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saturation [see Table 5 of Savage & Sembach (1991)]. For a grid of different intrinsic central line depths \(d_{line}\) we converted the optical depth profile to a normalized flux profile using \(F_{norm}=e^{-\tau(v)}\), where the intrinsic central optical depth \(\tau_{0}=-\mathrm{ln}(1-d_{line})\). The flux profiles were then convolved with the instrumental broadening function; the effect of this process is to decrease the intrinsic line depth to an apparent line depth (\(d\)), and increase the intrinsic line width to an apparent line width (\(\sigma\)). We then added different levels of random noise (drawn from a Gaussian distibution) to the data, scaled so that the S/N in the continuum reached the desired levels when rebinned to pixels equal in size to the resolution element. In the line, we scaled down the random noise contribution by \(\sqrt{F}\), in accordance with Poisson statistics. We then rebinned the data by different factors, converted the profiles to \(N_{a}(v)\) space, and finally integrated the profiles over velocity to yield \(N_{a}\), as a function of line depth, noise, and rebinning factor. The velocity integration limits used are \(\pm 2.5\sigma\) around the line center, corresponding to the points where the line recovers to 96% of the continuum in the absence of noise. These limits were chosen so as to reproduce the velocity integration ranges used in practice, determined by comparing the line widths and velocity integration ranges from a large spectroscopic data set (the _FUSE_ O VI survey; Wakker et al., 2003). For each model run, we determined the ratio of \(N_{a}\) to \(N_{true}\), where \(N_{true}\) is the true column density of the simulated component, then repeated the process 500 times; the mean overestimation factor \(<N_{a}>/N_{true}\), together with its dispersion, is then used in our results. For very optically thick lines, the random error can take the flux below zero, corresponding to negative \(N_{a}(v)\), which has no physical meaning. Therefore, a cutoff must be used, whereby all points with \(F(v)\) less than some value are placed at that value (in our case, 1% of the continuum). The cutoff value selected will depend on the reliability of the scattered light and background corrections for the particular instrument providing the observations. ## 3. Results Figure 1 shows a graphical example of the overestimation process for a resolved line with an intrinsic depth of 0.8, measured with _FUSE_. In the left column we show how the spectra would appear at different S/N levels, ranging from S/N=\(\infty\) at the bottom to S/N=5 at the top. Note that we quote the S/N per resolution element, rather than the S/N at the level of rebinning shown. The two are related by (S/N)\({}_{res.elem.}\)=\(\sqrt{}\)(number of bins per resolution element) \(\times\)(S/N)\({}_{bin}\). We verified this relation by measuring the S/N of the model spectra at different binning levels. In the next three columns we show the profiles in apparent column density space after different levels of rebinning. In Figure 2 we display the results of different parameter cases using a color-coded plot: resolved lines with _FUSE_ (top left), marginally resolved lines with _FUSE_ (top right), resolved lines with STIS (bottom left), and marginally resolved lines with STIS (bottom right). Within each panel, we show the overestimation factor as a function of signal-to-noise ratio and apparent line depth (both easily measurable quantities), for three different rebinning cases. In each panel, we have not shaded in regions that correspond to non-significant detections, i.e. those with \(W_{\lambda}<3\sigma(W_{\lambda})\); the minimum depth line that can be considered significant is proportional to (S/N)\({}^{-1}\), since at low S/N shallow lines will not be distinguished from the noise. Using Figure 2 an observer can find the likely error on \(N_{a}\) in a line with a given depth, width, and S/N, and correct for it. The overestimation factors for a range of cases are also presented in Tables 1 and 2, for _FUSE_/LiF and STIS/E140M data, respectively. Upon request we can also provide an IDL code that returns the overestimation factor when given the measured S/N, apparent line depth, and apparent line width. ## 4. Discussion The effects of several parameters combine to produce the trends seen in Tables 1 and 2 and Figures 1 and 2: S/N, level of rebinning, spectral resolution, line width, and line depth. We discuss each separately in this section. * ***Low S/N and Rebinning** - the non-linear distortion of the \(N_{a}(v)\) profile and resulting overestimate of \(N_{a}\) becomes worse as the S/N decreases (Fig. 1). Rebinning the spectrum before measurement can lessen the distortion, since the rebinning process increases the effective S/N. Once the data is rebinned to a level coarser than the resolution element, the gain in the \(N_{a}\) accuracy is made at the expense of resolution, so that kinematic information is given up. However, if the absorption line before rebinning is fully or marginally resolved, and if one is more interested in obtaining an accurate column density than obtaining knowledge about the detailed shape of the line profile, then overbinning is justified at low S/N. AOD measurements made at optimum sampling (two rebinned pixels per resolution element) on _FUSE_ and STIS data are overestimated by less than 10% for S/N per resolution element \(\gtrsim\)7. For data with lower S/N, rebinning beyond the resolution element will likely increase the accuracy of the derived column density. * ***Lack of Resolution and Line Width** - for marginally resolved lines, the apparent column density tends to underestimate the true column density at high line depths (purple shading on the right hand panels in Figure 2), since the high optical depth points are smoothed out to lower apparent optical depths by the instrumental blurring. This effect therefore works in the opposite sense to the S/N effect. The more unresolved the line is (i.e., the lower \(\sigma_{line}/\sigma_{ins}\)), the worse this effect becomes. Even full saturation can be hidden by the effects of instrumental broadening. Savage & Sembach (1991) and Jenkins (1996) discuss how this unresolved saturation can be corrected for when observations exist for more than one line of an ion. For resolved lines, increasing the ratio \(\sigma_{line}/\sigma_{ins}\) above 2 increases the number of pixels susceptible to noise and hence increases \(<\!N_{a}\!>/N_{true}\) slightly for a given S/N and line depth (by a few percent if \(\sigma_{line}/\sigma_{ins}=4\)); however, since the dependency on width is weak, we present results for two line width cases only

. * ***Line Depth** - for a given S/N and line width, the overestimation factor is worse for shallow lines than for deep lines. This is because the noise is Poissonian, so a pixel with low optical depth (shallow) has a higher error on the flux than a pixel with high optical depth (deep). For very deep lines, the cutoff used to eliminate negative pixels _underestimates_ the optical depth in very opaque parts of the profile. This effect works in the opposite sense to the S/N effect, so that measurements of very deep (\(F(v)/F_{c}(v)\leq 0.10\)) lines at low S/N are distorted by two competing effects. Note that if the noise were random rather than Poissonian (i.e. independent of the flux), the overestimation effect on deep lines would become worse since the flux errors deep in the lines are larger. In Figure 3 we show the histogram of \(N_{a}/N_{true}\) for one particular run (_FUSE_/LiF, \(\sigma_{line}=2\sigma_{ins}\), S/N=8, intrinsic depth=0.5, 500 runs) for three levels of rebinning. The overestimation factor has a Gaussian distribution, with a mean that decreases with rebinning. For any given absorption profile, the overestimation can take a range of values. We therefore advise a conservative error estimate when correcting for the overestimation. We note that the non-linear S/N distortion effect discussed here can influence the detailed intercomparisons of \(N_{a}(v)\) profiles of the same ion. Therefore, corrections for line saturation based on comparing \(N_{a}(v)\) profiles of weak and strong lines may not be valid for low S/N observations. In their survey of O VI absorption in the Galactic halo and high-velocity clouds, Wakker et al. (2003) rebinned _FUSE_ data with S/N\(<\)10 per resolution element by 5 pixels, and noisier data by up to 20 pixels, before measurement with the AOD technique. Our modelling shows that this was the correct procedure for measuring accurate O VI column densities, and we endorse a similar treatment of low S/N data in future studies. Without this rebinning, the column density measurements along sight lines with noisy spectra could be inflated by more than 20%. **Acknowledgements** The authors wish to thank Ken Sembach and Chris Howk for useful discussions. This research has been supported by NASA through grant NNG04GC70G to BDS and grant NAG5-7444. BDS also acknowledges support from the University of Wisconsin Graduate School. ## References * Jenkins (1996) Jenkins, E. B. 1996, ApJ, 471, 292 * Sahnow et al. (2000) Sahnow, D., et al. 2000, ApJ, 538, L7 * Savage & Sembach (1991) Savage, B. D., & Sembach, K. R. 1991, ApJ, 379, 245 * Sembach & Savage (1992) Sembach, K. R., & Savage, B. D. 1992, ApJS, 83, 147 * Wakker et al. (2003) Wakker, B. P., et al. 2003, ApJS, 146, 1 * Woodgate et al. (1998) Woodgate, B. E., et al. 1998, PASP, 110, 1183

# Did Boomerang hit MOND ? Anze Slosar\({}^{1}\), Alessandro Melchiorri\({}^{2}\), Joseph I. Silk\({}^{3}\) \({}^{1}\)Faculty of Mathematics and Physics, University of Ljubljana, Slovenia \({}^{2}\) Physics Department and sezione INFN, University of Rome "La Sapienza", Ple Aldo Moro 2, 00185 Rome, Italy \({}^{3}\) Astrophysics, Denys Wilkinson Building, Keble Road, OX13RH, Oxford, United Kingdom (October 11, 2023) ###### Abstract Purely baryonic dark matter dominated models like MOND based on modification of Newtonian gravity have been successfull in reproducing some dynamical properties of galaxies. More recently, a relativistic formulation of MOND proposed by Bekenstein seems to agree with cosmological large scale structure formation. In this work, we revise the agreement of MOND with observations in light of the new results on the Cosmic Microwave Anisotropies provided by the \(2003\) flight of Boomerang. The measurements of the height of the third acoustic peak, provided by several small scale CMB experiments have reached enough sensitivity to severely constrain models without cold dark matter. Assuming that acoustic peak structure in the CMB is unchanged and that local measurements of the Hubble constant can be applied, we find that the cold dark matter is strongly favoured with Bayesian probability ratio of about one in two hundred. ## I Introduction The measurements of the Cosmic Microwave Background (CMB) anisotropies, most notably by the Wilkinson Microwave Anisotropy Probe (WMAP) mission Bennett03 , have truly marked the beginning of the era of precision cosmology. In particular, the shape of the measured temperature and polarisation angular power spectra are in spectacular agreement with the expectations of the standard model of structure formation, based on primordial adiabatic and nearly scale invariant perturbations (see e.g. spergel ). More recently, ground based and balloon borne CMB experiments like extended VSA vsa , CBI cbi , Acbar acbar1 , DASI dasipol and BOOMERANG-03 boom03 , have probed the CMB power spectra at smaller scales, confirming the presence of acoustic oscillations and providing the first unambiguous detection of polarisation. Moreover, new, complementary, results from the Sloan Digital Sky Survey (SDSS) on galaxy clustering (see e.g. Tg04 ) and, more recently, on Lyman-\(\alpha\) Forest clouds Se04 are now further constraining the scenario. Since all these measurements appear in spectacular agreement with the \(\Lambda\)CDM model, based on a cosmological constant and on cold dark matter, is definitely timely to investigate what space is left for alternative theories. Perhaps the most exotic alternative to the standard model one could consider is MOdified Newtonian Dynamics (MOND, M1 ) where a purely baryonic model with modifications to standard (Newtonian) gravity is suggested. In MOND the departure from Newtonian law \(\mathbf{a}=-\bm{\nabla}\Phi_{\rm N}\) is given by: \[\tilde{\mu}(|\mathbf{a}|/\mathfrak{a}_{0})\mathbf{a}=-\bm{\nabla}\Phi_{\rm N}\] (1) where \(\Phi_{\rm N}\) is the Newtonian potential of the visible matter, \(\mathfrak{a}_{0}\) is an acceleration scale while \(\tilde{\mu}(x)\approx x\) for \(x\ll 1\) and \(\tilde{\mu}(x)\to 1\) for \(x\gg 1\). If \(\mathfrak{a}_{0}\approx 1\times 10^{-8}\) cm s\({}^{-2}\) the Newtonian law is recovered in the solar system where accelerations are large compared to \(\mathfrak{a}_{0}\). The above empirical formula (1) has been originally proposed to explain the fact that rotation curves of disk galaxies become flat outside their central parts. While in the standard dark matter paradigm flat rotation curves are explained by assuming a spherical halo of invisible dark matter around visible disk galaxies, in MOND there is no need to include non baryonic dark matter since, thanks to the Eq.1, galaxies far out exhibit an approximately spherical Newtonian potential without the inclusion of the dark matter. Attempts were made to confront MOND with clusters of galaxies (see e.g. sand03 ; poi05 ) and the large scale structure (e.g. adi ) with mixed success. While the non-baryonic dark matter paradigm is definitely more compelling for its aesthetic simplicity than a modification to Newtonian gravity, the MOND model has been claimed successful in other aspects (see e.g. mcg98 ; san2k ) and MOND proponents insist that this alternative model for gravity merits serious examination. The MOND theory has suffered from a lack of a successful relativistic formulation, that would allow one to compare it to observations of CMB and Large Scale Structure. Nevertheless, there were some attempts to confront CMB data gaugh04 , which find that the first \(2\) observed acoustic peaks in the CMB spectrum are compatible with MOND at the price of a substantial neutrino mass, which is barely compatible with current laboratory bounds fogli , or at the price of including curvature lmg , which is at odds with the inflationary scenario. A major step in the direction of developing the sim

ple MOND formula into a more robust theory of gravity has been recently proposed by Bekenstein bekenstein . In this paper, a relativistic gravitational theory has been presented whose nonrelativistic weak acceleration limit accords with MOND while its nonrelativistic strong acceleration regime is Newtonian. Moreover, Bekenstein's model provides a specific formalism for constructing cosmological models and testing MOND using cosmological data. Indeed, more recently, Skordis et al. skordis produced the first theoretical prediction for CMB anisotropies and Large Scale Structure in the case of Bekenstein's model. It has been shown that the Bekenstein model may be put in agreement with the WMAP data and Large Scale Structure observations. Similar to previous results authors find agreement if neutrinos ensure that peak positions are unchanged. The results are obviously of great relevance since the model has no cold dark matter in it and may therefore be considered as an important alternative to the present cosmological scenario, which assumes a fine-tuned cosmological constant and yet to be discovered dark matter particles. In this brief report we point out that recent, small scale, CMB data already provide discriminating power between these two scenarios. In the standard cold dark matter scenario, the amplitude of the CMB peaks is sensitive to the amount of dark matter because of two effects: increasing the matter density on one hand decreases the radiation driving while on the other hand it increases the depth of potential wells. These two effects nearly cancel out in the amplitude of the second acoustic peak, but conspire to produce a higher amplitude of the third peak (see hufu ). The height of the second peak to the first peak therefore contains information on the baryonic content of the Universe, while the ratio of the third peak to the first peak height tells us about the matter density. A generic prediction of purely baryonic dominated models like MOND is therefore that peaks in the CMB power spectrum should be strictly decreasing in amplitude. Extraordinary WMAP results on the first two peaks, coupled with the recent small scale CMB data on the third peak now have enough power to discriminate between these two scenarios and to determine the amount of cold dark matter. The goal of this brief report is to examine the data on the third peak, with special emphasis on the recent measurements of the CMB fluctuations by the Boomerang experiment. The ultimate test of MOND, would be a full confrontation of the relativistic theory with the data. This is a daunting task, given that the theory is very complicated with yet to be fully understood perturbation theory and several free parameters including a free function. We note, however, that models discussed in skordis are in a complete agreement with generic \(\Lambda\)-CDM predictions in the range \(\ell>200\). We therefore assume that this is a generic prediction of the Bekenstein's theory and proceed by fitting the \(\ell>200\) region of the CMB data with the standard \(\Lambda\)-CDM models to see whether models with zero cold dark matter density are compatible with the data. Whether our assumption is a justified one is to be seen, however, we feel it nevertheless provides a first order confrontation of the data with the theory. Our approach is orthogonal to that of skordis in the sense that it provides constraints on any theory that leaves the CMB physics unchanged on scales smaller or roughly equal to that of the first acoustic peak. ## II Analysis We use the Cosmo-MC package (cosmomc ) to perform parameter estimation on standard flat \(\Lambda\)-CDM models using top-hat priors on the following 6 parameters: \(\omega_{\rm b}=\Omega_{\rm b}h^{2}\) (the baryon density of the universe), \(\omega_{\rm dm}\) (the dark matter density of the universe), \(\theta\) (ratio of the sound horizon to the angular diameter distance to the surface of last scattering, multiplied by 100), \(\nu_{\rm frac}\) (the fraction of dark matter in form of massive neutrinos), \(n_{\rm s}\) (spectral index of primordial fluctuations), \(\log A_{\rm s}\) (the amplitude of primordial scalar fluctuations). The priors used are listed in the Table 1. In our parametrisation the density of the _cold_ dark matter is given by \[\Omega_{\rm cdm}=\frac{\omega_{\rm dm}\left(1-\nu_{\rm frac}\right)}{h^{2}}\] (2) We intentionally omitted \(\tau\), the optical depth to the last scattering, from our parametrisation as it is completely degenerate with the amplitude in the multipoles of interest. The following datasets were used in our parametrisation: WMAP Bennett03 ; verde , VSA vsa , CBI cbi , Acbar acbar1 , and the latest Boomerang results boom03 . In these datasets we have used the default Cosmo-MC distribution datasets for VSA, CBI and Acbar experiments. In all datasets any points with \(\ell<200\) were removed and additionally all points with \(\ell<375\) were removed \begin{table} \begin{tabular}{c c} Parameter & Prior \\ \hline \(\omega_{\rm b}\) & BBN (see text) \\ \(\omega_{\rm dm}\) & (0,0.99) \\ \(\theta\) & (0.5,10) \\ \(\nu_{\rm frac}\) & (0,1) \\ \(n_{\rm s}\) & (0.5,1.5) \\ \(\log 10^{10}A_{\rm s}\) & (2,5) \\ \(n_{\rm run}\) & (-0.2,0.2) \\ \end{tabular} \end{table} Table 1: Flat priors on the cosmological parameters. Notation \((x,y)\) implies a a flat prior between \(x\) and \(y\). Running spectral index (last parameter) was used only in the part discussed in the last paragraph of section III.

from Boomerang temperature data (to prevent cosmic variance coupling to the WMAP dataset). The basis of our analysis are the heavily oversampled chains of the WMAP dataset (with about \(\sim\)260,000 independent points) on the parametrisation described above, together with a Big Bang Nucleosynthesis (BBN) prior of \(\omega_{b}=0.020\pm 0.002\)bbn . There is an additional prior on \(0.4<h<1.0\) hard-coded into the Cosmo-MC code and our posterior space is cut by the lower end of this prior. Releasing this prior would weaken our constraints, but \(h<0.4\) models would face many difficulties with other cosmological probes. We importance sample these chains with additional data in order to get improved constraints. Apart from savings in the CPU time, the importance sampled chains still include models from the low \(\Omega_{\rm dm}\) region which is of interest for the MOND models and would otherwise be present only far into the tails of the probability distribution. We also made a similar run without the BBN prior but with very wide flat prior on \(\omega_{\rm b}\) instead, to check the effect of BBN prior dependence. ## III Results The parameter of major interest here is \(\Omega_{\rm cdm}\). A MOND predicts a zero \(\Omega_{\rm cdm}\), while the standard prediction is that of a \(\Omega_{\rm cdm}\) of about 0.3. In the Figure 1 we plot the data we used (note that some points were omitted from the plot - see caption) and a few theoretical predictions. The solid line model corresponds to a standard \(\Lambda\)CDM flat model and fits the data very well. The dashed and dotted models were cherry-picked from the models that have the highest likelihood of models that satisfy \(\Omega_{m}<0.01\) in each individual MCMC chain (using WMAP data alone). The dashed model illustrates the common wisdom that it is possible to construct models that have nearly identical peak positions and heights of even peaks with zero dark matter. Finally, the dotted model shows an example of a zero dark matter model that is allowed by the WMAP data but obviously at odds with measurements of the small scale power. In the Figure 2 we plot the marginalised probability distribution for \(\Omega_{\rm cdm}\) for the WMAP dataset and the WMAP dataset after inclusion of all the other CMB data. We note that the WMAP alone admits the zero cold dark matter solutions, in agreement with previous investigations skordis ; gaugh04 . The addition of other datasets, however, strongly rejects this region of the parameter space, without resorting to non-CMB experiments. In order to quantify this further, we use two statistical tests. Firstly, we compare two basic models, namely the flat CDM model with \(\Omega_{\rm cdm}\) between 0 and 1 and the MOND model for which \(\Omega_{\rm cdm}=0\) using Bayesian model comparison slal . In order to do this we compute the logarithm of evidence ratio with a version of the Savage-Dickey test, equivalent to that described in the Appendix of ss04 . Secondly we estimate the number of "sigmas" in a frequentist manner by comparing the likelihoods of the \(\Omega_{\rm cdm}=0\) point and the most likely point in the marginalised probability distribution for \(\Omega_{\rm cdm}\). The likelihood ratio can be converted to a number of standard deviations using the prescription \(n_{\sigma}=\sqrt{2\frac{\mathcal{L}_{\rm max}}{\mathcal{L}_{\rm MOND}}}\), which returns the expected result in the Gaussian case. In such short communication it is impossible to compare the two methods in depth, but we Figure 1: This plot shows the experimental data used and a few theoretical spectra. Points with large error-bars were removed from the plot (but actually used in the parameter estimation chains) to maintain clarity. The experiments are as follows: WMAP (bars), VSA (triangles), CBI (crosses), ACBAR (crossed circles), Boomerang (circles). The theoretical graphs plotted are most likely model in our chains for the all CMB data (solid line) and two models picked from best fit models with \(\Omega_{m}<0.01\) from each chain sampling WMAP data only. Parameters for dashed model are \((\omega_{b},\omega_{\nu},h,n_{s})=(0.22,0.096,0.76,0.59)\) and those for the dotted are \((0.22,0.15,0.78,0.43)\). See text for discussion. Figure 2: This plot shows the marginalised probability distribution for \(\Omega_{\rm cmd}\) for the WMAP dataset alone (thin line) and WMAP/VSA/ACBAR/CBI/Boomerang datasets (thick line). Curves are normalised to the same total area under the curve.

note that frequenstist approaches neary always give higher "detection" confidences. Bayesian evidence ratio has an advantage that it directly encodes the probabiltiy ratio. The results are summarised in the Table 2. The exact numbers somewhat depend on the binning width and therefore the numbers in the table are accurate to about \(0.1\) in both columns. Some row state the constraints upon adding two extra constraints on top of all CMB data. HST label denotes the Hubble Space Telescope (HST) constraint on the Hubble's constant freedman , which is conveniently described as a Gaussian around \(h=H_{0}/100{\rm km/s/Mpc}=.72\) with 1-\(\sigma\) dispersion of \(0.8\). The HST data actually has a rather strong effect on our results as the Hubble constant favoured by the \(\Omega_{\rm cdm}=0\) models is rather low. SN label denotes the gold dataset of the riess supernovae data. These results must be taken with some caution, because it is not entirely clear that the standard interpretation of these two cosmological probes is applicable in the MONDian setting. Finally, we have also considered running of the spectral index, defined by \(n_{\rm run}={\rm d}n_{\rm s}/{\rm d}\ln k\) with pivot scale set to \(k=0.05\,\,\mbox{Mpc}\,{h}^{-1}\). Using a top-hat prior between -0.2 and 0.2 on \(n_{\rm run}\) we find that this parameter is completely unconstrained by the WMAP data and only weakly constrained by the all CMB data. However, the very high \(\ell\) points from Acbar seem to favour _negative_ running indices, thus even lowering the third peak required by MOND. Consequently we find that the bound on \(\Omega_{\rm cdm}\) is unaffected when all CMB data are included. ## IV Discussion and Conclusions In this brief report we have analysed the latest CMB data in light of the recently renewed interest in the MOND theories of gravity. We simplified (and potentially oversimplified) the theory by assuming that the small scale CMB fluctuations are unmodified by the MOND theory in accordance with recent attempt skordis to model linear fluctuations in the relativistic theory of MOND recently proposed by Bekenstein. Under this assumption we find that the WMAP data alone is fully consistent with the \(\Omega_{\rm dm}=0\) required by MOND, in accordance with previous findings. A component of massive sterile neutrinos is required with \(\omega_{\nu}\gtrsim 0.1\), which is marginally consistent with earth-based beta electron decay experiments. Addition of other CMB data constrains the third peak height, which encodes the information on the presence of the cold dark matter. The data before the latest Boomerang dataset weakly favour the cold dark matter but only at 1 in 8 probability ratio for a Bayesian analysis and less than 3-\(\sigma\) for the more conventional approach. The VSA's measurement of power at the top of the third peak is probably crucial in absence of Boomerang data. Addition of the third peak from latest Boomerang data gives crucial extra information. The Bayesian probability ratio in favour of cold dark matter models increases to 1 in 36, while the likelihood ratio breaks the 3-\(\sigma\) "barrier". We note that using less general models for the CDM setting would make the Bayesian model selection even stronger in favour of cold dark matter models. Releasing the BBN prior somewhat weakens the constraints. We note however, that there is no obvious mechanism how could a MOND theory evade BBN constraints and that such models are additionally characterised by very low values of \(h\) and \(n_{s}\). Marginalised value of \(\omega_{b}\sim 0.025\) for these models. Finally, we have added two other standard cosmological probes, the HST measurements of the Hubble's constant and the recent supernovae measurements of the luminosity distance. Taken at the face value, they seem to blow the MOND model into oblivion. Care must be taken, however, in interpreting these two datasets as it is not clear whether it is appropriate to include them in the MONDian scenarios without detailed treatment of possible MONDian effects on the background evolution. We have shown that running of the spectral index cannot rescue the third peak, at least for \(|n_{\rm run}|<0.2\). We note that our results are somewhat prior dependent: the \(\Omega_{\rm cdm}\) parameter is a derived parameter in the standard parametrisation used by the Cosmo-MC package and therefore the implied prior on it is certainly not flat. However, we feel that priors employed are actually a sound set of physical priors and therefore our results should be fairly insensitive to any sensible reparametrisations. Finally, we note that there is still a possibility that a version of MOND theory with a high third peak is constructed. However, this would seem rather artificial. The ratio of height of third to the first peak encodes the amount of the baryonic drag and in order to get a high third peak one needs some cold dark matter like element. Even if this eventually turns out to be a scalar field in a MONDian theory, the present

