then stack the individual one-halo terms to obtain the mean.
 The dotted curve in Figure 5 is the wean ouc-hialo term. or sources in LOMATAL. halos., The dotted curve in Figure \ref{fig:stackSB_1h2h} is the mean one-halo term for sources in $10^{11}\hMsun$ halos.
 The shape is similar o that seen in Figure. L., The shape is similar to that seen in Figure \ref{fig:PSF}.
 The dashed curve is the two- term. inferred frou subtracting the ouc-halo term. roni the total surface brightuess profile.," The dashed curve is the two-halo term, inferred from subtracting the one-halo term from the total surface brightness profile."
 The two-halo erm can be expressed as a convolution (Equation 1)). with the couvolution kernel being the onc-halo term of he clustered star-forming halos ofeM masses.," The two-halo term can be expressed as a convolution (Equation \ref{eqn:2halo}) ), with the convolution kernel being the one-halo term of the clustered star-forming halos of masses."
 The shape of the oue-halo term at different halo mass is similar o that shown in Figure 5.., The shape of the one-halo term at different halo mass is similar to that shown in Figure \ref{fig:stackSB_1h2h}.
 Iu the two-halo term. a slater reaches out to a radius of 2htMpe. which is around the cutoff scale of the mass-averaged ouc-lalo erm.," In the two-halo term, a plateau reaches out to a radius of $\hMpc$, which is around the cutoff scale of the mass-averaged one-halo term."
 This is not a coincidence., This is not a coincidence.
 The scale where the ateau in the two-halo term ends marks the spatial extent of the extended emission of the clustered sources. since on scales larger than this the smoothiug effect from the source PSF is simall.," The scale where the plateau in the two-halo term ends marks the spatial extent of the extended emission of the clustered sources, since on scales larger than this the smoothing effect from the source PSF is small."
 As the two-halo term dominates on large scales. the above scale is just the outer characteristic scale Roy seen in the total surface brightuess profile.," As the two-halo term dominates on large scales, the above scale is just the outer characteristic scale $R_{\rm out}$ seen in the total surface brightness profile."
" The πι characteristic scale Ri, marks the transition from the ouc-halo term: dominated reeinue to the two-halo term dominated regine.", The inner characteristic scale $R_{\rm in}$ marks the transition from the one-halo term dominated regime to the two-halo term dominated regime.
 The realistic decomposition of the surface brightness profile confirms the results of the test in Figure 2. that the origin of the plateau between the two characteristic scales im the total surface brightuess profile is the extended CLUISSIOL., The realistic decomposition of the surface brightness profile confirms the results of the test in Figure \ref{fig:stack_tophat_M11} that the origin of the plateau between the two characteristic scales in the total surface brightness profile is the extended emission.
 The euvironment dependent radiative transfer couples the observed cinission with the circtunealactic and intergalactic cuvirouments., The environment dependent radiative transfer couples the observed emission with the circumgalactic and intergalactic environments.
 Alay consequences of such a coupling are studied in Paper I and Paper IL., Many consequences of such a coupling are studied in Paper I and Paper II.
 For the stacked surface brightuess profile. the enviroment dependence also appears. as detailed below.," For the stacked surface brightness profile, the environment dependence also appears, as detailed below."
 At fixed halo mass. which corresponds to fixed intrinsic lhnuumnositv or UV hinunositv in our model. the observed. huninosity has ai broad distribution. reflecting the distribution of cuviroumeuts.," At fixed halo mass, which corresponds to fixed intrinsic luminosity or UV luminosity in our model, the observed luminosity has a broad distribution, reflecting the distribution of environments."
 Iu our model. for cach source we link together the pixels above a surface brightuess threshold similar to that used in Ouchietal.(2008) to define the observed emission. aud if noue of the pixels around the central source exceeds the threshold. we simply take the flux in the pixel at the source position as the observed. cussion (sec Paper I for details).," In our model, for each source we link together the pixels above a surface brightness threshold similar to that used in \citet{Ouchi08} to define the observed emission, and if none of the pixels around the central source exceeds the threshold, we simply take the flux in the pixel at the source position as the observed emission (see Paper I for details)."
 The observed. Iuninuositv is only a fraction of the extended cussion. comme from the central. high surface brightuess part of the source.," The observed luminosity is only a fraction of the extended emission, coming from the central, high surface brightness part of the source."
 The one-lalo term of the surface brightucss profile is expected to be closely related to the enviroment., The one-halo term of the surface brightness profile is expected to be closely related to the environment.
 We divide the sources mto two samples of equal size. according to the observed Iuniuositvy.," We divide the sources into two samples of equal size, according to the observed luminosity."
 In Fieure 6.. we show the stacked surface brightuess profile for the bright half and faint half. respectively.," In Figure \ref{fig:stackSB_halfhalf}, we show the stacked surface brightness profile for the bright half and faint half, respectively."
 The dotted curves show the correspouding one-halo terms., The dotted curves show the corresponding one-halo terms.
 We note that the fluxes inferred from the one-halo terms of the two cases are nof necessarily the same., We note that the fluxes inferred from the one-halo terms of the two cases are not necessarily the same.
 The reason is that the scattered ciuission is not isotropic. being sensitive to the density and velocity structures around the source.," The reason is that the scattered emission is not isotropic, being sensitive to the density and velocity structures around the source."
 Overall. the sample of sources with lower observed luninosity has a shallower stacked surface brightness profile at small radius aud there is no clear scale of the transition from the imucr cusp to the approximate plateau.," Overall, the sample of sources with lower observed luminosity has a shallower stacked surface brightness profile at small radius and there is no clear scale of the transition from the inner cusp to the approximate plateau."
 The result implies that the stacked narrowband nage for star-forming galaxies with weaker observed cuiission would appear to be less conipact., The result implies that the stacked narrowband image for star-forming galaxies with weaker observed emission would appear to be less compact.
 So far we have focused ou the surface brightucss profile for sources in halos of 1015.TAL..., So far we have focused on the surface brightness profile for sources in halos of $10^{11}\hMsun$.
 The profile is expected to be a function of the halo mass., The profile is expected to be a function of the halo mass.
 We show the dependence on halo mass in Figure 7.. both for halo in narrow nass bius (left paucl) aud above different mass thresholds (wight panel).," We show the dependence on halo mass in Figure \ref{fig:SB_Mh}, both for halo in narrow mass bins (left panel) and above different mass thresholds (right panel)."
 Since iu our model the UV Iuiminositv is tightly correlated with halo mass. the plot also represeuts a sequence of profiles as a function of UV. luminosity.," Since in our model the UV luminosity is tightly correlated with halo mass, the plot also represents a sequence of profiles as a function of UV luminosity."
 The amplitude of the stacked profile increases with halo ass., The amplitude of the stacked profile increases with halo mass.
 Ou small scales this increase is larecly a reflection of the fact that halos of higher masses host sources of higher hunuinositv. while ou large scales there is an additional coutributiou from stronger source clusterimg around more massive halos.," On small scales this increase is largely a reflection of the fact that halos of higher masses host sources of higher luminosity, while on large scales there is an additional contribution from stronger source clustering around more massive halos."
 On small scales ΕΕ the inner characteristic radius). where the ouc-halo profile makes a substantial contribution. sources m higher mass halos show a steeper profile.," On small scales (inside the inner characteristic radius), where the one-halo profile makes a substantial contribution, sources in higher mass halos show a steeper profile."
 The inner characteristic scale δημ. where the profile starts to level off. iucreases with halo mass.," The inner characteristic scale $R_{\rm in}$, where the profile starts to level off, increases with halo mass."
 It inuples that sources in higher mass halos have more extended emission., It implies that sources in higher mass halos have more extended emission.
 The outer characteristic scale, The outer characteristic scale
or strip the galaxy.,or strip the galaxy.
 As a result. these simulations should provide a pure test of ram pressure stripping and should be easier to model than the second type of simulations.," As a result, these simulations should provide a pure test of ram pressure stripping and should be easier to model than the second type of simulations."
 On the other hand. if the lessons learnt [rom mocelling the uniform medium runs do not also generally apply to more realistic situations. such as those in the 2-svstenmi runs. they will be of little practical use.," On the other hand, if the lessons learnt from modelling the uniform medium runs do not also generally apply to more realistic situations, such as those in the 2-system runs, they will be of little practical use."
 This is why we have elected to use both tvpes of simulations to study this problem., This is why we have elected to use both types of simulations to study this problem.
 The galaxies (and the groups into which they fall. in the case of the 2-svstem runs) are represented. by spherically-svmametrie svstenis composed of a realistic mixture of dark matter and οπρο barvons.," The galaxies (and the groups into which they fall, in the case of the 2-system runs) are represented by spherically-symmetric systems composed of a realistic mixture of dark matter and diffuse baryons."
" The dark matter is assumed to follow the NEW distribution (Navarro et 11996: 1997): where p,=Als(απ) and lere. 17200 is the radius within which the mean density is 200 times the critical density. pog. and Aloo—Mí(rso9)(A3),20 Perit."," The dark matter is assumed to follow the NFW distribution (Navarro et 1996; 1997): where $\rho_s = M_s/(4 \pi r_s^3)$ and Here, $r_{200}$ is the radius within which the mean density is 200 times the critical density, $\rho_{\rm crit}$, and $M_{200} \equiv M(r_{200}) = (4/3) \pi r_{200}^3 \times 200
\rho_{\rm crit}$ ."
" The only ""free parameter of the NEW. profile is the scale radius. rs."," The only `free' parameter of the NFW profile is the scale radius, $r_s$."
 Phe scale radius isoften expressed in terms ofa concentration parameter. esog=rÁoofrs.," The scale radius isoften expressed in terms of a concentration parameter, $c_{200} \equiv r_{200}/r_s$."
 By default. we adopt the mean mass-concentration (Alsou— 6200) relation derived. from theShinulalion. (Springel et 22005) by Neto et ((2007).," By default, we adopt the mean mass-concentration $M_{200}-c_{200}$ ) relation derived from the (Springel et 2005) by Neto et (2007)."
 Phis relationship is similar to that derived previously by Ike et ((2001)., This relationship is similar to that derived previously by Eke et (2001).
" For simplicity. the diffuse. barvons. are. assumed. to initially trace the dark matter distribution. with the ratio of gas to total mass set to the universal ratio fj,=0,/0,,0.022h.7/03= 0.141. where f is the Hubble constant. in units of 100 km Mpe.|."," For simplicity, the diffuse baryons are assumed to initially trace the dark matter distribution, with the ratio of gas to total mass set to the universal ratio $f_b = \Omega_b/\Omega_m = 
0.022 h^{-2}/0.3 = 0.141$ , where $h$ is the Hubble constant in units of $100$ km $^{-1}$ $^{-1}$."
 Phe other properties of the clilfuse eas (i.e. temperat+ure ancl pressure profiles) are fixed bv ensuring the gas is initially eravitationally bound and in hyerostatic equilibrium. While the assumption that the gas initially traces the dark matter is reasonable for the bulk of the barvons in massive groups and clusters (e.g... Vikhlinin et 22006: MeCarthy et 220075). it is almost certainly not a very realistic approximation for relatively low-mass svstenis. such as galaxies.," The other properties of the diffuse gas (i.e., temperature and pressure profiles) are fixed by ensuring the gas is initially gravitationally bound and in hydrostatic equilibrium, While the assumption that the gas initially traces the dark matter is reasonable for the bulk of the baryons in massive groups and clusters (e.g., Vikhlinin et 2006; McCarthy et 2007b), it is almost certainly not a very realistic approximation for relatively low-mass systems, such as galaxies."
 Phe reason. of course. is that non-gravitational physics. such as cooling ancl feedback. due. lor example. to supernovae and/or AGN. which are neglected in our simulations. can significantly alter the propertics of the eas in these svstenis.," The reason, of course, is that non-gravitational physics, such as cooling and feedback due, for example, to supernovae and/or AGN, which are neglected in our simulations, can significantly alter the properties of the gas in these systems."
 Phese processes are poorly understood and the properties of the eas will likely depend: sensitively on the assumed. feedback model., These processes are poorly understood and the properties of the gas will likely depend sensitively on the assumed feedback model.
 Pherefore. any clistribution we select. for the hot gaseous halo of the galaxies will be somewhathoc.," Therefore, any distribution we select for the hot gaseous halo of the galaxies will be somewhat."
 The important point. however. is that one can use the simulations to develop aphysicad model for ram. pressure stripping that can. with some confidence. x applied more generally.," The important point, however, is that one can use the simulations to develop a model for ram pressure stripping that can, with some confidence, be applied more generally."
 We argue that the analytic model developed. below is just such. a model., We argue that the analytic model developed below is just such a model.
 As will be demonstrated. tuning the model to match just one of our simulations results in very good agreement with all the other simulations. in spite of their widely varving physical conditions.," As will be demonstrated, tuning the model to match just one of our simulations results in very good agreement with all the other simulations, in spite of their widely varying physical conditions."
 The reader is referred to 82 of ALOT for a. detailed discussion. of how we establish equilibrium. configurations of dark matter and gas particles that follow an NEWtribution’., The reader is referred to 2 of M07 for a detailed discussion of how we establish equilibrium configurations of dark matter and gas particles that follow an NFW.
 In the case of the 2-svstemi runs. the more massive system is set to have a total mass of Alouy=LOM AL... while the less massive svstems have masses in the range 2LOMAL.xMou (Lo. mass ratios from 50:1 to 10:1).," In the case of the 2-system runs, the more massive system is set to have a total mass of $M_{200} = 10^{14} M_\odot$ , while the less massive systems have masses in the range $2 \times 10^{12} M_\odot 
\leq M_{200} \leq 10^{13} M_\odot$ (i.e., mass ratios from 50:1 to 10:1)."
 Thus. the 2-svstem runs represent galaxies with masses comparable to or larger than a normal elliptical falling into à moderate mass group/low mass cluster.," Thus, the 2-system runs represent galaxies with masses comparable to or larger than a normal elliptical falling into a moderate mass group/low mass cluster."
 Note that for galaxies within this mass range. the mean temperature of their gaseous halos ranges between zl3.lO? Ww. In 11. we show the initial gas density and temperature profiles for the hot gaseous halo of one of the galaxies and for the ICM of the LOYAL. group.," Note that for galaxies within this mass range, the mean temperature of their gaseous halos ranges between $\approx 1-3\times10^6$ K. In 1, we show the initial gas density and temperature profiles for the hot gaseous halo of one of the galaxies and for the ICM of the $10^{14} M_\odot$ group."
" The default gas particle nmiass. nis... is set to 210f, Ad. while the default dark matter particle mass. naa. is set to 2.107(1fo)M.."," The default gas particle mass, $m_{\rm gas}$, is set to $2\times10^{8} f_b \ M_\odot$ , while the default dark matter particle mass, $m_{\rm dm}$ , is set to $2\times10^{8} 
(1-f_b) \ M_\odot$."
 In the 2-svstem runs. these masses are fixed for both the group and the galaxy.," In the 2-system runs, these masses are fixed for both the group and the galaxy."
 This, This
that the cuuission liue spectrum of 5 Cas is not well represcuted by Menzel case B recombination liue theory.,that the emission line spectrum of $\gamma$ Cas is not well represented by Menzel case B recombination line theory.
 Many line fluxes correlate with the local coutimmn aud are independent of the intrinsic line strength (Einstein A coctiicicut}., Many line fluxes correlate with the local continuum and are independent of the intrinsic line strength (Einstein A coefficient).
 The observed line fluxes and widths suggest that these lines are formed im an iuner region with welldetermined size. aud that ouly the intrinsically strougest lines have a coutribution from outer lavers.," The observed line fluxes and widths suggest that these lines are formed in an inner region with well-determined size, and that only the intrinsically strongest lines have a contribution from outer layers."
 This paper is organized as follows., This paper is organized as follows.
 Iu Sect., In Sect.
 2 we briefly discuss the observations aud data reduction., 2 we briefly discuss the observations and data reduction.
 Section 3 discusses the contimumun and Sect., Section 3 discusses the continuum and Sect.
 { deals with the line spectra., 4 deals with the line spectrum.
 Section 5 discusses some plications of our nicasureimoenuts for the structure of the disc of +Cas., Section 5 discusses some implications of our measurements for the structure of the disc of $\gamma$Cas.
" The Be star 5 Cas was observed with the SWS ou hoard ISO on July 22nd. 1996. as part of the SWS euuantecd time programme BESTARS,."," The Be star $\gamma$ Cas was observed with the SWS on board ISO on July 22nd, 1996, as part of the SWS guaranteed time programme BESTARS."
 A full spectral scan (2.1-15 sau) using Astronomical ObservationTemplate (AQT) no., A full spectral scan (2.4-45 $\mu$ m) using Astronomical ObservationTemplate (AOT) no.
 Le speed L(?) was obtained. while also several AOTO2 line scans were taken.," 1, speed 4 \citep{1996A&A...315L..49D} was obtained, while also several AOT02 line scans were taken."
 The observations were reduced using the SWS Interactive Aualvsis (IA?) software package. with calibration filles equivalent to pipeline version 7.0.," The observations were reduced using the SWS Interactive Analysis $^3$ ) software package, with calibration files equivalent to pipeline version 7.0."
 Further processing consisted of bad data removal aud rebinning on an equidistant waveleueth exid., Further processing consisted of bad data removal and rebinning on an equidistant wavelength grid.
 The fiux levels are accurate to within 5 per ceut for the wavelengths shortward of 7 jun. The observations between 7 and 12 jaa (band. 2€) suffer from momnory. effects: this has little influence ou the measured line properties but does increase he uncertainty of the coutimuun flux level to 15 per ceut., The flux levels are accurate to within 5 per cent for the wavelengths shortward of 7 $\mu$ m. The observations between 7 and 12 $\mu$ m (band 2C) suffer from memory effects; this has little influence on the measured line properties but does increase the uncertainty of the continuum flux level to 15 per cent.
 At even kreer waveleugths the signal to noise ratio decreases dramatically aud only the strongest lines cau be neasuredd with reasonable accuracy., At even longer wavelengths the signal to noise ratio decreases dramatically and only the strongest lines can be measured with reasonable accuracy.
 Most of the emission ines are partially resolved with a ratio of FWIIM to the FWIIM of the oeκαποια. profile between 1.1-3.5., Most of the emission lines are partially resolved with a ratio of FWHM to the FWHM of the instrumental profile between 1.4-3.5.
 Ouly 6 of the enission lines are considered unresolved having lis ratio below 1.l., Only 6 of the emission lines are considered unresolved having this ratio below 1.4.
 Since the SWS iustruneutal profile is approximately Ciaussimn (7) and the observed lines are well fitted) by Crassians. we estimate the original line width from: where (uns ds the observed ΕΑΝΗΝΕν «ope is the original FWIIA aud Uis is the FWIIM of the lustrimental profile.," Since the SWS instrumental profile is approximately Gaussian \citep{1996A&A...315L..60V} and the observed lines are well fitted by Gaussians, we estimate the original line width from: where $w_\mathrm{obs}$ is the observed FWHM, $w_\mathrm{org}$ is the original FWHM and $w_\mathrm{inst}$ is the FWHM of the instrumental profile."
 The latter value varies with wavelength., The latter value varies with wavelength.
 To determüne (gua. We use nieasured hue widths of euülssiou lines of planetary nebulae: aud6302.. observed in the same observiug modo.," To determine $w_\mathrm{inst}$, we use measured line widths of emission lines of planetary nebulae; and, observed in the same observing mode."
 No siguificaut line profile viuiatious are observed., No significant line profile variations are observed.
 We show the final AOTOL spectrin in Fig. 1.., We show the final AOT01 spectrum in Fig. \ref{fig:swsspec}.
 The contimuni enerev clistribution of  Cas at IR wavelengths is donmünated by free-free and bouud-free chussion from the ionized part of the circumstellar eas (e.c.7?7)..," The continuum energy distribution of $\gamma$ Cas at IR wavelengths is dominated by free-free and bound-free emission from the ionized part of the circumstellar gas \citep[e.g.][]{1978ApJ...220..940P,1987A&A...185..206W}."
 The stellar contribution to the total flux is about 20 per cent at 2.1 qun. based on extrapolation of a Ixurucz model atinosphere fitted to the UV. contiuuua (?)..," The stellar contribution to the total flux is about 20 per cent at 2.4 $\mu$ m, based on extrapolation of a Kurucz model atmosphere fitted to the UV continuum \citep{1993A&A...270..355T}."
" The spectruii can be well represented. by a sinele power-law. S, X Μον with a = 0.99 + 0.05."," The spectrum can be well represented by a single power-law, $_{\nu}$ $\propto$ $\nu^{\alpha}$, with $\alpha$ = 0.99 $\pm$ 0.05."
 This spectra slope is slightly. but significantly flatter. than that derive by ?.. based on IRAS broad-band plotometiy taken iu 1983.," This spectral slope is slightly, but significantly flatter, than that derived by \citet{1987A&A...185..206W}, based on IRAS broad-band photometry taken in 1983."
" We have usec the simple isothermal disc iode of ? to estimate the radial densitv eradient iu the dise. asstuning a power-law p(r) = ρα εν). "". aud fine n — 2.5 0.1."," We have used the simple isothermal disc model of \citet{1986A&A...162..121W} to estimate the radial density gradient in the disc, assuming a power-law $\rho$ (r) = $\rho_{0}$ $_*$ $^{-n}$ , and find n = 2.8 $\pm$ 0.1."
 The value of py depeuds on the assume opening angle 0 of the disc. as well as on the stellar radius and disc temperature.," The value of $\rho_0$ depends on the assumed opening angle $\theta$ of the disc, as well as on the stellar radius and disc temperature."
" We use = JO RR. anTai, = 104 IK (seo below).", We use $_*$ = 10 $_{\sun}$ and$_\mathrm{disc}$ = $^{4}$ K (see below).
 Analysis of the optical linear polarisation and interferometric miaeme of (7) suggests a half opening anele of 2.57., Analysis of the optical linear polarisation and interferometric imaging of \citep{1997ApJ...477..926W} suggests a half opening angle of $\degr$.
" We use a 1l"" half opening angele.", We use a $\degr$ half opening angle.
 The derived density at the stellar surface is py = 3.5410 H © Coonn enisslon naienasure EM = 1.5109 7 was found., The derived density at the stellar surface is $\rho_0$ = $\times$ $^{-11}$ g $^{-3}$; an emission measure EM = $\times$ $^{61}$ $^{-3}$ was found.
 There are some wavelength ranges that show a deviation from the power-law behavior of the continua discussed above., There are some wavelength ranges that show a deviation from the power-law behavior of the continuum discussed above.
 Near 3.28 jnu the mereing of the cinrissio1 lues of the Ihuuphlirevs series. with lower quanti level P=6. causes a jump.," Near 3.28 $\mu$ m the merging of the emission lines of the Humphreys series, with lower quantum level $n=6$, causes a jump."
 This Ihuuphireys jump (seen i- enission). which is simular to the Baluer jump at optical wavelengths. can be used to derive the average electrou temperature of the emitting region.," This Humphreys jump (seen in emission), which is similar to the Balmer jump at optical wavelengths, can be used to derive the average electron temperature of the emitting region."
 The difference in fiux ou both sides of the Ihuuphnrevs jump is caused by a discoutimuty in bouud-free Gri ie) Opacity of the gas i- the disc., The difference in flux on both sides of the Humphreys jump is caused by a discontinuity in bound-free $\kappa_\mathrm{ff+bf}$ ) opacity of the gas in the disc.
 We write for the total continui opacity., We write for the total continuum opacity.
" where A.T) aud b(A.T) are the yee-free and bouud-free eauut factors. respectively,"," where $\lambda$ ,T) and $\lambda$ ,T) are the free-free and bound-free gaunt factors, respectively."
 b(A.T) is a sensitive function of the temperature: the jump in b(A.T) (and in flux) increases towards lower clectron teniperature.," $\lambda$ ,T) is a sensitive function of the temperature: the jump in $\lambda$ ,T) (and in flux) increases towards lower electron temperature."
 The change in efA .T) is negligible over the waveleneth rauge of interest.," The change in $\lambda$ ,T) is negligible over the wavelength range of interest."
 The jump im b(A.T) is thus a diagnostic of the temperature in the disc.," The jump in $\lambda$ ,T) is thus a diagnostic of the temperature in the disc."
 We use the following method to determine the size of this jump: We define the normalized excess fluxas ὧν 1 = (Fy-Fy..)/Fy.. where Fy. is the stellar photospheric fiux. soe Fig. 2..," We use the following method to determine the size of this jump: We define the normalized excess fluxas $_{\lambda}-$ 1 = $_{\lambda}$ $_{\lambda,*}$ $_{\lambda,*}$, where $_{\lambda,*}$ is the stellar photospheric flux, see Fig. \ref{fig:humpschema}."
 Za lis normalized o the source function of the eas in the disc modulo a coustaut since both the dise aud the star raciate in the Ravleigh-Jeaus limit in this waveleneth regiae and thus wave the same waveleneth dependence., $_{\lambda}-$ 1 is normalized to the source function of the gas in the disc modulo a constant since both the disc and the star radiate in the Rayleigh-Jeans limit in this wavelength regime and thus have the same wavelength dependence.
 Ou the blue side of the ciscoutinuity b(A.T) las a certain value. with a correspondiug value of Hey pe of THepe for cach Lue of sight hrough the dise and thus a correspoucding value of Z4. 1.," On the blue side of the discontinuity $\lambda$ ,T) has a certain value, with a corresponding value of $\kappa_\mathrm{ff+bf}$ , of $\tau_\mathrm{ff+bf}$ for each line of sight through the disc and thus a corresponding value of $_{\lambda}-$ 1."
 Devonud the discontiuuitv there isa drop iu b(A.T). ey pe. Trying tad Z4 1.," Beyond the discontinuity there isa drop in $\lambda$ ,T), $\kappa_\mathrm{ff+bf}$ , $\tau_\mathrm{ff+bf}$ and $_{\lambda}-$ 1."
 Siuce there is a wide range of zur for different ues of sight Z4 Lois not a simple function of ACT).," Since there is a wide range of $\tau_\mathrm{ff+bf}$ for different lines of sight $_{\lambda}-$ 1 is a simple function of $\lambda$ ,T)."
" Dowever teeῃ], steadilv increases with waveleneth. e.g. Equ. 2.. "," However $\kappa_\mathrm{ff+bf}$ steadily increases with wavelength, e.g. Eqn. \ref{eqn:totalkappa}, ,"
and thus there is a wavelength (A) where the, and thus there is a wavelength $\lambda^{\prime}$ ) where the
"even shorter in the limit of low densities, when radiative decay dominates collisional de-excitation.","even shorter in the limit of low densities, when radiative decay dominates collisional de-excitation."
" To validate the assumption of s-e, one must compare this population transfer time-scale with a dynamical time-scale, such as the flow time of the neutral particles through the shock region, that corresponds to the width of the neutral temperature profile shown in the upper panels."," To validate the assumption of s-e, one must compare this population transfer time-scale with a dynamical time-scale, such as the flow time of the neutral particles through the shock region, that corresponds to the width of the neutral temperature profile shown in the upper panels."
" Adopting the representative values of 10* cm? for the density and 107! cm? for the collisional de-excitation rate coefficient results in a population transfer time-scale of 0.03 yr, much less than the flow time of the neutral particles through the C-type shock considered."," Adopting the representative values of $^4$ $^{-3}$ for the density and $^{-10}$ $^{-3}$ for the collisional de-excitation rate coefficient results in a population transfer time-scale of 0.03 yr, much less than the flow time of the neutral particles through the C-type shock considered."
" In the case of the reference CJ-type shock model, this condition is verified for most of the transitions, as the overall agreement between light and dark blue open circles in Figure 6 confirms."," In the case of the reference CJ-type shock model, this condition is verified for most of the transitions, as the overall agreement between light and dark blue open circles in Figure \ref{Figure6} confirms."
" For the brightest transitions, our independent LVG calculation is consistent with that denoted ‘FP10’."," For the brightest transitions, our independent LVG calculation is consistent with that denoted `FP10'."
" In this case, the discrepancies with the red filled circles are larger, owing to the differences in the water abundance profiles, which are attributable in turn to the temperature differences arising from: the small displacement of J-discontinuity; the treatment of the cooling due to water; and the strength of the grain-gas interaction as the post-shock region is approached."," In this case, the discrepancies with the red filled circles are larger, owing to the differences in the water abundance profiles, which are attributable in turn to the temperature differences arising from: the small displacement of J-discontinuity; the treatment of the cooling due to water; and the strength of the grain–gas interaction as the post-shock region is approached."
" We note that the pattern created by each set of points is similar for the brightest, and hence observable, transitions, and that the pattern is shifted vertically from one set of results to the other."," We note that the pattern created by each set of points is similar for the brightest, and hence observable, transitions, and that the pattern is shifted vertically from one set of results to the other."
" Such a shift is indistinguishable from that arising from the uncertainty in the filling factor, when comparisons are made with observations."," Such a shift is indistinguishable from that arising from the uncertainty in the filling factor, when comparisons are made with observations."
 We conclude from the above analysis that the use of the s-e approximation is justified in the present context of the study of water emission., We conclude from the above analysis that the use of the s-e approximation is justified in the present context of the study of water emission.
 As a preamble to this section — aimed at providing predictions of water line intensities for use in the interpretation of observations — we study the evolution of the optical depth of the fundamental transitions of both o-H2O and p-H5O0 in each of our reference models., As a preamble to this section – aimed at providing predictions of water line intensities for use in the interpretation of observations – we study the evolution of the optical depth of the fundamental transitions of both $_2$ O and $_2$ O in each of our reference models.
" This evolution, together with the total optical depths, integrated through the shock wave, are shown in Figure 7.."," This evolution, together with the total optical depths, integrated through the shock wave, are shown in Figure \ref{Figure7}."
" Owing to the one-dimensional nature of our approach, we probably overestimate the optical depths and find that the transitions are optically thick in most parts of our shock models; this is especially the case of the C-type shock, as the water accumulates in the large post-shock region."," Owing to the one-dimensional nature of our approach, we probably overestimate the optical depths and find that the transitions are optically thick in most parts of our shock models; this is especially the case of the C-type shock, as the water accumulates in the large post-shock region."
" The example of the CJ-type shock shows the spread of values of the optical depths in the emitting region — low when water is dissociated in the high-temperature regime, followed by higher values when water reforms."," The example of the CJ-type shock shows the spread of values of the optical depths in the emitting region – low when water is dissociated in the high-temperature regime, followed by higher values when water reforms."
 This figure underlines the requirement for an adequate treatment of the radiative transfer., This figure underlines the requirement for an adequate treatment of the radiative transfer.
" As already mentioned, Hz, SiO and H20 are believed to have coincident regions of emission, at least to the resolution of currently available observations (e.g. ?))."," As already mentioned, $_2$, SiO and $_2$ O are believed to have coincident regions of emission, at least to the resolution of currently available observations (e.g. \citealt{Nisini10}) )."
" For completeness, we provide predictions of water line intensities for the models that were found to fit the H» pure rotational excitation diagram acceptably at position of the SiO knot."," For completeness, we provide predictions of water line intensities for the models that were found to fit the $_2$ pure rotational excitation diagram acceptably at position of the SiO knot."
" Given the relative uniformity of the shock conditions in the inner parts of the outflow, revealed by the similarity of the H» excitation diagrams at the different positions considered, our models should be applicable to water observations at any position."," Given the relative uniformity of the shock conditions in the inner parts of the outflow, revealed by the similarity of the $_2$ excitation diagrams at the different positions considered, our models should be applicable to water observations at any position."
" Stationary, C-type shock models are excluded, for the reasons given in Section 3.3.."," Stationary, C-type shock models are excluded, for the reasons given in Section \ref{sub:mr}."
" The results are given in Tables B1 and B2 for o-H5O and p-H20, respectively."," The results are given in Tables \ref{tableb1} and \ref{tableb2} for $_2$ O and $_2$ O, respectively."
 The transitions that appear in the Tables are the ones that will be the target of observations., The transitions that appear in the Tables are the ones that will be the target of observations.
 The first three transitions in each table will be observed by, The first three transitions in each table will be observed by
"that the emission is slightly extended along an arc of the same radius, as would be expected if it were distributed in a ring around the star.","that the emission is slightly extended along an arc of the same radius, as would be expected if it were distributed in a ring around the star."
" It is impossible to determine from the images alone the underlying radial distribution of the dust grains or the degree of azimuthal (a)symmetry of the emission, due to the low signal-to-noise ratio and incomplete sampling of the (u,v) plane."," It is impossible to determine from the images alone the underlying radial distribution of the dust grains or the degree of azimuthal (a)symmetry of the emission, due to the low signal-to-noise ratio and incomplete sampling of the $u$ $v$ ) plane."
" In Section 4,, we therefore model the underlying dust distribution to constrain its extent and to search for asymmetries in the residuals."," In Section \ref{sec:analysis}, we therefore model the underlying dust distribution to constrain its extent and to search for asymmetries in the residuals."
 We detect the CO(3-2) emission reported by ? and demonstrated by ? to be at an LSR velocity coincident with that of HR 8799., We detect the CO(3-2) emission reported by \citet{wil06} and demonstrated by \citet{su09} to be at an LSR velocity coincident with that of HR 8799.
" The line emission is quite narrow, appearing in only two of the 0.7kkmss~! channels, indicating a linewidth of <1.4kkmss~!."," The line emission is quite narrow, appearing in only two of the $^{-1}$ channels, indicating a linewidth of $\lesssim$ $^{-1}$."
" The line does not image cleanly in the interferometric data, exhibiting striping from northeast to southwest across the image."," The line does not image cleanly in the interferometric data, exhibiting striping from northeast to southwest across the image."
" There are two likely reasons for this: (1) the position angle of the stripes matches that of the CO filament in Figure 4 of ?,, and the separation between stripes is equal to that between the peak of the synthesized beam and its largest (3096)) sidelobes, and (2) there is a knot of bright CO emission visible in the JOMT map to the northwest of the SMA map center at a distance of approximately the width of the SMA primary beam, which coincides with a peak in the SMA map."," There are two likely reasons for this: (1) the position angle of the stripes matches that of the CO filament in Figure 4 of \citet{wil06}, and the separation between stripes is equal to that between the peak of the synthesized beam and its largest ) sidelobes, and (2) there is a knot of bright CO emission visible in the JCMT map to the northwest of the SMA map center at a distance of approximately the width of the SMA primary beam, which coincides with a peak in the SMA map."
" Not only are interferometers inherently poorly suited to imaging extended emission like the CO filament observed with the JCMT, but the presence of a bright source outside the primary beam on its own would be expected to cause striping across the image."," Not only are interferometers inherently poorly suited to imaging extended emission like the CO filament observed with the JCMT, but the presence of a bright source outside the primary beam on its own would be expected to cause striping across the image."
" Nevertheless, there is no evidence of a velocity gradient across the line, which is characteristic of rotation and would be expected if the CO(3-2) emission were associated with the disk."," Nevertheless, there is no evidence of a velocity gradient across the line, which is characteristic of rotation and would be expected if the CO(3-2) emission were associated with the disk."
" Given the spatial resolution of the SMA, such a gradient should be easily detectable if it were present."," Given the spatial resolution of the SMA, such a gradient should be easily detectable if it were present."
" Assuming a gas disk spatially coincident with the observed dust emission, the CO(3-2) line should be concentrated well within the 30"" SMA primary beam and should exhibit centroid shifts across the line by ~5” between the red and blue channels, which is not observed."," Assuming a gas disk spatially coincident with the observed dust emission, the CO(3-2) line should be concentrated well within the 30” SMA primary beam and should exhibit centroid shifts across the line by $\sim$ 5” between the red and blue channels, which is not observed."
" We therefore conclude that the CO emission does not originate from the disk around HR. 8799, although the coincidence in spatial location and velocity are suggestive that the disk may be associated with the CO filament."," We therefore conclude that the CO emission does not originate from the disk around HR 8799, although the coincidence in spatial location and velocity are suggestive that the disk may be associated with the CO filament."
" In order to constrain the spatial distribution of circumstellar dust in these systems, we model simultaneously the spectral energy distribution (SED) and spatially resolved um visibilities."," In order to constrain the spatial distribution of circumstellar dust in these systems, we model simultaneously the spectral energy distribution (SED) and spatially resolved $\mu$ m visibilities."
" Section 4.1 describes the modeling procedure used for HD 107146, including anposteriori comparison between the model of the SMA data and previous spatially resolved observations of HD 107146 with CARMA."," Section \ref{sec:hd_analysis} describes the modeling procedure used for HD 107146, including an comparison between the model of the SMA data and previous spatially resolved observations of HD 107146 with CARMA."
 Section 4.2 describes how we modify this procedure for the low signal-to-noise case of HR 8799., Section \ref{sec:hr_analysis} describes how we modify this procedure for the low signal-to-noise case of HR 8799.
 The bottom right panel of Figure 1 shows the HD IRASand2MASS ," The bottom right panel of Figure \ref{fig:hd107146} shows the HD 107146 SED assembled from the literature \citep[][plus IRAS and 2MASS fluxes]{lan83,
wil04,car05,moo06,hil08,cor09}. ."
"We model the SED with three components: (1) afluxes).. Kurucz model stellar photosphere with surface gravity log g=4.5 and effective temperature Te KK (?7); (2) a dust belt with a temperature of ¢¢=585969KK, which is required to reproduce the mid-IR fluxes but does not contribute substantially to the millimeter-wavelength flux; and (3) an outer debris belt with the properties described below."," We model the SED with three components: (1) a Kurucz model stellar photosphere with surface gravity $\log{g}$ =4.5 and effective temperature $T_{eff}$ K \citep{car08,hil08}; (2) a dust belt with a temperature of K, which is required to reproduce the mid-IR fluxes but does not contribute substantially to the millimeter-wavelength flux; and (3) an outer debris belt with the properties described below."
" It is this latter component that accounts for effectively all of the um flux, and it must therefore be modeled as a spatially extended component to reproduce both the observed visibilities and the SED."," It is this latter component that accounts for effectively all of the $\mu$ m flux, and it must therefore be modeled as a spatially extended component to reproduce both the observed visibilities and the SED."
" As in ?,, we assume a dust grain emission efficiency QxX=1—exp[-(Ao/A)g£], where Ao is a critical wavelength; this has the desired asymptotic behavior that Q4= for λ>>Ao and Q»= for A<<Ao, while (Ao/A)®varying smoothly between the1 two extremes."," As in \citet{wil04}, , we assume a dust grain emission efficiency $Q_\lambda = 
1 - \exp{[-(\lambda_0/\lambda)^{\beta}]}$, where $\lambda_0$ is a critical wavelength; this has the desired asymptotic behavior that $Q_\lambda = 
(\lambda_0/\lambda)^\beta$ for $\lambda >> \lambda_0$ and $Q_\lambda = 1$ for $\lambda << \lambda_0$, while varying smoothly between the two extremes."
" However, unlike ? who fit the SED with a single dust temperature, we require the dust grains to be in radiative equilibrium with the star and allow the disk to be spatially extended."," However, unlike \citet{wil04} who fit the SED with a single dust temperature, we require the dust grains to be in radiative equilibrium with the star and allow the disk to be spatially extended."
" With these assumptions, using the textbook formulation from ?,, the dust temperature is given by where L, is the stellar luminosity, o is the Stefan-Boltzmann constant, r is the distance fromthe star, 8 is the dust grain emissionefficiency power law index, ¢ is the Riemann zeta function, and Qo is the dust grain efficiency at the critical wavelength Ao= 27a."," With these assumptions, using the textbook formulation from \citet{tie05}, the dust temperature is given by where $L_*$ is the stellar luminosity, $\sigma$ is the Stefan-Boltzmann constant, $r$ is the distance fromthe star, $\beta$ is the dust grain emissionefficiency power law index, $\zeta$ is the Riemann zeta function, and $Q_0$ is the dust grain efficiency at the critical wavelength $\lambda_0 = 2 \pi a$ ."
 We assume, We assume
From this ligure. we find that the D4 D5 runs with E(D.V)-—0 and the €5 G6 run with οV)—0.15 appear to have reasonable number densities. while all runs with 001)=0.3 seem to uncerprecict the number densitv.,"From this figure, we find that the D4 D5 runs with $E(B-V)=0$ and the G5 G6 run with $E(B-V)=0.15$ appear to have reasonable number densities, while all runs with $E(B-V)=0.3$ seem to underpredict the number density."
 “Phe O3 (no-wind) and P3 (weak wind) runs with £(BV)=O overprediet the number density. significantly., The O3 (no-wind) and P3 (weak wind) runs with $E(B-V)=0$ overpredict the number density significantly.
 Apparently. without strong feedback by. galactic winds and extinction. the LDBGs simply become too bright and. hence too abundant above a given. brightness limit.," Apparently, without strong feedback by galactic winds and extinction, the LBGs simply become too bright and hence too abundant above a given brightness limit."
 Other null results of the Q-series. are allectecd by the small box size of the simulation., Other null results of the Q-series are affected by the small box size of the simulation.
 We will show the cllect of the box size more explicitly when we discuss the luninosity function of ealaxies in Section 6.., We will show the effect of the box size more explicitly when we discuss the luminosity function of galaxies in Section \ref{section:lf}.
 In Figure 3.. we show the distribution of galaxies at 2=3 in the 0-run on the plane of Ai-band apparent magnitude and C—P colour.," In Figure \ref{Rmag_GRcol.eps}, we show the distribution of galaxies at $z=3$ in the `G6'-run on the plane of $R$ -band apparent magnitude and $G-R$ colour."
 We here chose the GO-run because it gives a reasonable fit to the observed Luminosity functions and the number density. and it has higher resolution than the 5 run.," We here chose the `G6'-run because it gives a reasonable fit to the observed luminosity functions and the number density, and it has higher resolution than the G5 run."
 Again. we use three dillerent symbols for three cilferent values of extinction: (D.V)=0.0 (blue dots). 0.15 (green crosses). and 0.32 (red open squares).," Again, we use three different symbols for three different values of extinction: $E(B-V)=0.0$ (blue dots), 0.15 (green crosses), and 0.3 (red open squares)."
 The Iong-dashed lines and the arrows indicate the colour-selection criteria applied bv Steideletal.(2003) to select LBG candidates at z23., The long-dashed lines and the arrows indicate the colour-selection criteria applied by \citet{Ste03} to select LBG candidates at $z\sim 3$.
 We see that most of the galaxies brighter than £2=25.5 automatically satisfy the criterion C22«12. and only a small [fraction of galaxies with /?«25.5fall out of the region.," We see that most of the galaxies brighter than $R=25.5$ automatically satisfy the criterion $G-R<1.2$, and only a small fraction of galaxies with $R<25.5$fall out of the region."
 There is a significant population of dim (2?7 28) galaxies ΑΠΕ (812., There is a significant population of dim $R>28$ ) galaxies with $G-R>1.2$.
" We will see below that these are low-mass ealaxies with stellar masses AM,<1017).TALL.", We will see below that these are low-mass galaxies with stellar masses $M_{\star}\le 10^{10}\himsun$.
 In Figure 4.. we show the Zi-band apparent magnitude vs. stellar mass of simulated galaxies at 2=3.," In Figure \ref{Rmag_Mstar_all.eps}, we show the $R$ -band apparent magnitude vs. stellar mass of simulated galaxies at $z=3$."
 As before. we plot results for three values of extinction. using cdillerent symbols.," As before, we plot results for three values of extinction, using different symbols."
 We also mark the magnitude limit 2«25.5 used by Steideletal.(2003) with a vertical lone-dashed line and ALLONS., We also mark the magnitude limit $R<25.5$ used by \citet{Ste03} with a vertical long-dashed line and arrows.
" From this Figure. we see that the LBGs in the Q- with 2<25.5 have typically stellar masses. in the range AM,=lo’1027A TALL. while those in ορ take a somewhat wicler interval. nearly covering the range"," From this Figure, we see that the LBGs in the Q-series with $R<25.5$ have typically stellar masses in the range $M_{\star}=10^9 -
10^{10}\himsun$ , while those in `D5' take a somewhat wider interval, nearly covering the range"
LR cliagrams extensively. and testing the robustness of the method to changes in the initialization condition of the algorithm.,"HR diagrams extensively, and testing the robustness of the method to changes in the initialization condition of the algorithm."
 An independent test of the validity of the results was also implemented. and is described in section 4.," An independent test of the validity of the results was also implemented, and is described in section 4."
 The main advantages of our method. over. other maximum. likelihood schemes. are (1). the totally non parametric approach the variational calculus. treatment allows. and (2) the ellicient computational procedure. where no time consuming repeated Comparisons between synthetic and. observational CMD. are necessary. as the optimal SEBIG) is solved for clirectLy.," The main advantages of our method over other maximum likelihood schemes are (1) the totally non parametric approach the variational calculus treatment allows, and (2) the efficient computational procedure, where no time consuming repeated comparisons between synthetic and observational CMD are necessary, as the optimal $SFR(t)$ is solved for directly."
 We now present two examples of the method's performance. in cases similar to the Llipparcos samples CMDs.," We now present two examples of the method's performance, in cases similar to the Hipparcos samples CMDs."
 Phe left panel of Figure (1) shows à svnthetie CMD produced from. the first input S4AD. resulting in a number of stars similar to what the LHipparcos samples vield for small errors in V/ (<0.12 mag) and. Ady (<<0.02 mag).," The left panel of Figure (1) shows a synthetic CMD produced from the first input $SFR(t)$, resulting in a number of stars similar to what the Hipparcos samples yield for small errors in $V-I$ $<0.12$ mag) and $M_{V}$ $(<0.02$ mag)."
 The positions of the simulated stars are then usec to construct the likelihood matrix.which is used to recover the inferred S42). through an iterative numerical procedure. (see paper D).," The positions of the simulated stars are then used to construct the likelihood matrix,which is used to recover the inferred $SFR(t)$, through an iterative numerical procedure (see paper I)."
 The right panel of Figure (1) shows the last 3 iterations of the method (solid curves) and 1e input. S£. a three burst SE) (clotted curve)," The right panel of Figure (1) shows the last 3 iterations of the method (solid curves) and the input $SFR(t)$, a three burst $SFR(t)$ (dotted curve)."
 lt can be seen that the main features of the input S£) are accurately recovered., It can be seen that the main features of the input $SFR(t)$ are accurately recovered.
 The age. duration and shape of the input S£) are clearly well represented bv the final inferred. SPIG).," The age, duration and shape of the input $SFR(t)$ are clearly well represented by the final inferred $SFR(t)$."
 As the cilference between successive isochrones diminishes with age. since the errors remain constant. the accuracy of the recovery procedure diminishes with the age of the stellar populations being treated.," As the difference between successive isochrones diminishes with age, since the errors remain constant, the accuracy of the recovery procedure diminishes with the age of the stellar populations being treated."
 This is seen in that the first burst is very accurately recovered. whilst the last one appears somewhat spread out.," This is seen in that the first burst is very accurately recovered, whilst the last one appears somewhat spread out."
 The last example is shown in Figure (2). which is analogous to Figure (1).," The last example is shown in Figure (2), which is analogous to Figure (1)."
 Here a SE) which is constan over a large period is treated., Here a $SFR(t)$ which is constant over a large period is treated.
 The LR diagram of this case appears by sight. almost identical to that of the previous case. however. given the extremely small errors. assume (tvpical of the Lipparcos data) the method. is capable of istinguish and accurately recover the input S£I) of these wo cases.," The HR diagram of this case appears by sight almost identical to that of the previous case, however, given the extremely small errors assumed (typical of the Hipparcos data) the method is capable of distinguish and accurately recover the input $SFR(t)$ of these two cases."
 Phe small number of stars (450) result in a egree of shot noise. which has to be artificially suppressec using a smoothing procedure. the result of which is seen in 16 residual short period oscillations of the inferred S£HG).," The small number of stars $(\sim 450)$ result in a degree of shot noise, which has to be artificially suppressed using a smoothing procedure, the result of which is seen in the residual short period oscillations of the inferred $SFR(t)$."
 This smoothing procedure reduces the effective resolution of 1e method to 50 Myr., This smoothing procedure reduces the effective resolution of the method to $50$ Myr.
 Note that as in the previous example. 10 inversion method successfully recovers the main features of the input S£AU.," Note that as in the previous example, the inversion method successfully recovers the main features of the input $SFR(t)$."
 In these two tests only stars blucwards of VO£0.7 where considered in the inversion procedure (sce below)., In these two tests only stars bluewards of $V-I=0.7$ where considered in the inversion procedure (see below).
 In order to apply the method described in the preceding section to the Lipparcos data. we would like to construct a voltune-limited sample. where no biases appear between stars of dillerent ages.," In order to apply the method described in the preceding section to the Hipparcos data, we would like to construct a volume-limited sample, where no biases appear between stars of different ages."
 Further. such a sample should contain a sullicient number of stars coming from all age groups being considered Le. it must eo down in magnitude to," Further, such a sample should contain a sufficient number of stars coming from all age groups being considered i.e. it must go down in magnitude to"
When we take into account the different PN populations. we see that gradients are much steeper lor the voung Type I than for the old Type II disk PNe. consistently for both the oxveen and the neon data sets.,"When we take into account the different PN populations, we see that gradients are much steeper for the young Type I than for the old Type III disk PNe, consistently for both the oxygen and the neon data sets."
 This result goes in the opposite direction to the [Iattening with time. which Maciel et al. (," This result goes in the opposite direction to the flattening with time, which Maciel et al. ("
2003) have proposed based on PNe.,2003) have proposed based on PNe.
 We discuss (his important result further in Section 5., We discuss this important result further in Section 5.
 In the previous section we noted that the gradients derived for non-Tvpe I PNe are typically not steeper than -0.032 dex 1. consistent with the most recent determinations (e. e.. Stanghellini οἱ al.," In the previous section we noted that the gradients derived for non-Type I PNe are typically not steeper than -0.03 dex $^{-1}$, consistent with the most recent determinations (e. g., Stanghellini et al."
 2006. POG).," 2006, P06)."
 To check the stability of our results i( is worth going through (hie exercise of calculating the oxvgen gradients with different assumptions., To check the stability of our results it is worth going through the exercise of calculating the oxygen gradients with different assumptions.
" First. if we include the few halo PNe in our sample the eradients would not change noliceably, even if it would change the meaning of the sample."," First, if we include the few halo PNe in our sample the gradients would not change noticeably, even if it would change the meaning of the sample."
 A different areument should be applied for bulge PNe. since it is hard to separate bulee and disk populations.," A different argument should be applied for bulge PNe, since it is hard to separate bulge and disk populations."
 If we do not exclude bulge PNe from our sample. ancl leave all other selection as for the set of Table 3. we obtain oxveen gradient slopes of -0.02540.005 dex + for the complete sample. compared with -0.02340.005 dex ! obtained if we exclude the bulee population.," If we do not exclude bulge PNe from our sample, and leave all other selection as for the set of Table 3, we obtain oxygen gradient slopes of $\pm$ 0.005 dex $^{-1}$ for the complete sample, compared with $\pm$ 0.005 dex $^{-1}$ obtained if we exclude the bulge population."
 For this and all other PN samples. the effect of including bulee PNe is to increase (he (negative) eradient slopes.," For this and all other PN samples, the effect of including bulge PNe is to increase the (negative) gradient slopes."
 This could have contributed in part to the sleeper gradients slopes of some of the published metallicity gradients [rom PNe. where an accurate selection of PN populations was not in effect.," This could have contributed in part to the steeper gradients slopes of some of the published metallicity gradients from PNe, where an accurate selection of PN populations was not in effect."
 Past metallicity MESgradient. analvses have included bipolar PNe., Past metallicity gradient analyses have included bipolar PNe.
 By including5 bipolar PNe in the gradient calculation we would obtain different. gradients onlv [or the Type I PNe (.Alog( /.NBG;—-0.0242:0.02 dex 1). where the bipolar constitute a very," By including bipolar PNe in the gradient calculation we would obtain different gradients only for the Type I PNe $\Delta$ $\Delta{\rm R_G}$ $\pm$ 0.02 dex $^{-1}$ ), where the bipolar constitute a very"
fraction of the radio data image covered by the V aud Is catalogues are ~95% and ντο.,fraction of the radio data image covered by the V and K catalogues are $\sim$ and $\sim$.
 These objects shown as circles. are teutativelv assigned a classification on the basis of the available colour (see figure caption).," These objects, shown as circles, are tentatively assigned a classification on the basis of the available colour (see figure caption)."
 Fig., Fig.
 Ll shows the 6 cn radio flux versus the I baud magnitude for all the 63 radio sources (I baud upper limits are shown for the 5 radio sources with uo optical counterpart)., \ref{F14} shows the 6 cm radio flux versus the I band magnitude for all the 63 radio sources (I band upper limits are shown for the 5 radio sources with no optical counterpart).
 Superimiposed are the lines correspondiusg to coustaut values or the observed radio-to-optical ratios R. defined as R= S 10911224 where S aud I are the racio fux iu uJv aud the appareut magnitude of sources respectively.," Superimposed are the lines corresponding to constant values for the observed radio-to-optical ratios $\it R$, defined as $\it R$ = S $\times$ $^{0.4(I-12.5)}$, where S and I are the radio flux in mJy and the apparent magnitude of sources respectively."
 The svinbols are the same as those defined in the previous figure. except for the crosses. which represent the objects for which only au I baud magnitude is available aud therefore were not shown in the colour colour diagran.," The symbols are the same as those defined in the previous figure, except for the crosses, which represent the objects for which only an I band magnitude is available and therefore were not shown in the colour – colour diagram."
 This figure.c» althoughC» Iuuited to a relatively narrow range of radio fluxes (soe Fig.," This figure, although limited to a relatively narrow range of radio fluxes (see Fig."
 Sa iu ντου et al. (, 8a in Kron et al. (
1995) for a similar plot at higher flux level). shows that the two classes of objects defined ou the basis of the colour diagram. have a different distribution iu the radio fiuxoptical magnitude diaerauu.,"1995) for a similar plot at higher flux level), shows that the two classes of objects defined on the basis of the colour–colour diagram have a different distribution in the radio flux--optical magnitude diagram."
 Iu particular. all the objects at large radio-to-optical ratios (Ro 2 1000) have colours typical of passively evolving galaxies at relatively uch redshift.," In particular, all the objects at large radio-to-optical ratios $\it R$ $\ge$ 1000) have colours typical of passively evolving galaxies at relatively high redshift."
 Ou the basis of this plot we would conclude hat also the five radio sources without optical identification are likely to beloug to this class., On the basis of this plot we would conclude that also the five radio sources without optical identification are likely to belong to this class.
 No object of this class. instead. appears in this plot at low values of 77 (Rs ). consistent with previous findings (sec. for cxample. Cuauppioni et al.," No object of this class, instead, appears in this plot at low values of $\it R$ $\it R$ $\le$ 30), consistent with previous findings (see, for example, Gruppioni et al.,"
 1999) hat objects with these values of BRoare mainly identified with starforming galaxies., 1999) that objects with these values of R are mainly identified with star–forming galaxies.
 The situation is less well defined for iuteriuediate values of & (30 «Ro< 1000) where the two populations defined ou the basis of Fie., The situation is less well defined for intermediate values of $\it R$ ( 30 $ < \it R < $ 1000) where the two populations defined on the basis of Fig.
 13 are not clearly separated im this plot., \ref{F13} are not clearly separated in this plot.
 Ouly spectroscopic data can help iu better defining the relative proportions of the two populations in this ranee of R., Only spectroscopic data can help in better defining the relative proportions of the two populations in this range of $\it R$.
" Th any case. this analysis already allows us to conclude that at least about of the radio sources in ah GIIz selected sample with limiting fux 9644, 20.05 mJw is associated to carlytype galaxies."," In any case, this analysis already allows us to conclude that at least about of the radio sources in a 5 GHz selected sample with limiting flux $_{\rm 6~cm}\geq$ 0.05 mJy is associated to early–type galaxies."
 A sinl conclusion was reach by Cruppioui et al. (, A similar conclusion was reached by Gruppioni et al. (
"1999) for a 1.1 CIIz selected sample (Soyeq, 20.2 ιν). or Which a substantial fraction of spectroscopic identifications was available.","1999) for a 1.4 GHz selected sample $_{\rm 21cm}\geq$ 0.2 mJy), for which a substantial fraction of spectroscopic identifications was available."
 Iu Fie., In Fig.
 15. we show the LIX’ colour as a function of the radio flux. of the I inagnitude aud of the radio-to-optical ratio R.," \ref{F15} we show the $^{\prime}$ colour as a function of the radio flux, of the I magnitude and of the radio-to-optical ratio $\it R$."
 While uo obvious correlation is seen between LK and radio dux. there appear to be significant correlations between TIN’ and both I iiaenitude and radio-to-optical ratio &.," While no obvious correlation is seen between $^{\prime}$ and radio flux, there appear to be significant correlations between $^{\prime}$ and both I magnitude and radio-to-optical ratio $\it R$ ."
widely accepted theory for the acceleration of nonthermal particles (Blanclord&Eichelar1987:Heavens&DruryLO8s:Ixirketal. 2000).,"widely accepted theory for the acceleration of nonthermal particles \citep{Blandford87,
Heavens88, Kirk00}."
. The produced electron spectrum has the spectral index of ac2.5—3.0. twpically found in the optically thin svnchrotron emission ol AGNs.," The produced electron spectrum has the spectral index of $\alpha\simeq 2.5-3.0$, typically found in the optically thin synchrotron emission of AGNs."
" The hard N-ravs created by electron svnchrotron emission has the photon index ofa,2La—2.0. which is not consistent with the observed index of SPL state."," The hard X-rays created by electron synchrotron emission has the photon index of $\alpha_p\simeq 1.7-2.0$, which is not consistent with the observed index of SPL state."
" In fact the hard X-ray. svnchrotron photons will be down-scattered by the surrounding corona and form a softer spectiun where the photon index increases by unit a,—+1.", In fact the hard X-ray synchrotron photons will be down-scattered by the surrounding corona and form a softer spectrum where the photon index increases by unit $\alpha_p \rightarrow \alpha_p +1$.
 since (he energv of hard photons is higher (han the electron energy in (he corona. the Conmptonization is described by the following equation (Sunvaev&Tilarchuk1980) where Zr—nbr. ji2-5(n«5ay7» corresponding. to the mean number. ofB scatterings.. 7j is (he optical depth through the corona. anc f/(Z) is the original spectrum of the photons.," Since the energy of hard photons is higher than the electron energy in the corona, the Comptonization is described by the following equation \citep{Sunyaev80}
 where $Z=\frac{h\nu}{m_e c^2}$, $\beta^{-1}=\frac{3}{\pi^2}(\tau_0+\frac{2}{3})^2$ corresponding to the mean number of scatterings, $\tau_0$ is the optical depth through the corona, and $f(Z)$ is the original spectrum of the photons."
" The solution of the above equation is as follows: For a power law spectrum of the hard photons /(Z)xZ"""" with Z/3>1 corresponding to large optical depth (7;2 1) and high energy photon (Z~ 1). we have the Compton scattered spectrum F(Z)xZ""D! that can explain the observed spectra with the photon index of 2.4—3.0."," The solution of the above equation is as follows: For a power law spectrum of the hard photons $f(Z)\propto
Z^{-\alpha_p}$ with $Z/\beta\gg 1$ corresponding to large optical depth $\tau_0\gg 1$ ) and high energy photon $Z\sim 1$ ), we have the Compton scattered spectrum $F_{\nu}(Z)\propto Z^{-\alpha-1}$ that can explain the observed spectra with the photon index of $2.4-3.0$."
 For hard X-ray svuchrotvon photons (fvz 1). the net effect of Compton scattering process is a (vausler of energy. [rom the photon to the electron.," For hard X-ray synchrotron photons $h\nu \gg 1$ ), the net effect of Compton scattering process is a transfer of energy from the photon to the electron."
 The average fractional enerev change per scattering is large for high energy photons. the spectral shape at higher energv bands is seriously affected by Compton scattering.," The average fractional energy change per scattering is large for high energy photons, the spectral shape at higher energy bands is seriously affected by Compton scattering."
 It implies that most HE(ODOs appear more signilicantlv in higher energy bands., It implies that most HFQPOs appear more significantly in higher energy bands.
 The light curves actually have large, The light curves actually have large
lt is generally believed that. large. scale. structures. like ealaxies and clusters of galaxies formed. from small initial inhomogencities via gravitational collapse.,It is generally believed that large scale structures like galaxies and clusters of galaxies formed from small initial inhomogeneities via gravitational collapse.
 One implication of this picture is a distinct epoch when structures. [ike »oto-galaxies and proto-clusters decoupled from the largely iomniogeneous universe., One implication of this picture is a distinct epoch when structures like proto-galaxies and proto-clusters decoupled from the largely homogeneous universe.
 Present observations suggest tha us epoch is around z~5 for galaxies., Present observations suggest that this epoch is around $z\sim 5$ for galaxies.
 Observations of structures in this stage of formation. if made. can be a very »owerful constraint on the models of structure formation.," Observations of structures in this stage of formation, if made, can be a very powerful constraint on the models of structure formation."
 uluch observations will also improve our understanding of 10 process of structure formation., Such observations will also improve our understanding of the process of structure formation.
 Sunvaev and. Zel'dovich (L972) also sec Sunvaey ane Zel'dovich. (1975)] pointed out that the formation of firs structures may be probed by observing the redshifted 21cm line emitted. by the neutral hydrogen in these structures., Sunyaev and Zel'dovich (1972) [also see Sunyaev and Zel'dovich (1975)] pointed out that the formation of first structures may be probed by observing the redshifted $21$ cm line emitted by the neutral hydrogen in these structures.
 Several searches have been made to look for such structures at high redshifts., Several searches have been made to look for such structures at high redshifts.
 In absence of a detection. these searches have only been able to put [limits on the mass of neutral hydrogen present in clumped form.," In absence of a detection, these searches have only been able to put limits on the mass of neutral hydrogen present in clumped form."
 For a summary of these surveys see Wieringa. de Bruyn and Watecrt (1992). and references cited in that paper.," For a summary of these surveys see Wieringa, de Bruyn and Katgert (1992) and references cited in that paper."
 The Giant Meter-wave Raclio Telescope CGMBT) oesentiv being constructed. in India should be able to improve the observational situation considerably as regards he detection and study of proto condensates containing neutral hvdrogen (Swarup1984)., The Giant Meter-wave Radio Telescope (GMRT) presently being constructed in India should be able to improve the observational situation considerably as regards the detection and study of proto condensates containing neutral hydrogen \cite{swarup84}.
. Phe CMICE will be able (» probe the redshifted 21cm line [rom three epochs centred a.=3.34. 5.1] and 8.5.," The GMRT will be able to probe the redshifted $21$ cm line from three epochs centred at $z=3.34$, $5.1$ and $8.5$."
 In this paper we will discuss the »ossibilitv of detection at the two lower redshifts., In this paper we will discuss the possibility of detection at the two lower redshifts.
 Subramanian and Padmanabhan (1993) have computed he expected [lux at these redshifts for some models structure formation., Subramanian and Padmanabhan (1993) have computed the expected flux at these redshifts for some models of structure formation.
 They. used. the Press-Schechter imalism. (Pressand.Sehechter1975). to compute the expected number densities of proto-clusters in the CDM and DM models., They used the Press-Schechter formalism \cite{ps75} to compute the expected number densities of proto-clusters in the CDM and HDM models.
 In à later paper (Ixumzar.Padmanabhananeubramanian1995). they computed linc profiles assuming 16 proto-clusters to be spherically svmmetric., In a later paper \cite{nhline} they computed line profiles assuming the proto-clusters to be spherically symmetric.
 These studies gsugeest that it should be possible to detect. proto-clusters in 1ο standard CDM model using the (ΑΔΗ with 10 to 20 hours of observations., These studies suggest that it should be possible to detect proto-clusters in the standard CDM model using the GMRT with $10$ to $20$ hours of observations.
" In this paper we will use N-Bocly simulations to follow eravitational collapse of dark. matter and. some. simple approximations for estimating the collapsed: anc neutral fraction in dense regions to construct ""radio maps” with same specifications as the GM.", In this paper we will use N-Body simulations to follow gravitational collapse of dark matter and some simple approximations for estimating the collapsed and neutral fraction in dense regions to construct “radio maps” with same specifications as the GMRT.
 We will study these maps and suggest simple methods to optimise the signal to noise ratio., We will study these maps and suggest simple methods to optimise the signal to noise ratio.
 Some authors have studied the distribution of neutral hwdrogen at high. redshifts using simulations that include gas dynamics. ionisation and other astrophysical processes.," Some authors have studied the distribution of neutral hydrogen at high redshifts using simulations that include gas dynamics, ionisation and other astrophysical processes."
 where we assumed that the product waves propagate approximately along the field Lue. and wave 2 propagates backward.,"V= -i _X - _2) where we assumed that the product waves propagate approximately along the field line, and wave 2 propagates backward."
 Two couclusions may be made on analyzing Eq. CÀ))., Two conclusions may be made on analyzing Eq. \ref{V}) ).
 First. for the decay to occur. the initial O node should be obliquely propagating (04 0).," First, for the decay to occur, the initial O mode should be obliquely propagating $\theta \neq 0$ )."
 Secondly. the polarizations of the product wave are completely random with respect to the initial O mode aud approximately orthogonal to cach other.," Secondly, the polarizations of the product wave are completely random with respect to the initial O mode and approximately orthogonal to each other."
 Thus. the decay of the linearly polavized O mode produces unpolarized waves.," Thus, the decay of the linearly polarized O mode produces unpolarized waves."
 Microscopicallv. this is due to the fact that it is the + component of the initial O mode that couples to the product modes.," Microscopically, this is due to the fact that it is the $z$ component of the initial O mode that couples to the product modes."
 A more plivsical description of the 3 wave interaction in pair plasiua may be fouud in Machabeli Rogava 1982., A more physical description of the 3 wave interaction in pair plasma may be found in Machabeli Rogava 1983.
 Civeu the matrix element (Aj) we can find the the probability of emission in the random plase approximation (which assumes that radiation is broadband) (Melrose 1978) ky ko) , Given the matrix element \ref{V}) ) we can find the the probability of emission in the random phase approximation (which assumes that radiation is broadband) (Melrose 1978) u = 4 (2 )^7 V^2 _0 - _X - _2) _0 - _X _2).
(ww, Then the characteristic nonlinear decay time is
FU Orionis is the prototvpe of a small. but quite remarkable class of low-nass Young Stellar Objects (YSOs) normally referred. to as FU Ori objects (ΕΙΟΠΣ).,"FU Orionis is the prototype of a small, but quite remarkable class of low-mass Young Stellar Objects (YSOs) normally referred to as FU Ori objects (FUORs)."
 For the first meuibers of this class an outburst in optical light of up to 4-6 magnitudes over short time scales. followed. by a decrease in Dunminosi(v over several vears or decades. was observed (Ilerbig1977).," For the first members of this class an outburst in optical light of up to 4-6 magnitudes over short time scales, followed by a decrease in luminosity over several years or decades, was observed \citep{herbig1977}."
. Other objects were included in the class as thev shared. common specific spectroscopic features. e.g.. double-peaked line proliles. a spectral (wpe varving wilh waveleneth and often CO bancdhead absorption features.," Other objects were included in the class as they shared common specific spectroscopic features, e.g., double-peaked line profiles, a spectral type varying with wavelength and often CO bandhead absorption features."
 As for one object (V1057 νο) the pre-outburst spectrum is known ancl as it resembles that of a classical TT star (Welin1971)... it is commonly assumed that FUORs should be low-mass YSOs.," As for one object (V1057 Cyg) the pre-outburst spectrum is known and as it resembles that of a classical TTauri star \citep{welin}, it is commonly assumed that FUORs should be low-mass YSOs."