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# A 2.1 Solar Mass Pulsar Measured by Relativistic Orbital Decay David J. Nice and Eric M. Splaver Physics Department, Princeton University Princeton, NJ 08544 Ingrid H. Stairs Department of Physics and Astronomy, University of British Columbia 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada Oliver Lohmer and Axel Jessner Max-Planck-Institut fur Radioastronomie Auf dem Hugel 69, D-53121 Bonn, Germany Michael Kramer University of Manchester, Jodrell Bank Observatory Macclesfield, Cheshire, SK11 9DL, UK James M. Cordes Astronomy Department and NAIC, Cornell University Ithaca, NY 14853 (Submitted to the Astrophysical Journal, 15 June 2005; Revised, 31 July 2005) ###### Abstract PSR J0751+1807 is a millisecond pulsar in a circular 6 hr binary system with a helium white dwarf secondary. Through high precision pulse timing measurements with the Arecibo and Effelsberg radio telescopes, we have detected the decay of its orbit due to emission of gravitational radiation. This is the first detection of the relativistic orbital decay of a low-mass, circular binary pulsar system. The measured rate of change in orbital period, corrected for acceleration biases, is \(\dot{P_{b}}=(-6.4\pm 0.9)\times 10^{-14}\). Interpreted in the context of general relativity, and combined with measurement of Shapiro delay, it implies a pulsar mass of \(2.1\pm 0.2\) \({\rm M}_{\odot}\), the most massive pulsar measured. This adds to the emerging trend toward relatively high neutron star masses in neutron star-white dwarf binaries. Additionally, there is some evidence for an inverse correlation between pulsar mass and orbital period in these systems. We consider alternatives to the general relativistic analysis of the data, and we use the pulsar timing data to place limits on violations of the strong equivalence principle. Subject headings: gravitation--binaries: general--pulsars: individual (PSR 0751+1807) + Footnote †: journal: Submitted to the Astrophysical Journal ## 1. Introduction A fundamental prediction of general relativity is the emission of gravitational radiation by binary systems. The consequent loss of energy and angular momentum from these systems causes their orbital periods to decrease (Peters 1964). Previous to the present work, relativistic orbit decay had been detected in five binary pulsar systems. Four of these systems consist of a mildly recycled pulsar bound to a second neutron star in an eccentric orbit (Taylor & Weisberg 1989; Stairs et al. 2002; Deich & Kulkarni 1996; Kramer et al. 2005). The fifth system, that of PSR J1141\(-\)6545, contains a young pulsar and a \(\sim\)1 \({\rm M}_{\odot}\) white dwarf in an eccentric orbit (Bailes et al. 2003). In this paper, we report the measurement of the relativistic decay of PSR J0751+1807, a millisecond pulsar in a 6 hr orbit (Lundgren et al. 1995). This system differs in several ways from the other binaries in which relativistic decay has been detected. First, its rotation period of 3.4 ms is an order of magnitude smaller than the rotation periods of the pulsars in the other systems, implying greater accumulation of angular momentum during its binary accretion phase. Second, its magnetic field is substantially lower than those of the other systems, presumably because of differences in orbital evolution and accretion (Bhattacharya 2002). Third, its orbit is extremely circular, with eccentricity under \(2\times 10^{-6}\), a consequence of tidal circularization during the late stages of the secondary (Phinney 1992). Fourth, the secondary to PSR J0751+1807 is a low mass helium white dwarf, several times lighter than the secondary stars in the other systems. Measurements of relativistic orbital phenomena in binary systems yield constraints on the masses of the stellar components of the systems. Neutron star mass measurements, in turn, serve as probes of the properties of nuclear matter at high densities (e.g., Lattimer & Prakash 2001). The maximum achievable neutron star mass depends on the equation of state of nuclear matter. Soft equations of state, expected if the core of the neutron star is composed of non-nucleonic matter, predict the maximum neutron star mass \(\lesssim\)2 \({\rm M}_{\odot}\), while stiffer equations of state allow higher values. Reviewing the field several years ago,

function. The confidence intervals derived from these probability distributions were: \[\cos i=\left\{\begin{array}[]{ll}0.41^{+0.11}_{-0.07}&\mbox{(68\% confidence)} \\[4.0pt] 0.41^{+0.27}_{-0.13}&\mbox{(95\% confidence),}\\ \end{array}\right.\] (7) \[m_{1}=\left\{\begin{array}[]{r@{}l@{\,}ll}2.1&\pm 0.2&{\rm M}_{\odot}&\mbox{(6 8\% confidence)}\\[3.0pt] 2.1&{}^{+0.4}_{-0.5}&{\rm M}_{\odot}&\mbox{(95\% confidence),}\\ \end{array}\right.\] (8) and \[m_{2}=\left\{\begin{array}[]{r@{}l@{\,}ll}0.191&\pm 0.015&{\rm M}_{\odot}& \mbox{(68\% confidence)}\\[3.0pt] 0.191&{}^{+0.033}_{-0.029}&{\rm M}_{\odot}&\mbox{(95\% confidence).}\\ \end{array}\right.\] (9) ### Lower Limit on Pulsar Mass from \(\dot{P_{b}}\) Alone While there is no reason to doubt the detection of Shapiro delay, it is worth noting that the orbit decay measurement alone provides some evidence for a very massive neutron star. We calculated a probability distribution function for \(m_{1}\) assuming a uniform _a priori_ distribution for \(\cos i\), appropriate for randomly oriented orbits, and assuming \(\dot{P_{b}}\) is drawn from the Gaussian distribution implied by its measurement uncertainty. The distribution of \(m_{1}\) calculated under these assumptions gives lower limits \(m_{1}\!>\!1.75\,{\rm M}_{\odot}\) (68% confidence) and \(m_{1}\!>\!0.88\,{\rm M}_{\odot}\) (95% confidence). ### Solar Wind Radio signals are dispersed by electrons in the interstellar medium and in the solar wind. Because the solar wind is variable and unpredictable, its contribution can degrade the accuracy of pulsar timing models. The problem is particularly acute for PSR J0751+1807 because of its low ecliptic latitude. Dispersion by the solar wind imposed delays of up to \(\sim\)12 \(\mu\)s in the TOAs in our data set. We excluded all observations for which the line of sight to the pulsar passed within \(15^{\circ}\) of the sun. We found that changing this cutoff to \(30^{\circ}\) or to \(0^{\circ}\) had little impact on our results. In principle, observations at multiple radio frequencies at every epoch would allow the dispersion to be measured and removed; in practice, it is difficult to measure high precision TOAs at two or more widely spaced frequencies, so it becomes necessary to use an analytic model of the solar wind and average the results over many epochs. We modeled the electron density in the solar wind as \(n_{e}(r)=n_{0}(1\mbox{\sc AU}/r)^{2}\), where \(r\) is the distance to the Figure 4.— Constraints on pulsar and secondary masses from the general relativistic timing model. Confidence limits of 68% and 95% are shown. These are the same constraints as the right plot of figure 3, cast into a different parameterization. The shaded region in the lower left is disallowed by the Keplerian mass function. Dashed lines show constraints from \(\dot{P_{b}}\) alone. A dotted line indicates inclination \(i=60^{\circ}\). Figure 3.— Constraints on \(\cos i\) and \(m_{2}\). Dashed lines indicate values of \(m_{1}\) according to equation 6. (a) _Left plot:_ Constraints from the basic timing model, with three post-Keplerian parameters (orbital decay and two Shapiro delay parameters), cast into inclination and mass values via equations 3 through 6. (b) _Right plot:_ Constraints from the general relativistic timing model, with two post-Keplerian parameters (inclination and secondary mass). In each plot, inner and outer contours correspond to 68% and 95% confidence limits.

sun and \(n_{0}\) is the electron density at 1 AU. We found the best fits to the data had \(n_{0}=9.6\pm 3.0\) pc cm\({}^{-3}\). Within this uncertainty range, the particular value of \(n_{0}\) used had little impact in the rotation and binary parameters derived in the timing fit; we used a fixed value of \(n_{0}=9.6\) cm\({}^{-3}\) to calculate the rotation and binary parameters in Table 2. The pulsar's astrometric parameters--position, proper motion, and parallax--exhibit high covariances with \(n_{0}\) and with time changes in \(n_{0}\). To estimate values and uncertainties for these parameters, we fit a grid of timing solutions with \(n_{0}\) between 6.6 and 12.6 pc cm\({}^{-3}\), and with the time derivative of \(n_{0}\) between \(-\)1.5 and +1.5 pc cm\({}^{-3}\) yr\({}^{-1}\). We use the extreme values from these timing fits to calculate the uncertainties on position, proper motion, and parallax given in Table 2. Observations of another pulsar, J1713+0747, over a similar period of time found a marginally smaller solar wind electron density, \(n_{0}=5\pm 4\) pc cm\({}^{-3}\)(Splaver et al. 2005). Despite differing by a factor of two, the \(n_{0}\) values from the two pulsars are in statistical agreement. ## 4. Probing Strong Field Gravity Pulsars are well established testbeds for relativity. Observations of the neutron star-neutron star binary PSR B1913+16 have established that its orbit decays at the rate predicted by general relativity within 0.3% (Taylor & Weisberg 1989; Weisberg & Taylor 2003). However, this test of relativity is of limited use for constraining violations of the strong equivalence principle (SEP) because of the similar self-energies of the two neutron stars. More useful for probing this aspect of gravitation are neutron star-white dwarf binaries, in which the radically different self-energies of the two stars would generate excess gravitational wave energy loss under SEP-violating theories. A succinct review is given by Arzoumanian (2003)(see also Stairs 2003; Will & Zaglauer 1989; Goldman 1992; Lange et al. 2001; Gerard & Wiaux 2002). The observed change in the orbital period of PSR J0751+1807 is \((\dot{P_{b}}/P_{b})_{\rm obs}=(-2.7\pm 0.4)\times 10^{-18}\,{\rm s}^{-1}\). We consider five possible mechanisms for generating changes in the orbital period: acceleration of the binary system relative to the Earth; changes in the gravitational constant, i.e., nonzero \(\dot{G}\); changes in the masses of the component stars; energy loss from the binary due to quadrupole gravitational radiation, as in general relativity; and energy loss due to dipole radiation, as in SEP-violating theories. Contributions from tidal interactions between the two stars are likely not to be important (e.g., Smarr & Blandford 1976). The observed decay rate is the sum of the five contributions: \[\left(\frac{\dot{P_{b}}}{P_{b}}\right)_{\!\rm obs} = \left(\frac{\dot{P_{b}}}{P_{b}}\right)_{\!A}+\left(\frac{\dot{P_{ b}}}{P_{b}}\right)_{\!\dot{G}}+\left(\frac{\dot{P_{b}}}{P_{b}}\right)_{\!\dot{ m}}\] (10) \[\hskip 36.0pt+\left(\frac{\dot{P_{b}}}{P_{b}}\right)_{\!Q}+\left( \frac{\dot{P_{b}}}{P_{b}}\right)_{\!D}.\] We address each of these terms in turn. The first term, acceleration biases, arises from the proper motion of the pulsar, acceleration toward the Galactic plane (\(z\)-acceleration), and Galactic rotation (see Damour & Taylor 1991, for details). The biases for PSR J0751+1807 are listed in Table 3. These values were calculated using the measured proper motion of 6 mas yr\({}^{-1}\), and using a distance of 1.15 kpc, derived from the dispersion measure of the pulsar using the NE2001 galactic electron density model (Cordes & Lazio 2002). To be conservative, we assign an uncertainty equal to the total bias (i.e., 100% uncertainty). The bias of \(\dot{P_{b}}\) is much smaller than its measurement uncertainty and essentially negligible.2 Footnote 2: The same phenomena shift the pulse period derivative, \(\dot{P}=\nu_{1}/\nu_{0}^{2}\), a few percent away from its intrinsic value, but this is of no practical consequence. The second term in Equation 10, due to \(\dot{G}\), can be shown negligible by appeal to other binary pulsars. The change in orbital period due to nonzero \(\dot{G}\) is approximately \((\dot{P_{b}}/P_{b})_{\dot{G}}\simeq-2(\dot{G}/G).\) This expression neglects the effects of \(\dot{G}\) on the energy content of the stars themselves; a more precise expression is given in Nordtvedt (1990), but is not necessary for the purposes of the present paper. Because the same expression for \((\dot{P_{b}}/P_{b})_{\dot{G}}\) holds for _any_ binary pulsar system, the binary with the lowest value of this expression sets an upper limit on it for _all_ pulsars. The best limit comes from PSR J1713+0737, for which \(\dot{P_{b}}/P_{b}\leq 1\times 10^{-19}\,{\rm s}^{-1}\)(Splaver et al. 2005), more than an order of magnitude smaller than our value for PSR J0751+1807. A comparable limit on \((\dot{P_{b}}/P_{b})_{\dot{G}}\) can be set using limits on \(\dot{G}\) from lunar laser ranging measurements, which have found \(\dot{G}/G=(1.3\pm 2.9)\times 10^{-20}\,{\rm s}^{-1}\)(Williams et al. 2004). In any case, \(\dot{G}\) effects are unimportant for PSR J0751+1807. The third term arises if one of the component stars is losing mass (Esposito & Harrison 1975; Lavagetto et al. 2005). First, we consider mass loss from the pulsar. The pulsar's measured spin down rate implies that it is losing energy at a rate \(\dot{E}=4\pi^{2}\nu_{0}\nu_{1}I_{1},\) where \(I_{1}\) is the moment of inertia of the pulsar. Assuming the pulsar outflow is relativistic, this energy loss rate is equivalent to a mass loss rate of \(\dot{m_{1}}=\dot{E}/c^{2}=4\pi^{2}\nu_{0}\nu_{1}I_{1}/c^{2}=-4\times 10^{-21} \,{\rm M}_{\odot}\,{\rm s}^{-1}(I_{1}/10^{45}\,{\rm g\,cm})\). The resulting change in the orbital period is \((\dot{P_{b}}/P_{b})_{\!\dot{m}}=-2\dot{m_{1}}(m_{1}+m_{2})^{-1}\simeq-4\times 1 0^{-21}\,{\rm s}^{-1}\), depending on the precise values of \(m_{1}\), \(m_{2}\), and \(I_{1}\). This is three orders of magnitude smaller than the measured value an \begin{table} \begin{tabular}{l r r} \hline \hline Quantity & \multicolumn{1}{c}{\(\dot{P}\)} & \multicolumn{1}{c}{\(\dot{P_{b}}\)} \\ \hline \multicolumn{3}{l}{_Measurement …_} \\ & \(7.7860\times 10^{-21}\) & \(-6.2\times 10^{-14}\) \\ Uncertainty & \(\pm 0.0005\times 10^{-21}\) & \(\pm 0.8\times 10^{-14}\) \\ \multicolumn{3}{l}{_Acceleration biases …_} \\ Proper motion & \(0.35\phantom{0}\phantom{0}\times 10^{-21}\) & \(0.2\times 10^{-14}\) \\ \(z\)-acceleration & \(-0.19\phantom{0}\phantom{0}\times 10^{-21}\) & \(-0.1\times 10^{-14}\) \\ Galactic rotation & \(0.19\phantom{0}\phantom{0}\times 10^{-21}\) & \(0.1\times 10^{-14}\) \\ \multicolumn{3}{l}{_Intrinsic value …_} \\ Measurement\(-\)Bias & \(7.44\phantom{0}\phantom{0}\times 10^{-21}\) & \(-6.4\times 10^{-14}\) \\ Uncertainty & \(\pm 0.4\phantom{0}\phantom{0}\phantom{0}\times 10^{-21}\) & \(\pm 0.9\times 10^{-14}\) \\ \hline \end{tabular} \end{table} Table 3Biases of pulsar and orbital period derivatives

d, so mass loss can be neglected. Next, we consider mass loss from the white dwarf companion. I. Wasserman (private communication) has pointed out that mass flow from the white dwarf could arise from irradiation of the white dwarf by the pulsar. If such an outflow were directed predominantly opposite the motion of the white dwarf, it would induce a negative \(\dot{P_{b}}\). Given the geometry of the PSR J0751+1807 system, a white dwarf of low mass might capture sufficient the pulsar flux to produce such an outflow, although there is no reason to expect the flow to be collimated tangential to the orbit. The presence of an ionized outflow would give rise to variations in the dispersion measure of the pulsar over the course of its orbit and, depending on the orbital geometry, might even cause eclipses. However, PSR J0751+1807 exhibits neither eclipses nor orbital variability in its dispersion measure. To search for the latter, we analyzed multi-frequency observations made in January 2004 by dividing the orbit into ten equal length sections and separately measuring the dispersion measure in each section. We found no significant variation in dispersion measure over the course of the orbit, with a conservative upper bound of \(\Delta{\rm DM}<4\times 10^{-4}\,{\rm pc}\,{\rm cm}^{-3}=1\times 10^{15}\,{\rm cm }^{-2}\). This is strong, but not definitive, evidence against an outflow; it is possible to imagine scenarios with small orbital inclinations in which the pulsar irradiation directs the outflow away from our line of sight. Optical observations of the companion find it to be relatively cool, further evidence that a significant wind is unlikely (van Kerkwijk et al. 2005; M. van Kerkwijk, private communication). The expressions for \((\dot{P_{b}}/P_{b})_{Q}\) and \((\dot{P_{b}}/P_{b})_{D}\) in Equation 10 depend on gravitational theory. In general relativity, \((\dot{P_{b}}/P_{b})_{Q}\) is given by Equation 3, while \((\dot{P_{b}}/P_{b})_{D}=0\). In some SEP-violating theories, the quadrupole term equals the general relativistic expression, while the dipole contribution has the form \[\left(\frac{\dot{P_{b}}}{P_{b}}\right)_{\!D}=-\left(\!\frac{2\pi}{P_{b}}\! \right)^{\!2}T_{\odot}\left(\!\frac{G_{*}}{G}\!\right)\frac{m_{1}m_{2}}{m_{1}+ m_{2}}(\alpha_{c1}-\alpha_{c2})^{2}.\] (11) where \(\alpha_{c1}\) and \(\alpha_{c2}\) are the couplings of the pulsar and the secondary star, respectively, to the scalar field, and \(G_{*}\) is the "bare" gravitational constant. To measure or constrain the dipole term \((\dot{P_{b}}/P_{b})_{D}\) using Equation 10, it is necessary to know the quadrupole term \((\dot{P_{b}}/P_{b})_{Q}\), which in turn requires knowing \(m_{1}\) and \(m_{2}\) by means other than the measured \(\dot{P_{b}}\). For PSR J0751+1807, there are no independent high precision measurements of \(m_{1}\) and \(m_{2}\), so we must consider all combinations of \(m_{1}\) and \(m_{2}\) which fall within the Shapiro delay 95% confidence contour (Fig 3a) and have reasonable neutron star masses, \(1\,{\rm M}_{\odot}\!<\!m_{1}\!<\!3\,{\rm M}_{\odot}\)(Lattimer & Prakash 2004). For these masses, the predicted general relativistic values of \((\dot{P_{b}}/P_{b})_{Q}\) range from \(-1.1\times 10^{-18}\,{\rm s}^{-1}\) to \(-1.4\times 10^{-17}\,{\rm s}^{-1}\). The largest negative allowed value of \((\dot{P_{b}}/P_{b})_{D}=(\dot{P_{b}}/P_{b})_{\rm obs}-(\dot{P_{b}}/P_{b})_{Q}\), is \(-4.1\times 10^{-18}\,{\rm s}^{-1}\) (95% confidence). This arises at the smallest values of \(m_{1}\) and \(m_{2}\) that fall within the constraints, and corresponds to a difference in coupling strengths \[(\alpha_{c1}-\alpha_{c2})^{2}<7\times 10^{-5}.\] (12) This improves by a factor of a few on previously published upper limits from PSRs B0655+64 and J1012+5307 (Arzoumanian 2003; Lange et al. 2001). A result comparable to it can be derived from the measurements of the PSR J1141\(-\)6545 orbit presented in Bailes et al. (2003). In fact, in generalized tensor-scalar theories of gravity, the latter pulsar is likely to be the most constraining among known pulsar-white dwarf binaries. Its eccentric orbit gives rise to several relativistic phenomena, allowing its stellar masses to be measured independently of \(\dot{P_{b}}\)(Esposito-Farese 2004). In Brans-Dicke theory, the coupling to star \(i\) is \(\alpha_{ci}=2s_{i}(2+\omega_{\rm BD})^{-1}\), where \(s_{i}=-\partial\ln m_{i}/\partial\ln G\), the "sensitivity" of star \(i\), is the change in its binding energy as a function of \(G\), and where \(\omega_{\rm BD}\) is the Brans-Dicke coupling constant. Estimates of \(s_{1}\) range from 0.1 to 0.3, depending on the neutron star equation of state (Will & Zaglauer 1989). The sensitivity of the white dwarf is negligible. The limit on coupling strengths (Eqn. 12) places a lower limit \(w_{\rm BD}>1300(s_{1}/0.2)^{2}\) on the Brans-Dicke coupling constant. This limit is higher than previous constraints from pulsar work, but lower than the best limit attained by other means, \(\omega_{\rm BD}>40000\), from radio ranging to the Cassini probe (Bertotti et al. 2003). ## 5. Discussion The mass of PSR J0751+1807 is the largest measured for any pulsar. As shown in Figure 5, pulsars in circular orbits with helium white dwarf companions tend to have masses greater than the canonical value of 1.35 \({\rm M}_{\odot}\). This is in contrast to pulsars and secondary stars in neutron star-neutron binaries, which fall within the range 1.18\(-\)1.44 \({\rm M}_{\odot}\) (SS1). The relatively high masses of pulsars in neutron star-white dwarf systems presumably result from extended mass accretion during the late stages of their evolution. An inverse correlation between orbital period and pulsar mass is apparent in Figure 5. Any such relation is likely to be complicated by the different evolutionary paths followed by different systems. The four systems with the longest orbital periods, those of PSRs J1713+0747, B1855+09, J0437\(-\)4715, and J1909\(-\)3744, are classical wide millisecond pulsar-helium white dwarf binaries, which underwent extended stable Figure 5.— Measured pulsar masses in circular pulsar–helium white dwarf binary systems as a function of orbital period. Data are from this paper, Jacoby et al. (2005), Lange et al. (2001), van Straten et al. (2001), and Nice et al. (2005), and references therein.

mass transfer. In the library of evolutionary tracks calculated by Podsiadlowski et al. (2002), such systems show an inverse correlation between orbital period and pulsar mass, although there is a wide spread in pulsar mass for a given orbital period. In these calculations, it was assumed that half of the mass lost by the secondary was accreted onto the neutron star; whether the mass accreted onto the neutron star is, in fact, proportional to the mass lost by the secondary remains an open question. PSRs J0751+1807 and J1012+5307, with their short orbital periods, provide a challenge to binary evolution theories. Evolution calculations tend not to produce systems with binary periods close to the orbital period of PSR J0751+1807 at the end of mass transfer. Its orbital period falls above the periods of ultracompact systems but below the periods of standard pulsar-white dwarf binaries (e.g., Podsiadlowski et al. 2002). Ergma et al. (2001) are able to produce the properties of the PSR J0751+1807 system by invoking magnetic braking and heating of the secondary by irradiation from the pulsar. The latter effect drives mass loss in the secondary, increasing the orbital separation and preventing the binary from shrinking into an ultracompact system. This picture is supported by optical observations, which find that the secondary lacks a hydrogen envelope and that it has cooled rapidly (van Kerkwijk et al. 2005). ## 6. Summary The orbit of PSR J0751+1807 decays at a rate of \(\dot{P_{b}}=-(6.4\pm 0.9)\times 10^{-14}\). This is in line with the expected value from general relativity. Combined with Shapiro delay measurements, it implies the pulsar and secondary star masses are \(2.1\pm 0.2\) \({\rm M}_{\odot}\) and \(0.191\pm 0.15\) \({\rm M}_{\odot}\), respectively. The mass of PSR J0751+1807 is the largest recorded for a pulsar, and it may imply greater mass is transferred in tighter low mass neutron star binary systems than in wider systems. The maximum mass attainable by a neutron star depends on the stars composition and the equation of state of nuclear matter. Lattimer & Prakash (2001) calculated neutron star mass-radius relationships for a number of plausible equations of state. They found that models with exotic components, such as pure quark stars or mixed phases with kaon condensate or strange quark matter, allow neutron stars to attain masses no higher than \(\sim 2\) \({\rm M}_{\odot}\). While the measurement of the PSR J0751+1807 mass is nominally above this limit, the measurement uncertainty is not yet small enough to draw firm conclusions on this point. The uncertainty in the measurement of \(\dot{P_{b}}\) scales with observation span to the \(-\)2.5 power for uniformly sampled data. 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# Transit Photometry of the Core-Dominated Planet HD 149026b David Charbonneau, Joshua N. Winn1 , David W. Latham, Gaspar Bakos1 , Emilio E. Falco, Matthew J. Holman, Robert W. Noyes, and Balazs Csak2 Footnote 1: In addition to HD 209458b and TrES-1, the OGLE photometric survey (Udalski et al. 2002, 2004) and spectroscopic follow-up efforts have located 5 such objects. Recent estimates of the planetary radii have been given by Bouchy et al. (2004), Holman et al. (2005), Konacki et al. (2003), Moutou et al. (2004), Pont et al. (2004), and references therein. Footnote 1: In addition to HD 209458b and TrES-1, the OGLE photometric survey (Udalski et al. 2002, 2004) and spectroscopic follow-up efforts have located 5 such objects. Recent estimates of the planetary radii have been given by Bouchy et al. (2004), Holman et al. (2005), Konacki et al. (2003), Moutou et al. (2004), Pont et al. (2004), and references therein. Footnote 2: With more accurate photometry and better time sampling of the ingress or egress, it would be possible to solve for the stellar radius, rather than assuming a certain value (see, for example, Brown et al. 2001, Winn et al. 2005, Wittenmyer et al. 2005, and Holman et al. 2005). In this case, we found that the stellar radius is not well determined by the photometry. Rather, the constraint on the stellar radius based on stellar parallax and spectral modeling is tighter. Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138; dcharbonneau@cfa.harvard.edu Gilbert A. Esquerdo and Mark E. Everett Planetary Science Institute, 1700 East Fort Lowell, Tucson, AZ 85719 Francis T. O'Donovan California Institute of Technology, 1200 East California Blvd., Pasadena, CA 91125 ###### Abstract We report \(g\), \(V\), and \(r\) photometric time series of HD 149026 spanning predicted times of transit of the Saturn-mass planetary companion, which was recently discovered by Sato and collaborators. We present a joint analysis of our observations and the previously reported photometry and radial velocities of the central star. We refine the estimate of the transit ephemeris to \(T_{c}~{}[{\rm HJD}]=(2453527.87455^{+0.00085}_{-0.00091})+(2.87598^{+0.00012}_ {-0.00017})\ N\). Assuming that the star has a radius of \(1.45\pm 0.10~{}R_{\odot}\) and a mass of \(1.30\pm 0.10~{}M_{\odot}\), we estimate the planet radius to be \(0.726\pm 0.064\ R_{\rm Jup}\), which implies a mean density of \(1.07^{+0.42}_{-0.30}\ {\rm g\,cm^{-3}}\). This density is significantly greater than that predicted for models which include the effects of stellar insolation and for which the planet has only a small core of solid material. Thus we confirm that this planet likely contains a large core, and that the ratio of core mass to total planet mass is more akin to that of Uranus and Neptune than that of either Jupiter or Saturn. planetary systems -- stars: individual (HD 149026) -- techniques: photometry ## 1 Introduction Sato et al. (2005) recently presented the discovery of a planetary companion to the bright G0 iv star HD 149026. The star exhibits a time-variable Doppler shift that is consistent with a sinusoid of

amplitude \(K=43\) m s\({}^{-1}\) and period \(P=2.9\) days, which would be produced by the gravitational force from an orbiting planet with \(M_{\rm P}\sin i=0.36\)\(M_{\rm Jup}\). Furthermore, at the predicted time of planet-star conjunction, the star's flux declines by 0.3% in the manner expected of an eclipse by a planet of radius \(0.72\)\(R_{\rm Jup}\) (given an estimate of the stellar radius, 1.45 \(R_{\odot}\), that is based on the stellar parallax and effective temperature). Sato et al. (2005) observed three such eclipses. This discovery is extraordinary for at least two reasons. Firstly, the occurrence of eclipses admits this system into the elite club of bright stars with detectable planetary transits. Of all the previously-known transiting systems, only HD 209458 (Charbonneau et al. 2000; Henry et al. 2000) and TrES-1 (Alonso et al. 2004; Sozzetti et al. 2005) have parent stars brighter than \(V=12\), and therefore only they are amenable to a number of fascinating measurements requiring a very high signal-to-noise ratio. Among these studies are (i) the search for satellites and rings (Brown et al. 2001), (ii) the search for period variations due to additional companions (Wittenmyer et al. 2005), (iii) the detection of (or upper limits on) atmospheric absorption features in transmission (Charbonneau et al. 2002; Brown, Libbrecht, & Charbonneau 2002; Deming et al. 2005a), (iv) the characterization of the exosphere (Bundy & Marcy 2000; Moutou et al. 2001, 2003; Vidal-Madjar et al. 2003, 2004; Winn et al. 2004; Narita et al. 2005), (v) the measurement of the angle between the sky-projected orbit normal and stellar rotation axis (Queloz et al. 2000; Winn et al. 2005), and (vi) the search for spectroscopic features near the times of secondary eclipse (Richardson et al. 2003a, 2003b), and (vii) the direct detection of thermal emission from the planet (Charbonneau et al. 2005; Deming et al. 2005b). Charbonneau (2004) reviews these techniques and related investigations. Secondly, the planet is the smallest and least massive of the 8 known transiting extrasolar planets1. This makes HD 149026b an important test case for theories of planetary structure. Sato et al. (2005) argued that, once the effects of stellar insolation are included, the small planetary radius implies that the planet has a large and dense core. In particular, assuming a core density \(\rho_{c}=5.5\ {\rm g\,cm^{-3}}\), their models predict a prodigious core mass of 78 Earth masses, or 74% of the total mass of the planet. This, in turn, would seemingly prove that the planet formed through core accretion, as opposed to direct collapse through a gravitational instability. Footnote 1: In addition to HD 209458b and TrES-1, the OGLE photometric survey (Udalski et al. 2002, 2004) and spectroscopic follow-up efforts have located 5 such objects. Recent estimates of the planetary radii have been given by Bouchy et al. (2004), Holman et al. (2005), Konacki et al. (2003), Moutou et al. (2004), Pont et al. (2004), and references therein. A system of such importance should be independently confirmed, and the determination of its basic parameters should be refined through multiple observations. With this as motivation, we performed photometry of HD 149026 on two different nights when transits were predicted by Sato et al. (2005). These observations and the data reduction procedures are described in SS 2. The model that we used to determine the system parameters is described in SS 3, and the results are discussed in SS 4. Our data are available in digital form in the electronic version of this article, and

from the authors upon request. ## 2 The Observations and Data Reduction ### FLWO 1.2m \(g\) and \(r\) Photometry We observed HD 149026 (\(V=8.16\), \(B-V=0.56\)) on UT 2005 June 6 and UT 2005 July 2 with the 48-inch (1.2m) telescope of the F. L. Whipple Observatory (FLWO) located at Mount Hopkins, Arizona. We used Minicam, an optical CCD imager with two \(2048\times 4608\) chips. In order to increase the duty cycle of the observations, we employed \(2\times 2\) binning, which reduced the readout and overhead time to 20 s. Each binned pixel subtends approximately \(0\farcs 6\) on the sky, giving an effective field of view of about \(10\arcmin\times 23\arcmin\) for each CCD. Fortunately, there exists a nearby object of similar brightness and color (HD 149083; \(V=8.05\), \(B-V=0.40\), \(\Delta\alpha\)\(=5.1\arcmin\), \(\Delta\delta=-17\arcmin\)), which we employed as an extinction calibrator. We selected the telescope pointing so that both stars were imaged simultaneously. We defocused the telescope so that the full-width at half-maximum (FWHM) of a stellar image was typically 15 binned pixels (9\(\arcsec\)), and we used automatic guiding to ensure that the centroid of the stellar images drifted no more than 3 binned pixels over the course of the night. In addition to enabling longer integration times, this served to mitigate the effects of pixel-to-pixel sensitivity variations that were not perfectly corrected by our flat-fielding procedure. On UT 2005 June 6, we gathered 5.5 hrs of SDSS \(g\)-band observations with typical integration times of 8 s and a cadence of 28 s. The conditions were photometric, and the frames span an airmass from 1.01 to 1.74. On UT 2005 July 2, we gathered 4.4 hrs of SDSS \(r\)-band observations with integration times of 6 s and a median cadence of 26 s. The field appeared to remain free of clouds for the duration of the observations, which spanned an airmass range of 1.01 to 1.43, although occasional patches of high cirrus could be seen in images from the MMT all-sky camera. We converted the image time stamps to Heliocentric Julian Day (HJD) at mid-exposure. The images were overscan-subtracted, trimmed, and divided by a flat-field image. We performed aperture photometry of HD 149026 and the comparison star HD 149083, using an aperture radius of 15 binned pixels (9\(\arcsec\)) for the UT 2005 June 6 data, and an aperture radius of 20 binned pixels (12\(\arcsec\)) for the UT 2005 July 2 data. We subtracted the underlying contribution from the sky for both the target and calibrator by estimating the counts in an annulus exterior to the photometric aperture. The relative flux of HD 149026 was computed as the ratio of the fluxes within the two apertures. Normalization and residual extinction corrections are described in SS 3. ### TopHAT \(V\) Photometry at FLWO TopHAT is an automated telescope located on Mt. Hopkins, Arizona, which was designed to

perform multi-color photometric follow-up of transiting extrasolar planet candidates identified by the HAT network (Bakos et al. 2004). Since TopHAT has not previously been described in the literature, we digress briefly to outline the principal goals and features of the instrument. Wide-field transit surveys must contend with a large rate of astrophysical false positives, which result from stellar systems that contain an eclipsing binary and precisely mimic the single-color photometric light curve of a Jupiter-sized planet transiting a Sun-like star (Brown 2003; Charbonneau et al. 2004; Mandushev et al. 2005; Torres et al. 2004). Although multi-epoch radial velocity follow-up is an effective tool for identifying these false positives (e.g. Latham 2003), instruments such as TopHAT and Sherlock (Kotredes et al. 2004) can be fully-automated, and thus offer a very efficient means of culling the bulk of such false positives. TopHAT is a 0.26m diameter f/5 commercially-available Baker Ritchey-Chretien telescope on an equatorial fork mount developed by Fornax Inc. A 1\(\fdg\)25-square field of view is imaged onto a 2k\(\times\)2k Peltier-cooled, thinned CCD detector, yielding a pixel scale of 2\(\farcs\)2. The time for image readout and associated overheads is 25 s. Well-focused images have a typical FWHM of 2 pixels. A two-slot filter-exchanger permits imaging in either \(V\) or \(I\). The components are protected from inclement weather by an automated asymmetric clamshell dome. We observed HD 149026 on UT 2005 July 2, the same night as the FLWO 1.2m \(r\) observations described above. In order to extend the integration times and increase the duty cycle of the observations, we broadened the point spread function (PSF) by performing small, regular motions in RA and DEC according to a prescribed pattern that was repeated during each 13 s integration (see Bakos et al. 2004 for details). The resulting PSF had a FWHM of 3.5 pixels (7\(\farcs\)7). We gathered 4.8 hrs of \(V\) observations with a cadence of 68 s, spanning an airmass range of 1.01 to 1.45. We converted the time stamps in the image headers to HJD at mid-exposure. We calibrated the images by subtracting the overscan bias and a scaled dark image, and dividing by an average sky flat from which large outliers had been rejected. We evaluated the centroids of the target and the three brightest calibrators in each image. For each star, we summed the flux within an aperture with a radius of 8 pixels (17\(\farcs\)6), and subtracted a local sky estimate based on the median flux in an annulus exterior to the photometric aperture. We divided the resulting time series for the target by the statistically-weighted average of the time series for the three calibrator stars. The resulting relative flux time series was then corrected for normalization and residual extinction effects as described in the following section. ## 3 The Model We attempted to fit simultaneously (i) the 3 photometric time series discussed above, (ii) the \((b+y)/2\) photometry of 3 transits presented by Sato et al. (2005), and (iii) the 7 radial velocities that were measured by Sato et al. (2005) when the planet was not transiting. We did not attempt to fit the 4 radial velocities measured during transits, which would have required a model of the Rossiter-McLaughlin effect (Queloz et al. 2002; Ohta, Taruya, & Suto 2004; Winn et al. 2005).

We modeled the system as a circular Keplerian orbit. Following Sato et al. (2005), we assumed the stellar mass (\(M_{\rm S}\)) to be \(1.30~{}M_{\odot}\) and the stellar radius2 (\(R_{\rm S}\)) to be \(1.45~{}R_{\odot}\). The free parameters were the planetary mass (\(M_{\rm P}\)), planetary radius (\(R_{\rm P}\)), orbital inclination (\(i\)), orbital period (\(P\)), central transit time (\(T_{c}\)), and the heliocentric radial velocity of the center of mass (\(\gamma\)). We included 2 free parameters for each of our 3 photometric time series: an overall flux scaling \(C\); and a residual extinction coefficient (\(k\)) to correct for differential extinction between the target star and the comparison object, which have somewhat different colors. These are defined such that the relative flux observed through an airmass \(X\) is \(C\exp(-kX)\) times the true relative flux. The residual extinction corrections were small but important at the millimagnitude level; for example, in the \(g\) band, we found \(k\approx-2\times 10^{-3}\). The 3 time series presented by Sato et al. (2005) were already corrected for airmass, so we allowed each of these to have only an independent flux scaling. Finally, we allowed the data from each spectrograph (Keck/HIRES and Subaru/HDS) to have an independent value of \(\gamma\). Footnote 2: With more accurate photometry and better time sampling of the ingress or egress, it would be possible to solve for the stellar radius, rather than assuming a certain value (see, for example, Brown et al. 2001, Winn et al. 2005, Wittenmyer et al. 2005, and Holman et al. 2005). In this case, we found that the stellar radius is not well determined by the photometry. Rather, the constraint on the stellar radius based on stellar parallax and spectral modeling is tighter. We computed the model radial velocity at each observed time as \(\gamma+\Delta v_{r}\), where \(\Delta v_{r}\) is the line-of-sight projection of the orbital velocity of the star. We calculated the model flux during transit using the linear limb-darkening law \(B_{\lambda}(\mu)=1-u_{\lambda}(1-\mu)\), where \(B_{\lambda}\) is the normalized stellar surface brightness profile and \(\mu\) is the cosine of the angle between the normal to the stellar surface and the line of sight. We employed the "small planet" approximation as described by Mandel & Agol (2002). We held the limb darkening parameter \(u_{\lambda}\) fixed at a value appropriate for a star with the assumed properties, and for the bandpass concerned, according to the models of Claret & Hauschildt (2003) and Claret (2004). These values were \(u_{g}=0.73\), \(u_{r}=0.61\), \(u_{V}=0.62\), and \(u_{b+y}=0.67\). The goodness-of-fit parameter is \[\chi^{2}=\chi^{2}_{v}+\chi^{2}_{f}=\sum_{n=1}^{N_{v}}\left(\frac{v_{O}-v_{C}}{ \sigma_{v}}\right)^{2}+\sum_{n=1}^{N_{f}}\left(\frac{f_{O}-f_{C}}{\sigma_{f}} \right)^{2},\] (1) where \(v_{O}\) and \(v_{C}\) are the observed and calculated radial velocities, of which there are \(N_{v}=7\), and \(f_{O}\) and \(f_{C}\) are the observed and calculated fluxes, of which there are \(N_{f}=2310\). Of the flux measurements, 679 are our \(g\)-band measurements, 574 are our \(r\)-band measurements, 237 are our \(V\)-band measurements, and 820 are the \((b+y)\)/2 measurements of Sato et al. (2005). We minimized \(\chi^{2}\) using an AMOEBA algorithm (Press et al. 1992). The radial velocity uncertainties \(\sigma_{v}\) were taken from Table 2 of Sato et al. (2005). To estimate the uncertainties in our photometry, we performed the following procedure. We expect the two

dominant sources of uncertainty to be scintillation noise (\(\sigma_{S}\)) and Poisson noise (\(\sigma_{P}\)). Young (1967) advocated an approximate scaling law for the fractional error due to scintillation noise (see also Dravins et al. 1998): \[\sigma_{S}=0.06\ X^{7/4}\left(\frac{D}{{\rm 1~{}cm}}\right)^{-2/3}\left(\frac{ t_{\rm exp}}{{\rm 1~{}s}}\right)^{-1/2}\exp\left(-\frac{h}{{\rm 8000~{}m}} \right),\] (2) where \(X\) is the airmass, \(D\) is the diameter of the aperture, \(t_{\rm exp}\) is the exposure time, and \(h\) is the altitude of the observatory. For each of our 3 time series, we assumed that the noise in each point obeyed \[\sigma=\sqrt{\sigma_{P}^{2}+(\beta\sigma_{S})^{2}},\] (3) where \(\sigma_{S}\) was calculated with Eq. 2. We determined the constant \(\beta\) by requiring \(\chi^{2}/N_{\rm DOF}=1\) for that particular time series. Thus we did _not_ attempt to use the \(\chi^{2}\) statistic to test the validity of the model; rather, we assumed the model is correct, and sought the appropriate weight for each data point. The results for \(\beta\) ranged from 1.2 to 1.5. To estimate the uncertainties in each of the three Sato et al. (2005) time series (which were already corrected for airmass), we simply assigned an airmass-independent error bar to all the points such that \(\chi^{2}/N_{\rm DOF}=1\). The results agreed well with the RMS values quoted in Table 5 of Sato et al. (2005). After assigning the weight of each data point in this manner, we analyzed all the data simultaneously and found the best-fitting solution. This solution is overplotted on the data in Figure 1. Our photometry, after correcting for the overall flux scale and for airmass, is given in Table 1. We estimated the uncertainties in the model parameters using a Monte Carlo algorithm, in which the optimization was performed on each of \(7\times 10^{4}\) synthetic data sets, and the distribution of best-fitting values was taken to be the joint probability distribution of the parameters. Each synthetic data set was created as follows: 1. 1.We randomly drew \(N_{f}=2310\) flux measurements \(\{t_{n},f_{n}\}\) from the real data set. We drew these points with replacement, i.e., we allowed for repetitions of the original data points. This procedure, recommended by Press et al. (1992), estimates the probability distribution of the measurements using the measured data values themselves, rather than the more traditional approach of assuming a certain model for the underlying process. 2. 2.This procedure was impractical for the radial velocity measurements, because the number of data points is too small. Instead, in each realization, we discarded a single radial velocity measurement chosen at random. This was intended as a test of the robustness of the results to single outliers. To each of the remaining \(N_{v}=6\) radial velocities, we added a random number drawn from a Gaussian distribution, with zero mean and a standard deviation equal to the quoted 1 \(\sigma\) uncertainty. 3. 3.To account for the uncertainty in the stellar properties, we assigned a stellar mass by picking a random number from a Gaussian distribution with mean \(1.30~{}M_{\odot}\) and standard deviation

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# The dependence on environment of Cold Dark Matter Halo properties Vladimir Avila-Reese1 , Pedro Colin2 , Stefan Gottlober3 Footnote 1: Instituto de Astronomía, U.N.A.M., A.P. 70-264, 04510, México, D.F., México Footnote 2: Centro de Radioastronomía y Astrofísica, U.N.A.M., A.P. 72-3 (Xangari), Morelia, Michoacán 58089, México Footnote 3: Astrophysical Institute Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany Claudio Firmani4,1, and Christian Maulbetsch\({}^{3}\) Footnote 4: Osservatorio Astronomico di Brera, via E.Bianchi 46, I-23807 Merate, Italy (Received 2005 March 15) ###### Abstract A series of high-resolution \(\Lambda\)CDM cosmological N-body simulations are used to study the properties of _galaxy-size_ dark halos as a function of global environment. We analyse halos in three types of environment: "cluster" (cluster halos and their surroundings), "void" (large regions with density contrasts \(\lesssim-0.85\)), and "field" (halos not contained within larger halos). We find that halos in clusters have a median spin parameter \(\sim 1.3\) times lower, a minor-to-major axial ratio \(\sim 1.2\) times lower (more spherical), and a less aligned internal angular momentum than halos in voids and the field. For masses \(\lesssim 5\times 10^{11}\mbox{$h^{-1}$M${}_{\odot}$}\), halos in cluster regions are on average \(\sim 30-40\%\) more concentrated and have \(\sim 2\) times higher central densities than halos in voids. While for halos in cluster regions the concentration parameters decrease on average with mass with a slope of \(\sim 0.1\), for halos in voids these concentrations do not seem to change with mass. When comparing only parent halos from the samples, the differences are less pronounced but they are still significant. We obtain also the maximum circular velocity- and rms velocity-mass relations. These relations are shallower and more scattered for halos in clusters than in voids, and for a given circular velocity or rms velocity, the mass is smaller at \(z=1\) than at \(z=0\) for all environments. At \(z=1\), the differences in the halo properties with environment almost dissapear, suggesting this that the differences were stablished mainly after \(z\sim 1\). The halos in the cluster regions undergo more dramatic changes than those in the field or the voids. The differences in halo properties with environment are owing to (i) the dependence of halo formation time on global environment, and (ii) local effects as tidal stripping and the tumultuos histories that halos suffer in high-density regions. We calculate seminumerical models of disk galaxy evolution using halos with the concentrations and spin parameters found for the different environments. For a given disk mass, the galaxy disks have higher surface density, larger maximum circular velocity and secular bulge-to-disk ratio, lower gas fraction, and are redder as one goes from cluster to void environments. Although all these trends agree with observations, the latter tend to show more differences, suggesting this that physical ingredients not considered here as missalignment of angular momentum, halo triaxility, merging, ram pressure stripping, harassment, etc. play an important role for galaxy evolution, specially in high-density environments. cosmology:dark matter -- galaxies:formation -- galaxies:halos -- methods:\(N-\)body simulations

et al., 2002; Kauffmann et al., 2004; Hogg et al., 2004; Tanaka et al., 2004), the steepest correlation being for intermediate mass galaxies (Kauffmann et al., 2004) or faint galaxies (Tanaka et al., 2004). The dependences of both properties on environment extend typically to lower local densities than the dependence for morphology. These properties are tightly related to the galaxy SF history, which in turn depends on internal formation/evolution processes related directly to initial cosmological conditions (e.g., Kauffmann et al., 1993; Baugh et al., 1996; Somerville & Primack, 1999; Avila-Reese & Firmani, 2000) as well as to external astrophysical mechanisms able to inhibit or induce SF activity. It is difficult to disantangle the role of these internal or external factors, in particular in the densest environments. An analysis of the influence of environment on the CDM halo properties and their evolution certainly would help to understand the role of initial conditions. There are also some pieces of evidence that the scale lenghts of spirals in clusters are systematically smaller than those of spirals in the field (Aguerri et al., 2004). Besides, it was shown that the fraction of low surface brightness (LSB), blue galaxies increases toward low-density environments (e.g., Bothun et al., 1993; Rojas et al., 2004), mainly in the outskirts of filamentes and in voids (Rosenbaum & Bomans, 2004). The LSB galaxies may have formed in halos with high and well-aligned angular momentum (e.g., Dalcanton et al., 1997; Firmani & Avila-Reese, 2000; Avila-Reese & Firmani, 2000; Boissier et al., 2003) and/or have had a low SF rate history in comparison with high surface brightness galaxies due to their low-density environment. To explore which one of these processes dominate it would be helpful to know if there are any differences in the halo angular momentum distribution and its alignment between voids and other environments. ### Theoretical results and expectations From the analysis of a \(60\mbox{$h^{-1}$Mpc}\) box simulation with a particle mass of \(1.57\times 10^{9}\mbox{M${}_{\odot}$}\), Avila-Reese et al. (1999) found that the outer density profiles of galaxy-size halos in cluster cores decline sharper and their concentrations are higher than for "field" halos (see also Ghigna et al., 1998; Okamoto & Habe, 1999; Klypin et al., 1999; Bullock et al., 2001a). The last authors explored also the differences in concentration between distinct or parent halos (halos not contained within larger ones) and subhalos (halos contained inside larger halos), with the result that the latter have typically larger concentrations than the former. As suggested by the referee, one should differentiate the effect of the "local" environment, which is simply due to a halo being subhalo, from the global (large-scale) environment. Some dependence of the halo mass-circular velocity relation on global environment was also reported by Avila-Reese et al. (1999). Lemson & Kauffmann (1999) explored how halo mass function, formation redshift, concentration, shape and spin parameter \(\lambda\) change with the density contrast of the local halo environment. The particle mass in their simulations was \(2\times 10^{10}\mbox{M${}_{\odot}$}\) or more. They found that only the mass function varies with environment, suggesting that any dependence of observable galaxy properties on environment can be established because only the halo mass influences on these properties. Antonuccio-Delogu et al. (2002) used constrained initial conditions in order to produce in the same box two extreme environments, a void and two clusters (the particle mass of their simulation was \(4.2\times 10^{9}\mbox{M${}_{\odot}$}\)). They found some differences in the distribution of the spin parameter and the mass-velocity dispersion relation between cluster and void environments. A general conclusion of all previous numerical works is that present-day CDM halo properties and correlations do not strongly change with global environment. However, as mentioned above, some influence of environment on halo properties and correlations has been reported. Halos in dense environments, as clusters, are expected to collapse earlier than halos in less dense environments. Besides, halos in the high density environments suffer tidal stripping and frequent violent mergers. It is still an open issue the extent of the influence of environment on halo properties as well as its potential effects on the baryonic galaxies which form within these halos. In this paper we will analyze high-resolution simulations of extreme environments, namely selected cluster and void regions, and compare the properties and correlations of the galaxy-size CDM halos from these simulations, both at redshift \(z=0\) and \(z=1\). Our aim is to explore