 Most observational data can be explained by (he presence of an accretion disk surrounding (he voung stars (Herbigetal.2003.late-0(vpestarswithstrongstellar winds).," Most observational data can be explained by the presence of an accretion disk surrounding the young stars \citep[][however, found that some spectral properties are well explained in the context of rapidly rotating late-type stars with strong stellar winds]{herbig}."
 A dramatic temporal increase in the accretion rate. where the disk outshines tlie star by several orders of magnitude. can account for the observed outbursts in luminosity.," A dramatic temporal increase in the accretion rate, where the disk outshines the star by several orders of magnitude, can account for the observed outbursts in luminosity."
 Several scenarios. possibly triggering such an increased accretion rate. have (thus lar been proposed.," Several scenarios, possibly triggering such an increased accretion rate, have thus far been proposed."
 They include (a) interactions of binary or multiple svstems where tidal forces disturb the circumstellar disk (Bonnell 1992).. (b) planet-disk interactions. where thermal instabilies in the disk are caused by the presence of a massive planet (Lodato&Clarke2004).. or (c) thermal instabilities in the clisk alone (Belletal.1995).," They include (a) interactions of binary or multiple systems where tidal forces disturb the circumstellar disk \citep{bonnell}, (b) planet-disk interactions, where thermal instabilities in the disk are caused by the presence of a massive planet \citep{lodato}, or (c) thermal instabilities in the disk alone \citep{bell}."
. For a detailed overview concerning the FU Ori phenomenon we reler to Hartmann&IXenvon(1996)., For a detailed overview concerning the FU Ori phenomenon we refer to \citet{hartmann}.
. Apart [rom revealing the mechlianism leading to the observed outbursts. it is also important to investigate whether all Tauri stars undergo such epochs of enhanced accretion or whether ΕΤΟΣ are a special class of YSOs.," Apart from revealing the mechanism leading to the observed outbursts, it is also important to investigate whether all TTauri stars undergo such epochs of enhanced accretion or whether FUORs are a special class of YSOs."
 Most observations of classical TTauri stars show that the derived accretion rates of 10.!!—TAL./yr etal.L998) are not sullicient to build up a low-mass star over lime scales of a few Myr.," Most observations of classical TTauri stars show that the derived accretion rates of $10^{-10}-10^{-7}M_{\sun}/yr$ \citep[e.g.,][]{gullbring} are not sufficient to build up a low-mass star over time scales of a few Myr."
 Even if part of the matter is supposed to be accreted in (he very early phases of a YSO. FUOR-phases might provide an elegant solution to this problem as they would speed up the accretion process.," Even if part of the matter is supposed to be accreted in the very early phases of a YSO, FUOR-phases might provide an elegant solution to this problem as they would speed up the accretion process."
 As so [ar only a dozen or so well established FUORs are known and as the has significant impact on the voung str-disk svstem il is crucial to. combine as much observational information as possible for these objects to eventually derive a coherent theoretical picture., As so far only a dozen or so well established FUORs are known and as the FUOR-phase has significant impact on the young star-disk system it is crucial to combine as much observational information as possible for these objects to eventually derive a coherent theoretical picture.
 Dased on near-infrared (NIB) and/or mid-infrared (MIT interferometry as a technique to study the inner few AU of the accretion disks new insights to some of the best studied FUOLs were provided recently., Based on near-infrared (NIR) and/or mid-infrared (MIR) interferometry as a technique to study the inner few AU of the accretion disks new insights to some of the best studied FUORs were provided recently.
" Millaa-Gabetetal.(2006) Found that accretion disks alone can not reproduce the SED and observed low Ix-band visibiliies for V1057 (να, V1515 Cvg and Z CMa-SE simultaneously."," \citet{millan-gabet} found that accretion disks alone can not reproduce the SED and observed low K-band visibilities for V1057 Cyg, V1515 Cyg and Z CMa-SE simultaneously."
 Thev concluded that additional uneorrelated [lux may arise due (o seattering by large dusty envelopes., They concluded that additional uncorrelated flux may arise due to scattering by large dusty envelopes.
 Abrahametal.(2006) presented the, \citet{abraham} presented the
The integral in Eqn. (1)),The integral in Eqn. \ref{integral}) )
 ts then evaluated using the trapezium method where f| is a dimensionless tolerance parameter of order unity controlling the integration step. and /1; is the smoothing lengthof evaluation point /.," is then evaluated using the trapezium method where $f_1$ is a dimensionless tolerance parameter of order unity controlling the integration step, and $h_{j'}$ is the smoothing lengthof evaluation point $j'$."
 The identifier Ξ0 denotes the evaluation point placed at the position of the star. and consecutive evaluation points are then located according to Thus Πρ represents the adaptive step along the line of sight from the tonizing star towards the ionization front.," The identifier $j'=0$ denotes the evaluation point placed at the position of the star, and consecutive evaluation points are then located according to Thus $f_1h_{j'}$ represents the adaptive step along the line of sight from the ionizing star towards the ionization front."
 Fig., Fig.
 | shows a representation of the method., \ref{fig: evalpoints} shows a representation of the method.
" Acceptable accuracy is obtained with f,=0.25 and this ts the value we use in the simulations presented here.", Acceptable accuracy is obtained with $f_1=0.25$ and this is the value we use in the simulations presented here.
 The use of ray splitting allows us to maintain good resolution while achieving significant speed-up in comparison with uniform ray tracing (cf., The use of ray splitting allows us to maintain good resolution while achieving significant speed-up in comparison with uniform ray tracing (cf.
 Abel Wandelt 2002)., Abel Wandelt 2002).
 In our scheme à ray Is split into four child-rays as soon as its linearseparation from neighbouring rays. r;jA6;. exceeds ή).," In our scheme a ray is split into four child-rays as soon as its linearseparation from neighbouring rays, $r_j\Delta\theta_{\ell}$, exceeds $f_2h_j$."
 Here r; is the distance from the tonizing star to evaluation point j. f» is a dimensionless parameter controlling the angular resolution of the ensemble of rays representing the ionizing radiation. and {η is the smoothing length of the local evaluation point j.," Here $r_j$ is the distance from the ionizing star to evaluation point $j$, $f_2$ is a dimensionless parameter controlling the angular resolution of the ensemble of rays representing the ionizing radiation, and $h_j$ is the smoothing length of the local evaluation point $j$ ."
 Hence we require Acceptable results are obtained with £ in the range (1.0.1.3)," Hence we require Acceptable results are obtained with $f_2$ in the range $(1.0,1.3)$."
 A smaller f£ gives greater accuracy. but at the expense of more HEALPix rays.," A smaller $f_2$ gives greater accuracy, but at the expense of more HEALPix rays."
 As one moves outwards away from the central star. rays are only ever split. they are never merged.," As one moves outwards away from the central star, rays are only ever split, they are never merged."
 The version of HEALPix allocates identifiers to rays according to the scheme illustrated in Fig. 2.. ," The version of HEALPix allocates identifiers to rays according to the scheme illustrated in Fig. \ref{fig: healpixtessel},"
which shows asmall patch on the celestial sphere., which shows a small patch on the celestial sphere.
 Here the mother-ray of ray 1Η has ID and the four child-rays of ray i have IDs Here #=0 corresponds to the child-ray to the South. 7=| corresponds to the child-ray to the West. 2= corresponds to the child-ray to the East and 723 corresponds to the child-ray to the North.," Here the mother-ray of ray $m$ has ID and the four child-rays of ray $m$ have IDs Here $n=0$ corresponds to the child-ray to the South, $n=1$ corresponds to the child-ray to the West, $n=2$ corresponds to the child-ray to the East and $n=3$ corresponds to the child-ray to the North."
 This numbering scheme makes it very simple to trace a ray back to the star at the origin. provided you know the ID of the ray its level.," This numbering scheme makes it very simple to trace a ray back to the star at the origin, provided you know the ID of the ray its level."
" To avoid numerical artifacts due discretization in the directions of rays. we rotate the ensemble of HEALPix rays through three random angles (about the z-. αι and z""—axes). each time we build the ensemble."," To avoid numerical artifacts due discretization in the directions of rays, we rotate the ensemble of HEALPix rays through three random angles (about the $z-$, $x'-$, and $z''-$ axes), each time we build the ensemble."
 This process is necessary to prevent the formation of artificial corrugations in the ionization front. as explained in detail in Krumholz et al. (," This process is necessary to prevent the formation of artificial corrugations in the ionization front, as explained in detail in Krumholz et al. ("
2007).,2007).
 At each evaluation point we estimate the value of 7(rj) using Eqn. (13)., At each evaluation point we estimate the value of $I(r_j)$ using Eqn. \ref{sumint}) ).
 If the calculation returns {η<7... then the evaluation point lies in the interior of the.," If the calculation returns $I(r_j)<I_{_{\rm MAX}}$, then the evaluation point lies in the interior of the."
 Therefore. some of the particles that belong to its neighbour list should be ionized.," Therefore, some of the particles that belong to its neighbour list should be ionized."
 We flag a particle as ionized. if it passes the following two tests: (a) its coordinates are inside the solid angle of the ray: and (b) its distance from the star is smaller than the distance of the evaluation point (7j).," We flag a particle as ionized, if it passes the following two tests: (a) its coordinates are inside the solid angle of the ray; and (b) its distance from the star is smaller than the distance of the evaluation point $r_j$ )."
 If a particle is ionized. it is given a temperature 7=73i.," If a particle is ionized, it is given a temperature $T=T_{\rm i}$."
 Otherwise it remains neutral with temperature 7=7., Otherwise it remains neutral with temperature $T=T_{\rm n}$.
 Fig.3 illustrates the location of the neighbours of evaluation point j. and the ones which pass these tests.," \ref{fig: givet} illustrates the location of the neighbours of evaluation point $j$, and the ones which pass these tests."
 We store in memory the value of the integral in Eqn. (13)), We store in memory the value of the integral in Eqn. \ref{sumint}) )
 and the coordinates of the evaluation point at the end of a given ray segment., and the coordinates of the evaluation point at the end of a given ray segment.
" The distance R, of the ionization front from the star along a given ray is given by the condition 7Z(R,)=LL."," The distance $R_{_{\rm IF}}$ of the ionization front from the star along a given ray is given by the condition $I\left(R_{_{\rm IF}}\right)\,=\,I_{_{\rm MAX}}$."
" It is determined using a binary chop algorithm between the last two evaluation points rj, and r; for which Hrii)SESI(r;) The binary chop algorithm i5 stopped once the adjustment to r; becomes smaller than 1077,4.", It is determined using a binary chop algorithm between the last two evaluation points $r_{j-1}$ and $r_j$ for which $I\left(r_{j-1}\right)<I_{_{\rm MAX}}<I\left(r_j\right)$ .The binary chop algorithm is stopped once the adjustment to $r_j$ becomes smaller than $10^{-3}h_{j-1}$.
 If the material of the cloud along the line of sight of à ray is sufficiently rarefied. 7Z(r) may never reach J. within the computational domain.," If the material of the cloud along the line of sight of a ray is sufficiently rarefied, $I\left(r\right)$ may never reach $I_{_{\rm MAX}}$ within the computational domain."
 We therefore estimate the maximum distance fpinay Of all gas particles and if rj> We stop calculating the sum.," We therefore estimate the maximum distance $r_{p,{\rm max}}$ of all gas particles and if $r_j>r_{p,{\rm max}}$ we stop calculating the sum."
 Any ray that satisfies this condition is characterized as and the position of the ionization front is not determined along such rays (see Fig. 4))., Any ray that satisfies this condition is characterized as and the position of the ionization front is not determined along such rays (see Fig. \ref{fig: openray}) ).
 It is not feasible to resolve the ionization. front in a standard SPH simulation. of an evolving (see Appendix Appendix A:))., It is not feasible to resolve the ionization front in a standard SPH simulation of an evolving (see Appendix \ref{ap.tempsmoothing}) ).
 Consequently we have to smooth the temperature gradient artificially across the tonization front., Consequently we have to smooth the temperature gradient artificially across the ionization front.
 To demonstrate why this is necessary. we model a uniform density spherical cloud consisting of 10° pre-settled SPH particles.," To demonstrate why this is necessary, we model a uniform density spherical cloud consisting of $10^6$ pre-settled SPH particles."
 The total mass of the cloud is M.= 1000M... and the radius 1s R= Ipe.," The total mass of the cloud is $M\,=\,1000{\rm M_{\odot}}$ , and the radius is $R\,=\,1{\rm pc}$ ."
 At the centre of the cloud therets a single star emitting N=10” ≻↼↼↼ionizing photons per second.," At the centre of the cloud thereis a single star emitting $\dot{\cal{N}}_{_{\rm LyC}}\,=\,10^{49}$ ionizing photons per second."
 There are no gravitational forces., There are no gravitational forces.
 We simulate this system in two ways: in Case A. the temperature gradient is unsmoothed: and in Case B. the temperature gradient 1s smoothed.," We simulate this system in two ways: in Case A, the temperature gradient is unsmoothed; and in Case B, the temperature gradient is smoothed."
for νο. Ay. p? and pr.,"for $v_{\parallel2}$ , $b_{\parallel2}$ , $p_2$ and $\rho_2$."
 Here we need to make a note., Here we need to make a note.
 It follows from Eqs. (95)), It follows from Eqs. \ref{eq:secondexpansion1}) )
" and (96)) that the ratio of ps to p, is of the order of e577. and the same Is true for vip. Sy. and pz."," and \ref{eq:secondexpansion2}) ) that the ratio of $\rho_2$ to $\rho_1$ is of the order of $\epsilon\delta^{-2}$ , and the same is true for $v_{\parallel2}$, $b_{\parallel2}$ and $p_2$."
 It seems to be inconsistent with the regular perturbation method where it is assumed that the next order approximation is always smaller than the previous one., It seems to be inconsistent with the regular perturbation method where it is assumed that the next order approximation is always smaller than the previous one.
 However. this problem is only apparent.," However, this problem is only apparent."
" To show this we need to clarify the exact mathematical meaning of the statement ""in the asymptotic expansion each subsequent term is much smaller than the previous one”."," To show this we need to clarify the exact mathematical meaning of the statement “in the asymptotic expansion each subsequent term is much smaller than the previous one""."
 To do this we introduce the nine-dimensional vector U=(uy.vLbbib.LP.p.p) and consider it as an element of a Banach space.," To do this we introduce the nine-dimensional vector $\mathbf{U}=\left(u,v_{\parallel},v_{\perp},b_x,
b_{\parallel},b_{\perp},P,p,\rho\right)$ and consider it as an element of a Banach space."
 The norm in this space can be introduced in different ways., The norm in this space can be introduced in different ways.
 One possibility 15 where L is the period., One possibility is where $L$ is the period.
 The asymptotic expansion in the dissipative layer. Eq. (68)).," The asymptotic expansion in the dissipative layer, Eq. \ref{eq:reynoldsexpansion}) ),"
" can be rewritten as U=Uo+eU,€Us ει...", can be rewritten as $\mathbf{U}=\mathbf{U}_0+\epsilon\mathbf{U}_1+\epsilon^2\mathbf{U}_2+\ldots$ .
" Then the mathematical formulation of the statement ""each subsequent term is much smallerthan theprevious one"" is [[U,l|<JU,|) 2=1.2.2...Et ts straightforward to verify that. inaccordance with Eqs. (68)). (69)). (95))"," Then the mathematical formulation of the statement “each subsequent term is much smallerthan theprevious one"" is $||\mathbf{U}_{n+1}||\ll||\mathbf{U}_n||$, $n=1,2,\ldots$.It is straightforward to verify that, inaccordance with Eqs. \ref{eq:reynoldsexpansion}) ), \ref{eq:reynoldsexpansionlarge}) ), \ref{eq:secondexpansion1}) )"
 and (96)). IU||«Uy].," and \ref{eq:secondexpansion2}) ), $||\mathbf{U}_2||\ll||\mathbf{U}_1||$."
 Once the expansions (95)) and (96)) are substituted into Eqs. (86))-(94)).," Once the expansions \ref{eq:secondexpansion1}) ) and \ref{eq:secondexpansion2}) ) are substituted into Eqs. \ref{eq:epsilon2ndapprox1}) \ref{eq:epsilon2ndapprox9}) ),"
 we can express the variables in this order of approximation as For the total pressure we obtain that In addition. we obtain that the equation which determines ily( b:IS Since the large variables in this order of approximation are vp and bp. we can deduce that the linear order of approximation of resonant waves in the dissipative layer excite modes in the second order of approximation.," we can express the variables in this order of approximation as For the total pressure we obtain that In addition, we obtain that the equation which determines $u_2^{(1)}$ is Since the large variables in this order of approximation are $v_{\parallel2}$ and $b_{\parallel2}$, we can deduce that the linear order of approximation of resonant waves in the dissipative layer excite modes in the second order of approximation."
 The excitation comes from the nonlinear term found in the second order approximation of the pressure equation. this drives the parallel components of the velocity and magnetic field perturbations.," The excitation comes from the nonlinear term found in the second order approximation of the pressure equation, this drives the parallel components of the velocity and magnetic field perturbations."
 Since we are focussed on the resonance only. these waves are not resonant.," Since we are focussed on the resonance only, these waves are not resonant."
 These waves act to cancel the very small pressure and density perturbations created by the first order approximation., These waves act to cancel the very small pressure and density perturbations created by the first order approximation.
 We now calculate the third order approximation with respect to e., We now calculate the third order approximation with respect to $\epsilon$.
" On analyzing the third order system.of equations we deduce that the large variables in this order ofκ approximationul: are⊀∣↼ Alfvénnic Gv.≼∣↠ 5th)κ), so we. only: need the perpendicular components of momentum and induction equations given by Eqs. (59))"," On analyzing the third order systemof equations we deduce that the large variables in this order of approximation are Alfvénnic $v_{\perp3}^{(1)}$, $b_{\perp3}^{(1)}$ ), so we only need the perpendicular components of momentum and induction equations given by Eqs. \ref{eq:momconservationperp}) )"
 and (62)). respectively.," and \ref{eq:inductnewperp}) ), respectively."
" First. since some of the first order approximation. terms contribute to the third order approximation in integral form we must introduce à new notation The third order approximation of the perpendicular component of momentum is while the perpendicular component of magnetic induction equation is Note that in obtaining the third order approximations we have employed all the relations we have for variables in the first and second order of approximation,"," First, since some of the first order approximation terms contribute to the third order approximation in integral form we must introduce a new notation The third order approximation of the perpendicular component of momentum is while the perpendicular component of magnetic induction equation is Note that in obtaining the third order approximations we have employed all the relations we have for variables in the first and second order of approximation."
 Equations (104)) and (105)) clearly show that the nonlinear terms on the right-hand sides do not cancel., Equations \ref{eq:epsilon3rdapprox1}) ) and \ref{eq:epsilon3rdapprox2}) ) clearly show that the nonlinear terms on the right-hand sides do not cancel.
 This implies that the expansion of v.3 and 5.3 should be of the form We should state. for completeness. that if we derive the third order approximation for all the Eqs. (57))-(65))," This implies that the expansion of $v_{\perp3}$ and $b_{\perp3}$ should be of the form We should state, for completeness, that if we derive the third order approximation for all the Eqs. \ref{eq:massconservation1}) \ref{eq:totalpressurenew}) )"
" we obtain the expansions for us. bya. vis. bis. ps. p and P3 to be The expansions calculated for all the variablescan nowbe collected together and we canwrite the expansions for ""large? and ‘small’ variables in the dissipative layer when studying resonant waves."," we obtain the expansions for $u_3$, $b_{x3}$, $v_{\parallel3}$, $b_{\parallel3}$, $p_3$, $\rho_3$ and $P_3$ to be The expansions calculated for all the variablescan nowbe collected together and we canwrite the expansions for `large' and `small' variables in the dissipative layer when studying resonant waves."
" Large variables (v_ and 4_) have the expansion and the expansion of small variables (u. ὃν, vy. bj. p. p and P) is defined as"," Large variables $v_{\perp}$ and $b_{\perp}$ ) have the expansion and the expansion of small variables $u$ , $b_x$ , $v_{\parallel}$ , $b_{\parallel}$ , $p$ , $\rho$ and $P$ ) is defined as"
"calculating the area of the larges patch oei the ΕΟΝ formed. exclusively. by profiles of the paricular family one finds that network. patches. nanlv associated wili and4.. can reach dineINIOUS 11» to few tels , ⋜∐⋅","calculating the area of the largest patch in the FOV 	formed, exclusively, by profiles of the particular 	family one finds that network 	patches, mainly associated with 	and, can reach dimensions up to few 	tens $^2$."
↸⊳↴∖↴↸∖↸⊳−∙⊀≚∐∪↑∐↸∖↥⋅↕⋜∐⊔∏↕↸∖↴∖↴∐⋜∏↽↸∖↑⋅↖↴⋟⋅⋅ vical patch dinieusiols of. few. teuths of al arcsecD (sce for a οκunuparison tie detail amage iu Fig, All other families have typical 	patch dimensions of few tenths of $1$ $^2$ 	(see for a comparison the detail image in Fig.
 5n i which coutoir liehliehtiis the erauular scale are reported).," \ref{fig2}
 	in which contour highlighting the granular scale are reported)."
" This means that out of network regions the profie shape of the analyzed proῃCR change over very small scales, snidler than the typical eranular scale."," 	This means that out of network regions the profile 	shape of the analyzed profiles change over very 	small scales, smaller than the typical granular scale."
 The results presented in this seclon were derived from a sinee classification run., 	 	The results presented in this section were derived from a single classification run.
 As specified in 3 it is lunvortaut to study the dependence of the results on cdiffereiw random nmüfializatious.," As specified in \ref{Analysis}
 	it is important to study the dependence of the results 	on different random initializations."
 To do this. we derived the average abundances of the differcut Γαμος fro uten classification rus: Table1 allows oue. to colmpare the averaec BIts with those preseuted above.," To do this, we derived 	the average abundances of the different families from ten 	classification runs; Table \ref{table} allows one 	to compare the average results with those presented 	above."
 Frou. this we can concluce that the results presented are sound aud hat the classification does not depend ou the random iuitializatio1, From this we can conclude that the results presented 	are sound and that the classification does not depend on the 	random initialization.
 Theoily class we did not consider so far in the preseifation of the results is29.. representative of 1.1 of the analyzed xofiles.," 	 	The only class we did not consider so far in the presentation 	of the results is, representative of $1.1$ 	of the analyzed profiles."
 Tus can be considered a fake class since it contains auonmalko» profiles., This 	can be considered a fake class since it contains anomalous 	profiles.
 Tere we define as anonmalous. for cxample. jose profiles on which the procedure adopted or the definition of the iuput dataset 5.10) did uot worz properly.," Here we define as anomalous, for example, those profiles 	on which the procedure adopted for the definition of the input dataset \ref{Dataarch}) ) did not work properly."
 A sinele fake class is found in all tje Classification rus: Us is always representative of abo of the analyzed xofiles., A single fake 	class is found in all the classification runs; this is always 	representative of about $1$ of the analyzed profiles.
 This can be verified also in Table 1.. indeed by ackine up the. percentages from all families one ects 00 of 1ο analyzed profiles.," This can 	be verified also in Table \ref{table}, indeed by adding up the 	percentages from all families one gets $99$ of the 	analyzed profiles."
 Au miportaut point to e1iphasize is that the wmuber of classes representative of all. the profiles observed by SOT/SP (3543) is sinall compared to the tota nuniber of profiles iu f1ο analyzed dataset. (535165)., 	 	An important point to emphasize 	is that the number of classes representative of all 	the profiles observed by SOT/SP $35\pm3$ ) is small 	compared to the total number of profiles 	in the analyzed dataset $535465$ ).
 Aloreover. when the major features of the classes are coisidered. the analyzed profiles can be organized im six families (ic. network. bluc-lobe. red-lohe. Q-like. asvnnetric. aud autisviuuietric) so thata few shape tvpokCOS cal represent SOT/SP quie Sun data.," Moreover, 	when the major features of the classes are considered, 	the analyzed profiles can be organized in six 	families (i.e., network, blue-lobe, 	red-lobe, $Q$ -like, asymmetric, and antisymmetric) 	so that	a few shape typologies can represent SOT/SP 	quiet Sun data."
 Nevertheless. if is -uportaunt to note ha aluost all these shapes are stronglv asviunietric.," Nevertheless, it is important to note 	that almost all these shapes are strongly asymmetric."
 Δost SOT/SP data have been so far iuterpreted through ME codes (OrozcoSuarezctal.20072:AscensioRamos20t)f))..but the classes iu Fis.," 	 	Most SOT/SP data have been so far interpreted through 	ME codes \citep[][]{OroS07,AseR09}, but 	the classes in Fig."
1 show that such a1 hypothesis has to be replaced o analvze the whole variety of profile shapes observed xw SOT/SP iu the «uet Sun.," \ref{fig1}
 	show that such an hypothesis has to be replaced 	to analyze the whole variety of profile shapes observed 	by SOT/SP in the quiet Sun."
 Except for he classes whose profile shapes cau © reasonablv consiered to be quasi-antisvunuetric (sce 1). we can conclue that ME codes cannot reproduce f16 observed profiles oserved. by SOT/SP.," 	Except for the classes whose profile shapes can be reasonably 	considered to be quasi-antisymmetric (see \ref{Results}) ), 	we can conclude that ME codes cannot reproduce 	the observed profiles observed by SOT/SP."
 OrozcoSuárezetal.(2010) recently showed that ÀIE coxes can be used to derive average propertics of fully resoved magnetized atinospheres {echuically speaking wit1nieuetic fillug factors equal o 1l) even when imvertiis extremely αποο profiles.," \citet{OroS10}
 	recently showed that ME codes can be used to derive 	average properties of fully resolved magnetized 	atmospheres (technically speaking withmagnetic 	filling factors equal to $1$ ) even when inverting 	extremely asymmetric profiles."
 This good LOWS does not eliminate the need for more refined inversions., This good news 	does not eliminate the need for more refined 	inversions.
 Tje asvnunetries provide inforinatiou on f nresolved sructure and/or eradieuts along the LOS 16 mnaenetic field that ire washed out uuless the li1C VAiapes are acequately interpreted., The asymmetries provide information 	on the unresolved structure and/or gradients along the 	LOS of the magnetic field that are washed out unless the 	line shapes are adequately interpreted.
 Moreover. the present angular resoutious do not eraut treating all EN. inagnetic eatures as fiIly: resolved.," Moreover, the present 	angular resolutions do not grant treating all IN 	magnetic features as fully resolved."
 These cousiderations cau IO used iu a coustructive wav when thinking about future strategies for the interpretation of spectropolarinietric data either from or. trom future telescopes., 	 	These considerations can 	be used in a constructive way when thinking 	about future strategies for the interpretation of 	spectropolarimetric data either from or 	from future telescopes.
 One needs different hypotheses. in order to interpret (aud fit) the different polarization profiles emiergiug from the quiet Sun., One needs different hypotheses 	in order to interpret (and fit) the different polarization 	profiles emerging from the quiet Sun.
" As an cxalple. et us consider two extreme cases from our classificatiol. οο,οἱ iud25."," 	As an example, let us consider two extreme cases 	from our classification, e.g., 	and."
. The first one. qlasi-antisvunuuetric. can be interpreted adoting AE hypotheses.," The first one, quasi-antisymmetric, 	can be interpreted adopting ME hypotheses."
 The second One Is a class that. for exanuple. could be interpreted iu terius of ήχος polaritics iua sinele xel ofHINODE.. with a two maeetic Conionent uodel atmosphere. Ποσο]. As," The 	second one is a class that, for example, 	could be interpreted in 	terms of mixed polarities in a single pixel of, 	i.e., with a two magnetic component model atmosphere. 	Recently,"
cusioRamos(201) put Kkward an dnversion procedure based ou Bayesian echniqies., \citet{AseR10spw6} put forward 	an inversion procedure based on Bayesian techniques.
 This procedure follows directly frou1 the approach adopted im AscusioRamos (2009).. based exclusively on ME. hypothesis.," 	This procedure follows directly from the approach 	adopted in \citet{AseR09}, based exclusively on ME hypothesis."
 new code is ade to automatically recognize the siniplest model. from those provided bv the user that can reproduce the examined polarization profiles.," 	The new code is able to automatically 	recognize the simplest model, from those 	provided by the user that can reproduce the examined polarization 	profiles."
 Iu other words. the code recognizes the minim degree of colplexity of a model atinosphere needed to reproduce the Oservations.," In other words, 	the code recognizes the minimum degree of complexity 	of a model atmosphere needed to reproduce the 	observations."
 This means tha different inversiou livpotreses can be used in a single inversion procedure., 	This means that 	different inversion hypotheses can be used in a 	single inversion procedure.
" From our poiut of view such an ayproach is extremely promising because it allows to avoid an a-priori choice of livpotCSCS for the description of f16 solar photosphere that. Ἡ Sole Cases, can turn out to be wrong i reproucing observations."," 	From our point 	of view such an approach is extremely promising because 	it allows to avoid an a-priori choice of hypotheses 	for the description of the solar photosphere 	that, in some cases, can turn out to be wrong in reproducing 	observations."
 Adoie the profile shapes in Fie.,	 	 	Among the profile shapes in Fig.
 l1 ταν single lobe profiles can be recognized., \ref{fig1} many single lobe 	profiles can be recognized.
 Naev. according to the definition adopted in Steiner e 17.6 of the analyzed profiles are blue-lobe- while 9.6 aro red-lobe-oul.," Namely, according to the definition 	adopted in \citet{Ste00}, , $17.6$ of the analyzed profiles are 	blue-lobe-only, while $9.6$ are red-lobe-only."
 Such extremely asvuuuetric profiles have been the object of receut stucies, 	Such extremely asymmetric profiles have been 	the object of recent studies
Possible implications of this soft seed photon energy estimate will be discussed in §3..,Possible implications of this soft seed photon energy estimate will be discussed in \ref{sequence}.
" Other model parameter estimates based on these observables are D=28. B=2.2 € 10P em. f;=64x10.1L1(4/100).""2. implying Lj6.4x102(5,/100)°° eres !."," Other model parameter estimates based on these observables are $D = 28$ , $B = 2.2$ G, $R_{\rm sc} = 1.2 \times 10^{18} 
\, \sqrt{L_{46} \, (\taur / 0.1)}$ cm, $R_b = 1.7 \times 
10^{15}$ cm, $f_j = 6.4 \times 10^{-4} \, L_{46}^{-1} \, 
(\gamma_1 / 100)^{-0.2}$, implying $L_j \sim 6.4 \times 10^{42}
\, (\gamma_1 / 100)^{-0.2}$ ergs $^{-1}$."
 The high-energy cut-off of both the svnchrotron and the Compton components are poorly known in 3€ 279 and other FSRQs. so no reliable constraint on (he maxinnun electron energy 5» can be derived in the FSRQ case.," The high-energy cut-off of both the synchrotron and the Compton components are poorly known in 3C 279 and other FSRQs, so no reliable constraint on the maximum electron energy $\gamma_2$ can be derived in the FSRQ case."
 The parameter estimates for the FSRQ case quoted above are in good agreement. with those found by Ghisellinietal.(1993). [or FSRQs in general. and through more detailed spectral modeling of ος 279 in particular (e.g.. Hartmanetal.(2001))). which indicates (hat our analvtic estimates max indeed be useful to assess a convenient starting point lor more detailed spectral modeling of FSRQs.," The parameter estimates for the FSRQ case quoted above are in good agreement with those found by \cite{ghisellini98} for FSRQs in general, and through more detailed spectral modeling of 3C 279 in particular (e.g., \cite{hartman01}) ), which indicates that our analytic estimates may indeed be useful to assess a convenient starting point for more detailed spectral modeling of FSRQs."
 In the previous section. we obtained (vpical parameter values for IDEs. and FSRQs.," In the previous section, we obtained typical parameter values for HBLs and FSRQs."
 These estimates indicate that the most significant differences between model parameters of FSRQs and HIIDLEs are found in the values of the jet power £; and the magnetic field D. which are both found to decrease by more than an order of magnitude [roi FSRQs to IDEs.," These estimates indicate that the most significant differences between model parameters of FSRQs and HBLs are found in the values of the jet power $L_j$ and the magnetic field $B$, which are both found to decrease by more than an order of magnitude from FSRQs to HBLs."
" The lack of evidence for a significant. contribution of an external Compton component to the -rav spectra of HLBLEs indicates that the energy density of (he external soft photon field porameterized through Lp. Tepe. and Ai decreases by ο2,3D orders of magnitude along the sequence of blazar twpes."," The lack of evidence for a significant contribution of an external Compton component to the $\gamma$ -ray spectra of HBLs indicates that the energy density of the external soft photon field — parameterized through $L_D$, $\taur$, and $R_{\rm
sc}$ — decreases by $\gs 3$ orders of magnitude along the sequence of blazar types."
 This is in agreement with the results of Ghisellinietal.(1995)., This is in agreement with the results of \cite{ghisellini98}.
. The decreasing energv densitv of the external soft photon field along the sequence FSRQ — LBL — IIBL. in tandem with the decreasing jel power suggests that (liis is a consequence ol a decreasing accretion rate along (this sequence.," The decreasing energy density of the external soft photon field along the sequence FSRQ $\to$ LBL $\to$ HBL, in tandem with the decreasing jet power suggests that this is a consequence of a decreasing accretion rate along this sequence."
 This. in turn. is in very good agreement with the suggestion of DElia&Cavaliere(2000) ancl Cavaliere of an evolutionary sequence from FSRQs to DL Lacs characterized by such a decline in the accretion rate.," This, in turn, is in very good agreement with the suggestion of \cite{delia00} and \cite{cavaliere01} of an evolutionary sequence from FSRQs to BL Lacs characterized by such a decline in the accretion rate."
 We are (hus motivated (o tay to reconstruct the evolutionary sequence FSRQ — LBL — UBL by varying the accretion rate (aud other model parameters dependent on (he accretion rate) in our specific spectral blazar model described in (he previous section., We are thus motivated to try to reconstruct the evolutionary sequence FSRQ $\to$ LBL $\to$ HBL by varying the accretion rate (and other model parameters dependent on the accretion rate) in our specific spectral blazar model described in the previous section.
 In order to do so. we are starting out will parameters appropriate to reproduce the broadband spectrum of a typical FSRQ.," In order to do so, we are starting out with parameters appropriate to reproduce the broadband spectrum of a typical FSRQ."
 The FSRQ phase constitutes an early phase of blazar evolution in which the central regions of the galaxy are rich in gas and dust. leading to a high accretion rale onto the central. supermassive black hole.," The FSRQ phase constitutes an early phase of blazar evolution in which the central regions of the galaxy are rich in gas and dust, leading to a high accretion rate onto the central, supermassive black hole."
 At (he same time. the cireumnuclear material efficiently reprocesses and scatters (he accretion-disk radiation. leading to the observed strong optical emission lines in the broad line region and to a high energy densityof the external," At the same time, the circumnuclear material efficiently reprocesses and scatters the accretion-disk radiation, leading to the observed strong optical emission lines in the broad line region and to a high energy densityof the external"
Finally. the false positive rate as a function of AZ; (at all values of 2 and ¢;) is shown in Figure 10..,"Finally, the false positive rate as a function of $M_i$ (at all values of $P_i$ and $e_i$ ) is shown in Figure \ref{fig:mfp}."
 While the large numbers of false positives at low mass might at first appear troubling. it must be remembered that there is a significant selection οσοι finding objects at. very. low masses.," While the large numbers of false positives at low mass might at first appear troubling, it must be remembered that there is a significant selection effect finding objects at very low masses."
 Vherefore the number of correct. detections will. decline steeply at very low masses (as low mass planets are very hare to detect). while the incorrect detection rate should remain roughly constant.," Therefore the number of correct detections will decline steeply at very low masses (as low mass planets are very hard to detect), while the incorrect detection rate should remain roughly constant."
 This will lead to à systematic increase in the false positive rate at very low masses., This will lead to a systematic increase in the false positive rate at very low masses.
 We test this idea by showing the false positives as a function of the total number of simulations for cach star in the top panel of Figure 11.., We test this idea by showing the false positives as a function of the total number of simulations for each star in the top panel of Figure \ref{fig:correct_all}.
 The detections seem to be approximately constant for 1179949. and 220782. with valuesof ~1-2% for the former ancl ~2- for the latter.," The detections seem to be approximately constant for 179949 and 20782, with valuesof $\sim$ for the former and $\sim$ for the latter."
 In the case of 338382. however. there is an increase from about αμ up to around.," In the case of 38382, however, there is an increase from about $M_{\mathrm{Jup}}$ up to around."
 Comparing 338382 to the 1:10three subsets of 1179940 (bottom panel of Figure 11)). we see the cause of the increase is observation density.," Comparing 38382 to the three subsets of 179949 (bottom panel of Figure \ref{fig:correct_all}) ), we see the cause of the increase is observation density."
 The subset with W=14 approximately the same as 338382. suffers from the same elfect., The subset with $N=14$ – approximately the same as 38382 – suffers from the same effect.
 The No=28 subset shows the effect to a Lesser degree and it is almost completely removed in the N=56 subset., The $N=28$ subset shows the effect to a lesser degree and it is almost completely removed in the $N=56$ subset.
 This shows one weakness in our detection criteria and we are currently investigating wavs to minimise the problem., This shows one weakness in our detection criteria and we are currently investigating ways to minimise the problem.
 Our automated detection criteria. and a means to analyse alse positive rates. place us in à position to examine in etail the observational biases present in our data for the iree stars under simulation.," Our automated detection criteria, and a means to analyse false positive rates, place us in a position to examine in detail the observational biases present in our data for the three stars under simulation."
 We define the detectability aas the detection rate as a function of £5. ος and AJ; in 10 case of our simulations we performed. 100 realisations at ach point in (£2.06; M;) space. so we divide the number of etections by 100.," We define the detectability as the detection rate as a function of $P_i$, $e_i$, and $M_i$ – in the case of our simulations we performed 100 realisations at each point in $P_i$ $e_i$ $M_i$ ) space, so we divide the number of detections by 100."
 False positives have been removed. from o for each set e;of Mi)simulations., False positives have been removed from the for each set of simulations.
 In Figure 12.. we show contour maps of detectability. for cach star. as a function of input," In Figure \ref{fig:Pselfunc1}, , we show contour maps of detectability, for each star, as a function of input"
following the evolution of substructures.,following the evolution of substructures.
 Fig., Fig.
 1 shows the projected correlation functions at three different stellar mass bins at redshift of around 0.8., \ref{fig:VVDS} shows the projected correlation functions at three different stellar mass bins at redshift of around $0.8$.
" Symbols with error bars are results from VVDS observation(?),, and dashed lines are the derived results from our simple model."," Symbols with error bars are results from VVDS \citep{meneux2008}, and dashed lines are the derived results from our simple model."
 The projected correlation functions predicted by the model are in reasonably good agreement with the observation from VVDS., The projected correlation functions predicted by the model are in reasonably good agreement with the observation from VVDS.
 Fig., Fig.
" 2. shows the observed stellar mass functions at different redshifts(symbols), compared with the stellar mass functions derived from our model(lines), with the Mstars-Minfau relation taken the same as that of present day."," \ref{fig:SMF} shows the observed stellar mass functions at different redshifts(symbols), compared with the stellar mass functions derived from our model(lines), with the $M_{stars}$ $M_{infall}$ relation taken the same as that of present day."
" Considering the fact that different initial mass functions(IMF) were adopted in different observations, we convert all stellar masses to the case of the Chabrier IMF(?),, in this figure and all the figures of stellar mass functions hereafter."," Considering the fact that different initial mass functions(IMF) were adopted in different observations, we convert all stellar masses to the case of the Chabrier \citep{chabrier2003}, in this figure and all the figures of stellar mass functions hereafter."
" The galaxy mass obtained with the Salpeter IMF(?) is divided by 1.70, and that with the Kroupa(?) IMF is divided by 1.104(?).."," The galaxy mass obtained with the Salpeter \citep{salpeter1955} is divided by $1.70$ , and that with the \citep{kroupa2001} IMF is divided by $1.104$ \citep{cowie2008}."
 It is clear from Fig., It is clear from Fig.
 2 that the stellar mass functions are not reproduced under the simple assumption that Mstars-Minfat relation does not evolve with time., \ref{fig:SMF} that the stellar mass functions are not reproduced under the simple assumption that $M_{stars}$ $M_{infall}$ relation does not evolve with time.
" Observationally, the number of galaxies with low stellar mass decreases dramatically towards higher redshifts, while the number of high mass galaxies stays roughly unchanged with different redshifts."," Observationally, the number of galaxies with low stellar mass decreases dramatically towards higher redshifts, while the number of high mass galaxies stays roughly unchanged with different redshifts."
" 'The model derived results, however, show an opposite trend."," The model derived results, however, show an opposite trend."
" The number of low mass galaxies evolves quite slowly, and remains almost the same till redshift 2, while the number of high mass galaxies evolves a lot, with a much smaller number of galaxies existing at higher redshifts."," The number of low mass galaxies evolves quite slowly, and remains almost the same till redshift $2$, while the number of high mass galaxies evolves a lot, with a much smaller number of galaxies existing at higher redshifts."
 T'hese results show that the Mstars-Minfait relation must vary at different redshifts., These results show that the $M_{stars}$ $M_{infall}$ relation must vary at different redshifts.
 A reasonable model should in general give more massive galaxies and fewer low mass galaxies at higher redshifts than at the local universe., A reasonable model should in general give more massive galaxies and fewer low mass galaxies at higher redshifts than at the local universe.
" As shown in Fig.3 of ?,, the stellar mass function is more sensitive to the change of model parameters, while the x? of correlation functions stays flatter around minimum in a large range of parameter sets."," As shown in Fig.3 of \citet{moster2009}, the stellar mass function is more sensitive to the change of model parameters, while the $\chi^2$ of correlation functions stays flatter around minimum in a large range of parameter sets."
 This explains why the correlation functions can be well reproduced while the stellar mass functions show such a large discrepancy., This explains why the correlation functions can be well reproduced while the stellar mass functions show such a large discrepancy.
" Therefore, correlation function alone is not enough to constrain the Mstars-Minfau relation at z~0.8."," Therefore, correlation function alone is not enough to constrain the $M_{stars}$ $M_{infall}$ relation at $z\sim
0.8$."
" At the end of this section, we will show that stellar mass function alone is not enough either to give a good constraint on the relation, at least in fitting the current observational data results."," At the end of this section, we will show that stellar mass function alone is not enough either to give a good constraint on the relation, at least in fitting the current observational data results."
 From Fig., From Fig.
 1 and Fig., \ref{fig:VVDS} and Fig.
 2 we know that we need to fit both the stellar mass function and the two point correlation functions to constrain the underlying Mstars- Minfau relation at higher redshifts., \ref{fig:SMF} we know that we need to fit both the stellar mass function and the two point correlation functions to constrain the underlying $M_{stars}$ $M_{infall}$ relation at higher redshifts.
 Current studies of VVDS observation give both the stellar mass function(?) and correlation functions indifferent stellar mass, Current studies of VVDS observation give both the stellar mass \citep{pozzetti2007} and correlation functions indifferent stellar mass
NGC 2257. and Hodge 11 te.g.. Johnson et al. (1999)}):,"NGC 2257, and Hodge 11 (e.g., Johnson et al. \shortcite{johnson:99}) );"
 NGC 1754. 1835. 1898. 1916. 2005. and 2019 te.g.. Olsen et al. (1998)):," NGC 1754, 1835, 1898, 1916, 2005, and 2019 (e.g., Olsen et al. \shortcite{olsen}) );"
 and NGC 1786. 1841 and 2210 te.g.. Brocato et al. (1996))).," and NGC 1786, 1841 and 2210 (e.g., Brocato et al. \shortcite{brocato}) )."
 Several published CMDs show the remote outer cluster Reticulum to be very old (Johnsonetal.1999:Marconi2002: 2003): however a full age analysis is yet to be published for this cluster.," Several published CMDs show the remote outer cluster Reticulum to be very old \cite{johnson:99,marconi,monelli}; however a full age analysis is yet to be published for this cluster."
 In addition there are two more clusters located in the LMC bar region - NGC 1928 and 1939 — which integrated spectroscopy suggests could be old (Dutraetal.1999).. but which are so compac and lie against such highly crowded LMC fields that it has no previously been possible to obtain accurate CMDs for them (see for example. the search for old LMC clusters conducted by Geisler et al. (1997))).," In addition there are two more clusters located in the LMC bar region – NGC 1928 and 1939 – which integrated spectroscopy suggests could be old \cite{dutra}, but which are so compact and lie against such highly crowded LMC fields that it has not previously been possible to obtain accurate CMDs for them (see for example, the search for old LMC clusters conducted by Geisler et al. \shortcite{geisler}) )."
 The census of old LMC clusters is therefore stil incomplete., The census of old LMC clusters is therefore still incomplete.
" We have used the Advanced Camera for Surveys (ACS) onAST to obtain images of NGC 1928. 1939, and Reticulum as par of program 989] — a snapshot survey of 40 LMC and 40 SMC clusters."," We have used the Advanced Camera for Surveys (ACS) on to obtain images of NGC 1928, 1939, and Reticulum as part of program 9891 – a snapshot survey of $40$ LMC and $40$ SMC clusters."
 This program is primarily designed to extend the detailed investigation of Mackey Gilmore (2003a:2003b) concerning the structural evolution of Magellanic Cloud clusters.," This program is primarily designed to extend the detailed investigation of Mackey Gilmore \shortcite{sbp1,sbp2} concerning the structural evolution of Magellanic Cloud clusters."
 However. the ACS observations are of sufficient quality and resolution as to allow colour-magnitude diagrams (CMDs) to be constructed for NGC 1928 and NGC 1939 for the first time. as well as a high quality CMD for Reticulum.," However, the ACS observations are of sufficient quality and resolution as to allow colour-magnitude diagrams (CMDs) to be constructed for NGC 1928 and NGC 1939 for the first time, as well as a high quality CMD for Reticulum."
" In this paper. we present the results of these observations (Section 29) and the measured colour-magnitude ""iagrams (Section 3))."," In this paper, we present the results of these observations (Section \ref{s:obsred}) ) and the measured colour-magnitude diagrams (Section \ref{s:colourmag}) )."
 Abundances and reddenings are derived for each cluster. and it is demonstrated that NGC 1928 and 1939. along with Reticulum. are coeval with both well studied Galactic globular clusters (such as M92. M3 and M3) and other old LMC objects (such as NGC 2257 and Hodge |1) (Section 4)).," Abundances and reddenings are derived for each cluster, and it is demonstrated that NGC 1928 and 1939, along with Reticulum, are coeval with both well studied Galactic globular clusters (such as M92, M3 and M5) and other old LMC objects (such as NGC 2257 and Hodge 11) (Section \ref{s:clusterprop}) )."
 The observations were taken duringHST Cycle 12 using the ACS Wide Field Channel (WFC)., The observations were taken during Cycle 12 using the ACS Wide Field Channel (WFC).
 As snapshot targets. the clusters were observed for only one orbit each.," As snapshot targets, the clusters were observed for only one orbit each."
 This allowed two exposures to be taken per cluster — one through the F555W filter and one through the FSIJW filter., This allowed two exposures to be taken per cluster – one through the F555W filter and one through the F814W filter.
 Details of the individual exposures are listed in Table |.., Details of the individual exposures are listed in Table \ref{t:observations}.
 Exposure durations were 330 sin F555W and 200 s in F8I4W. The ACS WFC consists of a mosaic of two 2048.«.4096 SITe CCDs with a scale of ~0.05 arcsee per pixel. and separated by a gap of ~50 pixels.," Exposure durations were $330$ sin F555W and $200$ s in F814W. The ACS WFC consists of a mosaic of two $2048 \times 4096$ SITe CCDs with a scale of $\sim 0.05$ arcsec per pixel, and separated by a gap of $\sim 50$ pixels."
 Each image therefore covers a field of view (FOV) of approximately 202. areseconds., Each image therefore covers a field of view (FOV) of approximately $202 \times 202$ arcseconds.
 The clusters were centred at the reference point WFCI. located on chip | at position (2072.1024).," The clusters were centred at the reference point WFC1, located on chip 1 at position $(2072\,,\,1024)$."
" This allowed any given cluster to be observed up to a radius 7~150"" from its centre. while also ensuring the cluster core did not fall near the inter-chip gap."," This allowed any given cluster to be observed up to a radius $r\sim 150 \arcsec$ from its centre, while also ensuring the cluster core did not fall near the inter-chip gap."
 In order to maximise the efficiency of the limited imaging strategy afforded by a snapshot program. all observations were made with the ACS/WFC GAIN parameter set to 2 rather than the default (GAIN = 1).," In order to maximise the efficiency of the limited imaging strategy afforded by a snapshot program, all observations were made with the ACS/WFC GAIN parameter set to $2$ rather than the default (GAIN $=1$ )."
 This allowed the full well depth to be sumpled (as opposed to only ~75 per cent of the full well depth for GAIN = 1)with only a modest increase in read noise (~θ extra rms). thus increasing the dynamic range of the observations by greater than 0.3 mag.," This allowed the full well depth to be sampled (as opposed to only $\sim 75$ per cent of the full well depth for GAIN $=1$ ) with only a modest increase in read noise $\sim 0.3$ $^{-}$ extra rms), thus increasing the dynamic range of the observations by greater than $0.3$ mag."
 In addition. the second image of each cluster was offset by 2 pixels in both the .r and y directions. to help facilitate the removal of hot pixels and cosmic rays.," In addition, the second image of each cluster was offset by $2$ pixels in both the $x$ and $y$ directions, to help facilitate the removal of hot pixels and cosmic rays."
 With only two images per cluster. through different filters. it is not possible to completely eliminate the inter-chip gap using such an offset.," With only two images per cluster, through different filters, it is not possible to completely eliminate the inter-chip gap using such an offset."
 Before being made available for retrieval from the STScI archive. all images were passed through the standard ACS/WFC reduction pipeline.," Before being made available for retrieval from the STScI archive, all images were passed through the standard ACS/WFC reduction pipeline."
 This process includes bias and dark subtractions. flattield division. masking of known bad pixels and columns. and the calculation of photometry header keywords.," This process includes bias and dark subtractions, flatfield division, masking of known bad pixels and columns, and the calculation of photometry header keywords."
 In addition the STScI software is used to correct the (significant) geometric distortion present in WFC images., In addition the STScI software is used to correct the (significant) geometric distortion present in WFC images.
 The products obtained from the STScI archive are hence fully calibrated and distortion-corrected images. in units of counts per second.," The products obtained from the STScI archive are hence fully calibrated and distortion-corrected images, in units of counts per second."
" The F555W images of NGC 1928. 1939, and Reticulum may be seen in Figure I.."," The F555W images of NGC 1928, 1939, and Reticulum may be seen in Figure \ref{f:images}."
 Both NGC 1928 and NGC 1939 are extremely compact clusters set against heavily populated background fields. while Reticulum is at the other end of the scale — extremely diffuse with almost no background population evident.," Both NGC 1928 and NGC 1939 are extremely compact clusters set against heavily populated background fields, while Reticulum is at the other end of the scale – extremely diffuse with almost no background population evident."
 A second cluster is visible in the image of NGC 1939. slightly to the lower left of the main cluster.," A second cluster is visible in the image of NGC 1939, slightly to the lower left of the main cluster."
 This is another LMC member. NGC 1938 (see Section 44 and Figure 85).," This is another LMC member, NGC 1938 (see Section \ref{ss:1938} and Figure \ref{f:1938}) )."
 Foreach cluster. photometry was performed on the two images individually. using the software inIRAF.," For each cluster, photometry was performed on the two images individually, using the software in."
 The detailed procedure was as follows., The detailed procedure was as follows.
 First the task was used with a detection threshold of 4a above background to locate all the brightness peaks in each image., First the task was used with a detection threshold of $4\sigma$ above background to locate all the brightness peaks in each image.
 The two output lists were matched against each other to find objects falling at identical positions in the two frames., The two output lists were matched against each other to find objects falling at identical positions in the two frames.
 Objects detected in the first image but with no matching counterpart in the second image (and vice versa) were discarded., Objects detected in the first image but with no matching counterpart in the second image (and vice versa) were discarded.
 Performing this cross-matching was not as simple a task as it might at first appear., Performing this cross-matching was not as simple a task as it might at first appear.
 Because of the significant geometric distortion present in the ACS/WFC observations. a 2 pixel offset in the telescope position (i.e.. in the object's position on the detector) between the two exposures does not correspond to a 2.2 pixel offset between the two distortion-corrected images.," Because of the significant geometric distortion present in the ACS/WFC observations, a $2\times 2$ pixel offset in the telescope position (i.e., in the object's position on the detector) between the two exposures does not correspond to a $2\times 2$ pixel offset between the two distortion-corrected images."
 In fact. the value of the offset is position-dependent in the corrected images.," In fact, the value of the offset is position-dependent in the corrected images."
 There are at least two possible ways to overcome this., There are at least two possible ways to overcome this.
 The simplest is to use the header information in each of the two images to overlay a common coordinate system (e.g.. J2000.0 (a.0) coodinates) and match between the lists via a transformation from pixel coordinates to the common coordinate system.," The simplest is to use the header information in each of the two images to overlay a common coordinate system (e.g., J2000.0 $(\alpha\,,\,\delta)$ coodinates) and match between the lists via a transformation from pixel coordinates to the common coordinate system."
 However. this procedure is completely dependent on the accuracy of the header information in each of the two datasets and the consistency between them. and we possessed no independent means of verifying this for all the observations.," However, this procedure is completely dependent on the accuracy of the header information in each of the two datasets and the consistency between them, and we possessed no independent means of verifying this for all the observations."
 Instead. we preferred a more generally applicable and physically grounded procedure.," Instead, we preferred a more generally applicable and physically grounded procedure."
 We applied the distortion models used in to transform the observed F555W positions from the distortion-corrected frame to detector positions (.e.. in the distorted frame).," We applied the distortion models used in to transform the observed F555W positions from the distortion-corrected frame to detector positions (i.e., in the distorted frame)."
 The new coordinates were then subjected to the 2. pixel offset and transformed into the FSIJW distortion-corrected frame., The new coordinates were then subjected to the $2\times 2$ pixel offset and transformed into the F814W distortion-corrected frame.
 This allowed a direct match against the list of object positions measured by from this frame., This allowed a direct match against the list of object positions measured by from this frame.
 Given that the distortion models are accurate to a small fraction of a pixel. a match was defined as the transformed F555W position lying within a 0.5 pixel radius of an Γ5ΑΝ position.," Given that the distortion models are accurate to a small fraction of a pixel, a match was defined as the transformed F555W position lying within a $0.8$ pixel radius of an F814W position."
 Experimentation showed, Experimentation showed
already consumed. their gas both in internal processes and in previous mergers. cannot fuel the central starburst and. hence. their cry merger will not result in a blue core galaxy.,"already consumed their gas both in internal processes and in previous mergers, cannot fuel the central starburst and, hence, their dry merger will not result in a blue core galaxy."
 Acdditionallv. the enhancement: with redshift. of the gas fraction at the disposal of progenitor galaxies could explain not only the increasing presence of blue core galaxies at higher redshift. but also their compact dimensions.," Additionally, the enhancement with redshift of the gas fraction at the disposal of progenitor galaxies could explain not only the increasing presence of blue core galaxies at higher redshift, but also their compact dimensions."
 In fact. the blue core galaxies. due to the central starburst they underwent in the early strong dissipative merger. will have surface brightness profiles more centrally peaked. hence with smaller Ry. than Ες formed in non-dissipative mergers.," In fact, the blue core galaxies, due to the central starburst they underwent in the early strong dissipative merger, will have surface brightness profiles more centrally peaked, hence with smaller $_{e}$, than ETGs formed in non-dissipative mergers."
 As a consequence. 1ας formed in early. mergers will tend to have both bluer cores and to be more compact.," As a consequence, ETGs formed in early mergers will tend to have both bluer cores and to be more compact."
 Supporting this scenario. recently it has been found that high-z," Supporting this scenario, recently it has been found that $z$ \citep{saracco10b}."
 (2).. ," \nocite{}
 "
Direct imaging of extra-solar planetary-mass companions to solar-type stars is complicated by problems of contrast and resolution.,Direct imaging of extra-solar planetary-mass companions to solar-type stars is complicated by problems of contrast and resolution.
 At the time of writing. no planet has been directly imaged around a solar-type star.," At the time of writing, no planet has been directly imaged around a solar-type star."
 An alternative solution to these difficulties is to target intrinsically faint stars instead. such as white dwarfs.," An alternative solution to these difficulties is to target intrinsically faint stars instead, such as white dwarfs."
 Stellar evolution lends two huge advantages when searching for very faint companions: white dwarfs are up to ~104 times fainter than their main sequence progenitors. and the orbits of any planetary-mass companions that lie outside the stellar envelopes during the giant phases will expand outwards as mass is lost from the central star. increasing the projected separation by a maximum factor Ανν/Mwp (O2.," Stellar evolution lends two huge advantages when searching for very faint companions: white dwarfs are up to $\sim10^4$ times fainter than their main sequence progenitors, and the orbits of any planetary-mass companions that lie outside the stellar envelopes during the giant phases will expand outwards as mass is lost from the central star, increasing the projected separation by a maximum factor $M_{\rm MS} / M_{\rm WD}$ \citep{jeans}."
 Thus. the problems of contrast and resolution are greatly reduced.," Thus, the problems of contrast and resolution are greatly reduced."
 The possible evolution of planetary systems in the post-main sequence phase is discussed in more detail by 2.. 2.. 2 and ?..," The possible evolution of planetary systems in the post-main sequence phase is discussed in more detail by \citet{duncan}, \citet*{burleigh02}, \citet{Debes02} and \citet{villaver}."
 The direct detection of such low mass companions to white dwarfs opens up the possibility for spectroscopic investigation of a previously unobserved class of object: evolved low-mass brown dwarfs and planetary-mass gas giants as low in temperature as Zip=300 KK. In contrast. the directly imaged planetary-mass (€ {ων} companion to the brown dwarf IJ1207 has the spectrum of a mid-L dwarf (22). because it is still young (~10° years old).," The direct detection of such low mass companions to white dwarfs opens up the possibility for spectroscopic investigation of a previously unobserved class of object: evolved low-mass brown dwarfs and planetary-mass gas giants as low in temperature as $T_{\rm eff}\approx300$ K. In contrast, the directly imaged planetary-mass $\approx5\mjup$ ) companion to the brown dwarf J1207 has the spectrum of a mid-L dwarf \citep{chauvina,chauvinb}, because it is still young $\sim10^7$ years old)."
 The coolest known brown dwarf. J003402.77—005206.7. has a temperature GOOK< TOOK (2) and a spectral type 88.5.," The coolest known brown dwarf, $003402.77-005206.7$, has a temperature $600$ $< T_{\rm eff} < 700$ K \citep{warren07} and a spectral type 8.5."
" The letter ""Y"" has been suggested for the next. cooler. spectral type (2)... which migh include evolved. planetary-mass companions to white dwarfs."," The letter “Y” has been suggested for the next, cooler, spectral type \citep{Kirkpatrick}, which might include evolved planetary-mass companions to white dwarfs."
 Alternatively. if no obvious spectral change triggers the use of a new letter. then the T classification will need to be extended beyonce 88.5.," Alternatively, if no obvious spectral change triggers the use of a new letter, then the T classification will need to be extended beyond 8.5."
 The idea of using white dwarfs το. find intrinsically faint. low mass companions is not new.," The idea of using white dwarfs to find intrinsically faint, low mass companions is not new."
 ? and ? usec the low luminosity of white dwarfs to search for brown dwarf companions as near-infrared photometric excesses.," \citet{probst83} and \citet{becklin88} used the low luminosity of white dwarfs to search for brown dwarf companions as near-infrared photometric excesses,"
in Sec.,in Sec.
 [., 4.
 We eive our coucludiug remarks in Sec., We give our concluding remarks in Sec.
 5., 5.
" We use a stellar evolution code with eas mass accretion developed bv Olkuboetal(2006,2009):Unedaetal. (20095."," We use a stellar evolution code with gas mass accretion developed by \citet{ohkubo06, ohkubo09, umeda09}."
.. We implement enerev ecneration bv DAL amuihilation rate iu the code in the following manner., We implement energy generation by DM annihilation rate in the code in the following manner.
 We consider a primordia (proto-)star enmibedded at the ceuter of a small mass DAL halos., We consider a primordial (proto-)star embedded at the center of a small mass DM halos.
 The DAI density profile. py. is calculated using the analytical method of Bhunenthalctal.(1986): when the primordia eas cools and collapses. DAL particles are also “drageed” iuto the eravitational poteutial well.," The DM density profile, ${\rho}_{\chi}$, is calculated using the analytical method of \citet{blumenthal86}; when the primordial gas cools and collapses, DM particles are also “dragged” into the gravitational potential well."
 The adiabatic contraction model uses au adiabatic iuvariant., The adiabatic contraction model uses an adiabatic invariant.
 For spherically distributed DAL and barvous with a total mass of A(R)= A). an adiabatic invariant is Freeseetal.(2009). conipared the difference of DM density profile calculated using this method and a more accurate ioethod developed by Young (1980).," For spherically distributed DM and baryons with a total mass of $M(R) = M_{\mathrm{gas}}(R) + M_{\mathrm{DM}}(R)$ , an adiabatic invariant is \citet{freese09} compared the difference of DM density profile calculated using this method and a more accurate method developed by \citet{young80}."
.. They conclude that the difference is not more than a factor of two., They conclude that the difference is not more than a factor of two.
 We have performed direct numerical simulations of carly structure formation to check the accuracy of this analytical method., We have performed direct numerical simulations of early structure formation to check the accuracy of this analytical method.
 To this eud we have used the parallel N-body/S1ioothed Particle Uvdrodvnaimics (SPIT) solver CADCET-2 (SpringelWw105) in its version suitably adopted to follow radiative cooling processes at very high densities (Yoshidaetal.2006)., To this end we have used the parallel $N$ -body/Smoothed Particle Hydrodynamics (SPH) solver GADGET-2 \citep{springel05} in its version suitably adopted to follow radiative cooling processes at very high densities \citep{yoshida06}.
. We have found that the DAL deusity calculated by Blumeuthal’s method is indeed in good agreement with the result of our direct nunerncal sinulations., We have found that the DM density calculated by Blumenthal's method is indeed in good agreement with the result of our direct numerical simulations.
 Figue 1 compares the results from the analytic model and the simulations., Figure \ref{f1} compares the results from the analytic model and the simulations.
 Details will be preseuted elsewhere (Iirauo et al..," Details will be presented elsewhere (Hirano et al.,"
 in preparation)., in preparation).
 We note hat. although these two resis aeree very well. confirnune the validity of the analytic model. the simulations do not resolve the DM density down ο length scales of astronomical units.," We note that, although these two results agree very well, confirming the validity of the analytic model, the simulations do not resolve the DM density down to length scales of astronomical units."
 Because the eas density profile itself evolves iu a self-similar namner (Omumisai&Nishi1998). we asstue that he DA continue to contract adiabatically aud he evolution of DM deusity can be calculated by Bhuneuthal’s uethoct.," Because the gas density profile itself evolves in a self-similar manner \citep{omukai98}, we assume that the DM continue to contract adiabatically and the evolution of DM density can be calculated by Blumenthal's method."
 Tn this work. we onulv consider the DM density evolution based ou adiabatic contraction.," In this work, we only consider the DM density evolution based on adiabatic contraction."
 lu principle. DAL anmihilation can occur even more cficicutly in the star by capture.," In principle, DM annihilation can occur even more efficiently in the star by capture."
 If the density of the stellar core increases enough to scatter and trap DAL particles. the DAL particles can rapidly siuk tow the center. to selt-auniliüla5 cficicuth.," If the density of the stellar core increases enough to scatter and trap DM particles, the DM particles can rapidly sink toward the center, to self-annihilate efficiently."
 During the dark star phase. however. the effect of DM capture is uuiiportaut because the star has expanded extremely and the eas clensity is low.," During the dark star phase, however, the effect of DM capture is unimportant because the star has expanded extremely and the gas density is low."
" Suppose a ""cloud"" of DAL particles. contract frou a radial position fij to fü. aud the total mass distribution changes from My) to Mryow(2)."," Suppose a “cloud” of DM particles contract from a radial position $R_{\mathrm{pre}}$ to $R_{\mathrm{new}}$, and the total mass distribution changes from $M_{\mathrm{pre}}(R)$ to $M_{\mathrm{new}}(R)$."
 Then the following relation holds during adiabatic contraction: The “new DAL density profile can be simply calculated from the above equation., Then the following relation holds during adiabatic contraction: The “new” DM density profile can be simply calculated from the above equation.
 Note that. iu our case. the gas distribution also changes because of the eas accretion onto the central primordial protostar.," Note that, in our case, the gas distribution also changes because of the gas accretion onto the central primordial protostar."
 We model the gas mass accretion rate in a siniple parameterized form as a function of the stellar mass., We model the gas mass accretion rate in a simple parameterized form as a function of the stellar mass.
 We use the accretion rate calculated by cosinological simulations of Gaootal.(2007)., We use the accretion rate calculated by cosmological simulations of \citet{gao07}.
 They found a large variation of accretion rates., They found a large variation of accretion rates.
 Tn particular. the accretion rates for rotationally supported disks are typically sialler than for the other cases.," In particular, the accretion rates for rotationally supported disks are typically smaller than for the other cases."
 As our fiducial model. we choose the accretion rate of their R5 ruu. which is well described as a power-law Tereatter we call this rate “Crate” (seo Figure 2)).," As our fiducial model, we choose the accretion rate of their R5 run, which is well described as a power-law Hereafter we call this rate “G-rate” (see Figure \ref{f2}) )."
 The rate is for a cosmological halo forming fron a very ligh-opeak. aud is ποτ larger than that adopted iu a previous work (Spolvaretal. 2009).," The rate is for a cosmological halo forming from a very $\sigma$peak, and is slightly larger than that adopted in a previous work \citep{spolyar09}."
". We also run models with three different accretion rates 1.0.0.5.0,2 «Cirate."," We also run models with three different accretion rates $1.0,\ 0.5,\ 0.2 \times $ G-rate."
 The intermediate value. 0.5 \Cerate. is close to that used in Spolvarctal. (2009)...," The intermediate value, $0.5 \times $ G-rate, is close to that used in \citet{spolyar09}. ."
 We use this model to compare with their result., We use this model to compare with their result.
 The energy generation rate of DM annihilation Is given by, The energy generation rate of DM annihilation is given by
Mapping the matter distribution in the outer reaches of the Galaxy. which is expected to be dark-matter dominated. is currently one of the central tasks in| astrophysics.,"Mapping the matter distribution in the outer reaches of the Galaxy, which is expected to be dark-matter dominated, is currently one of the central tasks in astrophysics."
 Recent surveys of the outer Galaxy have revealed numerous enhancements in the coensitv of stars that have been securely identified as tidal streamers from Galactic satellites 2006)., Recent surveys of the outer Galaxy have revealed numerous enhancements in the density of stars that have been securely identified as tidal streamers from Galactic satellites .
. Such structures cllectively delineae the orbit in the Galactic force-Deld of the parent body 2003)., Such structures effectively delineate the orbit in the Galactic force-field of the parent body .
. Ixnowledge of the phase- coordinates along an individual orbit provides strong constraints on the force-ficld that confines. the orbit. and thus on the matter distribution that gives rise to the force field.," Knowledge of the phase-space coordinates along an individual orbit provides strong constraints on the force-field that confines the orbit, and thus on the matter distribution that gives rise to the force field."
 Consequently. in recent vears considerable elfort has been devoted to the problem of determining the orbit of a satellite from. observations of its tidal stream2007).," Consequently, in recent years considerable effort has been devoted to the problem of determining the orbit of a satellite from observations of its tidal stream."