to what extent the CDM halo properties that affect observable galaxy properties change with the global environments. We will analyze also distinct galaxy-size halos ("field" halos) and compare them with those in the cluster and void simulations. Seminumerical and semianalytical models have shown that most of the properties and correlations of galaxies formed within CDM halos depend on (i) the halo mass aggregation history (MAH) and its dominating regime (accretion or merging) as well as on the halo concentration that is determined mainly by the MAH (in particular the typical formation time) for a given mass, (ii) the halo spin parameter and angular momentum distribution, and (iii) the halo mass function (e.g., Kauffmann et al., 1993; Baugh et al., 1996; Mo et al., 1998; Avila-Reese & Firmani, 2000; Firmani & Avila-Reese, 2000; van den Bosch, 2000). The dependence on environment of the halo mass function has been extensively analyzed in numerical works (Lemson & Kauffmann, 1999; Gottlober et al., 2003; Mo et al., 2004). Our comparative study here will be focused on some halo structural and angular momentum parameters: concentration, central density, shape, spin parameter, and the angular momentum internal alignment. Elsewhere we will present results related to halo evolution (MAH) depending on environment (see also Gardner, 2001; Gottlober, Klypin & Kravtsov, 2001). In SS2 we describe the method and simulations carried out and present the halo samples to be analyzed. In SSSS3.1 several concentration parameters as well as the central density of halos from the different environments (samples) are presented and disscused for \(z=0\) and \(z=1\). The ellipticity distribution function of halos for the different samples is computed in SSSS3.2. Section 4 is devoted to the analysis of the spin parameter and internal angular momentum alignment of halos as a function of environment. In SS5 we present and discuss the maximum circular velocity- and velocity dispersion-mass relations of halos in the different environments. In SS6 we discuss the implications that the differences in the halo properties as a function of environment can have on the properties of the disks formed inside these halos. A summary of the results and our main conclusions are given in SS7. ## 2 Method and simulations In our numerical simulations we adopt the flat cosmological model with a non-vanishing cosmological constant (\(\Lambda\)CDM) using the following cosmological parameters: \(\Omega_{0}=0.3\), \(\Omega_{\Lambda}=0.7\), and \(h=0.7\). The matter power spectrum is normalized to \(\sigma_{8}=0.9\), where \(\sigma_{8}\) is the present linear rms amplitude of mass fluctuations in spheres of radius 8\(h^{-1}\)Mpc. The simulations were run with the Adaptive Refinement Tree (ART) code (Kravtsov et al., 1997). The ART code achieves high spatial resolution by refining the base uniform grid in all high-density regions with an automated refinement algorithm. Initial conditions have been calculated either with the transfer function given by Klypin & Holtzman (1997) (boxes of 60 and 80 \(h^{-1}\)Mpc) or using the numerical results of the Boltzmann code kindly provided by W. Hu. Up to a few percent both transfer functions coincide and at the same level they coincide also with the transfer function provided by CMBfast. For the multiple mass simulations we have used the mass refinement technique described by Klypin et al. (2001). The halos are identified by the Bound Density Maxima (BDM) algorithm (Klypin & Holtzman, 1997; Klypin et al., 1999). The BDM algorithm first finds positions of local maxima in the density field. Once centers of potential halos are found, the algorithm identifies halos around them and removes particles which are not bound to those halos. This procedure also detects subhalos of larger objects - halos inside halos (for example, satellites of galaxies or galaxies in clusters). Particles of a subhalo are bound to both the subhalo and to the larger halo. Our study is focused on the analysis of the properties of galaxy-size CDM halos formed in two extreme environments: the high density environment of clusters and the low density environment of voids. To this end we have at first performed simulations with low mass resolution. However, already for this simulation the initial displacements and velocities of the particles were calculated using all waves ranging from the fundamental mode \(k=2\pi/L\) to the Nyquist frequency \(k_{\rm Ny}=2\pi/L\times N_{1}/2\), where \(N_{1}=1024\) corresponds to the maximum possible mass resolution (cf. Table 1). To get the initial conditions of the low reso

lution run we merge \(8^{3}\) particles to a more massive one. After running an inexpensive simulation with the resulting \(128^{3}\) particles we can select regions of interest. Then we use the original sample of small-mass particles to resimulate the regions of interest using the multi-mass technique described in Klypin et al. (2001). As high density regions we have selected spheres centered on 14 clusters. The radius of these spheres was typically about three virial radii of the cluster. Thus a significant fraction of resimulated halos are not within the virial radius of one of the clusters, but these halos are in the high-density environment around clusters. Voids have been selected as described in Gottlober et al. (2003). The radius of resimulation area centered on voids has been taken typically about 10% smaller than the estimated void radius to be sure that no massive objects around the low density region will enter the region with high mass and force resolution, otherwise all the integration time would be allocated to such a massive object. We have performed high resolution simulations of selected regions in a 80 \(h^{-1}\)Mpc box and in a 50 \(h^{-1}\)Mpc box (simulations 80 and 50, respectively). For comparison purposes, we have also analyzed a sample of galaxy-size "field" halos from two 60\(h^{-1}\)Mpc box simulations with the same cosmological parameters as simulation 80 (simulations 60A and 60B). The parameters of the simulations are summarized in Table 1. The brackets around the particle numbers denote that all low mass particles were merged outside the regions of interest. The "field" halos in the 60\(h^{-1}\)Mpc box are those called distinct or parent, i.e. halos which are not contained inside larger halos (Avila-Reese et al., 1999; Bullock et al., 2001a). Most of the parent halos are truly isolated (\(\sim 80\%\)); the rest are mostly 'binary' halos, i.e. with companions of masses larger than 1/3 the mass and within distances up to 3 times the radius of the given halo. ### The halo samples according to the environment From the simulations described above, we have five independent subsamples of halos (see Table 2): two cluster subsamples selected from simulation 80, one made up of halos from the very high-resolution run Cl\({}_{6}^{\rm hr}\), and the other built from the sum of the halos belonging to the 14 clusters, Cl\({}_{\rm all}\); both subsamples constitute the CLUSTER sample, where \(\sim 55\%\) of the galaxy-size halos are parent (those outside the clusters), and \(\sim 45\%\) are subhalos (mostly those within the cluster virial radii); two void subsamples, one consisting of halos from the simulation \(V_{50}^{\rm hr}\), and the other built of halos from the 5 voids resimulated from the 80 simulation, \(V_{\rm all}\); boths subsamples constitute the VOID sample, where more than \(90\%\) of the galaxy-size halos are parent ones; one FIELD halo sample composed of two subsamples of galaxy-size parent halos from both the 60A and 60B simulations. \begin{table} \begin{tabular}{c c c c c c} \hline \hline simulation & Box & N\({}_{\rm part}\) & Mass resolution & Force resolution & \(z_{\rm start}\) \\ & (\(h^{-1}\)Mpc) & & (\(h^{-1}\)M\({}_{\odot}\)) & (\(h^{-1}\)kpc) & \\ \hline Full box & & & & & \\ 80 & 80 & \(128^{3}\) & \(2.0\times 10^{10}\) & 9.8 & 50 \\ 60A & 60 & \(256^{3}\) & \(1.1\times 10^{9}\) & 2.0 & 35 \\ 60B & 60 & \(256^{3}\) & \(1.1\times 10^{9}\) & 2.0 & 35 \\ 50 & 50 & \(128^{3}\) & \(5.0\times 10^{9}\) & 6.2 & 60 \\ Multiple mass & & & & & \\ Cl\({}_{\rm all}\) & 80 & \((512^{3})\) & \(3.2\times 10^{8}\) & 2.4 & 50 \\ Cl\({}_{6}^{\rm hr}\) & 80 & \((1024^{3})\) & \(4.0\times 10^{7}\) & 0.6 & 50 \\ \(V_{\rm all}\) & 80 & \((1024^{3})\) & \(4.0\times 10^{7}\) & 1.2 & 50 \\ \(V_{50}^{\rm hr}\) & 50 & \((1024^{3})\) & \(2.5\times 10^{7}\) & 0.8 & 60 \\ \hline \end{tabular} \end{table} Table 1: Parameters of simulations

Column (2) of Table 2 gives the number of regions (clusters or voids) in each (sub)sample resimulated with high resolution; this does not apply for the FIELD sample, where all the parent galaxy-size halos in the boxes are taken into account. The number of halos with more than 500 particles in each one of the samples is given in column (3). We set an upper limit mass of \(3\ 10^{13}\mbox{$h^{-1}$M${}_{\odot}$}\) for that we define as a galaxy-size halo. In column (4) we give an estimate of the density contrast [\((\bar{\rho}_{\rm region}-\rho_{u})/\rho_{u}\)] of our different environments. For the samples where several regions were used (Cl\({}_{\rm all}\) and \(V_{\rm all}\)), the mean of the density contrasts and the standard deviation are reported; for the "field" halos, the density contrast is around zero. The mean halo mass (\(N_{p}>500\) particles) and the median spin parameter of each sample are given in columns (5) and (6), respectively. Finally, we note that in multimass simulations we discard the halos contaminated by massive particles if their fraction is larger than 5% of the total halo mass. Also fake halos (recognized by a too low central density or flat or decreasing density profiles toward the center) have been removed; the criteria to remove these halos are a density in the central bin below \(\sim 5\ 10^{15}\)h\({}^{2}\)M\({}_{\odot}\)Mpc\({}^{-3}\) and/or similar or increasing with radius densities in the the first 5 radial bins. To study the spin parameter distribution we demand a halo to have a minimum of 500 particles. For concentration and central density determinations we demand more than 2500 particles. ## 3 Structural properties The virialized CDM halos present a diversity of spherically averaged density profiles (Avila-Reese et al., 1998, 1999; Jing, 1999; Tasitsiomi et al., 2004) that cluster around the Navarro, Frenk & White (1997; hereafter NFW) fit. High-resolution simulations show that in the center the density profile is typically steeper than the NFW profile (Moore et al., 1999; Klypin et al., 2001; Power et al., 2003; Navarro et al., 2004). Unfortunately, there is not still a clear theoretical understanging of the origin of the CDM halo density profiles (see for some interesting results Manrique et al., 2003, and more references therein). Several works have shown that the shape of the profiles or their concentration parameter if they are fitted by a NFW profile -which is not always a good fit, depend on the halo MAH (Avila-Reese et al., 1998; Firmani & Avila-Reese, 2000; Wechsler et al., 2002) or even on the cosmological initial conditions (Avila-Reese et al., 2003). It was shown in Avila-Reese et al. (1999) that the outer density profile of CDM halos change with environment. Following, we will explore whether or not the halo concentrations, central density, and internal shape alignment change with environment. ### Concentrations and inner density We construct spherically averaged density profiles for all the halos studied here. We can roughly characterize the profiles by a concentration parameter only, because the profiles have approximately similar shapes. The use of one parameter allows us to attain an easy statistical comparison between VOID, CLUSTER and FIELD samples. In the CDM hierarchical scenario one expects that the concentration of halos will be typically higher for less massive halos, because they assemble most of their mass earlier than larger mass halos (e.g., NFW). For the NFW profile, the concentration is defined as \(\mbox{c${}_{\rm NFW}$}\equiv\mbox{$R_{\rm vir}$}/r_{s}\), where \(R_{\rm vir}\) is the virial radius and \(r_{s}\) the radius where \(d\)ln\(\rho/d\)ln\(r=-2\) (NFW). The virial radius \(R_{\rm vir}\) is defined as the radius where the average halo density is \(\Delta\) times the background density according to the spherical top-hat model. The parameter \(\Delta\) depends on epoch and cosmological parameters (\(\Omega_{0}\),\(\Omega_{\Lambda}\)); for a flat \(\Lambda\)CDM model, \(\Delta\sim 337\) and 203 at \(z=0\) and \(z=1\), respectively. As mentioned above, not all halos can be well fitted by a NFW profile. One may introduce a concentration parameter that does not depend on a particular fitting profile, for example the c\({}_{\rm 1/5}\) concentration defined as \(\mbox{c${}_{\rm 1/5}$}\equiv\mbox{$R_{\rm vir}$}/r_{1/5}\), where \(r_{1/5}\) is the radius where 1/5 of the virial mass is contained. For both the c\({}_{\rm NFW}\) and c\({}_{\rm 1/5}\) concentrations one needs to measure \(R_{\rm vir}\). On one hand, this is not possible for a large fraction of subhalos because they are typically truncated at a radius \(\mbox{$R_{\rm tr}$}<\mbox{$R_{\rm vir}$}\). On the other hand, both c\({}_{\rm NFW}\) and c\({}_{\rm 1/5}\) trace the global halo concentration, while galaxies form only in the inner parts of the halos. Thus, it is desirable to introduce a concentration parameter whose definition is independent of the virial ra

dius, and which measures concentration in the inner/intermediate halo regions. We introduce here the concentration parameter c\({}_{\delta}\). To calculate c\({}_{\delta}\), we find the radii within which the halo average density is equal to \(4\times 10^{4}\) and \(4\times 10^{3}\) times the background density, respectively, and compute the enclosed mass within these radii. The ratio of these masses is c\({}_{\delta}\). For NFW profiles in the range of galaxy-size halos, the typical radii where the halo overdensities become \(4\times 10^{4}\) and \(4\times 10^{3}\) are in the range of \(\sim 0.10-0.45\)\(R_{\rm vir}\), respectively, tracing therefore the inner to intermediate regions. For example, for c\({}_{\rm NFW}\)=12, these radii are 0.11 and 0.35\(R_{\rm vir}\), respectively, and the ratio of the masses enclosed within these radii is c\({}_{\delta}\)=0.33. We define formally the truncation radius \(R_{\rm tr}\) as the radius where the outer density profile begins to systematically flatten out or increase (d\(\rho(r)\)/d\(t>0\)). The radius of the halo, \(R_{h}\) is defined as the minimum beetwen \(R_{\rm vir}\) and \(R_{\rm tr}\). The mass enclosed within \(R_{h}\) is the halo mass \(M_{h}\). According to our resolution tests, halos with more than \(\sim 2500\) particles are needed in order to estimate reliable concentration parameters. This leaves us with halos more massive than \(\sim 10^{11}\)\(h^{-1}\)M\({}_{\odot}\) and \(\sim 8\times 10^{11}\)\(h^{-1}\)M\({}_{\odot}\) in the void \(V_{\rm all}\) and cluster Cl\({}_{\rm all}\) samples, respectively. Since the voids are defined in such a way that they contain only halos less massive than \(\sim 4\times 10^{11}\)\(h^{-1}\)M\({}_{\odot}\)(Gottlober et al., 2003), the ranges of masses in both samples do not overlap and our comparisons should be based on extrapolations of the mass-concentration dependences. However, we have one cluster resimulated with the same resolution as the voids, Cl\({}_{6}^{\rm hr}\). Therefore, in this simulation the halos resolved with more than 2500 particles have masses larger than \(\sim 10^{11}\)\(h^{-1}\)M\({}_{\odot}\). There is also a void simulation, \(V_{50}^{\rm hr}\), for which halos resolved with more than 2500 particles have masses larger than \(\sim 5\ 10^{10}\)\(h^{-1}\)M\({}_{\odot}\), allowing us to expand the range of masses of void halos. #### 3.1.1 Results at z=0 Upper panel of Fig. 1 shows c\({}_{\rm NFW}\) vs \(M_{\rm vir}\) for the VOID (circles), Cl\({}_{\rm all}\) (crosses), Cl\({}_{6}^{\rm hr}\)(squeletal triangles) and FIELD (dots) _non-truncated_ halos with an acceptable NFW profile fit. Non-truncated halos are those that attain the virial radius without any systematical flattening or increasing of the outer density profile. They are mostly parent halos. The quality of the NFW fit is evaluated roughly through the variance of the fit divided by the weighted average of the individual variances of the data (each radial bin is assigned a weight according to the number of particles inside it). Since the fit is in logarithmic variables, the root square of this quantitiy can be interpreted as a measure of the logarithmic difference between the model fit and the data. The latter can be expressed as a percentage deviation; from visual inspections, we have found that an acceptable NFW fit to the density profile is when this deviation is less than \(\sim 15\%\). More than 80% of the non-truncated halos obey this condition. The parent halos in the CLUSTER sample are highlighted with an open square. As expected, most of the non-truncated halos are parent ones. In the VOID sample, more than 95% of the halos with more than 2500 particles are parent ones, then, we do not highlight these halos in the figures in order to avoid overplotting. The FIELD sample has been constructed only with parent halos. \begin{table} \begin{tabular}{c c c c c c} \hline \hline sample & \(N_{\rm regions}\) & \(n_{h}(>500)\) & contrast & \(<M_{h}>\) & \(\lambda^{\prime}_{med}\) \\ & & & & (\(h^{-1}\)M\({}_{\odot}\)) & \\ \hline Cl\({}_{\rm all}\) & 14 & 421 & \(37.8\pm 18.2\) & \(5.3\times 10^{11}\) & 0.024 \\ Cl\({}_{6}^{\rm hr}\) & 1 & 318 & 44.7 & \(1.0\times 10^{11}\) & 0.024 \\ \(V_{\rm all}\) & 5 & 333 & \(-0.85\pm 0.05\) & \(4.9\times 10^{10}\) & 0.030 \\ \(V_{50}^{\rm hr}\) & 1 & 249 & -0.85 & \(2.2\times 10^{10}\) & 0.033 \\ FIELD & .. & 2990 & \(\sim 0\) & \(2.2\times 10^{12}\) & 0.033 \\ \hline \end{tabular} \end{table} Table 2: Samples of halos

-Reese et al., 1999; Bullock et al., 2001a), at least in the range of masses explored here. In Figs. 1 and 2 we show a toy-model prediction for c\({}_{\rm NFW}\) and \(\rho_{-2}\) (long-dashed lines) following Eke, Navarro, & Steinmetz (2001) for the same cosmological parameters than in our simulations and \(\sigma_{8}=0.9\). The toy model for c\({}_{\rm NFW}\) was normalized to a set of isolated halos in a wide range of masses (re)simulated with very high resolution (Eke, Navarro, & Steinmetz, 2001). The toy model roughly agrees with our FIELD halo results. Interestingly, studies aiming at infering the halo c\({}_{\rm NFW}\) concentration from galaxy observables show that the slope of the \(\mbox{c${}_{\rm NFW}$}-\mbox{$M_{\rm vir}$}\) relation is significantly steeper for halos of elliptical galaxies (e.g., Sato et al., 2000), which are localized typically deep inside the clusters, than for halos of spiral galaxies (Jimenez, Verde & Oh, 2003), which are localized in less dense environments. Our main interest here is to compare the properties of halos in low and high-density environments. From Figs. 1 and 2, one concludes that the concentrations and \(\rho_{-2}\) of the VOID sample are lower on average than those of the CLUSTER sample, although the scatter in both samples is large. In fact this conclusion is based mostly on extrapolations of trends because the VOID and CLUSTER samples almost do not overlap in mass. At \(\sim 10^{11}\)\(h^{-1}\)M\({}_{\odot}\), the concentrations c\({}_{\rm NFW}\), c\({}_{\rm 1/5}\) and c\({}_{\delta}\) are on average 40% smaller for halos in the VOID sample than for halos in the CLUSTER sample, and the inner density \(\rho_{-2}\) is on average two times lower for the former than for the latter. For larger masses, all these differences reduce. There are also differences in the scatters: they are larger for the CLUSTER sample than for the VOID and FIELD ones (see Table 3). The halos from the FIELD sample also tend to have on average lower concentrations and central density than those halos from the CLUSTER sample, although the differences are smaller than those between VOID and CLUSTER halos, in particular for \(\rho_{-2}\). If we assume that the prediction for c\({}_{\rm NFW}\) given by the Eke, Navarro, & Steinmetz (2001) toy-model is a good fit to our FIELD sample data, then its extrapolation to lower masses shows that the difference in c\({}_{\rm NFW}\) between FIELD and CLUSTER halos remains roughly the same (Fig. 1). For \(\rho_{-2}\), the difference seems to increase at lower masses (Fig. 2). We have also compared only the parent halos from the CLUSTER sample with those from the VOID and FIELD samples. The differences in concentrations and \(\rho_{-2}\) become less pronounced than in the case when the subhalos were included. The slopes of the c\({}_{\rm NFW}\), c\({}_{\rm 1/5}\), c\({}_{\delta}\) and \(\rho_{-2}\) vs mass relations for the CLUSTER parent halos reduce to -0.07, -0.06, -0.07 and -0.16, respectively (to be compared with those given in Table 3), becoming closer to those of the FIELD sample, but still steeper. As expected, c\({}_{\delta}\) changes more than c\({}_{\rm NFW}\) and c\({}_{\rm 1/5}\) because the definition of the latter concentrations imply that the halos should be non-truncated, and the non-truncated halos are mostly parent ones, so that the fraction of CLUSTER subhalos in Fig. 1 is small in any case. We have also compared the concentrations and \(\rho_{-2}\) of the very few subhalos from the VOID sample with the extrapolations of these parameters to the corresponding masses from the CLUSTER subhalo sample. All the VOID subhalo concentrations and \(\rho_{-2}\) lie below the corresponding extrapolations from the CLUSTER subhalos. Our results show that halos in dense environments are on average more concentrated, with higher central densities and with larger scatters in these parameters than halos in low-density environments. We find that these differences are owing to both nature and nurture reasons. Related to the former is mainly the fact that _halos in dense regions typically assemble most of their masses earlier than halos in low dense regions_, through violent MAHs. Sheth & Tormen (2004) indeed have shown that halos in dense regions form at earlier times than do halos of the same mass in less dense regions. Related to "nurture" is the effect of steepening of the outer (sub)halo profile due to tidal stripping by the parent halo (Ghigna et al., 1998; Okamoto & Habe, 1999; Avila-Reese et al., 1999; Klypin et al., 1999). This effect tends to make the subhalos more concentrated and it is subject to a local condition rather than to the global environment. Subhalos are indeed systematically more concentrated than parent halos, however, both increase also their concentrations as the environment density increases (see also Bullock et al., 2001a). The effect of the formation epoch, related to the global environment, affects likely more the central halo density than concentrations, while the inverse is expected for the local

evolutionary effects. As will be seen below, the differences with environment from \(z=1\) to \(z=0\) are more pronounced for concentrations than for \(\rho_{-2}\). #### 3.1.2 Results at z=1 We analyze the CLUSTER, VOID and FIELD samples at \(z=1\) in the same statistical sense as done at \(z=0\). Similar to Figs. 1 and 2, we show in Figs. 3 and 4 the concentrations and \(\rho_{-2}\) versus mass but now at \(z=1\), and in Table 3 the parameters of the corresponding linear regressions are given. The first impresion is that the differences in the concentrations and central density seen at \(z=0\) among the three halo samples are hardly present at \(z=1\). Our results thus show that at this epoch the c\({}_{\rm NFW}\), c\({}_{\rm 1/5}\), c\({}_{\delta}\) and \(\rho_{-2}\) versus mass relations do not depend on environment. The central concentration \(\rho_{-2}\) for the CLUSTER halos is on average only a little larger at \(z=1\) than at \(z=0\). Halos in dense environments assemble their present-day mass early in such a way that their central densities are stablished likely before \(z=1\). For the VOID halos, the mean of \(\rho_{-2}\) at \(z=1\) is larger than the one at \(z=0\) by \(\sim 70\%\). Halos in low-density environments assemble slowly, incorporating most of their mass lately. The concentration parameters change more with \(z\) than the central density. As previously reported (e.g., Bullock et al., 2001a; Eke, Navarro, & Steinmetz, 2001; Navarro et al., 2004), the c\({}_{\rm NFW}\) concentration parameter is lower at higher redshifts for a given mass. In the upper panel of Fig. 3, the dashed curve shows the \(\mbox{c${}_{\rm NFW}$}-\mbox{$M_{\rm vir}$}\) dependence at \(z=1\) given by the toy model of Eke, Navarro, & Steinmetz (2001). According to this model \(\mbox{c${}_{\rm NFW}$}\propto(1+z)^{-1}\) approximately (see also Bullock et al., 2001a). In Figs. 3 and 4 are also shown (thin solid lines) the linear regression for the CLUSTER sample and the 1\(\sigma\) scatter of the VOID sample plotted in Figs. 1 and 2 (\(z=0\)). The concentration c\({}_{\rm NFW}\) is on average \(\sim 1.5\) and 2.1 times lower at \(z=1\) than at \(z=0\) for the VOID and CLUSTER samples, respectively. For the latter sample, the comparison is made at \(10^{12}\mbox{$h^{-1}$M${}_{\odot}$}\). For the FIELD sample, the differences of c\({}_{\rm NFW}\) between \(z=0\) and \(z=1\) are on average slightly less than a factor of two, at least in the range of masses explored here. Thus, the evolution of c\({}_{\rm NFW}\) seems to be slightly different in the different environments. A similar behaviour is seen for c\({}_{\rm 1/5}\) and c\({}_{\delta}\). The scatters in all the measured parameters are larger at \(z=1\) than at \(z=0\), reflecting likely the fact that at \(z=1\) the halos are in general less relaxed than at \(z=0\). The increase of concentration with time is more pronounced in the cluster environment. We analyze the behaviour of concentration for halos inside the present-day cluster virial radius (subhalos) in simulation Cl\({}_{6}^{\rm hr}\). Because for this simulation we have the halo MAHs, concentrations for a given halo can be measured at \(z=0\) and \(z=1\). We find that the ratios of concentrations measured Figure 3: Same as in Fig. 1 but for a snapshot at \(z=1\). Thick lines and error bar correspond to the current samples (\(z=1\)), while thin line and error bar are the same ones as shown in Fig. 1 (\(z=0\)). The bars were slightly shifted to avoid overlapping.

## 4 Spin parameter and angular momentum alignment ### Spin parameter distribution We compute the halo total angular momentum as \[\mbox{\boldmath$J$}=\sum_{i=1}^{n}m_{i}\mbox{\boldmath$r_{i}$}\times\mbox{ \boldmath$v_{i}$},\] (3) where \(r_{i}\) and \(v_{i}\) are the position and velocity of the _i_th particle with respect to the halo center of mass. We follow Bullock et al. (2001b) and define a modified spin parameter \(\lambda^{\prime}\) to characterize the global angular momentum of a halo \[\lambda^{\prime}\equiv\frac{J_{h}}{\sqrt{2}M_{h}V_{h}R_{h}},\] (4) where \(J_{h}\) is the angular momentum inside the halo radius \(R_{h}\) (see SS3.1), and \(V_{h}\) is the circular velocity at \(R_{h}\). Hereafter, in this section, we drop the prime in \(\lambda^{\prime}\). Figure 8 shows the spin parameter distributions for our different galaxy-size halo samples. In this case, halos with more than 500 particles were used. The halos that are subhalos are cut at the truncation radius. The spin distributions of the Cl\({}_{\rm all}\) and VOID samples are shown in left and right panels, respectively. Curves on panels are the corresponding lognormal best fits to the data. The lognormal fit of sample FIELD is shown as a dotted line in both panels for comparison purposes. The (\(\sigma\),\(\lambda_{0}\)) parameters of the lognormal distributions are given inside the panels. The median values of \(\lambda\) for the different samples are presented in Table 2. The conclusion from Fig. 8 and Table 2 is clear: halos from the Cl\({}_{\rm all}\) sample have on average lower Figure 8: Spin parameter distribution (histograms) for halos with more than 500 particles drawn from a cluster environment (Cl\({}_{\rm all}\) sample, left panel) and from a void environment (VOID sample, right panel). Curves on each panel are lognormal best fits to the data. The lognormal fit of the \(\lambda\) distribution for halos in the FIELD sample is shown in both panels for comparison purposes. The values of the parameters of the fits (\(\lambda_{0},\sigma_{\lambda}\)) are also shown in panels. Figure 6: The average ellipticity, \(\epsilon=1-s\), as a function of halo mass at two redshifts \(z=0\) and 1 for halos in the FIELD sample. Error bars reflect the Poisson uncertainty associated with the number of halos within the bin and not the scatter in the relation. Figure 7: Ellipticity distribution (histograms) for halos with more than 500 particles drawn from a cluster environment (left panel) and from a void environment (right panel). Curves on each panel are lognormal best-fits to the data. The lognormal fit of the \(\epsilon\) distribution for the FIELD sample of halos is shown in both panels for comparison purposes. The values of the parameters of the fits \((\sigma_{\epsilon},\epsilon_{0})\) are also shown in panels.

spin parameters and a wider distribution than halos from the VOID and FIELD samples. The \(\lambda_{0}\) and \(\sigma\) parameters of the former sample are 30-40% and \(\sim 15\%\) times smaller than for the latter samples, respectively. The difference between the \(\lambda\) distributions of halos in the Cl\({}_{\rm all}\) and VOID samples is confirmed by a KS test: the probability that both samples belong to the same parent distribution is \(1.17\times 10^{-5}\). Our result agrees with that obtained by Reed et al. (2005). They also found that halos in high-density environments have smaller spins than halos in the field. Are these differences due to global environment effects or to the fact that CLUSTER subsamples have a higher fraction of subhalos? To address this question we compare the \(\lambda\) distributions of the parent halos and subhalos of the CLUSTER subsamples. By applying a KS test we find only slight differences in these distributions: the probabilities that both samples belong to the same parent distribution are 0.89 for the Cl\({}_{6}^{\rm hr}\) sample and 0.45 for the Cl\({}_{\rm all}\) sample. On the other hand, the \(\lambda\) medians (or \(\lambda_{0}\)) of the halo and subhalo samples in both cases agree within 5%. We notice that the FIELD sample is by construction composed of only parent halos, and the VOID halos are esentially parent ones (more than 90%). How much of the difference we have found can be attributed to cluster-to-cluster scatter? Unfortunately, we only have one cluster, Cl\({}_{6}^{\rm hr}\), with hundreds of halos, each one with more than 500 particles inside its virial or tidal radius. The other clusters are less resolved and they thus have less halos than Cl\({}_{6}^{\rm hr}\) by far. We avoid the halo _low-number_ problem by combining these clusters to form only one, which in principle is independent from Cl\({}_{6}^{\rm hr}\). We measure \(P(\lambda)\) for the independent Cl\({}_{6}^{\rm hr}\) halo sample and test whether this distribution is similar to the one obtained for the composite Cl\({}_{\rm all}\) sample. We found differences in the values of the fitting parameters (\(\sigma\),\(\lambda_{0}\)) of less than 5%. Slightly higher differences are measured when the comparison is made between the \(P(\lambda)\) distribution from the same sample Cl\({}_{\rm all}\) but at two close snapshots. Our results show that present-day halos in dense environments have a spin parameter distribution shifted to lower values with respect to those of halos in the field or in the voids. Does \(\lambda\) decrease due to the lost of high angular momentum material by halos that suffer strong tidal stripping in dense regions? A way of testing this hypothesis is by simply measuring \(P(\lambda)\) in the cluster environment at much earlier time, when most halos have yet to experiment strong tidal stripping. We find a median value \(\lambda_{med}=0.036\) at \(z=1\) for the CLUSTER sample, which is comparable to \(\lambda_{med}=0.033\) for the FIELD sample at present time. This result is consistent with the hypothesis above but does not actually prove it. On the other hand, we showed above that subhalos and parent halos have, according to a KS test, similar \(P(\lambda)\) distributions. These results appear to contradict each other. Notice, however, that the histories of parent halos in high-density regions can be very different from their counterparts in low-density environments because the former undergo a "tumultuous life". They may have suffered, for instance, tidal stripping in the past, from close encounters with major substructures, or their mass accretion could have been stopped (Kravtsov et al., 2004b). We also looked for a cluster-centric radial \(\lambda\) dependence in Cl\({}_{\rm all}\) and Cl\({}_{6}^{\rm hr}\) samples. Unlike Reed et al. (2005), we did not find any systematical decreasing of \(\lambda_{med}\) as the cluster-centric radius is smaller. Notice that Reed et al. (2005) analyzed subhalos with more than 144 particles, while our subhalos have more than 500 particles; many subhalos are below this limit, but the measure of \(\lambda\) for them is not reliable. For the VOID and FIELD samples, \(\lambda_{med}=0.034\) and 0.036 at \(z=1\), respectively. Therefore, \(\lambda\) for these halo samples also decreases on average from \(z=1\) to \(z=0\), but very little. In this case, the small decreasing of \(\lambda\) with time could be explained by the accretion mode proposed by Peirani et al. (2004). In summary, while halos in low-dense regions seem to keep constant or slightly decrease their \(\lambda\) values from \(z=1\) to \(z=0\), halos from the cluster-like regions tend to decrease significantly their \(\lambda\) values. We interpret the latter as a consequence of two effects: (i) the earlier halo assembly epochs typical of higher density regions, and (ii) the subhalo tidal stripping and the the tumultuous mass assembly history of halos in clusters and their surroundings. For a more detailed discussion of these effects it is necessary to follow the individual mass and angular momentum assembly histories of the halos. In a subsequent paper we will construct and analyze these

individual histories for each one of our samples. ### Internal angular momentum alignment In previous subsection we explored the distribution of the magnitude of the angular momentum as a function of environment. Now we will explore possible differences in the distribution of the angular momentum internal alignment. We measure the typical alignment by the angle \(\theta_{1/2}\) between the mean angular momentum of the particles in the inner sphere of half-mass radius and the mean angular momentum of the particles in the outer half-mass spherical shell (Bullock et al., 2001b). As discussed by Bullock et al. (2001b) large errors are involved in the determination of the direction of the angular momentum vectors and thus in \(\cos\theta_{1/2}\). The error in \(\cos\theta_{1/2}\) is estimated in two manners. In the first one, we assign errors to each component of the angular momentum, in both inner and outer half-mass regions, using a Monte Carlo procedure similar to the one built to estimate the error in the axial ratios (SS3.2), and perform a standard propagation of errors. In the second one, the Monte Carlo procedure is applied directly on \(\cos\theta_{1/2}\). The first method gives larger errors. This is so likely because the internal and external angular momentum are not entirely independent quantities. We found that the error depends not only on the number of particles, \(N_{p}\), and \(\lambda\) but also on the intrinsic alignment: a more aligned halo have a smaller error. For \(N_{p}\) as low as \(\sim 500\), the \(1\sigma\) error in \(\cos\theta_{1/2}\) can reach 50% of the measurement. _Bearing this in mind_, we now proceed to present our results (still uncertain) and their possible intepretations. The distributions of \(\cos\theta_{1/2}\) for our different environments at \(z=0\) are shown in Fig. 9. As it was the case for \(P(\lambda)\), we use halos with more than 500 particles. Figure 9 shows that the Cl\({}_{\rm all}\) halos are on average less aligned than the halos from the FIELD and VOID samples. The median values of \(\cos\theta_{1/2}\) for the Cl\({}_{\rm all}\) FIELD, and VOID samples are 0.51, 0.80, and 0.83, respectively. In order to find a possible explanation for these differences with environment, we have also measured the alignment distributions at a much earlier time, \(z=1\) (Fig. 10). Figures 9 and 10 show that the population of VOID and FIELD halos at \(z=0\) is more aligned on average than the one at \(z=1\). A more quantitative estimate of this difference is confirmed by the KS test: for the FIELD sample, for example, the probability that the populations at \(z=0\) and \(z=1\) belong to the same parent distribution is \(4.5\times 10^{-5}\), with \(\cos\theta_{\rm 1/2,med}=0.80\) and 0.75, respectively. Regarding the Cl\({}_{\rm all}\) sample, there is no any significant difference in the alignment distributions of halos at \(z=0\) and \(z=1\). We remark that the results presented above need to be confirmed by future analysis with better resolved halos. If confirmed, we find the following explanation for the evolutionary effect seen in the internal angular momentum alignment of FIELD and VOID sample halos. On one hand, most of the angular momentum of the outer sphere, which is where essentially most of the halo angular momentum resides, was acquired during the linear grow. On the other hand, it is expected that most of the angular momentum of the inner sphere comes from the violent, initial merger-growth phase (Vitvitska et al., 2002; Peirani et al., 2004). The material accreted by the halo at later times brings angular momentum oriented in the direction of the angular momentum of the outer shell. As part of this material is incorporated into the inner sphere the alignment increases. This Figure 9: Angular momentum alignment distributions for our four samples of halos at \(z=0\). Two different distributions are shown in each panel for comparison purposes. Distributions shown as dotted histograms are also shaded for more clarity. Halos in voids and those in the field present similar distributions but they both are on average more aligned than their counterpart in clusters.

mechanism is not expected to apply to halos in clusters or their outskirts because they typically do not incorporate material as soon as they fall into the cluster halo; in some cases the halos in clusters even loose mass due to tidal stripping. Regarding the question of why present-day halos in clusters are less aligned than those in the field or in voids, a comparison between Cl\({}_{\rm all}\) and FIELD halos at \(z=1\) shows that they are equally well aligned. This is probably so because at \(z=1\) these environments are still not too disimilar. However, unlike halos in the field and voids, halos in clusters evolve under the influence of strong tidal fields. Halos in sample CLUSTER have a mass assembly history very different from their counterparts in samples FIELD or VOID. In the cluster environment, a significant fraction of halos present at \(z=1\) do not survive until \(z=0\), others end up with their masses significantly reduced, while some others, those that at present day are at cluster outskirts, may grow as what is typical of a halo in field and void environments. Figures 9 and 10 show that halos in sample Cl\({}_{6}^{\rm hr}\) at \(z=0\) are more disaligned than halos at \(z=1\). For the subset of halos of sample Cl\({}_{6}^{\rm hr}\) that are within \(R_{\rm vir}\) at \(z=0\) (subhalos), which were also identified at \(z=1\), we find the same trend: the halos at \(z=1\) are on average more aligned than the halos at \(z=0\). A halo by halo comparison, however, shows that the trend is not systematic; i.e., there are halos that exhibit a higher alignment at \(z=0\). In summary, it seems that in an environment in which halos stop growing, an increase in alignment is not expected, but even more, it seems that a cluster-like environment acts on the halo angular momentum internal alignment in a non-trivial way: the change in alignment varies halo by halo. ### Alignment between the halo shape and angular momentum Halo axis ratios as well as the directions of the principal axes are determined as explained in SS3.2. We denote with \(\theta\) the angle between the angular momentum axis within \(R_{h}\) and the direction of the minor principal axis. In Fig. 11 we show the distributions of \(\theta\) at \(z=0\) for our different halo samples. We use here also halos with more than 500 particles, although the iterative procedure sometimes need more than that to converge. The number of halos used to draw the histograms in Fig. 11 can thus be lower than those shown in Table 2 (see SS2). We repeat here the procedure we follow to evaluate the \(1\sigma\) error in axial ratios and \(\cos\theta_{1/2}\) to obtain the corresponding \(1\sigma\) error in \(\cos\theta\). Errors in \(\cos\theta\) are smaller than those ones in \(\cos\theta_{1/2}\). They amount to about 20% for halos with 500 particles. Taking into account that this particle number is a lower limit, we expect errors in \(\cos\theta\) to be on average less than 20%. On the other hand, errors in \(\cos\theta\) are also dependent on the degree of alignment but they seem to be less sensitive to it than the errors in \(\cos\theta_{1/2}\). The angular momentum axis of halos tends to align to the minor axis of the halo ellipsoids (in a plot like Fig. 11, a random oriented distribution would be uniform). This appears to be a generic prediction of the CDM cosmology (see also Faltenbacher et al., 2002; Bailin & Steinmetz, 2004). Besides, we find some trend of decreasing the alignment angle \(\theta\) from Cl\({}_{\rm all}\) to FIELD and VOID halo samples. This visual result is mildly supported by a KS test: the probability that the Cl\({}_{\rm all}\) and VOID samples belong to the same parent distribution is \(2.4\times 10^{-2}\). The relative orientations of the halo angular Figure 10: Angular momentum alignment distributions for our four samples of halos at \(z=0\) and \(z=1\). Each panel correspond to a halo sample. Distributions shown as dotted histograms are also shaded for more clarity. Halos in voids and those in the field are on average less aligned at \(z=1\) than at \(z=0\).

difference becomes very small when the central velocity dispersion is used. ## 6 The halo-galaxy connection Our study shows that present-day halos in the cluster environment are on average more concentrated, more spherical, disaligned and rotate slower than halos in the void or field environments. Our study also suggests differences in the evolution history of halos depending on the environment: halos in dense environments assemble their masses apparently earlier than halos in low-density regions (see also Sheth & Tormen, 2004). The question is whether all these differences in the halos produce visible differences in the luminous galaxies formed inside them. A common method in galaxy modeling is to build-up a luminous galaxy linked directly to a present-day CDM halo. Several numerical and analytical works show indeed that the present-day properties of the halos keep some memory of their evolution history (typical formation epoch, average shape of the MAH, major mergers, etc.). For example, the \(z=0\) halo concentration depends on the shape of the MAH (Avila-Reese et al., 1998; Firmani & Avila-Reese, 2000; Wechsler et al., 2002; Zhao et al., 2003), in such a way that fixing the concentration at \(z=0\), the main feature of the halo MAH (and of the corresponding baryon matter infall history) remains roughly determined. However, a direct (\(z=0\) halo)-galaxy connection may fail for subhalos (specially for the massive ones and in cluster regions). The tumultous history of galaxy-size subhalos, since they infall in the cluster halo, affects in a complex way their present-day properties and distributions. The main effect is that of tidal stripping, or even total disruption, of subhalos as they penetrate into the cluster potential (e.g., Ghigna et al., 1998, 2000; Colin et al., 1999, 2000; Taffoni et al., 2003; De Lucia et al., 2004; Kravtsov et al., 2004a, b; Diemand et al., 2004; Gao et al., 2004a; Reed et al., 2005). Thus, the halo mass function and the halo-to-galaxy mass ratio of galaxies in clusters is expected to change dramatically with time. The study of galaxy evolution in clusters, at least in their inner regions, requires a full treatment of halo evolution and baryonic physics (Springel et al. 2001; Diaferio et al. 2001; Gao et al. 2004b). Following, we will carry out a very preliminar exploration of the effects on the _disk_ galaxy properties when varying the _present-day_ CDM halo concentration and \(\lambda\), according to the results obtained above for different environments. For this, seminumerical models of disk galaxy evolution (Avila-Reese & Firmani, 2000; Firmani & Avila-Reese, 2000) will be used (see also van den Bosch, 2000). These models include in a self-consistent way the processes of formation and evolution of a spherical CDM halo and a disk in centrifugal equilibrium inside it, the adiabatic gravitational contraction of the halo due to disk formation, self-regulated SF and feedback, secular bulge formation and other evolutionary processes. Most of the Figure 13: Same as in Fig. 11 but for a snapshot at \(z=1\). For comparative purposes, the linear regressions of the CLUSTER and VOID samples at \(z=0\) (Fig. 11) are shown (thin solid and dashed lines, respectively).

\(z=0\) galaxy properties depend mainly on (i) the present-day \(M_{\rm vir}\), (ii) the halo MAH (that determines the concentration), (iii) the spin parameter \(\lambda\), and (iv) the disk mass fraction \(f_{d}\) (\(\equiv M_{d}/\mbox{$M_{\rm vir}$}\)). A brief description of the main ingredients of the model is presented in the Appendix. We notice that the \(\lambda\) parameter in this case follows its standard definition (e.g., Peebles, 1969). This \(\lambda\) parameter is larger than the \(\lambda^{\prime}\) one measured for halos in SS4 by factors typically of 1.25-1.50, depending on the halo concentration (Bullock et al., 2001b). We model disk galaxies of a given baryon mass (\(M_{d}\)) in halos with different concentration and spin parameters, emulating void and cluster environments. The seminumerical method is well suited for isolated (field and void) galaxies. For "void" galaxies, we assign the (high) median \(\lambda\) (calculated from \(\lambda^{\prime}\)) found for VOID halos and fix the \(z=0\)\(M_{\rm vir}\) (\(=M_{d}/f_{d}\)). We then select, from random realizations, MAHs for this mass so that they yield the typical (low) concentrations of VOID halos at \(z=0\); these MAHs are extended, implying late halo assembling. We carefully choose roughly regular MAHs, without dramatic changes in their shapes. The emulation of "cluster" galaxies with our method is more difficult. We will assume that the (sub)halo was accreted into the cluster halo at \(z=0.3\) (3.4 Gyr ago, for the cosmology used here). Ours and previous simulations show that most subhalos in present-day cluster halos were accreted recently (\(\sim 70\%\) after \(z=0.5\)), and that since then, these halos have lost typically 30-50% of their masses due to tidal striping (e.g., De Lucia et al., 2004; Nagai & Kravtsov, 2005; Zentner et al., 2005; van den Bosch et al., 2005). Thus, we fix \(M_{\rm vir}\) at \(z=0.3\) rather than at \(z=0\), and we assign a low \(\lambda\), typical of our CLUSTER halos at \(z=0.3\), which is slightly larger than at \(z=0\). Regarding concentrations, we fix them to the typical (high) concentrations of our CLUSTER halos by selecting the appropiate MAHs. These MAHs and the fact that the halo is fixed at \(z=0.3\), imply an early assembling of the halo/disk system. Since \(z\lesssim 0.3\) the disk does not accretes more gas but it continues evolving. Models for two disk (baryonic) masses are calculated, \(M_{d}=10^{9}\mbox{M${}_{\odot}$}\) and \(10^{11}\mbox{M${}_{\odot}$}\). For each mass, we calculate two galaxy models corresponding roughly to the extreme environments, void and cluster regions, as explained above. We set the disk mass fraction in all cases to be \(f_{d}=0.03\). The cosmologycal parameters are the same ones used in our N-body simulations (SS2). Table 5 summarizes the main halo and disk input parameters as well as the obtained properties of our simulated galaxies. Recall that in the case of the "cluster" galaxies, the halo growth and gas infall are truncated at \(z=0.3\) to account for the fact that it was accreted into the cluster at this time. The late-accreted halos are typically located in the periphery of the cluster halo (e.g., De Lucia et al., 2004; Nagai & Kravtsov, 2005) and are expected to host mostly spiral or S0 galaxies. Looking at Table 5, one sees that the dependence of halo concentration and \(\lambda\) on environment found in this work should produce some changes in the disk galaxy properties. As previously reported (Avila-Reese & Firmani, 2000), \(\lambda\) influences mainly the disk scale length and surface \begin{table} \begin{tabular}{l c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\(M_{d}\)} & Env.a [FOOTNOTE:a]Footnote a: Environment: V=void, Cl=cluster[ENDFOOTNOTE] & c\({}_{\rm NFW}\) & \(\lambda\) & \(\lg\Sigma_{0}\) & \(f_{g}\) & \(B-V\) & b/d & \(r_{s}\) & \(M_{s}\) & \(V_{\rm max}\) \\ \(10^{9}\mbox{M${}_{\odot}$}\) & & & & \(\mbox{M${}_{\odot}$}/\)pc\({}^{2}\) & & & \(10^{-2}\) & kpc & \(10^{8}M_{\odot}\) & km/s \\ \hline 1 & V & 12 & 0.048 & 1.75 & 0.64 & 0.54 & 1.1 & 1.1 & 3.61 & 55 \\ & Cl & 19 & 0.035 & 2.42 & 0.39 & 0.74 & 12.3 & 0.7 & 6.18 & 71 \\ 100 & V & 10 & 0.048 & 2.30 & 0.50 & 0.53 & 8.8 & 6.3 & 512 & 212 \\ & Cl & 13 & 0.035 & 2.83 & 0.27 & 0.72 & 24.5 & 3.8 & 730 & 278 \\ \hline \end{tabular} \end{table} Table 5: Main properties of simulated disk galaxies

brightness, the gas fraction and the secular bulge-to-disk ratio, while the MAH fixes the halo concentration and influences mainly the SF history, galaxy integral color and the scatter of the TFR. Thus, our expectation is that disk galaxies of a given mass \(M_{d}\) formed in low-\(\lambda\) and highly concentrated halos, with a gas infall history truncated early (cluster environment), are preferentially of earlier morphologycal types, redder, shifted to the higher velocity side in the TFR, and have higher surface brightness, smaller scale lengths, and lower gas fractions than disk galaxies formed in high-\(\lambda\) and low-concentration halos (void environment). All these trends are namely seen in Table 5. The stellar central surface density, \(\Sigma_{0}\), and disk scale radius, \(r_{d}\), are the parameters of the exponential-law fit to the model stellar disk. In fact, the disks formed in CDM halos typically are not exactly exponentials, but their surface density profiles are more concentrated in the center and with an excess in the periphery compared with the exponential law (Firmani & Avila-Reese, 2000; Bullock et al., 2001b). Our results show that owing to only differences in the halo properties (related to the environment), the galaxy disks can have significant differences. According to Table 5, disks formed in halos with properties typical of halos in voids are \(\sim 0.2\) mag bluer in \((B-V)\) color, have central stellar surface densities lower by \(\sim 4\) times (1.5 mag/arcsec\({}^{2}\)), and gas fractions higher by 1.5-2 times than disks formed in halos with properties typical of the cluster-periphery environment. According to our models, the low mass disks have lower central surface brightnesses and higher gas fractions than the high mass ones, while the \((B-V)\) colors do not change significantly with mass. The (secular) bulge-to-disk ratio depends strongly on mass, being this ratio larger for massive disks. There is also a significant increasing of this ratio from halos typical of voids to those typical of the cluster periphery. This implies that _part of the morphology-density relation is due to changes in the properties of the galaxy halos with environment_. As mentioned in SS5.1, one expects also differences with environment in the TFR. The slope of the model stellar TFR is \(\sim 3.4\)(Firmani & Avila-Reese, 2000). By using this slope, we correct the velocities due to the variations in the stellar masses of each one of the models with \(M_{d}=10^{9}\mbox{M${}_{\odot}$}\) and \(M_{d}=10^{11}\mbox{M${}_{\odot}$}\) presented in Table 5. We obtain that at \(M_{d}=10^{11}\mbox{M${}_{\odot}$}\), the difference in \(V_{\rm max}\) for our void and cluster-periphery galaxies is about 20%; the difference in mass, expressed in magnitudes, is 0.6 mag, i.e. we predict that the zero-point of the TFR of void galaxies at \(M_{d}=10^{11}\mbox{M${}_{\odot}$}\) should be brighter by \(\sim 0.6\) mag than the one of cluster-periphery galaxies. At \(M_{d}=10^{9}\mbox{M${}_{\odot}$}\), the predicted difference is \(\sim 0.4\) mag. Real galaxies show likely more pronounced differences in their observational properties as a function of the environment than those obtained with our models (see SS1.1 for references). Thus, other physical processes not considered here should certainly play an important role in galaxy dynamics and evolution. For example, we did not treat in detail the angular momentum distribution misalignment and did not take into account the halo triaxiality and the shape-to-rotation axis misalignment. These properties change with environment as was shown in SSSS3 and 4. Besides, deep in the cluster regions, the external effects such as tidal and ram pressure stripping, strong interactions at early epochs, and galaxy harassment (Moore et al., 1996), are likely the dominant ones in shaping morphology and other galaxy properties (see the references above). Finally, we note that most of the differences in the halo properties with environment seen at \(z=0\) dissapear at \(z=1\), although the scatters in the latter epoch are very large. As mentioned in SS1.1, observations also show that the morphology-density relations flattens at higher redshifts. The main morphological evolution is seen for the galaxies in the high-density environment. Halos in clusters are also those that change most their properties. ## 7 Summary and Conclusions Observations show that morphology and several properties of galaxies change systematically with environment. According to the current paradigm of galaxy formation, galaxies assemble inside CDM halos. We state then two questions: (i) do the properties of _galaxy-size_ CDM halos/subhalos change systematically with environment?, and if this the case, (ii) do these changes in the halo/subhalo properties affect the luminous