. Since tidal streams are generally discovered as enhancements in the density of stars on the sky. the phase-space coordinates of the satellite orbit that are Casiest [o determine are its Galactic coordinates /().b(u)]. where η is an arbitrary parameter that increases along the orbit.," Since tidal streams are generally discovered as enhancements in the density of stars on the sky, the phase-space coordinates of the satellite orbit that are easiest to determine are its Galactic coordinates $[l(u),b(u)]$, where $u$ is an arbitrary parameter that increases along the orbit."
 With a moderate observational follow-up effort. it is always possible to augment these data with linc-of-sight. velocities ," With a moderate observational follow-up effort, it is always possible to augment these data with line-of-sight velocities $\vlos(u)$ ."
Phe other three coordinates (heliocentric distance 5 and ο).proper motion components) are much harder to obtain. and are generally. either. unknown or measured with very low accuracy.," The other three coordinates (heliocentric distance $s$ and proper motion components) are much harder to obtain, and are generally either unknown or measured with very low accuracy."
 Given the incomplete nature of the data. the standard approach to orbit fitting is to adopt a gravitational potential. and then to seek an orbit in this potential that is consistent with the data2007).," Given the incomplete nature of the data, the standard approach to orbit fitting is to adopt a gravitational potential, and then to seek an orbit in this potential that is consistent with the data."
.. The fitting procedure is generally trial-anc-error. and the final fit is often imperfect2006).," The fitting procedure is generally trial-and-error, and the final fit is often imperfect."
. Lore we show that given the three coordinates (7.5.64) along a section of an orbit in a gravitational potential bor). one can uniquely determine what the remaining three phase-space coordinates must be if the data are to be part of an orbit in a trial potential í(r).," Here we show that given the three coordinates $(l,b,\vlos)$ along a section of an orbit in a gravitational potential $\Phi_0(\b
r)$, one can uniquely determine what the remaining three phase-space coordinates must be if the data are to be part of an orbit in a trial potential $\Phi_{\rm t}(\b r)$."
 Lob= Po. the recovered. phase-space coordinates are. consistent with conservation of energy. while when the trial and true potentials cilfer. energy conservation appears to be violated.," If $\Phi_{\rm t}=\Phi_0$ , the recovered phase-space coordinates are consistent with conservation of energy, while when the trial and true potentials differ, energy conservation appears to be violated."
 Therefore this procedure. can be used to hunt. for the Galaxys gravitational potential. ancl vields. predictions for distances ancl proper motions along a tidal stream that can be tested observationally.," Therefore this procedure can be used to hunt for the Galaxy's gravitational potential, and yields predictions for distances and proper motions along a tidal stream that can be tested observationally."
 We work in the inertial coordinate system in which the Galactic centre is a rest., We work in the inertial coordinate system in which the Galactic centre is at rest.
 Consequently. line-of-sight velocities in this frame will diller from measured heliocentric velocities bv the projection of the Sun's velocity (wheh we assume known) onto the ine of sight.," Consequently, line-of-sight velocities in this frame will differ from measured heliocentric velocities by the projection of the Sun's velocity (whch we assume known) onto the line of sight."
 Let s be the position vector of the satellite with respect to an observer at theposition of the Sun. and let Fy(8) be the trial gravitational," Let $\b s$ be the position vector of the satellite with respect to an observer at theposition of the Sun, and let $\b F_{\rm t}(\b s)$ be the trial gravitational"
been matched to four standard stars (Landolt 1992) observed under photometric conditions in (he D-band.,been matched to four standard stars (Landolt 1992) observed under photometric conditions in the B-band.
 Then. all the ~100 stars in our catalog in common with the D-band catalog published by Ferraro et al. (," Then, all the $\sim 100$ stars in our catalog in common with the B-band catalog published by Ferraro et al. ("
2003) have been used to derive the photometric zero-point.,2003) have been used to derive the photometric zero-point.
 The two resulting calibrations are fully consistent within a few hundredths of magnitude., The two resulting calibrations are fully consistent within a few hundredths of magnitude.
 A periodicity search was carried out on the photometric dataset using GRATIS (GhRaphyeal Analyzer of TIme Series). a software package developed at the Bologna Astronomical Observatory (see previous applications in Ferraro et al.," A periodicity search was carried out on the photometric data set using GRATIS (GRaphycal Analyzer of TIme Series), a software package developed at the Bologna Astronomical Observatory (see previous applications in Ferraro et al."
 2001)., 2001).
 Since the period (2?=0.839+0.002 dav) obtained from the variability curve turned. out to be fully consistent with that obtained from the radio time series of PSR J1911—5958A. a phased light eurve has been produced (Figure 3)) assuming the same orbital parameters used in 32.," Since the period $P=0.839\pm
0.002$ day) obtained from the variability curve turned out to be fully consistent with that obtained from the radio time series of PSR $-$ 5958A, a phased light curve has been produced (Figure \ref{LC}) ) assuming the same orbital parameters used in 2."
 The different svinbols in Figure 3. mark series of D-magnitudes obtained in different observing nights (hence different companions orbits): in parücular. empty and starred svmbols are used for the pointines of 2004. whereas filled svanbols (clustering al about phase 0.6) refer to observations of 2003.," The different symbols in Figure \ref{LC} mark series of B-magnitudes obtained in different observing nights (hence different companion's orbits): in particular, empty and starred symbols are used for the pointings of 2004, whereas filled symbols (clustering at about phase 0.6) refer to observations of 2003."
 The result is really surprising: shows two phases of strong enhancement of the luminosity located close to the equadratures and extending for about 20% of the orbit each., The result is really surprising: shows two phases of strong enhancement of the luminosity located close to the quadratures and extending for about $20\%$ of the orbit each.
 The primary maximuni occurs between phases 0.5 and 0.6 (a more precise positioning is prevented by (he lacking of useful data in that range) wilh a flix variation of 20.3 mag in less than 1 hr: orbital location and rapidity of the brightening are confirmed in (wo clilferent orbits., The primary maximum occurs between phases 0.5 and 0.6 (a more precise positioning is prevented by the lacking of useful data in that range) with a flux variation of $\gapp 0.3$ mag in less than $1$ hr: orbital location and rapidity of the brightening are confirmed in two different orbits.
 A secondary maximumn. corresponding to a brightening of ~0.2 mag appears ad about phase 0.05. presenting a less steep raise wilh respect to the primary peak (in (his case onlv the decay from the maximum is observed in (wo different orbits).," A secondary maximum, corresponding to a brightening of $\sim 0.2$ mag appears at about phase 0.05, presenting a less steep raise with respect to the primary peak (in this case only the decay from the maximum is observed in two different orbits)."
 Outside the peaks. the source displays an almost steady luminosity al an average D=22.1120.02. In particular the D-band luminosity at orbital phase ~0.6 does not show anv significant [Iuctuation between the 2003 and the 2004 data (the poinüngs of 2003 unfortunately did not cover other orbital phases).," Outside the peaks, the source displays an almost steady luminosity at an average $B=22.11\pm
0.02.$ In particular the B-band luminosity at orbital phase $\sim 0.6$ does not show any significant fluctuation between the 2003 and the 2004 data (the pointings of 2003 unfortunately did not cover other orbital phases)."
 These features are unusual and intriguing., These features are unusual and intriguing.
 The modulation of the optical light curve of ihe companion to a MSP is most often driven by the heating of one emisphere of the star (whose rotation is svncronized with the orbital period) due to the radiation coming from the pulsar: see for example the cases of PSR D1957—20 (Callanan. van Paradijs. Reneelink 1995) and PSR J2051-082T (Stappers οἱ al.," The modulation of the optical light curve of the companion to a MSP is most often driven by the heating of one emisphere of the star (whose rotation is syncronized with the orbital period) due to the radiation coming from the pulsar: see for example the cases of PSR B1957+20 (Callanan, van Paradijs, Rengelink 1995) and PSR J2051-0827 (Stappers et al."
 2001) in the Galactic field and 47 Tuc U and 47 Tue W in the GC! 47 Tucanae (Edmonds et al., 2001) in the Galactic field and 47 Tuc U and 47 Tuc W in the GC 47 Tucanae (Edmonds et al.
 2001. 2002).," 2001, 2002)."
 For the square of the ratio (£4~ 100) between the orbital separation (~4.5—5I.. ) and the radius of (he companion (inferred from the off-peaks huninosity ancl (he effective temperature. Ferraro et al.," For the square of the ratio $\xi_1\sim 100$ ) between the orbital separation $\sim 4.5-5 {\rm
R_\odot}$ ) and the radius of the companion (inferred from the off-peaks luminosity and the effective temperature, Ferraro et al."
 2003a) is much larger than (he ratio (£o~ 25) between (he rotational power of the, 2003a) is much larger than the ratio $\xi_2\sim 25$ ) between the rotational power of the
central velocity dispersion is not likely to be affected by the stripping.,central velocity dispersion is not likely to be affected by the stripping.
 'There is observational evidence of overmassive MBHs for a given M. in Virgo., There is observational evidence of overmassive MBHs for a given $M_*$ in Virgo.
" Kormendyetal.(1997) used ground-based spectroscopic observations of NGC 4486B, the satellite galaxy to NGC 4486 (M87), along with isotropic dynamical models to find a central dark object of mass M=6*3x10*Μο, though three-integral, axisymmetric models cannot rule out absence of a MBH."," \citet{Kormendyetal1997} used ground-based spectroscopic observations of NGC 4486B, the satellite galaxy to NGC 4486 (M87), along with isotropic dynamical models to find a central dark object of mass $M=6^{+3}_{-2}\times10^8\msun$, though three-integral, axisymmetric models cannot rule out absence of a MBH."
" Magorrianetal.(1998) later modeled NGC 4486B with two-integral, axisymmetric dynamical models to find a mass of M—9.2*0059x10° Mo."," \citet{Magorrian1998} later modeled NGC 4486B with two-integral, axisymmetric dynamical models to find a mass of $M=9.2^{+0.055}_{-0.033}\times10^9\msun$ ."
" The galaxy contains a double nucleus, which may pose problems for isotropic and axisymmetric models, but the presence of a double nucleus, itself, is explained by an eccentric disk of stars, which requires a MBH as in M31 (Tremaine1995) So while the mass estimate may be uncertain, there is strong evidence for a MBH in NGC 4486B. Even if the mass estimate is high by a factor of a few, with a stellar mass of ~6x10?Mc (Kormendyetal.1997) the MBH is more massive than those in galaxies with comparable bulge mass (see,e.g.,Magorrianetal. 1998)."," The galaxy contains a double nucleus, which may pose problems for isotropic and axisymmetric models, but the presence of a double nucleus, itself, is explained by an eccentric disk of stars, which requires a MBH as in M31 \citep{Tremaine1995} So while the mass estimate may be uncertain, there is strong evidence for a MBH in NGC 4486B. Even if the mass estimate is high by a factor of a few, with a stellar mass of $\sim6\times10^9\msun$ \citep{Kormendyetal1997} the MBH is more massive than those in galaxies with comparable bulge mass \citep[see, e.g.,][]{Magorrian1998}."
" NGC 4486B is almost certainly tidally stripped, though this could be primarily a result of much stronger interactions with M87 (Evstigneevaetal.2007) rather than milder stripping from the cluster potential."," NGC 4486B is almost certainly tidally stripped, though this could be primarily a result of much stronger interactions with M87 \citep{Evstigneevaetal2007} rather than milder stripping from the cluster potential."
" Another potential example in Virgo is the SO galaxy NGC 4342 with a measured black hole mass of M=3.0*1x10°Mc and bulge mass of M=1.2x101?Mc (Cretton&5vandenBosch 1999),, making it another extreme high outlier by a factor of ~ 30(Haring&Rix2004)."," Another potential example in Virgo is the S0 galaxy NGC 4342 with a measured black hole mass of $M=3.0^{+1.7}_{-1.0}\times10^8\msun$ and bulge mass of $M=1.2\times10^{10}\msun$ \citep{Cretton1999}, making it another extreme high outlier by a factor of $\sim 30$ \citep{Haring2004}."
". We note that the population of “undermassive” MBHs, signature of the gravitational recoil, described, e.g. in Volonteri(2007);etal.(2007) is basically absent here, due to the more simplistic modeling we performed."," We note that the population of “undermassive"" MBHs, signature of the gravitational recoil, described, e.g. in \cite{Volonteri2007, Volonterietal2007} is basically absent here, due to the more simplistic modeling we performed."
" We have in fact assumed that whenever two galaxies with MBHs merge, with a mass ratio larger than 1:10, the MBHs are placed directly on the Mgy—ox."," We have in fact assumed that whenever two galaxies with MBHs merge, with a mass ratio larger than $1:10$, the MBHs are placed directly on the $M_{BH}-\sigma_*$."
 This consequently puts MBHs preferentially on the Maz—Moai correlation., This consequently puts MBHs preferentially on the $M_{BH}-M_{gal}$ correlation.
" The cases where the MBH is below the mass predicted by the Meu—Mga are those in which the galaxy has not had any major merger recently, so the MBH mass has not grown, while the galaxy mass has (viaminormergers,cfr.thedis-cussioninVolonterietal."," The cases where the MBH is below the mass predicted by the $M_{BH}-M_{gal}$ are those in which the galaxy has not had any major merger recently, so the MBH mass has not grown, while the galaxy mass has \citep[via minor mergers, cfr. the discussion in][]{VHM}."
"2003).. We explored the influence of formation epoch of MBHs, bias of their hosts, and MBHs dynamical evolution on the occupation distribution of MBHs in galaxy clusters."," We explored the influence of formation epoch of MBHs, bias of their hosts, and MBHs dynamical evolution on the occupation distribution of MBHs in galaxy clusters."
 The possible decrease of the occupation fraction at low galaxy mass proposed by Wehner&Harris(2006) and Ferrareseetal.(2006) is not a surprising result and follows naturally from the evolution of the MBH population of galaxies in clusters., The possible decrease of the occupation fraction at low galaxy mass proposed by \cite{Wehner2006} and \cite{Ferrareseetal2006} is not a surprising result and follows naturally from the evolution of the MBH population of galaxies in clusters.
 We emphasize that our models do not in any way imply that MBHs and nuclear clusters are mutually exclusive., We emphasize that our models do not in any way imply that MBHs and nuclear clusters are mutually exclusive.
 We however predict that the occupation fraction decreases with galaxy mass., We however predict that the occupation fraction decreases with galaxy mass.
" If, as suggested by Wehner Harris (2006), lacking a MBH is a necessary condition for nuclear cluster formation, radio or hard X-ray observations will inform us of the complementary or mutually exclusive essence of MBHs and nuclear clusters."," If, as suggested by Wehner Harris (2006), lacking a MBH is a necessary condition for nuclear cluster formation, radio or hard X-ray observations will inform us of the complementary or mutually exclusive essence of MBHs and nuclear clusters."
" Galloetal.(2007) recently observed 32 galaxies in Virgo with the Chandra X-ray Observatory, and found, in agreement with Decarlietal.(2007) that nuclear X-ray activity increases with the mass of the host galaxy."," \cite{Gallo2007} recently observed 32 galaxies in Virgo with the Chandra X-ray Observatory, and found, in agreement with \cite{Decarli2007} that nuclear X-ray activity increases with the mass of the host galaxy."
" Intriguingly, at least in one case, VCC1178, a nuclear X-ray source is detected jointly with a central star cluster."," Intriguingly, at least in one case, VCC1178, a nuclear X-ray source is detected jointly with a central star cluster."
 Seth also report that a small AGN might be hosted within the core of the nuclear star cluster in NGC 4206., \cite{Seth2006} also report that a small AGN might be hosted within the core of the nuclear star cluster in NGC 4206.
seven orders of magnitude smaller than the measured value. thus there can be no massive third body orbiting the system.,"seven orders of magnitude smaller than the measured value, thus there can be no massive third body orbiting the system."
" The third term. 73,"" is the contribution from the mass loss of the binary."," The third term, $\dot{P_{\rm b}}^{\dot{m}}$, is the contribution from the mass loss of the binary."
 If we consider. a circular orbit. no mass loss from the pulsar ερ= 0) and a rate of mass loss from the companion meoc7 O02). we obtain: and therefore: where Af is the total mass of the system.," If we consider a circular orbit, no mass loss from the pulsar $\dot{m_{\rm p}} = 0$ ) and a rate of mass loss from the companion $\dot{m_{\rm c}} > 0$ \citep{jea24}, we obtain: and therefore: where $M$ is the total mass of the system."
 This number is six orders of magnitude larger than expected (ascalculatedby2). and hard to reconcile with the low electron densities measured in the eclipse region (?)..," This number is six orders of magnitude larger than expected \citep[as calculated
 by][]{sbl+96} and hard to reconcile with the low electron densities measured in the eclipse region \citep{sbl+96}."
 In addition. for the second of the epochs we would need mass injection to the companion in order to explain the orbital decay — an infeasible scenario for this system.," In addition, for the second of the epochs we would need mass injection to the companion in order to explain the orbital decay – an infeasible scenario for this system."
 Tidal forces in tight synchronous binaries may also be responsible for interactions which would change the orbital period., Tidal forces in tight synchronous binaries may also be responsible for interactions which would change the orbital period.
 This could be the case if. for example. a companion star suddenly contracts or expands and thereby changes its spin angular momentum.," This could be the case if, for example, a companion star suddenly contracts or expands and thereby changes its spin angular momentum."
 Tidal locking of the orbit would then result in exchange of spin and orbital angular momentum. e.g. ?..," Tidal locking of the orbit would then result in exchange of spin and orbital angular momentum, e.g. \citet{ts01}."
 However. in wwe do not see reasons for any sudden major radial changes in the structure of the companion star — especially not changes that would not result in detection of X-ray bursts (A. Levine and D. Altamirano. private communication).," However, in we do not see reasons for any sudden major radial changes in the structure of the companion star – especially not changes that would not result in detection of -ray bursts (A. Levine and D. Altamirano, private communication)."
 Hence. we neglect the term hs.," Hence, we neglect the term $\dot{P_{\rm b}}^{\rm T}$."
 Since all the above contributions are much smaller than the observed variation. of the orbital period. we conclude that they must originate from the last term of Equation (359. which represents variations of the gravitational quadrupole moment of the companion star.," Since all the above contributions are much smaller than the observed variation of the orbital period, we conclude that they must originate from the last term of Equation \ref{eq:period}) ), which represents variations of the gravitational quadrupole moment of the companion star."
 The gravitational quadrupole coupling (GQC) mechanism (22?) has been applied successfully to the eclipsing binary system PSR | 20 (?).. explaining the orbital period variations seen by ?..," The gravitational quadrupole coupling (GQC) mechanism \citep{app92,
 as94} has been applied successfully to the eclipsing binary system PSR $+$ 20 \citep{as94}, explaining the orbital period variations seen by \cite{aft94}."
 In addition. it was proposed by ? as the main mechanism for producing the orbital period variations of0827.," In addition, it was proposed by \cite{dlk+01} as the main mechanism for producing the orbital period variations of."
. However. as we will present below. the latter publication considered only a small part of these variations. which led to an underestimation in their calculations.," However, as we will present below, the latter publication considered only a small part of these variations, which led to an underestimation in their calculations."
 In the GQC model (2).. magnetic activity is driven by energy flows in convective layers of the irradiated companion.," In the GQC model \citep{as94}, magnetic activity is driven by energy flows in convective layers of the irradiated companion."
 This. in combination with wind mass loss. results in a torque on its spin. which holds it slightly out of synchronous rotation. causing tidal dissipation of energy and heating of the companion.," This, in combination with wind mass loss, results in a torque on its spin, which holds it slightly out of synchronous rotation, causing tidal dissipation of energy and heating of the companion."
 The resultant time-dependent gravitational quadrupole moment (e.g. variations of the oblateness) causes modulation of the orbital period on a short. in principle dynamical. time scale.," The resultant time-dependent gravitational quadrupole moment (e.g. variations of the oblateness) causes modulation of the orbital period on a short, in principle dynamical, time scale."
 An increase in the quadrupole moment causes the two stars to move closer together and a decrease in the quadrupole moment results in a widening of the orbit — in Applegate's model total orbital angular momentum is assumed to remain constant and the neutron star is treated as a point mass., An increase in the quadrupole moment causes the two stars to move closer together and a decrease in the quadrupole moment results in a widening of the orbit – in Applegate's model total orbital angular momentum is assumed to remain constant and the neutron star is treated as a point mass.
 The details of the hydrodynamic dynamo and its activity cycle remain unspecitied for our purposes (also given the unknown nature of the companion star — see Section ??)) and it is simply assumed that the variable quadrupole moment. AQ. is caused by cyclicspin-up and spin-down of the outer layers of the companion. which leads to orbital period changes equal to (23:," The details of the hydrodynamic dynamo and its activity cycle remain unspecified for our purposes (also given the unknown nature of the companion star – see Section \ref{subsec:companion}) ) and it is simply assumed that the variable quadrupole moment, $\Delta Q$, is caused by cyclicspin-up and spin-down of the outer layers of the companion, which leads to orbital period changes equal to \citep{as94}: :"
N-ray binaries are among the brightest XN-rav sources in the skv.,X-ray binaries are among the brightest X-ray sources in the sky.
 Au ταν binary consists of a compact object (neutron star or black hole) aud a normal colupanion star. orbiting around each other.," An X-ray binary consists of a compact object (neutron star or black hole) and a normal companion star, orbiting around each other."
 At certain stage of the binary, At certain stage of the binary
of ω(θ) due to smaller number of particles in the bin (see below).,of $w(\theta)$ due to smaller number of particles in the bin (see below).
" We also consider three narrower redshift bins, with photo-z ranges [0.45— 0.5], [0.5—0.55] and [0.55—0.6]."," We also consider three narrower redshift bins, with photo-z ranges $\left[0.45-0.5\right]$ , $\left[0.5-0.55\right]$ and $\left[0.55-0.6\right]$."
 The redshift distribution for these cases are shown in Fig. 8.., The redshift distribution for these cases are shown in Fig. \ref{fig:dndz_narrowbins}.
 They are clearly highly correlated and not narrower than the wider top-hat bin discussed above., They are clearly highly correlated and not narrower than the wider top-hat bin discussed above.
" The number of LRGs in these 3 bins are 451753, 317882 and 346988 respectively."," The number of LRGs in these 3 bins are $451753$, $317882$ and $346988$ respectively."
" In addition to an increase of shot-noise and overlap, one expects the estimation of N(z) to be not so robust for a bin narrower than the intrinsic photo-z (a possible evidence for this is discussed in Sec. 4.3))."," In addition to an increase of shot-noise and overlap, one expects the estimation of $N(z)$ to be not so robust for a bin narrower than the intrinsic photo-z (a possible evidence for this is discussed in Sec. \ref{sec:systematics}) )."
" These are the reasons why we decided to concentrate in a single redshift bin, and repeat our analysis in these 3 bins as consistency checks."," These are the reasons why we decided to concentrate in a single redshift bin, and repeat our analysis in these 3 bins as consistency checks."
 Redshifts bins lower than z—0.45 and higher than z=0.6 do not have enough number of LRGs to obtain precise measurements ofthe angular correlation (we find 52845 LRGs in the photometric range [0.4—0.45] and 30412 in [0.6— 0.65])., Redshifts bins lower than $z=0.45$ and higher than $z=0.6$ do not have enough number of LRGs to obtain precise measurements ofthe angular correlation (we find $52845$ LRGs in the photometric range $\left[0.4-0.45\right]$ and $30412$ in $\left[0.6-0.65\right]$ ).
 At those extreme bins our measurements also become too sensitive to ours cuts (e.g. in galactic latitude and/or photo-z quality)., At those extreme bins our measurements also become too sensitive to ours cuts (e.g. in galactic latitude and/or photo-z quality).
" This might be due to various reasons, for example, large magnitude errors that correlate with galactic latitude and lead to large photo-z errors."," This might be due to various reasons, for example, large magnitude errors that correlate with galactic latitude and lead to large photo-z errors."
 But perhaps the most worrisome issue happens at z0.6 where we find a large extra-power over a broad range of large angular scales (already for 0> 1°)., But perhaps the most worrisome issue happens at $z>0.6$ where we find a large extra-power over a broad range of large angular scales (already for $\theta > 1^\circ$ ).
 Excess of on large scales has already been found and discussed in different LRG selections based on SDSS DR5 in ?) and SDSS DR7 in ??) (see also 7) and ?))).," Excess of on large scales has already been found and discussed in different LRG selections based on SDSS DR5 in \cite{2009arXiv0912.0511S} and SDSS DR7 in \cite{2011MNRAS.412.1669T,2010arXiv1012.2272T} (see also \cite{2007MNRAS.374.1527B} and \cite{2007MNRAS.378..852P}) )."
" Nonetheless, we only encounter this problem in the redshift bin [0.6—0.65]."," Nonetheless, we only encounter this problem in the redshift bin $\left[0.6-0.65\right]$."
 We defer a discussion of possible reasons for Appendix A and proceed to discard these bins from our study hereafter., We defer a discussion of possible reasons for Appendix \ref{sec:appendix} and proceed to discard these bins from our study hereafter.
 The angular correlation function measurements were performed starting from angular maps as described in Sec., The angular correlation function measurements were performed starting from angular maps as described in Sec.
" 2.2 (Nsiae=512, pixel size of ~0.01 deg?) and using a standard pixel estimator (?),, ?))) where δὲν=Nia— is the fluctuation in number of galaxies in the i-th /Noatpixel 1with respect to the mean in the angular map, pixels 7 and 7 are separated by an angle 0 and Npairs(@) is the corresponding number of pixel pairs."," \ref{sec:angularmask} $N_{side} = 512$, pixel size of $\sim 0.01$ ${\rm deg}^2$ ) and using a standard pixel estimator \cite{2002MNRAS.333..443B}, , \cite{2004ApJS..151....1E}) ) where $\delta_G^i=N_{gal}^i/\hat{N}_{gal} -1$ is the fluctuation in number of galaxies in the $th$ pixel with respect to the mean in the angular map, pixels $i$ and $j$ are separated by an angle $\theta$ and $N_{pairs}(\theta)$ is the corresponding number of pixel pairs."
 Pixels were weighted by 0 or 1 according to the angular mask discussed in Sec. 2.2.., Pixels were weighted by 0 or 1 according to the angular mask discussed in Sec. \ref{sec:angularmask}.
" We have also implemented a standard Landy Szalay (7) estimator, and the resulting measured correlations were within 1% of that from Eq. (5))."," We have also implemented a standard Landy Szalay \citep{1993ApJ...412...64L} estimator, and the resulting measured correlations were within $1\%$ of that from Eq. \ref{eq:pixelestimator}) )."
 The measured correlations in the three bins of width 0.05 as well as in the bin 0.1 are shown in Fig. 9.., The measured correlations in the three bins of width $0.05$ as well as in the bin $0.1$ are shown in Fig. \ref{fig:plg}.
 Error bars displayed in this figure were obtained using jack-knife resampling., Error bars displayed in this figure were obtained using jack-knife resampling.
 In what follows we discuss our different error estimates., In what follows we discuss our different error estimates.
 We estimate the error and covariance between angular bins in the measured correlation function using two independent methods., We estimate the error and covariance between angular bins in the measured correlation function using two independent methods.
" One method was implementing the standard jack-knife resampling technique, that to date has been widely used in clustering analysis with correlation functions (for a summary see ?) and ?) and references therein)."," One method was implementing the standard jack-knife resampling technique, that to date has been widely used in clustering analysis with correlation functions (for a summary see \cite{2007MNRAS.381.1347C} and \cite{2009MNRAS.396...19N} and references therein)."
 To this end we divided the angular mask in 81 jack-knife (JK) zones of similar area (~90deg? each) and shape.," To this end we divided the angular mask in 81 jack-knife (JK) zones of similar area $\sim 90 \,
{\rm deg}^2$ each) and shape."
 Thesezones are shown in grey levels in Fig. 5.., Thesezones are shown in grey levels in Fig. \ref{fig:mask}. .
 One then takes different realizations to be all the sampled areaexcept from one JK zone at a time., One then takes different realizations to be all the sampled areaexcept from one JK zone at a time.
 The covariance is then computed from the dispersion among the measurements of w(0) in the Nyx=81 resulting, The covariance is then computed from the dispersion among the measurements of $w(\theta)$ in the $N_{JK}=81$ resulting
Point spread. functions can be determined: observationallv by studying the scattering of stellar light.,Point spread functions can be determined observationally by studying the scattering of stellar light.
 Numerous papers have been devoted to this. problem. (e.g. Molfat |1969: ine 1971: Bendinelli et al., Numerous papers have been devoted to this problem (e.g. Moffat 1969; King 1971; Bendinelli et al.
 1990)., 1990).
 Among the analytical approximations. the Molfat. function (see Eq. ," Among the analytical approximations, the Moffat function (see Eq. ["
1]) has been widely used. to model the PSE (c.g. Dendinelli. Zavatti DParmegegiani 19882.b: Young et al.,"1]) has been widely used to model the PSF (e.g. Bendinelli, Zavatti Parmeggiani 1988a,b; Young et al."
 1998): for instance. the IRAP data reduction package Clody 1986) adopts the Molfat function as à standard PSE.," 1998); for instance, the IRAF data reduction package (Tody 1986) adopts the Moffat function as a standard PSF."
 In Fig., In Fig.
 1 we plot both the Gaussian function anc Mollat. function having a range of 1., 1 we plot both the Gaussian function and Moffat function having a range of $\beta$.
 Note that as 3 increases the Alollat [function tends to approximate the core of the Gaussian. profile., Note that as $\beta$ increases the Moffat function tends to approximate the core of the Gaussian profile.
 In fact. a Alollat function contains the Gaussian PSE as a limiting case (see Appendix A).," In fact, a Moffat function contains the Gaussian PSF as a limiting case (see Appendix A)."
 Moreover. the Molfat. PSE has two clear advantages over the Gaussian PSE: Very accurate convolutions between the PSE and the model profiles of the galaxies are required in order to obtain reliable results.," Moreover, the Moffat PSF has two clear advantages over the Gaussian PSF: Very accurate convolutions between the PSF and the model profiles of the galaxies are required in order to obtain reliable results."
 Current reduction packages use Fast Fourier Fransforms to evaluate the convolutions., Current reduction packages use Fast Fourier Transforms to evaluate the convolutions.
 This is in [act inappropriate where there are strong changes in the intensity eracients of the galaxy profiles., This is in fact inappropriate where there are strong changes in the intensity gradients of the galaxy profiles.
 Phe inner parts of galaxy profiles are steep. and this demands a very accurate measurement of the high frequencies in the Fourier domain.," The inner parts of galaxy profiles are steep, and this demands a very accurate measurement of the high frequencies in the Fourier domain."
 απο PSEs (such as those of the 451) maenily this xoblem because they also present a steeper profile., Narrow PSFs (such as those of the ) magnify this problem because they also present a steeper profile.
 Working in theread domain does not exempt. us from trouble either: in fact. one can encounter several numerical problems when »erforming accurate convolutions when using a Gaussian o model narrow PSEs.," Working in the domain does not exempt us from trouble either; in fact, one can encounter several numerical problems when performing accurate convolutions when using a Gaussian to model narrow PSFs."
 Current. computers can manage numbers of the order of —« PEE . ⋅ ↴−⊔⋡∐, Current computers can manage numbers of the order of $\sim e^{200}$.
↥∢⊾⊳∖⋖⋅↓⊔⊔∠⇂⊳∖∪⇂⊔⊔⊔↓∣⋊⊾↓⋅⊳∖ can be easily obtained when working with Gaussians which nave m< lin units of pixels (see the exponential expressions at play when performing a Gaussian convolution in Eq. , These kinds of numbers can be easily obtained when working with Gaussians which have $\sigma<1$ in units of pixels (see the exponential expressions at play when performing a Gaussian convolution in Eq. [
4] in POL).,4] in T01).
 The use of Molfat functions avoids this problem due o the use of polynomials instead of exponential expressions (see Eq. , The use of Moffat functions avoids this problem due to the use of polynomials instead of exponential expressions (see Eq. [
3]).,3]).
" In this sense. Molfat functions are numerically »etter. behavecl than Gaussians when dealing with narrow ""SES."," In this sense, Moffat functions are numerically better behaved than Gaussians when dealing with narrow PSFs."
 We will use a circular. Molfat. function to model the point spread. function: with the full width al half maximum. PWHAI=PaVote?]. where PSEC(GWILIN2) = (1/2)PSE(0) and the total flux is normalized to 1.," We will use a circular Moffat function to model the point spread function: with the full width at half maximum, $2\alpha\sqrt{2^{1/\beta}-1}$, where PSF(FWHM/2) = (1/2)PSF(0) and the total flux is normalized to 1."
 Consider a case where. in the absence of secing. the surfaces brightness distribution. /(r). of a galaxy is. ellipticallv symmetric.," Consider a case where, in the absence of seeing, the surfaces brightness distribution, $I({\bf {r}})$, of a galaxy is elliptically symmetric."
 This means that the isophotes of the object all have the same constant ellipticity € (€=θα. where a and b are respectively the semi-major and semi-minor axes of the isophotes).," This means that the isophotes of the object all have the same constant ellipticity $\epsilon$ $\epsilon=1-b/a$, where $a$ and $b$ are respectively the semi-major and semi-minor axes of the isophotes)."
 As shown in ‘VOL elliptical coordinates (€.4) are the most appropriate for this type of problem.," As shown in T01 elliptical coordinates $\xi,\theta)$ are the most appropriate for this type of problem."
 In this coordinate system. thesurface brightness distribution. Z(r). of an elliptical. source. depends. only on ὃν J(r)=L(€).," In this coordinate system, thesurface brightness distribution, $I({\bf {r}})$, of an elliptical source depends only on $\xi$: $I({\bf {r}})=I(\xi)$."
 The convolution equation that represents the ellect of seeing on the surface brightness distribution is given by: £.80) is the Mollat PSE given by: The subseript ce” shall be used. from. here on to refer seeingconvolved. quantities.," The convolution equation that represents the effect of seeing on the surface brightness distribution is given by: where $(\xi^{'}, \theta^{'}, \xi, \theta)$ is the Moffat PSF given by: The subscript “c” shall be used from here on to refer seeing–convolved quantities."
 Along the major axis of the object. 6-0. the angular integral can be solved: analytically (c =O): where and C(/) and Bs.uw) are the Gegenbauer polynomials (Cradshteyn livzhik 1980. p. 1029) and beta functionsCXbramowitz Steeun 1964. p. 258) respectively.," Along the major axis of the object, $\theta$ =0, the angular integral can be solved analytically $\epsilon>$ 0): where and $C_n^\lambda(t)$ and $B(z,w)$ are the Gegenbauer polynomials (Gradshteyn Ryzhik 1980, p. 1029) and beta functions(Abramowitz Stegun 1964, p. 258) respectively."
" A simpler expression is obtained. for the convolution in the circularly svmametric Case (e =O): where and P,Cr) is the Leeencdre function. of first. class (Abramowitz Stegun 1964. p. 332)."," A simpler expression is obtained for the convolution in the circularly symmetric case $\epsilon=0$ ): where and $P_n(x)$ is the Legendre function of first class (Abramowitz Stegun 1964, p. 332)."
 For any intensity distribution with elliptical symmetry. Z(£). the seeing convolved central intensity. £.(€= 0). is such that," For any intensity distribution with elliptical symmetry, $I(\xi)$ , the seeing convolved central intensity, $I_{\rm c}(\xi=0)$ , is such that"
gas. these lines are clearly the dominant process even near the ionization threshold.,"gas, these lines are clearly the dominant process even near the ionization threshold."
 Interestingly. the right panel of Figure 3. shows that the ratio fica/foxcite IS nearly independent of both energy and .e;: it depends almost entirely on the atomic physics of HI.," Interestingly, the right panel of Figure \ref{fig:excite-lya} shows that the ratio $f_{\rm Ly\alpha}/f_{\rm excite}$ is nearly independent of both energy and $x_i$: it depends almost entirely on the atomic physics of HI."
 The weak energy dependence near threshold occurs because the different levels feed into in different ways., The weak energy dependence near threshold occurs because the different levels feed into in different ways.
 The (very) weak dependence on .r;. with the fraction increasing slightly with νε. is probably because efficient electron-electron interactions in. highly-ionized gas bring electrons to the threshold energy more rapidly.," The (very) weak dependence on $x_i$, with the fraction increasing slightly with $x_i$, is probably because efficient electron-electron interactions in highly-ionized gas bring electrons to the threshold energy more rapidly."
 The overall fraction of ~SO% can easily be estimated from the oscillator strengths (2).., The overall fraction of $\sim 80\%$ can easily be estimated from the oscillator strengths \citep{pritchard07}.
 The remaining energy. shown in the right panel of Figure 2.. heats the IGM.," The remaining energy, shown in the right panel of Figure \ref{fig:ion-heat}, heats the IGM."
 The curves vary only slowly at large £7. but the behavior at £—100eV is complicated by the ionization and line thresholds.," The curves vary only slowly at large $E$, but the behavior at $E \la 100 \eV$ is complicated by the ionization and line thresholds."
 Note that the features here are caused by the combination of these processes., Note that the features here are caused by the combination of these processes.
considered for the full scope of model selection optimization that we wish to consider. the Savage-Dickey Density Ratio (SDDR) is investigated.,"considered for the full scope of model selection optimization that we wish to consider, the Savage–Dickey Density Ratio (SDDR) is investigated."
 The SDDR is a simplification of the Bayes factor that assumes a less complex model is nested within a more complex model and that the priors are separable., The SDDR is a simplification of the Bayes factor that assumes a less complex model is nested within a more complex model and that the priors are separable.
" For example. ACDAL is nested within the evolving dark energy models parameter space where wyΞ Land i,=0. and furthermore the priors concerned with these two dark energy parameters (20) and those concerned with the nuisance parameters (IV) of the models can be separated. pha.IN)=p(awe)p(IN)."," For example, $\Lambda\rm CDM$ is nested within the evolving dark energy model's parameter space where $w_0=-1$ and $w_a=0$, and furthermore the priors concerned with these two dark energy parameters $\boldsymbol{w}$ ) and those concerned with the nuisance parameters $\boldsymbol{N}$ ) of the models can be separated, $p(\boldsymbol{w},\boldsymbol{N})=p(\boldsymbol{w})p(\boldsymbol{N})$."
 The SDDR is given by equation 8.. where 2” represents the simpler models” nested values. being a special case of the more complex model's parameter vector το.," The SDDR is given by equation \ref{eq:SDDR1}, where $\boldsymbol{w^*}$ represents the simpler models' nested values, being a special case of the more complex model's parameter vector $\boldsymbol{w}$."
 For a derivation of this see Appendix B of Trotta (20072)., For a derivation of this see Appendix B of Trotta (2007a).
 This allows the Bayes factor to be evaluated by considering the marginalised posterior probability of the more complex model and its prior at the parameter values of the nested simpler model., This allows the Bayes factor to be evaluated by considering the marginalised posterior probability of the more complex model and its prior at the parameter values of the nested simpler model.
 This removes the need for the computationally expensive integral as required to calculate the evidence via equation 5.., This removes the need for the computationally expensive integral as required to calculate the evidence via equation \ref{eq:evi}.
 Both assumptions made in deriving equation 8. are true for the dark energy models under consideration and nothing has been assumed about the likelihood. therefore it is exact in this case.," Both assumptions made in deriving equation \ref{eq:SDDR1} are true for the dark energy models under consideration and nothing has been assumed about the likelihood, therefore it is exact in this case."
 However. we now make a further assumption that makes this implementation approximate.," However, we now make a further assumption that makes this implementation approximate."
" To minimise alteration to the original DETF optimization and hence calculation time. our SDDR calculation assumes Gaussianity of the posterior in ay and w,, having marginalized over all other parameters."," To minimise alteration to the original DETF optimization and hence calculation time, our SDDR calculation assumes Gaussianity of the posterior in $w_0$ and $w_a$ having marginalized over all other parameters."
" The Bayes factor can therefore be forecast with only a few simple additions to the DETF optimization. by application of the following: In this equation 7 and ;; ean have values of either O or |: a£"" are the nested values of the simpler model: ej=wo: Auwy and Aw, are the width of the flat prior ranges: and {ιν is the marginalised Fisher matrix."," The Bayes factor can therefore be forecast with only a few simple additions to the DETF optimization, by application of the following: In this equation $\nu$ and $\mu$ can have values of either 0 or 1; $\boldsymbol{w^{*}}$ are the nested values of the simpler model; $w_1=w_a$; $\Delta w_{0}$ and $\Delta w_{1}$ are the width of the flat prior ranges; and $F_{\mu\nu}$ is the marginalised Fisher matrix."
 A numerical approach using finite-differencing was used to determine the Fisher matrix. the details of which are described in Appendix A of PIO.," A numerical approach using finite-differencing was used to determine the Fisher matrix, the details of which are described in Appendix A of P10."
 Recall that values larger than unity (1n2 0) support the simpler model. and values less than unity (1n2« 0) support the more complex model.," Recall that values larger than unity $\ln B > 0$ ) support the simpler model, and values less than unity $\ln B < 0$ ) support the more complex model."
 We see then that the pre-factor of equation 9 acts as an amplitude. measuring the ratio of the area of tj— ts parameter space allowed by the more complex model to the area of the error ellipse: this term therefore penalises the more complex model for unjustified parameter space.," We see then that the pre-factor of equation \ref{eq:SDDR2}
 acts as an amplitude, measuring the ratio of the area of $w_0$ $w_a$ parameter space allowed by the more complex model to the area of the error ellipse; this term therefore penalises the more complex model for unjustified parameter space."
 The exponential part measures the distance between the two models and can lend support for the more complex model by suppressing the amplitude term., The exponential part measures the distance between the two models and can lend support for the more complex model by suppressing the amplitude term.
 This SDDR approach allows investigation of both model selection FoMs., This SDDR approach allows investigation of both model selection FoMs.
" However for the + FoM to be practical for full MCMC optimizations it needs refining: for example. InDu.t,) calculations could be parallellized and MCMC could be used to determine the +."," However for the $^{-1}$ FoM to be practical for full MCMC optimizations it needs refining; for example, $\ln B(w_0,w_a)$ calculations could be parallellized and MCMC could be used to determine the $^{-1}$."
 The prior range mentioned in section ?? is the same as that used in MO. but we acknowledge that the choice of priors is arbitrary to a degree.," The prior range mentioned in section \ref{sec:modselFoM} is the same as that used in M06, but we acknowledge that the choice of priors is arbitrary to a degree."
 Whilst changing the prior range. Aas and Aw. will quantitatively affect lo calculations it will not qualitatively change the FoMs we are considering.," Whilst changing the prior range, $\Delta w_{0}$ and $\Delta w_{1}$, will quantitatively affect $\ln B$ calculations it will not qualitatively change the FoMs we are considering."
 Furthermore. as discussed in MO6. different (sensible) prior choices will not have a serious impact on the interpretation of the resulting Bayes factors.," Furthermore, as discussed in M06, different (sensible) prior choices will not have a serious impact on the interpretation of the resulting Bayes factors."
 Early in the process of adding the new FoM options to the optimization we became aware of a coding error that made the original results in PIO incorrect., Early in the process of adding the new FoM options to the optimization we became aware of a coding error that made the original results in P10 incorrect.
 We have fixed this error and present the updated results in Appendix A. The main differences are a reduction in the DETF FoM by a factor of 3 and that the optimization is qualitatively unchanged by including eurvature as a nuisance parameter., We have fixed this error and present the updated results in Appendix A. The main differences are a reduction in the DETF FoM by a factor of 3 and that the optimization is qualitatively unchanged by including curvature as a nuisance parameter.
 The latter of these results is found to be also true of the model selection FoMs we investigate in the following. therefore we do not explicitly consider curvature in any of our presented findings.," The latter of these results is found to be also true of the model selection FoMs we investigate in the following, therefore we do not explicitly consider curvature in any of our presented findings."
 As mentioned. both the nested InD(.1.0) and SDDR + computations are quite slow.," As mentioned, both the nested $\ln B(-1,0)$ and SDDR $^{-1}$ computations are quite slow."
 To deal with this issue. discrete. mmanual. optimizations are considered.," To deal with this issue, discrete, manual, optimizations are considered."
 Large-seale surveys such as this are designed with the number of fibres tuned to the required source density. therefore repeated observations of the same area of sky are rarely needed.," Large-scale surveys such as this are designed with the number of fibres tuned to the required source density, therefore repeated observations of the same area of sky are rarely needed."
 Furthermore the minimum exposure time is nearly always sufficient to achieve the required S/N on large populations of the the observed galaxies C- 80669) which is why the DETF optimization prefers to maximise the area (Parkinsonetal.2010)., Furthermore the minimum exposure time is nearly always sufficient to achieve the required S/N on large populations of the the observed galaxies $\sim$ ) which is why the DETF optimization prefers to maximise the area \cite{par2010}.
. We therefore chose to set the time and area to maximum and then manually vary the maximum and minimum redshift limits., We therefore chose to set the time and area to maximum and then manually vary the maximum and minimum redshift limits.
 In doing so we have essentially maximised over all other survey parameters. which allows clearer interpretation of the FoM performance.," In doing so we have essentially maximised over all other survey parameters, which allows clearer interpretation of the FoM performance."
 The findings of our nested sampling discrete optimization are, The findings of our nested sampling discrete optimization are
"Figure 6 shows how i, is influenced specifically by the spectral tvpe of the binary in the blend for different transit percentages.",Figure 6 shows how $\eta_\star$ is influenced specifically by the spectral type of the binary in the blend for different transit percentages.
 Here (oo it is evident that later main-sequence spectral ivpes in the binary. produce lower diagnostics., Here too it is evident that later main-sequence spectral types in the binary produce lower diagnostics.
 As this is due to the shorter transit cdurations (from the lower stellar radii). eiant and sub-eiant binaries in blends would produce very. high diagnostics that would be easily separable [rom exoplanets.," As this is due to the shorter transit durations (from the lower stellar radii), giant and sub-giant binaries in blends would produce very high diagnostics that would be easily separable from exoplanets."
 The shaded regions in (his ligure are identical to those in Fig., The shaded regions in this figure are identical to those in Fig.
 5., 5.
 This figure also shows (hat a relatively hieh percentage of blends can be separated [rom exoplanets. especially those orbiüng late spectral-type parent slars.," This figure also shows that a relatively high percentage of blends can be separated from exoplanets, especially those orbiting late spectral-type parent stars."
 Incorporating an estimate of (he primary radius improves (he performance of the diagnostic., Incorporating an estimate of the primary radius improves the performance of the diagnostic.
 Figure 7 is similar to Figure 6. except that stellar raclii are assumed to be known to within (top) and (bottom).," Figure 7 is similar to Figure 6, except that stellar radii are assumed to be known to within (top) and (bottom)."
 For claritv. only the highest (F2/F2 binary) and the lowest (M3/MS3 binary) of the transit percentage contours are shown.," For clarity, only the highest (F2/F2 binary) and the lowest (M3/M3 binary) of the transit percentage contours are shown."
 Information on stellar racii affects the locations of the exoplanet regions so that central Gransits have a diagnostic close to one. within the limits of the errors. which is quite different [rom earlier figures.," Information on stellar radii affects the locations of the exoplanet regions so that central transits have a diagnostic close to one, within the limits of the errors, which is quite different from earlier figures."
 Aloreover. the imprecision in the estimate of stellar radius affects the diagnostics of the blends as well.," Moreover, the imprecision in the estimate of stellar radius affects the diagnostics of the blends as well."
" In (his figure. the information on spectral tvpe show that blends in which ihe ""primarv is a late spectral (ype will be the easiest to separate Irom exoplanels. while (hose involving the earliest spectral types will not gain much from the use of the diagnostic."," In this figure, the information on spectral type show that blends in which the “primary” is a late spectral type will be the easiest to separate from exoplanets, while those involving the earliest spectral types will not gain much from the use of the diagnostic."
 To date. only about of exoplanets discovered with either radial velocity or transits have been around F stars.," To date, only about of exoplanets discovered with either radial velocity or transits have been around F stars."
 This of course could be affected bv the choice of stars in radial velocity searches., This of course could be affected by the choice of stars in radial velocity searches.
 We have devised an exoplanet diagnostice 7 and shown that it can be an effective tool in choosinge transit. candidates worthy of follow-up observation., We have devised an exoplanet diagnostic $\eta$ and shown that it can be an effective tool in choosing transit candidates worthy of follow-up observation.
 Usinge our diagnotic.c» many eclipsing binary stars. especially those involving giants. and blends can be excluded from further consideration.," Using our diagnotic, many eclipsing binary stars, especially those involving giants, and blends can be excluded from further consideration."
" Specifically, we suggest that OGLE-TR-33 is unlikely (ο be planetary. while our analysis indicated (hat OGLE-TR-10 had a high likelihood of begin planetary belore it was confirmed (Bouchyetal.2004)."," Specifically, we suggest that OGLE-TR-33 is unlikely to be planetary, while our analysis indicated that OGLE-TR-10 had a high likelihood of begin planetary before it was confirmed \citep{bouchy}."
. Estimates of stellar radii improve (he performance of the diagnostic. giving it an even greater ability to identify the events that are non-exoplanetary in origin.," Estimates of stellar radii improve the performance of the diagnostic, giving it an even greater ability to identify the events that are non-exoplanetary in origin."
 The diagnostic will be particularly. useful for bodies (such as hot Jupiters) (hat have circular orbits., The diagnostic will be particularly useful for bodies (such as hot Jupiters) that have circular orbits.
 The addition of eccentricity to (hie analvsis leads to an increased spread im the diagnostic. but does not critically impair the method.," The addition of eccentricity to the analysis leads to an increased spread in the diagnostic, but does not critically impair the method."
 Transits are more likely (o occur in portions of an eccentric orbit where ὃς exceeds vou leading to a reduction in (he average diagnostic [or exoplanetary svstems with a given period.," Transits are more likely to occur in portions of an eccentric orbit where $v_{\rm t}$ exceeds $v_{\rm circular}$, leading to a reduction in the average diagnostic for exoplanetary systems with a given period."
 Overall.," Overall,"
To see the sensitivity of the PCA results to the small differences in the choice of the threshold density. we compared the results of the PCA for superclusters chosen at higher and lower threshold density levels.,"To see the sensitivity of the PCA results to the small differences in the choice of the threshold density, we compared the results of the PCA for superclusters chosen at higher and lower threshold density levels."
 As an example we show in Table 7. the coefficients of the principal components for the superclusters chosen at the threshold density level D=5.5., As an example we show in Table \ref{tab:pca55} the coefficients of the principal components for the superclusters chosen at the threshold density level $D = 5.5$.
 At this density level. determined superclusters in the SDSS-DR7 for volume-limited samples of galaxies.," At this density level, determined superclusters in the SDSS-DR7 for volume-limited samples of galaxies."
 We used flux-limited samples. thus the density levels cannot be compared directly. but we can still choose this level for the present test.," We used flux-limited samples, thus the density levels cannot be compared directly, but we can still choose this level for the present test."
 Table 8 shows the results of the Spearman’s correlation test for this density level., Table \ref{tab:rank55} shows the results of the Spearman's correlation test for this density level.
 The comparison with Tables 4 and 3 shows that the coefficients are almost the same., The comparison with Tables \ref{tab:pca90} and \ref{tab:rank} shows that the coefficients are almost the same.
 Therefore the results of the correlation test and the PCA are not very sensitive to the choise of the density level., Therefore the results of the correlation test and the PCA are not very sensitive to the choise of the density level.
 We studied the properties of superclusters drawn from the SDSS DR7 using the principal component analysis and Spearman's correlation test., We studied the properties of superclusters drawn from the SDSS DR7 using the principal component analysis and Spearman's correlation test.
 Several earlier studies have shown that the properties of superclusters are correlated (see the references in Sect. 1)., Several earlier studies have shown that the properties of superclusters are correlated (see the references in Sect. \ref{sect:intro}) ).
 However. it i$ surprising that the correlations between the various properties of superclusters are so tight.," However, it is surprising that the correlations between the various properties of superclusters are so tight."
 The first two principal components account for most of the variance in the data., The first two principal components account for most of the variance in the data.
 Different physical parameters (the luminosity. volume. and diameter) and the morphological parameters (the clumpiness and the shape parameters) are almost equally important m shaping the properties of superclusters.," Different physical parameters (the luminosity, volume, and diameter) and the morphological parameters (the clumpiness and the shape parameters) are almost equally important in shaping the properties of superclusters."
 This suggests that superclusters. as described by their overall physical and morphological properties and by their inner morphology and peak density. are objects that can be described with a few parameters.," This suggests that superclusters, as described by their overall physical and morphological properties and by their inner morphology and peak density, are objects that can be described with a few parameters."
 We derived the scaling relation for superclusters in which we combine their lummosities. diameters. and shapetinders.," We derived the scaling relation for superclusters in which we combine their luminosities, diameters, and shapefinders."
 We saw in Fig., We saw in Fig.
 7. that more elongated and less elongated high-luminosity superclusters populate the ορ” Lepredicwdy plane differently., \ref{fig:scl90scale} that more elongated and less elongated high-luminosity superclusters populate the $L_{g(observed)}$ $L_{g(predicted)}$ plane differently.
 This suggests that luminous superclusters can be divided into two populations according to their shapes — more elongated systems with the shape parameter ΚΚ.-ϱ0.5 and less elongated ones with K\/K>>0.5., This suggests that luminous superclusters can be divided into two populations according to their shapes – more elongated systems with the shape parameter $K_1/K_2 < 0.5$ and less elongated ones with $K_1/K_2 > 0.5$.
 got a similar result using multidimensional normal mixture modelling., got a similar result using multidimensional normal mixture modelling.
 It is remarkable that two different multivariate methods reveal information about the data in such good agreement., It is remarkable that two different multivariate methods reveal information about the data in such good agreement.
 However. there are few high-luminosity superclusters in our sample.," However, there are few high-luminosity superclusters in our sample."
" There are 14 systems with the shape parameter K,/K>«0.5 among them. and 17 systems with. Aj/&5>0.5."," There are 14 systems with the shape parameter $K_1/K_2 < 0.5$ among them, and 17 systems with $K_1/K_2 > 0.5$."
 A larger sample of superclusters has to be analysed to confirm this result., A larger sample of superclusters has to be analysed to confirm this result.
 Parameters used to characterise superclusters in the present study do not reflect all the properties of superclusters., Parameters used to characterise superclusters in the present study do not reflect all the properties of superclusters.
 For example. rich superclusters contain high-density cores that may contain merging X-ray clusters and may be collapsing(222222).," For example, rich superclusters contain high-density cores that may contain merging X-ray clusters and may be collapsing."
. A supercluster environment with a wide range of densities affects the properties of galaxies. groups. and clusters located there(22222222?2).," A supercluster environment with a wide range of densities affects the properties of galaxies, groups, and clusters located there."
. showed that the dynamical evolution of one of the richest superclusters in the Sloan Great Wall (SCL 111. SCI 024 in LIO catalogue) is almost finished. while the richest member of the Wall. SCI] 126 (SCI 061) ts still dynamically active.," showed that the dynamical evolution of one of the richest superclusters in the Sloan Great Wall (SCL 111, SCl 024 in L10 catalogue) is almost finished, while the richest member of the Wall, SCl 126 (SCl 061) is still dynamically active."
 Therefore our results reflect only certain aspects of the properties of superclusters., Therefore our results reflect only certain aspects of the properties of superclusters.
 Systems of galaxies determined in the SDSS have been studied by a number of authors(, Systems of galaxies determined in the SDSS have been studied by a number of authors.
???22222222222) The overall shapes of superclusters have been described by the shape parameters or approximated by triaxial ellipses(222222222)., The overall shapes of superclusters have been described by the shape parameters or approximated by triaxial ellipses.
 These studies showed that elongated. prolate structures dominate among superclusters.," These studies showed that elongated, prolate structures dominate among superclusters."
 The results obtained using the moments of inertia tensor or the Minkowski functionals are ina good agreement??)., The results obtained using the moments of inertia tensor or the Minkowski functionals are in a good agreement.
. In addition. analysed correlations between supercluster properties from simulations and find that the amplitude of the supercluster - cluster alignment increases. (weakly) with superclusters filamentarity.," In addition, analysed correlations between supercluster properties from simulations and find that the amplitude of the supercluster - cluster alignment increases (weakly) with superclusters filamentarity."
 The properties of superclusters are determined by their formation and evolution., The properties of superclusters are determined by their formation and evolution.
 show that the shapes of superclusters agree better with à ACDM model than with a TCDM model., show that the shapes of superclusters agree better with a $\Lambda$ CDM model than with a $\tau$ CDM model.
 Also found that the shapes of observed superclusters agree with those in the ACDM model., Also found that the shapes of observed superclusters agree with those in the $\Lambda$ CDM model.
" In the ACDM concordance cosmological model. the matter density O,, dominated in the early universe and the structures formed by hierarhical clustering driven by gravity."," In the $\Lambda$ CDM concordance cosmological model, the matter density $\Omega_{\mathrm{m}}$ dominated in the early universe and the structures formed by hierarhical clustering driven by gravity."
 As the universe expands. the average matter density decreases.," As the universe expands, the average matter density decreases."
 At, At
of 6589 days in Fig. 8(a)..,of 6589 days in Fig. \ref{fig.hd22468_per}.
" In this figure we also show the 10, 50 and FAP levels computed with this method."," In this figure we also show the 10, 50 and FAP levels computed with this method."
" This period of 18.05+3.21 years is in concordance, within the statistical error, with the ones found by the authors cited above."," This period of $18.05\pm 3.21$ years is in concordance, within the statistical error, with the ones found by the authors cited above."
"In Fig. 8(b),,","In Fig. \ref{fig.hd22468_fas},"
" we plot the mean annual (S) phased with the period obtained and we found that a harmonic function fits these points with a reduced x?=1.5, which corroborates the period found."," we plot the mean annual $\langle S \rangle$ phased with the period obtained and we found that a harmonic function fits these points with a reduced $\chi^2=1.5$, which corroborates the period found."
" Berdyugina&Henry(2007) also found a 5-year flip-flop cycle, derived from the cyclic pattern of the peak-to-peak V magnitude which reflects the non-axisymmetric redistribution of the spotted area."," \cite{2007ApJ...659L.157B} also found a 5-year flip-flop cycle, derived from the cyclic pattern of the peak-to-peak V magnitude which reflects the non-axisymmetric redistribution of the spotted area."
 The photometric observations analysed by (2006) also reflected this short-term oscillation with a period of 3-5 years superposed on the long-term spot activity cycle., The photometric observations analysed by \cite{2006A&A...455..595L} also reflected this short-term oscillation with a period of 3-5 years superposed on the long-term spot activity cycle.
" To search for a chromospheric flip-flop cycle, we analysed the peak-to-peak Mount Wilson index for several seasons of measurements, since these variations are proportional to the difference of the area of plages between opposite hemispheres of HD 22468."," To search for a chromospheric flip-flop cycle, we analysed the peak-to-peak Mount Wilson index for several seasons of measurements, since these variations are proportional to the difference of the area of plages between opposite hemispheres of HD 22468."
" To do this, we built individual light curves for the sets of data indicated with arrows in Fig. 6,,"," To do this, we built individual light curves for the sets of data indicated with arrows in Fig. \ref{fig.hd22468},"
 which are shown in Fig. 9.., which are shown in Fig. \ref{fig.hd22468_curvas}.
 We excluded from these datasets those points associated with flares., We excluded from these datasets those points associated with flares.
" Following Díazetal. (2007),, we phased each light-curve with the"," Following \cite{2007A&A...474..345D}, , we phased each light-curve with the"
The total. phase-dependent specific intensities from (he spot are (hen obtained by integrating the local emission in each mode over the observable surface. accounting for the gravitational redishilt of the radiation (?):: where the local specific intensity in each mode 7; (J=X.O) is set to zero outside of the boundaries on @ and 42 set above.,"The total, phase-dependent specific intensities from the spot are then obtained by integrating the local emission in each mode over the observable surface, accounting for the gravitational redishift of the radiation \citep[][]{Page95a}: where the local specific intensity in each mode $I_j$ $j=\mbox{X, O}$ ) is set to zero outside of the boundaries on $\theta$ and $\varphi$ set above."
 The energy observed at infinity is given by Ey.=Ec wilh The phase-dependent Stokes parameters ave then readily calculated using the methods of refsubsect:Observed Polarization..," The energy observed at infinity is given by $E_{\infty}=E e^{\Lambda}$, with The phase-dependent Stokes parameters are then readily calculated using the methods of \\ref{subsect:Observed Polarization}."
 We present results [rom our magnetar models with fullv ionized hwdrogen atmospheres. magnetic field strengths 7x107 οκ10! G. and ellective temperature Typ=5x10 Ix (a value which is in (he (vpical magnetar range).," We present results from our magnetar models with fully ionized hydrogen atmospheres, magnetic field strengths $7 \times 10^{13}$ G – $5\times 10^{14}$ G, and effective temperature $T_{\rm eff}=5\times 10^6$ K (a value which is in the typical magnetar range)."
" We explore four representative geometries: ag=905. ag,=90° (herealter denoted G1): ay=90°. ag,=45° (hereafter denoted C32): ag=45°. n3;=45° (herealter denoted G3): and ay=457. ag,=0* (herealter denoted G4)."," We explore four representative geometries: $\alpha_R=90^{\circ}$, $\alpha_M=90^{\circ}$ (hereafter denoted G1); $\alpha_R=90^{\circ}$, $\alpha_M=45^{\circ}$ (hereafter denoted G2); $\alpha_R=45^{\circ}$, $\alpha_M=45^{\circ}$ (hereafter denoted G3); and $\alpha_R=45^{\circ}$, $\alpha_M=0^{\circ}$ (hereafter denoted G4)."
 As discussed above. quiescent magnetar emission spectra are well fit bv a blackbody plus power-law and do not contain absorption features.," As discussed above, quiescent magnetar emission spectra are well fit by a blackbody plus power-law and do not contain absorption features."
 Thus. it is difficult to distinguish magnetic atmosphere models [rom phenomenological fits.," Thus, it is difficult to distinguish magnetic atmosphere models from phenomenological fits."
 However. the linear polarization is strongly dependent on the magnetic field and viewing geometry. aud. importantly. cannot be predicted without a detailed plivsical model for the surface emission.," However, the linear polarization is strongly dependent on the magnetic field and viewing geometry, and, importantly, cannot be predicted without a detailed physical model for the surface emission."
 lu (his section. we describe the dependence of TI... on magnetic field ancl geometry.," In this section, we describe the dependence of $\Pi_{\rm em}$ on magnetic field and geometry."
 Figures 1 and 2 show the linear polarization Iraction calculated using NS atmosphere models at magnetic field strengths B=5x10! G (solid curves). B=10!! G (dotted curves). and B=7xLOM G (dashed curves).," Figures \ref{fig:pfracE5} and \ref{fig:pfracE20} show the linear polarization fraction calculated using NS atmosphere models at magnetic field strengths $B=5\times 10^{14}$ G (solid curves), $B=10^{14}$ G (dotted curves), and $B=7\times 10^{13}$ G (dashed curves)."
 Each panel in the figure corresponds (to one of (he NS geometries described above., Each panel in the figure corresponds to one of the NS geometries described above.
" The polar cap size is set to 9= 5°,", The polar cap size is set to $\beta = 5^{\circ}$ .
population parametersa and mo. while the second. term concerns the probability of finding cach galaxy / at position 4;.,"population parameters$\alpha$ and $n_0$, while the second term concerns the probability of finding each galaxy $i$ at position $\theta_i$."
 By maximizing / we find the most likely parameter(s) for a given lens model., By maximizing $l$ we find the most likely parameter(s) for a given lens model.
 In the subsequent sections. we examine two single-parameter mass models.," In the subsequent sections, we examine two single-parameter mass models."
 The derivation of this expression is) presented in Appendix A. Laportanth. this appendix also generalizes the likelihooc method of SKE to include the elfect of incompleteness.," The derivation of this expression is presented in Appendix A. Importantly, this appendix also generalizes the likelihood method of SKE to include the effect of incompleteness."
 We showed that. as long as the intrinsic uünlensed counts. follow. a power lav. incompleteness is very simple to account for: one simply uses the observed (incomplete) unlensec density 20 in place of the intrinsic (complete) unlensed. density ro in the likelihood. function.," We showed that, as long as the intrinsic unlensed counts follow a power law, incompleteness is very simple to account for: one simply uses the observed (incomplete) unlensed density $\tilde{n}_{0}$ in place of the intrinsic (complete) unlensed density $n_{0}$ in the likelihood function."
 This allows us to include. in our sample. galaxies which are fainter than the completeness. limit ancl therefore. of improving our signal-to-noise. without fear of introducing a bias.," This allows us to include, in our sample, galaxies which are fainter than the completeness limit and therefore of improving our signal-to-noise, without fear of introducing a bias."
 First. we model the cluster according to a singular isothermal sphere (SES) parametrized with the Einstein racius. Ge: The filled circles in Fig.," First, we model the cluster according to a singular isothermal sphere (SIS) parametrized with the Einstein radius, $\theta_{\rm E} $: The filled circles in Fig."
 S. show the resulting log-ikelihood curve., \ref{fig-mlplot} show the resulting log-likelihood curve.
 The sharp dips are a result. of the contribution of the second term of Equation 3. (concerning he galaxy positions) to the log-likelihood function., The sharp dips are a result of the contribution of the second term of Equation \ref{eqn-l} (concerning the galaxy positions) to the log-likelihood function.
 As the ikelihood is calculated. for increasing. values of the input 0p. a galaxy may happen to lie on the critical line (6;= θε).," As the likelihood is calculated for increasing values of the input $\theta_E$, a galaxy may happen to lie on the critical line $\theta_i=\theta_E$ )."
 Since the magnification (ancl hence the depletion) is ormallv infinite at this radius. the probability. of finding a galaxy vanishes. and the method. rejects this particular model.," Since the magnification (and hence the depletion) is formally infinite at this radius, the probability of finding a galaxy vanishes, and the method rejects this particular model."
 This results from the fact that we have cllectively moclelled the galaxies as point sources., This results from the fact that we have effectively modelled the galaxies as point sources.
 In practice. galaxies are extended objects and therefore are not subject to infinite magnifications. but instead are stretched into giant. arcs on he critical Line.," In practice, galaxies are extended objects and therefore are not subject to infinite magnifications, but instead are stretched into giant arcs on the critical line."
 In. our analysis. we simply identified the oak as the absolute maximum. without any interpolation.," In our analysis, we simply identified the peak as the absolute maximum, without any interpolation."
 As we will see below. this does not introduce any observable jas in the determination of the model parameters.," As we will see below, this does not introduce any observable bias in the determination of the model parameters."
 The peak of the likelihood. function. is reached. ataresec.. which is consistent with the location of he red ogiant arc located. 13 aresee from the cluster centre (shown in Fig. 6)).," The peak of the likelihood function is reached at, which is consistent with the location of the red giant arc located 13 arcsec from the cluster centre (shown in Fig. \ref{fig-arczoom}) )."
 We perform a test of the depletion by applving the same maximunm-likelihood test on one of the olfset fields., We perform a test of the depletion by applying the same maximum-likelihood test on one of the offset fields.
 Using he same colour selection criteria to define a population of red objects we find no evidence for anv depletion. effect., Using the same colour selection criteria to define a population of red objects we find no evidence for any depletion effect.
" Furthermore. we also test the population of ""foreground"" galaxies (those with colours bluer than the cluster sequence) in the eluster field. anc again find as expected no evidence for depletion."," Furthermore, we also test the population of `foreground' galaxies (those with colours bluer than the cluster sequence) in the cluster field, and again find as expected no evidence for depletion."
 The log-likelihood functions for these two samples. both peaking at 8g=0 aresec. are also shown as open svmbols in Fig. δ..," The log-likelihood functions for these two samples, both peaking at $\theta_E=0$ arcsec, are also shown as open symbols in Fig. \ref{fig-mlplot}."
 An alternative model to the SIS is the universal density profile for dark matter halos proposed. by Navarro. Erenk White (L097. 1996. 1995).," An alternative model to the SIS is the universal density profile for dark matter halos proposed by Navarro, Frenk White (1997, 1996, 1995)."
 Given the uncertainties in the data it is unlikely that we could use this technique to distinguish between two moclels., Given the uncertainties in the data it is unlikely that we could use this technique to distinguish between two models.
 It is nevertheless of interest to demonstrate how the method could be applied to a second model., It is nevertheless of interest to demonstrate how the method could be applied to a second model.
" The NEW density. profile follows where p, is the eritical density at the redshift of the lens.", The NFW density profile follows where $\rho_c$ is the critical density at the redshift of the lens.
 The two parameters of the model are contained in the scale radius ες and the concentration parameter e. so that the characteristic overdensity is In contrast to the SIS. this profile Hattens towards the core and is capable of producing radial as well as tangential ares (Bartelmann 1996).," The two parameters of the model are contained in the scale radius $r_s$ and the concentration parameter $c$, so that the characteristic overdensity is In contrast to the SIS, this profile flattens towards the core and is capable of producing radial as well as tangential arcs (Bartelmann 1996)."
 For a projected radial distance 2. we can define a dimensionless distance.τοι.," For a projected radial distance $R$ , we can define a dimensionless distance,."
 Wright Drainerd (1999) give the formulation for the racial dependence of the surface density XGr) and the shear 5(24)., Wright Brainerd (1999) give the formulation for the radial dependence of the surface density $\Sigma(x)$ and the shear $\gamma(x)$.
 The convergence is then simply Αα)=XGr)/ Noa. where the critical surface number mass density depends on the angular diameter distances J...D.Du.from observer to source. observer to lens. and source to lens.," The convergence is then simply $\kappa(x)=\Sigma(x)/\Sigma_{\rm crit}$ , where the critical surface number mass density depends on the angular diameter distances $D_s,D_d,D_{ds}$from observer to source, observer to lens, and source to lens,"
The change of expansion velocity of the central cemitting torus from 14.5 to 21.2 iin the morphological/kinematical model in Meaburn et al (2005b) makes only minor cosmetic differences to the predictions of the model for comparison with the previous observations along cuts 6 7 in Fig.,The change of expansion velocity of the central emitting torus from 14.5 to 21.2 in the morphological/kinematical model in Meaburn et al (2005b) makes only minor cosmetic differences to the predictions of the model for comparison with the previous observations along cuts 6 7 in Fig.
 |., 1.
" In fact, the detailed comparison is improved quantitatively but will not be repeated here."," In fact, the detailed comparison is improved quantitatively but will not be repeated here."
 The tilt to more positive velocities from the southeastern to the northwestern (bottom to top) is clear in Fig., The tilt to more positive velocities from the southeastern to the northwestern (bottom to top) is clear in Fig.
 2 as predicted by the same bipolar/torus model., 2 as predicted by the same bipolar/torus model.
" Firstly, the outer CO ring appears to have been detected at optical wavelengths for the first time in the new pv array along cut 4."," Firstly, the outer CO ring appears to have been detected at optical wavelengths for the first time in the new pv array along cut 4."
" The very deep, negative. greyscale image of this is presented in Fig."," The very deep, negative, greyscale image of this is presented in Fig."
 4 and two sets of velocity ‘spikes’ (A and B in Fig., 4 and two sets of velocity `spikes' (A and B in Fig.
 4) can be seen over the approaching and receding maxima depicted in Fig., 4) can be seen over the approaching and receding maxima depicted in Fig.
 6., 6.
 These have the same radial velocity ranges as the corresponding CO features of Young ct al (1999)., These have the same radial velocity ranges as the corresponding CO features of Young et al (1999).
" The higher angular resolution of the present ddata compared with the CO maps (30"")) appears to have resolved this outer neutral/ionized torus into a double ring structure with its axis along PA = ccompared with PA = ffor the inner torus (Sect.", The higher angular resolution of the present data compared with the CO maps ) appears to have resolved this outer neutral/ionized torus into a double ring structure with its axis along PA = compared with PA = for the inner torus (Sect.
 3.2.1)., 3.2.1).
 There is no easy way to estimate directly the tilt of the axis of this outer torus to the sight line for it does not appear on optical images and most of its extent gets confused in the CO maps as it crosses the central nebula. consequently an estimation of only a lower limit of its expansion velocity can be made i.c. > 27/|.," There is no easy way to estimate directly the tilt of the axis of this outer torus to the sight line for it does not appear on optical images and most of its extent gets confused in the CO maps as it crosses the central nebula, consequently an estimation of only a lower limit of its expansion velocity can be made i.e. $\geq$ 27."
. The possible bipolar lobes L1 and L2 in Fig., The possible bipolar lobes L1 and L2 in Fig.
 6 (Sect., 6 (Sect.
 3.1.1) associated with this outer torus would have receding and approaching radial velocities respectively., 3.1.1) associated with this outer torus would have receding and approaching radial velocities respectively.
 Neither have vet been measured., Neither have yet been measured.
 Also the axis of the outer CO torus and the common axis of these possibily related bipolar lobes would expected to be the same., Also the axis of the outer CO torus and the common axis of these possibily related bipolar lobes would expected to be the same.
" Evidence for some type of outer bipolar structure, as suggested on morphological grounds in Sect."," Evidence for some type of outer bipolar structure, as suggested on morphological grounds in Sect."
" 3.1, enveloping the inner one. is also present in this new kinematical data."," 3.1, enveloping the inner one, is also present in this new kinematical data."
 As the pv array crosses from the bright helical structure to the NE outer arc in Fig., As the pv array crosses from the bright helical structure to the NE outer arc in Fig.
 3 along cut 5 the profiles stay on 22-50 until they reach -95 tto then come back to, 3 along cut 5 the profiles stay on = -50 until they reach -95 to then come back to
"The angular iiomieutiim loss rate follows M/M;,j.",The angular momentum loss rate follows ${\dot M}/{\dot M}_{inj}$.
 Tuterestinely. the maxima of the average angular nunomenutuia of the disk coicides with the minima of the emission. miass-loss rate aud the angular uomentuna loss rate.," Interestingly, the maxima of the average angular momentum of the disk coincides with the minima of the emission, mass-loss rate and the angular momentum loss rate."
" The bottom panel of Figure 9 sugeests that if the average angular moment of the disk mereases. then e, should decrease in a aree regiono of the disk. which should reduce the rate of matter actually accreted outo the ca- role."," The bottom panel of Figure 9 suggests that if the average angular momentum of the disk increases, then $v_r$ should decrease in a large region of the disk, which should reduce the rate of matter actually accreted onto the black hole."
 Aud the average augulu momentum (<7>) of the disk lnereases with the increase of the veal and the width of the aneular momnenutuu distribution of the disk. which corresponds tc [um dips in emission. niass-loss parameter and angular uonentuni loss rate.," And the average angular momentum $<l>$ ) of the disk increases with the increase of the peak and the width of the angular momentum distribution of the disk, which corresponds to the dips in emission, mass-loss parameter and angular momentum loss rate."
 Although <7> oscillates with the same period as that of shock. but the disk interestingly prefers to stav in the state ↕↴∖↴∶↴∙⊾↥⋅↸∖⋜↧↑↸∖↥⋅↑∐⋜⋯∣∣⊽⊓∕∙≋↕∐," Although $<l>$ oscillates with the same period as that of shock, but the disk interestingly prefers to stay in the state $<l>$ is greater than $l_{inj}$."
∩∖↑∐↸∖≼∐↴∖↴↘↽↕↑↴∖↴↸∖∐⋟ ↕↴∖↴∪↴∖↴↸⊳∐↕⋜↧↑↕∐∶↴⋁∙⋜↧↕↑∐↸∖↴∖↴↸∖∏∪↖↖⇁↻⋜∐⋅⋜∐⊔↸∖↑↸∖↥⋅↴∖↴↴∖↴∐∪∏∐ oscillate with the same period.," Since the disk itself is oscillating, all these flow parameters should oscillate with the same period."
 And indeed the brelusstralliue cussion. the mass loss rate. the aueular momentum loss rate etc all oscillate with the same period of shock oscillation.," And indeed the bremsstrahlung emission, the mass loss rate, the angular momentum loss rate etc all oscillate with the same period of shock oscillation."
 The dynamics of the disk with higher viscosity parameter is different from that due to the lower one., The dynamics of the disk with higher viscosity parameter is different from that due to the lower one.
 For higher viscosity paraicter the difference in the disk dvuamics will arise from more efficieut aneular momentum transfer as well as higher viscous dissipation of leat. even if the outer boundary condition remains the same.," For higher viscosity parameter the difference in the disk dynamics will arise from more efficient angular momentum transfer as well as higher viscous dissipation of heat, even if the outer boundary condition remains the same."
 Iu Figure 10. we have plotted the shock location with time op) and the broemsstraliluug cussion with time Xttoni) for a fid with the same injection yaralneters as the inviscid flow described in Ll. ie. Vin?= Ομη)=2.97010.2Te. and ο1).=LN27«10ὃς and the viscosity xuanmeter isa=0.1.," In Figure 10, we have plotted the shock location with time (top) and the bremsstrahlung emission with time (bottom) for a fluid with the same injection parameters as the inviscid flow described in 4.1, i.e., $r_{inj}=1000r_g$, $v_r(inj)=2.970 \times 10^{-2}c$, and $c_s(inj)=4.827 \times 10^{-3}c$ and the viscosity parameter is $\alpha=0.1$."
 The time variation of shock or a=0. (Fig., The time variation of shock for $\alpha=0.1$ (Fig.
 10) is distinctly different from jii of à=0.01 Fig., 10) is distinctly different from that of $\alpha=0.01$ Fig.
 7)., 7).
 The iuner shock Orns. expands. and at some epoch collides with ie contracting outer shock. while at some other epoch it disappears before colliding with the outer shock.," The inner shock forms, expands, and at some epoch collides with the contracting outer shock, while at some other epoch it disappears before colliding with the outer shock."
 The immer shock is weaker compared to the disk with lower o., The inner shock is weaker compared to the disk with lower $\alpha$.
 The time evolution of the two shocks are somewhat similar to the initial phases of the shock variation for a=0.01., The time evolution of the two shocks are somewhat similar to the initial phases of the shock variation for $\alpha=0.01$.
 Comparison of the time variation of bremsstrahlung cussion with the time variation of the shock shows uo correlation between shock münunua and cussion mania uulike the case for a=0.01., Comparison of the time variation of bremsstrahlung emission with the time variation of the shock shows no correlation between shock minima and emission maxima unlike the case for $\alpha=0.01$.
" Iu Figure 1a llb. e, (dashed-dot) and ος (solid) are plotted corresponding to the ciaission Inaxinia (Fig."," In Figure 11a – 11b, $v_r$ (dashed-dot) and $c_s$ (solid) are plotted corresponding to the emission maxima (Fig."
 lla) aud enmuüssion minuna (Fie., 11a) and emission minima (Fig.
 11b)., 11b).
 Sinularly the corresponding specific angular moment distributions are plotted for the cmission maxima (Fie., Similarly the corresponding specific angular momentum distributions are plotted for the emission maxima (Fig.
 Lic) aud munima (Fig., 11c) and minima (Fig.
 11d). aud the deusity too ave plotted for he enüssion maxiua (Fie.," 11d), and the density too are plotted for the emission maxima (Fig."
 11ο) and minima (Fie., 11e) and minima (Fig.
 l1f)., 11f).
 The maxima of the brenisstrahnluus cussion occurs when the imnuer shock is tending to form. while the nininia occurs when the tuner shock has not been formed (also refer Fie.," The maxima of the bremsstrahlung emission occurs when the inner shock is tending to form, while the minima occurs when the inner shock has not been formed (also refer Fig."
 10)., 10).
" This change in the behavior of the VArock and the cussion properties compared to ji of the a=0,01. actually depends on the litferent rate of angular moment transfer."," This change in the behavior of the shock and the emission properties compared to that of the $\alpha=0.01$, actually depends on the different rate of angular momentum transfer."
 Since 1 Viscosity in the present case is ten fold higher wna =0.01. the outward augular 1io1uentuin rausport is very efficient.," Since the viscosity in the present case is ten fold higher than $\alpha=0.01$, the outward angular momentum transport is very efficient."
 So close to the black role. the aneular momentum rises steeply outward uulike the flow with lower viscosity Fig.," So close to the black hole, the angular momentum rises steeply outward unlike the flow with lower viscosity Fig."
 Le lid may be compared with Fie., 11c – 11d may be compared with Fig.
 6a 6d)., 6a – 6d).
 If he shock is closer to the black hole then the ovk of the angular momentum distribution is very close to the outer shock (Fig., If the shock is closer to the black hole then the peak of the angular momentum distribution is very close to the outer shock (Fig.
 lld): this Causes natter to accrete more yeely between the iorizon and the peak of the angular moment distribution. aud hence the deusitv is lower (Fig.," 11d); this causes matter to accrete more freely between the horizon and the peak of the angular momentum distribution, and hence the density is lower (Fig."
 llb. Lid and 11f).," 11b, 11d and 11f)."
 This causes the cussion » dip., This causes the emission to dip.
 As the shock MOVCS out the aneular uonmientuni peak is situated further inside (Fig., As the shock moves out the angular momentum peak is situated further inside (Fig.
 lc), 11c).
 Aud this causes the matter to madly fall inwards between the outer shock and the iuuer | peak., And this causes the matter to madly fall inwards between the outer shock and the inner $l$ peak.
 As the in falling matter encounters tle aueular momentum pile it decelerates drastically increasing the deusitv considerably. and hence enhances the broiisstralbung cussion (Fie.," As the in falling matter encounters the angular momentum pile it decelerates drastically increasing the density considerably, and hence enhances the bremsstrahlung emission (Fig."
 lla. lle and 11e).," 11a, 11c and 11e)."
 LEwvoeutuallyv it forms an inner shock but the cuhanced energy deposition in the post-inner shock region causes the iuner shock to expand aud thereby reducing density and cluission., Eventually it forms an inner shock but the enhanced energy deposition in the post-inner shock region causes the inner shock to expand and thereby reducing density and emission.
 Iu this connection one may polit out that the iuuediate post-shock (for both iunuer and outer shocks) region maw be decelerating or acceleratiug Figs., In this connection one may point out that the immediate post-shock (for both inner and outer shocks) region may be decelerating or accelerating Figs.
 5i-5d. 11a-11b).," 5a-5d, 11a-11b)."
" However. it was predicted by Nakaviuua(1992):Nobuta& that post-shock acceleration aud deceleration correspoud to uustable aud stable shocks. respectively,"," However, it was predicted by \citet{n92,nh94} that post-shock acceleration and deceleration correspond to unstable and stable shocks, respectively."
 The reason for this is that no, The reason for this is that no
"analvses show that the correlation between Z4; and. My, is not caused by the common redshift dependence.",analyses show that the correlation between $l_{\rm core}$ and $M_{\rm bh}$ is not caused by the common redshift dependence.
 I. scons that the effect of the angular resolution limit of. VLBI observations is not important in our analyses., It seems that the effect of the angular resolution limit of VLBI observations is not important in our analyses.
 There is no significante correlation between the linear eneth |obscore (without [requeney. correction to the rest frame of the sources) and Adiga for the whole sample. while a correlation is present only for those sources observed at he same frequency 8.55 11.," There is no significant correlation between the linear length $l_{\rm core}^{\rm obs}$ (without frequency correction to the rest frame of the sources) and $M_{\rm bh}$ for the whole sample, while a correlation is present only for those sources observed at the same frequency 8.55 GHz."
 The dependence of the core size on observing frequency seems to be important in the correlation analyses. which is in consistent with inhomogencous spherejet models.," The dependence of the core size on observing frequency seems to be important in the correlation analyses, which is in consistent with inhomogeneous sphere/jet models."
 The linear core length foe is a measurement on the size οἱ optically thick emission. region of the plasma in inhomogeneous sphere/jet models (Marscher 1977: Wonniel 1981)., The linear core length $l_{\rm core}$ is a measurement on the size of optically thick emission region of the plasma in inhomogeneous sphere/jet models (Marscher 1977; Könnigl 1981).
 The length four. is mainly determined by the electron number density. the magnetic field strength in the plasma and the bulk velocity of the plasma. which may be regulated bv the central black hole mass.," The length $l_{\rm core}$ is mainly determined by the electron number density, the magnetic field strength in the plasma and the bulk velocity of the plasma, which may be regulated by the central black hole mass."
 Lt is therefore naturally to expect that a larger black hole has a larger radio emission region., It is therefore naturally to expect that a larger black hole has a larger radio emission region.
 But the slope of the Adjlae ds rather Dat. i.c.. the length four. increases slowly with Mi (not a linear relation).," But the slope of the $M_{\rm bh}~-~l_{\rm core}$ is rather flat, i.e., the length $l_{\rm core}$ increases slowly with $M_{\rm bh}$ (not a linear relation)."
 We plot the relation between the length ἐς in unit of the Schwarsehild radius ο and the hole mass Ay in Fig.," We plot the relation between the length $l_{\rm core}$ in unit of the Schwarschild radius $r_{\rm g}
=2GM/c^2$ and the hole mass $M_{\rm bh}$ in Fig."
 6., 6.
 Ht shows that the dimensionless linear length foorefry decreases with the hole mass., It shows that the dimensionless linear length $l_{\rm core}/r_{\rm g}$ decreases with the hole mass.
 As cdiscussec in Sect., As discussed in Sect.
 4. rw results. seem to be consistent with the inhomogeneous jet model.," 4, the results seem to be consistent with the inhomogeneous jet model."
 Lt is worth noting that a similar trend of feae/tyMy seems to be present for three φον[οι galaxies observed. by Ulvestad Ilo (2001)., It is worth noting that a similar trend of $l_{\rm core}/r_{\rm g}-M_{\rm bh}$ seems to be present for three Seyfert galaxies observed by Ulvestad Ho (2001).
 LO max imply that the origin of the radio emission. from these Sevfer ealaxies is similar to that of racdio-Ioud AGNs., It may imply that the origin of the radio emission from these Seyfert galaxies is similar to that of radio-loud AGNs.
 Their radio emission is generated by compact jets (Falcke 1996: Faleke AlarkolT 2000). though the power of the jets in these Sevfer ealaxies is significantly lower than that in the racio-LIou AGINs discussed in present. work.," Their radio emission is generated by compact jets (Falcke 1996; Falcke Markoff 2000), though the power of the jets in these Seyfert galaxies is significantly lower than that in the radio-loud AGNs discussed in present work."
 Lt was pointed out that the core Luminosity is à goo indicator of jet. power for core dominated. quasars (Cao Jiang 2001)., It was pointed out that the core luminosity is a good indicator of jet power for core dominated quasars (Cao Jiang 2001).
 The intrinsic correlation found in this work between the core luminosity and hole mass confirms some previous similar results (AleLure 1999: Laor 2000)., The intrinsic correlation found in this work between the core luminosity and hole mass confirms some previous similar results (McLure 1999; Laor 2000).
 The jet formation in an AGN is regulated by the central black hole., The jet formation in an AGN is regulated by the central black hole.
 We are grateful to the referee; Mark. Lacy. for his helpful comments ancl suggestions on the paper.," We are grateful to the referee, Mark Lacy, for his helpful comments and suggestions on the paper."
 NC thanks the support from NSEC(No., XC thanks the support from NSFC(No.
 10173016). the NABRSE (No.," 10173016), the NKBRSF (No."
 €:11909075403). and Pandeng Project.," G1999075403), and Pandeng Project."
 This research has made use of the NASA/IPAC Extragalactic Database (NED). which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Acronautic and Space Administration.," This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautic and Space Administration."
Find the density ancl potential ou the PM grid again. aud update the acceleration for PM particles (eq.,"Find the density and potential on the PM grid again, and update the acceleration for PM particles (eq."
 [ibb])., \ref{eqn:leapfrog}b b]).
 All tree particles are at the PM imidstep. the proper location for computing the force on PM particles.," All tree particles are at the PM midstep, the proper location for computing the force on PM particles."
 Integrate each tree region forward to the end of the PM step., Integrate each tree region forward to the end of the PM step.
 Update PM particle velocities and positions to the eud of the time step (eqs., Update PM particle velocities and positions to the end of the time step (eqs.
 [1cc-d])., \ref{eqn:leapfrog}c c-d]).
" TPM exploits the fact that graviational instability in au expalding universe creates spatially isolated. high density peaks: for typieal CDM models these peaks wi| contain a significant [raction of the mass (~ 1/1) but occupy a tiy fraction of the volue (10"": see for example Fig. 22 of Mo&White (2002))).", TPM exploits the fact that gravitational instability in an expanding universe creates spatially isolated high density peaks; for typical CDM models these peaks will contain a significant fraction of the mass $\sim 1/4$ ) but occupy a tiny fraction of the volume $\sim 10^{-3}$ ; see for example $.$ 2 of \citet{MoWhite02}) ).
 As described i1 detail inBOX. this is accomdlished by taggingMDoo active mesh cells based ou the cell density (which as already been caleulated in «der to perform the PM step).," As described in detail in, this is accomplished by tagging active mesh cells based on the cell density (which has already been calculated in order to perform the PM step)."
 Adjacent cells are linked together. «ividiug the cells into groups 1La frieuds-ol-lrieuds ianuer.," Adjacent cells are linked together, dividing the cells into groups in a friends–of–friends manner."
 Thus isolated high-density regions of space are ideutified. separate by at least one cell width.," Thus isolated high–density regions of space are identified, separated by at least one cell width."
 InBOX. the criterion used to decide if à cell 7 was active was if its clensity p; exceeded a global threshold density where p is the mean density at do is the dispersion of cell deusities.," In, the criterion used to decide if a cell $i$ was active was if its density $\rho_i$ exceeded a global threshold density where $\bar{\rho}$ is the mean density and $\sigma$ is the dispersion of cell densities."
 While temporally adaptive (in the sense that the threshold is ower at early times wieu peaks are rare). this criterion las two iuain drawbacks.," While temporally adaptive (in the sense that the threshold is lower at early times when peaks are rare), this criterion has two main drawbacks."
 First. small. peaks iu isolated regions «o» voids will not be picked up. especially when σ is large. because the total 1lass in sucha halo wotId not puta PM cell above pij.," First, small peaks in isolated regions or voids will not be picked up, especially when $\sigma$ is large, because the total mass in such a halo would not put a PM cell above $\rho_{\rm thr}$ ."
" Secondly. in the case of a region with peak cleusity near pog, whether or not a give1 PM ce Lis above pity can depeud on the offset of the grid with respect to tlie particles— the haο Mass 1vay be cliviclect into two or more cells."," Secondly, in the case of a region with peak density near $\rho_{\rm thr}$, whether or not a given PM cell is above $\rho_{\rm thr}$ can depend on the offset of the grid with respect to the particles— the halo mass may be divided into two or more cells."
 We have developed au unprovec| criterion for selectine tree reelois involving the contrast of a cell with its surrouucdiugs (rather than a sinele global threshold valiιο) found by comparing the density smoothed on two scales., We have developed an improved criterion for selecting tree regions involving the contrast of a cell with its surroundings (rather than a single global threshold value) found by comparing the density smoothed on two scales.
 For each ce| three deInilies are compute., For each cell three densities are computed.
 Firs Ως. fcmud by boxcar smoothing over a leneth of 5 cells alor[n]e each dimension. (," First $\rho_s$, found by boxcar smoothing over a length of 5 cells along each dimension. ("
A110her type of sinootli1 wilh a CGatssian. would be possible. but the boxcar cau be clone with minimal interprocessor communication).,"Another type of smoothing, with a Gaussian, would be possible, but the boxcar can be done with minimal interprocessor communication)."
 Second. pe. the mean density in the eight-cell cube of which the cell under consideration is the lower octaut(wheu using CIC. a particle in thiscell would also assign mass to," Second, $\rho_c$, the mean density in the eight–cell cube of which the cell under consideration is the lower octant(when using CIC, a particle in thiscell would also assign mass to"
"apparent dimensions of the host galaxies are mostly below10’,, i.e. smaller than the point spread function of the iin the major part of the considered energy range.","apparent dimensions of the host galaxies are mostly below, i.e. smaller than the point spread function of the in the major part of the considered energy range."
" In the modelled reconstruction of the sources, all the objects included in the 1FGL catalogue (?) are accounted for."," In the modelled reconstruction of the sources, all the objects included in the 1FGL catalogue \citep{2010ApJS..188..405A} are accounted for."
" Moreover, other sources, for which test statistics (TS,see?) are above 25 — roughly equivalent to a 5c detection — and which are not reported in the 1FGL catalogue, are also included in the source models."," Moreover, other sources, for which test statistics \citep[TS, see e.g.][]{1996ApJ...461..396M} are above 25 – roughly equivalent to a $\sigma$ detection – and which are not reported in the 1FGL catalogue, are also included in the source models."
" These potential source candidates were selected from the ccount maps above GGeV, where the ppoint spread function is below ~0.5°.."," These potential source candidates were selected from the count maps above GeV, where the point spread function is below $\sim$."
" For each object added in this way to the model, as well as for the source of interest, we first run a likelihood test, usinggtlike,, to assess whether the new introduced source is significant."," For each object added in this way to the model, as well as for the source of interest, we first run a likelihood test, using, to assess whether the new introduced source is significant."
" If the corresponding TS is above 25, revealing a detection, the position of the new source is optimised using the toolf£indsrc,, whereas for the sources included in the IFGL catalogue, we fixed their position to the values from the catalogue."," If the corresponding TS is above 25, revealing a detection, the position of the new source is optimised using the tool, whereas for the sources included in the 1FGL catalogue, we fixed their position to the values from the catalogue."
" The spectral parameters of the additional source are then refined on the corresponding best-fit position, usinggtlike."," The spectral parameters of the additional source are then refined on the corresponding best-fit position, using."
". For all the sources of interest in the sample, the corresponding TS are found to be below 25."," For all the sources of interest in the sample, the corresponding TS are found to be below 25."
 We thus computed upper limits at 2σ confidence level on their flux in the GGeV energy range., We thus computed upper limits at $\sigma$ confidence level on their flux in the GeV energy range.
" No specific energy spectra are assumed to derive these upper limits, the photon indices of the sources of interest are left free to vary in the models."," No specific energy spectra are assumed to derive these upper limits, the photon indices of the sources of interest are left free to vary in the models."
" Table summarises the results of our analysis on the source sample, [I]as well as results for other galaxies studied in the era."," Table \ref{tab-ana_results} summarises the results of our analysis on the source sample, as well as results for other galaxies studied in the era."
 Following are some notes concerning peculiar sources., Following are some notes concerning peculiar sources.
" For the search of y--ray emission from 881, the strong starburst emitter 882 is located aaway from M881, hence contaminating the region around M881, given that the point spread function of the LAT degrades strongly at low energies, which prevents us from deriving constraining upper limits on the flux of M881."," For the search of -ray emission from 81, the strong starburst emitter 82 is located away from 81, hence contaminating the region around 81, given that the point spread function of the LAT degrades strongly at low energies, which prevents us from deriving constraining upper limits on the flux of 81."
 The corresponding upper limit given in Table [I] should thus be considered as conservative., The corresponding upper limit given in Table \ref{tab-ana_results} should thus be considered as conservative.
" A significant signal is found in the vicinity of 883, with a TS=30.1 (5.507)."," A significant signal is found in the vicinity of 83, with a TS=30.1 $\sigma$ )."
" However, the best-fit position of the excess turns out to be compatible with the nominal position of a blazar, 33100, lying at ffrom the position of 883."," However, the best-fit position of the excess turns out to be compatible with the nominal position of a blazar, 3100, lying at from the position of 83."
" The ssource is not spatially compatible with 883, as can be seen in the count map shown in Fig."," The source is not spatially compatible with 83, as can be seen in the count map shown in Fig."
 [I] for the GGeV energy range., \ref{fig-M83_map} for the GeV energy range.
 3342 lies at ffrom the Galactic plane., 342 lies at from the Galactic plane.
" Given the proximity of the Galactic plane for this source lying at b=+10.6deg, we extracted the events from a region of oof radius centred on a position displaced by ttowards north-east compared to the nominal position of 3342, in order to reduce the fraction of the emission from the Galactic background in the region of interest."," Given the proximity of the Galactic plane for this source lying at $b=+10.6\deg$, we extracted the events from a region of of radius centred on a position displaced by towards north-east compared to the nominal position of 342, in order to reduce the fraction of the emission from the Galactic background in the region of interest."
" For this analysis, four sources were added to the source model in addition to those from the 1FGL catalogue, and the signal extracted around 3342 amounts to 1.3σ."," For this analysis, four sources were added to the source model in addition to those from the 1FGL catalogue, and the signal extracted around 342 amounts to $\sigma$."
" The two galaxies 11 and 22 are separated by only0.68°,, making it difficult to derive high-energy properties for these two objects separately withFermi/LAT,, given the angular resolution of theLATI]."," The two galaxies 1 and 2 are separated by only, making it difficult to derive high-energy properties for these two objects separately with, given the angular resolution of the."
" Moreover, they are located at less than ffrom the Galactic plane."," Moreover, they are located at less than from the Galactic plane."
" For this reason, no precise constraints on their supernova rate or the total gas mass were found in the literature."," For this reason, no precise constraints on their supernova rate or the total gas mass were found in the literature."
 994 is a spiral galaxy viewed almost face-on., 94 is a spiral galaxy viewed almost face-on.
" The closest source from the 1FGL catalogue lies at ~4° ffrom 994, easing any analysis of this region."," The closest source from the 1FGL catalogue lies at $\sim$ from 94, easing any analysis of this region."
 The signal extraction from 994 amounts to 0.00., The signal extraction from 94 amounts to $\sigma$ .
S. Turck-Chiezze and It. Ciarcia for stimulating discussions and helioseismic analysis.,S. Turck-Chièzze and R. Garcia for stimulating discussions and helioseismic analysis.
 The authors would like also to thank the referee D. Jungman for his valuable suggestions that [σας to. improve the original manuscript., The authors would like also to thank the referee D. Jungman for his valuable suggestions that lead to improve the original manuscript.
 SIL is supported by a Marie. Curie Fellowship of the European Community under the contract LIPAIFCT-2000-00607., SHH is supported by a Marie Curie Fellowship of the European Community under the contract HPMFCT-2000-00607.
 LPL is grateful for support by a grant from FundactikzmarkmainDocdyvInd5107mainBodystart5108a00 para a Cienneia e Tecnologia., IPL is grateful for support by a grant from Funda\c{c}\\tikzmark{mainBodyEnd5107}\~\tikzmark{mainBodyStart5108}aoo para a Ciênncia e Tecnologia.
formation rates are very different.,formation rates are very different.
 The use of simulation ALATIS allows us to determine the aceretion epoch of a satellite aud follow its mass loss due to tidal stripping. G, The use of simulation MAHs allows us to determine the accretion epoch of a satellite and follow its mass loss due to tidal stripping. (
i) At cach time output we calculate the accreted mass since the last time step. AM.,"ii) At each time output we calculate the accreted mass since the last time step, $\Delta M$."
" We increase the total eas mass. M. ta the satellite bv the amouut of cold gas iu a single halo with the mass AAL at that epoch: AM,=modelsF,UM. )AM."," We increase the total gas mass, $M_g$, in the satellite by the amount of cold gas in a single halo with the mass $\Delta M$ at that epoch: $\Delta M_g = f_g(M,z) \Delta M$ ."
" The fraction f, takes into account the of barvous by extragalactic UV flux. using the filtering scale parametrization of αμα taking the redshift of reionization to be 2,=7."," The fraction $f_g$ takes into account the photoevaporation of baryons by extragalactic UV flux, using the filtering scale parametrization of and taking the redshift of reionization to be $z_r =
7$."
 See Appeucdix Bo aud equation (D 19) for details., See Appendix \ref{sec:filter} and equation \ref{eq:fg}) ) for details.
 After the satellite enters the host halo. the accretion of new eas is halted aud the disk scale length is fixed. although stars may continue to form from the reaming reservoir of cold gas.," After the satellite enters the host halo, the accretion of new gas is halted and the disk scale length is fixed, although stars may continue to form from the remaining reservoir of cold gas."
 We distribute the eas on a spherically svuuuctric eric of 50 radial shells. according to the surface deusity of an expoucutial disk: X4(r)=XMXoexp(παν ," We distribute the gas on a spherically symmetric grid of 50 radial shells, according to the surface density of an exponential disk: $\Sigma_g(r) = \Sigma_0 \exp{(-r/r_{\rm d})}$."
"We use the observed Sclunidt law of star formation to estimate the star formationrate: X,=2.5«10.!(Ny/AL.pe2)L-1ALD~ "," We use the observed Schmidt law of star formation to estimate the star formation rate: $\dot{\Sigma}_* = 2.5\times 10^{-4} \, (\Sigma_g / M_{\sun} \,
\mbox{pc}^{-2})^{1.4} \, M_{\sun} \, \mbox{kpc}^{-2}$."
"Onlv the shells above the threshold X,2X=5AL.pe form stars(?)"," Only the shells above the threshold $\Sigma_g > \Sigma_{\rm th} \equiv 5 \
M_{\sun} \, \mbox{pc}^{-2}$ form stars. ("
.. i) The scale leugth of the disk is determined by its aueular momentum.,iii) The scale length of the disk is determined by its angular momentum.
 For a rotationally-supported disk it is approximately rg=27Aray.," For a rotationally-supported disk it is approximately $r_{\rm d}
= 2^{-1/2} \lambda \, r_{\rm vir}$."
" The value of the angular 1ionmientun parameter is draw raudouly from the probability distribution with A=0.015. a,= 0.56. according to the latest measurement by?7."," The value of the angular momentum parameter is drawn randomly from the probability distribution with $\bar{\lambda} = 0.045$, $\sigma_\lambda = 0.56$ , according to the latest measurement by."
. This is a kev assuuption of the models of ealaxy formation., This is a key assumption of the semi-analytic models of galaxy formation.
" However, suall halos at high redshift could oulv cool by atomic hydrogen to about 10 Is. Tf their virial temperature is only slightly above that equilibrium temperature. the gas would uot be able to dissipate enough to reach a supported state."," However, small halos at high redshift could only cool by atomic hydrogen to about $10^4$ K. If their virial temperature is only slightly above that equilibrium temperature, the gas would not be able to dissipate enough to reach a rotationally-supported state."
 Instead. its distribution would be more extended. which can have important implication for the star formation with a density threshold X.," Instead, its distribution would be more extended, which can have important implication for the star formation with a density threshold $\Sigma_{\rm th}$."
 This effect is particularly inportaut for dwarf halos, This effect is particularly important for dwarf halos.
 We inodel the effect of inefiicicut dissipation by adopting the expausion factor that depends on the ratio of the viral temperature to the equilibrium temperature of 10! Ix. The eas would reach a Doltzinaun distribution with the density. ALroyexp(®f/AT). where © is the potentiμασι energv.," We model the effect of inefficient dissipation by adopting the expansion factor that depends on the ratio of the virial temperature to the equilibrium temperature of $10^4$ K. The gas would reach a Boltzmann distribution with the density $M/r^3 \propto
\exp{(-\Phi/kT)}$, where $\Phi$ is the potential energy."
 Using the maxima circular velocityinstead of the temperature and ignoring the slow variation of the potential. we can express the scale leneth of the gas as rqκexpDuu. where eds a normalization factor and VW)=16.7 hans + is the virial velocity corresponding to Των=10! K. We find that e=10 is a best fit to the abundance aud radial distribution of the Local Gxoup ealaxies (see refsecisfresults)).," Using the maximum circular velocityinstead of the temperature and ignoring the slow variation of the potential, we can express the scale length of the gas as $r_{\rm d} \propto \exp{\left[c (V_4/V_{\rm m})^2\right]}$, where $c$ is a normalization factor and $V_4 = 16.7$ km $^{-1}$ is the virial velocity corresponding to $T_{\rm vir} = 10^4$ K. We find that $c = 10$ is a best fit to the abundance and radial distribution of the Local Group galaxies (see \\ref{sec:sfresults}) )."
 This scaling also provides a good description of the extent of the eas within halos in cosmological galaxy formation simulation described in?., This scaling also provides a good description of the extent of the gas within halos in cosmological galaxy formation simulation described in.
. Thus. we set tle size of the gascous disk at cach time step to he Of course. rq is not allowed to exceed the tidal radius of the halo. (;.," Thus, we set the size of the gaseous disk at each time step to be Of course, $r_{\rm d}$ is not allowed to exceed the tidal radius of the halo, $r_{\rm t}$."
" The eas in large halos with Vj,2Vy cau cool cficicutly aud reach rotational support. but for small halos with Vi,2V, the extended distribution reduces the central concentration of the eas aud hinders star formation. ("," The gas in large halos with $V_{\rm m} \gg V_4$ can cool efficiently and reach rotational support, but for small halos with $V_{\rm m} \gtrsim V_4$ the extended distribution reduces the central concentration of the gas and hinders star formation. ("
iv) Strong tidal forces. such as in the interacting or mereine galaxies. may lead to a burst of star formation throughout the dwarf galaxy.,"iv) Strong tidal forces, such as in the interacting or merging galaxies, may lead to a burst of star formation throughout the dwarf galaxy."
 The association of starbursts with strong peaks of the tidal force is motivated by theoretical and. to a certain extent. by observatious(?).," The association of starbursts with strong peaks of the tidal force is motivated by theoretical models and, to a certain extent, by observations."
. photoevaporfibielut ter suggest that the tidally-trigecred star formation in the SMC can be accurately modeled as au mstautaueous burst of star formation., The latter suggest that the tidally-triggered star formation in the SMC can be accurately modeled as an instantaneous burst of star formation.
 find the best fit to them data when the star formation rate (SFR) varies as kr.£P with the distance to the Galaxy., find the best fit to their data when the star formation rate (SFR) varies as $r^{-4.6}$ with the distance to the Galaxy.
 The tidal interaction parameter. La (seo oq. [AT].," The tidal interaction parameter, $I_{\rm tid}$ (see eq. \ref{eq:Itidsum}] ]),"
 that reflects the integrated effect. of a single tidal shock. is the most natural candidate for he parainetrization of the tidallv-trigeered SER.," that reflects the integrated effect of a single tidal shock, is the most natural candidate for the parametrization of the tidally-triggered SFR."
 Tenorine he adiabatic correction. it varies with the distance to he perturber approximately as TigXs| (but sec the discussion ins 6.2)).," Ignoring the adiabatic correction, it varies with the distance to the perturber approximately as $I_{\rm tid} \propto r^{-4}$ (but see the discussion in \ref{sec:sfresults}) )."
 We allow for the starburst modeof star formation. when the tidal+ interaction+- parameter exceeds a threshold value.," We allow for the starburst modeof star formation, when the tidal interaction parameter exceeds a threshold value."
 After experimenting with different thresholds. we find that La=ds10° 7 provides the best simultaneous fit to the velocity function aud spatial distribution of the satellites.," After experimenting with different thresholds, we find that $I_{\rm tid,th} = 4\times 10^3$ $^{-2}$ provides the best simultaneous fit to the velocity function and spatial distribution of the satellites."
 Iu all radial shells. a fraction f.=Tigεν10!Gyr.? Qvith a masinnun of f.=0.5) of the available gas is converted iuto stars iustanutancously," In all radial shells, a fraction $f_* = {I_{\rm tid} / 4\times 10^4 \ \mbox{Gyr}^{-2}}$ (with a maximum of $f_* = 0.5$ ) of the available gas is converted into stars instantaneously."
 The normalization of f. is somewhat arbitrary aud cau be adjusted to fit the stellar masses of the satellites., The normalization of $f_*$ is somewhat arbitrary and can be adjusted to fit the stellar masses of the satellites.
 Since the starburst changes drastically the distribution of gas in the ealaxy. new iufalliug gas may have a very differcut augular momentum.," Since the starburst changes drastically the distribution of gas in the galaxy, new infalling gas may have a very different angular momentum."
 Therefore. after cach starburst we recalculate the value of A according to eq. (3)).," Therefore, after each starburst we recalculate the value of $\lambda$ according to eq. \ref{eq:lambda}) )."
" The external tidal force determines the triucation radius PR, of the satellite. outside which all stars aud gas are lost."," The external tidal force determines the truncation radius $R_{\rm t}$ of the satellite, outside which all stars and gas are lost."
 Tn a static eravitational field. the radius of the Roche lobe is set by the condition that the average deusity ofmatter n rotationallv-the satellite equals twice the local ambiceut density (for tho isothermal sphere potential).," In a static gravitational field, the radius of the Roche lobe is set by the condition that the average density of matter in the satellite equals twice the local ambient density (for the isothermal sphere potential)."
 Ina dyuauidc situation of the satellite on an eccentric orbit experiencing tidal shocks. the truncatiou depends on the time-varving tidal force.," In a dynamic situation of the satellite on an eccentric orbit experiencing tidal shocks, the truncation depends on the time-varying tidal force."
 However. using N-body simulations of the dvuamical evolution of galaxies in clusters. πόνος that the truncation radius can be accurately described by the same condition. PR)=2pra. where the effective tidal deusity pri is related to the trace of the tidal tensor via The truncation occurs near the maxi of the tidal force along the orbit. usually at the perigalactic distance.," However, using $N$ -body simulations of the dynamical evolution of galaxies in clusters, showed that the truncation radius can be accurately described by the same condition, $\rho_{\rm av}(R_{\rm t}) = 2 \, \rho_{\rm tid}$, where the effective tidal density $\rho_{\rm tid}$ is related to the trace of the tidal tensor via The truncation occurs near the maximum of the tidal force along the orbit, usually at the perigalactic distance."
 The knowledge of the external tidal force also allows us to estimate the tidal heating of stars im the satellite., The knowledge of the external tidal force also allows us to estimate the tidal heating of stars in the satellite.
 After cach tidal shock. typically once per orbit. the velocity dispersion of stars in cach radial shell increases by the amount The mass-weighted dispersion σ may serve as an indicator of the morphological type of the satellite.," After each tidal shock, typically once per orbit, the velocity dispersion of stars in each radial shell increases by the amount The mass-weighted dispersion $\sigma$ may serve as an indicator of the morphological type of the satellite."
 In 86.2.. we adopt the ratio of the rotation velocity to the velocity dispersion. (ror /0. a8 à possible criterion.," In \ref{sec:sfresults}, , we adopt the ratio of the rotation velocity to the velocity dispersion, $v_{\rm rot}/\sigma$ , as a possible criterion."
 In practice. we compute (i as the circular velocity of the NEW. haloat the radius enclosing all bouud stars.," In practice, we compute $v_{\rm rot}$ as the circular velocity of the NFW haloat the radius enclosing all bound stars."
main elements of the calculation.,main elements of the calculation.
 The eigenvalue problem is formulated in terms of perturbation variables that are conserved when advected., The eigenvalue problem is formulated in terms of perturbation variables that are conserved when advected.
" These are the perturbed mass flux |2óp/p-v,/v,. Bernoulli flux f=vv,c/(— 1). entropy ó$2(5—1)![spp-5óàp p]. and an entropy-vortex combination 6K27v(V.«ów)-((641p/pS (see also eq. [A33]D."," These are the perturbed mass flux $h = \delta\rho/\rho +\delta v_r/v_r$, Bernoulli flux $f = v_r\delta v_r + \delta c^2/(\gamma-1)$ , entropy $\delta S = (\gamma-1)^{-1}\left[\delta p/p - \gamma\delta \rho/\rho\right]$ , and an entropy-vortex combination $\delta K = r^2\mathbf{v}\cdot(\nabla\times\delta\mathbf{w}) +
\ell(\ell+1)(p/\rho)\delta S$ (see also eq. \ref{eq:K_redef}] ]),"
 with c2sp/p. v the velocity. and w the vorticity.," with $c^2 = \gamma p/\rho$, $\mathbf{v}$ the velocity, and $\mathbf{w}$ the vorticity."
 Perturbations are decomposed in Fourier modes in time and spherical harmonics in the angular direction. having the general form where dg(r) is the complex amplitude. Υ is a spherical harmonic. and the complex frequency satisfies w=vo.+ Ross.," Perturbations are decomposed in Fourier modes in time and spherical harmonics in the angular direction, having the general form where $\delta \tilde{q}(r)$ is the complex amplitude, $Y_\ell^m$ is a spherical harmonic, and the complex frequency satisfies $\omega = \omega_{\rm{osc}} + i\omega_{\rm{grow}}$ ."
" This choice results in all thermodynamic variables along with àv, being proportional to Υ (corresponding to modes. e.g. ?))."," This choice results in all thermodynamic variables along with $\delta v_r$ being proportional to $Y_\ell^m$ (corresponding to modes, e.g. \citealt{andersson01}) )."
" The transverse components of the velocity involve angular derivatives of the Y"". and have the same radial amplitude (Appendix A)). The system of ordinary differential equations that determines the complex amplitudes is independent of— the azimuthal number # of the mode."," The transverse components of the velocity involve angular derivatives of the $Y_\ell^m$, and have the same radial amplitude (Appendix \ref{sec:v_trans}) ), The system of ordinary differential equations that determines the complex amplitudes is independent of the azimuthal number $m$ of the mode."
 Boundary conditions at the shock are expressed in terms proportional to the shock displacement AC. or the shock velocity Av2—iwAc.," Boundary conditions at the shock are expressed in terms proportional to the shock displacement $\Delta \xi$, or the shock velocity $\Delta v = -i\omega \Delta \xi$."
" By imposing àv,(7.)=O at the inner boundary. a complex eigenvalue το is obtained for a given set of flow parameters."," By imposing $\delta \tilde{v}_r(r_*) = 0$ at the inner boundary, a complex eigenvalue $\omega$ is obtained for a given set of flow parameters."
 For each {. a discrete set of overtones is obtained. which are related to the number of nodes in the radial direction (??)..," For each $\ell$, a discrete set of overtones is obtained, which are related to the number of nodes in the radial direction \citep{F07,FT09a}."
 The resulting eigenmodes have both real and imaginary eigenfrequencies., The resulting eigenmodes have both real and imaginary eigenfrequencies.
 For fixed 5. ντι. and functional form of the cooling function. the eigenfrequencies of the SASI depend only on the relative size of the shock and accreting star. quantified by the ratio r../7o.," For fixed $\gamma$, $\mathcal{M}_1$ , and functional form of the cooling function, the eigenfrequencies of the SASI depend only on the relative size of the shock and accreting star, quantified by the ratio $r_*/\rs0$."
 Time-dependent studies of individual SASI modes are possible by choosing model parameters such that only the fundamental mode is unstable. for a given (.," Time-dependent studies of individual SASI modes are possible by choosing model parameters such that only the fundamental mode is unstable, for a given $\ell$ ."
 Based on the fact that the relevant modes in more realistic core-collapse simulations are (=1. and 2. we adopt two configurations for single-mode studies: 7./79=0.5 for (=1. and οςπρ=0.6 for (2 (see ?| and ? for more extended parameter studies of the SASI e1genfrequencies).," Based on the fact that the relevant modes in more realistic core-collapse simulations are $\ell =1$, and $2$, we adopt two configurations for single-mode studies: $r_*/\rs0 = 0.5$ for $\ell=1$, and $r_*/\rs0 = 0.6$ for $\ell=2$ (see \citealt{F07} and \citealt{FT09a} for more extended parameter studies of the SASI eigenfrequencies)."
 In addition. we explore a configuration with a larger postshock cavity. r.{ro=0.2. to more closely resemble actual stalled supernova shocks.," In addition, we explore a configuration with a larger postshock cavity, $r_*/\rs0 = 0.2$, to more closely resemble actual stalled supernova shocks."
 In this case unstable overtones of (=| and (2 are present., In this case unstable overtones of $\ell=1$ and $\ell=2$ are present.
 To facilitate visualization. and unless otherwise noted. we employ the representation of spherical harmonies.," To facilitate visualization, and unless otherwise noted, we employ the representation of spherical harmonics."
 For I. one has This basis is entirely equivalent to the one involving complex exponentials imn azimuth (e.g.. ?)) but has a straightforward interpretation: equations (4)). (5)). and (6)) are dipoles in the z-. x-. and y-directions. respectively.," For $\ell=1$ , one has This basis is entirely equivalent to the one involving complex exponentials in azimuth (e.g., \citealt{arfken05}) ), but has a straightforward interpretation: equations \ref{eq:Y_z}) ), \ref{eq:Y_x}) ), and \ref{eq:Y_y}) ) are dipoles in the z-, x-, and y-directions, respectively."
" Por (22, we have corresponding to the usual z-symmetrie quadrupole (Y?). and a series of 4-striped ""beach balls"" with alternating polarity and symmetry axis along x (Y). y ο, and z (27)."," For $\ell=2$, we have corresponding to the usual z-symmetric quadrupole $Y_2^0$ ), and a series of 4-striped ""beach balls"" with alternating polarity and symmetry axis along $\hat x$ $Y_2^1$ ), $\hat y$ $Y_2^{-1}$ ), and $\hat z$ $Y_2^{\pm 2}$ )."
" Whenever necessary. we will denote the traditional as Y""."," Whenever necessary, we will denote the traditional as $\Upsilon_\ell^m$."
 We perform time-dependent hydrodynamic calculations to verify the evolution of linear SASI eigenmodes in. three dimensions. covering the linear and nonlinear phases.," We perform time-dependent hydrodynamic calculations to verify the evolution of linear SASI eigenmodes in three dimensions, covering the linear and nonlinear phases."
 To this end. we employ the publicly available code Zeus-MP (?).. which solves the Euler equations using a finite difference algorithm that includes artificial viscosity for the treatment of shocks.," To this end, we employ the publicly available code Zeus-MP \citep{hayes06}, which solves the Euler equations using a finite difference algorithm that includes artificial viscosity for the treatment of shocks."
 The default version. of the code supports an ideal gas equation of state and point mass gravity., The default version of the code supports an ideal gas equation of state and point mass gravity.
 We have extended it to account for optically thin cooling and a tensor artificial viscosity. for a better shock treatment in curvilinear coordinates (e.g.. 2.. 2.. 2)).," We have extended it to account for optically thin cooling and a tensor artificial viscosity, for a better shock treatment in curvilinear coordinates (e.g., \citealt{stone92}, \citealt{hayes06}, \citealt{iwakami08}) )."
 Issues associated with implementing the latter are discussed in Appendix 2.., Issues associated with implementing the latter are discussed in Appendix \ref{sec:zeus}. .
 The initial conditions are set by the steady-state accretion flow used in linear stability calculations., The initial conditions are set by the steady-state accretion flow used in linear stability calculations.
 To prevent runaway cooling at the base of the flow. we impose a gaussian cutoff in the cooling with entropy (?)..," To prevent runaway cooling at the base of the flow, we impose a gaussian cutoff in the cooling with entropy \citep{FT09a}."
 The normalization of the cooling function is adjusted so that the Mach number at the surface of the accreting star is ME~1077., The normalization of the cooling function is adjusted so that the Mach number at the surface of the accreting star is $\mathcal{M}\sim 10^{-2}$.
 Spherical polar coordinates (7.7.0) are used. covering the whole sphere minus a cone of half-opening angle 5 degrees around the polar axis.," Spherical polar coordinates $r,\theta,\phi$ ) are used, covering the whole sphere minus a cone of half-opening angle $5$ degrees around the polar axis."
 This prescription does not significantly alter the flow dynamics. and ameliorates the severe Courant-Friedrichs-Lewy restriction around the polar axis (H-Th.," This prescription does not significantly alter the flow dynamics, and ameliorates the severe Courant-Friedrichs-Lewy restriction around the polar axis (H-Th."
 Janka. private communication).," Janka, private communication)."
 We present convergence studies in Appendix 2 showing that only ~10% differences relative to using the full sphere are introduced with this prescription., We present convergence studies in Appendix \ref{sec:zeus} showing that only $\sim 10\%$ differences relative to using the full sphere are introduced with this prescription.
 Cells are uniformly spaced in the polar and azimuthal directions. while ratioed in radius.," Cells are uniformly spaced in the polar and azimuthal directions, while ratioed in radius."
 The choice of grid spacing is key to a achieve a stable background solution and to adequately capture linear growth rates. while minimizing the computational cost.," The choice of grid spacing is key to a achieve a stable background solution and to adequately capture linear growth rates, while minimizing the computational cost."
 The radial size of the cells at r= 7. Arn. determines how stable the unperturbed shockremains. because near hydrostatic equilibrium needs to be maintained.," The radial size of the cells at $r=r_*$ , $\Delta r_{\rm min}$, determines how stable the unperturbed shockremains, because near hydrostatic equilibrium needs to be maintained."
 At the shock. the angular size determines howwell growth rates are captured.," At the shock, the angular size determines howwell growth rates are captured."
 Based on numerical experiments. we have found that μμ<1074 is required to obtain a stable shockwithin 500 dynamical times. and that 36 cells in thepolar direction is the minimum needed to obtain a clean shockoscillation (oy within =10% and wo. within ~20% from the linear stability value: convergence," Based on numerical experiments, we have found that $\Delta r_{\rm min} < 10^{-3}\rs0$ is required to obtain a stable shockwithin $500$ dynamical times, and that 36 cells in thepolar direction is the minimum needed to obtain a clean shockoscillation $\omega_{\rm osc}$ within $\lesssim 10\%$ and $\omega_{\rm grow}$ within $\sim 20\%$ from the linear stability value; convergence"
 (e.@.Macauetal.1993:Laarsma2000:Calzetà2007:etal.2005:TakeuchiMannucei2007:Martin2008).," \citep[e.g. ][]{mad98,haa00,cal07,lef05,tak05,man07,mar08}."
. (5pilzer) Spitzer e ~ (e.g.Genzeletal.1998:Rigopoulou2000:Peetersοἱ2004:2," $Spitzer$ $Spitzer$ $\sim$ $\sim$ \citep[e.g. ][]{gen98,rig00,pee04,for04}."
004).. (Drandletal.2006)  etal.2008).," \citep{bra06} $\sim$ \citep{pop08,far08}."
. << , $<$$\la$ 
The form of this conic section is that of an ellipse.,The form of this conic section is that of an ellipse.
 From this it is now possible to conclude that the peak of the normal moveout curve will trace an elliptical trajectory in the ./—f plane. with a continuous change in the dip angle. 0.," From this it is now possible to conclude that the peak of the normal moveout curve will trace an elliptical trajectory in the $x$ $t$ plane, with a continuous change in the dip angle, $\theta$."
 While this entire algebraic exercise looks very elegant in principle. it fails hopelessly in addressing a serious practical problem.," While this entire algebraic exercise looks very elegant in principle, it fails hopelessly in addressing a serious practical problem."
 The derivation of Eq. (4)), The derivation of Eq. \ref{hyper2}) )
 has been done with the help of a single source-receiver patr., has been done with the help of a single source-receiver pair.
 Πο that every source-receiver pair in a full array of sources and receivers will have a point of reflection from the inclined subsurface., It that every source-receiver pair in a full array of sources and receivers will have a point of reflection from the inclined subsurface.
 this is not possible to achieve in practice., this is not possible to achieve in practice.
 If anything. for a realistic arrangement of source-receiver arrays.point.," If anything, for a realistic arrangement of source-receiver arrays,."
 Therefore. unlike the simple representation in Fig. 1..," Therefore, unlike the simple representation in Fig. \ref{f1},"
 there will be no common depth point vertically below the common midpoint of the source receiver arrays., there will be no common depth point vertically below the common midpoint of the source receiver arrays.
 Being unmindful of this crucial point will only serve to furnish an erroneous impression of the subsurface depth. of the kind that has been schematically shown in Fig. 4..," Being unmindful of this crucial point will only serve to furnish an erroneous impression of the subsurface depth, of the kind that has been schematically shown in Fig. \ref{f3}."
" This fact categorically precludes the simple approach of determining the value of ο, using the arguments which have been presented following Eq. (3))."," This fact categorically precludes the simple approach of determining the value of $d$, using the arguments which have been presented following Eq. \ref{nmo}) ),"
 at the end of Section 1.., at the end of Section \ref{sec1}.
 The difficulties do not end here., The difficulties do not end here.
 In actual fact the situation is vastly more complicated., In actual fact the situation is vastly more complicated.
 The dipping reflectors will have a varying gradient from one spatial position to another. as opposed to being at a constant incline with respect to the horizontal. shown in Fig. 3..," The dipping reflectors will have a varying gradient from one spatial position to another, as opposed to being at a constant incline with respect to the horizontal, shown in Fig. \ref{f2}."
 Besides this. there will be geological faults. and the propagation velocity of the seismic waves will also have a variation with respect to the depth.," Besides this, there will be geological faults, and the propagation velocity of the seismic waves will also have a variation with respect to the depth."
 All of these facts will combine to render the accurate imaging of the subsurface a quite formidable task., All of these facts will combine to render the accurate imaging of the subsurface a quite formidable task.
 Nevertheless. all reflection seismic records must be corrected for non-vertical reflections.," Nevertheless, all reflection seismic records must be corrected for non-vertical reflections."
 This evidently complicated process of correction is what is. for all practical purposes. implied by the termmigration.," This evidently complicated process of correction is what is, for all practical purposes, implied by the term."
 It purports to shift all dipping reflections to their true subsurface positions 2001)..," It purports to shift all dipping reflections to their true subsurface positions \citep{lowrie, yilmaz}."
 Another important point has to be stressed here., Another important point has to be stressed here.
 So far the entire discussion has accounted for dip and subsurface variations in the direction (Yilmaz2001).. 1.8. the direction along which the source-receiver arrays have been lined up.," So far the entire discussion has accounted for dip and subsurface variations in the direction \citep{yilmaz}, i.e. the direction along which the source-receiver arrays have been lined up."
 This means that the analytical treatment presented so far has been confined to a 2D plane only — along the vertical depth (given by the - coordinate) and along the offset direction (given by the ο coordinate)., This means that the analytical treatment presented so far has been confined to a $2D$ plane only — along the vertical depth (given by the $z$ coordinate) and along the offset direction (given by the $x$ coordinate).
 However. practically speaking. variations im the subsurface will also take place in the direction (Yilmaz206010.. 1.8. along the y axis.," However, practically speaking, variations in the subsurface will also take place in the direction \citep{yilmaz}, i.e. along the $y$ axis."
 So a comprehensive migration process must account for all variations along all the three spatial, So a comprehensive migration process must account for all variations along all the three spatial
Tn this paper. we discuss the properties of the iuner ouffed-up rim which forms in circumstellar disks wheu dust evaporates.,"In this paper, we discuss the properties of the inner puffed-up rim which forms in circumstellar disks when dust evaporates."
 The rim existence has been arene or. starting from the work of Natta ct al. (," The rim existence has been argued for, starting from the work of Natta et al. ("
2001). voth on theoretical aud observational grounds.,"2001), both on theoretical and observational grounds."
 Tere. we investigate the shape of the illuniuated face of the rim.," Here, we investigate the shape of the illuminated face of the rim."
 We argue that this shape is controlled. by a fundamental xopertv of circtuustellar disks. namely their verv large vertical density eradicut. through the dependence of eran evaporation temperature on density.," We argue that this shape is controlled by a fundamental property of circumstellar disks, namely their very large vertical density gradient, through the dependence of grain evaporation temperature on density."
" As a result. the bright side of the vim is naturallyeurveed. rather thanvertical, as expected when a constant evaporation temperature is asstuned."," As a result, the bright side of the rim is naturally, rather than, as expected when a constant evaporation temperature is assumed."
 We lave COMM?)5 a nmunber of riu models. which take into account this effect in a selfconsisteut wav.," We have computed a number of rim models, which take into account this effect in a self-consistent way."
 A ΠΤΙΟΙ of approximations have been necessary to perform the calculations. and we discuss their validitv.," A number of approximations have been necessary to perform the calculations, and we discuss their validity."
" We thiuk tha the basic result νο, the curved shape of the rin iluuinate face) is in fact quite robust."," We think that the basic result (i.e., the curved shape of the rim illuminated face) is in fact quite robust."
 For a ogiven star. the rin properties depend imostlv ou the properties of the erains. aud very little on those of the disk itself. or example the exact value of the surface densitv.," For a given star, the rim properties depend mostly on the properties of the grains, and very little on those of the disk itself, for example the exact value of the surface density."
 The distauce of he riu from the y.star ls eteyruiued bv the evaporation temperature (at the density of the disk midplane) of the dust species that has the highest evaporation temperature. as loug as its opacity is sufficient to make the disk very optically thick: in the model of Pollack et al. (019913) ," The distance of the rim from the star is determined by the evaporation temperature (at the density of the disk midplane) of the dust species that has the highest evaporation temperature, as long as its opacity is sufficient to make the disk very optically thick; in the model of Pollack et al. \cite{PH94}) )"
of the dust. in accretion disks. silicates have the highest evaporation temperature.," of the dust in accretion disks, silicates have the highest evaporation temperature."
 Therefore. we have assmmed in our models dust mace of astronomical silicates. aud varied their size over a large range of values.," Therefore, we have assumed in our models dust made of astronomical silicates, and varied their size over a large range of values."
 We find that the run properties do not depend on size as soon as ez 1.540: the values of the rim radi observed with interferometers sugeest that i many pre-aunainsequence disks eras have erown to sizes of fow san at least., We find that the rim properties do not depend on size as soon as $a \simgreat 1.3\mu$ m; the values of the rim radii observed with interferometers suggest that in many pre-main–sequence disks grains have grown to sizes of 1--few $\mu$ m at least.
 The curved riui fas the vertical ria) cuits most of its radiation in the near aud mid-IR. aud provides a simple explanation to the observed values of the near-IR excess (the “3 yan bump” of Herbie. Ac stars}.," The curved rim (as the vertical rim) emits most of its radiation in the near and mid-IR, and provides a simple explanation to the observed values of the near-IR excess (the “3 $\mu$ m bump"" of Herbig Ae stars)."
" Contrary. to the vertical rin. for curved rus the near-IR excess does not depend much on the inclination. bee maxinuun for face-on objects and ouly somewhat sinaller for Lighly inclined ones,"," Contrary to the vertical rim, for curved rims the near-IR excess does not depend much on the inclination, being maximum for face-on objects and only somewhat smaller for highly inclined ones."
 This is in agrecment with the apparent similarity of the observed near-IR SED between objects secu face-on and close to edge-on., This is in agreement with the apparent similarity of the observed near-IR SED between objects seen face-on and close to edge-on.
" Finally, we have computed svuthetic nuages of the curved rim seen uuder differeut inclinatious."," Finally, we have computed synthetic images of the curved rim seen under different inclinations."
 Face-on rius are seen as bright. centrally sviuuetric riugs on the sky: increasing the inclination. the rim takes an elliptical shape. with oue side brighter than the other.," Face-on rims are seen as bright, centrally symmetric rings on the sky; increasing the inclination, the rim takes an elliptical shape, with one side brighter than the other."
 However. the brightness distribution of curved rims remains at any iuclination much more centrally svuuuetric than that of vertical ones.," However, the brightness distribution of curved rims remains at any inclination much more centrally symmetric than that of vertical ones."
 In a forthcoming paper (Isella et al., In a forthcoming paper (Isella et al.
 2005) we will discuss the application of the curved rim models to the interpretation of uear-IR interferometric observations of disks., 2005) we will discuss the application of the curved rim models to the interpretation of near-IR interferometric observations of disks.
svmametrey axes of the central elliptical lens.,symmetry axes of the central elliptical lens.
 Comparing the crosses to the circles we find that the introduction. of foreground SIS [enses does little to alfect the ratio of the tangential shears when the intrinsic svmmctry axes of the central elliptical lens are used for the calculation., Comparing the crosses to the circles we find that the introduction of foreground SIS lenses does little to affect the ratio of the tangential shears when the intrinsic symmetry axes of the central elliptical lens are used for the calculation.
 The squares in Figures 13-15 show 5(0)/5(0) for the case that the source galaxies are lensecl by both the central elliptical lens. as well as all foregrouncl SIS lenses.," The squares in Figures 13-15 show $\gamma^+ (\theta) / \gamma^- (\theta)$ for the case that the source galaxies are lensed by both the central elliptical lens, as well as all foreground SIS lenses."
 In addition. the central. elliptical lens has been lensed by all foreerouncl SIS lenses.," In addition, the central, elliptical lens has been lensed by all foreground SIS lenses."
 Here the svmimetry axes. used for the calculation are theobserved symmetry axes of the central elliptical lens (ic. the svimmetry axes after lensing bv the foreground. SIS. lenses)," Here the symmetry axes used for the calculation are the symmetry axes of the central elliptical lens (i.e., the symmetry axes after lensing by the foreground SIS lenses)."
 From Figures 13-15. the degree to which the observed. function. 5.(86)/*(8). is suppressed. compared to what one would obtain using the intrinsic symmetry axes of the elliptical lens is a function of the velocity. clispersion that is adopted.," From Figures 13-15, the degree to which the observed function, $\gamma^+ (\theta) /
\gamma^- (\theta)$, is suppressed compared to what one would obtain using the intrinsic symmetry axes of the elliptical lens is a function of the velocity dispersion that is adopted."
" ""Ehe lower is the velocity dispersion of the lenses. the less the observed function is suppressed."," The lower is the velocity dispersion of the lenses, the less the observed function is suppressed."
 This is due to the fact that the frequeney and strength of the multiple weak delleetions are lower for lenses with low velocity dispersions than for lenses with high velocity. dispersions (see. e... Brainercl 2010).," This is due to the fact that the frequency and strength of the multiple weak deflections are lower for lenses with low velocity dispersions than for lenses with high velocity dispersions (see, e.g., Brainerd 2010)."
 In contrast. the ellipticity. of the projected. dark matter halo of the central elliptical lens has relatively little effect on the degree to which the observed function. 5(0)/*5.(8) is suppressed. (," In contrast, the ellipticity of the projected dark matter halo of the central elliptical lens has relatively little effect on the degree to which the observed function, $\gamma^+ (\theta) / \gamma^- (\theta)$ is suppressed. ("
Note that the vertical scales in Figures 13-15 are very different from cach other due to the fact that the more elliptical is the central elliptical lens. the greater is the anisotropy that it induces.),"Note that the vertical scales in Figures 13-15 are very different from each other due to the fact that the more elliptical is the central elliptical lens, the greater is the anisotropy that it induces.)"
" In an attempt to ""inoculate one's analysis of galaxy-galaxy lensing by non-spherical haloes against the above ellects. one might consider simply rejecting bright centres with small image ellipticities from the caleulation of .(6) and (6)."," In an attempt to “inoculate” one's analysis of galaxy-galaxy lensing by non-spherical haloes against the above effects, one might consider simply rejecting bright centres with small image ellipticities from the calculation of $\gamma^+ (\theta)$ and $\gamma^- (\theta)$."
 That is. one could hope to avoid the extreme situation where a lens-source pair that is truly in the 75. 7 configuration is swapped to the 75.  configuration due to the cllipticity of the image ofthe lens being very small (and. hence. making it more susceptible to having its svmmetry axes altered significantly by weak lensing due to foreground ealaxies).," That is, one could hope to avoid the extreme situation where a lens-source pair that is truly in the $\gamma^+$ ” configuration is swapped to the $\gamma^-$ ” configuration due to the ellipticity of the image of the lens being very small (and, hence, making it more susceptible to having its symmetry axes altered significantly by weak lensing due to foreground galaxies)."
 Naivelv. one might hope that the suppression X the observed. function. .(0)(8). could. be eliminated simplv by choosing to compute the mean tangential shear using bright centres whose images are hiehly elliptical.," Naively, one might hope that the suppression of the observed function, $\gamma^+ (\theta) /
\gamma^- (\theta)$, could be eliminated simply by choosing to compute the mean tangential shear using bright centres whose images are highly elliptical."