galaxies in the direction that observations show? We studied the first question by means of high-resolution \(\Lambda\)CDM cosmological N-body simulations. Several clusters with their surroundings (CLUSTER sample) and void regions (VOID sample) were selected from large-box simulations, and they were resimulated with high resolution. We also use other simulations, in particular two 60\(h^{-1}\)Mpc-box simulations from which the FIELD sample of parent halos was extracted. The local density contrast in our CLUSTER, VOID and FIELD samples are on average larger than 34, smaller than -0.8 and roughly 0, respectively. The second question, in a first attempt, was disscused by using standard seminumerical models of disk galaxy evolution. Disk galaxies were modeled inside CDM halos with properties that we have found they have in the different environments. Following, we summarize our main results: \(\bullet\) For masses \(\lesssim 5\times 10^{11}\mbox{$h^{-1}$M${}_{\odot}$}\), halos from the CLUSTER sample are on average \(\sim 40\%\) more concentrated and have \(\sim 2\) times higher central densities \(\rho_{-2}\) than halos in voids at \(z=0\). While for halos in cluster regions the concentration parameters c\({}_{\rm NFW}\), c\({}_{\rm 1/5}\) and c\({}_{\delta}\), and the density \(\rho_{-2}\) decrease on average with mass, for halos in voids these concentrations and \(\rho_{-2}\) do not seem to change with mass. The slope of the \(\mbox{c${}_{\rm NFW}$}-\mbox{$M_{\rm vir}$}\), \(\mbox{c${}_{\rm 1/5}$}-\mbox{$M_{\rm vir}$}\) and \(\mbox{c${}_{\delta}$}-\mbox{$M_{h}$}\) dependences for the former sample is \(\sim-0.1\). In the mass range of the parent FIELD halos analyzed here, concentrations and \(\rho_{-2}\) are also smaller on average than those of halos in clusters. The concentrations and \(\rho_{-2}\) of FIELD halos decrease on average with mass but less rapid than halos from the CLUSTER sample. The scatters of all of these parameters are larger for CLUSTER halos than for halos in less dense environments. For example, for reasonably well fitted NFW halos from the CLUSTER and VOID samples, \(\Delta\)(logc\({}_{\rm NFW}\))\(\approx 0.13\) and \(\approx 0.09\), respectively. \(\bullet\) All the differences mentioned above become less pronounced when comparing only the parent halos from the different samples (CLUSTER: \(\sim 60\%\); VOID: \(\sim 95\%\); FIELD: all). Therefore, the CLUSTER halos are more concentrated and internally denser than the VOID and FIELD ones due partially to a local halo-subhalo effect (subhalos are a significant fraction of the CLUSTER sample, and subhalos are systematically more concentrated than their parent halos, see also, e.g., Bullock et al. 2001a). However, we find that the parent halos and subhalos from the CLUSTER sample are still significanlty different on average than the parent halos and subhalos from the VOID and FIELD samples. Therefore, the differences in halo properties are certainly also due to a pure global environmental effect, related mainly to the typical halo formation epoch: _halos in dense environments assemble their masses earlier than halos in low-density regions_. \(\bullet\) Halos in dense environments are more spherical than halos in less dense environments at \(z=0\). The minor-to-major axis ratios of CLUSTER halos are on average \(\sim 1.2\) times lower than those of the FIELD halos. For a given epoch, the ellipticity of the halos tends to increase with mass. For a given mass, the ellipticity changes with age, the younger halos having on average larger ellipticities than the older halos. \(\bullet\) The spin parameter of CLUSTER halos is on average \(1.3-1.4\) times lower than the one of VOID or FIELD halos at \(z=0\). This is likely a consequence of both global (environmental) and local effects, i.e. the dependence of halo formation epoch on environment, and the tidal stripping and "tumultuos" histories that halos suffer in locally high-density regions, respectively. We do not find significant differences in the \({\lambda^{\prime}}\) distribution of parent halos and subhalos from the CLUSTER sample. The CLUSTER halos appear to have a less aligned intrinsic angular momentum distribution than the VOID and FIELD ones, but this result needs to be confirmed by future analysis because of the large errors involved in the determination of \(\cos\theta_{1/2}\). The spin parameter does not change significantly with mass in any environment and its distribution is well approximated by a lognormal function with a larger width and a lower peak \({\lambda^{\prime}}\) in cluster regions than in voids and the field. The angular momentum axis of halos tends to be aligned with their minor principal axis, this behaviour being more common in the less dense environments than in the high-density ones. \(\bullet\) A tight \(\mbox{$V_{\rm max}$}-\mbox{$M_{h}$}\) relation is seen for halos in all the environments. The relation is shallower (slope of 0.30) and more scattered for clusters and their surroundings than for the void and field environments (slopes of \(\sim 0.33-0.34\)). If this relation is the basis of the observed TFR, then slight dif

ferences in the TFR are expected in different environments. The \(\mbox{$V_{\rm max}$}-\mbox{$M_{h}$}\) relation slightly shifts to the lower mass side at \(z=1\) in all the environments, but in particular in the voids. Similar results to the \(\mbox{$V_{\rm max}$}-\mbox{$M_{h}$}\) relation are obtained for the \(\mbox{$\sigma_{c}$}-\) and \(\mbox{$\sigma_{t}$}-\mbox{$M_{h}$}\) relations, showing that most of the halos are close to their equilibrium state. \(\bullet\) The differences in halo properties with environment seen at \(z=0\) drastically diminish at \(z=1\). Interestingly enough, a similar result was found for the observed morphology-environment relation. As expected, the concentration parameters decrease as we go from \(z=0\) to \(z=1\), being this change more pronounced for the CLUSTER halos, particularly for the less massive ones. The spin parameter of CLUSTER halos at \(z=1\) is on average significantly larger than at \(z=0\), while for less dense environments, the spin parameter at \(z=1\) is on average only slightly larger than at \(z=0\); thus, \(\lambda^{\prime}\) evolves in a different way for halos in cluster-like regions than for halos in less dense environments. Halos in the void and field environments are systematically less aligned at \(z=1\) than at \(z=0\), while halos in the cluster regions do not show any systematical change with redshift in a statistical sense. \(\bullet\) Disk galaxies modeled in a self-consistent fashion inside \(\Lambda\)CDM halos with the present-day concentrations and spin parameters found here for halos in the different environments present systematical differences: the galaxies formed in halos typical of cluster-periphery environment have higher surface density, circular velocity and secular bulge-to-disk ratio, lower gas fraction, and are redder than for those formed in halos typical of void environment. These trends agree qualitatively with observations but are not enough to explain the observed differences of galaxy properties with environment. We predict that the TFR of galaxies in low and high-density environment is different. From our study we conclude that most of the properties of galaxy-size halos at \(z=0\) change with environment in a statistical sense, the largest differences in the structural properties being for the less massive halos (sub-\(L_{*}\) galaxies). The main changes with environment occured after \(z\sim 1\) and the most affected halos are the subhalos in the CLUSTER sample. The differences in halo concentrations and spin parameters along the different environments influence on the properties of galaxy disks formed inside these halos and in the same direction that observations show. However, the inclusion of angular momentum dissalignment, triaxiality, and shape-rotation axis dissalingment -halo properties that also change with environment- in the models of disk galaxy evolution is necessary in order to attempt to reproduce in more detail the observed relations of disk galaxy properties with environment. The halo merging history and its influence on luminous galaxies should also be taken into account, in particular for modelling galaxies in the high-density environments. The halo properties discussed above and their changes with environmnet are ultimately related to the _initial cosmological conditions_. Based on our results, we claim that the observed galaxy properties-environment relations are partially established by the initial cosmological conditions (nature), in the sense that galaxy halos in more dense environments assemble earlier. However, our results point out that the _external astrophysical factors_ (nurture) should play also an important role in the observed trends of changing galaxy properties with environment, specially in the highest density regions (clusters). Computer simulations presented in this paper were done at the Leibnizrechenzentrum (LRZ) in Munich and at the John von Neumann Institute for Computing Julich. We acknowledge the anonymous referee whose helpful comments and suggestions improved several aspects of the paper. We are also grateful to Ricardo Flores for kindly providing a copy of his program to compute the halo ellipticities. This work has been supported by a bilateral CONACyT-DFG (Mexico-Germany) grant, and by CONACyT grants 36584-E and 40096-F. **APPENDIX** Here we present the main physical ingredients of the self-consistent evolutionary models used in SS6. For details see Firmani & Avila-Reese (2000); Avila-Reese & Firmani (2000). The disk is built up within a growing \(\Lambda\)CDM halo. An extended Press-Schechter approach (Lacey & Cole, 1993;

# Star Formation in Isolated Disk Galaxies. II. Schmidt Laws and Efficiency of Gravitational Collapse Yuexing Li124 , Mordecai-Mark Mac Low12 and Ralf S. Klessen3 Footnote 1: affiliationmark: Footnote 2: affiliationmark: Footnote 4: affiliationmark: Footnote 1: affiliationmark: Footnote 2: affiliationmark: Footnote 3: affiliationmark: \({}^{1}\)Department of Astronomy, Columbia University, New York, NY 10027, USA \({}^{2}\)Department of Astrophysics, American Museum of Natural History, 79th Street at Central Park West, New York, NY 10024-5192, USA \({}^{3}\)Astrophysikalisches Institut Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany \({}^{4}\) Current address: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA, 02138 yxli@cfa.harvard.edu, mordecai@amnh.org, rklessen@aip.de ###### Abstract We model gravitational instability in a wide range of isolated disk galaxies, using GADGET, a three-dimensional, smoothed particle hydrodynamics code. The model galaxies include a dark matter halo and a disk of stars and isothermal gas. Absorbing sink particles are used to directly measure the mass of gravitationally collapsing gas. Below the density at which they are inserted, the collapsing gas is fully resolved. We make the assumption that stars and molecular gas form within the sink particle once it is created, and that the star formation rate is the gravitational collapse rate times a constant efficiency factor. In our models, the derived star formation rate declines exponentially with time, and radial profiles of atomic and molecular gas and star formation rate reproduce observed behavior. We derive from our models and discuss both the global and local Schmidt laws for star formation: power-law relations between surface densities of gas and star formation rate. The global Schmidt law observed in disk galaxies is quantitatively reproduced by our models. We find that the surface density of star formation rate directly correlates with the strength of local gravitational instability. The local Schmidt laws of individual galaxies in our models show clear evidence of star formation thresholds. The variations in both the slope and the normalization of the local Schmidt laws cover the observed range. The averaged values agree well with the observed average, and with the global law. Our results suggest that the non-linear development of gravitational instability determines the local and global Schmidt laws, and the star formation thresholds. We derive from our models the quantitative dependence of the global star formation efficiency on the initial gravitational instability of galaxies. The more unstable a galaxy is, the quicker and more efficiently its gas collapses gravitationally and forms stars. Subject headings: galaxy: evolution -- galaxy: spiral -- galaxy: kinematics and dynamics -- galaxy: ISM -- galaxy: star clusters -- stars: formation ## 1. INTRODUCTION Stars form at widely varying rates in different disk galaxies (Kennicutt, 1998a). However, they appear to follow two simple empirical laws. The first is the correlation between the star formation rate (SFR) density and the gas density, the "Schmidt law" as first introduced by Schmidt (1959): \[\Sigma_{\rm SFR}=A\ \Sigma_{\rm gas}^{\rm N}\] (1) where \(\Sigma_{\rm SFR}\) and \(\Sigma_{\rm gas}\) are the surface densities of SFR and gas, respectively. When \(\Sigma_{\rm gas}\) and \(\Sigma_{\rm SFR}\) are averaged over the entire star forming region of a galaxy, they give rise to a global Schmidt law. Kennicutt (1998b) found a universal global star formation law in a large sample that includes 61 normal spiral galaxies that have \(\rm H_{\alpha}\), H\({}_{\rm I}\) and CO measurements and 36 infrared-selected starburst galaxies. The observations show that both the slope \(N\sim\) 1.3-1.5 and the normalization \(A\) appear to be remarkably consistent from galaxy to galaxy. There are some variations, though. For example, Wong & Blitz (2002) reported \(N\sim\) 1.1-1.7 for a sample of seven molecule-rich spiral galaxies, depending on the correction of the observed \(\rm H_{\alpha}\) emission for extinction in deriving the star formation rate. Boissier et al. (2003) examined 16 spiral galaxies with published abundance gradients and found \(N\sim\) 2.0. Gao & Solomon (2004a) surveyed HCN luminosity, a tracer of dense molecular gas, from 65 infrared or CO-bright galaxies including nearby normal spiral galaxies, luminous infrared galaxies, and ultraluminous infrared galaxies. Based on this survey, Gao & Solomon (2004b) suggested a shallower star formation law with a power-law index of 1.0 in terms of dense molecular gas content. When \(\Sigma_{\rm gas}\) and \(\Sigma_{\rm SFR}\) are measured radially within a galaxy, a local Schmidt law can be measured. Wong & Blitz (2002) investigated the local Schmidt laws of individual galaxies in their sample. They found similar correlations in these galaxies but the normalizations and slopes vary from galaxy to galaxy, with \(N\sim\) 1.2-2.1 for total gas, assuming that extinction depends on gas column density (or, \(N\sim\) 0.8-1.4 if extinction is assumed constant). Heyer et al. (2004) reported that M33 has a much deeper slope, \(N\simeq 3.3\). The second empirical law is the star formation threshold. Stars are observed to form efficiently only above a critical gas surface density. Martin & Kennicutt (2001) studied a sample of 32 nearby spiral galaxies with well-measured \(\rm{H_{\alpha}}\) and H\({}_{2}\) profiles, and demonstrated clear surface-density thresholds in the star formation laws in these galaxies. They found that the threshold gas density (measured at the outer threshold radius where SFR

drops sharply) ranges from 0.7 to 40 \(\rm{M_{\odot}\ pc^{-2}}\) among spiral galaxies, and the threshold density for molecular gas is \(\sim\)5-10 \(\rm{M_{\odot}\ pc^{-2}}\). However, they found that the ratio of gas surface density at the threshold to the critical density for Toomre (1964) gravitational instability, \(\alpha_{Q}=\Sigma_{\rm gas}/\Sigma_{\rm crit}\), is remarkably uniform with \(\alpha_{Q}=0.69\pm 0.2\). They assumed a constant velocity dispersion of the gas, the effective sound speed, of \(c_{s}=6\) km s\({}^{-1}\). Such a density threshold applies to normal disk galaxies (e.g., Boissier et al. 2003), elliptical galaxies (e.g., Vader & Vigroux 1991), low surface brightness galaxies (van der Hulst et al., 1993), and starburst galaxies (Elmegreen, 1994). However, there are a few exceptions, such as dwarf and irregular galaxies (e.g., Hunter, Elmegreen & Baker 1998). Furthermore, inefficient star formation can be found well outside the threshold radius (Ferguson et al., 1998). What is the origin of the Schmidt laws and the star formation thresholds? The mechanisms that control star formation in galaxies, such as gravitational instability, supersonic turbulence, magnetic fields, and rotational shear are widely debated (Shu et al. 1987; Elmegreen 2002; Larson 2003; Mac Low & Klessen 2004). At least four types of models are currently discussed. The first type emphasizes self-gravity of the galactic disk (e.g., Quirk 1972; Larson 1988; Kennicutt 1989; Elmegreen 1994; Kennicutt 1998b). In these models, the Schmidt laws do not depend on the local star formation process, but are simply the results of global gravitational collapse on a free-fall time. In the second type, the global star formation rate scales with either the local dynamical time, invoking cloud-cloud collisions (e.g. Wyse 1986; Wyse & Silk 1987; Silk 1997; Tan 2000), or the local orbital time of the galactic disk (e.g. Elmegreen 1997; Hunter et al. 1998). A third type, which invokes hierarchical star formation triggered by turbulence, has been proposed by Elmegreen (2002). In this model, the Schmidt law is scale-free, and the star formation rate depends on the probability distribution function (PDF) of the gas density produced by galactic turbulence, which appears to be log-normal in simulations of turbulent molecular clouds and interstellar medium (e.g., Scalo et al. 1998; Passot & Vazquez-Semadeni 1998; Ostriker, Gammie, & Stone 1999; Klessen 2000; Wada & Norman 2001; Ballesteros-Paredes & Mac Low 2002; Padoan & Nordlund 2002; Li, Klessen & Mac Low 2003; Kravtsov 2003; Mac Low et al. 2005). Recently, Krumholz & McKee (2005) extended this analysis with additional assumptions such as the virialization of the molecular clouds and star formation efficiency to derive the star formation rate from the gas density PDFs. They successfully fitted the global Schmidt law, but their theory still contains several free or poorly constrained parameters, and does not address the observed variation in local Schmidt laws among galaxies. A fourth type appeals to the gas dynamics and thermal state of the gas to determine the star formation behavior. Struck-Marcell (1991) and citetstruck99, for example, suggest that galactic disks are in thermohydrodynamic equilibrium maintained by feedback from star formation and countercirculating radial gas flows of warm and cold gas. There is considerable debate on the star formation threshold as well. Martin & Kennicutt (2001) suggest that the threshold density is determined by the Toomre criterion (Toomre, 1964) for gravitational instability. Hunter et al. (1998) argued that the critical density for star formation in dwarf galaxies depends on the rotational shear of the disk. Wong & Blitz (2002) claimed no clear evidence for a link between \(\alpha_{Q}\) and star formation. Instead, they suggested that \(\alpha_{Q}\) is a measurement of gas fraction. Boissier et al. (2003) found that the gravitational instability criterion has limited application to their sample. Note all the models above are based on an assumption of constant sound speed for the gas. Schaye (2004) proposed a thermal instability model for the threshold, in which the velocity dispersion or effective temperature of the gas is not constant, but drops from a warm (i.e. 10\({}^{4}\) K) to a cold phase (below 10\({}^{3}\) K) at the threshold. He suggested that such a transition is able to reproduce the observed threshold density. While each of these models has more or less succeeded in explaining the Schmidt laws or the star formation threshold, a more complete picture of star formation on a galactic scale remains needed. Meanwhile, observations of other properties related to star formation in galaxies have provided more clues to the dominant mechanism that controls global star formation. An analysis of the distribution of dust in a sample of 89 edge-on, bulgeless disk galaxies by Dalcanton, Yoachim & Bernstein (2004) shows that dust lanes are a generic feature of massive disks with \(V_{\rm rot}>120\) km s\({}^{-1}\), but are absent in more slowly rotating galaxies with lower mass. These authors identify the \(V_{\rm rot}=120\) km s\({}^{-1}\) transition with the onset of gravitational instability in these galaxies, and suggest a link between the disk instability and the formation of the dust lanes which trace star formation. Color gradients in galaxies help trace their star formation history by revealing the distribution of their stellar populations (Searle, Sargent & Bagnuolo, 1973). A comprehensive study of color gradients in 121 nearby disk galaxies by Bell & de Jong (2000) shows that the star formation history of a galaxy is strongly correlated with the surface mass density. Similar conclusions were drawn by Kauffmann et al. (2003) from a sample of over \(10^{5}\) galaxies from the Sloan Digital Sky Survey. Recently, MacArthur et al. (2004) carried out a survey of 172 low-inclination galaxies spanning Hubble types S0-Irr to investigate optical and near-IR color gradients. These authors find strong correlations in age and metallicity with Hubble type, rotational velocity, total magnitude, and central surface brightness. Their results show that early type, fast rotating, luminous, or high surface brightness galaxies appear to be older and more metal-rich than their late type, slow rotating, or low surface brightness counterparts, suggesting an early and more rapid star formation history for the early type galaxies. These observations show that star formation in disks correlates well with the properties of the galaxies such as rotational velocity, velocity dispersion, and gas mass, all of which directly determine the gravitational instability of the galactic disk. This suggests that, on a galactic scale, gravitational instability controls star formation. The nonlinear development of gravitational instability and its effect on star formation on a galactic scale can be better understood through numerical modeling. There

have been many simulations of disk galaxies, including isolated galaxies with various assumptions of the gas physics and feedback effects (e.g., Thacker & Couchman 2000; Wada & Norman 2001; Noguchi 2001; Barnes 2002; Robertson et al. 2004; Li, Mac Low & Klessen 2005a; Okamoto et al. 2005), galaxy mergers (e.g., Mihos & Hernquist 1994; Barnes & Hernquist 1996; Li, Mac Low & Klessen 2004), and galaxies in a cosmological context, with different assumptions about the nature and distribution of dark matter (e.g., Katz & Gunn 1991; Navarro & Benz 1991; Katz 1992; Steinmetz & Mueller 1994; Navarro, Frenk & White 1995; Sommer-Larsen, Gelato & Vedel 1999; Steinmetz & Navarro 1999; Springel 2000; Sommer-Larsen & Dolgov 2001; Sommer-Larsen, Gotz & Portinari 2003; Springel & Hernquist 2003; Governato et al. 2004). However, in most of these simulations gravitational collapse and star formation are either not numerically resolved, or are followed with empirical recipes tuned to reproduce the observations _a priori_. There are only a handful of numerical studies that focus on the star formation laws. Early three-dimensional smoothed particle hydrodynamics (SPH) simulations of isolated barred galaxies were carried out by Friedli & Benz (1993); Friedli, Benz & Kennicutt (1994), and Friedli & Benz (1995). In Friedli & Benz (1993), the secular evolution of the isolated galaxies was followed by modeling of a two-component (gas and stars) fluid, restricting the interaction between the two to purely gravitational coupling. The simulations were improved later in Friedli & Benz (1995) by including star formation and radiative cooling. These authors found that their method to simulate star formation, based on Toomre's criterion, naturally reproduces both the density threshold of \(7\ \rm M_{\odot}\ pc^{-2}\) for star formation, and the global Schmidt law in disk galaxies. They also found that the nuclear starburst is associated with bar formation in the galactic center. Gerritsen & Icke (1997) included stellar feedback in similar two-component (gas and stars) simulations that yielded a Schmidt law with power-law index of \(\sim\) 1.3. However, these simulations included only stars and gas, and no dark matter. More recently, Kravtsov (2003) reproduced the global Schmidt law using self-consistent cosmological simulations of high-redshift galaxy formation. He argued that the global Schmidt law is a manifestation of the overall density distribution of the interstellar medium, and that the global star formation rate is determined by the supersonic turbulence driven by gravitational instabilities on large scales, with little contribution from stellar feedback. However, the strength of gravitational instability was not directly measured in this important work, so a direct connection could not be made between instability and the Schmidt laws. In order to investigate gravitational instability in disk galaxies and consequent star formation, we model isolated galaxies with a wide range of masses and gas fraction. In Li et al. (2005a, hereafter Paper I) we have described the galaxy models and computational methods, and discussed the star formation morphology associated with gravitational instability. In that paper it was shown that the nonlinear development of gravitational instability determines where and when star formation takes place, and that the star formation timescale \(\tau_{\rm SF}\) depends exponentially on the initial Toomre instability parameter for the combination of collisonless stars and collisional gas in the disk \(Q_{sg}\) derived by Rafikov (2001). Galaxies with high initial mass or gas fraction have small \(Q_{sg}\) and are more unstable, forming stars quickly, while stable galaxies with \(Q_{sg}>1\) maintain quiescent star formation over a long time. Paper I emphasized that to form a stable disk and derive the correct SFR from a numerical model, the gravitational collapse of the gas must be fully resolved (Bate & Burkert, 1997; Truelove et al., 1997) up to the density where gravitationally collapsing gas decouples from the flow. If this is done, stable disks with SFRs comparable to observed values can be derived from models using an isothermal equation of state. With insufficient resolution, however, the disk tends to collapse to the center producing much higher SFRs, as found by some previous work (e.g. Robertson et al., 2004). We analyze the relation between the SFR and the gas density, both globally and locally. In SS 2 we briefly review our computational method, galaxy models and parameters. In SS 3 we present the evolution of the star formation rate and radial distributions of both gas and star formation. We derive the global Schmidt law in SS 4, followed by a parameter study and an exploration of alternative forms of the star formation law. Local Schmidt laws are presented in SS 5. In SS 6 we investigate the star formation efficiency. The assumptions and limitations of the models are discussed in SS 7. Finally, we summarize our work in SS 8. Preliminary results on the global Schmidt law and star formation thresholds were already presented by Li, Mac Low & Klessen (2005b). ## 2. COMPUTATIONAL METHOD We here summarize the algorithms, galaxy models, and numerical parameters described in detail in Paper I. We use the SPH code GADGET, v1.1 (Springel, Yoshida & White, 2001), modified to include absorbing sink particles (Bate, Bonnell & Price, 1995) to directly measure the mass of gravitationally collapsing gas. Paper I and Jappsen et al. (2005) give detailed descriptions of sink particle implementation and interpretation. In short, a sink particle is created from the gravitationally bound region at the stagnation point of a converging flow where number density exceeds values of \(n=10^{3}\) cm\({}^{-3}\). It interacts gravitationally and inherits the mass, and linear and angular momentum of the gas. It accretes surrounding gas particles that pass within its accretion radius and are gravitationally bound. Regions where sink particles form have pressures \(P/k\sim 10^{7}\) K cm\({}^{-3}\) typical of massive star-forming regions. We interpret the formation of sink particles as representing the formation of molecular gas and stellar clusters. Note that the only regions that reach these high pressures in our simulations are dynamically collapsing. The measured mass of the collapsing gas is insensitive to the value of the cutoff-density. This is not an important free parameter, unlike in the models of Elmegreen (2002) and Krumholz & McKee (2005). Our galaxy model consists of a dark matter halo, and a disk of stars and isothermal gas. The initial galaxy structure is based on the analytical work by Mo, Mao & White (1998), as implemented numeri