 1n acdcdition. in a search for the signature of anisotropic ealaxv-galaxy lensing. one might be tempted. to restrict the analysis to source galaxies that are very. close to the svinmetry axes of the bright. centres that are used to calculate the mean tangential shear.," In addition, in a search for the signature of anisotropic galaxy-galaxy lensing, one might be tempted to restrict the analysis to source galaxies that are very close to the symmetry axes of the bright centres that are used to calculate the mean tangential shear."
" “Phat is. in all of the analyses above. (0) and >(@) were computed using all sources whose azimuthal coordinates. ὡς. placed them within E45"" of the symmetry axes of the bright centres."," That is, in all of the analyses above, $\gamma^+(\theta)$ and $\gamma^-(\theta)$ were computed using all sources whose azimuthal coordinates, $\varphi$, placed them within $\pm 45^\circ$ of the symmetry axes of the bright centres."
 At fixed angular separation from an elliptical lens. the maximal ilference in the shear experienced by two sources will. of course. occur when one source is located along the minor axis of the lens anc the other is located along the major axis of the lens.," At fixed angular separation from an elliptical lens, the maximal difference in the shear experienced by two sources will, of course, occur when one source is located along the minor axis of the lens and the other is located along the major axis of the lens."
" Pherefore. one might expect that if one narrowed the analysis region. [rom 445° to. sav. x25"" or"," Therefore, one might expect that if one narrowed the analysis region from $\pm 45^\circ$ to, say, $\pm 25^\circ$ or"
is sieuificautlv altered by mass loading. we require that siunultaueouxslv o and 0 axe both πα].,"is significantly altered by mass loading, we require that simultaneously $\phi$ and $\theta$ are both small."
 The similavity equations were inteeratedwith a fifth-order accurate adaptive step-size Dulirsch-Stoer method using polvuonial extrapolation to infinitesimal step size., The similarity equations were integratedwith a fifth-order accurate adaptive step-size Bulirsch-Stoer method using polynomial extrapolation to infinitesimal step size.
 Ouce the CD was reached. the similarity variables were rescaled using he relationships defined in Eq.," Once the CD was reached, the similarity variables were rescaled using the relationships defined in Eq."
" 21 so that nm""l.", \ref{eq:norm} so that $x_{cd} =1$.
 The1nass. and kinetic and thermal energies of thebubble were calculated. as were the kinetic energy of the shell aud he euergv radiated from it.," The mass, and kinetic and thermal energies of the bubble were calculated, as were the kinetic energy of the shell and the energy radiated from it."
 The correct normalization o satisfv elobal euergv conservation was then obtained., The correct normalization to satisfy global energy conservation was then obtained.
 Finally. for given values of E.Q aud f. the ΠΕ varialdes esfog aud hb may be scaled iuto the physical variables Περιd and © ," Finally, for given values of $\dot{E}, Q$ and $t$, the similarity variables $x, f, g$ and $h$ may be scaled into the physical variables $r, \rho, u$ and $\varepsilon$ ."
We fist check«de our work agaiist the solutions obtained x Dyson (1973 )) for WBBs with no mass loading., We first checked our work against the solutions obtained by Dyson \cite{D1973}) ) for WBBs with no mass loading.
 For this colparison if was required that À—3 and that o was argo., For this comparison it was required that $\lambda = -3$ and that $\phi$ was large.
 For A=) the radius ¢of wiiju nass loading lucreases as f., For $\lambda = -3$ the radius of minimum mass loading increases as $t$.
 Excelleut agreenent with Dyson (1973)) was found over a luge range of isuds, Excellent agreement with Dyson \cite{D1973}) ) was found over a large range of $x_{is}/x_{cd}$.
 For arge o icelieible mass loadiug) the value of wey.) Las 10 effect on he resulting solution., For large $\phi$ negligible mass loading) the value of $x_{ml}$ has no effect on the resulting solution.
 Fig., Fig.
 1 SLOWS a sunuple solution., \ref{fig:neg_ml} shows a sample solution.
 Tn Fie., In Fig.
 we show results for À= doc-100. with ciffereut values of Vande," \ref{fig:neg_xml} we show results for $\lambda=-3$ , $\phi=100$, with different values of $x_{ml}$."
 The amass loadi1s i1i these results is small.|»t not uceligiljo. SO that the precise value of veya |las ΠΟΥ «ώμοςueuces for f1ο solution obtained.," The mass loading in these results is small, but not negligible, so that the precise value of $x_{ml}$ has minor consequences for the solution obtained."
 In TzUle πο tabulate iiportaut piarineters from these soliions., In Table \ref{tab:xml_var} we tabulate important parameters from these solutions.
 Iu particular. woe fiud hat values for the ratio Stssup and the οjiergv fractio1s nro Very simular.," In particular, we find that values for the ratio $x_{is}/x_{cd}$ and the energy fractions are very similar."
 The freictional mass loaine of the Inble. δρ. is somewhat more seusitive to the value of η]. axd increases when the “tureon radius for mass loading is decreased. as one would expect.," The fractional mass loading of the bubble, $\Phi_{b}$, is somewhat more sensitive to the value of $x_{ml}$, and increases when the `turn-on' radius for mass loading is decreased, as one would expect."
 The presrocks Mach προ also reflects the degree of preshock mass loading. again as expected.," The preshock Mach number also reflects the degree of preshock mass loading, again as expected."
 Interestingly. the profiles of postshock Mach πο are. however. very inscusitive to the preshock Mach iuber.," Interestingly, the profiles of postshock Mach number are, however, very insensitive to the preshock Mach number."
 With tje asstuuption of constant o. we note tha κος t;tsn» varies for the above results it was nuportaun to see whetjer this was a possible factor for sole of the ciffereuces in these solutions.," With the assumption of constant $\phi$, we note that since $x_{is}/x_{cd}$ varies for the above results it was important to see whether this was a possible factor for some of the differences in these solutions."
 Therefore we also invesigated the eff(CE of different values of ο whlülst seepiug tjdug constait and varving o as necessary., Therefore we also investigated the effect of different values of $x_{ml}$ whilst keeping $x_{is}/x_{cd}$ constant and varying $\phi$ as necessary.
 We find that the resulting solutious are again fairly simular. and differ at about the samc level as t10 Yosts in the op half of Table 1..," We find that the resulting solutions are again fairly similar, and differ at about the same level as the results in the top half of Table \ref{tab:xml_var}."
" Trerefore it seenus hat varvine 0, its a direct effect on tfle results. aud uot just a1 dudirect oeuence through chauges iuduced in e;fcu and/or o."," Therefore it seems that varying $x_{ml}$ has a direct effect on the results, and not just an indirect influence through changes induced in $x_{is}/x_{cd}$ and/or $\phi$."
" Iu 1¢ following. therefore. we will vary sc, whilst keeping o xed."," In the following, therefore, we will vary $x_{ml}$ whilst keeping $\phi$ fixed."
 At the other extrel110 Fie.," At the other extreme, Fig."
 EMi shows results where 1ο value of Lapp Call have large consequeices for the Xdutious Obtained., \ref{fig:nonneg_xml} shows results where the value of $x_{ml}$ can have large consequences for the solutions obtained.
 This occurs for values of o for which je resulting mass loacling of thebub leiIs Ónporta, This occurs for values of $\phi$ for which the resulting mass loading of the bubble is important.
 Parameters frou these solutions are tabuated iu ower half of Table 1, Parameters from these solutions are tabulated in the lower half of Table \ref{tab:xml_var}.
 Although the ratio τεςcud YOU relatively iusensitive to the value of μμ. the fractio nass loadiug Q4. the ratio of the shell nass to 5 mbble mass AM/Ms. and the euergyv partition are senificautlv aflected. as Table 1 shows.," Although the ratio $x_{is}/x_{cd}$ remains relatively insensitive to the value of $x_{ml}$, the fractional mass loading $\Phi_{b}$, the ratio of the shell mass to the bubble mass $M_{sh}/M_{b}$, and the energy partition are all significantly affected, as Table \ref{tab:xml_var} shows."
 This is expec oeiven that inost of tho mass loading OCCULS near 5 nininuni nis5 loadinge radius for A=Mi2, This is expected given that most of the mass loading occurs near the minimum mass loading radius for $\lambda = -3$.
 An interesme consequence of mass loading the wine xior to f1ο Iunershock is that if the mass IoaΠιο is large. he Mach. uuuber of the flow can be reduced so iuch hat the fiOW ¢rectly connects to the contact ciscontiuuitv without t1e presenceof an imner shock.," An interesting consequence of mass loading the wind prior to the innershock is that if the mass loading is large, the Mach number of the flow can be reduced so much that the flow directly connects to the contact discontinuity without the presenceof an inner shock."
 In Fig., In Fig.
 Ll we show one solution where this happens., \ref{fig:direct_con} we show one solution where this happens.
" Iu this examje. the flow is contiuuouslv supersonic with respect to he clumps. and we obtain d;1.25 andM,Al,= 0.07."," In this example, the flow is continuously supersonic with respect to the clumps, and we obtain $\Phi_{b} = 1.25$ and$M_{sh}/M_{b} = 0.07$ ."
 This, This
"spectrum at small scales will influence το,",spectrum at small scales will influence $z_*$.
 Precise high redshift micasurements of the contributions of these two »pulatious to the f£üut-eud of the luminosity function in future surveys with e.g. the TST WEC3 will help to xu down +., Precise high redshift measurements of the contributions of these two populations to the faint-end of the luminosity function in future surveys with e.g. the HST WFC3 will help to pin down $z_*$.
 One potential problem for future survevs will be a possible bias towards cluster galaxies as they welt experieuce induced starformation (Alarcillacetal. 2007). iucreasing their surface brightuess aud makine hem more easily detectable.," One potential problem for future surveys will be a possible bias towards cluster galaxies as they might experience induced star-formation \citep{2007ApJ...654..825M}, increasing their surface brightness and making them more easily detectable."
 This effect will shift : o higher redshifts and needs to be taken iuto account carefully., This effect will shift $z_*$ to higher redshifts and needs to be taken into account carefully.
 Observational selection effects will affect the observed faiut-cnd LF-slope in Fig., Observational selection effects will affect the observed faint-end LF-slope in Fig.
 2., 2.
" Some observational selection effects (1.6.catalogueiucompletenessaudnat-uralcoufusion.Windhorstetal.2007) can make the observed faint-eud slope flatter than the true one. while others (οιοι, SB-dinunine) could make the observed slope somewhat steeper than the true one. depending on the exact intrinsic object size distribution."," Some observational selection effects \citep[i.e. catalogue incompleteness
and natural confusion,][]{2007astro.ph..3171W} can make the observed faint-end slope flatter than the true one, while others (e.g., SB-dimming) could make the observed slope somewhat steeper than the true one, depending on the exact intrinsic object size distribution."
 A nunuber of eroups correct for immconipleteness either through MC-siauulatious (e.g.Yan&Windhorst200Lb) or through cloning techniques (e.g.Dowweusoetal.2006).. and fud similar fünt-eud slopes when following differeut procedures.," A number of groups correct for incompleteness either through MC-simulations \citep[e.g.][]{2004ApJ...600L...1Y} or through cloning techniques \citep[e.g.][]{2006ApJ...653...53B}, and find similar faint-end slopes when following different procedures."
 When judging the data. however. one must keep these observational biases in iinud.," When judging the data, however, one must keep these observational biases in mind."
 Ultimately. these issues can onlv be resolved with deeper JWST data to AB=31-32 mas.," Ultimately, these issues can only be resolved with deeper JWST data to AB=31-32 mag."
 Tidal disruption of dwarf galaxies iu clusters as seen in high resolution sinulatious (Tormenctal.1998). cau iu principle change the slope à., Tidal disruption of dwarf galaxies in clusters as seen in high resolution simulations \citep{1998MNRAS.299..728T} can in principle change the slope $\alpha$.
 Our results. however. sugeest that at a transition redshitt of τν=2. the evolution of à. changes from beiug dominated by cluster ealaxics to being dominated by field galaxies.," Our results, however, suggest that at a transition redshift of $z_*=2$, the evolution of $\alpha$ changes from being dominated by cluster galaxies to being dominated by field galaxies."
 It is therefore not Likely that a large amount of the evolution Ina at iosot. as driven by tidal disruption of fuut ealaxies., It is therefore not likely that a large amount of the evolution in $\alpha$ at $z<z_*$ is driven by tidal disruption of faint galaxies.
 Au additional implication from the transition at το is that the evolution of a(2) is better fit by a linear function with a break at το., An additional implication from the transition at $z_*$ is that the evolution of $\alpha(z)$ is better fit by a linear function with a break at $z_*$.
 The flattening of the slope a with respect to the nuderlving dark matter slope sugeests the interesting possibility. of estimating the time-scale over which supernovae operate., The flattening of the slope $\alpha$ with respect to the underlying dark matter slope suggests the interesting possibility of estimating the time-scale over which supernovae operate.
 Asstuine that the first Pop II stars were formed sometime before reiouizatioun (Yau&Windhorst2001b).. and that supernovae type la originate roughlv <12 Cer after the bulk of the first Pop II star-formation. oue would expect au increase In energv injection iuto the interstellar πού. at a redshift correspouding to this time lag.," Assuming that the first Pop II stars were formed sometime before reionization \citep{2004ApJ...600L...1Y}, and that supernovae type Ia originate roughly $ \le 1-2$ Gyr after the bulk of the first Pop II star-formation, one would expect an increase in energy injection into the interstellar medium at a redshift corresponding to this time lag."
 This additional enerev input will hinder star-formation aud contribute to a further increase in the mass-to-light ratio of galaxies and lence to an even stronger flattening of the slope a., This additional energy input will hinder star-formation and contribute to a further increase in the mass-to-light ratio of galaxies and hence to an even stronger flattening of the slope $\alpha$.
 It will be crucial to have robust micasurcments of a over a wide range of redshifts to probe the ouset of the first significaut feedback contribution from type Ta supernovac., It will be crucial to have robust measurements of $\alpha$ over a wide range of redshifts to probe the onset of the first significant feedback contribution from type Ia supernovae.
" Furthermore. probing the faint-eud slope at redshifts 26. before the significant onset of type I supernovae will allow us to measure the uuderlviug dar matter slope very accurately,"," Furthermore, probing the faint-end slope at redshifts $ z>6 $, before the significant onset of type II supernovae will allow us to measure the underlying dark matter slope very accurately."
 Our approach has certain shortcomines., Our approach has certain shortcomings.
 The model presented here did not include any time delay prescriptions for the various SN types. but imstead assumed instautaueous feedback.," The model presented here did not include any time delay prescriptions for the various SN types, but instead assumed instantaneous feedback."
 More detailed modeling of the time delavs aud its influence on the faünut-eud slope will he presented clsewhere Gu. preparation)., More detailed modeling of the time delays and its influence on the faint-end slope will be presented elsewhere (in preparation).
 Our treatinent of supernovae feedback is very simplistic. and more detailed bydrodvuamical simulations imcliding a anulti-phase medium will show if this general trend which we report can be recovered.," Our treatment of supernovae feedback is very simplistic, and more detailed hydrodynamical simulations including a multi-phase medium will show if this general trend which we report can be recovered."
 First seenuerationus of such simulations indeed show that SN type II that are ecnuerated in dense star clusters explode imto bubbles of hot gas and are therefore less efficient at feedback iuto the ISM. (Mac.Low&Ferrara1999) compared to SN type Ia. which eo off at random places in the galaxy and. cau have more effect on the carly ISAL.," First generations of such simulations indeed show that SN type II that are generated in dense star clusters explode into bubbles of hot gas and are therefore less efficient at feedback into the ISM \citep{1999ApJ...513..142M} compared to SN type Ia, which go off at random places in the galaxy and, can have more effect on the early ISM."
 We would like to thank Seth Cohen. Evan Scannapieco and Richard Dowweus for helpful discussions aud the anonviious referee for lis useful comunents.," We would like to thank Seth Cohen, Evan Scannapieco and Richard Bouwens for helpful discussions and the anonymous referee for his useful comments."
 This work was supported by IST erants IIST-CGO-10530.07. (to RAW) and TST-AR-1097LOL (to RER) from STScI. which is operated by AURA for NASA under coutract NAS 5-26555. and by NASA JWST eraut NAC 5-12160 (to RAW).," This work was supported by HST grants HST-GO-10530.07 (to RAW) and HST-AR-10974.01 (to RER) from STScI, which is operated by AURA for NASA under contract NAS 5-26555, and by NASA JWST grant NAG 5-12460 (to RAW)."
defined before can then be written as and {αν(he)=PG).,"defined before can then be written as and $P_{\mathrm{h},11}(k)=b_1^2 P_{11}(k)$."
 By taking the limit &+0 of the foregoing equations. one can study the behaviou of the SPT halo power spectrum on large scales:," By taking the limit $k\rightarrow 0$ of the foregoing equations, one can study the behaviour of the SPT halo power spectrum on large scales:"
the oscillation frequency. which becomes a function of the amplitude of oscillations and explicitly on time because (he proper orbital. racial and. vertical epicvelic frequencies vary when matter approaches the neutron star surface.,"the oscillation frequency which becomes a function of the amplitude of oscillations and explicitly on time because the proper orbital, radial and vertical epicyclic frequencies vary when matter approaches the neutron star surface."
 This was discarded so far., This was discarded so far.
 However. in (his new extended. picture. the spin frequency still plavs an important role by triggering (he resonance al some prelerred radius. bringing the disk into off-plane oscillations that. are slowly advected by the flow and drift downwards to the neutron star.," However, in this new extended picture, the spin frequency still plays an important role by triggering the resonance at some preferred radius, bringing the disk into off-plane oscillations that are slowly advected by the flow and drift downwards to the neutron star."
" Therefore. 1, does nol give a clear imprint (o the precise kIIz-QDPO frequencies as it seems (nol) seen in the data. but serves to launch (the mechanism."," Therefore, $\nu_*$ does not give a clear imprint to the precise kHz-QPO frequencies as it seems (not) seen in the data, but serves to launch the mechanism."
 Moreover. these motions occur due (o matter flow influenced bv eravily in a strong field regime. and thus the ISCO plays a central role.," Moreover, these motions occur due to matter flow influenced by gravity in a strong field regime, and thus the ISCO plays a central role."
 It is not the purpose of this paper to study the drifting and non-linear terms. which will deserve full attention in another work.," It is not the purpose of this paper to study the drifting and non-linear terms, which will deserve full attention in another work."
 Here. to give a taste. we only draw the basic lines of the consequences of these effects in Appendix A..," Here, to give a taste, we only draw the basic lines of the consequences of these effects in Appendix \ref{sec:Appendix}."
 Anv model predicting a fixed frequency ratio faces difficulties to explain the data since this frequency. ratio is not only 3/2 or 4/3 (where most of the observations cluster). but covers a wider range as seen by Bellonietal.(2005).," Any model predicting a fixed frequency ratio faces difficulties to explain the data since this frequency ratio is not only 3/2 or 4/3 (where most of the observations cluster), but covers a wider range as seen by \cite{2005A&A...437..209B}."
. Although a strong linear correlation exists. it differs significantly from the 3/2 ratio. see Bellonietal.(2005) and (2005b.a)..," Although a strong linear correlation exists, it differs significantly from the 3/2 ratio, see \cite{2005A&A...437..209B} and \cite{2005AN....326..864A,
 2005ragt.meet....1A}."
 In addition. the frequency ratio clustering around the 3/2 value first found bv Abramowiczetal.(2003a) could be well explained by a uniform distribution of the lower and upper kIIz QPO set in the source.," In addition, the frequency ratio clustering around the 3/2 value first found by \cite{2003A&A...404L..21A} could be well explained by a uniform distribution of the lower and upper kHz QPO set in the source."
 The 3/2 peak in the observed ratio distribution comes [rom selection effects (sensitivity of measurement tools) since there is only a very narrow range of [requency ratio where both QPOs are sufficiently strong in order to be detected., The 3/2 peak in the observed ratio distribution comes from selection effects (sensitivity of measurement tools) since there is only a very narrow range of frequency ratio where both QPOs are sufficiently strong in order to be detected.
 The details can be found in works of Toroketal.(20088.b) and who elaborated this issue.," The details can be found in works of \cite{2008AcA....58...15T,2008AcA....58..113T} and \cite{2010MNRAS.401.1290B} who elaborated this issue."
 We emphasize that their results do not contradiet the parametric resonance model., We emphasize that their results do not contradict the parametric resonance model.
 The question of the viability of such models remains fully open and subject to strong debates., The question of the viability of such models remains fully open and subject to strong debates.
 Moreover. Barret&Boutelier(2003). looked. carefully al 4U1820-30 and found a gap of roughly 100 Hz in the QPO frequency distribution that," Moreover, \cite{2008NewAR..51..835B} looked carefully at 4U1820-30 and found a gap of roughly 100 Hz in the QPO frequency distribution that"
(http:www.ast.cam.ac.uk/dwwe/SRE eextinction.htal).,(http://www.ast.cam.ac.uk/ extinction.html).
 We selected. as photometric nights those satisfving the Following requirements: (i) the total number of observing hours is lareerὃν than seven: (ii) the total number of photometric data taken is larger than of the total number of observing hours: and (ii) the average Ix47 along the night is smaller than 0.2., We selected as photometric nights those satisfying the following requirements: (i) the total number of observing hours is larger than seven; (ii) the total number of photometric data taken is larger than of the total number of observing hours; and (iii) the average $_V$ along the night is smaller than 0.2.
 of the nights from June 2001 to December 2008 in the CAAIC database follow. the selection criteria., of the nights from June 2001 to December 2008 in the CAMC database follow the selection criteria.
 PWV. measurements derived. [rom GPS data during photometric nights were then used to derived the statistical values of PWV. (see table 4))., PWV measurements derived from GPS data during photometric nights were then used to derived the statistical values of PWV (see table \ref{statistic_photometric}) ).
 Statistical values (average anc median) of PWV strongly improve when specific weather conditions are selected. which is usually imposed by the techniques used to retrive PW values.," Statistical values (average and median) of PWV strongly improve when specific weather conditions are selected, which is usually imposed by the techniques used to retrive PWV values."
 Therefore. the comparison of PWV values from dillerent.V. sites is only. possible when the same technique and. procedure have been used to. acquire and analvse the data.," Therefore, the comparison of PWV values from different sites is only possible when the same technique and procedure have been used to adquire and analyse the data."
 ORAL has been an astronomical site traditionally. dedicate to optical ancl near-Ht observations (from OA to 2.5 jam)., ORM has been an astronomical site traditionally dedicated to optical and near-IR observations (from 0.4 to 2.5 $\mu$ m).
 The 10 meters Gran Telescopic de Canarias wil extend this range to the mic-LR. with CanariCum. a camera and spectrograph working in the thermal infrarec between ~7.5 and 25 yam. dn this section. we explore the implications in terms of atmospheric transmission of DWV values in the standard near and mid-Ili. windows in astronomy.," The 10 meters Gran Telescopio de Canarias will extend this range to the mid-IR, with CanariCam, a camera and spectrograph working in the thermal infrared between $\sim$ 7.5 and 25 $\mu$ m. In this section, we explore the implications in terms of atmospheric transmission of PWV values in the standard near and mid-IR windows in astronomy."
 We have modelled the theoretical near anc mic-Lh transmission spectrum for La Palma site using the ATRAN modelling software (Lord. S.D. 1902. NASA ‘Technical Memor.," We have modelled the theoretical near and mid-IR transmission spectrum for La Palma site using the ATRAN modelling software (Lord, S.D. 1992, NASA Technical Memor."
 103957) throughout the web-based. form at httpi/Zatran.sofia.usra.edu/cgi-bin/atran/atran.cgi., 103957) throughout the web-based form at http://atran.sofia.usra.edu/cgi-bin/atran/atran.cgi.
 We selected the closest [atitude to the site allowed (30 degrees). the altitude of the site (2400 m) scanning the PWV from 1l to 10 mm.," We selected the closest latitude to the site allowed (30 degrees), the altitude of the site (2400 m), scanning the PWV from 1 to 10 mm."
 The transmission spectrum. derived. [rom each PWW value was integrated. in the spectral range covering the standard. filters windows and these values were refered. to the integrated. transmission. asuniming a DWV equal to 1 mm (see table 5))., The transmission spectrum derived from each PWV value was integrated in the spectral range covering the standard filters windows and these values were refered to the integrated transmission asumming a PWV equal to 1 mm (see table \ref{trans}) ).
 The theoretical transmission spectrum for Mauna Ixea was extracted from a model available at the GIZMINI Observatory web pages (http://stall-geminiecuy kvolk/linkpage.html) which is also based on the APRAN modeling software. although it is limited in. PAVY values.," The theoretical transmission spectrum for Mauna Kea was extracted from a model available at the GEMINI Observatory web pages (http://staff.gemini.edu/ kvolk/linkpage.html) which is also based on the ATRAN modeling software, although it is limited in PWV values."
 We followed. the some procedure than in the case of La Palma. integrating the transmission spectrum in cach filter window and refering the value to the derived for Imm of PW'V.," We followed the some procedure than in the case of La Palma, integrating the transmission spectrum in each filter window and refering the value to the derived for 1mm of PWV."
 In both cases. similar results were found.," In both cases, similar results were found."
 The atmospheric transmission in. bands II. Ix. and IN. decrease less than for PWY variations from 1 to LO mm.," The atmospheric transmission in bands H, K, and N decrease less than for PWV variations from 1 to 10 mm."
 The atmospheric transmission in windows J. L. and AL slowly decrease when PWY increase (up to lrom 1 to 10 mm).," The atmospheric transmission in windows J, L, and M slowly decrease when PWV increase (up to from 1 to 10 mm)."
 The most significant effect occurs in band (Q. where atmospheric transmission is around smaller when PWV increase from 1 to 5 mm.," The most significant effect occurs in band Q, where atmospheric transmission is around smaller when PWV increase from 1 to 5 mm."
 When PWV is 10 mm. the atmospheric transmission is almost of the transmission with 1 mm of PWV in Q-band.," When PWV is 10 mm, the atmospheric transmission is almost of the transmission with 1 mm of PWV in Q-band."
 Lt is also important to note that high. levels of water vapor also increase the thermal IR. background. which is one of the major factors limiting the atmospheric transparency in mid-Lt observations from eround-based sites.," It is also important to note that high levels of water vapor also increase the thermal IR background, which is one of the major factors limiting the atmospheric transparency in mid-IR observations from ground-based sites."
 The effects. of observing conditions (water vapor column. airmass. cloud cover. etc) in the quality of cata recorded. in. mic-LR bands was illustrated in Masonctal.(2008). using real data obtained in Mauna Ixea.," The effects of observing conditions (water vapor column, airmass, cloud cover, etc) in the quality of data recorded in mid-IR bands was illustrated in \cite{2008SPIE.7016E..63M} using real data obtained in Mauna Kea."
 We have analised the water vapor content for the period from June 2001 to December 2008 above the ORAL using DWV estimations [rom GPS data., We have analised the water vapor content for the period from June 2001 to December 2008 above the ORM using PWV estimations from GPS data.
 We have verified. the consistency. of 940nm-radiometer and GPS estimation. of PWV. removing the olfset. between both techniques.," We have verified the consistency of 940nm-radiometer and GPS estimation of PWV, removing the offset between both techniques."
 We have also presented statitical results for Alauna hea for the same period. analysing the GPS close to Alauna hea site with Tooscu.; measurements.," We have also presented statitical results for Mauna Kea for the same period, analysing the GPS close to Mauna Kea site with $\tau_{225GHz}$ measurements."
 Our main results ancl conclusions may be summarized as follows: GPS is a promising technique to unify the PWV estimations at many astronomical sites., Our main results and conclusions may be summarized as follows: GPS is a promising technique to unify the PWV estimations at many astronomical sites.
 This paper is based on GPS data recor ded from the GPS station at the Roque de los Muchachos Observatory on the island of La Palma and from the labelled: MINIZA station at Alauna Ixea on the island of Hawaii., This paper is based on GPS data recor ded from the GPS station at the Roque de los Muchachos Observatory on the island of La Palma and from the labelled MKEA station at Mauna Kea on the island of Hawaii.
 Both GPS stations are part of the international network of GPS stations EUREL (www.eurefeu)., Both GPS stations are part of the international network of GPS stations EUREF (www.euref.eu).
 Aleasurements of the 225 Cllz optical depths ab Alauna Wea were recorded. from the web page of the Caltech Submillimeter Observatory (CSO) (http://puuoo.subnmun.caltech.edu ), Measurements of the 225 GHz optical depths at Mauna Kea were recorded from the web page of the Caltech Submillimeter Observatory (CSO) (http://puuoo.submm.caltech.edu/ ).
 The coellicient-extinction data were downloaded from. the. database (httpz//wwew.ast.cam.ac.uk eextinction.html) of the Carlsberg Meridian Circle of the Isaac Newton Group on., The coefficient-extinction data were downloaded from the database (http://www.ast.cam.ac.uk/ extinction.html) of the Carlsberg Meridian Circle of the Isaac Newton Group on.
 Thanks are due to M. Widger who managed the waler vapor monitoring campaigns at the ORAL from, Thanks are due to M. Kidger who managed the water vapor monitoring campaigns at the ORM from
"Flux density variability at radio wavelengths in the conrpact cores of radio loud AGNs on time scales of qmouths or even vears is generally associated with ejection of coniponents dn parsec-scale relativistic jets (c.g, Valtaoja ct al. 1988)).",Flux density variability at radio wavelengths in the compact cores of radio loud AGNs on time scales of months or even years is generally associated with ejection of components in parsec-scale relativistic jets (e.g. Valtaoja et al. \cite{valtaoja}) ).
 Such behavior has been observed in nauv radio sources (e.g. DPauliu-Toth e al. 19871) , Such behavior has been observed in many radio sources (e.g. Pauliny-Toth et al. \cite{pauliny}) )
and is successfully reproduced by theoretical work (e.g. Ilughes et al. 1991..," and is successfully reproduced by theoretical work (e.g. Hughes et al. \cite{hughes},"
 Cónunez et al. 1997)]., Gómmez et al. \cite{gomez}) ).
 However. here are objects which. appareutlv do no fit into this scenario.," However, there are objects which, apparently, do not fit into this scenario."
 One of these. the quasar 3395 εν= 0.635). exlibits significaut fiux clensity variability which is clearly associated with activity im its compac Core (Lara et al. 1991. 1997) ," One of these, the quasar 395 $z=0.635$ ), exhibits significant flux density variability which is clearly associated with activity in its compact core (Lara et al. \cite{lara1, lara2}) );"
however. Very Lone Baseline Interferometry (VLBI) observations since 198 show a stationary morphology. with no evidence of the expected correlation between flux deusity variability aux he ejection of new jet components (Lara et al. 1997)).," however, Very Long Baseline Interferometry (VLBI) observations since 1984 show a stationary morphology, with no evidence of the expected correlation between flux density variability and the ejection of new jet components (Lara et al. \cite{lara2}) )."
 Tn this paper we present new VLBI observations of he quasar 23395 at Ls GIIz. made with the Very Long Bascline Array (VLBA) and the Japanese satellite Talca.," In this paper we present new VLBI observations of the quasar 395 at 4.8 GHz, made with the Very Long Baseline Array (VLBA) and the Japanese satellite Halca."
 These observations not only take profit of the culancec aneular resolution of Spacc-VLDI. but also of the high sensitivity achieved by the coutiunous observation of a sinele source at a single frequency with the VLBA.," These observations not only take profit of the enhanced angular resolution of Space-VLBI, but also of the high sensitivity achieved by the continuous observation of a single source at a single frequency with the VLBA."
 The new data shed belt on the link between flux density variability aud the structural properties of 3395., The new data shed light on the link between flux density variability and the structural properties of 395.
 We made continuum observations of 30°3395 with the VLBA and Hala on Mav dst 1998 at ai frequency of Ls GIIz., We made continuum observations of 395 with the VLBA and Halca on May 1st 1998 at a frequency of 4.8 GHz.
 The observing bandwidth was 32 MIIEZ., The observing bandwidth was 32 MHz.
 Two tracking stations. Robledo (Spain) aud. Creeu Bank (USA). participated in the observations providing mascr referenced timing tones to the satellite.," Two tracking stations, Robledo (Spain) and Green Bank (USA), participated in the observations providing maser referenced timing tones to the satellite."
" At the same time. they received the astronomical data from Halca through a Ίναας, downlink. recording them ou magnetic tapes for later processing ina VLBI correlator."," At the same time, they received the astronomical data from Halca through a Ku-band downlink, recording them on magnetic tapes for later processing in a VLBI correlator."
 In Fig., In Fig.
 1 we display the uv-coverage achieved in our observations to illustrate the improvement in angular resolution provided by the orbiting auteuna., \ref{fig1} we display the uv-coverage achieved in our observations to illustrate the improvement in angular resolution provided by the orbiting antenna.
 The correlation of the data was done by the staff of the VLBA correlator in Socorro (NAL USA).," The correlation of the data was done by the staff of the VLBA correlator in Socorro (NM, USA)."
 After correlation. we used the NRAO AIPS package to determine the bandpass response fictions of the antennas. to correct for iustrunenutal phase and delay offsets between the separate baseband converters in each anteuua. to determine antenua-based fringe correc10119 and to apply the aurplitude calibration.," After correlation, we used the NRAO AIPS package to determine the bandpass response functions of the antennas, to correct for instrumental phase and delay offsets between the separate baseband converters in each antenna, to determine antenna-based fringe corrections and to apply the amplitude calibration."
 Data Πασάς in toal inteusitv was finally performed with the Diftuap package (Shepherd ο al. LOOL))., Data imaging in total intensity was finally performed with the Difmap package (Shepherd et al. \cite{shepherd}) ).
 The imaging process consisted of two main steps: initially. we started mapping the VLBA data alone. i.c. without erounud-space baselines. a low anenlarOo resolution by reducing the weieht of the longer VLBA baselines.," The imaging process consisted of two main steps: initially, we started mapping the VLBA data alone, i.e. without ground-space baselines, at low angular resolution by reducing the weight of the longer VLBA baselines."
 Ouce a satisfactory low resolution map of 3395 was obtained. the weight of the long baselines was progressively restored to its original values. so that we finally oained a lap Wii the VLBA alone at ifs iuaxiniuni aueular resolution.," Once a satisfactory low resolution map of 395 was obtained, the weight of the long baselines was progressively restored to its original values, so that we finally obtained a map with the VLBA alone at its maximum angular resolution."
 Iu this process. we also derived. accurate selbcalibration solutions for the VLBA auteuuas.," In this process, we also derived accurate self-calibration solutions for the VLBA antennas."
 We then included data from Halca ina second mapping step. improving the source model at sub-nulliaresecoud resolution aud obtaining a high resolutiou map frou the whole data set.," We then included data from Halca in a second mapping step, improving the source model at sub-milliarcsecond resolution and obtaining a high resolution map from the whole data set."
 Finally. we calibrated the absolute. flux chsity scale mapping the compact calibrator source 0:33|176. also observed durus the," Finally, we calibrated the absolute flux density scale mapping the compact calibrator source 0133+476, also observed during the"
"Recent ASCA. RATE. Chandra and XMM-Newton observations of Sevfert galaxies demonstrated the existence of the wide iron A, line (6.4 keV) in their spectra along with a number of other weaker lines (Ne N. Si NIHILXIV. 8 AWL Ar NVILXVILL Ca NIN. ete.) (","Recent ASCA, RXTE, Chandra and XMM-Newton observations of Seyfert galaxies demonstrated the existence of the wide iron $K_\alpha$ line (6.4 keV) in their spectra along with a number of other weaker lines (Ne X, Si XIII,XIV, S XIV-XVI, Ar XVII,XVIII, Ca XIX, etc.) ("
see for example. Fabian(2001b):Ogleetal. (2000))).,"see for example, \citet{fabian1,tanaka1,nandra1,nandra2,malizia,sambruna,
yacoob4,ogle1}) )."
 Alagnetic [fields play ai Κον role. in. dynamics of accretion dises and jet formation., Magnetic fields play a key role in dynamics of accretion discs and jet formation.
 Disnovatvi-Ixogan&Ituz-maikin(1974.1976) considered. a scenario to generate superstrong magnetic fields near black holes.," \cite{Bis74,Bis76} considered a scenario to generate superstrong magnetic fields near black holes."
" According to their results magnetic fields near the mareinally stable orbit. could be about 44—102""I1017 Cs.", According to their results magnetic fields near the marginally stable orbit could be about $H \sim 10^{10} - 10^{11}$ Gs.
4 hardashevt(1995.2001a.b.c) considered a generation of svnchrotron radiation. acceleration of ο pairs and cosmic ravs in magnetospheres of supermassive black holes.," \citet{Kard95,Kard00,Kard01a,Kard01} considered a generation of synchrotron radiation, acceleration of $e^{+/-}$ pairs and cosmic rays in magnetospheres of supermassive black holes."
 Lt is magnetic field. which plavs a key role in these models.," It is magnetic field, which plays a key role in these models."
" Below. based on the analysis of iron. A, line profile in the presence of a strong magnetic field. we describe how to detect. the field itself or at least obtain an upper limit of the magnetic field."," Below, based on the analysis of iron $K_\alpha$ line profile in the presence of a strong magnetic field, we describe how to detect the field itself or at least obtain an upper limit of the magnetic field."
" For cases when the spectral resolution is good enough the emission. spectral line demonstrates. typical two-peals profile with the high ""blue"" peak. the low ""red peak and the long “red” wing which drops gradually to the background level (Tanakactal.(1995):Yaqoobet (1997)))."," For cases when the spectral resolution is good enough the emission spectral line demonstrates typical two-peak profile with the high ""blue"" peak, the low ""red"" peak and the long ""red"" wing which drops gradually to the background level \cite{tanaka1,yaqoob2}) )."
 Ehe Doppler line width corresponds to the velocity of the matter motion of tens of thousanels kilometers per second5. eg. the maximum value is about οzzSOOO0—100000 kms for the ealaxy MCG63015 (Tanakaetal.(1995):Fabian (2002))) and οzc48000 kms for (Weawerctal. (1998))).," The Doppler line width corresponds to the velocity of the matter motion of tens of thousands kilometers per second, e.g. the maximum value is about $v \approx 80000 - 100000$ km/s for the galaxy MCG–6–30–15 \cite{tanaka1,Fabian02}) ) and $v \approx 48000$ km/s for \cite{krolik1}) )."
 For both galaxies the line profiles are known rather well., For both galaxies the line profiles are known rather well.
 Fabianetal.(2002) analyzed results of long-time observations of MCG-6-30-15. galaxy using andLX., \cite{Fabian02} analyzed results of long-time observations of MCG-6-30-15 galaxy using and.
" The long monitoring confirmed the qualitative conclusions about the features of the Fe A, line. which were discovered by ASCA satellite."," The long monitoring confirmed the qualitative conclusions about the features of the Fe $K_\alpha$ line, which were discovered by ASCA satellite."
 Yaqoobctal.(2002). discussed. the essential importance of Ας calibrating and the reliability of obtained. results., \citet{yaqoob02} discussed the essential importance of ASCA calibrating and the reliability of obtained results.
 Leeetal.(2002). compared SCA results with IUNTIS and Chandra observations for the MCCG-6-30-15., \cite{Lee02} compared ASCA results with RXTE and Chandra observations for the MCG-6-30-15.
" Lwasawaetal.(19990):Leeetal.(1999):Shih(2002). analyzed in detail the variabilitv in continuum and in Fe A, line for the MC-6-30-15. galaxy."," \cite{Iwa99,Lee99,Shih02}
 analyzed in detail the variability in continuum and in Fe $K_\alpha$ line for the MCG-6-30-15 galaxy."
 The phenomena of the broad. emission. lines are supposed to be related with accreting matter around. black holes., The phenomena of the broad emission lines are supposed to be related with accreting matter around black holes.
 Wilmsetal.(2001):Ballantyne&FabianMar- proposed physical mocels of accretion disces for the MC€:-6-30-15 galaxy and their influence on the," \cite{Wilms01,Ball01,Mart02} proposed physical models of accretion discs for the MCG-6-30-15 galaxy and their influence on the"
The issue of Jupiter and Saturns provenance. as well as that of the known extrasolar eas glant planets. remains a subject of intense study.,"The issue of Jupiter and Saturn's provenance, as well as that of the known extrasolar gas giant planets, remains a subject of intense study."
 Over the last decade. several computational groups. using an array of different. techniques and disk models. have examined theiustabilitv mechanism. where eas-phase gravitational instabilities (GIs) produce spiral waves (hat [fragment into protoplanetary clumps (Boss1997.1998.2000.2007:Stamatellos&Whitworth2008:Forganetal. 2009).," Over the last decade, several computational groups, using an array of different techniques and disk models, have examined the mechanism, where gas-phase gravitational instabilities (GI's) produce spiral waves that fragment into protoplanetary clumps \citep{boss97,boss98, boss00, boss01, boss02, boss03, boss04, boss05, boss07, boss09, pickett98, pickett00a, pickett00b, pickett03, nelson98, nelson00, nelson06, gammie01, mayer02, mayer04, mayer07, johnson03, rice03, rice05, mejia05, cai06, cai08, boley06, boley07, stam08, forg09}."
. Researchers agree that Gis are triggered when disks are massive and cold ancl that. once GUs occur. cooling on time scales comparable to the dynamic time is required for disk fragmentation (Lorareview.Durisenetal. 2007).," Researchers agree that GI's are triggered when disks are massive and cold and that, once GI's occur, cooling on time scales comparable to the dynamic time is required for disk fragmentation \citep[for a review, see][]{durisen07}."
. The questions are whether cooling by radiative (ransport will realistic opacilies is rapid enough anvwhere in protoplanetary disks (ο cause fragmentation and whether champs that do form remain physically intact. gravitationally bound entities before the eas disk clissipates (e.g..Haischetal.2001).," The questions are whether cooling by radiative transport with realistic opacities is rapid enough anywhere in protoplanetary disks to cause fragmentation and whether clumps that do form remain physically intact, gravitationally bound entities before the gas disk dissipates \citep[e.g.,][]{haisch01}."
. There have been sharp disagreements on these points among the different groups attacking the problem. and so it is important to evaluate how and why clifferent methodologies may lead to strikingly different conclusions.," There have been sharp disagreements on these points among the different groups attacking the problem, and so it is important to evaluate how and why different methodologies may lead to strikingly different conclusions."
 For moderate mass disks with a radial extent of tens of AU around solar-twpe stars. simulations with radiative (ranusport and realistic opacities presented in hereafterBOT) support disk fragmentation. in partial agreement wilh but in severe disagreement with simulations bv our own group Caietal.2006.2008:Dolev&Durisen2008) and others (Stamatellos&2008:Forganetal. 2009).," For moderate mass disks with a radial extent of tens of AU around solar-type stars, simulations with radiative transport and realistic opacities presented in \citet[][hereafter B07]{boss07} support disk fragmentation, in partial agreement with \cite{mayer07} but in severe disagreement with simulations by our own group \citep{boley06, boley07, cai06, cai08, bd08} and others \citep{stam08,forg09}."
. In DOT. Boss considers a variety of [actors that may account for the disagreement between his results ancl ours.," In B07, Boss considers a variety of factors that may account for the disagreement between his results and ours."
 We as well have explored some of the, We as well have explored some of the
We use a new. refined. semi-numerie algorithm. FFRT. presented in ? to generate ionization fields. yiCx.2).,"We use a new, refined, semi-numeric algorithm, FFRT, presented in \citet{Zahn10} to generate ionization fields, $\nf({\bf x}, z)$."
 The ionization fields have been exhaustively compared against cosmological RT codes in ?.. yielding good agreement across a broad range of statistical diagnostics on moderate to large scales.," The ionization fields have been exhaustively compared against cosmological RT codes in \citet{Zahn10}, yielding good agreement across a broad range of statistical diagnostics on moderate to large scales."
 Thus. we will not present further tests here.," Thus, we will not present further tests here."
 Instead. we merely outline the procedure. and motivate some aspects with regards to the goals of 21emFAST: speed and efficiency.," Instead, we merely outline the procedure, and motivate some aspects with regards to the goals of 21cmFAST: speed and efficiency."
 We use the excursion-set approach for identifying HII regions. pioneered by ?..," We use the excursion-set approach for identifying HII regions, pioneered by \citet{FZH04}."
 The foundation of this approach is to require that the number of ionizing photons inside a region be larger than the number of hydrogen atoms it contains., The foundation of this approach is to require that the number of ionizing photons inside a region be larger than the number of hydrogen atoms it contains.
 Then ionized regions are identified via an exeursion-set approach. starting at large scales and progressing to small scales. analogous to the derivation of the Press-Schechter (PS) mass functions (22)..," Then ionized regions are identified via an excursion-set approach, starting at large scales and progressing to small scales, analogous to the derivation of the Press-Schechter (PS) mass functions \citep{Bond91, LC93}."
 Specifically. we flag fully ionized cells in our box as those which meet the criteria [ωμίχ.τI)>¢+ where ¢ is some efficiency parameter and μία.z./2) is the collapse fraction smoothed on decreasing scales. starting from a maximum 4 Mpc and going down to the cell size. oc.," Specifically, we flag fully ionized cells in our box as those which meet the criteria $\fcoll \geq \zeta^{-1}$, where $\zeta$ is some efficiency parameter and $\fcoll$ is the collapse fraction smoothed on decreasing scales, starting from a maximum $R_{\rm max}$ Mpc and going down to the cell size, $R_{\rm cell}$."
 Additionally. we allowfor partially-ionized cells by setting the cell's ionized fraction to Cfion(x.z.Reo) at the last filter step for those cells which are not fullyionized”.," Additionally, we allowfor partially-ionized cells by setting the cell's ionized fraction to $\zeta f_{\rm coll}({\bf x}, z, R_{\rm cell})$ at the last filter step for those cells which are not fully."
.. The ionizing photon horizon. Aus. is a free parameter which can be chosen to match the extrapolated ionizing photon mean free path. in the ionized IGM. at 2— (e.g. 2229).," The ionizing photon horizon, $R_{\rm max}$, is a free parameter which can be chosen to match the extrapolated ionizing photon mean free path, in the ionized IGM, at $z\sim$ 7--10 (e.g. \citealt{Storrie-Lombardi94, Miralda-Escude03, CFG08}) )."
 The photon sinks dominating the mean free path of ionizing photons are likely too small to be resolved in reionization simulations., The photon sinks dominating the mean free path of ionizing photons are likely too small to be resolved in reionization simulations.
 An effective horizon due to photon sinks can delay the completion of reionization (e.g. 22)). and cause a drop in large scale 2|-em power. as we shall see below.," An effective horizon due to photon sinks can delay the completion of reionization (e.g. \citealt{CHR09, FM09}) ), and cause a drop in large scale 21-cm power, as we shall see below."
" There are two main differences between FFRT used in 2|emFAST and the previous incarnation of our HII bubble finder used in DexM (MFEO7): (1) the use of the halo finder to generate ionization fields in DexM (MFO7) vs. using the evolved density field and conditional PS to generate ionization fields in 21emFAST: and (2) the bubble flagging algorithm. which in MFO7 is taken to paint the entire spherical region enclosed by the filter as ionized (“flagging-the-entire-sphere”). whereas for 21emFAST we just flag the central cell as ionized (""flagging-the-central-cell"": for more information. see 2? and the appendix in ?.."," There are two main differences between FFRT used in 21cmFAST and the previous incarnation of our HII bubble finder used in DexM (MF07): (1) the use of the halo finder to generate ionization fields in DexM (MF07) vs. using the evolved density field and conditional PS to generate ionization fields in 21cmFAST; and (2) the bubble flagging algorithm, which in MF07 is taken to paint the entire spherical region enclosed by the filter as ionized (“flagging-the-entire-sphere”), whereas for 21cmFAST we just flag the central cell as ionized (“flagging-the-central-cell”; for more information, see \citealt{Zahn07, MF07} and the appendix in \citet{Zahn10}."
 These default settings of 21emFAST were chosen to maximize speed and dynamic range. while minimizing the memory requirements.," These default settings of 21cmFAST were chosen to maximize speed and dynamic range, while minimizing the memory requirements."
 Nevertheless. they are left as user-adjustable options in the codes.," Nevertheless, they are left as user-adjustable options in the codes."
 The first difference noted above means that 2lemFASThalos., The first difference noted above means that 21cmFAST.
 In MFO07. we made use of a semi-numerically generated halo field. which accurately reproduces N-body halo fields down to non-linear scales (MFO7: Mesinger et al.," In MF07, we made use of a semi-numerically generated halo field, which accurately reproduces N-body halo fields down to non-linear scales (MF07; Mesinger et al.,"
 in preparation)., in preparation).
 As in numerical reionization simulations. these halos were assumed to host ionizing sources.," As in numerical reionization simulations, these halos were assumed to host ionizing sources."
 However. the intermediate step of generating such halo source fields adds additional computation time. and generally requires many GB of RAM for typical cosmological uses.," However, the intermediate step of generating such halo source fields adds additional computation time, and generally requires many GB of RAM for typical cosmological uses."
 As for numerical simulations. this memory requirement means that simulation boxes are limited to <200 Mpe if they wish to resolve atomically-cooled halos at += 7—10. and even smaller sizes if they wish o resolve these at higher redshifts or resolve molecularly-cooled idos.," As for numerical simulations, this memory requirement means that simulation boxes are limited to $\lsim 200$ Mpc if they wish to resolve atomically-cooled halos at $z=$ 7–10, and even smaller sizes if they wish to resolve these at higher redshifts or resolve molecularly-cooled halos."
 Although DexM's halo finder is much faster than N-body codes. and can generate halo fields at a given redshift in a ew hours on a single processor. extending the dynamic range even further without hundreds of GB of RAM would be very useful.," Although DexM's halo finder is much faster than N-body codes, and can generate halo fields at a given redshift in a few hours on a single processor, extending the dynamic range even further without hundreds of GB of RAM would be very useful."
 Alternatives to extending the dynamic range have been oroposed by ??..," Alternatives to extending the dynamic range have been proposed by \citet{McQuinn07, Santos09}."
 These involve stochastically populating cells with alos below the resolution threshold., These involve stochastically populating cells with halos below the resolution threshold.
 Although computationally efficient. it is unclear if these alternatives preserve higher-order statistics of the non-Gaussian fiu(x.z.£2) field. as each cell is reated independently from the others.," Although computationally efficient, it is unclear if these alternatives preserve higher-order statistics of the non-Gaussian $\fcoll$ field, as each cell is treated independently from the others."
 More fundamentally. the stochasticity involved makes it difficult to deterministically track he redshift evolution of a single realization: halos effectively pop in and out of existence from one redshift output to the next.," More fundamentally, the stochasticity involved makes it difficult to deterministically track the redshift evolution of a single realization: halos effectively pop in and out of existence from one redshift output to the next."
 Therefore. to increase speed and dynamic range. we use he FFRT algorithm. which uses the conditional PS formalism (??) to generate the collapsed mass (i.e. ionizing source) field.," Therefore, to increase speed and dynamic range, we use the FFRT algorithm, which uses the conditional PS formalism \citep{LC93, SK99} to generate the collapsed mass (i.e. ionizing source) field."
 Since conditional PS operates directly on the density field. without needing to resolve halos. one can have an enormous dynamic range with a relatively small loss in accuracy (compare FFRT and FFRT-S in ο).," Since conditional PS operates directly on the density field, without needing to resolve halos, one can have an enormous dynamic range with a relatively small loss in accuracy (compare FFRT and FFRT-S in \citealt{Zahn10}) )."
 Most importantly. when computing fiai(x.z.22) we use thenon-linear density field. generated according to 32.1.. instead of the standard linear density field.," Most importantly, when computing $\fcoll$ we use the density field, generated according to \ref{sec:den}, instead of the standard linear density field."
 The resulting ionization fields are a much better match to RT simulations than those generated from the linear density field (2:: foreshadowed also by the ICs panel in Fig., The resulting ionization fields are a much better match to RT simulations than those generated from the linear density field \citealt{Zahn10}; foreshadowed also by the ICs panel in Fig.
 | above)., \ref{fig:den_pics} above).
" We normalize the resulting collapsed mass field to match the Sheth-Tormen (ST) mean collapse fraction, which in turn matches numerical simulations (see eq."," We normalize the resulting collapsed mass field to match the Sheth-Tormen (ST) mean collapse fraction, which in turn matches numerical simulations (see eq."
 1+ and. associated discussion)., \ref{eq:fcoll} and associated discussion).
 The other major difference is that by default. FFRT in 2lemFAST flags just the central filter cell. instead of the entire sphere enclosed by the filter. as in MFO7.," The other major difference is that by default, FFRT in 21cmFAST flags just the central filter cell, instead of the entire sphere enclosed by the filter, as in MF07."
 The main motivation for this switch is that the former algorithm is O(N). while the later is slower: QUV) αμ~1 but approaching O(N7) as. gp50.," The main motivation for this switch is that the former algorithm is ${\cal O}(N)$, while the later is slower: ${\cal O}(N)$ at $\avenf\sim1$ but approaching ${\cal O}(N^2)$ as $\avenf \rightarrow 0$."
 There are some other minor differences between the FFRT and the ionization scheme in MFO7. such as the use of a sharp k-space filter instead of a spherical top-hat. but these have a smaller impact on the resulting ionization maps.," There are some other minor differences between the FFRT and the ionization scheme in MF07, such as the use of a sharp k-space filter instead of a spherical top-hat, but these have a smaller impact on the resulting ionization maps."
" Redshift space distortions. accounted for with the dr,/dr term in eq. (L9..."," Redshift space distortions, accounted for with the $dv_r/dr$ term in eq. \ref{eq:delT}),"
 are often ignored when simulating the 21-em signal., are often ignored when simulating the 21-cm signal.
 In the linear regime. redshift space distortions of the 2|-em field are similar to the well-studied Kaiser effect (e.g. 3). and the power spectrum of fluctuations is enhanced on all scales by a geometric factor of 1.87. (22)...," In the linear regime, redshift space distortions of the 21-cm field are similar to the well-studied Kaiser effect (e.g. \citealt{Kaiser87}) ), and the power spectrum of fluctuations is enhanced on all scales by a geometric factor of 1.87 \citep{BA04, BL05}. ."
 However. the small scale overdensities. where redshift space distortions are most important. are also the regions whose 2l-em emission is first erased by “inside-out” reionization.," However, the small scale overdensities, where redshift space distortions are most important, are also the regions whose 21-cm emission is first erased by “inside-out” reionization."
 Preliminary studies therefore concluded that redshift space distortions would only be, Preliminary studies therefore concluded that redshift space distortions would only be
spectrmm aud the effect of propagation.,spectrum and the effect of propagation.
 Figure H1 shows how clearly Augcr will test the spectrun im spite of their clustering properties., Figure 11 shows how clearly Auger will test the spectrum in spite of their clustering properties.
 The cosmuograpliy of sources should aso become clear aAC able to discrimuuate between plausible populations for UIIECR sources., The cosmography of sources should also become clear and able to discriminate between plausible populations for UHECR sources.
 The CCrelation of arrival directious for events with energies abovο 1029 eV. with so11e known structure such as the Galaxy. the Calactic halo. he Local Growp or the Local Supercluster would be key in differcutiating beween differcut models.," The correlation of arrival directions for events with energies above $10^{20}$ eV with some known structure such as the Galaxy, the Galactic halo, the Local Group or the Local Supercluster would be key in differentiating between different models."
 For iustanee. a correlation with the Galactic ceuter aud disk should become apparent at extremely hiel energies for the case of vouugC» neutron star winds. while a correlation with the laree[m] scale galaxy distribution should become clear for the case of quasar remmS," For instance, a correlation with the Galactic center and disk should become apparent at extremely high energies for the case of young neutron star winds, while a correlation with the large scale galaxy distribution should become clear for the case of quasar remnants."
 If SIIBs or nono»olouia are respousible for UITEC'R. production. the arrival directions should correlate with the dark matter distribution aud show the halo asvuuuetry.," If SHRs or monopolonia are responsible for UHECR production, the arrival directions should correlate with the dark matter distribution and show the halo asymmetry."
 For these signatures to be tested. full «kv coverage is essenti:d.," For these signatures to be tested, full sky coverage is essential."
 Finally. an excellent discriminator would be au waaASMONS coniposition cletermunation of the primavies.," Finally, an excellent discriminator would be an unambiguous composition determination of the primaries."
 Iu general Calactie disk models invoke mon uuclei to be cousistcut wih the isotropic distribution. extragalactic Zevatrous tend to favor proton primaries. while photon primarics are more cπο for carly universe relies.," In general, Galactic disk models invoke iron nuclei to be consistent with the isotropic distribution, extragalactic Zevatrons tend to favor proton primaries, while photon primaries are more common for early universe relics."
 The hybrid detector of the Auger Project siould help determine 4the conrpositiont wincasuring the depth of shower maxim and the monu coiteut of the same shower., The hybrid detector of the Auger Project should help determine the composition by measuring the depth of shower maximum and the muon content of the same shower.
 The prospect of testing extremely high euergy plysics as well as solving the UITECT ivstery awaits improved observatious that should be comüug in the next decade with experiments muder construction such as Auge! or in- the plauning. stages such as the TelescopeJj Array’?D EUSO! , The prospect of testing extremely high energy physics as well as solving the UHECR mystery awaits improved observations that should be coming in the next decade with experiments under construction such as \cite{Auger} or in the planning stages such as the Telescope \cite{TA} \cite{EUSO} 
A simple solution of the expanding magnetic loops is that the poloidal magnetic field is dipolar near the surface of the star (Low1982)..,A simple solution of the expanding magnetic loops is that the poloidal magnetic field is dipolar near the surface of the star \citep{1982ApJ...261..351L}.
 Phe magnetic field should be tangential to the spherical surface r=ΠΕ) at all time., The magnetic field should be tangential to the spherical surface $r=R(t)$ at all time.
" Such a solution can be constructed by where zl, and a are constants.", Such a solution can be constructed by where $A_0$ and $a$ are constants.
" The radius A2(/) where 4,1=0 is given by We hereafter call the solution constructed (rom equation (37)) assolulion.", The radius $R(t)$ where $\tilde{A}=0$ is given by We hereafter call the solution constructed from equation \ref{sol1:A}) ) as.
 Solid curve in Fig., Solid curve in Fig.
 L shows the ux function Las a function of y for the dipolar solution., \ref{fig:shellflux} shows the flux function $\tilde{A}$ as a function of $\eta$ for the dipolar solution.
 Contour plots of 1 for dipolar solution is shown in the left panel of Fig. 2.., Contour plots of $\tilde{A}$ for dipolar solution is shown in the left panel of Fig. \ref{fig:flux}.
 When the Iux function is given by equation (37)). the magnetic Lux crossing the annulus at the equatorial plane 6=7/2 decreases with radius (see Fig. 1).," When the flux function is given by equation \ref{sol1:A}) ), the magnetic flux crossing the annulus at the equatorial plane $\theta=\pi/2$ decreases with radius (see Fig. \ref{fig:shellflux}) )."
 In actual ΑΔΗ explosion. the magnetic Dux can be swept up into a thin shell just behind the loop top.," In actual MHD explosion, the magnetic flux can be swept up into a thin shell just behind the loop top."
 The shell boundaries are assumed to be at r=bf and rk—ef (region LL. see Fig. 1).," The shell boundaries are assumed to be at $r=bt$ and $r=at$ (region II, see Fig. \ref{fig:shellflux}) )."
 Such a self-similar field can be constructed by where and a.b and & are constants (Low 1982).. ," Such a self-similar field can be constructed by where and $a$,$b$ and $k$ are constants \citep{1982ApJ...261..351L}. ."
The flux functions in region L (7)& 5) and region LE (b<η& a) are connected smoothly at a=5.," The flux functions in region I $\eta \lid b$ ) and region II $b < \eta
\lid a$ ) are connected smoothly at $\eta=b$."
 The loop boundary locates at r=af. where οἱ=0.," The loop boundary locates at $r=at$, where $\tilde{A}=0$."
 The Hux function for this solution is shown by a dashed curve in Fig. 1.., The flux function for this solution is shown by a dashed curve in Fig. \ref{fig:shellflux}.
 lt can be casily shown that the magnetic field lines projected on to the ry @ plane are all racial in region I. We call the solution constructed from equation (39)) as solution., It can be easily shown that the magnetic field lines projected on to the $r-\theta$ plane are all radial in region I. We call the solution constructed from equation \ref{sol2:A}) ) as .
 Themiddle panel of Fig., Themiddle panel of Fig.
 2. shows the contours of ;l Dor the shell solution., \ref{fig:flux} shows the contours of $\tilde{A}$ for the shell solution.
dispersion.,dispersion.
 Mergers may then alfect the CMIC by building more luminous galaxies with the same composition as their less massive progenitors. which would tend to Ilatten the CAIR slope at L2L luminosities ," Mergers may then affect the CMR by building more luminous galaxies with the same composition as their less massive progenitors, which would tend to flatten the CMR slope at $L>L^*$ luminosities (eg."
Skelton. Bell and Somerville 2009).," Skelton, Bell and Somerville 2009)."
 Age also has a (secondary) role in explaining the colour trend - the most massive IE/80s formed early and rapidly (in <1 Gyr). while those of lower luminosity formed stars over longer timescales. giving slightly vounger [ux-weighted ages.," Age also has a (secondary) role in explaining the colour trend - the most massive E/S0s formed early and rapidly (in $<1$ Gyr), while those of lower luminosity formed stars over longer timescales, giving slightly younger flux-weighted ages."
 ‘There is also evidence that LE/SO galaxy formation MM slightly earlier in dense environments (eg., There is also evidence that E/S0 galaxy formation occurred slightly earlier in dense environments (eg.
 Sheth et al., Sheth et al.
 2c Jermardi 2009). while galaxies in cluster centres may had an unusual and extreme merger history (c.g. Bovlan-Ixolchin. Ma and Quatacrt 2006)," 2006, Bernardi 2009), while galaxies in cluster centres may have had an unusual and extreme merger history (e.g. Boylan-Kolchin, Ma and Quataert 2006)."
 ‘Thus merger history ancl cluster environment may both inlluence the CALR., Thus merger history and cluster environment may both influence the CMR.
 Our studies of the CMBR. in. Roche. Bernardi and 1Ivde 2009 (hereafter Paper I) suggested. (see Section. 3.1) that the radial colour gradients in E/SO galaxies might be correlated with their other properties ancl it would. be fruitful to investigate this further.," Our studies of the CMR in Roche, Bernardi and Hyde 2009 (hereafter Paper I) suggested (see Section 3.1) that the radial colour gradients in E/S0 galaxies might be correlated with their other properties and it would be fruitful to investigate this further."
 These colour. gradients are of interest in that they are sensitive tracers of evolution processes and. vary strongly. between the individual I2/80s, These colour gradients are of interest in that they are sensitive tracers of evolution processes and vary strongly between the individual E/S0s.
 Most EYSO galaxies have negative colour eracients. meaning that the centres are. τοσο and colours become. bluer outwards.," Most E/S0 galaxies have negative colour gradients, meaning that the centres are reddest and colours become bluer outwards."
 This could be the result of a negative eracicnt in age. metallicity or dust. or some combination of these.," This could be the result of a negative gradient in age, metallicity or dust, or some combination of these."
 Tamura et al. (, Tamura et al. (
2000) and Tomura anc Ohta (2003) estimate the mean colour eracient in E/SOs as ABAilesdh0.09 mae ον (with a scatter of 0.04). and attributed this to a racial gradient. of metallicity (rather than age) diosdilosZi0.3c0.1. approximately constant to zc1.,"2000) and Tamura and Ohta (2003) estimate the mean colour gradient in E/S0s as ${{\Delta(B-R)}\over{\Delta(\rm log~r)}}=-0.09$ mag $\rm dex^{-1}$ (with a scatter of 0.04), and attributed this to a radial gradient of metallicity (rather than age) ${{d(\rm log~Z)}\over{d(\rm log~r)}}= -0.3\pm 0.1$, approximately constant to $z\simeq 1$."
 Wu et al. (, Wu et al. (
2005) similarly. estimated πα=0.25 with a large scatter σ=0.19.,2005) similarly estimated ${{d({\rm log}~Z)}\over{d(\rm log~r)}}= -0.25$ with a large scatter $\sigma=0.19$.
 Mehlert. et al. (, Mehlert et al. (
2003). found negative metallicity. gradients in. Coma-cluster ellipticals. out. negligible. gradients in age or afle.,"2003) found negative metallicity gradients in Coma-cluster ellipticals, but negligible gradients in age or $\alpha$ /Fe."
 Alichard (2005) concluded: colour. gradients in 50 nearby cllipticals were oimarilv due to metallicity eracicnts and the elfects of dust. were usually small., Michard (2005) concluded colour gradients in 50 nearby ellipticals were primarily due to metallicity gradients and the effects of dust were usually small.
 La Barbera and Carvalho (2009) compare optical ancl near-LR colour eracicnts aud again conclude they are produced: by negative gradients in metallicity (hey find the radial age gradients in E/SOs may oc even be positive)., La Barbera and Carvalho (2009) compare optical and near-IR colour gradients and again conclude they are produced by negative gradients in metallicity (they find the radial age gradients in E/S0s may be even be positive).
 Ixobavashi (2004) performed. detailed chemocdynamical simulations of a set of over LOO model elliptical. galaxies. with star-formation anc merging. and predicted. that spheroidals which formed. monolithicallv. or at least. with only minor mergers. would have steeper metallicity gradients (sues(uem21(.3 to -0.5) than those formed. by major mereers (diedc0.2).," Kobayashi (2004) performed detailed chemodynamical simulations of a set of over 100 model elliptical galaxies, with star-formation and merging, and predicted that spheroidals which formed monolithically, or at least with only minor mergers, would have steeper metallicity gradients ${{d({\rm log}~Z)}\over{d(\rm log~r)}}\simeq -0.3$ to -0.5) than those formed by major mergers ${{d({\rm log}~Z)}\over{d(\rm log~r)}}\simeq -0.2)$."
 Within the simulated galaxy set. merger history was the primary determinant (more so than mass or luminosity) of present-cay metallicity/colour eracicnt.," Within the simulated galaxy set, merger history was the primary determinant (more so than mass or luminosity) of present-day metallicity/colour gradient."
" ""This might account for the observed. wide distribution. in colour gradients if similar numbers of spheroidals had. monolithic. minor-merger or major-merger histories. and might also leack to an. environmental dependence."," This might account for the observed wide distribution in colour gradients if similar numbers of spheroidals had monolithic, minor-merger or major-merger histories, and might also lead to an environmental dependence."
 In this paper we focus especially on Brightest: Cluster Galaxies (BCGs). of which several thousand have been identified in the SDSS.," In this paper we focus especially on Brightest Cluster Galaxies (BCGs), of which several thousand have been identified in the SDSS."
" Previously. the BCCGs in the SDSS have been found follow à steeper relation of radius to uninosity (r.ppxL) than the other E/SOs (ppxL""): (Bernardi et al."," Previously, the BCGs in the SDSS have been found to follow a steeper relation of radius to luminosity ${\rm r}_{eff}\propto L$ ) than the other E/S0s ${\rm r}_{eff}\propto L ^{0.6}$ ); (Bernardi et al."
 2007: Bernardi 2009)., 2007; Bernardi 2009).
" In this paper. we look or svstematic dillerences in their CAI ancl racial colour eradients with respect to other 0/90 galaxies. especially hose in the same luminosity range (AL,<22.5 to Al,c25)."," In this paper, we look for systematic differences in their CMR and radial colour gradients with respect to other E/S0 galaxies, especially those in the same luminosity range $M_r<-22.5$ to $M_r\simeq -25$ )."
 Some models. for example. predict a much. Latter CAIR for the BCGs. as a result of formation [rom a relatively aree number of mergers of (already)iold ancl red. galaxics indicationsde Lucia ancl Blaizot 2007).," Some models, for example, predict a much flatter CMR for the BCGs, as a result of formation from a relatively large number of mergers of (already) old and red galaxies (de Lucia and Blaizot 2007)."
 ko Im (2005) found that the colour gradients of ellipticals in. dense cluster environments tended to be less strong than in field environments. which again could be due to (more) mergers.," Ko and Im (2005) found indications that the colour gradients of ellipticals in dense cluster environments tended to be less strong than in field environments, which again could be due to (more) mergers."
 In Section 2 of this paper we describe the data used and our selection of earlv-tvpe galaxies and. DOCs., In Section 2 of this paper we describe the data used and our selection of early-type galaxies and BCGs.
 In Sections 3 and 4 we investigate and compare their CALR and 6 relation., In Sections 3 and 4 we investigate and compare their CMR and $\sigma$ relation.
 In. Section 5 we use an estimator of colour eracient based on the ratio of g and r-band etlective radii to compare the colour gradients of BCCGs and other [ος and examine the dependenees on luminosity. radius. aud density.," In Section 5 we use an estimator of colour gradient based on the ratio of $g$ and $r$ -band effective radii to compare the colour gradients of BCGs and other E/S0s and examine the dependences on luminosity, radius, and density."
 In Section 6 we look at the influence ofstellar age. as estimated from the spectra.," In Section 6 we look at the influence of stellar age, as estimated from the spectra."
 We conclude in Section 7 with summary and further discussion., We conclude in Section 7 with summary and further discussion.
 SDSS magnitudes are given in the AB system where mip=48.602.5 log P. (in eres emsilziy equivalentIy. mig=0 is 3631 Jy.," SDSS magnitudes are given in the AB system where $m_{AB}=-48.60-2.5$ log $F_{\nu}$ (in ergs $\rm cm^{-2}s^{-1}Hz^{-1}$ ); equivalently, $m_{AB}=0$ is 3631 Jy."
" We assume throughout a spatially flat cosmology with //j=10 km sINpei Oy,=0.27 and O4=0.73. giving the age of the Universe as 13.88 Cir."," We assume throughout a spatially flat cosmology with $H_0=70$ km $\rm 
s^{-1}Mpc^{-1}$, $\Omega_{M}=0.27$ and $\Omega_{\Lambda}=0.73$, giving the age of the Universe as 13.88 Gyr."
 We first describe the selection of EYSO and BCC. galaxies used in the colour-magnitude relation analysis., We first describe the selection of E/S0 and BCG galaxies used in the colour-magnitude relation analysis.
 For the following analysis of colour gradients. we exclude. some objects to give somewhat smaller samples. as described in Section 5.1.," For the following analysis of colour gradients, we exclude some objects to give somewhat smaller samples, as described in Section 5.1."
 In Paper Lowe selected 70378. LE and SO galaxies out of a total of 367471 galaxies in the DRA spectroscopic sample of the Sloan DigitalSky survey. with parameters updated: to DRG," In Paper I we selected 70378 E and S0 galaxies out of a total of 367471 galaxies in the DR4 spectroscopic sample of the Sloan DigitalSky survey, with parameters updated to DR6."
" Strict criteria were applied: the I2/80s had to have de Vaucouleurs profile fractions (Lracqoy) from the SDSS cisk-plus-bulee fits of 1.0 in both g and r (ie. galaxies with any significant disk component are excluded). ""eclass! spectroscopic classification. parameters «0 (signifving absorption-line spectra). ancl dereddened i:xxl model magnitudes 14.5«r17.5."," Strict criteria were applied; the E/S0s had to have de Vaucouleurs profile fractions $\rm frac_{deV}$ ) from the SDSS disk-plus-bulge fits of 1.0 in both $g$ and $r$ (i.e. galaxies with any significant disk component are excluded), `eclass' spectroscopic classification parameters $<0$ (signifying absorption-line spectra), and dereddened $r$ -band model magnitudes $14.5<r<17.5$."
 Redshilt range is per20.3., Redshift range is $0<z<0.36$.
 Phe same sample is used here. and (as in Paper D we include the small ‘sky subtraction corrections from Livele and Bernardi (2009): applied to the SDSS photometry hese have the ellect of slightly increasing the elfective radii and brightening the model magnitudes (in all passbands) for he galaxies of larger angular size.," The same sample is used here, and (as in Paper I) we include the small `sky subtraction' corrections from Hyde and Bernardi (2009); applied to the SDSS photometry these have the effect of slightly increasing the effective radii and brightening the model magnitudes (in all passbands) for the galaxies of larger angular size."
 Lere we make use of two samples of BCGs. both selected rom the SDSS.," Here we make use of two samples of BCGs, both selected from the SDSS."
" The first are the ""C4 BCCGs’. a subsample of the lirst-ranked galaxies within the catalog of clusters detected: using a ""CX cluster-detection algorithm on the SDSS-DR2 data (Miller et al."," The first are the `C4 BCGs', a subsample of the first-ranked galaxies within the catalog of clusters detected using a `C4' cluster-detection algorithm on the SDSS-DR2 data (Miller et al."
 2005)., 2005).
 )ernardi et al. (, Bernardi et al. (
"2007) selected a subset of 286 (ol the original list of 748) XCis as those with M, 2]. velocity dispersion (0) measurements and at least LO other A,2] galaxies within 1.4 Alpe.","2007) selected a subset of 286 (of the original list of 748) BCGs as those with $M_r<-21$ , velocity dispersion $\sigma$ ) measurements and at least 10 other $M_r<-21$ galaxies within 1.4 Mpc."
 We, We
throughout the observing run to check the performance of the telescope.,throughout the observing run to check the performance of the telescope.
 We found. that at worst the pointing was accurate to within 3 arcsec., We found that at worst the pointing was accurate to within $\sim$ 3 arcsec.
 Once the receivers had. been tuned to the correct frequency. a bright standard source was observed to check the chopper wheel calibration.," Once the receivers had been tuned to the correct frequency, a bright standard source was observed to check the chopper wheel calibration."
 The data obtained were in the form of a series of spectra sampled at different positions that could be built into a data cube., The data obtained were in the form of a series of spectra sampled at different positions that could be built into a data cube.
 Phe basic data format is a spectrum whose intensity is eiven in terms of the antenna temperature T7., The basic data format is a spectrum whose intensity is given in terms of the antenna temperature $ \rm T_a^*$.
 Phe spectra were calibrated regularly using the usual chopper wheel methocl (Ixutner Ulich 1981) in addition to the standard observations described above., The spectra were calibrated regularly using the usual chopper wheel method (Kutner Ulich 1981) in addition to the standard observations described above.
 Since the beam of the telescope is not expected to be perfectly. coupled. to the source. a correction factor 1 has to be applied. to TZ in order to caleulate the radiation temperature of the source Tas.," Since the beam of the telescope is not expected to be perfectly coupled to the source, a correction factor $\eta$ has to be applied to $ \rm T_a^*$ in order to calculate the radiation temperature of the source $ \rm T_{mb}$."
 This coupling constant is dependent on the spatial extent of the source., This coupling constant is dependent on the spatial extent of the source.
 Taking into account the observations of standard sources discussed above ancl using the suggested coupling factor of Matthews (1999). np. for a source filling the beam. we used the following conversions from antenna temperature to main beam temperature for receiver À2: Tus=Ες/0.65(45%): and for receiver. Bai: Van=Pe/O-4(4£10%).," Taking into account the observations of standard sources discussed above and using the suggested coupling factor of Matthews (1999), $\eta_{\rm B}$, for a source filling the beam, we used the following conversions from antenna temperature to main beam temperature for receiver A2: $\rm T_{mb} = T_a^* / 0.65 (\pm 5\%)$; and for receiver B3i: $\rm T_{mb} = T_a^* / 0.4 (\pm 10\%)$."
 These conversion [actors are slightly lower than the canonical values. which may have been due to minor receiver problems at the time of the observations.," These conversion factors are slightly lower than the canonical values, which may have been due to minor receiver problems at the time of the observations."
 LI1GSOD data cubes in the CO el) and Ὁ 2) transitions are presented in Figures 1 and 2., L1689B data cubes in the $ \rm ^{18}$ O $ \rm \rightarrow$ 1) and $ \rm ^{18}$ O $ \rm \rightarrow$ 2) transitions are presented in Figures 1 and 2.
 The source is Clearly detected in both transitions at. virtually all positions in the maps., The source is clearly detected in both transitions at virtually all positions in the maps.
 The brightness distribution of the core appears relatively uniform across the area mapped. and it is not strongly peaked.," The brightness distribution of the core appears relatively uniform across the area mapped, and it is not strongly peaked."
 “Phe noise level per channel in the spectra is 0.6 IX for CIO 1) and 0.4 for CLO 52)., The noise level per channel in the spectra is 0.6 K for $ \rm ^{18}$ O $ \rm \rightarrow$ 1) and 0.4 for $ \rm ^{18}$ O $ \rm \rightarrow$ 2).
" For most positions Tyun(peak) for 450(,—2 +1) lies between 5 and 6 I. Ehe C100(J23 +2) Tai intensity at most positions lies in the range 3.8 to 4.8 Ix. The most clearly detected variation in intensity seenis to be a drop oll towards the North-East of both maps. most noticeably in CH 19)."," For most positions $ \rm T_{mb}$ (peak) for $ \rm ^{18}$ $ \rm \rightarrow$ 1) lies between 5 and 6 K. The $ \rm ^{18}$ $ \rm \rightarrow$ 2) $ \rm T_{mb}$ intensity at most positions lies in the range 3.8 to 4.8 K. The most clearly detected variation in intensity seems to be a drop off towards the North-East of both maps, most noticeably in $ \rm ^{18}$ $ \rm \rightarrow$ 2)."
 The full-width at half maximum CENHIM) width of the lines is 0.6O.Skm/s. The C 0(J23. +2) map had too little signal to noise to reveal any kinematic information. but a channel map of the Οι 21) map was produced and is shown in Figure 3.," The full-width at half maximum (FWHM) width of the lines is 0.6–0.8km/s. The $ \rm ^{18}$ $ \rm \rightarrow$ 2) map had too little signal to noise to reveal any kinematic information, but a channel map of the $ \rm ^{18}$ $ \rm \rightarrow$ 1) map was produced and is shown in Figure 3."
 The map shows no evidence of rotation which would. be revealed by the red and. blue shifted: maps peaking at opposite positions either side of the centre of the core., The map shows no evidence of rotation which would be revealed by the red and blue shifted maps peaking at opposite positions either side of the centre of the core.
 However some evidence exists for the points 20 areseconds cast and west of centre being blue shifted: with respect to the central. position., However some evidence exists for the points 20 arcseconds east and west of centre being blue shifted with respect to the central position.
 Detailed inspection of the individual lines shows this to be true. as they are shifted by approximately 0.20.3 kms. However. there is no clear evidence for line asymmetry.," Detailed inspection of the individual lines shows this to be true, as they are shifted by approximately 0.2–0.3 km/s. However, there is no clear evidence for line asymmetry."
 We hypothesise that this may be due to slow contraction of the core. but. this would," We hypothesise that this may be due to slow contraction of the core, but this would"
some gas begins to condense down onto the central galaxy: a small proportion of that gas is driven down to the central regions of the galaxy. fuelling a new cycle of AGN activity: the resulting radio source re-heats the gas and cuts off the cooling once again.,"some gas begins to condense down onto the central galaxy; a small proportion of that gas is driven down to the central regions of the galaxy, fuelling a new cycle of AGN activity; the resulting radio source re-heats the gas and cuts off the cooling once again."
 One interesting question is why. in this scenario. the AGN fraction should scale as Abg.," One interesting question is why, in this scenario, the radio--loud AGN fraction should scale as $M_{\rm BH}^{1.6}$."
 Best shortcitebesOSb found that the occurrence of low luminosity radio— AGN activity was completely independent of that of optical (emission-line) AGN activity. and therefore argued that radio—loud AGN were fuelled by the accretion of hot gas (as opposed to the cold gas which fuels optical AGN through a standard thin accretion disk).," Best \\shortcite{bes05b} found that the occurrence of low luminosity radio--loud AGN activity was completely independent of that of optical (emission–line) AGN activity, and therefore argued that radio–loud AGN were fuelled by the accretion of hot gas (as opposed to the cold gas which fuels optical AGN through a standard thin accretion disk)."
" Croton shorteitecro0S showed that the Bondi-Hoyle accretion rate of hot gas is ""npoàChinAlaafX (their Eq.", Croton \\shortcite{cro05} showed that the Bondi–Hoyle accretion rate of hot gas is $\dot{m}_{\rm Bondi} \approx G \mu m_p k T M_{\rm BH} / \Lambda$ (their Eq.
" 28). where qon, is the mean mass of particles in the gas. and A is the cooling function."," 28), where $\mu m_p$ is the mean mass of particles in the gas, and $\Lambda$ is the cooling function."
 For an isothermal gas. £x στ. which from the black hole mass versus velocity dispersion relation gives ZxMg.," For an isothermal gas, $T \propto
\sigma^2$ , which from the black hole mass versus velocity dispersion relation gives $T \propto M_{\rm BH}^{0.5}$."
 Ais relatively independent of temperature (and hence black hole mass) at the temperature of elliptical galaxy haloes. and therefore the Bondi accretion rate scales roughly as Al}y. remarkably similar o the sealing of the radio-loud fraction: the higher proportion of radio-loud AGN in more massive galaxies may therefore arise naturally from the higher accretion rates.," $\Lambda$ is relatively independent of temperature (and hence black hole mass) at the temperature of elliptical galaxy haloes, and therefore the Bondi accretion rate scales roughly as $M_{\rm BH}^{1.5}$, remarkably similar to the scaling of the radio–loud fraction: the higher proportion of radio–loud AGN in more massive galaxies may therefore arise naturally from the higher accretion rates."
 The physics underlying his accretion must be more complicated. since the Bondi accretion rate is for continual infall of gas whilst the mass—scaling of the radio-loud AGN fraction represents a scaling of the fraction of time hat a given black hole is active. but it is certainly intriguing that he two scale with mass in the same way. and that this mass scaling matches that required in the Croton mmodel to solve the current problems in the semi—analytic models.," The physics underlying this accretion must be more complicated, since the Bondi accretion rate is for continual infall of gas whilst the mass–scaling of the radio–loud AGN fraction represents a scaling of the fraction of time that a given black hole is active, but it is certainly intriguing that the two scale with mass in the same way, and that this mass scaling matches that required in the Croton model to solve the current problems in the semi–analytic models."
 In conclusion. therefore. observations show that the time—averaged mechanical energy output associated with radio-source activity in massive galaxies is found to almost exactly balance the cooling radiation losses from the hot haloes of those galaxies. across a wide range of galaxy masses.," \nocite{bic95}
 In conclusion, therefore, observations show that the time--averaged mechanical energy output associated with radio–source activity in massive galaxies is found to almost exactly balance the cooling radiation losses from the hot haloes of those galaxies, across a wide range of galaxy masses."
 This implies that the cooling of the gas may be feedback controlled by the radio activity., This implies that the cooling of the gas may be feedback controlled by the radio activity.
 This feedback will control the growth rate of all galaxies in haloes in which a quasi-static cooling halo of hot gas has been established: in practice this means all dark matter haloes more massive than 23.JOAL. (e.g. Bower 22005. Croton 22005).," This feedback will control the growth rate of all galaxies in haloes in which a quasi–static cooling halo of hot gas has been established; in practice this means all dark matter haloes more massive than $2-3 \times 10^{11} M_{\odot}$ (e.g. Bower 2005, Croton 2005)."
 The mass—scaling of the mechanical energy output due to radio source activity matches both that predicted if they are fuelled by Bondi accretion of hot gas from the cooling haloes. and that required for radio-AGN feedback to successfully solve the problem of the over-growth of massive galaxies in semi-analytic models.," The mass–scaling of the mechanical energy output due to radio source activity matches both that predicted if they are fuelled by Bondi accretion of hot gas from the cooling haloes, and that required for radio–AGN feedback to successfully solve the problem of the over-growth of massive galaxies in semi–analytic models."
 PNB would like to thank the Royal Society for generous financial support through its University Research Fellowship scheme., PNB would like to thank the Royal Society for generous financial support through its University Research Fellowship scheme.
 The authors thank Simon White and Darren Croton for illuminating discussions about the cooling and heating rates in the semi-analytic models. Ed Pope for usefuldiscussions about the recurrent radio source activity. and the referee for helpful comments.," The authors thank Simon White and Darren Croton for illuminating discussions about the cooling and heating rates in the semi–analytic models, Ed Pope for usefuldiscussions about the recurrent radio source activity, and the referee for helpful comments."
The dwarf nova (DN) eruption. is one of the most distinctive features of the cataclysmic variables (CVs).,The dwarf nova (DN) eruption is one of the most distinctive features of the cataclysmic variables (CVs).
 Such stars brighten by typically 3ο magnitudes. for durations of 48 d every 2060 d. There are also longer. brighter ‘superouthursts’ and other related phenomena (for a comprehensive review sce Warner 1995a).," Such stars brighten by typically 3–5 magnitudes for durations of 4–8 d every 20–60 d. There are also longer, brighter `superoutbursts' and other related phenomena (for a comprehensive review see Warner 1995a)."
 The near unanimous opinion is that the outhursts are caused. by instabilities in the acerction disc surrounding the white dwarf in these close binaries., The near unanimous opinion is that the outbursts are caused by instabilities in the accretion disc surrounding the white dwarf in these close binaries.
 Because of the hydrogen ionization instability a disc with the right conditions can choose either of two states (one hot and. viscous. the other cooler and more Luicl) for à given surface density.," Because of the hydrogen ionization instability a disc with the right conditions can choose either of two states (one hot and viscous, the other cooler and more fluid) for a given surface density."
 The disc evcles between the states. dumping material onto the white chvarl at a higher rate when it is hot and viscous (reviewed by Osaki 1996).," The disc cycles between the states, dumping material onto the white dwarf at a higher rate when it is hot and viscous (reviewed by Osaki 1996)."
 Phe alternative proposal. that instabilites in the secondary star increase the mass transfered into the disc. is decreasingly favoured for typical DN eruptions. but might still have a role to play in explaining the full phenomenology of CVs.," The alternative proposal, that instabilites in the secondary star increase the mass transfered into the disc, is decreasingly favoured for typical DN eruptions, but might still have a role to play in explaining the full phenomenology of CVs."
 While outbursts in non-magnetic Όλο are well studied. far fewer have been seen in magnetic svstems.," While outbursts in non-magnetic DNe are well studied, far fewer have been seen in magnetic systems."
 In AM 11ου stars. which don't have clises. the lack of outbursts is expected.," In AM Her stars, which don't have discs, the lack of outbursts is expected."
 The intermediate polars (LPs). which have weaker fields and. are not. phase-locked. but do possess at. least partial clises. show several variations on the DN theme.," The intermediate polars (IPs), which have weaker fields and are not phase-locked, but do possess at least partial discs, show several variations on the DN theme."
 These are reviewed below to set the scene for this paper., These are reviewed below to set the scene for this paper.
 XY An is an IP ἵνα behind a molecular cloud (Patterson Ullalpern 1990) and so cannot be seen in the optical., XY Ari is an IP lying behind a molecular cloud (Patterson Halpern 1990) and so cannot be seen in the optical.
 X-ray and infra-red. studies (Ixamata. Tawara IxIxovama 1991: Zuckerman 11993: Allan. Lellier liltamsever 1996) show it have a 6.06-h orbital period anc a 206-5 spin period. and reveal deep eclipses implving an inclination of 280.," X-ray and infra-red studies (Kamata, Tawara Koyama 1991; Zuckerman 1993; Allan, Hellier Ramseyer 1996) show it have a 6.06-h orbital period and a 206-s spin period, and reveal deep eclipses implying an inclination of $>$."
.. To use the X-ray eclipse to study the accretion regions we observed 20 eclipses of NY Ari with (Dract. Rothschild SSwank 1993).," To use the X-ray eclipse to study the accretion regions we observed 20 eclipses of XY Ari with (Bradt, Rothschild Swank 1993)."
 The results are reported in Llellier (190972), The results are reported in Hellier (1997a).
 Llowever. NY. Avi went into outburst. during the observations. the first ever seen of this star.," However, XY Ari went into outburst during the observations, the first ever seen of this star."
 It is also only the second magnetic CV to have been observed in outburst in N-ravs. after Gly Por (Watson. Wine OOsborne 1985).," It is also only the second magnetic CV to have been observed in outburst in X-rays, after GK Per (Watson, King Osborne 1985)."
 This paper reports the outburst and discusses its implications for LPs and other CVs., This paper reports the outburst and discusses its implications for IPs and other CVs.
 ‘Table 1 lists the six well-established IPs which have shown outbursts. together with the relevant literature (see Lellicr 1993a and Warner 1997 for previous compilations).," Table 1 lists the six well-established IPs which have shown outbursts, together with the relevant literature (see Hellier 1993a and Warner 1997 for previous compilations)."
 (αν Per has a long orbit and an evolved secondary. and its month-long outbursts can be explained. as dise instabilities when the parameters are adjusted for CAN Per's peculiarities (Ixim. Wheeler," GK Per has a long orbit and an evolved secondary, and its month-long outbursts can be explained as disc instabilities when the parameters are adjusted for GK Per's peculiarities (Kim, Wheeler"
extended.,extended.
 We note. however. that even the most massive high baryon fraction galaxies with the Uattest halo axial ratios are still rather round in their outskirts.," We note, however, that even the most massive high baryon fraction galaxies with the flattest halo axial ratios are still rather round in their outskirts."
 At the mass scales explored in these simulations. disks exert. significant pressure support. which leads to thicker star forming clisks than those tvpical in higher mass galaxies (e.g. 2)).," At the mass scales explored in these simulations, disks exert significant pressure support, which leads to thicker star forming disks than those typical in higher mass galaxies (e.g. \citet{Kaufmann2007}) )."
 tecent. cleep observations of regions surrounding Local Group Dwarfs have shown structure in. their. stellar »opulations in the form of old stellar populations at. large radii and broken exponential surface densitv profiles.," Recent, deep observations of regions surrounding Local Group Dwarfs have shown structure in their stellar populations in the form of old stellar populations at large radii and broken exponential surface density profiles."
 In arger galaxies. these extended. stellar halos are thought to »e the result. of hierarchical merging.," In larger galaxies, these extended stellar halos are thought to be the result of hierarchical merging."
 In our simulations. we ind that even galaxies are able to form extended 1alos. explaining why so many cdwarls have halos. even when he expected masses of the merging sub-halos are thought ο be too low to form stars.," In our simulations, we find that even galaxies are able to form extended halos, explaining why so many dwarfs have halos, even when the expected masses of the merging sub-halos are thought to be too low to form stars."
 1n our simulations. three mechanisms contributed to an age gradient in the outer galaxy.," In our simulations, three mechanisms contributed to an age gradient in the outer galaxy."
 First. the envelope inside which star formation occurred contracted as the supply of eas diminished and. pressure support was reduced.," First, the envelope inside which star formation occurred contracted as the supply of gas diminished and pressure support was reduced."
 Second. &gas-driven disk instabilities caused bulk motion of the stellar disk over time so that stars that. formed. the longest. ago are the farthest from the current center.," Second, gas-driven disk instabilities caused bulk motion of the stellar disk over time so that stars that formed the longest ago are the farthest from the current center."
 Third. some stars were ejected far out into the halo after forming in supernova driven shocks.," Third, some stars were ejected far out into the halo after forming in supernova driven shocks."
 The ejection was somewhat more cllective at early times because of the active carly star formation., The ejection was somewhat more effective at early times because of the active early star formation.
 The importance of the three cilferent mechanisms varied with mass anc barvon fraction of the model., The importance of the three different mechanisms varied with mass and baryon fraction of the model.
 For example. the contracting star formation envelope occurred in all of our models. but began earliest in the lowest mass models.," For example, the contracting star formation envelope occurred in all of our models, but began earliest in the lowest mass models."
" The higher mass models were able to initially grow disks from the ""inside-out using their large gas reservoir.", The higher mass models were able to initially grow disks from the “inside-out” using their large gas reservoir.
 However. dwindling gas supplies halted the steady disk erowth and star formation contracted. back towards: the ealaxvecenters.ed- in a similar folnto the lower mass mocoels.," However, dwindling gas supplies halted the steady disk growth and star formation contracted back towards the galaxy centers, in a similar manner to the lower mass models."
 cb Qu th lisk were the most notable in the models with lowdearvon fraction. which replicate the οσοι of reionization by removing barvons from. low mass halos.," Bulk motions of the stellar disk were the most notable in the models with low baryon fraction, which replicate the effect of reionization by removing baryons from low mass halos."
 Lowering the barvon fraction leads to low density eas disks that can only form stars at their center., Lowering the baryon fraction leads to low density gas disks that can only form stars at their center.
 The low barvon fraction disks therefore remain gas rich and are more prone to instabilities that lead to sloshing of the embedded stellar clisk., The low baryon fraction disks therefore remain gas rich and are more prone to instabilities that lead to sloshing of the embedded stellar disk.
 The ejection of stars formed in supernova-driven shocks is most prominent in the lowest mass mocels., The ejection of stars formed in supernova-driven shocks is most prominent in the lowest mass models.
 At these mass scales. the depth of the potential well is shallow enough that supernovae can drive significant outllows. making stellar ection more likely.," At these mass scales, the depth of the potential well is shallow enough that supernovae can drive significant outflows, making stellar ejection more likely."
 Each of these three scenarios plaved a role in producing a stellar distribution with a remarkable amount of structure., Each of these three scenarios played a role in producing a stellar distribution with a remarkable amount of structure.
 Although we have not ruled out. the possibility that the structure in dwarf stellar halos is the result of hierarchical mereing. tical interactions. or cold accretion along filaments. it dis possible to produce extended stellar structures without mereing.," Although we have not ruled out the possibility that the structure in dwarf stellar halos is the result of hierarchical merging, tidal interactions, or cold accretion along filaments, it is possible to produce extended stellar structures without merging."
 We would like to thank the anonvmous referee lor many relpful comments that. significantly improved. this paper., We would like to thank the anonymous referee for many helpful comments that significantly improved this paper.
 We would also like to thank Rok Itoskar. Peter Yoachim. Yvan Maas. Anil Seth. Chris Brook anc Ben Williams. or helpful conversations ancl LOL help during this project.," We would also like to thank Rok $\check{s}$ kar, Peter Yoachim, Ryan Maas, Anil Seth, Chris Brook and Ben Williams, for helpful conversations and IDL help during this project."
 Adrienne Stilp kindly reran all the simulations after they were lost in a disk crash., Adrienne Stilp kindly reran all the simulations after they were lost in a disk crash.
" This work was made possible by he facilities of the Shared. Hierarchical Academic Research Computing Network (SILAICNIZEswvww.sharenet.ca): and acilities provided bv the University of Washington Student ""Technology ", This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET:www.sharcnet.ca) and facilities provided by the University of Washington Student Technology Fee.
Gs and PO were supported by NSE LETT erant. PIIY-0205413., GS and TQ were supported by NSF ITR grant PHY-0205413.
".- -QP3RGRA.JD was partially supported. by NSE CAREER ""1", JD was partially supported by NSF CAREER AST-0238683.
 TH acknowledges financial support from the Swiss National Science Foundation., TK acknowledges financial support from the Swiss National Science Foundation.
The weak G-band (hereafter WGB) stars are G and K giants whose spectra show very weak or absent G-bands of the CH A*A - Χ-Π system at4300A.,The weak G-band (hereafter WGB) stars are G and K giants whose spectra show very weak or absent G-bands of the CH $^{2}\Delta$ - $^{2}\Pi$ system at.
. These stars were first identified as stellar class by ?.. and have been mainly studied in the late seventies. early eighties with a total number of dedicated papers not exceeding 20 (seee.g.forinstance????)..," These stars were first identified as stellar class by \citet{bidelman1951}, and have been mainly studied in the late seventies, early eighties with a total number of dedicated papers not exceeding 20 \citep[see e.g. for
instance][]{sneden1978,rao1978,partha1980,day1980}."
 They are rare with less than 30 known to date among the population of G-K giants in the Chemical composition. studies (2?) demonstrated that they are very much underabundant in carbon (typical |C/Fe = —].4) and present small overabundanees of nitrogen and normal oxygen.," They are rare with less than 30 known to date among the population of G-K giants in the Chemical composition studies \citep{sneden1978,cottrell1978}
 demonstrated that they are very much underabundant in carbon (typical [C/Fe] $\approx -1.4$ ) and present small overabundances of nitrogen and normal oxygen."
 ? analyzed the CN red-system features in the high resolution spectra of weak G-band stars and found = 4.," \citet{sneden1978}
 analyzed the $^{13}$ CN red-system features in the high resolution spectra of weak G-band stars and found = 4."
 ?. from the photometry of the 2.3um CO vibration-rotation bands confirmed the underabundances of carbon m a large sample of weak G-band stars., \citet{hartoog1977} from the photometry of the $\mu$ m CO vibration-rotation bands confirmed the underabundances of carbon in a large sample of weak G-band stars.
 The CH band strengths observed by ? also indicate that the weakening of the G-band is due to underabundance of carbon., The CH band strengths observed by \citet{rao1978} also indicate that the weakening of the G-band is due to underabundance of carbon.
 ? obtained high resolution spectra of the 24m first-overtone CO bands in the weak G-band giants and found excellent agreement between the carbon abundances derived from CO data anc those determined using features of the CH G-band., \citet{sneden1984} obtained high resolution spectra of the $\mu$ m first-overtone CO bands in the weak G-band giants and found excellent agreement between the carbon abundances derived from CO data and those determined using features of the CH G-band.
 They have found x 4 which is in agreement with the predicted ratio for the CN-cyele in equilibrium., They have found $\le$ 4 which is in agreement with the predicted ratio for the CN-cycle in equilibrium.
 The normal abundance of oxygen and sodium shows that the atmospheres of WGB stars are probably not mixed with ON-cycle processed material (??)..," The normal abundance of oxygen and sodium shows that the atmospheres of WGB stars are probably not mixed with ON-cycle processed material \citep{sneden1978,drake1994}."
 Additional chemical constraints are given by lithium and and beryllium abundance Li abundances have been derived for several WGB stars and several stars were found to be lithium rich. e.g. with >[4 (see?) and reaching up to A(Li) = 3 (??)..," Additional chemical constraints are given by lithium and and beryllium abundance Li abundances have been derived for several WGB stars and several stars were found to be lithium rich, e.g. with $\ge 1.4$ \citep[see][]{brown1989} and reaching up to A(Li) = 3 \citep{lambert1984,partha1980}."
 ?. also report or the possible presence of ?Li in HR 1299. but the profile of the 6707 A'Li line that is better reproduced. with *Li/?Li4 0. could also be reproduced without having to invoke the presence of °Li.," \citet{lambert1984} also report on the possible presence of $^6{\rm Li}$ in HR 1299, but the profile of the 6707 $^7{\rm Li}$ line that is better reproduced with $^6{\rm
Li}/^7{\rm Li} \ne 0$ , could also be reproduced without having to invoke the presence of $^6{\rm Li}$."
 BBe abundances were derived from [IUE spectra for 3 Li-rich weak G-band stars by ?.., Be abundances were derived from IUE spectra for 3 Li-rich weak G-band stars by \citet{partha1984}.
 Providing a differential analysis between the WGB stars and K giants in the Hyades. Be is found to be similar in both groups. and compatible within presumably largeerrorbars.. with the expected post dredge-up Be abundances according to standard stellar evolution models.," Providing a differential analysis between the WGB stars and K giants in the Hyades, Be is found to be similar in both groups, and compatible within presumably large, with the expected post dredge-up Be abundances according to standard stellar evolution models."
 Due to their relative low temperature and gravity. WGB stars are classified as giants and fall amidst the very crowded area of the HR diagram populated with stars on the subgiant branch. the RGB. the core helium burning phase and the AGB.," Due to their relative low temperature and gravity, WGB stars are classified as giants and fall amidst the very crowded area of the HR diagram populated with stars on the subgiant branch, the RGB, the core helium burning phase and the AGB."
 This has made the definition of their evolutionary status and initial mass difficult., This has made the definition of their evolutionary status and initial mass difficult.
 They seem however to have been unanimously qualified as core helium burning star., They seem however to have been unanimously qualified as core helium burning star.
 In particular ? tentatively attribute à mass of =1M. to HR 6766 (e.g. HD 165634) and exclude it from being nore massive than 3 because of the magnitude they derive.," In particular \citet{sneden1978} tentatively attribute a mass of $\approx 1
\msun$ to HR 6766 (e.g. HD 165634) and exclude it from being more massive than 3 because of the magnitude they derive."
 With such a low-mass. that star should then have undergone the He flash.," With such a low-mass, that star should then have undergone the He flash."
 Let us note that their conjecture is based on a very crude estimation for the lummosity due to the large error bars impairing the parallax of HR 6766., Let us note that their conjecture is based on a very crude estimation for the luminosity due to the large error bars impairing the parallax of HR 6766.
 ? also identify WGB stars in their sample as being in the mass range 1.5 € M € 3 past the He flash., \citet{cottrell1978} also identify WGB stars in their sample as being in the mass range 1.5 $\leq$ M $\leq$ 3 past the He flash.
 Later on. ? proposed that WGB stars could be the progeny of magnetic Ap stars. with initial masses of 2-3 that have undergone a dredge-up. but they do not make any clear statement of their evolutionary status.," Later on, \citet{lambert1984} proposed that WGB stars could be the progeny of magnetic Ap stars, with initial masses of 2-3 that have undergone a dredge-up, but they do not make any clear statement of their evolutionary status."
 Much recently ??. suggest that WGBstars," Much recently \citet{partha2000,partha2002} suggest that WGBstars"
The radiative acceleration of the wind was calculated by following the fate of the photous emitted from below the photosphere with the MC technique.,The radiative acceleration of the wind was calculated by following the fate of the photons emitted from below the photosphere with the MC technique.
 To this purpose the atmosphere is divided iuto a large nuuber of concentric. thin shells with radius r. thickness Ar containing a mass Αι).," To this purpose the atmosphere is divided into a large number of concentric, thin shells with radius $r$, thickness $\Delta r$ containing a mass $\Delta m(r)$."
 The loss of photon energy due to all scatterines that occur within each shell are calculated to retrieve the total line acceleration gp(7) per shell., The loss of photon energy due to all scatterings that occur within each shell are calculated to retrieve the total line acceleration $g_{\rm L}(r)$ per shell.
 The total Bine acceleration per shell sumuued over all line scatterings in that shell equals where p(r) is the momentum of the ious in the shell., The total line acceleration per shell summed over all line scatterings in that shell equals where $p(r)$ is the momentum of the ions in the shell.
 The mmoimentim gained by the ious in the shell is equal to the momentum lost by the photons due to imteractions 1u that shell., The momentum gained by the ions in the shell is equal to the momentum lost by the photons due to interactions in that shell.
 Using the relationship between Am(r) aud Ar for thin conceutrie shells. Aon(r)=Iz?ptr)Av. and the derived relation between momentum and energy. transfer of the photons Ap=AL/e (Eq. 25)).," Using the relationship between $\Delta m(r)$ and $\Delta r$ for thin concentric shells, $\Delta m(r) = 4 \pi r^{2} \rho(r) \Delta r$, and the derived relation between momentum and energy transfer of the photons $\Delta p = \Delta E /v $ (Eq. \ref{e_gp}) ),"
 ο) can be rewritten as where MAF(rr) is sun of the οποίον loss of all the photous that are scattered in the shell., $g_{\rm L}(r)$ can be rewritten as where $\Sigma \Delta E(r)$ is sum of the energy loss of all the photons that are scattered in the shell.
 Now using mass continuity (Eq. 2)), Now using mass continuity (Eq. \ref{eq:continuity}) )
 and the fact that the total cnerey transfer XAF(r) divided by the time interval At equals the rate at which the radiation field loses enerey. ALC). e XAE(Q)/AtFΑΙ) the expression for ο(η). which is valid for each shell. πρίν becomes (Abbott Lucy 1985) The line list that is used for the ALC calculatious consists of over LO? of the strougest lines of the clemeuts II - Zu from a line List constructed by Iurucz(1988).," and the fact that the total energy transfer $\Sigma~\Delta E(r)$ divided by the time interval $\Delta t$ equals the rate at which the radiation field loses energy, $- \Delta L(r)$, i.e. $\Sigma~\Delta E(r) / \Delta t = - \Delta L(r)$, the expression for $g_{\rm L}(r)$, which is valid for each shell, simply becomes (Abbott Lucy 1985) The line list that is used for the MC calculations consists of over $10^5$ of the strongest lines of the elements H - Zn from a line list constructed by Kurucz(1988)."
 Lines in the wavelength region- between 50 aud 7000 Aare included in the calculations with ionization stages up to stageVl., Lines in the wavelength region between 50 and 7000 are included in the calculations with ionization stages up to stage.
 Typically about 210? photon packets. distributed over the spectrum at the lower bouudary of the atunosphere were followed for cach model. iie. for cach adopted set of stellar and wind parameters.," Typically about $2~10^5$ photon packets, distributed over the spectrum at the lower boundary of the atmosphere were followed for each model, i.e. for each adopted set of stellar and wind parameters."
 For several more detailed models we calculated the fate of 2LO! photon packets., For several more detailed models we calculated the fate of $2~10^7$ photon packets.
 The wind was divided iu about 50-60 concentric shells. with mauy narrow shells in the subsonic reeion and wider shells in supersonic lavers.," The wind was divided in about 50-60 concentric shells, with many narrow shells in the subsonic region and wider shells in supersonic layers."
 The division iu shells is esscutially mace on the basis of a Rosselaud optical depth scale., The division in shells is essentially made on the basis of a Rosseland optical depth scale.
 Typical changes in the logarithm of this optical depth are about 0.13., Typical changes in the logarithm of this optical depth are about 0.13.
 We predict the imass-loss rates for a grid of model atmospheres to study the behaviour of uuear the bistability jump., We predict the mass-loss rates for a grid of model atmospheres to study the behaviour of near the bi-stability jump.
 For a eiven set of stellar parameters we calculate the mass loss in the following wav: We note that Eq., For a given set of stellar parameters we calculate the mass loss in the following way: We note that Eq.
 32. oulw describes thevelobal” consistency of the iass-loss rate with the radiative acceleration., \ref{eq:consistency} only describes the“global” consistency of the mass-loss rate with the radiative acceleration.
 For the set-up of the model atinosphere the velocity law ο) is needed as input., For the set-up of the model atmosphere the velocity law $v(r)$ is needed as input.
 This means that, This means that
 2001).. Maoetal.(2002)," \citep[e.g.][]{bulge,lmc5}."
 Bennettοἱal.(2002) M~10—304L.. Agoletal.(2002) πι 9 (Gould, \citet{mao} \citet{bennett} $M\sim10-30M_\odot$ \citet{agol} $\piE$ $\thetaE$ \citep{gould}.
2000).. zi. ο1 z /j;lew ~15—20% /=2/5 , $\piE$ $\gtrsim 1$ $\piE$ $\tE\gtrsim$ $\sim15-20\%$ ${\hat t}=2\tE$ 
"Figure 3. reveals consistently higher peak frequencies. For Increasing observer angles peak»0«10,4]<7/2.","Figure \ref{fig:3d6gFig3_ions_int2} reveals consistently higher peak frequencies, $\omega_{peak}$, for increasing observer angles $0<|\theta_{peak}|<\pi/2$."
" For higher angles w),.,¢ stays approximately constant up to 0~w/2.", For higher angles $\omega_{peak}$ stays approximately constant up to $\theta\sim\pi/2$.
 Even at late times 3.. lower panel) peak frequencies ομως are observer dependent. and apparently with streaming axis inclination. angle.," Even at late times , lower panel) peak frequencies $\omega_{peak}$ are observer dependent, and apparently with streaming axis inclination angle."
" Stull. even though zc,0|>0) increases relative to the on (= 0) observer at a given time. it never exceeds the initial head-on maximum peak frequency. (0=0). in 3D. In the 2D case viewed in the peak frequency increases for all observersduring the FI. and cepeat2pρεip for all"," Still, even though $\omega_{peak}(|\theta|>0)$ increases relative to the head-on $\theta\equiv0$ ) observer at a given time, it never exceeds the initial head-on maximum peak frequency, $\omega_{peak}(\theta\equiv0)$, in 3D. In the 2D case viewed in the peak frequency increases for all observersduring the FI, and $\omega_{peak, 2D}>\omega_{peak, 3D}$ for all"
the smoothed frame cleaned from contaminating features. approximating the sky intensity distribution (measured. i1 boxes evenly placed in blank regions) by a tilted plane. using the least-squares method (rrrarsrskv command).,"the smoothed frame cleaned from contaminating features, approximating the sky intensity distribution (measured in boxes evenly placed in blank regions) by a tilted plane, using the least-squares method $\rm \scriptstyle FIT/FLATSKY$ command)."
 The frame areas having intensities above some threshold (giver the trial estimate of the sky background and its error basec on histogram analysis within the AIP package) were maskec prior to background estimation in order to avoid influence by contaminating features or the galaxy itself and to make the procedure more objective., The frame areas having intensities above some threshold (given the trial estimate of the sky background and its error based on histogram analysis within the AIP package) were masked prior to background estimation in order to avoid influence by contaminating features or the galaxy itself and to make the procedure more objective.
 To estimate sky backgrounc properly in the presence of eventual gradient. we placed the boxes relatively close to the galaxy outskirts.," To estimate sky background properly in the presence of eventual gradient, we placed the boxes relatively close to the galaxy outskirts."
 The adoptec error of the sky background. σον. equals the standard deviatior about the fitted plane.," The adopted error of the sky background, $\sigma_{\rm sky}$, equals the standard deviation about the fitted plane."
 Properly estimated sky background would show up in a asymptotically flat growth curve. whereas sky background estimation errors would cause a continuous increase or a maximum followed by a continuous decrease in the growth curve.," Properly estimated sky background would show up in an asymptotically flat growth curve, whereas sky background estimation errors would cause a continuous increase or a maximum followed by a continuous decrease in the growth curve."
 The shape of the growth curve can therefore be usec to fine-tune the sky background by simply adding/subtracting a constant to/from the frame (Binggelietal.1984)., The shape of the growth curve can therefore be used to fine-tune the sky background by simply adding/subtracting a constant to/from the frame \citep{BST_84}.
. In general. our procedures worked well though an unambiguous estimate of the sky background is not always possible. e.g.. in cases of a bright companion. an overcrowded field. or not enough field," In general, our procedures worked well though an unambiguous estimate of the sky background is not always possible, e.g., in cases of a bright companion, an overcrowded field, or not enough field"
while the enuüssiou from the jet must be related o hou-thermal processes.,while the emission from the jet must be related to non-thermal processes.
 During OM eveuts. the spectral component respousible for the variation nay display characteristic color chauges.," During OM events, the spectral component responsible for the variation may display characteristic color changes."
 Then. we developed a method with quasi-imnultaueous observations at three optical bands to analyze hese color changes that accompanied microvariability eveuts.," Then, we developed a method with quasi-simultaneous observations at three optical bands to analyze these color changes that accompanied microvariability events."
" This paper is organized as follows: iu Section ??7.. we shortly comment ou the data roatiment: in Section ο, we define a spectral variability iudex aud how to determine the OM origin: in Section ?7.. we analyze the data: finally. we discuss the results in Section ??:: while a sununary and conclusions are given in Section ??.."," This paper is organized as follows: in Section \ref{datos}, we shortly comment on the data treatment; in Section \ref{sed}, we define a spectral variability index and how to determine the OM origin; in Section \ref{results}, we analyze the data; finally, we discuss the results in Section \ref{discusion}; while a summary and conclusions are given in Section \ref{summary}."
 Details of the selection criteria. observation strategy. and data reduction have been. exposed in PL PIL and deDiego(2010).," Details of the selection criteria, observation strategy, and data reduction have been exposed in PI, PII, and \cite{de10}."
 These data consist of a sample of 22. core-dominated radio-loud quasars (CRLQ) and 22 radio quiet quasars (ROQs) observed iu diverse epochs., These data consist of a sample of 22 core-dominated radio-loud quasars (CRLQ) and 22 radio quiet quasars (RQQs) observed in diverse epochs.
 Each objec in the ΠΟΩ sample paired a CRLO objec in brightuess and redshift nuüniuiziug selection effects when properties of microvariability between both samples were compared im PIL, Each object in the RQQ sample paired a CRLQ object in brightness and redshift minimizing selection effects when properties of microvariability between both samples were compared in PII.
 Tere. we wil only discuss the data corresponding to OAL events reported in PI.," Here, we will only discuss the data corresponding to OM events reported in PII."
 This subsample is listed im Table l.., This subsample is listed in Table \ref{log5}.
 Four telescopes were used. which are locate in Mexico aud Spain.," Four telescopes were used, which are located in Mexico and Spain."
 BWR filters of Joluson-Cousins series were used., $BVR$ filters of Johnson-Cousins series were used.
" “The observationa strategv cousists of monitoring a CRLQ-RQQ couple dining the same night i overlapping sequences: five images of cach object in the BYR sequence are faken (~1 aunmmto of exposure time per image, although it depends of the object brightness. the filters and the telescope used)."," The observational strategy consists of monitoring a CRLQ-RQQ couple during the same night in overlapping sequences; five images of each object in the $BVR$ sequence are taken $\sim 1$ minute of exposure time per image, although it depends of the object brightness, the filters and the telescope used)."
 Each object was observed at moderated air inasses. always at least 30° above the horizon.," Each object was observed at moderated air masses, always at least $30^o$ above the horizon."
 Standard stars were observed to obtain the fiux level of. the frst; data set of. cach objects. in: cach welt., Standard stars were observed to obtain the flux level of the first data set of each objects in each night.
"ohn Tbhese starsi were observed| cachi ""tine that1 aea sequence of cach pair of objects was complete.", These stars were observed each time that a sequence of each pair of objects was complete.
 This nuplies] that BEENstandard stars: were observed cachB hour. approximately.," This implies that standard stars were observed each hour, approximately."
 All these stars are taken from Landolt(1992)., All these stars are taken from \citet{landolt92}.
. In addition. these standard stars are used to perform correction by atmospheric extinction.," In addition, these standard stars are used to perform correction by atmospheric extinction."
 Tn order to discern where the OMoriginates. the analysis is divided into two main steps: first. à SED model is fitted to theZifial data set. obtaining estimations of the values of the parameters of each spectral coniponent: then. the observed spectral variations are modeled using these values.," In order to discern where the OM originates, the analysis is divided into two main steps: first, a SED model is fitted to the data set, obtaining estimations of the values of the parameters of each spectral component; then, the observed spectral variations are modeled using these values."
 The simplest description of the σοι cnussion for quasars is given by a thermal aud non-thermal enission inixture (6.5. Malkin&Sargent1982: Malkan&Moore1986)).," The simplest description of the continuum emission for quasars is given by a thermal and non-thermal emission mixture (e.g., \citealt{Malkan82}; ; \citealt{Malkan86}) )."
" Thus. at any time f. the flux would be determined by the expression where the sub-iudex f£ refers to the time when aparticular data set was acquired: f; refers. to the total flux: f,; to its nou-thermal component: and fury to its thermal componcut (hereatter sub-indices Z and » indicate thermal aud non-thenual coluponcuts. respectively),"," Thus, at any time $t$, the flux would be determined by the expression where the sub-index $t$ refers to the time when aparticular data set was acquired; $f_{\nu t}$ refers to the total flux; $f_{\nu n t}$ to its non-thermal component; and $f_{\nu T t}$ to its thermal component (hereafter sub-indices $T$ and $n$ indicate thermal and non-thermal components, respectively)."
" Usually, thermal aud nou-thermal components are associated with the accretion disk and with the relativistic jet. respectively,"," Usually, thermal and non-thermal components are associated with the accretion disk and with the relativistic jet, respectively."
 Tereatter. we will adopt this asuniption.," Hereafter, we will adopt this assumption."
" At auv time f. the coutribution from cach component to the total flux can be described as dit=font?tie tor the uou-thermal component. and buo;=fore’fie for the thermal one (note that Dit,=1 yt)."," At any time $t$, the contribution from each component to the total flux can be described as $a_{\nu t} \equiv {f_{\nu n t} / f_{\nu t}}$ for the non-thermal component, and $ b_{\nu t} \equiv {f_{\nu T t} / f_{\nu t}}$ for the thermal one (note that $b_{\nu t_0}= 1-a_{\nu t_0}$ )."
 Ina naive description. the nou-tleruzad cussion Yvon the jot can be described by a simple power aw. while the thermal cuiission from the disk cau x0 modeled bv a simple blackbody.," In a naive description, the non-thermal emission from the jet can be described by a simple power law, while the thermal emission from the disk can be modeled by a simple blackbody."
 Although a shuple blackbody is au over-simplfication for the accretion disk. this is the suuplest model that fits our data (something similar has been made sroviously bv Malkan&Sargent1982: Moore LONG: auoug others).," Although a simple blackbody is an over-simplification for the accretion disk, this is the simplest model that fits our data (something similar has been made previously by \citealt{Malkan82}; \citealt{Malkan86}; among others)."
 When a giveu object is monitored ina particular üght. we cau determine au initial time. ty. which corresponds to the first⋅ data set of: observations.," When a given object is monitored in a particular night, we can determine an initial time, $t_0$, which corresponds to the first data set of observations."
i When a variation is detected we take the difference of. fluxes between a eiven⋅ data set obtained⋅at the time f. and that for the first data set: then. we normalize with respect to the initial total fiux.," When a variation is detected we take the difference of fluxes between a given data set obtainedat the time $t$ , and that for the first data set; then, we normalize with respect to the initial total flux."
 We consider that the variation is provoked bw ouly, We consider that the variation is provoked by only
The PDS of the data preceding the flare also show distinct peaks iu the low noise regime at 0.553nu,The PDS of the data preceding the flare also show distinct peaks in the low noise regime at mHz (Fig.
ullz (Fig. 3bb. label AMHM-Nowton) and nuulIz (Fig.," \ref{fig3}b b, label 4; ) and mHz (Fig."
 Ibb. label E: Cliaudra): a further peak appears in the PDS at 0.159nuualIz (label 5).," \ref{fig4}b b, label 4; ); a further peak appears in the PDS at mHz (label 5)."
 The power at this frequency is so high that the equivalent period of 2178ss can be identified by peaks iu the lieht curve (c.f., The power at this frequency is so high that the equivalent period of s can be identified by peaks in the light curve (c.f.
 arrows in Fig., arrows in Fig.
 laa}., \ref{fig1}a a).
 A PDS peak associated with or close to nuullz is clearly abseut in the flare precursor observation but there is a pea- at Luntz in the flare (abel 5)., A PDS peak associated with or close to mHz is clearly absent in the flare precursor observation but there is a peak at mHz in the flare (label 5).
" The PDS is a function of discrete frequencies. given by f, = $ with 1Xnxint 3a) and At the biuniug size.", The PDS is a function of discrete frequencies given by $\sb{n}$ = ${{n}\over{T}}$ with $\le n \le int({{T\over{2~\Delta t}}}$ ) and $\Delta$ t the binning size.
 Therefore. there is iu principle a svstematic relative frequency uncertaiutv possible of (1) = +(1I.," Therefore, there is in principle a systematic relative frequency uncertainty possible of $({{\Delta\rm f}\over{\rm f}})\sb{\rm n}$ = $\pm({{1}\over{\rm n -1}})$."
 Tn Table 2.. we sununuarize the results includius frequencyau f. wave umber p. period P. power spectral density psd and a label ID. which has the same value for frequeucies close to each other.," In Table \ref{freqlog}, , we summarize the results including frequency $f$, wave number $n$, period $P$, power spectral density psd and a label ID, which has the same value for frequencies close to each other."
 The same ID's are shown as labels in the PDS eraphs., The same ID's are shown as labels in the PDS graphs.
 We find in the aud he observations five eroups of periods. cach of which is a pair with oue member from aud one fromChandra.," We find in the and the observations five groups of periods, each of which is a pair with one member from and one from."
 The periods of the members of cach xdrare alanost identical. 1.0. ss (label 0). ss (1). TOL/G92s8 (3). 1173/1117ss (1). 2178/2307ss (5).," The periods of the members of each pair are almost identical, i.e. s (label 0), s (1), s (3), s (4), s (5)."
 They appear to be not exactly identical but concediug he naxiual possible uucertaiutv they are consistent with cach other., They appear to be not exactly identical but conceding the maximal possible uncertainty they are consistent with each other.
" This coiucideuce strouglv supports their existence aud suggests that cach pair represents the same LOCOS,", This coincidence strongly supports their existence and suggests that each pair represents the same process.
 Conzel et al. (2003)), Genzel et al. \cite{Ge2003}) )
 have published the discovery of a lG.5E2munuuin period iu the two infrared flares observed on June 15 aud June 16. 2003.," have published the discovery of a $\pm$ min period in the two infrared flares observed on June 15 and June 16, 2003."
 À look at the two published PDS shows that there are more peaks. which we have read off from their figure 2ec ancl added to Table 2. (IR/15. IR/16).," A look at the two published PDS shows that there are more peaks, which we have read off from their figure \ref{fig2}c c and added to Table \ref{freqlog} (IR/15, IR/16)."
 Except the peak at ss and wavenumber n = 16. appearing iu the June 16," Except the peak at s and wavenumber n = 16, appearing in the June 16"
We aclelress the question of the tux variability expected rom the simulations by calculating. the probability of variations larger than a given threshold as a function of time difference between steps.,We address the question of the flux variability expected from the simulations by calculating the probability of variations larger than a given threshold as a function of time difference between steps.
 The low time-resolution data has he advantage of spanning the entire runs. but is not useful o predict the expected variations on timescales shorter than 107 vr.," The low time-resolution data has the advantage of spanning the entire runs, but is not useful to predict the expected variations on timescales shorter than $10^2$ yr."
 We use the high time-resolution data sets to make an estimate of the Dux. variations over shorter timescales. out we caution that the analyzed time intervals may not be representative of the entire simulation.," We use the high time-resolution data sets to make an estimate of the flux variations over shorter timescales, but we caution that the analyzed time intervals may not be representative of the entire simulation."
 We use this approach because re-running the entire simulations to produce data al ~10 vr resolution is not feasible., We use this approach because re-running the entire simulations to produce data at $\sim 10$ yr resolution is not feasible.
 Figures 6 and 7 show the probabilities ofthreshold For time differences between 1 and 60 kvr for Run A and Run D respectively., Figures 6 and 7 show the probabilities of for time differences between 1 and 60 kyr for Run A and Run B respectively.
 The panels correspond. to [lux increments larger than 10X. the panels correspond to 50%. and the panels to 90%.," The panels correspond to flux increments larger than $10~\%$, the panels correspond to $50~\%$, and the panels to $90~\%$."
 On average. regions tend to expand. making a given Hux increment to be more likely to happen for larger time intervals than for shorter ones.," On average, regions tend to expand, making a given flux increment to be more likely to happen for larger time intervals than for shorter ones."
 Figures S and 9 show the probabilities ofthreshold (in modulus) for Run A and Run D respectively., Figures 8 and 9 show the probabilities of (in modulus) for Run A and Run B respectively.
 At Af730 kwr the negative-change, At $\Delta t > 30$ kyr the negative-change
Alethyl formate (HICOOCII;) is the simplest. example of an ester.,Methyl formate $_{3}$ ) is the simplest example of an ester.
 Lt ds derived. from the formic acid (1ςου. where a methyl group is attached to the carboxyl group.," It is derived from the formic acid (HCOOH), where a methyl group is attached to the carboxyl group."
 ]t is an important organic complex molecule that was first detected. by Brown et al. (, It is an important organic complex molecule that was first detected by Brown et al. (
1975) towards the Ser D2(N). the richest. molecular source in the galaxy. located in the Galactic Centre giant clouc Ser B2.,"1975) towards the Sgr B2(N), the richest molecular source in the galaxy located in the Galactic Centre giant cloud Sgr B2."
 It is considered to play a kev role in understanding the origin of life because. it leads to the synthesis of bio-polvmers., It is considered to play a key role in understanding the origin of life because it leads to the synthesis of bio-polymers.
 Methyl formate has two structural isomers. elvcolaldehvde (HOOCLHISOLD and acetic acid CCLI4COOLLD. but it has been reported that this molecule is the most abundant among these isomers (Hollis et al.," Methyl formate has two structural isomers, glycolaldehyde $_{2}$ OH) and acetic acid $_{3}$ COOH), but it has been reported that this molecule is the most abundant among these isomers (Hollis et al."
 2001)., 2001).
 Particularly. its column density in the Orion Llot Core was derived to be 9.4 x 107 em7 by Ikeda ct al. (," Particularly, its column density in the Orion Hot Core was derived to be 9.4 x $^{15}$ $^{-2}$ by Ikeda et al. ("
2001) and this value was confirmed. by Sakai et al. (,2001) and this value was confirmed by Sakai et al. (
2007).,2007).
 Methyl formate has also been detected in the G31.41|0.31 vot molecular core (HNIC): its column censitv is observed o be 3.4. x 107 cem7 around this region., Methyl formate has also been detected in the G31.41+0.31 hot molecular core (HMC); its column density is observed to be 3.4 x $^{18}$ $^{-2}$ around this region.
 Cazaux et al. (, Cazaux et al. (
2003) observed methyl formate in the hot core around the otostellar object LAS 16293-2422.,2003) observed methyl formate in the hot core around the protostellar object IRAS 16293-2422.
 Hence methyl formate seems to be ubiquitous in star forming Several studies have been carried out on methyl formate o understand. its formation mechanisms. but it ids still debated whether complex organic molecules form on dust icv mantles during the cold phase. on grains during the warm-up johase or in the gas phase.," Hence methyl formate seems to be ubiquitous in star forming Several studies have been carried out on methyl formate to understand its formation mechanisms, but it is still debated whether complex organic molecules form on dust icy mantles during the cold phase, on grains during the warm-up phase or in the gas phase."
 Despite a large activation energy oxwrier between protonated methanol and. formaldehyde (llorn et al., Despite a large activation energy barrier between protonated methanol and formaldehyde (Horn et al.
 2004). Garrod et al. (," 2004), Garrod et al. ("
2006) found that the alter route of formation is viable during the tev mantle sublimation phase.,2006) found that the latter route of formation is viable during the icy mantle sublimation phase.
 Moreover. very recently. Laas οἱ al. (," Moreover, very recently, Laas et al. ("
2011) have proposed. two Fischer esterification (the acid-catalysed reaction of a carboxylic acid with an alcohol to eive an ester) pathways that occur during the warming-up ohase. involving protonatecl formic acid. ancl methanol and protonated methanol and neutral formic acid. respectively.,"2011) have proposed two Fischer esterification (the acid-catalysed reaction of a carboxylic acid with an alcohol to give an ester) pathways that occur during the warming-up phase, involving protonated formic acid and methanol and protonated methanol and neutral formic acid, respectively."
 Both reactions have two channels that correlate to cis- trans- protonated methyl formate., Both reactions have two channels that correlate to cis- trans- protonated methyl formate.
 They emphasised that methanol ohotodissociation branching ratios ancl warni-up timescales influence the relative ratios between these two geonietries., They emphasised that methanol photodissociation branching ratios and warm-up timescales influence the relative ratios between these two geometries.
 The possibility that more complex species are formed at low temperatures on surfaces has been investigated: before (e.g. Charnley 1997. 2001: Herbst van Dishoeck 2009) and in particular methyl formate production on dust. surfaces was first. proposed. by Llerbst (2005): CO. € and O Lead to the formation of CLI4O and HCO radicals. both known as methyl formate precursors.," The possibility that more complex species are formed at low temperatures on surfaces has been investigated before (e.g. Charnley 1997, 2001; Herbst van Dishoeck 2009) and in particular methyl formate production on dust surfaces was first proposed by Herbst (2005): CO, C and O lead to the formation of $_{3}$ O and HCO radicals, both known as methyl formate precursors."
 Dased on this pathway and using energetic electrons at. LO Ix. laboratory experiments were performed by Bennet Ixaiser. (2007) in order to produce methyl formate and. estimate the rate coefficients [or this reaction.," Based on this pathway and using energetic electrons at 10 K, laboratory experiments were performed by Bennet Kaiser (2007) in order to produce methyl formate and estimate the rate coefficients for this reaction."
 Dillerent. experiments. involving methyl formate were also performed by Cerakines et al. (, Different experiments involving methyl formate were also performed by Gerakines et al. (
1996) and Obere et al. (,1996) and Oberg et al. (
2009). which obtained. this molecule alter UV. photolysis of pure methanol and ΟΙ ico mixtures.,"2009), which obtained this molecule after UV photolysis of pure methanol and $_{3}$ OH ice mixtures."
 Recenth. a laboratory study by Modica Palumbo (2010) has suggested a new solid state route of formation for this molecule.," Recently, a laboratory study by Modica Palumbo (2010) has suggested a new solid state route of formation for this molecule."
 By using infrared spectroscopy in the 4400 - 400 range for in situ. monitoring the sample during the experiments. they simulated a cosmic lon irradiation on a binary mixture containing ΟΙ and CO," By using infrared spectroscopy in the 4400 - 400 $^{-1}$ range for in situ monitoring the sample during the experiments, they simulated a cosmic ion irradiation on a binary mixture containing $_{3}$ OH and CO"
[rom allowing a rotation rate greater than 200 ! at the Pleiades age for (he mininunm LDD mass (Burke&Pinsonneault2000).,from allowing a rotation rate greater than 200 $^{-1}$ at the Pleiades age for the minimum LDB mass \citep{bur00}.
. Such high rotation rates are only observed [ου solur-niass stars. and our adopted 65 ! rotation rate at Pleiades age in this study is more appropriate for the lower mass stars relevant to the LDB ages.," Such high rotation rates are only observed for solar-mass stars, and our adopted 65 $^{-1}$ rotation rate at Pleiades age in this study is more appropriate for the lower mass stars relevant to the LDB ages."
 Our second limiting case lor (he rotational evolution examines the impact of efficient angular momentum loss., Our second limiting case for the rotational evolution examines the impact of efficient angular momentum loss.
 The stars are forced to evolve at a constant rotational velocity malched to (he Pleiades rotation rates as described in (he preceding paragraph up to an age of 120 Myr and henceforth evolve at constant angular momentum., The stars are forced to evolve at a constant rotational velocity matched to the Pleiades rotation rates as described in the preceding paragraph up to an age of 120 Myr and henceforth evolve at constant angular momentum.
 This results in vounger ages for the minimum LDD mass and vounger ages for the highest LDB mass., This results in younger ages for the minimum LDB mass and younger ages for the highest LDB mass.
 Open cluster members of a given mass have a wide range of rotation rates which indicates a varietv of evolutionary sequences (Ierndrupetal.2000)., Open cluster members of a given mass have a wide range of rotation rates which indicates a variety of evolutionary sequences \citep{ter00}.
.. Thus an open cluster of a given age mav have a less well defined LDB as a result of stars with dillering rotation rates depleting lithium slightly earlier or later than our reference case., Thus an open cluster of a given age may have a less well defined LDB as a result of stars with differing rotation rates depleting lithium slightly earlier or later than our reference case.
 Our limiting cases for the angular momentum evolution allows us to equantifv this rotational “smearing” of the LDB location., Our limiting cases for the angular momentum evolution allows us to quantify this rotational “smearing” of the LDB location.
" The rotational LDB ""smearing is quantified by calculating the difference in bolometric magnitude of the lithium depletion at fixed age.", The rotational LDB “smearing” is quantified by calculating the difference in bolometric magnitude of the lithium depletion at fixed age.
 By comparing our no angular momentum loss caleulation to the efficient angular momentum loss ealeulation. we find the difference in bolometric magnitude at [ixed age between these calculations is 0.12 and 0.04 mag lor voung and old clusters. respectively.," By comparing our no angular momentum loss calculation to the efficient angular momentum loss calculation, we find the difference in bolometric magnitude at fixed age between these calculations is 0.12 and 0.04 mag for young and old clusters, respectively."
 In conclusion. since these calculations that include rotation are limiting cases {hese deviations are conservatively considered as 2-6 effects.," In conclusion, since these calculations that include rotation are limiting cases these deviations are conservatively considered as $\sigma$ effects."
 Thus. rotation negligibly affects the LDB calculation and extent of the observed LDB in comparison to the other sources of (theoretical and observational errors.," Thus, rotation negligibly affects the LDB calculation and extent of the observed LDB in comparison to the other sources of theoretical and observational errors."
 Thus. we do not include a contribution of these effects in the overall error budget for the LDB age technique.," Thus, we do not include a contribution of these effects in the overall error budget for the LDB age technique."
 Input. physics that affect the superadiabatic and radiative regions of ihe aümosphere dominate the uncertainty in the LDD ages., Input physics that affect the superadiabatic and radiative regions of the atmosphere dominate the uncertainty in the LDB ages.
 Qualitativelv. results from the previous section imply that the uncertainty in the lithium age dating techuique is larger for the higher masses. even though (he input physics for the higher masses are relatively more secure.," Qualitatively, results from the previous section imply that the uncertainty in the lithium age dating technique is larger for the higher masses, even though the input physics for the higher masses are relatively more secure."
 This behavior in the LDD uncertainty is explained in the following wav., This behavior in the LDB uncertainty is explained in the following way.
 For a eiven sel of physical inputs. the LDB age as a function of luminosity is a sequence of mass.," For a given set of physical inputs, the LDB age as a function of luminosity is a sequence of mass."
 llowever. for (he lowest masses. variations in the effective temperature of a star move the resulting LDB ageand luminosityparallel to (he sequence in mass.," However, for the lowest masses, variations in the effective temperature of a star move the resulting LDB age–and luminosity–parallel to the sequence in mass."
 This effect results in the, This effect results in the
impossible to get for real galaxies. for which the formation timescale is probably much larger than a few Myr.,"impossible to get for real galaxies, for which the formation timescale is probably much larger than a few Myr."
 If we would use o-enhanced tsochrones (Salasnichetal.2000:VandenBergetal. 2000..VAZO3). required to get the correct [Mg/Fe] ratios in giant ellipticals. assuming a solar-like element partition for the [Mg/Ca| and [Fe/Ca]. we would predict even larger Ca indices (VAZO3).. increasing the discrepancy.," If we would use $\alpha$ -enhanced isochrones \citealt{salasnich00,vandenberg00}, ,VAZ03), required to get the correct [Mg/Fe] ratios in giant ellipticals, assuming a solar-like element partition for the [Mg/Ca] and [Fe/Ca], we would predict even larger Ca indices \citepalias{vazdekis03}, increasing the discrepancy."
 Next we discuss the apparent Ca underabundance at large “'eloeity dispersions in terms of a dwarf-enhanced IMF., Next we discuss the apparent Ca underabundance at large velocity dispersions in terms of a dwarf-enhanced IMF.
 The cuversality of the IMF has been a matter of controversy i1 the last decades (see Gilmore2001. and Eisenhauer2001. for current reviews of observational keys in favour and against this statement)., The universality of the IMF has been a matter of controversy in the last decades (see \citealt{gilmore01} and \citealt{eisenhauer01} for current reviews of observational keys in favour and against this statement).
 IMF time variations among ellipticals have beer studied by Cenarroetal.(2003). in detail., IMF time variations among ellipticals have been studied by \citet{cenletter} in detail.
 An advantage of this approach is its ability to explain both. the large Mg and the [Mg/Fe]| values observed in giant ellipticals (Vazdekisetal.1996;Cenarroetal. 2003).," An advantage of this approach is its ability to explain both, the large Mg and the [Mg/Fe] values observed in giant ellipticals \citep{vazdekis96,cenletter}."