The SFRs in most models shown in Figure 1 appear to decline exponentially. From Paper I, the accumulated mass of the stars formed in each galaxy can be fitted with an exponential function: \[\frac{M_{*}}{M_{\rm init}}=M_{0}\ \left[1-\exp\left({-t}/{\tau_{\rm SF}}\right )\right]\,,\] (3) where \[M_{0}=0.96\ \epsilon_{\ell}\ \{1-2.9\ \exp\left[{-1.7}/{Q_{sg,{\rm min}}} \right]\}\,,\] (4) \[\tau_{\rm SF}=\left(34\pm 7\ \mbox{Myr}\right)\ \exp\left[Q_{sg,{\rm min}}/0.2 4\right],\] (5) \(M_{\rm init}\) is the initial total gas mass, and \(\tau_{\rm SF}\) is the star formation timescale. The star formation rate can then be rewritten in the following form: \[\mbox{SFR}=\frac{dM_{*}}{dt}\propto\frac{1}{\tau_{\rm SF}}{\exp\left({-t}/{ \tau_{\rm SF}}\right)}\,.\] (6) A similar exponential form is also reported by MacArthur et al. (2004), as first suggested by Larson (1974) and Tinsley & Larson (1978). Sandage (1986) studied the star formation rate of different types of galaxies in the Local Group and proposed an alternative form for the star formation history, as explicitly formulated by MacArthur et al. (2004): \[\mbox{SFR}\propto\frac{t}{\tau_{\rm SF}^{2}}\exp\left({-t^{2}}/{\tau_{\rm SF}^ {2}}\right)\] (7) Figure 3a shows an example of model G220-1 (low-\(T\)) fitted with these two formula. Both formulae appear quite similar at intermediate times. The Sandage model captures the initial rise in star formation better, but the exponential form follows the late time behavior of our models more closely. As we only include stellar feedback implicitly by maintaining constant gas sound speed, we must be somewhat cautious about our interpretation of the late time results. In order to compare the fits, we define a parameter for relative goodness of the fit \[\chi^{2}=\sum\left([y_{s}-y_{f}]/y_{m}\right)^{2}\] (8) where \(y_{s}\) is the SFR from the simulation, \(y_{m}\) is the maximum of SFR, and \(y_{f}\) is the model function from equation (6) or (7). Note that since we do not take into account the uncertainty of each point, the absolute value of \(\chi^{2}\) has no meaning. We only compare the relative \(\chi^{2}\) values in Figure 3_b_. Both formulae fit equally well to many models, especially to those with high gas fractions that form a lot of stars early on. But for some models such as G100-1 (low-\(T\)) and G220-1 (high-\(T\)), the exponential function seems to fit noticeably better. Therefore we use the exponential form in the rest of the paper. This analysis implies that the star formation history depends quantitatively on the initial gravitational instability of a galaxy after its formation or any major perturbation. An unstable galaxy forms stars rapidly in an early time, so its stellar populations will appear older than those in a more stable galaxy. More massive galaxies are less stable than small galaxies with the same gas fraction. The different star formation histories in such galaxies may account for the downsizing effect that star formation first occurs in big galaxies at high redshift, while modern starburst galaxies are smaller (Cowie et al. 1996; Poggianti et al. 2004; Ferreras et al. 2004), and thus more stable. ### Radial Distribution of Gas and Star Formation Figure 4 shows the radial distribution of different gas components and the SFR of selected models. The gas distribution and SFR are calculated at the star formation timescale \(\tau_{\rm SF}\) derived from the fits given in Paper I. We assume that 70% of the gravitationally collapsed, high-density gas (as identified by sink particles) is in molecular form. Similarly, we identify unaccreted gas as being in atomic form. The total amount of gas is the sum of both components. Figure 4 shows that the simulated disks have gas dis Figure 3.— (_a_) Example fit of the SFR evolution curve with the exponential form (eq. 6) and the Sandage (1986) form (eq. 7) for model G220-1 (low-\(T\)) as an example. (_b_) The relative goodness of fit \(\chi^{2}\) (eq. 8) for all models for exponential (_red_) and Sandage (1986) (_black_) forms.

tributions that are mostly atomic in the outer disk but dominated by molecular gas in the central region. Observations by Wong & Blitz (2002) and Heyer et al. (2004) show that the density difference between the atomic and molecular components in the central region depends on the size and gas fraction of the galaxy. For example, \(\Sigma_{\rm H_{2}}\) in the center of NGC4321 is almost two orders of magnitude higher than \(\Sigma_{\rm H_{I}}\)(Wong & Blitz, 2002), while in M33, the difference is only about one order of magnitude (Heyer et al., 2004). A similar relation between the fraction of molecular gas and the gravitational instability of the galaxy is seen in our simulations. In our most unstable galaxies such as G220-4, the central molecular gas surface density exceeds the atomic gas surface density by more than two orders of magnitude, while in a more stable model like G220-1 (high \(T\)), the profiles of \(\Sigma_{\rm H_{2}}\) and \(\Sigma_{\rm H_{I}}\) are close to each other within one disk scale length \(R_{\rm d}\). We also find a linear correlation between the molecular gas surface density and the SFR surface density, as can be seen by their parallel radial profiles in Figure 4. (In operational terms, we find a correlation between the surface density in sink particles and the rate at which they accrete mass.) Gao & Solomon (2004b) found a tight linear correlation between the far infrared luminosity, a tracer of the star formation rate, and HCN luminosity, in agreement with our result that star formation rate and molecular gas have similar surface density profiles. The agreement between the simulations and observations supports our assumption that both molecular gas and stars form by the gravitational collapse of high density gas. Note, however, that we neglect recycling of gas from molecular clouds back into the warm atomic and dissociated or ionized medium represented by SPH particles in our simulation. Although it is possible that even that reionized gas may still quickly collapse again if the entire region is gravitationally unstable, this still constitutes an important limitation of our models that will Figure 4.— Radial profiles of atomic (SPH particles; _green dimond_), molecular (70% of sink particle mass; _blue square_), and total (_red dot_) gas surface density, as well as SFR surface density (_black dot_). \(R_{\rm d}\) is the radial disk scale length as given in Table 1. Note the solid lines are used to connect the symbols.

have to be addressed in future work. ## 4. GLOBAL SCHMIDT LAW To derive the global Schmidt law from our models, we average \(\Sigma_{\rm SFR}\) and \(\Sigma_{\rm gas}\) over the entire star forming region of each galaxy. We define the star forming region following Kennicutt (1989), using a radius chosen to encircle 80% of the mass accumulated in sink particles (denoted \(R_{80}\) hereafter). The SFR is taken from the SFR evolution curves at some chosen time. As mentioned in SS 3, 30% of the mass of sink particles is assumed to be stars, while the remaining 70% of the sink particle mass remains in molecular form. The atomic gas component is computed from the SPH particles not participating in localized gravitational collapse, that is, gas particles not accreted onto sink particles. The total is the sum of atomic and molecular gas. Figure 5 shows the global Schmidt laws derived from our simulations at the star formation time \(t=\tau_{\rm SF}\) as listed in Table 1. Note that for a few models this is just the maximum simulated time, as indicated in Table 1. (Results from different times and star formation regions are shown in the next section.) We fit the data to the total gas surface density of the models listed in Table 1 (both low \(T\) and high \(T\)). A least-square fit to the models we have run gives a simulated global Schmidt law \[\Sigma_{\rm{SFR}}=(1.1\pm 0.4\times 10^{-4}\mbox{ M}_{\odot}\mbox { yr}^{-1}\mbox{ kpc}^{-2})\] \[\times\left(\frac{\Sigma_{\rm{gas}}}{1\ \rm M_{\odot}\ {\rm pc}^{ -2}}\right)^{1.56\pm 0.09}\] (9) For comparison, the best fit to the observations by Kennicutt (1998b) gives a global Schmidt law for the total gas surface density in a sample that includes both the normal and starburst galaxies of \[\Sigma_{\rm{SFR}}=(2.5\pm 0.7\times 10^{-4}\mbox{ M}_{\odot}\mbox { yr}^{-1}\mbox{ kpc}^{-2})\] \[\times\left(\frac{\Sigma_{\rm{gas}}}{1\ \rm M_{\odot}\ {\rm pc}^{ -2}}\right)^{1.4\pm 0.15}.\] (10) The global Schmidt law derived from the simulations agrees with the observed slope within the observational errors, but has a normalization a bit lower than the observed range. There are three potential explanations for this discrepancy. First, we have not weighted the fit by the actual distribution of galaxies in mass and gas fraction. Second, as we discuss in the next subsection, we have not used models at different times in their lives weighted by the distribution of lifetimes currently observed. Third, we have only simulated isolated, normal galaxies. Our models therefore do not populate the highest \(\Sigma_{\rm SFR}\) values observed in Kennicutt (1998b), which are all starbursts occurring in interacting galaxies. These produce highly unstable disks that undergo vigorous starbursts with high SFR (e.g., Li, Mac Low & Klessen, 2004). Our result is supported by Boissier et al. (2003), who found a much deeper slope, \(N\sim 2\) in a sample of normal galaxies comparable to our more stable models. In the models, the local SFE \(\epsilon_{\ell}\) is fixed at 30%, independent of the galaxy model. A change of the assumed value of \(\epsilon_{\ell}\) changes the normalization but not the slope of our relation. For example, an extremely high value of \(\epsilon_{\ell}\sim 90\)% increases \(A\) to \(\sim 3.15\times 10^{-4}\mbox{ M}_{\odot}\mbox{ yr}^{-1}\mbox{ kpc}^{-2}\), which is just within the \(1\sigma\) upper limit of the observation by Kennicutt (1998b). If we decrease \(\epsilon_{\ell}\) to 10%, then \(A\) decreases to \(\sim 0.7\times 10^{-4}\mbox{ M}_{\odot}\mbox{ yr}^{-1}\mbox{ kpc}^{-2}\). These fairly extreme assumptions still produce results lying within the observed ranges (e.g., Wong & Blitz, 2002), suggesting that our overall results are insensitive to the exact value of the local SFE that we assume. The SFR surface densities \(\Sigma_{\rm SFR}\) change dramatically with the gas fraction in the disk. The most gas-rich models (M-4, circles) have the highest \(\Sigma_{\rm SFR}\), while the models poorer in gas (M-1, squares) have \(\Sigma_{\rm SFR}\) two orders of magnitudes lower than their gas-rich counterparts. Note that models with lower \(\Sigma_{\rm SFR}\) tend to have slightly higher scatter, because in these models fewer sink particles form, and they form over a longer period of time, resulting in higher statistical fluctuations. A resolution study is shown in Figure 6 that compares the global Schmidt law computed with different numerical resolutions. Runs with different resolution converge within 10% in both the \(\Sigma_{\rm SFR}\) and \(\Sigma_{\rm gas}\). Although numerical resolution affects the total mass collapsed, and the number and location of fragments, as shown in Paper I, the SFR at \(\tau_{\rm SF}\) seems to be less sensitive to the numerical resolution. ### A Parameter Study In order to test how sensitive the global Schmidt law is to the radius \(R\) and the time \(t\) chosen to measure it, we carry out a parameter study changing both \(R\) and \(t\) individually. To maintain consistency with the previous section, we continue to assume a constant local SFE \(\epsilon_{\ell}=30\)%. Figure 7 compares the global Schmidt laws in total gas at different radii for the star-forming region \(R=R_{50}\) and \(R_{100}\) (encircling 50% and 100% of the newly formed star clusters), while the time is fixed to \(t=\tau_{\rm SF}\). We can see that the case with \(R_{50}\) has larger scatter than that with \(R_{100}\). This is due to the larger statistical fluctuations caused by the smaller number of star clusters within this radius. The global Schmidt law with \(R=R_{100}\) is almost identical to that with \(R=R_{80}\) shown in Figure 5. Figure 8 compares the global Schmidt laws in total gas at different times \(t=0.5\tau_{\rm SF}\) and \(t=1.5\tau_{\rm SF}\) with the star formation radius fixed to \(R_{80}\). Compared to the \(t=\tau_{\rm SF}\) case, models in the \(t=0.5\tau_{\rm SF}\) case have higher \(\Sigma_{\rm SFR}\), because the SFR drops almost exponentially with time (SS 3.1). Similarly, models in the \(t=1.5\tau_{\rm SF}\) case shift to the lower right. Nevertheless, data derived from different times appear to preserve the power-law index of the Schmidt law, just differing in the normalizations. The global Schmidt law presented by Li et al. (2005b) was derived at a time when the total mass of the star clusters reached 70% of the maximum collapsed mass, which is close to 1.0 \(\tau_{\rm SF}\) in many models. The time interval \(\Delta t\) used to calculate the SFR was the time taken to grow from 30% to 70% of the maximum collapsed mass, rather than the \(\Delta t=50\) Myr used here. Nevertheless, the results presented here also agree well with those in Li et al. (2005b). Our parameter study demonstrates that the global Schmidt law depends only weakly on the details of how it is measured. The small scatter seen in Kennicutt (1998b) does suggest that additional physics not included in our modeling may be important. We should keep in mind that since we do not treat gas recycling, our models are

valid only within one gas consumption time \(\tau_{\rm SF}\). The evolution after that may become unrealistic as most of the gas is locked up in the sinks. Nevertheless, our results suggest that the Schmidt law is a universal description of gravitational collapse in galactic disks. ### Alternative Global Star Formation Laws Figure 5.— A comparison of the global Schmidt laws between our simulations and the observations. The red line is the least-square fit to the total gas of the simulated models, the black solid line is the best fit of observations from Kennicutt (1998b), while the black dotted lines indicate the observational uncertainty. The color of the symbol indicates the rotational velocity for each model (see Table 1); labels from M-1 to M-4 are sub-models with increasing gas fraction; and open and filled symbols represent low and high \(T\) models, respectively.

The existence of a well-defined global Schmidt law suggests that the star formation rate depends primarily on the gas surface density. As shown by several authors (e.g., Quirk 1972; Larson 1988; Kennicutt 1989; Elmegreen 1994; Kennicutt 1998b), a simple picture of gravitational collapse on a free-fall timescale \(\tau_{\rm ff}\propto\rho^{-1/2}\) qualitatively produces the Schmidt law. Assuming the gas surface density is directly proportional to the midplane density, \(\Sigma_{\rm gas}\propto\rho\), it follows that \(\Sigma_{\rm SFR}\propto\Sigma_{\rm gas}/\tau_{\rm ff}\propto\Sigma_{\rm gas}^{ 3/2}\). This suggests that the Schmidt law reflects the global growth rate of gas density under gravitational perturbations. An alternative scenario that uses the local dynamical timescale has been suggested by several groups (e.g. Wyse 1986; Wyse & Silk 1987; Silk 1997; Elmegreen 1997; Hunter et al. 1998; Tan 2000). In particular, Elmegreen (1997) and Hunter et al. (1998) proposed a kinematic law that accounts for the stabilizing effect of rotational shear, in which the global SFR scales with the angular velocity of the disk, \[\Sigma_{\rm SFR}\propto\frac{\Sigma_{\rm gas}}{t_{\rm orb}}\propto\Sigma_{\rm gas}\Omega\] (11) where \(t_{\rm orb}\) is the local orbital timescale and \(\Omega\) is the orbital frequency. Kennicutt (1998b) gave a simple form for the kinematical law, \[\Sigma_{\rm SFR}\simeq 0.017\ \Sigma_{\rm gas}\Omega\] (12) with the normalization corresponding to a SFR of 21% of the gas mass per orbit at the outer edge of the disk. For our analysis, we follow Kennicutt (1998b) and define \(t_{\rm orb}=2\pi R/V(R)=2\pi/\Omega(R)\), where \(V(R)\) is the rotational velocity at radius \(R\). We use the initial rotational velocity, which should not change much with time as it depends largely on the potential of the dark matter halo. Figure 9 shows the relationship between \(\Sigma_{\rm SFR}\) and \(\Sigma_{\rm gas}\Omega\) in our models. The densities of SFR \(\Sigma_{\rm SFR}\) and total gas \(\Sigma_{\rm gas}\) are calculated the same way as in Figure 5 at 1.0 \(\tau_{\rm SF}\) and \(R_{80}\), and \(\Omega(R)\) is calculated by using the ini Figure 6.— Same as Figure 5 but for the resolution study of low \(T\) models of G100-1 (_blue_) and G220-1 (_orange_). Models with total particle number of \(N_{\rm tot}=10^{5}\) (R1; _open triangle_), \(8\times 10^{5}\) (R8; _open circle_) and \(6.4\times 10^{6}\) (R64; _open square_) are shown. Models with regular resolution \(N_{\rm tot}=10^{6}\) (R10 _filled circle_) are also shown for comparison. Figure 7.— Same as Figure 5 but with different radii assumed for the star-forming region: (_a_) \(R=R_{50}\), and (_b_) \(R=R_{100}\). The time is fixed at \(t=\tau_{\rm SF}\).

tial total rotational velocity at \(R_{80}\). A least-square fit to the data gives \(\Sigma_{\rm SFR}=(0.036\pm 0.004)\times\left(\Sigma_{\rm gas}\Omega\right)^{1. 49\pm 0.1}\). This correlation has a steeper slope than the linear law given in equation (12), suggesting a discrepancy between the behavior of our models and the observed kinematical law. However, Boissier et al. (2003) recently reported a slope of \(\sim\) 1.5 for the kinematical law from observations of 16 normal disk galaxies, in agreement with our results. Examination of Figure 7 in Kennicutt (1998b) also shows that the normal galaxies, considered alone, seem to have a steeper slope than the galactic nuclei and starburst galaxies. Boissier et al. (2003) suggested several reasons for the discrepancy, the most important one being the difference between their sample of normal galaxies and the sample of Kennicutt (1998b) including many starburst galaxies and galaxy nuclei. More simulations, and models with higher SFR such as galaxy mergers are necessary to test this hypothesis. ### A New Parameterization The global Schmidt law describes global collapse in the gas disk. It does not seem to depend on the local star formation process. From Paper I and Li et al. (2005b) we know that \(\Sigma_{\rm SFR}\) correlates tightly with the strength of gravitational instability (see also Mac Low & Klessen 2004; Klessen et al. 2000; Heitsch et al. 2001). Here we quantify this correlation, using the Toomre Q parameter to measure the strength of instability. Figure 10 shows the correlation between \(\Sigma_{\rm SFR}\) and the local gravitational instability parameters \(Q_{\rm min}\). The parameters \(Q_{\rm min}\) are minimum values of the Toomre \(Q\) parameters for gas \(Q_{g,{\rm min}}(t)\), and the combination of stars and gas \(Q_{sg,{\rm min}}(t)\) at a given time \(t\), respectively. To obtain the \(Q\) parameters, we follow the approach of Rafikov (2001), as described in equations (1)-(3) of Paper I. We divide the entire galaxy disk at time \(t\) into 40 annuli, calculate the \(Q\) parameters in each annulus, then take the minimum. In the plots, the time when \(\Sigma_{\rm SFR}\) is computed is \(t=\tau_{\rm SF}\). This correlation does not change significantly with time, but the scatter becomes larger at later times because the disk becomes more clumpy, which makes the calculation of \(Q_{g,{\rm min}}(t)\) more difficult (see below). There is substantial scatter in the plots, at least partly caused by the clumpy distribution of the gas. Equations (1)-(3) for the \(Q\) parameters in Paper I are derived for uniformly distributed gas, such as in our initial conditions. As the galaxies evolve, the gas forms filaments or spiral arms probably leading to the fluctuations seen. The least-square fits to the data shown in Figure 10 give \[\Sigma_{\rm SFR}=\left(0.013\pm 0.003\ \mbox{ M}_{\odot}\mbox{ yr}^{-1}\mbox{ kpc}^{-2}\right)\] \[\times\left[Q_{sg,{\rm min}}(\tau_{\rm SF})\right]^{-1.54\pm 0.23}\] (13) \[\Sigma_{\rm SFR}=\left(0.019\pm 0.005\ \mbox{ M}_{\odot}\mbox{ yr}^{-1}\mbox{ kpc}^{-2}\right)\] \[\times\left[Q_{g,{\rm min}}(\tau_{\rm SF})\right]^{-1.12\pm 0.21}\] (14) If we take a first-order approximation, \(Q_{sg}\propto 1\ /\Sigma_{\rm gas}\), then equation (4.3) gives \(\Sigma_{\rm SFR}\propto\Sigma_{\rm gas}^{1.54}\) at \(t=\tau_{\rm SF}\), agreeing very well with the observations. The slopes derived from \(Q_{g}\) appear to be lower than those derived from \(Q_{sg}\), but are still within the slope range observed. Keep in mind that the local instability is a non-linear interaction between the stars and gas, and so is much more complicated than the linear stability analysis presented here. Also, the instability of the entire disk at a certain time is not fully represented by the minimum values of the Q parameters we employ here, although they do represent the region of fastest star formation. These factors limit our ability to derive the global Schmidt law directly from the instability analysis. Figure 8.— Same as Figure 5 but derived at different times (_a_) \(t=0.5\ \tau_{\rm SF}\) and (_b_) \(t=1.5\ \tau_{\rm SF}\). The radius for the star formation region is fixed at \(R_{80}\).

## 5. LOCAL SCHMIDT LAW The relationship between surface density of SFR \(\Sigma_{\rm SFR}\) and gas density \(\Sigma_{\rm gas}\) can also be measured as a function of radius within a galaxy, giving a local Schmidt law. Observations by Wong & Blitz (2002) and Heyer et al. (2004) show significant variations in both the indices \(N\) and normalizations \(A\) of the local Schmidt laws of individual galaxies. For example, Heyer et al. (2004) show that M33 follows the law Figure 9.— Relation between \(\Sigma_{\rm SFR}\) and \(\Sigma_{\rm gas}\Omega\). The legends are the same as in Figure 5. The black solid line is the linear relationg derived from the observations by Kennicutt (1998b), as given in our equation (12).

\[\Sigma_{\rm{SFR}}=(0.0035\pm 0.066\ \mbox{ M}_{\odot}\mbox{ yr}^{-1}\mbox{ kpc}^{-2})\] \[\times\left({\Sigma_{\rm{tot}}}/{1\ \rm M_{\odot}\ {\rm pc}^{-2}} \right)^{3.3\pm 0.07},\] (15) while Wong & Blitz (2002) show that \(N\) has a range of 1.23-2.06 in their sample. To derive local Schmidt laws, we again divide each individual galaxy into 40 radial annuli within 4 \(R_{\rm d}\), then compute \(\Sigma_{\rm gas}\) and \(\Sigma_{\rm SFR}\) in each annulus. The SFR is measured at \(t=\tau_{\rm SF}\) as in SS 4. For models where \(\tau_{\rm SF}>3\) Gyr or is beyond the simulation duration, the maximum simulated timestep is used instead, as listed in Table 1. ### Star Formation Thresholds Figure 11 shows the relation between \(\Sigma_{\rm SFR}\) and \(\Sigma_{\rm gas}\) correlations for all models in the simulations that form stars in the first 3 Gyr. With such a large number of models in one plot, it is straightforward to characterize the general features, and to compare with the observations shown in Figure 3 of Kennicutt (1998b). Similar to the individual galaxies in Kennicutt (1998b) and Martin & Kennicutt (2001), each model here shows a tight \(\Sigma_{\rm SFR}\)-\(\Sigma_{\rm gas}\) correlation, the local Schmidt law. However, \(\Sigma_{\rm SFR}\) drops dramatically at some gas surface density. This is a clear indication of a star-formation threshold. We therefore define a threshold radius \(R_{\rm th}\) as the radius that encircles 95% of the newly formed stars. The gas surface density at the threshold radius \(R_{\rm th}\) in Figure 11 has a range from \(\sim 4\rm{M}_{\odot}\ {pc}^{-2}\) for the relatively stable model G220-1 (low-\(T\)) to \(\sim 60\rm{M}_{\odot}\ {pc}^{-2}\) for the most unstable model G220-4 (high-\(T\)). Note that in some galaxies, there are also smaller dips in SFR at higher density. Martin & Kennicutt (2001) suggest that rotational shearing can cause an inner star-formation threshold. However, the inner dips in our simulations are likely due to the lack of accretion onto sink particles in the simulations after most of the gas in the central region has been consumed. Further central star formation in real galaxies would occur due to gas recycling, which we neglect, and, probably more important, after interactions with other galaxies. In the analysis of observations, a dimensionless parameter, \(\alpha_{Q}=\Sigma_{\rm th}/\Sigma_{\rm crit}=1/Q\) has been introduced to relate the star formation threshold to the Toomre unstable radius (Kennicutt, 1989). The critical radius is usually defined as the radius where \(Q_{g}=1\). With a sample of 15 spiral galaxies, Kennicutt (1989) found \(\alpha_{Q}\simeq 0.63\) by assuming a constant effective sound speed (the velocity dispersion) of the gas \(c_{s}=6\) km s\({}^{-1}\). This result was confirmed by Martin & Kennicutt (2001) with a larger sample of 32 well-studied nearby spiral galaxies, who reported a range of \(\alpha_{Q}\sim 0.3\)-1.2, with a median value of 0.69. However, Hunter et al. (1998) found \(\alpha_{Q}\simeq 0.25\) for a sample of irregular galaxies with \(c_{s}=9\) km s\({}^{-1}\). As pointed out by Schaye (2004), this derivation of \(\alpha_{Q}\) depends on the assumption of \(c_{s}\). The values of \(\alpha_{Q}\) derived from our models using their actual values of \(c_{s}\) as shown in Figure 12. We find that the value of \(\alpha_{Q}\) depends not only on the gas sound speed, but also on the gas fraction of the galaxy. For models with the same rotational velocity and gas fraction, lower gas sound speed results in a higher value of \(\alpha_{Q}\). For models with the same total mass and sound speed, higher gas fraction leads to higher \(\alpha_{Q}\). The gas-poor models in our simulations (\(f_{\rm g}=20\%\)) have a range of \(\alpha_{Q}\sim\) 0.2-1.0, agreeing roughly with observations. This again may reflect the relative stability of the nearby galaxies in the observed samples. There are several theoretical approaches to explain the presence of star formation thresholds. Martin & Kennicutt (2001) suggest that the gravitational instability model explains the thresholds well, with the deviation of \(\alpha_{Q}\) from one simply due to the non-uniform distribution of gas in real disk galaxies. Hunter et al. (1998) p Figure 10.— Correlations between \(\Sigma_{\rm SFR}\) and the minimum value of (_a_) the Toomre parameter for stars and gas \(Q_{sg}(t)\) and (_b_) the Toomre parameter for gas \(Q_{g}(t)\) at \(t=1\ \tau_{\rm SF}\). The legends are the same as in Figure 5. The solid black lines are the least-square fits to the data given in equation (4.3).

roposed a shear criterion for star forming dwarf irregular galaxies, as they appear to be sub-critical to the Toomre criterion. Schaye (2004) modeled the thermal and ionization structure of a gaseous disk. He found the critical density is about \(\Sigma_{\rm crit}\sim 3\)-10 \(\rm{M}_{\odot}\ \rm{pc}^{-2}\) with a gas velocity dispersion of \(\sim\) 10 km s\({}^{-1}\), and argued that thermal instability determines the star formation threshold in the outer disk. Our models suggest that the threshold depends on the gravitational instability of the disk. The derived \(\Sigma_{\rm crit}\) and \(\alpha_{Q}\) from our stable models (\(Q_{sg,{\rm min}}>1\)) agree well with observations, supporting the arguments of Martin & Kennicutt (2001). Figure 11.— Local Schmidt laws of all models with \(\tau_{\rm SF}<3\) Gyr. The legends are the same as in Figure 5: the color of the symbol indicates the rotational velocity for each model as given in Table 1, the shape indicates the sub-model classified by gas fraction, and open and filled symbols represent low and high \(T\) models, respectively.