. The effect of a dwarf-dominatec IMF is a weakening of the tindex (VAZO3; Cenarroetal. 2003))., The effect of a dwarf-dominated IMF is a weakening of the index (VAZ03; \citealt{cenletter}) ).
 This effect is stronger at high metallicities., This effect is stronger at high metallicities.
 As also mentioned in SAGO2.. there are four observational drawbacks against this hypothesis: first: indications of an IMF flatter than Salpeter in the bulge of our own Galaxy (Zoccalietal.2000).. second: the fact that the predicted FeH 9916 ffeature is significantly stronger than what it is observed (Carteretal.1986).. and third: the discrepancy between visual M/L ratios 10. Vazdekisetal.1996;Maraston 1998)) and dynamical estimates M/L6 (Gerhardetal.2001)..," As also mentioned in \citetalias{saglia02}, there are four observational drawbacks against this hypothesis: first: indications of an IMF flatter than Salpeter in the bulge of our own Galaxy \citep{zoccali00}, second: the fact that the predicted FeH 9916 feature is significantly stronger than what it is observed \citep{carter86}, and third: the discrepancy between visual M/L ratios $>$ 10, \citealt{vazdekis96,maraston98}) ) and dynamical estimates $\approx$ 6 \citep{gerhard01}."
 An additional drawback is that visual-infrared (V/— A) colors are just at the verge of what it is observed in Es. as pointed out by Cenarroetal.(2003).," An additional drawback is that visual-infrared $V-K$ ) colors are just at the verge of what it is observed in Es, as pointed out by \citet{cenletter}."
. The use of composite stellar populations is analysed by SAGO2., The use of composite stellar populations is analysed by \citetalias{saglia02}.
 Their analysis reveals that a combination of populations including a low-metallicity component was not able to explain the low value of aand ttogether with H./ for the most massive galaxies., Their analysis reveals that a combination of populations including a low-metallicity component was not able to explain the low value of and together with $\beta$ for the most massive galaxies.
 Our independent analysis confirms their result., Our independent analysis confirms their result.
 Ca is known to be highly depleted onto dust in the interstellar medium (Crinklawetal.1994)., Ca is known to be highly depleted onto dust in the interstellar medium \citep{crinklaw94}.
. Could it be that it is also depleted in stars?, Could it be that it is also depleted in stars?
 The evidence is not strong., The evidence is not strong.
 Such depletion in stars would require that. during star formation. interstellar dust is recycled less than interstellar gas.," Such depletion in stars would require that, during star formation, interstellar dust is recycled less than interstellar gas."
 Moreover. depletion would have to be stronger in more dusty galaxies. so one would expect a large scatter in the -— 7 relation due to depletion.," Moreover, depletion would have to be stronger in more dusty galaxies, so one would expect a large scatter in the – $\sigma$ relation due to depletion."
 At least. the scatter for bulges of spirals. which are generally more dusty than ellipticals. should be larger.," At least, the scatter for bulges of spirals, which are generally more dusty than ellipticals, should be larger."
 Since this is not seen. we argue that depletion can be excluded as the origin of the low vvalues.," Since this is not seen, we argue that depletion can be excluded as the origin of the low values."
 In summary. many mechanisms can be used to try to explain the apparent underabundance of Ca for massive galaxies.," In summary, many mechanisms can be used to try to explain the apparent underabundance of Ca for massive galaxies."
 However none of them alone seems to be able to explain all the observations., However none of them alone seems to be able to explain all the observations.
 In the light of the discrepancies found between all the possibilities. a combination of several effects could be in place.," In the light of the discrepancies found between all the possibilities, a combination of several effects could be in place."
 More work is still needed to provide an answer to this problem., More work is still needed to provide an answer to this problem.
 We thank Javier Cenarro and Javier Gorgas for providing us with software and data in electronic form. and for many useful discussions that have helped to improve this letter.," We thank Javier Cenarro and Javier Gorgas for providing us with software and data in electronic form, and for many useful discussions that have helped to improve this letter."
 JFB acknowledges the finantial support from a PPARC studentship., JFB acknowledges the finantial support from a PPARC studentship.
 The William Herschel Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de sica de Canarias., The William Herschel Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de sica de Canarias.
recent surveys are in good agreement within the error range (Ojha et al.,recent surveys are in good agreement within the error range (Ojha et al.
 1996. Robin et al.," 1996, Robin et al."
 1996. Duser et al 1998).," 1996, Buser et al 1998)."
" Table 3 shows that the value of Xy;tr.f,) predicted by the post-thin model are cousisteut with most of the previous results from Literatures. while Myyia(r..t,) predicted by the pre-thin model is larger than the previous data frou studies of «tar counts;"," Table 3 shows that the value of $\Sigma_{thick}(r_{\odot},t_g)$ predicted by the post-thin model are consistent with most of the previous results from literatures, while $\Sigma_{thick}(r_{\odot},t_g)$ predicted by the pre-thin model is larger than the previous data from studies of star counts."
 To illustrate this quantitatively. Fieure 2 shows the \? asa fuuction of the Xi;(rif) within reasouable rauge for both the pre-thin model (loug dashed curve) aud post-thin model (full curve) iu which other free parameters are fixed as rmOC. tg=l.OGyer aud ziLüCvr.," To illustrate this quantitatively, Figure 2 shows the $\chi^2$ as a function of the $\Sigma_{thick}(r_{\odot},t_g)$ within reasonable range for both the pre-thin model (long dashed curve) and post-thin model (full curve) in which other free parameters are fixed as $\tau_{t}$ =1.0Gyr, $t_{max}$ =1.0Gyr and $\tau_d$ =4.0Gyr."
 It is shown that the value of 4? is very scusitive 0 οty).," It is shown that the value of $\chi^2$ is very sensitive to $\Sigma_{thick}(r_{\odot},t_g)$."
 This suggests that the thick disk has great influence on the Galactic chemical evolution., This suggests that the thick disk has great influence on the Galactic chemical evolution.
 Iu figure 2. three short horizontal lines iudicate the model coufideutial evel of 3054. (dotted line). 50% (lone dashed line) aud 705€ (full line). respectively.," In figure 2, three short horizontal lines indicate the model confidential level of $30\%$ (dotted line), $\%$ (long dashed line) and $\%$ (full line), respectively."
" The )oiuts in Figure 2 indicate the different results of 47 if the value of Xo;tr.f,) frou en Literatures (Table 23/) are adopted for both the pre-thin model (open squares) aud »ost-thiu model (open circles). respectively."," The points in Figure 2 indicate the different results of $\chi^2$ if the value of $\Sigma_{thick}(r_{\odot},t_g)$ from ten literatures (Table 3 ) are adopted for both the pre-thin model (open squares) and post-thin model (open circles), respectively."
 Figure 2 shows that. for the post-thin model. five poiuts have model confidential level arecr than 70%. while only two points have confidential level laveer than 705€ for the model.," Figure 2 shows that, for the post-thin model, five points have model confidential level larger than $\%$, while only two points have confidential level larger than $\%$ for the pre-thin model."
 This suggestsOO that the post-thin model be better than pre-thiu model., This suggests that the post-thin model be better than pre-thin model.
 Other evidences tended to favour the post-thiu scenario for the formation of thick disk comes roni the following facts., Other evidences tended to favour the post-thin scenario for the formation of thick disk comes from the following facts.
 First. the thick disk is kinematically distinct from the thin disk and it shows no kincmatic gradients (Ojla et al 1991 a.b).," First, the thick disk is kinematically distinct from the thin disk and it shows no kinematic gradients (Ojha et al 1994 a,b)."
 Secoud. Cilmore et al (1995) studied metallicity distribution of thick disk stars up to about 3&pe from the Galactic plane.," Second, Gilmore et al (1995) studied metallicity distribution of thick disk stars up to about $3kpc$ from the Galactic plane."
 They found that thick disk stars show uo vertical abundance gradient., They found that thick disk stars show no vertical abundance gradient.
 This argues against dissipational setting as the formation process of the thick disk (Freeman 1996)., This argues against dissipational setting as the formation process of the thick disk (Freeman 1996).
 Based on the above discussions. we treat the post-thin model with 7521.0 Car. Πλ 00v. T=LO Cor aud Senin.ty j= LOOAL.pe2 as the best-fit model.," Based on the above discussions, we treat the post-thin model with $\tau_t$ =1.0 Gyr, $t_{max}$ =1.0Gyr, $\tau_d$ =4.0 Gyr and $\Sigma_{thick}(r_{\odot},t_g)$ = $M_\odot pc^{-2}$ as the best-fit model."
 Figure 3 presents the comparison between our best-fit model predictious for the AMR aud the observations., Figure 3 presents the comparison between our best-fit model predictions for the AMR and the observations.
 The full line is our model predictions aud the points arc observational data taken from Edvardsson et al (1993)., The full line is our model predictions and the points are observational data taken from Edvardsson et al (1993).
" Figure 3 shows that. at the oeinniug of the formation of the thick disk (f£=f,,,, 1.0Ggr). the iron abuudauce of ISM decreases a little due to the iucreasiug infall rate of the primordial eas."," Figure 3 shows that, at the beginning of the formation of the thick disk $t=t_{max}=1.0Gyr$ ), the iron abundance of ISM decreases a little due to the increasing infall rate of the primordial gas."
 After hat phase. the model predicts that the metallicity increases smoothly with time.," After that phase, the model predicts that the metallicity increases smoothly with time."
 The overall tendency for this relation is consistent with the mean observations. but the preseut nodel can not reproduce the large observed scatters.," The overall tendency for this relation is consistent with the mean observations, but the present model can not reproduce the large observed scatters."
 Nordstrom et al. (, Nordstrom et al. (
1997) discussed in detail the main hypotheses for the origin of this scatter. such as star formation im au Inhomogencous gaseous medium. orbital diffusion iu homogeneous galaxy and miergers or,"1997) discussed in detail the main hypotheses for the origin of this scatter, such as star formation in an inhomogeneous gaseous medium, orbital diffusion in homogeneous galaxy and mergers or"
The epoch of reionization (EoR). when the first luminous sources reionized the neutral hydrogen in the intergalactic medium (IGM). is currently the frontier of observational astronomy.,"The epoch of reionization (EoR), when the first luminous sources reionized the neutral hydrogen in the intergalactic medium (IGM), is currently the frontier of observational astronomy."
 Observations of the Cosmic Microwave Background Radiation (CMBR) (Komatsuetal.2011:Larson2011) and. high redshift quasar absorption spectra (Beckeretal.2001:Fan2006:Willottetal.2009) jointly suggest that reionization took place over an extended period spanning the redshift range 6x2:15 (seee.g.Mitraetal. 2011)..," Observations of the Cosmic Microwave Background Radiation (CMBR) \citep{komatsu11,larson11} and high redshift quasar absorption spectra \citep{becker01,fan06,willott09} jointly suggest that reionization took place over an extended period spanning the redshift range $6 \le
z \le 15$ \citep[see e.g.][]{2011MNRAS.413.1569M}. ."
 Observations of high redshift Ly a-emitting galaxies (Malhotra&Rhoads2004:Ouchietal.2010:Kashikawaetal.2011) and gamma ray bursts (Totanietal.2006) are also consistent with this picture.," Observations of high redshift Ly $ \alpha $ -emitting galaxies \citep{malhotra04,ouchi10,kashikawa11} and gamma ray bursts \citep{totani06} are also consistent with this picture."
 Observations of redshifted 21-em radiation are considered to constitute the most promising tool to probe the EoR tforareviewseeFurlanettoetal.20€ 06., Observations of redshifted 21-cm radiation are considered to constitute the most promising tool to probe the EoR \citep[for a review see][]{fur06}.
 For the past few years substantial efforts have been undertaken both on the theoretical and experimental side (reviewedinMorales&Wyithe2010)., For the past few years substantial efforts have been undertaken both on the theoretical and experimental side \citep[reviewed in][]{morales10}.
". The first generation of low frequency radio telescopes (GMRT*..LOFAR?..MWA*.. PAPER"")) is either operational or will be operational very soon."," The first generation of low frequency radio telescopes (, ) is either operational or will be operational very soon."
 Preliminary results from these facilities include foreground measurements at EoR frequencies (Alietal.2008:Bernardial.2009:PenetPaciga2010) as well as some constraints on reionization (Bowman&Rogers2010:Paciga 2010).," Preliminary results from these facilities include foreground measurements at EoR frequencies \citep{ali08,bernardi09,pen09,paciga10} as well as some constraints on reionization \citep{bowman10,paciga10}."
 Motivated by the detection possibility of theEoR 21-em signal and the subsequent science results. a wide range of efforts are ongoing on the theoretical side with the goal to understandthe physies of reionization and its expected 21-em signal.," Motivated by the detection possibility of the EoR 21-cm signal and the subsequent science results, a wide range of efforts are ongoing on the theoretical side with the goal to understandthe physics of reionization and its expected 21-cm signal."
 Furlanetto developed analytical models to calculate the ionized, \citet{fur04} developed analytical models to calculate the ionized
bottom) aud 2-D ruptures or tectonic pate spreading.,bottom) and 2-D ruptures or tectonic plate spreading.
 Landslides were found in a rauge of agzm1.7οιUo which also implies a mixed dimensionality of Dzz(0.9.L5. ranging from 1-1) avalanches guided alone local valleys to 2-D avalanches that spread over flat Lill sides.," Landslides were found in a range of $\alpha_E\approx 1.7-3.3$, which also implies a mixed dimensionality of $D \approx 0.9-1.8$, ranging from 1-D avalanches guided along local valleys to 2-D avalanches that spread over flat hill sides."
 Forest fires were reported to have powerlaw slopes of apxm]ολο01.05 (Turcotte 1999). which is perfectly consistent with 2-D area-spreading in exteuded forest reeious.," Forest fires were reported to have powerlaw slopes of $\alpha_E\approx 1.3-1.5$ (Turcotte 1999), which is perfectly consistent with 2-D area-spreading in extended forest regions."
 Even city sizes were found to folow a powerlaw slope of agzx1.1 (Zaucette 2007). which corresponds to the urxui sprawl over 2-D areas.," Even city sizes were found to follow a powerlaw slope of $\alpha_E\approx 1.4$ (Zanette 2007), which corresponds to the urban sprawl over 2-D areas."
 Deskles energy. distributions. also the distrilutions of spatial scales of SOC events cau shed some lielit iuto the ractal ecometry of the energy dissipation regions.," Besides energy distributions, also the distributions of spatial scales of SOC events can shed some light into the fractal geometry of the energy dissipation regions."
 According to Eq., According to Eq.
 3 we expect a fragmentation scaling o DN(L)wL°%., 3 we expect a fragmentation scaling of $N(L) \propto L^{-3}$.
 Such a spatial fragmentation scaling law is iudeed confirmed for tlie sizes or Saturn rugs. Lo. ΑΠ)xL? (Zoebker et al.," Such a spatial fragmentation scaling law is indeed confirmed for the sizes or Saturn rings, i.e., $N(L) \propto L^{-3}$ (Zebker et al."
 1985: Freuch and Nicholson 20003: for the sizes of asteroids. Ίο ANO)xL2L!m (Ivezie et al.," 1985; French and Nicholson 2000); for the sizes of asteroids, i.e., $N(L) \propto L^{-2.3}... L^{-4}$ (Ivezic et al."
 2001): and for sizes of lunar craters. i6. a cumulative distribution (Cross 1966). which corresponds to the differential distribution N(L)κE..m ," 2001); and for sizes of lunar craters, i.e., a cumulative distribution $N^{cum}(>L) \propto L^{-2}$ (Cross 1966), which corresponds to the differential distribution $N(L) \propto L^{-3}$."
"Iu conclusion. our universal model for fractal euergyOo, dissipation dominus nm svstenis with selforeanizedOo criticality predicts (1) the powerlaw shape of occurrence frequency distributions of energies. as well as (1) a relationship of ag=3/DMi between the he powerlaw slope ag and the fractal dimension D of the energv dissipation domain."," In conclusion, our universal model for fractal energy dissipation domains in systems with self-organized criticality predicts (i) the powerlaw shape of occurrence frequency distributions of energies, as well as (ii) a relationship of $\alpha_E=3/D$ between the the powerlaw slope $\alpha_E$ and the fractal dimension $D$ of the energy dissipation domain."
" Most observed occurrence frequency distributions of SOC events exhibit a powerlaw-like function with a slope of agz5,1.5. which is predicted for instabilitics that have 2-D area-like propagation characteristics. such as tectouic plate ruptures in earthquakes or current sheets iu magnetic reconnection regions."," Most observed occurrence frequency distributions of SOC events exhibit a powerlaw-like function with a slope of $\alpha_E \approx 1.5$, which is predicted for instabilities that have 2-D area-like propagation characteristics, such as tectonic plate ruptures in earthquakes or current sheets in magnetic reconnection regions."
 This now scaling law could be corroborated by investigating the geometric 1iorphlology of eucrev dissipation events aud their statistical frequency distributious iu observations with spatial imagine capabilities. while it provides gcoimoetric predictions for ποιασας astroplivsical observations.," This new scaling law could be corroborated by investigating the geometric morphology of energy dissipation events and their statistical frequency distributions in observations with spatial imaging capabilities, while it provides geometric predictions for non-imaging astrophysical observations."
 This work is partially supported by NASA coutract NAS5-98033 of the RIIESSI mission through University of California. Berkeley. (subcontract SA22LI-26308P," This work is partially supported by NASA contract NAS5-98033 of the RHESSI mission through University of California, Berkeley (subcontract SA2241-26308PG)."
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 "
"improvement in the fit, to x?/dof of 1278/1167.","improvement in the fit, to $\chi^{2}$ /dof of 1278/1167."
" The LAOR line still had a high EW of ~0.6-0.9 keV, with disc emissivity index 6~3.5, and inner radius Rin~1.5R,."," The LAOR line still had a high EW of $\sim$ 0.6-0.9 keV, with disc emissivity index $\beta$$\sim$ 3.5, and inner radius $R_{in}$$\sim$ $R_{g}$."
" The gaussian emission line component had an rms width c = 0.28+0.15 keV and EW = 0.25+0.11 keV. The (poorly constrained) joint line energy was ~6.2 keV, or ~6.7 keV in the source rest frame, implying reflection from ionised matter."," The gaussian emission line component had an rms width $\sigma$ = $\pm$ 0.15 keV and EW = $\pm$ 0.11 keV. The (poorly constrained) joint line energy was $\sim$ 6.2 keV, or $\sim$ 6.7 keV in the source rest frame, implying reflection from ionised matter."
" We then attempted to fit the narrow absorption features visible in figure 2, initially with gaussian shaped absorption lines in Xspec."," We then attempted to fit the narrow absorption features visible in figure 2, initially with gaussian shaped absorption lines in Xspec."
" Adding a gaussian line with energy, width and equivalent width free gave a significantly better fit to the absorption near 7 keV than an absorption edge."," Adding a gaussian line with energy, width and equivalent width free gave a significantly better fit to the absorption near 7 keV than an absorption edge."
" The observed line energy was 7.02+0.03 keV, with o «100 eV, and an EW of 986-28 eV. The addition of this gaussian absorption line improved the fit to x? /dof = 1246/1164."," The observed line energy was $\pm$ 0.03 keV, with $\sigma$$\leq$ 100 eV, and an EW of $\pm$ 28 eV. The addition of this gaussian absorption line improved the fit to $\chi^{2}$ /dof = 1246/1164."
 The most likely identifications of this line are Lya of FeXXVI or the primary 1s-2p resonance transition in He-like FeXXV., The most likely identifications of this line are $\alpha$ of FeXXVI or the primary 1s-2p resonance transition in He-like FeXXV.
" 'The rest energies of these lines are separated by 0.26 keV, which would be resolved (or at least produce a broad line) in the EPIC data."," The rest energies of these lines are separated by 0.26 keV, which would be resolved (or at least produce a broad line) in the EPIC data."
" The narrowness of the observed feature at ~7 keV suggests the former identification, with any absorption from the FeXXV line modifying the Fe K emission line. ("," The narrowness of the observed feature at $\sim$ 7 keV suggests the former identification, with any absorption from the FeXXV line modifying the Fe K emission line. ("
We recall evidence for variable line-of-sight absorption superposed on the Fe K emission line has been previously seen in an oobservation of Mkn 766; Pounds 22003b).,We recall evidence for variable line-of-sight absorption superposed on the Fe K emission line has been previously seen in an observation of Mkn 766; Pounds 2003b).
" A second narrow gaussian line at 7.90.04 keV was less significant, reducing x? to 1234 for 1161 dof."," A second narrow gaussian line at $\pm$ 0.04 keV was less significant, reducing $\chi^{2}$ to 1234 for 1161 dof."
" In this case a statistically better fit (x?/dof of 1228/1161) was obtained with an absorption edge at ~7.7 keV, or with a broader line of width σ ~0.3 keV centred at ~8.05 keV (EW of 452-12 eV)."," In this case a statistically better fit $\chi^{2}$ /dof of 1228/1161) was obtained with an absorption edge at $\sim$ 7.7 keV, or with a broader line of width $\sigma$ $\sim$ 0.3 keV centred at $\sim$ 8.05 keV (EW of $\pm$ 12 eV)."
" We choose to proceed with the latter, and provisionally identify it with a blend of the FeXXV 1s-3p line and FeXXVI Ly, while noting other contributions could be from absorption edges of less highly ionised Fe (XVII or higher), inner shell transitions as recently addressed by Palmeri ((2002), or Ni K. A higher (outflow) velocity component of the absorption line seen at ~7 keV is a further possibility."," We choose to proceed with the latter, and provisionally identify it with a blend of the FeXXV 1s-3p line and FeXXVI $\beta$, while noting other contributions could be from absorption edges of less highly ionised Fe (XVII or higher), inner shell transitions as recently addressed by Palmeri (2002), or Ni K. A higher (outflow) velocity component of the absorption line seen at $\sim$ 7 keV is a further possibility."
" Figure 2 suggests the presence of other narrow absorption features in the EPIC data, the most significant being at  2.7 keV, and near 1.5 keV. Fitting these 2 features by successively adding gaussians lines to the model yielded further reductions in y? of, respectively, 26 and 32 for 3 fewer dof in each case (figure 4)."," Figure 2 suggests the presence of other narrow absorption features in the EPIC data, the most significant being at $\sim$ 2.7 keV, and near 1.5 keV. Fitting these 2 features by successively adding gaussians lines to the model yielded further reductions in $\chi^{2}$ of, respectively, 26 and 32 for 3 fewer dof in each case (figure 4)."
 Details of the absorption lines thus identified in the EPIC data are summarised in Table 1., Details of the absorption lines thus identified in the EPIC data are summarised in Table 1.
" When corrected for the redshift ofPG12114-143,, each line energy indicates an origin in the same relativistic outflow, with a velocity of ~0.08-0.1c."," When corrected for the redshift of, each line energy indicates an origin in the same relativistic outflow, with a velocity of $\sim$ 0.08–0.1c."
" The best determined line profile, for the line at ~7.02 keV, is essentially unresolved, corresponding to a velocity dispersion of < 12000 km s!."," The best determined line profile, for the line at $\sim$ 7.02 keV, is essentially unresolved, corresponding to a velocity dispersion of $\leq$ 12000 km $^{-1}$."
 We shall see in Section 3.5 that a tighter line width constraint is obtained from the RGS data., We shall see in Section 3.5 that a tighter line width constraint is obtained from the RGS data.
" In summary, we find the 1-10 keV spectrum of ccan be described by a broad Fe K emission line, together with absorption features which are best fitted with gaussian line profiles rather than absorption edges."," In summary, we find the 1–10 keV spectrum of can be described by a broad Fe K emission line, together with absorption features which are best fitted with gaussian line profiles rather than absorption edges."
" The proposed identification of these lines, with resonance absorption from highly ionised Fe, S, and Mg, indicates an origin in outflowing ionised gas at a velocity of ~0.08-0.1c."," The proposed identification of these lines, with resonance absorption from highly ionised Fe, S, and Mg, indicates an origin in outflowing ionised gas at a velocity of $\sim$ 0.08–0.1c."
 To quantify the highly ionised matter responsible for the observed absorption features we then replaced the gaussian absorption lines in the above model with a grid of photoionised absorbers based on the XSTAR code., To quantify the highly ionised matter responsible for the observed absorption features we then replaced the gaussian absorption lines in the above model with a grid of photoionised absorbers based on the XSTAR code.
" These model absorbers cover a wide range of column density and ionisation parameter, with outflow (or inflow) velocities as a variable parameter."," These model absorbers cover a wide range of column density and ionisation parameter, with outflow (or inflow) velocities as a variable parameter."
 All abundant elements from C to, All abundant elements from C to
The structure of the high density cores οοσα iu rearby imnoleculu clouds is curreutly a uatter of ercat interest.,The structure of the high density cores embedded in nearby molecular clouds is currently a matter of great interest.
" The fate of a protostar depeuds scusitively ou the initial conditions prior to collapse and it is difficult to iufer his froui studi of ""protostars where a Iuniuous object ias already formed.", The fate of a protostar depends sensitively on the initial conditions prior to collapse and it is difficult to infer this from studies of “protostars” where a luminous object has already formed.
 Considerable observaional effort has herefore been expenuded in the attenip to detect a “pre-xotostellar core. which is taken to be a cold dense core Whose column deusitv aud imterual Oessure exeecd considerably those found iu tje surroundings.," Considerable observational effort has therefore been expended in the attempt to detect a ``pre-protostellar core”, which is taken to be a cold dense core whose column density and internal pressure exceed considerably those found in the surroundings."
1k The high deusity nucleus of the dark cloud L151 Is an example of such an object (Tafalla et al., The high density nucleus of the dark cloud L1544 is an example of such an object (Tafalla et al.
 1998. Wk'Thoupson ct al.," 1998, Ward–Thompson et al."
 1999. WiHaus et al.," 1999, Williams et al."
 1999. Ciock Basu 20002.) aud in fact the nodels of Ciolek Basu (200la. CB hereafter) suggest trat it will become uusable in around 300JO vears from now.," 1999, Ciolek Basu 2000a,b) and in fact the models of Ciolek Basu (2000a, CB hereafter) suggest that it will become unstable in around 30000 years from now."
 Iowever. these inferences depend o το ability to derive the «lensity distribution iu such sources from observaC SIC lias the millimeter cussion axd tasm IR absorXon {e.g. Dacimaun et al.," However, these inferences depend on our ability to derive the density distribution in such sources from observables such as the millimeter emission and the mid--IR absorption (e.g. Bacmann et al."
 200|., 2000).
 Iu particular. the cussion of dust eraius at millimeter and subanilliuxter wavelengths is sensitively depeudeut rot only on fi6 erain coluun densitv but also upon he erain teni)orature.," In particular, the emission of dust grains at millimeter and submillimeter wavelengths is sensitively dependent not only on the grain column density but also upon the grain temperature."
 Iu clouds such as LiSLL. the erain tempcranre is) mown to be of order 12 Kk ou he basis of ti6 observed sρουτα] ejiergv distribution (André oet al.," In clouds such as L1544, the grain temperature is known to be of order 12 K on the basis of the observed spectral energy distribution (André et al."
 2000) and it has been normal practise Q asse suci regions Το ο Isothermal., 2000) and it has been normal practise to assume such regions to be isothermal.
 However. it Las been known for sone tile tha One can expect appreciable teuiperature eracdicuts within cores heated by he (external) iiteystellay radiation field (e.g. Leung 1975: Mathis et al.," However, it has been known for some time that one can expect appreciable temperature gradients within cores heated by the (external) interstellar radiation field (e.g. Leung 1975; Mathis et al."
 19S2. hereafter MAIP) as well as temperature differeuces between grains of differing optical properties.," 1983, hereafter MMP) as well as temperature differences between grains of differing optical properties."
 For example. for silicate grains. MAIP predict eraiu temperatures as low as 6 Ik iu he uucleus of cores of visual extinction  50 magnitudes.," For example, for silicate grains, MMP predict grain temperatures as low as 6 K in the nucleus of cores of visual extinction $\sim$ 50 magnitudes."
 Suc1 low teniperature grains will contribute negligibly to the emission at waveleugthlis below 1 nuu aud this sugecsts flat a new study of eran temperatures in dense cloud cores simiir to L151 Is warranted., Such low temperature grains will contribute negligibly to the emission at wavelengths below 1 mm and this suggests that a new study of grain temperatures in dense cloud cores similar to L1544 is warranted.
 Another characteristic of the observed xeprotostellar cores is that they clearly show laree «epartures frou spherical svuuncetiv 1i both the maps of dust ciission and absorption (Bacinaun et al., Another characteristic of the observed pre–protostellar cores is that they clearly show large departures from spherical symmetry in both the maps of dust emission and absorption (Bacmann et al.
 2000)ο, 2000).
 Ελα is. often interpreted as beie due to flattening aloie the direction of the mean inagnetie field resulting in a disk-like configuration (Ciolek Basu 2000a.0).," This is often interpreted as being due to flattening along the direction of the mean magnetic field resulting in a disk-like configuration (Ciolek Basu 2000a,b)."
 Furthermore. as shown τουσ by Calli et al. (," Furthermore, as shown recently by Galli et al. ("
2001). a cloud core modeled as a thin disk perpeudicular to the larec-scale maenetic field aud supported against its solferavitv bv a colubination of eas pressure and imaenetic forces. is not uecessarily axisviunietric.,"2001), a cloud core modeled as a thin disk perpendicular to the large-scale magnetic field and supported against its self-gravity by a combination of gas pressure and magnetic forces, is not necessarily axisymmetric."
 Direct evideice for the miportance of a maeietic field iu determing the structure of L15LE comes both from polarization measurements at 850 ((WareThompson ct al., Direct evidence for the importance of a magnetic field in determining the structure of L1544 comes both from polarization measurements at 850 (Ward--Thompson et al.
 2000) and observation of OIL Zeeman splitting (Crutcher Trolaxd 2000)., 2000) and observation of OH Zeeman splitting (Crutcher Troland 2000).
 The magnetic fied iinferred from the Zeeman neasurenient is cousistent witli t1 model predietious of CB but this restIt is scnsitive to the assuned inclination ο he magnetic ποια relative to t16 plane of the sky (167. according to CD).," The magnetic field inferred from the Zeeman measurement is consistent with the model predictions of CB but this result is sensitive to the assumed inclination of the magnetic field relative to the plane of the sky $^{\circ}$, according to CB)."
 It is releva also hat the observed direction of polarization isnot consistent with naive CB model expectalous in that the inferred maeuetic field direction in the daue of the s deviaes by an angle of 30° from that expectec (paral to the L1511 umor axis)., It is relevant also that the observed direction of polarization is consistent with naive CB model expectations in that the inferred magnetic field direction in the plane of the sky deviates by an angle of $^{\circ}$ from that expected (parallel to the L1544 minor axis).
 This can be easily. explained the cloud is sightly non-axisviunietric {Basu 2100. Calli et al.," This can be easily explained if the cloud is slightly non-axisymmetric (Basu 2000, Galli et al."
 2001)., 2001).
" Thus. while it secs plausi( that t magnetic fiok plavs au important role iu the evolution of preprotostellar cores just prior to collaIBC, it possije tha the ""standard ambipolar ditmSon 11ος requires nioication."," Thus, while it seems plausible that the magnetic field plays an important role in the evolution of pre–protostellar cores just prior to collapse, it is possible that the “standard” ambipolar diffusion model requires modification."
 One notes however tha he effec of temperature eradients mentioned earlier wil have t qualiative effect of biasiug the 850 volarization lueasurenens towards the lower deusity oucr parts COLCS suchas LISLL., One notes however that the effects of temperature gradients mentioned earlier will have the qualitative effect of biasing the 850 polarization measurements towards the lower density outer parts of cores such as L1544.
 Thus it is clearly of importance to able ο assess how large such temperature eyacieuts rea are., Thus it is clearly of importance to be able to assess how large such temperature gradients really are.
high latitudes that we simulate.,high latitudes that we simulate.
" Assuming a Ry=3.1, this corresponds to a reddening rate of E(B—V)0.23 mag/kpc."," Assuming a $R_V$ =3.1, this corresponds to a reddening rate of $E(B-V)=0.23\,\magA/\kpc$ ."
 No additional dust clouds were added., No additional dust clouds were added.
" For the Galaxia model, we present results with the dust modelled by an exponential disk, with the reddening rate in the solar neighbourhood normalized to 0.23 and 0.53mag/kpc, where the latter is taken from Binney&Merrifield (1998)."," For the Galaxia model, we present results with the dust modelled by an exponential disk, with the reddening rate in the solar neighbourhood normalized to 0.23 and $0.53\,\magA/\kpc$, where the latter is taken from \cite{BinneyMerrifield}."
". Also, we present results for a model where the reddening at infinity is matched to that of the value in Schlegel maps."," Also, we present results for a model where the reddening at infinity is matched to that of the value in Schlegel maps."
 To convert E(B—V) to extinction in different photometric bands we used the conversion factors in Table 6 of Schlegeletal.(1998)., To convert $E(B-V)$ to extinction in different photometric bands we used the conversion factors in Table 6 of \citet{Schlegel1998}.
 The mock samples were created from Galaxia and Besangoon using analogous methodology., The mock samples were created from Galaxia and Besançoon using analogous methodology.
" Firstly, to create the Besangoon sample we queried AlxAb=50?x20? regions using the online query form imposing the [-band magnitude limits of RAVE of 9«I13, making no biases in spectral type."," Firstly, to create the Besançoon sample we queried $\Delta l\times \Delta b=50^\circ\times20^\circ$ regions using the online query form imposing the $I$ -band magnitude limits of RAVE of $9<I<13$, making no biases in spectral type."
 A distance limit of d—20kpc is imposed as most RAVE stars the exception of a few notable LMC stars - see Munari(withetal. (2009))) should be within 15 kpc (Breddelsetal.2010).," A distance limit of $d=20\,\kpc$ is imposed as most RAVE stars (with the exception of a few notable LMC stars - see \citet{Munari2009}) ) should be within 15 kpc \citep{Breddels2010}."
. Grid-steps of 10? in | and 5? in b were used in the query., Grid-steps of $10^\circ$ in $l$ and $5^\circ$ in $b$ were used in the query.
" To generate samples from Galaxia we simply generated a full catalog over the area specified by 0«1360, —90«b0 and 9«I13 and then extracted the required samples from it after correcting for extinction."," To generate samples from Galaxia we simply generated a full catalog over the area specified by $0<l<360$, $-90<b<0$ and $9<I<13$ and then extracted the required samples from it after correcting for extinction."
" Since Galaxia allows oversampling, the initial catalog was generated with an oversampling factor of 10, so that later on 10 independent random realizations could be created."," Since Galaxia allows oversampling, the initial catalog was generated with an oversampling factor of 10, so that later on 10 independent random realizations could be created."
 Using Monte Carlo techniques each model was then resampled first to create a uniform distribution in [-magnitude and then resampled again to exactly mimic the shape of the DENIS J-band distribution in a AlxAb—50?x20? region., Using Monte Carlo techniques each model was then resampled first to create a uniform distribution in $I$ -magnitude and then resampled again to exactly mimic the shape of the DENIS $I$ -band distribution in a $\Delta l\times \Delta b=50^\circ\times20^\circ$ region.
 This ensures that the distance distribution will be similar to the RAVE sample., This ensures that the distance distribution will be similar to the RAVE sample.
 Each generated sample is then further reduced to those stars with J>10.3 to mimic our sample selection in Section 2.., Each generated sample is then further reduced to those stars with $J> 10.3$ to mimic our sample selection in Section \ref{sec:Stream}.
" Finally, the number of stars in the mock sample is normalized to that of the RAVE sample in sub-regions of AlxAb=25?10°, where this division into sub-regions was required to better suit the curved boundary of the RAVE survey area."," Finally, the number of stars in the mock sample is normalized to that of the RAVE sample in sub-regions of $\Delta l\times \Delta b=25^\circ\times10^\circ$, where this division into sub-regions was required to better suit the curved boundary of the RAVE survey area."
" For the Besangoon sample, the | and b co-ordinates were smeared out to remove the discretization by adding a uniform randomization of the same extent (since the Galaxia sample was already smoothly distributed no such procedure was required)."," For the Besançoon sample, the $l$ and $b$ co-ordinates were smeared out to remove the discretization by adding a uniform randomization of the same extent (since the Galaxia sample was already smoothly distributed no such procedure was required)."
" Also, for Galaxia ten mock data samples were created for each dust modelling scenario, enabling a better handle on the statistical significance of the Aquarius stream."," Also, for Galaxia ten mock data samples were created for each dust modelling scenario, enabling a better handle on the statistical significance of the Aquarius stream."
" Finally, to simulate the RAVE radial velocity measurement errors a scatter of c=2kms~+ was added to the models' radial velocities."," Finally, to simulate the RAVE radial velocity measurement errors a scatter of $\sigma=2\,\kms$ was added to the models' radial velocities."
 Figure 2 shows the Besancoon and one of the Galaxia samples E(B—V)0.23 mag/kpc) for the same area of the (withsky as in Figure 1aa. We see that both models do a fair job of reproducing the gross features of the data.," Figure \ref{f2} shows the Besançoon and one of the Galaxia samples (with $E(B-V)=0.23\,\magA/\kpc$ ) for the same area of the sky as in Figure \ref{f1}a a. We see that both models do a fair job of reproducing the gross features of the data."
 A detailed analysis of comparing both the Besangoon and Galaxia models to RAVE will be presented in an upcoming papers by A. Ritter., A detailed analysis of comparing both the Besançoon and Galaxia models to RAVE will be presented in an upcoming papers by A. Ritter.
" In this analysis it is sufficient to note firstly that the Galaxia model produces a better representation of the density of halo stars (i.e., those stars with larger Vio,) than the Besangoon model."," In this analysis it is sufficient to note firstly that the Galaxia model produces a better representation of the density of halo stars (i.e., those stars with larger $\vrad$ ) than the Besançoon model."
" Moreover, the Galaxia model better reproduces the Vio, distribution as a function of Galactic"," Moreover, the Galaxia model better reproduces the $\RV$ distribution as a function of Galactic"
distributed throughout the jet volume. as would be expected from stellar mass loss. is a potential complication to our analvsis.,"distributed throughout the jet volume, as would be expected from stellar mass loss, is a potential complication to our analysis."
 Lt is of interest to compare the results of the present. mocel with the conservation-law analysis of LDO2b., It is of interest to compare the results of the present model with the conservation-law analysis of LB02b.
 The treatments are very similar in many respects. both relving on equasi-one-dimensional approximations ancl using Conservation of mass. momentum and energy in a realistic external environment.," The treatments are very similar in many respects, both relying on quasi-one-dimensional approximations and using conservation of mass, momentum and energy in a realistic external environment."
 The formulation of the conservation laws is identical in the two treatments., The formulation of the conservation laws is identical in the two treatments.
 The principal differences in the assumptions are as follows., The principal differences in the assumptions are as follows.
 LDBO2h discussed the cllects of varving the assumptions of their analysis., LB02b discussed the effects of varying the assumptions of their analysis.
 This led to à spread of values around those [or theirπού which we quote here., This led to a spread of values around those for their which we quote here.
 Table 2 compares values of Κον parameters for our model jet and that from LDO2b's reference model at the brightening point and at I2kkpe from the nucleus., Table \ref{tab:compare} compares values of key parameters for our model jet and that from LB02b's reference model at the brightening point and at kpc from the nucleus.
 The energy Buxes of the two model jets are. quite similar. despite the dilferences in starting assumptions.," The energy fluxes of the two model jets are quite similar, despite the differences in starting assumptions."
 In terms of the available energy. Lux & (with. the rest-mass component subtracted. as in Section 5.2.3. and LDO02b). we lind =L6.107 WW. compared with —L1107 NW for LBO2b.," In terms of the available energy flux $\Phi$ (with the rest-mass component subtracted, as in Section \ref{jetpower}
 and LB02b), we find $\Phi = 1.6 \times 10^{37}$ W, compared with $\Phi = 1.1
\times 10^{37}$ W for LB02b."
 ‘This is because the geometries of the two jets are identical: in the outer region their velocities are very similar and they are both close to pressure equilibrium with the surroundings., This is because the geometries of the two jets are identical; in the outer region their velocities are very similar and they are both close to pressure equilibrium with the surroundings.
 “Phe main difference is in the mass flax. which is à factor of 1.5 times larger at kkpe from the nucleus in the present mocdel.," The main difference is in the mass flux, which is a factor of 1.5 times larger at kpc from the nucleus in the present model."
 There is ai larger dillerence between the initial conditions for the two models at the brightening point., There is a larger difference between the initial conditions for the two models at the brightening point.
 The model jet of LBO2Zb has an initial density roughly 5 times lower than that cleseribed here. but is also overpressurect: its cnerey density is dominated. by the internal energy. of relativistic particle rather than by bulk kinetic energy. as can be seen from the cillercnees in the value of .# at the brightening point (Pable 2)).," The model jet of LB02b has an initial density roughly 5 times lower than that described here, but is also overpressured: its energy density is dominated by the internal energy of relativistic particle rather than by bulk kinetic energy, as can be seen from the differences in the value of $\mathscr{R}$ at the brightening point (Table \ref{tab:compare}) )."
 The very. low initial density in LDO2b's reference model is derived. from the requirement for ΕΙ jets to be able to decelerate from bulk Lorentz [actors 5 on parsec scales., The very low initial density in LB02b's reference model is derived from the requirement for I jets to be able to decelerate from bulk Lorentz factors $\sim$ 5 on parsec scales.
 HE this requirement is relaxed. as in the high-momoentunm solutions described in section 3.2.6 of that paper. results closer to those in the present. paper are obtained.," If this requirement is relaxed, as in the high-momentum solutions described in section 3.2.6 of that paper, results closer to those in the present paper are obtained."
 The entrainment rate at the beginning of the flaring region in both models is very low and. could, The entrainment rate at the beginning of the flaring region in both models is very low and could
in abundances of heavy ¢-process elements such as Eu at [Γο/Τ~3.,in abundances of heavy $r$ -process elements such as Eu at ${\rm [Fe/H]}\sim -3$.
 However. a complete model of r-process aud Fe production in the H aud £ events is still lacking aud should be investigated by future theoretical stucies.," However, a complete model of $r$ -process and Fe production in the $\cal{H}$ and $\cal{L}$ events is still lacking and should be investigated by future theoretical studies."
 Iu discussing r-process curichiment by NSMs I have asstuned that the iuaxinuni amount of ISAL to mix with the ejecta from an individual event is the same as swept up by a SN remnant., In discussing $r$ -process enrichment by NSMs I have assumed that the maximum amount of ISM to mix with the ejecta from an individual event is the same as swept up by a SN remnant.
 This is because the total energy. of the NSM ejecta seen iu numerical simulations (Rosswog et al., This is because the total energy of the NSM ejecta seen in numerical simulations (Rosswog et al.
 1999) is at most comparable to the SN. explosion enerev (710°! ove)., 1999) is at most comparable to the SN explosion energy $\sim 10^{51}$ erg).
 For eiven conditions of the ISM. the expausion/evolutiou of the ejecta is esseutiallv governed by its total energv.," For given conditions of the ISM, the expansion/evolution of the ejecta is essentially governed by its total energy."
 The large difference iu the amount of ejecta between a NSM and a SN has uo siguificaut effect here as m both cases the mass of the swept-up ISAL soon overwhehus that of the ejecta while the total enerey remains more or less the same., The large difference in the amount of ejecta between a NSM and a SN has no significant effect here as in both cases the mass of the swept-up ISM soon overwhelms that of the ejecta while the total energy remains more or less the same.
 I note that a small amouut (<10° AL.) of material unight be ejected iu üiehlv-relativistie jets in a NS-DII merger eveut (CJanka al.," I note that a small amount $\lesssim 10^{-5}\,M_\odot$ ) of material might be ejected in highly-relativistic jets in a NS-BH merger event (Janka et al."
 1999)., 1999).
 Tlowever. the total euergv of these jets is ES10i cre (Janka et al.," However, the total energy of these jets is $\lesssim 10^{51}$ erg (Janka et al."
 1999) aud their existeuce would iof increase siguificautly the amount of ISAL that could nix with the entire ejecta from the event., 1999) and their existence would not increase significantly the amount of ISM that could mix with the entire ejecta from the event.
 It takes ~109 vr or the enerev (~1071 cre) and the associated mnomentuui of the ejecta to be dispersed in the ISM (e.g... ThoruOl et al.," It takes $\sim 10^6$ yr for the energy $\sim 10^{51}$ erg) and the associated momentum of the ejecta to be dispersed in the ISM (e.g., Thornton et al."
 1998). where the next NSM or SN would occur on a uuch longer timescale (~1079 vr for NSMs and ~104 yr or SNe}.," 1998), where the next NSM or SN would occur on a much longer timescale $\sim 10^{10}$ yr for NSMs and $\sim 10^{7}$ yr for SNe)."
 This leaves substautial time for mixing of he ejecta with the swept-up ISAL, This leaves substantial time for mixing of the ejecta with the swept-up ISM.
 However. the details of he wining process require further studies.," However, the details of the mixing process require further studies."
" If. as argued here. SNe are the major sources for he r-process, then there are two possible direct observatioial ests: Gama ravs from decay of process nuclei iu SN remnants aud surface contamination of the companion wo SN reprocess ejecta in binaries,"," If, as argued here, SNe are the major sources for the $r$ -process, then there are two possible direct observational tests: gamma rays from decay of $r$ -process nuclei in SN remnants and surface contamination of the companion by SN $r$ -process ejecta in binaries."
 Qian et al. (, Qian et al. (
H998b. 1999) discussed eamunaray signals from decay of loue-jved r-process nuclei (with lifetimes ~107 107 yr) iu a nearby SN remnant aud from decay of short-lived rexocess nuclei (with lifetimes ~1 10 vr) produced iu a Galactic SN that may occur in the future.,"1998b, 1999) discussed gamma-ray signals from decay of long-lived $r$ -process nuclei (with lifetimes $\sim 10^3$ $10^5$ yr) in a nearby SN remnant and from decay of short-lived $r$ -process nuclei (with lifetimes $\sim 1$ –10 yr) produced in a Galactic SN that may occur in the future."
 The nuclide “6Su is of particular interest (Qian ct al., The nuclide $^{126}$ Sn is of particular interest (Qian et al.
 1905) as its ifetime (LO? wr) is much louger than the age (~10! yr) of the Vela SN remnant at a distance z250 pe., 1998b) as its lifetime $\sim 10^5$ yr) is much longer than the age $\sim 10^4$ yr) of the Vela SN remnant at a distance $\approx 250$ pc.
 In the victure of rprocess enrichment by SNe diseussed here (see alko QW: WO) the solar r-process mass fraction of πιο] with A<130 resulted from ~107 £ events (see 833)., In the picture of $r$ -process enrichment by SNe discussed here (see also QW; WQ) the solar $r$ -process mass fraction of nuclei with $A\leq 130$ resulted from $\sim 10^2$ $\cal{L}$ events (see 3).
" So a total mass NEPOSweος1*AF, of Su nuclei are produced in cach £ event. where XSPe=16«10? (KApppeler et al."," So a total mass $X_{\odot,r}^{A=126}M_{\rm mix}/10^2
\sim 5\times 10^{-7}\,M_\odot$ of $^{126}$ Sn nuclei are produced in each $\cal{L}$ event, where $X_{\odot,r}^{A=126}\approx
1.6\times 10^{-9}$ (Käpppeler et al."
 1989) is the solar r-process inass fraction of Te. the stable daughter of S.," 1989) is the solar $r$ -process mass fraction of $^{126}$ Te, the stable daughter of $^{126}$ Sn."
 If the SN associated with the Vela. reuueant was an £ eveut. then decay of Sn in this remuaut would produce euunuverav fluxes ~10oscurοςbat energies E.=115. 666. aud 695 keV. Detection of these fluxes would require future eamuna-ray experumuents such as the proposed Advanced Telescope for Πιο] Euerev Nucleay Ástroplivsies (ATHENA. INurfess 1991).," If the SN associated with the Vela remnant was an $\cal{L}$ event, then decay of $^{126}$ Sn in this remnant would produce gamma-ray fluxes $\sim 10^{-7}\,\gamma\ {\rm cm}^{-2}\ {\rm s}^{-1}$ at energies $E_\gamma=415$, 666, and 695 keV. Detection of these fluxes would require future gamma-ray experiments such as the proposed Advanced Telescope for High Energy Nuclear Astrophysics (ATHENA, Kurfess 1994)."
 As the Vela remuaut contains a pulsar. such detection would also provide evidence for the speculated association between £ events aud SNe producing ucutron stars (Qian et al.," As the Vela remnant contains a pulsar, such detection would also provide evidence for the speculated association between $\cal{L}$ events and SNe producing neutron stars (Qian et al."
 1998a)., 1998a).
 The other test mentioned above takes advantage of the occurrence of SNe in binaries., The other test mentioned above takes advantage of the occurrence of SNe in binaries.
 The rprocess ejecta from the SN would coutaminate the surface of its binary colupanion., The $r$ -process ejecta from the SN would contaminate the surface of its binary companion.
 Some biuaries would survive the SN explosion and acquire a NS or a DIT in place of the SN progenitor., Some binaries would survive the SN explosion and acquire a NS or a BH in place of the SN progenitor.
 Therefore. an ordinary star observed to be the binary colupanion of a NS or a DII Πο show r-process abundance anomalies on the surface.," Therefore, an ordinary star observed to be the binary companion of a NS or a BH might show $r$ -process abundance anomalies on the surface."
 To estimate the plausible level of such anomalies. Tassie that a fraction ~10? of the eutire SN ejecta (~10AZ... mostly r-process material) would be intercepted by a low mass (~LAL.) companion aud then mixed with ~10341. of the surface material.," To estimate the plausible level of such anomalies, I assume that a fraction $\sim 10^{-3}$ of the entire SN ejecta $\sim 10\,M_\odot$, mostly $r$ -process material) would be intercepted by a low mass $\sim 1\,M_\odot$ ) companion and then mixed with $\sim 10^{-2}\,M_\odot$ of the surface material."
 If the SN was an A eveut. — of r-process clemeuts with A>130 would be intercepted. while for an £ eveut ~10SAL. of ;- process elements with 2b<130 would be intercepted (sce 833).," If the SN was an $\cal{H}$ event, $\sim 10^{-9}\,M_\odot$ of $r$ -process elements with $A>130$ would be intercepted, while for an $\cal{L}$ event $\sim 10^{-8}\,M_\odot$ of $r$ -process elements with $A\leq 130$ would be intercepted (see 3)."
 These quantities are to be compared with ~Ls1019AZ. of the corresponding r-process elements in ~107AL. of the surface material iu a companion star of solar r-process composition.," These quantities are to be compared with $\sim 4\times 10^{-10}\,M_\odot$ of the corresponding $r$ -process elements in $\sim 10^{-2}\,M_\odot$ of the surface material in a companion star of solar $r$ -process composition."
 So à SN ina binary could chhance significantly the surface rprocess abundances imn the companion star. especially if the SN was an £ eveut.," So a SN in a binary could enhance significantly the surface $r$ -process abundances in the companion star, especially if the SN was an $\cal{L}$ event."
 Iu view of the large overabundance of O. Mg. Si. and S recently observed in the companion star of a probable BIT (Ixraelian et al.," In view of the large overabundance of O, Mg, Si, and S recently observed in the companion star of a probable BH (Israelian et al."
 1999). detection of i7- process euliauceimoenut In smnilar binary svstenis seenis promising.," 1999), detection of $r$ -process enhancement in similar binary systems seems promising."
 Such detection may also test directly the speculation by Qian ct al. (, Such detection may also test directly the speculation by Qian et al. (
1998a) that H eveuts are associated with SNe producing DIIs while £ eveuts are associated with SNe producing neutron stars.,1998a) that $\cal{H}$ events are associated with SNe producing BHs while $\cal{L}$ events are associated with SNe producing neutron stars.
 I thank Petr Vogel aud Jerry Wasserburg for many discussious on the r-process, I thank Petr Vogel and Jerry Wasserburg for many discussions on the $r$ -process.
 I zm also grateful to the referee. Friedel Thielemiaun. for detailed critieius that help iuprove the paper.," I am also grateful to the referee, Friedel Thielemann, for detailed criticisms that help improve the paper."
 This work was supported iu part by the Department of Encrey under eraut DE-FC02-, This work was supported in part by the Department of Energy under grant DE-FG02-87ER40328.
It has long been appreciated that stellaz evolutionary uodels have trouble predicting the masses and radii of AMI dwarts in detached eclipsing binary svstenis (366. 6.8. Iloxie 1973. Lacy 1977). in the seuse that the models eud to underprediet the observed radius for a given uass by about (Ribas 2006).,"It has long been appreciated that stellar evolutionary models have trouble predicting the masses and radii of M dwarfs in detached eclipsing binary systems (see, e.g., Hoxie 1973, Lacy 1977), in the sense that the models tend to underpredict the observed radius for a given mass by about (Ribas 2006)."
 Tt was for this reason hat Chirbonnueau et al. (, It was for this reason that Charbonneau et al. (
2009) discounted the results sed ou the evolutionary models. aud why subsequent authors have done the same iu thei diseussious of GJ 1211.,"2009) discounted the results based on the evolutionary models, and why subsequent authors have done the same in their discussions of GJ 1214."
 However. it has recently been argued that the zadliues of the evolutionary models are confined to the nass range 0.30.7 AL... and even more specifically to stars that have been tidally spun up (aud mace more active) by a close stellar companion (see. e.g.. Torres et al.," However, it has recently been argued that the failings of the evolutionary models are confined to the mass range 0.3–0.7 $M_\odot$, and even more specifically to stars that have been tidally spun up (and made more active) by a close stellar companion (see, e.g., Torres et al."
 2006. Lóppoez-Morales 2007. Morales et al.," 2006, Lóppez-Morales 2007, Morales et al."
 2008)., 2008).
 Stars below a threshold mass of ©0.32 AL. are expected to be fully convective. aud seem to be well described by the evolutionary imocdols (sec. c.g.. Lóppez-Morales 2007. Demory et al.," Stars below a threshold mass of $\approx$ 0.32 $M_\odot$ are expected to be fully convective, and seem to be well described by the evolutionary models (see, e.g., Lóppez-Morales 2007, Demory et al."
 2009. Vida et 22009).," 2009, Vida et 2009)."
 To the exteut this is true. we would not expect GJ 1211.a single. low-activity star of mass <0.3 AL. to he affected by the problems that plague the theories of carlicr-type M chwarfs i close binary svstenis.," To the extent this is true, we would not expect GJ 1214—a single, low-activity star of mass $<$ 0.3 $M_\odot$ —to be affected by the problems that plague the theories of earlier-type M dwarfs in close binary systems."
 We are thereby motivated. to seek alternative resolutions to the discrepancy between the two methods of estimating the mass and radius of CJ 1211., We are thereby motivated to seek alternative resolutions to the discrepancy between the two methods of estimating the mass and radius of GJ 1214.
 Of course there is always the possibility that a kev input such as the parallax or infraredl magnitude is faulty. but in the sections to follow we discuss some possible resolutions iu which all of the data are taken at face value.," Of course there is always the possibility that a key input such as the parallax or infrared magnitude is faulty, but in the sections to follow we discuss some possible resolutions in which all of the data are taken at face value."
 We have worked exclusively with solar ietallicity isochrones., We have worked exclusively with solar metallicity isochrones.
 Loweranetalliitv isochrones generally xediet a larger radius for a given mass. in the relevant reeion of parameter space.," Lower-metallicity isochrones generally predict a larger radius for a given mass, in the relevant region of parameter space."
 Sclilaufinan (2010) have xeseuted a simple iiethod to estimate the metallicity of an AL dwarf based ou its observed V. and Jv maguitucles., Schlaufman (2010) have presented a simple method to estimate the metallicity of an M dwarf based on its observed $V$ and $K$ magnitudes.
 For GJ 1211. his method gives |Fe/II]|2.—0.16. suggesting hat the star is only moderately metal-poor.," For GJ 1214, his method gives $=-0.16$, suggesting that the star is only moderately metal-poor."
 This value or the ietallicity would not affect the theoretically xedieted radius by enough to resolve the discrepancy., This value for the metallicity would not affect the theoretically predicted radius by enough to resolve the discrepancy.
 Lóppez-Morales (2007) found that the Baraffe oct al. (, Lóppez-Morales (2007) found that the Baraffe et al. (
1998) isochroucs predict a variation iu stellar radius of ouly about for metallicitics ranging frou 0.0 to 0.5.,1998) isochrones predict a variation in stellar radius of only about for metallicities ranging from 0.0 to $-0.5$ .
 Moreover. for a saauple of low-mass stars with 0.5 0. Demory ct ((2009) showed that there is no «|Fe/II]-sieuificant correlation between measured metallicity and the fractional differeuce between the measured stellar radius and that found assuming solar metallicity.," Moreover, for a sample of low-mass stars with $-0.5 < $ $ < 0$, Demory et (2009) showed that there is no significant correlation between measured metallicity and the fractional difference between the measured stellar radius and that found assuming solar metallicity."
 Therefore. while it is possible that CJ 1211 is a inctal-poor star. we do uot consider this to offer a likely resolution of the diserepaucy we have noted between the two methods of estimating the stellar radius.," Therefore, while it is possible that GJ 1214 is a metal-poor star, we do not consider this to offer a likely resolution of the discrepancy we have noted between the two methods of estimating the stellar radius."
 If the star were relatively ποσο aud still contracting outo the main sequence. then the evolutionary models would predict a larger radius. relieving the discrepancy.," If the star were relatively young and still contracting onto the main sequence, then the evolutionary models would predict a larger radius, relieving the discrepancy."
 To investigate this possibility we repeated our isochrone analysis. but this time with a flat prior on the stellar age and a Cassian prior on the stellar mean deusitv to conform with the transit helt curve analysis.," To investigate this possibility we repeated our isochrone analysis, but this time with a flat prior on the stellar age and a Gaussian prior on the stellar mean density to conform with the transit light curve analysis."
 The result was that the age of the star ust be about 100 Nr., The result was that the age of the star must be about 100 Myr.
 This would conflict with the evidence for an older age. namely. the observed lack of strong chromospheric activity aud the |duematics (see 6.2))5.," This would conflict with the evidence for an older age, namely, the observed lack of strong chromospheric activity and the kinematics (see \ref{sec:iso}) )."
 There is also the low probability that we would happen to observe this star at such an early phase of its long life., There is also the low probability that we would happen to observe this star at such an early phase of its long life.
 For these reasons. a voung age for CJ 1211 docs not secu to be a promising solution.," For these reasons, a young age for GJ 1214 does not seem to be a promising solution."
" It is conceivable that unideutilied starspot anomalics lave significantly biased our estimate of e/P, from the rausit light curves (see 3.13).", It is conceivable that unidentified starspot anomalies have significantly biased our estimate of $a/R_\star$ from the transit light curves (see \ref{sec:model:spots}) ).
" Could this be responsible or the To discrepancy in p, between the two methods of characterizing the star?", Could this be responsible for the $\sigma$ discrepancy in $\rho_\star$ between the two methods of characterizing the star?
" [f this were the case. then the nore trustworthy estimate of p, would be the value from he isochrone analysis."," If this were the case, then the more trustworthy estimate of $\rho_\star$ would be the value from the isochrone analysis."
 This sccis unlikelw. partly because the residuals to our transit light curves do not displav iu anomalies o'vond the two that we have already identified. aud xwtlv because in this scenario it would be difficult to uuderstand the collection of transit depths.," This seems unlikely, partly because the residuals to our transit light curves do not display any anomalies beyond the two that we have already identified, and partly because in this scenario it would be difficult to understand the collection of transit depths."
" Specifically. we can use the value of p, from the evolutionary models as an mput to Equation (5)). to derive the planet-to-star radius ratio."," Specifically, we can use the value of $\rho_\star$ from the evolutionary models as an input to Equation \ref{eq:duration-radratio}) ), to derive the planet-to-star radius ratio."
 The result is ΠοΠε=0.405+0.01., The result is $R_p/R_\star = 0.15\pm0.01$.
 This conflicts with the upper Tut <=0.1161 that we derived in 5. under the asstuuptionΠΠ that the transit depths are affected by cool spots ou the stellar disk.," This conflicts with the upper limit $R_p/R_\star \le 0.1161$ that we derived in \ref{sec:radrat}, under the assumption that the transit depths are affected by cool spots on the stellar disk."
 Thus. one would have to suppose that nearly all of the transit depths were biased tosmaller values by nunerous starspot crossings throughout the transits.," Thus, one would have to suppose that nearly all of the transit depths were biased to values by numerous starspot crossings throughout the transits."
 We do not consider a conspiracy of starpot anomalies to be a satisfactory solution to the problem., We do not consider a conspiracy of starpot anomalies to be a satisfactory solution to the problem.
" If the orbit of GJ 1211b is not circular. then the piuraueter that is beie determined by the light curve analvsis is not a/R, aud our application of Equation (8)) is erroneous."," If the orbit of GJ 1214b is not circular, then the parameter that is being determined by the light curve analysis is not $a/R_\star$ and our application of Equation \ref{eq:dens}) ) is erroneous."
 The correct procedure inst take iuto account the speed of the planet at inferior conjunction. which is a function of the eccentricity and argument of pericenter (sec. e.2.. Equs.," The correct procedure must take into account the speed of the planet at inferior conjunction, which is a function of the eccentricity and argument of pericenter (see, e.g., Eqns."
 16 aud 27 of Winn 2010 or Isipping 2010)., 16 and 27 of Winn 2010 or Kipping 2010).
 The cud result is that the mean deusity of the planet would be modified as follows where p.cre is the mean density that is calculated under the assmuption of a circular orbit.," The end result is that the mean density of the planet would be modified as follows where $\rho_{\star,~{\rm circ}}$ is the mean density that is calculated under the assumption of a circular orbit."
 Therefore. it πο]! be possible to reconcile the two differeut uretlhods for estimating the stellar density. for suitable choices of € and w.," Therefore, it might be possible to reconcile the two different methods for estimating the stellar density, for suitable choices of $e$ and $\omega$."
 The orbital eccentricity. has been assuned to be zero. because of the expectation that tidal dissipatiou has damped out auv initial eccentricity to 10? or below.," The orbital eccentricity has been assumed to be zero, because of the expectation that tidal dissipation has damped out any initial eccentricity to $10^{-3}$ or below."
 Iowever. the published BW data onlv permit a coarse upper lit of e«0.27 with coufideuce (Charbonneau ct al.," However, the published RV data only permit a coarse upper limit of $<$ 0.27 with confidence (Charbonneau et al."
 2009)., 2009).
 To investigate the possibility of an eccentricorbit. we assumed that the isochrone- estimate of the mean stellar deusitv (38.1x2.1 oe cnm 7) ds accurate.," To investigate the possibility of an eccentricorbit, we assumed that the isochrone-based estimate of the mean stellar density $38.4\pm2.1$ g $^{-3}$ ) is accurate."
 We then derived the constraints, We then derived the constraints
all the other orbits.,all the other orbits.
 Figure ο compares he orbit 999 LE spectrum to the (rescaled) best-fitting moel to orbits 10001003. the bottom panel shows the cata to moclel ratio.," Figure \ref{999LF_comp} compares the orbit 999 LF spectrum to the (rescaled) best-fitting model to orbits 1000--1003, the bottom panel shows the data to model ratio."
 The orbit 999 LE spectrum can be Lited by adding a black body component to the warm-abscxbed power Law. where the black body acts as a simple parametrisation of the soft. excess.," The orbit 999 LF spectrum can be fitted by adding a black body component to the warm-absorbed power law, where the black body acts as a simple parametrisation of the soft excess."
 “Phis approach procuces a good fit C dof17.92/14—1.28). with parameters KT-0.11343:0.004 keV. Photon Index =1.5540.08 and 0.7 keV edge parameters fixed to the best-fitting values for orbits 10001003.," This approach produces a good fit $\chi^2$ /dof=17.92/14=1.28), with parameters $\pm$ 0.004 keV, Photon Index $\pm$ 0.03 and 0.7 keV edge parameters fixed to the best-fitting values for orbits 1000--1003."
 The power law slope is very [at compared to the LE rms spectra of the other observations. which have a value of Photon Index. 2.2 (see Table 3)).," The power law slope is very flat compared to the LF rms spectra of the other observations, which have a value of Photon Index $\sim 2.2$ (see Table \ref{orbitfits}) )."
 Alternatively. it is possible that the variable component in this observation is alfected by stronger warm absorption than the other orbits.," Alternatively, it is possible that the variable component in this observation is affected by stronger warm absorption than the other orbits."
 To explore this possibility we used the spectral components identified in these data by Milleretal.(2007):Turneral.(2007) using higher spectral resolution.," To explore this possibility we used the spectral components identified in these data by \citet{miller,turner}
 using higher spectral resolution."
 In one of their interpretations of the spectral variability. the most variable components are a power law of slope EP—2.38 plus an ionised reflection component whose normalisation varies tied to that of the power Law. both under a warm absorber of column density Ny=24107lem2 and ionisation parameter £=18.2.," In one of their interpretations of the spectral variability, the most variable components are a power law of slope $\Gamma=2.38$ plus an ionised reflection component whose normalisation varies tied to that of the power law, both under a warm absorber of column density $N_H=2.4\times 10 ^{21} {\rm cm}^{-2}$ and ionisation parameter $\xi=18.2$."
 The reflection component is modelled bv the rellion! model of Ross&Fabian(2005).. with solar Fe abundance and €=1600 cre cm/s. Fitting this moclel. allowing the normalisations and power law slope to vary. does not produce a &ood fit to the LE sspectrum of this orbit. (4? cof = 7.5. for 15 dol) and requires a very Lat power law of slope 1.3640.08.," The reflection component is modelled by the `reflion' model of \citet{ross}, with solar Fe abundance and $\xi=1600$ erg cm/s. Fitting this model, allowing the normalisations and power law slope to vary, does not produce a good fit to the LF spectrum of this orbit $\chi^2/$ dof = 7.5, for 15 dof) and requires a very flat power law of slope $\pm 0.08$."
 Allowing the absorbing column to vary produces a significantly better fit with us dof = 4.2. for 14 dof with Ny=6.50.01lOLem.? and power law slope 1.77220.09.," Allowing the absorbing column to vary produces a significantly better fit with $\chi^2/$ dof = 4.2, for 14 dof with $N_H=6.5 \pm 0.07 \times 10 ^{21}
{\rm cm}^{-2}$ and power law slope $\pm0.09$."
 Fitting this model to the LE and ME sspectra simultaneously. with free. normalisations for the power law and reflion components. produces a reasonably good lit. with? dof = 2.89. for 30 dof.," Fitting this model to the LF and MF spectra simultaneously, with free normalisations for the power law and reflion components, produces a reasonably good fit, with $\chi^2/$ dof = 2.89, for 30 dof."
 ln this interpretation. the cillerence between the LE and. ME sspectra in this orbit is mainly. produced by a decrease in relative normalisation of the rellected. component. on shor time-scales.," In this interpretation, the difference between the LF and MF spectra in this orbit is mainly produced by a decrease in relative normalisation of the reflected component on short time-scales."
 The ratio of power law to rellion normalisation rises from. 107 in the LE to 107 in the ME., The ratio of power law to reflion normalisation rises from $\times10^4$ in the LF to $\times10^4$ in the MF.
 The 110 keV range of the energy spectrum of orbi 999 is probably not a single component. as Fig.," The 1–10 keV range of the energy spectrum of orbit 999 is probably not a single component, as Fig."
 3. shows that the fractional variability of the LE spectrum in this range changes from being uniform to dropping sharply a around 3 keV. X natural explanation for the aand fractional variability spectra of orbit 999 is that the very strong soft. excess ancl hard. power law in the energy spectrum. of this orbit. are weakly varving. diluting part of the fractional variability at [ow anc high energies but still contributing significantly to the total rms.," \ref{NXS_999} shows that the fractional variability of the LF spectrum in this range changes from being uniform to dropping sharply at around 3 keV. A natural explanation for the and fractional variability spectra of orbit 999 is that the very strong soft excess and hard power law in the energy spectrum of this orbit are weakly varying, diluting part of the fractional variability at low and high energies but still contributing significantly to the total rms."
 In. this interpretation of the spectrum. orbit 999 might be essentially equal to all the other observations with the only dillerence that the power law component Εκ is weak compared to strong-IHux. weakly varying additional components.," In this interpretation of the spectrum, orbit 999 might be essentially equal to all the other observations with the only difference that the power law component flux is weak compared to strong-flux, weakly varying additional components."
 Lf this is the case. then the difference between the LE and AIP sspectra of orbit 999 should. be due to the variability properties of these additional components only. as in all other observations the Le anc ALP spectra. have approximately the same shape.," If this is the case, then the difference between the LF and MF spectra of orbit 999 should be due to the variability properties of these additional components only, as in all other observations the LF and MF spectra have approximately the same shape."
 We fitted the LE aad. AIP 999 sspectra with the best-fitting warm-absorbed power law model of orbits 1000.1003. with all parameters fixed excep for the normalisation. plus a black body component. anc an additional hard. power law of Photon Index-l with an absorption edge at ~7 keV. These additional components are à simple parametrisation of the O-point in the principa component analysis of (Millerctal..2007).. where the ~7 keV. edge is detected. significantly.," We fitted the LF and MF 999 spectra with the best-fitting warm-absorbed power law model of orbits 1000–1003, with all parameters fixed except for the normalisation, plus a black body component, and an additional hard power law of Photon Index=1 with an absorption edge at $\sim$ 7 keV. These additional components are a simple parametrisation of the 0-point in the principal component analysis of \citep{miller}, where the $\sim 7$ keV edge is detected significantly."
 We did not use a single absorbed. or reflected. component. for the additional sof excess and hard power law since these features show cilleren ime-scale dependencies., We did not use a single absorbed or reflected component for the additional soft excess and hard power law since these features show different time-scale dependencies.
 Both absorption edges. at 0.7 anc 7 keV were applied to all components.," Both absorption edges, at 0.7 and 7 keV were applied to all components."
 Phe optical depth of he 7 keV edge and the black body temperature were fittec jointly to the LE and. ME spectra ancl the normalisations of all components were allowed to vary independently., The optical depth of the 7 keV edge and the black body temperature were fitted jointly to the LF and MF spectra and the normalisations of all components were allowed to vary independently.
 Note jowever that the variability. of independent components should act quacratically ancl our fitting procedure adds.— components— inearlv., Note however that the variability of independent components should add quadratically and our fitting procedure adds components linearly.
 This is only a problem in energy bins where the different components have similar amplitudes. so we expec o obtain the approximate normalisation of the cilleren components but not to reproduce the spectral shape exactly.," This is only a problem in energy bins where the different components have similar amplitudes, so we expect to obtain the approximate normalisation of the different components but not to reproduce the spectral shape exactly."
 The top panel of Fig., The top panel of Fig.
 7 shows the 999 LE sspectrum. fitted with a black body. component. ancl hare power law in addition to the warnme-absorbed. power lay model fitted to the other orbits. showing that it can describe," \ref{999LFMF} shows the 999 LF spectrum, fitted with a black body component and hard power law in addition to the warm-absorbed power law model fitted to the other orbits, showing that it can describe"
The kev assumptions (hat are refuted by items 1 and 2 a correlation between lower host metallicities and higher gammnma-ray energy releases. ancl a proposed upper metallicity cut-olf for LGRB host galaxies are based on the traditional collapsar model ancl current assumptions regarding the effects of metallicity on massive star evolution.,"The key assumptions that are refuted by items 1 and 2 – a correlation between lower host metallicities and higher gamma-ray energy releases, and a proposed upper metallicity cut-off for LGRB host galaxies – are based on the traditional collapsar model and current assumptions regarding the effects of metallicity on massive star evolution."
 Specilicallv. under (he assumption of the collapsar model. lower-netallicity host environments are expected (o produce progenitors with higher angular momentum. which should in turn produce LGRBs with higher gamma-ray energy releases (e.g. MacFadyen Woosley 2001. Lirschi et 22005. Yoon et 22006. Woosley Ileger 2006).," Specifically, under the assumption of the collapsar model, lower-metallicity host environments are expected to produce progenitors with higher angular momentum, which should in turn produce LGRBs with higher gamma-ray energy releases (e.g. MacFadyen Woosley 2001, Hirschi et 2005, Yoon et 2006, Woosley Heger 2006)."
 ILowever. current evolutionary models for massive stars do not properly address (he difficulties of modeling mass loss mechanisms. which max be anisotropic (Alevnet Maeder 2007) anc could also include complex effects such as wind clumpineg (Crowther et 22002) and rotation-driven mass loss effects (Alevnet Maecder 2000).," However, current evolutionary models for massive stars do not properly address the difficulties of modeling mass loss mechanisms, which may be anisotropic (Meynet Maeder 2007) and could also include complex effects such as wind clumping (Crowther et 2002) and rotation-driven mass loss effects (Meynet Maeder 2000)."
 According to Dessart et ((2008). current. magnetohycrodvnamic simulations of low-metallicity massive stars actually produce core angular momenta that are too high to eenerate GRB-producing collapsars.," According to Dessart et (2008), current magnetohydrodynamic simulations of low-metallicity massive stars actually produce core angular momenta that are too high to generate GRB-producing collapsars."
 Adopting complete and rigorous treatments of mass loss components and magnetic processes in massive stellar evolutionary models could potentially vield evolutionary pathways For collapsars that are not strongly dependent on a strict eut-olE for the progenitors natal metallicity., Adopting complete and rigorous treatments of mass loss components and magnetic processes in massive stellar evolutionary models could potentially yield evolutionary pathways for collapsars that are not strongly dependent on a strict cut-off for the progenitor's natal metallicity.
 It ds also possible (hat some of the variation seen in our comparison could be attributed to variations in the initial masses of the LGRB progenitor stars., It is also possible that some of the variation seen in our comparison could be attributed to variations in the initial masses of the LGRB progenitor stars.
 We are not able to extrapolate any information about stellar progenitor masses from the data., We are not able to extrapolate any information about stellar progenitor masses from the data.
" IIowever. it is clear (hat metallicity is not the sole determinant of fe.;,, or E in LGRB production. and that additional parameters must be considered in future studies."," However, it is clear that metallicity is not the sole determinant of $E_{\gamma,iso}$ or $E_{\gamma}$ in LGRB production, and that additional parameters must be considered in future studies."
 Alternatively. it is also possible that these recent results regarding LGhRDs and their host metalliities may be in better agreement with other alternative progenitor pathways. such as Diagnetar or binary scenarios.," Alternatively, it is also possible that these recent results regarding LGRBs and their host metallicities may be in better agreement with other alternative progenitor pathways, such as magnetar or binary scenarios."
 These models do not necessarily require a low-metallicity environment for the evolution and development of the critical mechanism that produces a, These models do not necessarily require a low-metallicity environment for the evolution and development of the critical mechanism that produces a
very well with the input power spectrum until the scales which are affected by the resolution of the grid of the matter field.,very well with the input power spectrum until the scales which are affected by the resolution of the grid of the matter field.
" Once we apply smoothing, this small-scale effect will disappear."," Once we apply smoothing, this small-scale effect will disappear."
 The P22-term from the integration and the SPT calculation fits the simulation very well on all applicable scales., The $P_{22}$ -term from the integration and the SPT calculation fits the simulation very well on all applicable scales.
" Finally, the Pi3-term from the SPT calculation is slightly lower than the power spectrum integration (a factor of ©1.1)."," Finally, the $P_{13}$ -term from the SPT calculation is slightly lower than the power spectrum integration (a factor of $\approx 1.1$ )."
 The lines that are shown in Fig., The lines that are shown in Fig.
" 5 are the integration result with limits corresponding to the scales which are available in our simulation box, but since the box only contains discrete modes and the power spectrum integration assumes a continuous frequency spectrum, choosing the same upper and lower bound for both methods does not necessarily give the same result."," \ref{fig:p11theo} are the integration result with limits corresponding to the scales which are available in our simulation box, but since the box only contains discrete modes and the power spectrum integration assumes a continuous frequency spectrum, choosing the same upper and lower bound for both methods does not necessarily give the same result."
 A consistency check for both methods is if the power spectra overlap in the k-region covered by both boxes., A consistency check for both methods is if the power spectra overlap in the $k$ -region covered by both boxes.
" We find that the grid-based method gives very consistent results in this region, while there is an offset for the power spectrum integration."," We find that the grid-based method gives very consistent results in this region, while there is an offset for the power spectrum integration."
" By slightly modifying the integration limits for P13(k), the discrepancy in the latter can be fixed, and both methods agree with each other."," By slightly modifying the integration limits for $P_{13}(k)$, the discrepancy in the latter can be fixed, and both methods agree with each other."
 Fig., Fig.
 6 shows the full third-order SPT matter power spectrum compared to the simulation., \ref{fig:psum} shows the full third-order SPT matter power spectrum compared to the simulation.
" The lines show the power spectra directly calculated from the linear and non-linear density contrast in the simulation, which have been ""glued together"" to show both volumes at the same time."," The lines show the power spectra directly calculated from the linear and non-linear density contrast in the simulation, which have been “glued together"" to show both volumes at the same time."
 The points show the result from our grid-based calculation., The points show the result from our grid-based calculation.
" For the large box, linear theory, SPT and non-linear evolution agree until k+0.1h/Mpc, but linear theory seems to be the better approximation for slightly larger k."," For the large box, linear theory, SPT and non-linear evolution agree until $k \approx 0.1\, h/\mathrm{Mpc}$, but linear theory seems to be the better approximation for slightly larger $k$."
" For the small box, the SPT matter power spectrum describes the non-linear evolution better than the linear power spectrum for scales 0.2h/Mpc«k0.3h/Mpc, while they are equivalent for larger scales."," For the small box, the SPT matter power spectrum describes the non-linear evolution better than the linear power spectrum for scales $0.2\, h/\mathrm{Mpc}<k< 0.3\, h/\mathrm{Mpc}$, while they are equivalent for larger scales."
 We stress again that these power spectra (or the density contrast used to compute them) are not smoothed at all in Fig., We stress again that these power spectra (or the density contrast used to compute them) are not smoothed at all in Fig.
 5 and Fig. 6.., \ref{fig:p11theo} and Fig. \ref{fig:psum}.
 This explains the discrepancy of the SPT power spectra on small scales with respect to the good agreement of the density contrasts shown in Fig. 1.., This explains the discrepancy of the SPT power spectra on small scales with respect to the good agreement of the density contrasts shown in Fig. \ref{fig:dxptvsdxm_high}.
" The fact that the points deviate from each other in the overlap region between the large and small box is due to Pis(K), as discussed above."," The fact that the points deviate from each other in the overlap region between the large and small box is due to $P_{13}(k)$, as discussed above."
 There is excess power on these scales for the full SPT power spectrum because Pi3(k)«0., There is excess power on these scales for the full SPT power spectrum because $P_{13}(k)< 0$.
 In this section we study dark matter haloes and how they relate to the underlying matter density field., In this section we study dark matter haloes and how they relate to the underlying matter density field.
 The haloes are split up in 3 mass bins for each box because the bias parameters are very sensitive to the mass of the objects (see also Fig. 12))., The haloes are split up in 3 mass bins for each box because the bias parameters are very sensitive to the mass of the objects (see also Fig. \ref{fig:massdep}) ).
 Table 1 shows the selection criteria for the binning., Table \ref{tab:bins} shows the selection criteria for the binning.
 Halo positions are assigned to the grid using the CIC algorithm to obtain a continuous halo density contrast field dn(x)., Halo positions are assigned to the grid using the CIC algorithm to obtain a continuous halo density contrast field $\delta_{\mathrm{h}}(\mathbf{x})$.
" The bins were chosen such that they are separated in mass, but still contain a large enough number of haloes to reduce the effect of shot noise."," The bins were chosen such that they are separated in mass, but still contain a large enough number of haloes to reduce the effect of shot noise."
 Many different bias models exist in the literature., Many different bias models exist in the literature.
" Here, we use the bias model implying that the halo density6n(x) depends only on the matter density dm(x) at the same point in space through a general function F."," Here, we use the bias model implying that the halo density$\delta_{\mathrm{h}}(\mathbf{x})$ depends only on the matter density $\delta_{\mathrm{m}}(\mathbf{x})$ at the same point in space through a general function $F$ ."
 A choice of F which is widely used is, A choice of $F$ which is widely used is
"where & is (he thermal conductivity coellicient. ¢, is the specilic heat al constant volume. and Z(p.T)=P—X. the energy loss rate.","where $\kappa$ is the thermal conductivity coefficient, $c_v$ is the specific heat at constant volume, and ${\cal L}(\rho, T) = \Gamma -
\Lambda$, the energy loss rate."
 Here. D represents the energy gains and A. the enerev losses.," Here, $\Gamma$ represents the energy gains and $\Lambda$, the energy losses."
 In (his work. we assume (that £ is approximately zero.," In this work, we assume that $\cal{L}$ is approximately zero."
 Thus. the energy gains are balanced by energy losses (Shu1992).," Thus, the energy gains are balanced by energy losses \citep{shu92}."
. In order to estimate the relative importance of thermal conduction in magnetic flux (tubes. we divide the first term by the second term on (he right hand side of equation (24)).," In order to estimate the relative importance of thermal conduction in magnetic flux tubes, we divide the first term by the second term on the right hand side of equation \ref{thermequ}) )."
 This givesNp eL The specilic heat at constant volume for a non relativistic. non degenerate. monoalonic ideal gas is Ore where M is (he molecular weight ancl is Boltzmann's constant.," This gives ) v. The specific heat at constant volume for a non relativistic, non degenerate, monoatomic ideal gas is = where $\cal{M}$ is the molecular weight and $k$ is Boltzmann's constant."
 ;From Spitzer(1962).. the thermal conductivity coefficient is where Z is (he particle charge and In is the Coulomblogaritlim.," >From \citet{spi62}, the thermal conductivity coefficient is 2 where $Z$ is the particle charge and ${\rm ln} \Lambda$ is the Coulomblogarithm."
 substituting equations (26)) and (27)) in equation (25)).we obtain ΗΕ The A parameter is given by," Substituting equations \ref{cv}) ) and \ref{kapa}) ) in equation \ref{razao}) ),we obtain The $\Lambda$ parameter is given by"
"the ""heated-downstream"" from Cases A ,B, and C to D, respectively.","the ""heated-downstream"" from Cases A ,B, and C to D, respectively."
" The value of the total energy spectral index (L;5;)4= 0.7094, (L;5;)pg= 0.7802, (Τα)=0.8208, and (yor)=0.8667 in each case indicates the Maxwellian distribution in the ""heated-downstream"" with a decreasing deviation to the “power-law” distribution from Cases A, B, and C to D, correspondingly."," The value of the total energy spectral index $(\Gamma_{tot})_{A}=0.7094$ $(\Gamma_{tot})_{B}=0.7802$ , $(\Gamma_{tot})_{C}=0.8208$, and $(\Gamma_{tot})_{D}=0.8667$ in each case indicates the Maxwellian distribution in the ""heated-downstream"" with a decreasing deviation to the “power-law"" distribution from Cases A, B, and C to D, correspondingly."
" But the value of the subshock’s energy spectral index (L'5,5)4=1.8668, (Lsu5)p=1.2413, (Es45)c=1.1819, and (L5,5)p=1.0094 present the energy spectrum distribution with a “power-law” tail in each case implying there is an increasing rigidity of the spectrum from the Cases A, B, and C to D, respectively."," But the value of the subshock's energy spectral index $(\Gamma_{sub})_{A}=1.8668$, $(\Gamma_{sub})_{B}=1.2413$, $(\Gamma_{sub})_{C}=1.1819$, and $(\Gamma_{sub})_{D}=1.0094$ present the energy spectrum distribution with a “power-law"" tail in each case implying there is an increasing rigidity of the spectrum from the Cases A, B, and C to D, respectively."
" The cutoff energy at the “power-law” tail in the energy spectrum is given with an increasing value of (Ej,4,)421.23 MeV, (Emax)B=1.93 MeV, (Ej,4,)c-2.80 MeV and (Emax)p=4.01 MeV from the Cases A, B, C and D, respectively."," The cutoff energy at the “power-law"" tail in the energy spectrum is given with an increasing value of $(E_{max})_{A} $ =1.23 MeV, $(E_{max})_{B}$ =1.93 MeV, $(E_{max})_{C}$ =2.80 MeV and $(E_{max})_{D}$ =4.01 MeV from the Cases A, B, C and D, respectively."
" In the precursor region, the final energy spectrum is divided into two very different parts in each case."," In the precursor region, the final energy spectrum is divided into two very different parts in each case."
 The part in the range from the low energy to the central peak shows an irregular fluctuation in each case., The part in the range from the low energy to the central peak shows an irregular fluctuation in each case.
" The irregular fluctuation indicates that the cold upstream fluid slows down and becomes the “thermal fluid"" by the nonlinear “back reaction"" processes."," The irregular fluctuation indicates that the cold upstream fluid slows down and becomes the “thermal fluid"" by the nonlinear “back reaction"" processes."
 And the other part in the range beyond the central peak energy shows a smooth “power-law” tail in each case.," And the other part in the range beyond the central peak energy shows a smooth “power-law"" tail in each case."
" As shown in Figure 7,, the two kinds of shock compression ratios are both apparently dependent on the energy losses with respect to these four presented simulations."," As shown in Figure \ref{fig:ratio-index}, the two kinds of shock compression ratios are both apparently dependent on the energy losses with respect to these four presented simulations."
" As viewed from Cases A, B, and C to D, the total compression ratio is a decreasing function of the energy losses and each value is larger than the standard value four, the subshock's compression ratio is an increasing function of the energy losses and each value is lower than four."," As viewed from Cases A, B, and C to D, the total compression ratio is a decreasing function of the energy losses and each value is larger than the standard value four, the subshock's compression ratio is an increasing function of the energy losses and each value is lower than four."
" However, both the total compression ratio and the subshock's compression ratio approximate the standard value of four as the energy loss decreases."," However, both the total compression ratio and the subshock's compression ratio approximate the standard value of four as the energy loss decreases."
" According to the DSA theory,if the energy loss is limited to be the minimum, the"," According to the DSA theory,if the energy loss is limited to be the minimum, the"
The generally accepted active galactic nucleus (AGN) model requires gas accretion onto a supermassive black hole (SMBH).,The generally accepted active galactic nucleus (AGN) model requires gas accretion onto a supermassive black hole (SMBH).
 There are a number of fueling mechanisms of different relative importance depending on mass accretion rates and spatial scales., There are a number of fueling mechanisms of different relative importance depending on mass accretion rates and spatial scales.
 Major mergers are most commonly involved to explaiαυ] the high accretion rates of the most luminous quasars: the more accretion rate decreases. the higher the number of efficiert mechanisms (e.g.. dynamical friction. viscous torques).," Major mergers are most commonly involved to explain the high accretion rates of the most luminous quasars; the more accretion rate decreases, the higher the number of efficient mechanisms (e.g., dynamical friction, viscous torques)."
 At Seyfert (Sy) luminosities. bars. tidal interactions. and minor mergers become important (see.e.g..thereviewsofMarti2004:Jogee 2006).," At Seyfert (Sy) luminosities, bars, tidal interactions, and minor mergers become important \citep[see, e.g., the reviews of][]{M_04,J_06}."
. Bars have long been considered an efficient mechanism for inward gas transport down to about kkpe (Schwarz1984;Shlosmanetal.1989:Piner1995): among the possibilities for further driving the gas within the gravitational influence of the central source are nested bars (Shlosmanetal.1989) and central spiral dust lanes (Regan&Mulchaey 1999).," Bars have long been considered an efficient mechanism for inward gas transport down to about kpc \citep{S_84,SFB_89,PST_95}; among the possibilities for further driving the gas within the gravitational influence of the central source are nested bars \citep{SFB_89} and central spiral dust lanes \citep{RM_99}."
. The relation between galaxy interactions and the onset of nuclear activity is founded upon the key studies of Toomre&(1972) and Gunn(1979)., The relation between galaxy interactions and the onset of nuclear activity is founded upon the key studies of \citet{TT_72} and \citet{G_79}.
. Minor mergers could induce gas inflow to the nuclear regions (e.g..Hernquist&Mihos 1995).," Minor mergers could induce gas inflow to the nuclear regions \citep[e.g.,][]{HM_95}."
. Finding clear evidence of a minor merger is generally hard. since the sinking satellite detectability depends on the stage and geometry of the merger and on the parameters of the galaxies involved; e.g.. the minor merger is hardly recognizable in its final stages (Walkeretal.1996).," Finding clear evidence of a minor merger is generally hard, since the sinking satellite detectability depends on the stage and geometry of the merger and on the parameters of the galaxies involved; e.g., the minor merger is hardly recognizable in its final stages \citep[][]{WMH_96}."
. Numerical simulations show that (minor) mergers. together with tidal interactions. could induce tails. bridges.shells. bars. and various types of disturbed spiral structure and asymmetries (e.g..Toomre&1972:HernquistQuinn1989:Mi-hosetal.1995:Hernquist&Mihos 1995).," Numerical simulations show that (minor) mergers, together with tidal interactions, could induce tails, bridges,shells, bars, and various types of disturbed spiral structure and asymmetries \citep[e.g.,][]{TT_72,HQ_89,MWH_95,HM_95}."
. Thus. asymmetries have often been associated with mergers (e.g..Conseliceetal.2000;Conselice2003;DeProprisetal.2007 ).," Thus, asymmetries have often been associated with mergers \citep[e.g.,][]{CBJ_00,C1_03,DCL_07}."
. The question. of statistical differences between Sy and inactive galaxies considering non-axisymmetric perturbations of the potential is somewhat controversial., The question of statistical differences between Sy and inactive galaxies considering non-axisymmetric perturbations of the potential is somewhat controversial.
 [tis a prevalent view that neither bars (e.g..Mulchaey&Regan1997).. companions (e.g..DeRobertisetal.1998;Schmitt2001).. minor mergers (e.g..Corbin2000).. nested bars (Erwin&Sparke2002).. nor nuclear dust spiral arms (Martinietal.2003) are specific signatures of Sy galaxies.," It is a prevalent view that neither bars \citep[e.g.,][]{MR_97}, companions \citep[e.g.,][]{RYH2_98,S_01}, minor mergers \citep[e.g.,][]{C_00}, nested bars \citep{ES_02}, nor nuclear dust spiral arms \citep{MRM2_03} are specific signatures of Sy galaxies."
 Some studies. however. prompt an excess of bars (e.g..Laineetal.2002).. outer rings (Hunt&Malkan 1999).. companions (e.g..Rafanellietal.1995).. and. considering early type galaxies. circumnuclear features (Xilouris&Papadakis2002) and dust (e.g..SimóesLopesetal.2007) in Sy galaxy samples.," Some studies, however, prompt an excess of bars \citep[e.g.,][]{LSK_02}, outer rings \citep{HM1_99}, companions \citep[e.g.,][]{RVB_95}, and, considering early type galaxies, circumnuclear features \citep[][]{XP_02} and dust \citep[e.g.,][]{SSF_07} in Sy galaxy samples."
 Taniguchi(1999). even suggestec (minor) mergers as a unified formation mechanism of (Iow-Iuminosity) AGNs in the local Universe., \citet{T_99} even suggested (minor) mergers as a unified formation mechanism of (low-luminosity) AGNs in the local Universe.
 It is now believed that the SMBH and its host galaxy have coevolved., It is now believed that the SMBH and its host galaxy have coevolved.
 A relation between SMBH mass and bulge luminosity was first established for inactive galaxies (Kormendy&Richstone1995) and then extended to active galaxies (Laor1998:Wandel1999).," A relation between SMBH mass and bulge luminosity was first established for inactive galaxies \citep{KR_95} and then extended to active galaxies \citep{L_98,W_99}."
. Similar relations link SMBH mass with bulge velocity dispersion and light concentration (forareviewseeFerrarese&Ford2005)., Similar relations link SMBH mass with bulge velocity dispersion and light concentration \citep[for a review see][]{FF_05}.
". In particular. the accurate photometric separation of the bulge from the other galactic components is of utmost importance for studying the ""SMBH mass — bulge luminosity” relation in depth."," In particular, the accurate photometric separation of the bulge from the other galactic components is of utmost importance for studying the “SMBH mass – bulge luminosity” relation in depth."
 The bulge luminosity obtained by decomposition tends to be systematically lower and leads to less scatter of the above relation (e.g..Mar- 2004).. than the luminosity estimate based on the empirical relation between the," The bulge luminosity obtained by bulge-disk decomposition tends to be systematically lower \citep[][]{W_02} and leads to less scatter of the above relation \citep[e.g.,][]{MH_03,EGC_04}, than the luminosity estimate based on the empirical relation between the"
forms the SX in RE J1034)105 (Zelziarski ct al.,forms the SX in RE J1034+105 (Zdziarski et al.
 2003: AMicelleton et al., 2003; Middleton et al.
 2009: Gladstone. Roberts Done 2009).," 2009; Gladstone, Roberts Done 2009)."
 In this paper we analyse three new observations of RE JL034)396 obtained byVALAL-New/on. together with the previous two data sets (including the one with the QPO detection).," In this paper we analyse three new observations of RE J1034+396 obtained by, together with the previous two data sets (including the one with the QPO detection)."
 Phe QPO is plainly not detected in the first and third of the new datasets. but we may be secing residual signs of its presence in the second.," The QPO is plainly not detected in the first and third of the new datasets, but we may be seeing residual signs of its presence in the second."
 We look at the corresponding spectral evolution of the source. to try to identify what triggers the appearance (ancl clisappearance) of the QPO.," We look at the corresponding spectral evolution of the source, to try to identify what triggers the appearance (and disappearance) of the QPO."
 In this paper we will compare the spectral ancl timing properties of all five observations of IIS J10341396. withAAMAI-Noiwlon., In this paper we will compare the spectral and timing properties of all five observations of RE J1034+396 with.
. For each. observation we use 45 regions and extract co-adcded MOS and PN. background subtracted lighteurves (using v9.0/L10.0) to maximise signal to noise (see details of extraction method in Cierliásski et al.," For each observation we use 45” regions and extract co-added MOS and PN, background subtracted lightcurves (using ) to maximise signal to noise (see details of extraction method in Gierlińsski et al."
 2008 and. Middleton et al., 2008 and Middleton et al.
 2009)., 2009).
 Phe cates. ODSIDs. total exposure time. useful exposure time and operational moce are provided in Table 1.," The dates, OBSIDs, total exposure time, useful exposure time and operational mode are provided in Table 1."
 The first. two observations (hereafter Obsl and. Obs?) were carried out in fullewindow moce and so are piled up in all 3 detectors due to the extremely soft nature of the source., The first two observations (hereafter Obs1 and Obs2) were carried out in full-window mode and so are piled up in all 3 detectors due to the extremely soft nature of the source.
 Obsl is also heavily contaminated. by soft. protons. with strong background [lares across almost all the observation.," Obs1 is also heavily contaminated by soft protons, with strong background flares across almost all the observation."
 Any conservative background. selection would. give almost no usable data., Any conservative background selection would give almost no usable data.
 Including all the data gives the lighteurve ga10wn in Fig la with the one low point marking the position of the largest background Iare., Including all the data gives the lightcurve shown in Fig 1a with the one low point marking the position of the largest background flare.
 Obs2 is much less alfected by background. anc we use 10 same good time intervals as Gicrlifisski et al. (, Obs2 is much less affected by background and we use the same good time intervals as Gierlińsski et al. (
2008).,2008).
 Pig 1 shows the ~50 ks segment of the ~90 ks in which the QPO is most coherent. and. this feature is discussed at length in Cierlitsski et al. (, Fig 1 shows the $\sim$ 50 ks segment of the $\sim$ 90 ks in which the QPO is most coherent and this feature is discussed at length in Gierlińsski et al. (
2008) and. Middleton et al. (,2008) and Middleton et al. (
2009).,2009).
 Two further observations have been taken of RE J1034|396 since the QPO detection. the first was through clirector’s cliscretionary time in AOS (Obs3 hereafter) where the level of Hus can be seen to have risen. ancl the second was taken in AOD and was broken into 2  50ks pointings (Obs4a and 4th hereafter).," Two further observations have been taken of RE J1034+396 since the QPO detection, the first was through director's discretionary time in AO8 (Obs3 hereafter) where the level of flux can be seen to have risen, and the second was taken in AO9 and was broken into 2 $\sim$ 50ks pointings (Obs4a and 4b hereafter)."
 ALL of these were taken in small window mode and so are not. piled up., All of these were taken in small window mode and so are not piled up.
 Figure 2. shows the corresponding PDS (plotted. as power. where power is normalised to fractional rms) of the lighteurves shown in Figure 1.," Figure 2 shows the corresponding PDS (plotted as $\times$ power, where power is normalised to fractional $^2$ ) of the lightcurves shown in Figure 1."
" The 100s inning of the lishteurves gives a Nyquist [requeney. (and renee upper limit on the frequency on which the PDS can be determined) of 10 ""Hz.", The 100s binning of the lightcurves gives a Nyquist frequency (and hence upper limit on the frequency on which the PDS can be determined) of $\times$ $^{-3}$ Hz.
 The PDS includes. the Poisson white noise component which starts to dominate at jieh frequencies. with normalisation given by the error bar variance on cach point as shown by the dotted line on each igure.," The PDS includes the Poisson white noise component which starts to dominate at high frequencies, with normalisation given by the error bar variance on each point as shown by the dotted line on each figure."
 While the PDS of Obs2 shows a significant QPO (δα. even when applving the most stringent Bayesian analyses - see. Vaughan 2010). the PDS of Obsl. Obs3 and Obs ja/b do not have a similarly significant [eature at this requeney.," While the PDS of Obs2 shows a significant QPO $>$ $\sigma$, even when applying the most stringent Bayesian analyses - see Vaughan 2010), the PDS of Obs1, Obs3 and Obs 4a/b do not have a similarly significant feature at this frequency."
 In. particular. Obs3 sets very. stringent. limits on he presence ofa similarly strong QDO. Thus the QPO is not »ersistent. strengthening its association with the transient ueh-[requeney. (LUE) QPOs seen in 115 (Middleton Done 2010) rather than the much more ubiquitous LEQDPOs (Remillard AleClintock 2006).," In particular, Obs3 sets very stringent limits on the presence of a similarly strong QPO, Thus the QPO is not persistent, strengthening its association with the transient high-frequency (HF) QPOs seen in BHBs (Middleton Done 2010) rather than the much more ubiquitous LFQPOs (Remillard McClintock 2006)."
 We use the maximum likelihood fitting routine of Vaughan (2010). assuming an intrinsic power law PDS (POP)xfo) plus white noise. where à is —0.90+0.11. 148£0.32 and 1.59—0.23 for Obs3. Obsda and th respectively. compared— το 1.802:0.20 for Obs2 (consistent at the 2e level with our more simplistic [it of -1.35 - see Ciüerliásski et al.," We use the maximum likelihood fitting routine of Vaughan (2010), assuming an intrinsic power law PDS $P(f)\propto f^{\alpha}$ ) plus white noise, where $\alpha$ is $-0.90\pm 0.17$, $-1.48 \pm 0.32$ and $-1.59 \pm 0.23$ for Obs3, Obs4a and 4b respectively, compared to $-1.80 \pm 0.20$ for Obs2 (consistent at the $\sigma$ level with our more simplistic fit of -1.35 - see Gierlińsski et al."
 2008)., 2008).
 These indices are poorly constrained in Obsda/b due to the relatively short. lengths of the continuous lighteurves. but Obs3 is significantly dilferent to Obs2.," These indices are poorly constrained in Obs4a/b due to the relatively short lengths of the continuous lightcurves, but Obs3 is significantly different to Obs2."
 This change in red noise and QPO properties means that the PDS is non-stationary., This change in red noise and QPO properties means that the PDS is non-stationary.
 This is even more dramatic than in NOGC4051 CMiller et al., This is even more dramatic than in NGC4051 (Miller et al.
 2010). which was the first non-stationary AGN PDS.," 2010), which was the first non-stationary AGN PDS."
 As both Obsl and 2 are heavily pilecl up we attempt to mitigate the worst of the ellects (i.e. migration of counts from soft to hard. energies)., As both Obs1 and 2 are heavily piled up we attempt to mitigate the worst of the effects (i.e. migration of counts from soft to hard energies).
 In the case of Obsl. centroid removal is prohibitively expensive in terms of counts. so instead we extract the X-ray spectrum from single patterns onlv.," In the case of Obs1, centroid removal is prohibitively expensive in terms of counts, so instead we extract the X-ray spectrum from single patterns only."
 Obs2 is substantially longer and so we remove an inner centroid of 1.57 to account for the worst ellects of pile-up., Obs2 is substantially longer and so we remove an inner centroid of 7.5” to account for the worst effects of pile-up.
 We extract and fit NOS spectra only. due to the mismatch between MOS and PN spectra at low energies. using v11.3.2.," We extract and fit MOS spectra only, due to the mismatch between MOS and PN spectra at low energies, using v11.3.2."
 We apply the best-fitting model. of Middleton et al. (, We apply the best-fitting model of Middleton et al. (
2009): a low-temperature. optically thick thermal Conmptonisation of (unobservable UV/EUV) clise seed photons. together with high-temperature. optically thin Comptonisation which dominates at high energies (in this is NTICOAMDP)).,"2009): a low-temperature, optically thick thermal Comptonisation of (unobservable UV/EUV) disc seed photons, together with high-temperature, optically thin Comptonisation which dominates at high energies (in this is )."
 The low temperature Comptonisation component here) is similar to that invoked for high signal-to-noise ULX (Gladstone et al., The low temperature Comptonisation component here) is similar to that invoked for high signal-to-noise ULX (Gladstone et al.
 2009) which. if composed of high stellar mass black holes ος LOOAL.) rather than intermediate mass Bilis. would share similar Eddington/super-Eeldington mass accretion rates as inferred for IUS JLO34|396.," 2009) which, if composed of high stellar mass black holes $\le$ $_{\odot}$ ) rather than intermediate mass BHs, would share similar Eddington/super-Eddington mass accretion rates as inferred for RE J1034+396."
 We fit this model to the spectra of all five observations (Fig 3). with model parameters and their confidence limits presented in Table 2.," We fit this model to the spectra of all five observations (Fig 3), with model parameters and their confidence limits presented in Table 2."
 Fig 4 shows the ratio between the MOSI data for each non-QPO observation to the best. fitting spectral mocol [or Obs2., Fig 4 shows the ratio between the MOS1 data for each non-QPO observation to the best fitting spectral model for Obs2.
 These ratio plots show that the soft component is relatively stronger in. Obsl and Obs3 than in Obs2. but Obsda/b have spectral shapes which are very similar to that seen when the QPO was observed. though with apparant stronger warm absorber features at  0.92 keV. The SX variability is clearly associated with an intrinsic change rather than decreased absorption as the column density pees at the lower limit of absorption in our Cialaxy 20 2 ⋅ ⊔⊳≟⋀↓∪≼∼⊔↓⊳⋯↓∡⋖⋅⊔⇂↓⋅∪⊔↓⇂↓↥⋖⋅⊔⊔↥∪∪⇂∩∢⋅⇀∖≼∙∢⋅↓≻↥⇂∪↓⋅ ⋅ ↻∣⋡⊳∖↓∖∖⊽↓↕∢⊾↓⋅∢⊾↓≻⊲⊔⋅⊔↓≻∣⋡⋯⇍↓⊊⋏∙≟↓⋅∪⊔⊔∠⊲↓⊳∖⊳∖⋯⋅⊳∖⊔↓⋖⋅⋜⋯↿↓↕∢⊾⊳∖↓≻⋖⋅≼⇍↿↓⋅⋜⊔⊔⋅⋖⊾ not reliable.," These ratio plots show that the soft component is relatively stronger in Obs1 and Obs3 than in Obs2, but Obs4a/b have spectral shapes which are very similar to that seen when the QPO was observed though with apparant stronger warm absorber features at $\sim$ 0.9–2 keV. The SX variability is clearly associated with an intrinsic change rather than decreased absorption as the column density pegs at the lower limit of absorption in our Galaxy $\times$ $^{20}$ $^{-2}$, taken from the $_{\rm H}$ ) except for Obs1 where pileup/background issues mean the spectra are not reliable."
 Whilst the first three observations appear to have broadly consistent parameters for the shape of the components. their normalisations differ. with Obs2 having a," Whilst the first three observations appear to have broadly consistent parameters for the shape of the components, their normalisations differ, with Obs2 having a"
will refer to this only as Ho.,will refer to this only as $\alpha$.
 J and Ix broad-band imaging cata were obtained using the Wide Field Camera on URIRT. covering 0.75 square degrees. centered on the cluster centre.," J and K broad-band imaging data were obtained using the Wide Field Camera on UKIRT, covering 0.75 square degrees, centered on the cluster centre."
 ALL photometric data were reduced by the Cambridge Astronomical Survey Unit. with standard. pipelines for INT/WEC and URIRD/WECAAL imagine data.," All photometric data were reduced by the Cambridge Astronomical Survey Unit, with standard pipelines for INT/WFC and UKIRT/WFCAM imaging data."
 As there are not many standard stars for zero-point calibration in the observed fields. we have used. published galaxy photometry as photometric standards.," As there are not many standard stars for zero-point calibration in the observed fields, we have used published galaxy photometry as photometric standards."
 Magnitudes. quoted. in. specific apertures were preferred. for. this calibration., Magnitudes quoted in specific apertures were preferred for this calibration.
 The zero-points in INTPE/WEC U-band and. B-bancl photometry used apertures sizes given in Buta(1996)., The zero-points in INT/WFC U-band and B-band photometry used apertures sizes given in \citet{buta96}.
. Phe zero-point for the lt-band. photometry was calibrated using the photometric lata [rom cdeVaucouleurs&Longo(1905) and Tavloretal. (2005)., The zero-point for the R-band photometry was calibrated using the photometric data from \citet{vl98} and \citet{taylor05}.
. Near-LR. imaging data were calibrated using 16 Two Micron All Sky Survey photometry., Near-IR imaging data were calibrated using the Two Micron All Sky Survey photometry.
 Photometry was corrected lor foreground. Galactic extinction. using the reddening maps of Schlegelctal.(1998)., Photometry was corrected for foreground Galactic extinction using the reddening maps of \citet{schlegel98}.
 We have not attempted to correct the photometry for internal extinction., We have not attempted to correct the photometry for internal extinction.
 |x-correction. as determined by Pogeianti(LOOT). was applied for all images in all filters.," K-correction, as determined by \citet{poggianti97}, was applied for all images in all filters."
 “Phe IVE/WEC B-band images were used to visually classify the morphologies of the galaxies in our sample., The INT/WFC B-band images were used to visually classify the morphologies of the galaxies in our sample.
 Signs of disturbance were defined for he sample galaxies that have clear structures. but show ic. asvnuuectrics. bridecs/tails. broken spiral arms. or ike morphologies.," Signs of disturbance were defined for the sample galaxies that have clear structures, but show i.e. asymmetries, bridges/tails, broken spiral arms, or merger-like morphologies."
 To select a sample of likely members of the cluster. we have proceeded as follows.," To select a sample of likely members of the cluster, we have proceeded as follows."
 Lhe sample selection started rom llo detections within the central area of the cluster., The sample selection started from $\alpha$ detections within the central area of the cluster.
 S6 emission line objects with signal-to-noise larger than five are detected., 86 emission line objects with signal-to-noise larger than five are detected.
 In order to remove the contamination [roni oreerouncl stars. objects with full width half. maximum: smaller than seven pixels. i.e... 5e above the stellar mean. were excluded.," In order to remove the contamination from foreground stars, objects with full width half maximum smaller than seven pixels, i.e., $\sigma$ above the stellar mean, were excluded."
 The emission. line. sample was used. to estimate the B-band magnitude limit of galaxies for which Lla emission could be detected., The emission line sample was used to estimate the B-band magnitude limit of galaxies for which $\alpha$ emission could be detected.
 Objects in this sample are all brighter than B=21 magnitude in D-band., Objects in this sample are all brighter than B=21 magnitude in B-band.
 This magnitude was adopted as the faint limit of our sample., This magnitude was adopted as the faint limit of our sample.
 These criteria were applied to all extended objects In order to minimise the contamination from background> objects. the surface number densities of ealaxies were used to estimate the cluster radius ancl the probable fraction of cluster members.," These criteria were applied to all extended objects In order to minimise the contamination from background objects, the surface number densities of galaxies were used to estimate the cluster radius and the probable fraction of cluster members."
 The surface number density. of objects brighter than 21 ancl full width half maximum smaller than seven pixels. is found το crop around. half of the Abell radius of the cluster. and these objects are distributed uniformly beyond this radius.," The surface number density of objects brighter than 21 and full width half maximum smaller than seven pixels, is found to drop around half of the Abell radius of the cluster, and these objects are distributed uniformly beyond this radius."
 Brigh objects appear in higher proportion within this radius., Bright objects appear in higher proportion within this radius.
 We iive then decided to consider only galaxies within half of the Abell radius., We have then decided to consider only galaxies within half of the Abell radius.
 Then the selection. of galaxies was imited by a diameter criterion to optimise the selection of true cluster. members., Then the selection of galaxies was limited by a diameter criterion to optimise the selection of true cluster members.
 Phe final selected: sample of ‘luster galaxy candidates comprised. 304. galaxies., The final selected sample of cluster galaxy candidates comprised 304 galaxies.
 bor jese galaxies. isophotal fo; apertures were determined to measure UDltJIx magnitudes and Lo Iuxes.," For these galaxies, isophotal $R_{24}$ apertures were determined to measure UBRJK magnitudes and $\alpha$ fluxes."
 ‘To determine the cluster membership for galaxies in the ohotometrically selected sample. spectroscopic observations rom the WYEEOS fibre-fec spectrograph on the William Lerschel Telescope were obtained το determine their redshifts.," To determine the cluster membership for galaxies in the photometrically selected sample, spectroscopic observations from the WYFFOS fibre-fed spectrograph on the William Herschel Telescope were obtained to determine their redshifts."
 Phe total area covered by WYEFFOS/WITL observations covers approximately the same field. as the INT/WEC imagingὃνe observations. with exposure times of 4.1500 seconds for four pointings and 3.2GOO seconds for one pointing.," The total area covered by WYFFOS/WHT observations covers approximately the same field as the INT/WFC imaging observations, with exposure times of $4\times1800$ seconds for four pointings and $3\times600$ seconds for one pointing."
 The erating used gives a spectral dispersion of approximately pixel.I. with a total coverage ofAA.. centred onAA... covering a number of absorption and emission lines.," The grating used gives a spectral dispersion of approximately $^{-1}$, with a total coverage of, centred on, covering a number of absorption and emission lines."
 The observations targeted: preferentially faint. blue. ane small angular size galaxies in the photometrically selected sample.," The observations targeted preferentially faint, blue, and small angular size galaxies in the photometrically selected sample."
 “Phe faintest object has a total B-bancl magnitude of 22. and most of the targeted objects are brighter than 21.5 in I-band.," The faintest object has a total B-band magnitude of 22, and most of the targeted objects are brighter than 21.5 in R-band."
 The spectroscopic data were reduced. using he WYERED package. a special pipeline for the reduction of multifibre. spectroscopy. obtained by NIEP/WYEFEFOS.," The spectroscopic data were reduced using the WYFRED package, a special pipeline for the reduction of multifibre spectroscopy obtained by WHT/WYFFOS."
 Dias-substracted. meclian-combined science frames for each »ointing. and ares and sky images used. as input for the WYERIED package.," Bias-substracted, median-combined science frames for each pointing, and arcs and sky images used as input for the WYFRED package."
 The redshifts measured. from several ines were averaged for each galaxy., The redshifts measured from several lines were averaged for each galaxy.
 Among the 304 galaxies selected. from. broacd-bancl photometry data. 128. galaxies ive measured redshifts.," Among the 304 galaxies selected from broad-band photometry data, 128 galaxies have measured redshifts."
 72 among them are associated with he Abell 1367. cluster. whereas 56 are background objects.," 72 among them are associated with the Abell 1367 cluster, whereas 56 are background objects."
 The new cluster members have velocities within 2.5 times he velocity dispersion from. the average velocity of the cluster as determined by Struble&Roock(1999)., The new cluster members have velocities within 2.5 times the velocity dispersion from the average velocity of the cluster as determined by \citet{sr99}.
. Most of galaxies with spectroscopically determined: membership lie within approximatelv half of the Abell radius of the clust«, Most of galaxies with spectroscopically determined membership lie within approximately half of the Abell radius of the cluster.
 The B-band magnitudes of t1e cluster members range fro 16 to 20. with all galaxies brighter than 16 magnitudes in t photometrically selected sample being cluster members.," The B-band magnitudes of the cluster members range from 16 to 20, with all galaxies brighter than 16 magnitudes in the photometrically selected sample being cluster members."
 The fraction of cluster members to the known recshilt galaxies decreases clramatically [rom SO% for galaxies with B-hanc magnitude ranging from 16 to 17. to for galaxies with magnitude between LO and 20.," The fraction of cluster members to the known redshift galaxies decreases dramatically from $\sim80\%$ for galaxies with B-band magnitude ranging from 16 to 17, to for galaxies with magnitude between 19 and 20."
 The observed. properties of the final sample of Abel 1367 used in the rest of the paper are given in the first live columns of Table 1.. giving the galaxy name (column 1) the morphological tvpe (column 2). the presence of morphological disturbance (column 3: v: ves. n: no) an optical/near-L colours (column 4 and 5).," The observed properties of the final sample of Abell 1367 used in the rest of the paper are given in the first five columns of Table \ref{gal_prop_obs1}, giving the galaxy name (column 1), the morphological type (column 2), the presence of morphological disturbance (column 3; y: yes, n: no), and optical/near-IR colours (column 4 and 5)."
 Figures 1. and 2. show the distribution of the galaxies in oursample in four optical/near-LRo colour-magnitude diagrams., Figures \ref{cmr_morph} and \ref{cmr_ew} show the distribution of the galaxies in oursample in four optical/near-IR colour-magnitude diagrams.
 The galaxies in both figures are coded on the basis of their morphological tvpe. equivalent width of the La emission line and the presence of morphological disturbance.," The galaxies in both figures are coded on the basis of their morphological type, equivalent width of the $\alpha$ emission line and the presence of morphological disturbance."
 ‘These illustrate the wide range in luminosity covered in our analysis. nearly six magnitudes. with galaxies with cilferent properties spread across this range. except the brightest two galaxies which are ellipticals.," These illustrate the wide range in luminosity covered in our analysis, nearly six magnitudes, with galaxies with different properties spread across this range, except the brightest two galaxies which are ellipticals."
 The colour-magnituce diagrams of our sample galaxies show the normal bimocal structure. in. Abell 1367 the blue. sequence of. [ate-tvpe ealaxies is Clearly visible. in agreement with previous stucdes of this cluster (Godwin&Peach1982).. but in contrast to the colour-magnitude diagrams of more relaxed clusters such as Coma ‘Lerlevichetal.(c.g. 2001)..," The colour-magnitude diagrams of our sample galaxies show the normal bimodal structure, in Abell 1367 the blue sequence of late-type galaxies is clearly visible, in agreement with previous studies of this cluster \citep{gp82}, but in contrast to the colour-magnitude diagrams of more relaxed clusters such as Coma \citet[e.g.][]{terlevich01}. ."
 Specifically Terlevichet.al.(2001) find that most spiral. irregular. and unclassified galaxies in their Coma sample lie on the," Specifically \citet{terlevich01}
 find that most spiral, irregular, and unclassified galaxies in their Coma sample lie on the"
in grey-bolometric light curve calculations such as employed here.,in grey-bolometric light curve calculations such as employed here.
" In particular. 1. demonstrated that the light curve computed from a uniform-density spherical model with (y,=lot kms ! ügrees very well with that obtained from the W7 model (see their figure 2)."," In particular, \citet{pinto00a} demonstrated that the light curve computed from a uniform-density spherical model with $v_{\mbox{\scriptsize max}} = 10^4$ km $^{-1}$ agrees very well with that obtained from the W7 model (see their figure 2)."
" Inside our toy SN models. the ""Ni is also given a spherical distribution but its centre-of-mass is offset in velocity relative to that of the SN: this offset (Ac. which will generally be specitied as a fraction of Όμως) Is one of the parameters of the models."," Inside our toy SN models, the $^{56}$ Ni is also given a spherical distribution but its centre-of-mass is offset in velocity relative to that of the SN; this offset $\Delta v$, which will generally be specified as a fraction of $v_{\mbox{\scriptsize max}}$ ) is one of the parameters of the models."
" Throughout the region which contains """"Ni. a uniform Htraction f is adopted — this is the second parameter of the model."," Throughout the region which contains $^{56}$ Ni, a uniform mass-fraction $f$ is adopted – this is the second parameter of the model."
" n all the models the total mass of ""Ni is fixed to 0.4 M.: (chojerefore. f. determines the volume of the region which contains ""Ni.", In all the models the total mass of $^{56}$ Ni is fixed to 0.4 $_{\odot}$; therefore $f$ determines the volume of the region which contains $^{56}$ Ni.
 In total. five models (A — E) are presented here: the structure of these models is illustrated in Figure |..," In total, five models (A – E) are presented here; the structure of these models is illustrated in Figure \ref{fig:toy-pics}."
 The parameters which differentiate the models (Aesena. f£) are indicated in the figure and also tabulated in Table |..," The parameters which differentiate the models $\Delta v/v_{\mbox{\scriptsize max}}$, $f$ ) are indicated in the figure and also tabulated in Table \ref{tab:toy}."
 In all the toy models. a uniform grey-absorption cross section of 0.1 em? + is adopted for the treatment of “bolometric” photons while the  -ray transport and deposition is treated in detail (see ?. for a full description).," In all the toy models, a uniform grey-absorption cross section of 0.1 $^{2}$ $^{-1}$ is adopted for the treatment of “bolometric” photons while the $\gamma$ -ray transport and deposition is treated in detail (see \citealt{sim07} for a full description)."
" Light eurves have been computed for each of the five models (A — E) for three interesting viewing directions: For each of these viewing angles in each of the models. the time (),) and magnitude (AZ) of maximum light have been extracted: these values are reported in Table I.."," Light curves have been computed for each of the five models (A – E) for three interesting viewing directions: For each of these viewing angles in each of the models, the time $t_{\rm p}$ ) and magnitude $M_{\rm p}$ ) of maximum light have been extracted; these values are reported in Table \ref{tab:toy}."
" The results in Table |. indicate that an off-centre distribution of ""Ni could introduce significant angular dependence in the light curve properties.", The results in Table \ref{tab:toy} indicate that an off-centre distribution of $^{56}$ Ni could introduce significant angular dependence in the light curve properties.
" In the models. the light curve peak is both earliest and brightest when viewed along the direction in which the ""Ni is displaced."," In the models, the light curve peak is both earliest and brightest when viewed along the direction in which the $^{56}$ Ni is displaced."
" This behaviour is as expected since the mean optical depth from the ""Ni to the edge of the ejecta is lowest in this direction: therefore. more energy packets escape more quickly."," This behaviour is as expected since the mean optical depth from the $^{56}$ Ni to the edge of the ejecta is lowest in this direction; therefore, more energy packets escape more quickly."
 Correspondingly. when viewed from the diametrically opposite direction. the peak magnitude occurs latest and is dimmest.," Correspondingly, when viewed from the diametrically opposite direction, the peak magnitude occurs latest and is dimmest."
" It can be seen that the viewing-angle sensitivity of AJ), 1s significantly affected by Av but is insensitive to the adopted value of f.", It can be seen that the viewing-angle sensitivity of $M_{\rm p}$ is significantly affected by $\Delta v$ but is insensitive to the adopted value of $f$.
" As Av is increased. the variation of AZ, with angle in a given model increases from about 0.5 mag for the models with ελΌμως=0.1 to more than 1.5 mag for the most extreme model considered (Ar/tpi,= 0.3)."," As $\Delta v$ is increased, the variation of $M_{\rm p}$ with angle in a given model increases from about 0.5 mag for the models with $\Delta v / v_{\mbox{\scriptsize max}} = 0.1$ to more than 1.5 mag for the most extreme model considered $\Delta v / v_{\mbox{\scriptsize max}} = 0.3$ )."
 To examine the angular behaviour of the light curve properties further. one model (model C) has been studied in greater detail.," To examine the angular behaviour of the light curve properties further, one model (model C) has been studied in greater detail."
 For this model. light curves have been extracted for an additional eight viewing directions.," For this model, light curves have been extracted for an additional eight viewing directions."
" These directions have been selected to give a uniform grid of viewing angles in cos@ (6 being the angle between the line of sight direction and the direction along which the ""Ni is displaced).", These directions have been selected to give a uniform grid of viewing angles in $\cos \theta$ $\theta$ being the angle between the line of sight direction and the direction along which the $^{56}$ Ni is displaced).
" Figures 2 and 3. show the variation of AZ, and /,, with cos6, respectively."," Figures \ref{fig:toy-mpeak} and \ref{fig:toy-tpeak} show the variation of $M_{\rm p}$ and $t_{\rm p}$ with $\cos \theta$, respectively."
 Figure 2. shows that the peak magnitude follows a near-linear dependence on cos6., Figure \ref{fig:toy-mpeak} shows that the peak magnitude follows a near-linear dependence on $\cos \theta$.
" The best-fit straight line Qvhich is drawn in the figure) is given by: The near-linear variation with cos@ is important since it means that the distribution of AZ, one obtains by selecting random is close to a top-hat function: thus the model predicts that if one were to observe it from a random viewing direction one would be equally likely to measure any value of 17, between about -18.2 and -19.2 with no bias towards the median.", The best-fit straight line (which is drawn in the figure) is given by: The near-linear variation with $\cos \theta$ is important since it means that the distribution of $M_{\mbox{\scriptsize p}}$ one obtains by selecting random is close to a top-hat function; thus the model predicts that if one were to observe it from a random viewing direction one would be equally likely to measure any value of $M_{\mbox{\scriptsize p}}$ between about -18.2 and -19.2 with no bias towards the median.
 Α similarly simple relationship is apparent in Figure 3.., A similarly simple relationship is apparent in Figure \ref{fig:toy-tpeak}.
" Again. a linear fit is an adequate description: the best-fit straight line being given by The absolute values for /,, obtained from the toy models are generally somewhat low compared to those deduced by fitting templates to observed light curves (e.g. typically ~ 19 days found in a recent study of light curves from the Supernova Legacy Survey by 23)."," Again, a linear fit is an adequate description; the best-fit straight line being given by The absolute values for $t_{p}$ obtained from the toy models are generally somewhat low compared to those deduced by fitting templates to observed light curves (e.g. typically $\sim$ 19 days found in a recent study of light curves from the Supernova Legacy Survey by \citealt{conley06}) )."
 This is most likely a consequence of the simple treatment of the radiation transport which we have adopted (namely. the use of a grey. time-independent scattering cross-section per gram). but it may also be. in part. a consequence of the chosen structure of the toy models.," This is most likely a consequence of the simple treatment of the radiation transport which we have adopted (namely, the use of a grey, time-independent scattering cross-section per gram), but it may also be, in part, a consequence of the chosen structure of the toy models."
 However. a full investigation of the sensitivity of ἐν to the assumptions made in the radiation transport and the construction of the models goes beyond what we require for this study: instead we focus only on the differential effects introduced by the departures from spherical symmetry.," However, a full investigation of the sensitivity of $t_{p}$ to the assumptions made in the radiation transport and the construction of the models goes beyond what we require for this study; instead we focus only on the differential effects introduced by the departures from spherical symmetry."
" The relative behaviour of fp and AM, is discussed below.", The relative behaviour of $t_{\mbox{\scriptsize p}}$ and $M_{\mbox{\scriptsize p}}$ is discussed below.
 The results obtained with the toy models described above can be used to gain some insight into how observable light curve properties behave., The results obtained with the toy models described above can be used to gain some insight into how observable light curve properties behave.
" In Figure 4.. the values of AZ, are plotted against /, for all the light curves summarised in Table I.."," In Figure \ref{fig:toy-arnett}, , the values of $M_{\mbox{\scriptsize p}}$ are plotted against $t_{\mbox{\scriptsize p}}$ for all the light curves summarised in Table \ref{tab:toy}."
 In addition. the grid of light curves computed to map out the angle dependence with Model C are also represented (eight additional points).," In addition, the grid of light curves computed to map out the angle dependence with Model C are also represented (eight additional points)."
" We emphasise that. since all the models considered adopt the same total mass of ""Ni. he variation in Ad), amongst the different points is entirely the result of the differences in the distribution of Ni with velocity."," We emphasise that, since all the models considered adopt the same total mass of $^{56}$ Ni, the variation in $M_{\rm p}$ amongst the different points is entirely the result of the differences in the distribution of Ni with velocity."
" Since here is no compelling reason to suppose that all observed SN Ta synthesise the same total mass of “°Ni— indeed. to the contrary. the otal mass of ""Ni is likely a dominant parameter in distinguishing SN Ia — our results (Figure +)) cannot be regarded as predictions or a model forthe directly observed distribution of SN Ta light curve xrameters."," Since there is no compelling reason to suppose that all observed SN Ia synthesise the same total mass of $^{56}$ Ni – indeed, to the contrary, the total mass of $^{56}$ Ni is likely a dominant parameter in distinguishing SN Ia – our results (Figure \ref{fig:toy-arnett}) ) cannot be regarded as predictions or a model forthe directly observed distribution of SN Ia light curve parameters."
 Instead. they should be correctly interpreted in terms," Instead, they should be correctly interpreted in terms"
Both N-rav aud azimuthal profiles peak at the same position angle ou the western limb of the outflow.,Both X-ray and azimuthal profiles peak at the same position angle on the western limb of the outflow.
 Iu both cases the castern limb of the outflow cone is 0.75 the intensity of the western lub. aud the surface briehtuess decreases juwards of the casteru Lib to a miuinauni value of ~0.3. OL of the peak brightness (although the rav peak is sheltly offset to the interior of the cone from the )).," In both cases the eastern limb of the outflow cone is $\sim 0.75$ the intensity of the western limb, and the surface brightness decreases inwards of the eastern limb to a minimum value of $\sim 0.3$ – $0.4$ of the peak brightness (although the X-ray peak is slightly offset to the interior of the cone from the )."
 There is not such a clear decrease in brightucss inwards of the western limb. but the images (Fie. 1))," There is not such a clear decrease in brightness inwards of the western limb, but the images (Fig. \ref{fig:n253_fig_geom}) )"
 show additional “clouds” appareutly within the outflow in both X-ray aud images., show additional “clouds” apparently within the outflow in both X-ray and images.
 These features might even be unrelated emission associated with the uncerling disk. rather than part of the outflow itself.," These features might even be unrelated emission associated with the underlying disk, rather than part of the outflow itself."
 We use a simple model to quantify the fraction of enission conuüues from within the core of the outflow. aud what fraction comes from the apparent shell.," We use a simple model to quantify the fraction of emission coming from within the core of the outflow, and what fraction comes from the apparent shell."
" We assume a conical outflow. with a uniform ciuissivity core £544. of opening augle θα surrounded by a shell of ciussivity Foy aud outer opeuing auele 0,54 (sec Fig. 1))."," We assume a conical outflow, with a uniform emissivity core $I_{\rm core}$ of opening angle $\theta_{\rm core}$, surrounded by a shell of emissivity $I_{\rm shell}$ and outer opening angle $\theta_{\rm shell}$ (see Fig. \ref{fig:n253_fig_geom}) )."
 Predicted azinuthal profiles are couvolved with Gaussian mask. to," Predicted azimuthal profiles are convolved with Gaussian mask, to"
that a significant fraction of its initial mass reaches (he core at once.,that a significant fraction of its initial mass reaches the core at once.
 The impactor then equilibrates with the core. material settles back into a new state of hvdrostatic equilibrium and the planet assumes the expected larger spherically sviumetric shape.," The impactor then equilibrates with the core, material settles back into a new state of hydrostatic equilibrium and the planet assumes the expected larger spherically symmetric shape."
 A portion of the impactor and impact energv are deposited high up in the gaseous envelope., A portion of the impactor and impact energy are deposited high up in the gaseous envelope.
 Eventually sedimentation of (hiis mass may release additional enerev on a much longer (ime scale., Eventually sedimentation of this mass may release additional energy on a much longer time scale.
 While the precise partitioning depends on impactor mass. velocity and orientation. il is clear (hat large impacts can deposit mass and energy in large parcels into both the core aud envelope.," While the precise partitioning depends on impactor mass, velocity and orientation, it is clear that large impacts can deposit mass and energy in large parcels into both the core and envelope."
 In addition. the final volumetric radius of the SPII result is in good agreement with those of our one-dimensional LIID model (see below) suggesting that longer term thermal evolution max be encapsulated using a more computationally convenient approach.," In addition, the final volumetric radius of the SPH result is in good agreement with those of our one-dimensional LHD model (see below) suggesting that longer term thermal evolution may be encapsulated using a more computationally convenient approach."
 The 3D-SPII scheme is not ideally suited for the demanding computation of the evolution of (he eas giant. planets., The 3D-SPH scheme is not ideally suited for the demanding computation of the long-term evolution of the gas giant planets.
 The results generated [rom the preliminary SPI scheme indicate (hat internal flow quickly isotropizes the densityv distribution of the merger product (see below)., The results generated from the preliminary SPH scheme indicate that internal flow quickly isotropizes the density distribution of the merger product (see below).
 Ii the limit of neeligible rotation. the structural response and evolution of the envelope. due to the release of thermal energy. during the core coalescence. can be computed with a 1D Lagrangian bydrodvnamic (LIID) scheme.," In the limit of negligible rotation, the structural response and evolution of the envelope, due to the release of thermal energy during the core coalescence, can be computed with a 1D Lagrangian hydrodynamic (LHD) scheme."
 This approach was firstly adopted by Wuchterl (Wuchterl1991). in his calculation of the planet lormation problem., This approach was firstly adopted by Wuchterl \citep{Wuchterl1991} in his calculation of the planet formation problem.
 Although a similar approach is used. our independently developed LHD scheme is based on a more conventional prescription for the convective heat transfer and an alternative approximation lor the computation of the thermal evolution of planets (see re[sec:convec)).," Although a similar approach is used, our independently developed LHD scheme is based on a more conventional prescription for the convective heat transfer and an alternative approximation for the computation of the thermal evolution of planets (see \\ref{sec:convec}) )."
 The basic equations for the LIID scheme include three conservation laws of momentum. mass and energv. ancl (lie equation of state for (hie relationship among the thermocdwvnanmieal quantities.," The basic equations for the LHD scheme include three conservation laws of momentum, mass and energy, and the equation of state for the relationship among the thermodynamical quantities."
 When wriüng them in the Lagrangian scheme. (hese equations are as Iollows:," When writing them in the Lagrangian scheme, these equations are as follows:"
Table 1 gives the parameters for the MERLIN observations.,Table 1 gives the parameters for the MERLIN observations.
 All measurements used the same phase calibrator source 2005-403 to retrieve the absolute position of the maser spots and therefore compare their locations from one line to another with high accuracy., All measurements used the same phase calibrator source 2005+403 to retrieve the absolute position of the maser spots and therefore compare their locations from one line to another with high accuracy.
 A bandpass calibrator was observed to calibrate the variation of instrumental gain and phase across the spectral bandpass., A bandpass calibrator was observed to calibrate the variation of instrumental gain and phase across the spectral bandpass.
 For OH. observations of 3C286 were also made during the observing run. with the same correlator configuration and bandwidth. to calibrate the polarisation characteristics.," For OH, observations of 3C286 were also made during the observing run, with the same correlator configuration and bandwidth, to calibrate the polarisation characteristics."
 The data were reduced in Jodrell Bank observatory using the AERLIN d-programs and the AIPS software package., The data were reduced in Jodrell Bank observatory using the MERLIN d-programs and the AIPS software package.
 IRAS 20126+4104 was observed in the 1665- and 1667-MHz OH maser trarsitions in January 2002 using six telescopes of the MERLIN network., IRAS $20126+4104$ was observed in the 1665- and 1667-MHz OH maser transitions in January 2002 using six telescopes of the MERLIN network.
 The frequencies were alternated during the observations. cycling between the two OH line frequencies. to provide data on both transitions spread over the whole observing track.," The frequencies were alternated during the observations, cycling between the two OH line frequencies, to provide data on both transitions spread over the whole observing track."
 The velocity resolution was 0.42 km s! for a total of 1 MHz spectrum bandwidth corresponding to 180 km s! velocity range., The velocity resolution was 0.42 km $^{-1}$ for a total of 1 MHz spectrum bandwidth corresponding to 180 km $^{-1}$ velocity range.
 The left- and right-hand eireular (LHC and RHC) polarisation data for each baseline were simultaneously correlated in order to obtain all Stokes parameters., The left- and right-hand circular (LHC and RHC) polarisation data for each baseline were simultaneously correlated in order to obtain all Stokes parameters.
 Using d-programs (see Diamond et al., Using d-programs (see Diamond et al.
 2003). the data were edited and corrected for gain-elevation effects.," 2003), the data were edited and corrected for gain-elevation effects."
 The flux density of the amplitude calibrator 3C84. was determined by comparing the visibility amplitudes on the shortest baselines with those of 3C286.," The flux density of the amplitude calibrator 3C84, was determined by comparing the visibility amplitudes on the shortest baselines with those of 3C286."
 Using flux densities of 13.6 Jy at 1665 MHz and 1667 MHz for 3C286 (Baars et al., Using flux densities of 13.6 Jy at 1665 MHz and 1667 MHz for 3C286 (Baars et al.
 1977). the flux density of 3C84 at the time of the observation was determined to be 23.2+0.6 Jy.," 1977), the flux density of 3C84 at the time of the observation was determined to be $23.2\pm0.6$ Jy."
 In AIPS the data were calibrated for all remaining instrumental and atmospheric effects., In AIPS the data were calibrated for all remaining instrumental and atmospheric effects.
 Starting from a point source model. the phase calibrator source was mapped. with a total of three rounds of phase self-calibration and the resulting corrections applied to the source. data.," Starting from a point source model, the phase calibrator source was mapped, with a total of three rounds of phase self-calibration and the resulting corrections applied to the source data."
 The polarisation leakage for each antenna was determined using 3C84 and the polarisation position angle correction was performed using 3C286., The polarisation leakage for each antenna was determined using 3C84 and the polarisation position angle correction was performed using 3C286.
 The AIPS task IMAGR was used to map the whole data set in Stokes I. Q. U and V in order to retrieve the polarisation information.," The AIPS task IMAGR was used to map the whole data set in Stokes I, Q, U and V in order to retrieve the polarisation information."
 The rms noise. after CLEANing. was typically 14 mJy/beam and the FWHM of the restoring beam is 174 x 137 mas at à position angle of —417.," The rms noise, after CLEANing, was typically 14 mJy/beam and the FWHM of the restoring beam is 174 $\times$ 137 mas at a position angle of $-41^\circ$."
 The positions of the maser components were determined by fitting two-dimensional Gaussian components to the brightest peaks m each channel map., The positions of the maser components were determined by fitting two-dimensional Gaussian components to the brightest peaks in each channel map.
 Components were considered as spectral features if they occurred in three or more consecutive channels., Components were considered as spectral features if they occurred in three or more consecutive channels.