(\(Q_{sg,{\rm min}}>1\)) agree well with observations, supporting the arguments of Martin & Kennicutt (2001). ### Local Correlations Between Gas and Star Formation Rate We fit the local Schmidt law to the total gas surface density within \(R_{\rm th}\), as demonstrated in Figure 13. The models in Figure 13 all have the same rotational velocity of 220 km s\({}^{-1}\) but different gas fractions and sound speeds. The local Schmidt laws of these models vary only slightly in slope and normalization. Figures 14_a_ and 14_b_ compare the slope \(N\) and normalization \(A\) of the local Schmidt laws for all models in Table 1 that form stars in the first 3 Gyr. The slope of the fit to the total gas in Figure 14a varies from about 1.2 to 1.7. Larger galaxies tend to have larger \(N\). However, the average slope is around 1.3, agreeing reasonably well with that of the global Schmidt law. There is substantial fluctuation in the normalization of fits to the total gas, as shown in Figure 14(_b_). The variation is more than an order of magnitude, with gas-rich models tending to have high \(A\). However, the average value of \(A\) settles around 2.2, agreeing surprisingly well with that of the global Schmidt law. Overall, the averaged local Schmidt law gives: \[\Sigma_{\rm{SFR}}=(2.46\pm 1.62\times 10^{-4}\ \mbox{ M}_{\odot} \ \mbox{ yr}^{-1}\mbox{ kpc}^{-2})\] \[\times\left(\frac{\Sigma_{\rm{tot}}}{1\ \rm M_{\odot}\ {\rm pc}^{ -2}}\right)^{1.31\pm 0.15}\] (16) The averaged local Schmidt law is very close to the global Schmidt law in SS 4. The _average_ slope in equation (5.2) is rather smaller than the value of \(N=3.3\) observed by Heyer et al. (2004) in M33. The galaxy M33 is very interesting. It is a nearly isolated, small disk galaxy with low luminosity and low mass. It has total mass of \(M_{\rm tot}\sim 10^{11}\ \rm M_{\odot}\) and a gas mass of \(\rm M_{\rm gas}\sim 8.0\times 10^{9}\ \rm M_{\odot}\)(Heyer et al., 2004). It is molecule-poor and sub-critical, with gas surface density is much smaller than the threshold surface density for star formation found by Martin & Kennicutt (2001). However, it is actively forming stars (Heyer et al., 2004). We do not have a model that exactly resembles M33, although a close one might be model G100-1 in terms of mass. However, the gas velocity dispersion of M33 is unknown, so we cannot make a direct comparison with our G100-1 models. In Figure 14, the low-\(T\) model G100-1 has \(N\sim 1.4\), but we have not derived a value for its high-\(T\) counterpart, as it does not form stars at all in the first 3 Gyrs. Any stars that form in a disk similar to this will likely form in spiral arms or other nonlinear density perturbations that are not well characterized by an azimuthally averaged stability analysis. If these perturbations occur in the highest surface density regions as might be expected, the local Schmidt law will have a very high slope as observed. This speculation will need to be confirmed with models reaching higher mass resolution in the future. The details of the feedback model and equation of state may also begin to play a role in this extreme case. The averaged values of our derived local Schmidt laws do agree well with the observations by Wong & Blitz (2002) of a number of other nearby galaxies. The similarity between the global and local Schmidt laws suggests a common origin of the correlation between \(\Sigma_{\rm{SFR}}\) and \(\Sigma_{\rm{gas}}\) in gravitational instability. ## 6. STAR FORMATION EFFICIENCY The SFE is poorly understood, because it is difficult in both observations and simulations to determine the timescale for gas removal and the gaseous and stellar mass within the star formation region. On the molecular cloud scale, observations of several nearby embedded clusters with mass \(M<1000\rm M_{\odot}\) indicate that the SFEs range from approximately 10-30% (Lada & Lada, 2003). However, it is thought that field stars form with SFE of only 1-5% in giant molecular clouds (e.g., Duerr, Imhoff, & Lada 1982), while the formation of a bound stellar cluster requires a local SFE \(\gtrsim\) 20-50% (e.g., Wilking & Lada 1983; Elmegreen & Efremov 1997). An analytical model including outflows by Matzner & McKee (2000) suggests that the efficiency of cluster formation is in the range of 30-50%, and that of single star formation could be anywhere in the range 25-70%. In the analysis of our simulations presented here, we convert the mass of the sink particles into stars using a fixed local SFE \(\epsilon_{\ell}=30\)%, consistent with both the observations and theoretical predictions mentioned above. This local efficiency is different from the global star formation efficiency in galaxies \(\epsilon_{g}\leq\epsilon_{\ell}\), which measures the fraction of the _total_ gas turned into stars. On a galactic scale, the star formation efficiency appears to be associated with the fraction of molecular gas (e.g., Rownd & Young 1999). The global SFE has had values derived from observations over a wide range, depend Figure 12.— The dimensionless parameter giving ratio of star formation threshold surface density to critical surface density for Toomre instability \(\alpha_{Q}=1/Q_{\rm th}\) is shown for low-\(T\) (in red) and high-\(T\) (in black) models. Open symbols give values derived using gas only, \(\alpha_{g}=1/Q_{g,{\rm th}}\), while filled symbols give values derived using both stars and gas, \(\alpha_{sg}=1/Q_{sg,{\rm th}}\). Gas fraction of disks increases from M-1 to M-4 (see Table 1).

ing on the gas distribution and the molecular gas fraction (Kennicutt, 1998b). For example, in normal galaxies \(\epsilon_{g}\simeq 2\)-10%, while in starburst galaxies \(\epsilon_{g}=10\)-50%, with a median value of 30%. One factor that appears to contribute to the differences in \(\epsilon_{g}\) is the gas content. The global SFE is generally averaged over all gas components, but since star formation correlates tightly with the local gravitational instability one expects higher global SFE in more unstable galaxies. In fact, as pointed out by Wong & Blitz (2002), most normal galaxies in the sample of Kennicutt (1998b) are molecule-poor galaxies, which seem to have high stability and low SFE, while molecule-rich starburst galaxies appear to be unstable, forming stars with high efficiency. Figure 13.— Comparisons of local Schmidt laws of galaxy models with the same rotational velocity of 220 km s\({}^{-1}\) but different gas fractions and sound speeds, as indicated in the legend. The solid lines are least-square fits to data points within the threshold radius \(R_{\rm th}\).

of Kennicutt (1998b) are molecule-poor galaxies, which seem to have high stability and low SFE, while molecule-rich starburst galaxies appear to be unstable, forming stars with high efficiency. The variation of the normalization of the local Schmidt laws in SS 5 also suggests that the global SFE varies from galaxy to galaxy. To quantitatively measure the SFE in our models, we apply the common definition of the global SFE, \[\epsilon_{g}=M_{*}/(M_{*}+M_{\rm gas})=M_{*}/M_{\rm init}\] (17) over a period of \(10^{8}\) years, an average timescale for star formation in galaxy. In this equation, \(M_{*}=\epsilon_{\ell}M_{\rm sink}\) is the mass of newly formed stars, and \(M_{\rm gas}\) includes both the remaining mass of the sink particles and the SPH particles, so that \(M_{*}+M_{\rm gas}=M_{\rm init}\) is the total mass of the initial gas. Figure 15(_a_) and (_b_) show the relation between the minimum values of the initial \(Q\) parameter \(Q_{sg,{\rm min}}\) and the global SFE normalized by the local SFE \(\epsilon_{\rm g}/\epsilon_{\ell}\). The time period is taken as the first 100 Myr after star formation starts. If we take \(\epsilon_{\ell}\) as a constant for all models, it appears that \(\epsilon_{g}\) declines as \(Q_{sg,{\rm min}}\) increases. Therefore, \(\epsilon_{g}\) is high in less stable galaxies with high mass or high gas fraction. A least-absolute-deviation fit of the data gives a linear fit of \(\epsilon_{g}/\epsilon_{\ell}=0.9-0.97\ Q_{sg,{\rm min}}\). This fit is good for values of \(Q_{sg,{\rm min}}\leq 1\). For more stable galaxies, with larger values of \(Q_{sg,{\rm min}}\), the SFE remains finite, deviating from the linear fit. Using the empirical relations we have derived from our models earlier in the paper, we can derive a better analytic expression for \(\epsilon_{g}\). Equation (17) can be combined with equation (3) in SS 3.1 to yield an equation for the global SFE \[\epsilon_{g}=M_{0}\left[1-\exp\left({-t}/{\tau_{\rm SF}}\right)\right]\] (18) We evaluate this at \(t=100\) Myr, taking the definitions of \(M_{0}\) and \(\tau_{\rm SF}\) derived from equations (4) and (5). Normalizing by the local SFE, we find \[\epsilon_{g}/\epsilon_{\ell}=0.96\times\left[1-2.88\exp\left({-1. 7}/{Q_{sg,{\rm min}}}\right)\right]\] \[\times\left[1-\exp\left(-2.9e^{-Q_{sg,{\rm min}}/0.24}\right)\right]\] (19) The function given by equation (6) is shown in Figure 15. For \(Q_{sg,{\rm min}}\leq 1.0\) it is well approximated by the much simpler linear function \[\epsilon_{g}/\epsilon_{\ell}\simeq 0.9-Q_{sg,{\rm min}}\] (20) as shown in Figure 15(_a_). At larger values of \(Q_{sg,{\rm min}}\), the exact function predicts the SFE in our models excellently as shown in Figure 15(_b_). Observational verification of this behavior is vital. ## 7. ASSUMPTIONS AND LIMITATIONS OF THE MODELS ### Isothermal Equation of State One of the two central assumptions in our model is the use of an isothermal equation of state to represent a constant velocity dispersion. This is of course a simplification, as the interstellar medium in reality has a broad range of temperatures 10 K\(<T<10^{7}\) K. However, neutral gas velocity dispersions in normal spiral galaxies cover a far more limited range, as reviewed by Kennicutt (1998b); Elmegreen & Scalo (2004); Scalo & Elmegreen (2004) and Dib et al. (2005). The characteristic \(\sigma\) increases when the averaged \(\Sigma_{\rm SFR}\) of a galaxy reaches tens of solar masses per year, but the normal galaxies in the sample with reliable measurements lie in the range \(\sim\)7-13 km s\({}^{-1}\) (e.g., Elmegreen & Elmegreen 1984; Meurer et al. 1996; van Zee et al. 1997; Stil & Israel 2002; Hippelein et al. 2003). At least two mechanisms appear viable for maintaining roughly constant velocity dispersion for the bulk of the gas in a galactic disk, supernova feedback Figure 14.— Local Schmidt law (_a_) slope \(N\) and (_b_) normalization \(A\) for all models with \(\tau_{\rm SF}<3\) Gyr. The fit is to the total gas surface density \(\Sigma_{\rm tot}\) within the threshold radius \(R_{\rm th}\). The symbols represent different models, as indicated in the legends. The dotted line in each panel indicates the linearly averaged value across the models shown.

and magnetorotational instability (Mac Low & Klessen, 2004). Three-dimensional simulations in a periodic box with parameters characteristic of the outer parts of galactic disks by Dib et al. (2005) show that supernova driving leads to constant velocity dispersions of \(\sigma\sim\) 6 km s\({}^{-1}\) for the total gas and \(\sigma_{\rm H_{\rm I}}\sim\) 3 km s\({}^{-1}\) for the H\({}_{\rm I}\) gas, independent of the supernova rate. Simulations of the feedback effects across whole galactic disks do suggest that the inner parts have slightly higher velocity dispersions (e.g. Thacker & Couchman 2000), though within the range that we consider. The magnetorotational instability in galactic disks was suggested by Sellwood & Balbus (1999) to maintain the observed velocity dispersion, a suggestion that has since been substantiated by both local (Piontek & Ostriker, 2005) and global (Dziourkevitch, Elstner, & Rudiger, 2004) numerical models. This may act even in regions with little or no active star formation. Recently, Robertson et al. (2004) presented simulations of galactic disks and claimed that an isothermal equation of state leads to a collapsed disk as the gas fragments into clumps that fall to the galactic center due to dynamical friction. However, similar behavior is seen in models by Immeli et al. (2004) who did not use an isothermal equation of state, but also ran at resolutions not satisfying the Jeans criterion (Bate & Burkert, 1997; Truelove et al., 1997). On the other hand, using essentially the same code and galaxy model as Robertson et al. (2004), but with higher resolution satisfying the Jeans criterion, we do not see this collapse. Insufficient resolution that fails to resolve the Jeans mass leads to spurious, artificial fragmentation and thus collapse. Simulations by Governato et al. (2004) suggest that some long-standing problems in galaxy formation such as the compact disk and lack of angular momentum may well be due to insufficient resolution or violation of numerical criteria. Our results lead us to agree that the isothermal equation of state is not the cause of the compact disk problem, but rather inadequate numerical resolution. Our assumption of an isothermal equation of state does, of course, rule out the treatment by our model of phenomena such as galactic winds associated with the hot phase of the interstellar medium (although the venting of supernova energy vertically may help maintain the isothermal behavior of the gas in the plane). The strong starbursts produced in some of our galaxy models will certainly cause strong galactic winds. It remains unclear whether even strong starbursts can remove substantial amounts of gas, though. Certainly they cannot in small galaxies (Mac Low & Ferrara, 1999), and larger galaxies would seem more resistant to stripping in starbursts than smaller ones. However, galactic winds will certainly influence the surroundings of starburst galaxies, as well as their observable properties. These effects should eventually be addressed in future simulations with more comprehensive gas physics and a more realistic description of the feedback from star formation. ### Sink Particles The use of sink particles enables us to directly identify high gas density regions, measure gravitational collapse, and follow the dynamical evolution of the system to a long time. We can therefore determine the star formation morphologies and rates, and study the Schmidt laws and star formation thresholds. However, one shortcoming of our sink particle implementation is that we do not include gas recycling. Once the gas collapses into the sinks, it remains locked up there. As discussed in Paper I, the bulk of the gas that does not form stars will remain in the disk and contribute to the next cycle of star formation. Also, the ejected material from massive stars will return into the gas reservoir for future star formation. Another problem is accretion. Figure 15.— The global SFE normalized by the local one \(\epsilon_{\rm g}/\epsilon_{\ell}\) versus the minimum initial gravitational instability parameter \(Q_{sg,{\rm min}}\) in linear (_a_) and log space (_b_). The legends are the same as in Figure 5. The black solid line is the least-absolute-deviation fit to the data, while the dotted line is the function given in equation (6).

In the current model, sink particles accrete until the surrounding gas is completely consumed. However, in real star clusters, the accretion would be cut-off due to stellar radiation, and the clusters will actually lose mass due to outflow and tidal stripping. These shortcomings of our sink particle technique may contribute to two limitations of our models: first, the decline of star formation rate over time due to consumption of the gas, as seen in Figure 1; second, the variation of SFR over time in the simulated global Schmidt laws in Figure 8. Nevertheless, as we have demonstrated in the previous sections, our models are valid within one gas consumption time \(\tau_{\rm SF}\), and are sufficient to investigate the dominant physics that controls gravitational collapse and star formation within that period. ### Initial Conditions of Galaxies Many nearby galaxies appear to be gas-poor and stable (\(Q_{sg}>1\)). However, their progenitors at high redshift were gas rich, so the bulk of star formation should have taken place early on. In order to test this, we vary the gas fraction (in terms of total disk mass) in the models. We also vary the total galaxy mass and thus the rotational velocity. These result in different initial stability curves. Massive, or gas-rich galaxies have low values of the \(Q\) parameters, so they are unstable, forming stars quickly and efficiently. There are no observations yet that directly measure the \(Q\) values in starburst galaxies. However, indirectly, observations by Dalcanton et al. (2004) show that dust lanes, which trace star formation, only form in unstable regions. Moreover, observations of color gradients in disk galaxies by MacArthur et al. (2004) show that massive galaxies form stars earlier and with higher efficiency. Both of these observations are naturally explained by our models. The Toomre \(Q\) parameter for gas \(Q_{g}\) differs from that for a combination of stars and gas \(Q_{sg}\) in some of our model galaxies. This leads to slightly different results in Figure 3 and Figure 10 where we compare \(Q_{sg,{\rm min}}\) and \(Q_{g,{\rm min}}\). However, we believe \(Q_{sg}\) is a better measure of gravitational instability in the disk, as it takes into account both the collisionless and the collisional components, and the interaction between them. We note that it is a simplified approach to quantify the instability of the entire disk with just a number \(Q_{sg,{\rm min}}\), as \(Q\) has a radial distribution, evolves with time, and is an azimuthally averaged quantity, but nevertheless, we find interesting regularities by making this approximation. ## 8. SUMMARY We have simulated gravitational instability in galaxies with sufficient resolution to resolve collapse to molecular cloud pressures in models of a wide range of disk galaxies with different total mass, gas fraction, and initial gravitational instability. Our calculations are based on two approximations: the gas of the galactic disk has an isothermal equation of state, representing a roughly constant gas velocity dispersion; and sink particles are used to follow gravitationally collapsed gas, which we assume to form both stars and molecular gas. With these approximations, we have derived star formation histories; radial profiles of the surface density of molecular and atomic gas and SFR; both the global and local Schmidt laws for star formation in galaxies; and the star formation efficiency. The star formation histories of our models show the exponential dependence on time given by equation 6 in agreement with, for example, the interpretation of galactic color gradients by MacArthur et al. (2004). The radial profiles of atomic and molecular gas qualitatively agree with those observed in nearby galaxies, with surface density of molecular gas peaking centrally at values much above that of the atomic gas (e.g. Wong & Blitz, 2002). The radial profile of the surface density of SFR correlates linearly with that of the molecular gas, agreeing with the observations of Gao & Solomon (2004b). Our models quantitatively reproduce the observed global Schmidt law (Kennicutt, 1998b)--the correlation between the surface density of star formation rate \(\Sigma_{\rm{SFR}}\) and the gas surface density \(\Sigma_{\rm{gas}}\)--in both the slope and normalization over a wide range of gas surface densities (eq. 4). We show that \(\Sigma_{\rm SFR}\) is strongly correlated with the gravitational instability of galaxies \(\Sigma_{\rm SFR}\propto\left[Q_{sg,{\rm min}}(\tau_{\rm SF})\right]^{-1.54\pm 0 .23}\), where \(Q_{sg,{\rm min}}(\tau_{\rm SF})\) is the local instability parameter at time \(t=\tau_{\rm SF}\) (see eq. 4.3). This correlation naturally leads to the Schmidt law. On the other hand, our models do not reproduce the correlation \(\Sigma_{\rm SFR}\sim\Sigma_{\rm gas}\Omega\) derived from kinematical models (Kennicutt, 1998b). However, they may agree better with the dependence of the normal galaxies on this quantity, as suggested by Boissier et al. (2003). The discrepancy may be caused by the lack of extreme starburst galaxies such as galaxy mergers in our set of models. The local Schmidt laws of individual galaxies clearly show evidence of star formation thresholds above a critical surface density. The threshold surface density varies with galaxy, and appears to be determined by the gravitational stability of the disk. The derived threshold parameters for our stable models cover the range of values seen in observations of normal galaxies. The local Schmidt laws have significant variations in both slope and normalization, but also cover the observational ranges reported by Wong & Blitz (2002), Boissier et al. (2003) and Heyer et al. (2004). The average normalization and slope of the local power-laws are very close to those of the global Schmidt law. Our models show that the global star formation efficiency (SFE) \(\epsilon_{g}\) can be quantitatively predicted by the gravitational instability of the disk. We have used a fixed local SFE \(\epsilon_{\ell}=30\%\) to convert the mass of the sink particles to stars in our analysis. This is a reasonable assumption for the SFE in dense, high pressure molecular clouds. The global SFE of a galaxy then can be shown to depend quantitatively on a nonlinear function (eq. 6) of the minimum Toomre parameter \(Q_{sg,{\rm min}}\) for stars and gas that can be approximated for \(Q_{sg,{\rm min}}\leq 1.0\) with the linear correlation \(\epsilon_{\rm g}/\epsilon_{\ell}\propto 0.9-Q_{sg,{\rm min}}\). More unstable galaxies have higher SFE. Massive, or gas-rich galaxies in our suite of models are unstable, forming stars quickly with high efficiency. They represent starburst galaxies. Small, or gas-poor galaxies are rather stable, forming stars slowly with low efficiency, corresponding to quiescent, normal galaxies. We thank V. Springel for making both GADGET and his galaxy initial condition generator available, as well as

\begin{table} \begin{tabular}{l l l l l l l l l l} \hline \hline \multicolumn{1}{c}{Modela [FOOTNOTE:a]Footnote a: First number is rotational velocity in km s\({}^{-1}\) at the virial radius, the second number indicates sub-model. Sub-models have varying fractions \(m_{\rm d}\) of total halo mass in their disks, and given values of \(f_{\rm g}\). Sub-models 1 – 3 have \(m_{\rm d}=0.05\), while sub-model 4 has \(m_{\rm d}=0.1\).[ENDFOOTNOTE] } & \multicolumn{1}{c}{\(f_{\rm g}\)b [FOOTNOTE:b]Footnote b: Fraction of disk mass in gas.[ENDFOOTNOTE] } & \multicolumn{1}{c}{\(R_{\rm d}\)c [FOOTNOTE:c]Footnote c: Stellar disk radial exponential scale length in kpc[ENDFOOTNOTE] } & \multicolumn{1}{c}{\(Q_{sg}\)(LT)d [FOOTNOTE:d]Footnote d: Minimum initial value of \(Q_{sg}(R)\) for low-\(T\) models.[ENDFOOTNOTE] } & \multicolumn{1}{c}{\(Q_{sg}\)(HT)e [FOOTNOTE:e]Footnote e: Minimum initial value of \(Q_{sg}(R)\) for high-\(T\) models.[ENDFOOTNOTE] } & \multicolumn{1}{c}{\(N_{\rm tot}\)f [FOOTNOTE:f]Footnote f: Total particle number in units of \(10^{6}\)[ENDFOOTNOTE] } & \multicolumn{1}{c}{\(h_{\rm g}\)g [FOOTNOTE:g]Footnote g: Gravitational softening length of gas in pc.[ENDFOOTNOTE] } & \multicolumn{1}{c}{\(m_{\rm g}\)h [FOOTNOTE:h]Footnote h: Gas particle mass in units of \(10^{4}\ \rm M_{\odot}\).[ENDFOOTNOTE] } & \multicolumn{1}{c}{\(\tau_{\rm SF}\)(LT)i [FOOTNOTE:i]Footnote i: Star formation timescale in Gyr of low-\(T\) model (from Paper I).[ENDFOOTNOTE] } & \multicolumn{1}{c}{\(\tau_{\rm SF}\)(HT)j [FOOTNOTE:j]Footnote j: Star formation timescale in Gyr of high-\(T\) model (from Paper I).[ENDFOOTNOTE] } \\ \hline G50-1 & 0.2 & 1.41 & 1.22 & 1.45 & 1.0 & 10 & 0.08 & 4.59 & \(\cdots\) \\ G50-2 & 0.5 & 1.41 & 0.94 & 1.53 & 1.0 & 10 & 0.21 & 1.28 & \(\cdots\) \\ G50-3 & 0.9 & 1.41 & 0.65 & 1.52 & 1.0 & 10 & 0.37 & 0.45 & \(\cdots\) \\ G50-4 & 0.9 & 1.07 & 0.33 & 0.82 & 1.0 & 10 & 0.75 & 0.15 & 0.53 \\ G100-1 & 0.2 & 2.81 & 1.08 & 1.27 & 6.4 & 7 & 0.10 & 2.66 & \(\cdots\) \\ G100-2 & 0.5 & 2.81 & \(\cdots\) & 1.07 & 1.0 & 10 & 1.65 & \(\cdots\) & \(\cdots\) \\ G100-3 & 0.9 & 2.81 & \(\cdots\) & 0.82 & 1.0 & 10 & 2.97 & \(\cdots\) & 1.92 \\ G100-4 & 0.9 & 2.14 & \(\cdots\) & 0.42 & 1.0 & 20 & 5.94 & \(\cdots\) & 0.15 \\ G120-3 & 0.9 & 3.38 & \(\cdots\) & 0.68 & 1.0 & 20 & 5.17 & \(\cdots\) & 0.46 \\ G120-4 & 0.9 & 2.57 & \(\cdots\) & 0.35 & 1.0 & 30 & 10.3 & \(\cdots\) & 0.16 \\ G160-1 & 0.2 & 4.51 & \(\cdots\) & 1.34 & 1.0 & 20 & 2.72 & \(\cdots\) & 3.1k [FOOTNOTE:k]Footnote k: Maximum simulation timestep instead of the star formation timescale \(\tau_{\rm SF}\).[ENDFOOTNOTE] \\ G160-2 & 0.5 & 4.51 & \(\cdots\) & 0.89 & 1.0 & 20 & 6.80 & \(\cdots\) & 0.58 \\ G160-3 & 0.9 & 4.51 & \(\cdots\) & 0.52 & 1.0 & 30 & 12.2 & \(\cdots\) & 0.30 \\ G160-4 & 0.9 & 3.42 & \(\cdots\) & 0.26 & 1.5 & 40 & 16.3 & \(\cdots\) & 0.11 \\ G220-1 & 0.2 & 6.20 & 0.65 & 1.11 & 6.4 & 15 & 1.11 & 0.28 & 3.0k [FOOTNOTE:k]Footnote k: Maximum simulation timestep instead of the star formation timescale \(\tau_{\rm SF}\).[ENDFOOTNOTE] \\ G220-2 & 0.5 & 6.20 & \(\cdots\) & 0.66 & 1.2 & 30 & 14.8 & \(\cdots\) & 0.39 \\ G220-3 & 0.9 & 6.20 & \(\cdots\) & 0.38 & 2.0 & 40 & 15.9 & \(\cdots\) & 0.25 \\ G220-4 & 0.9 & 4.71 & \(\cdots\) & 0.19 & 4.0 & 40 & 16.0 & \(\cdots\) & 0.096 \\ \hline \end{tabular} \end{table} Table 1Galaxy Models and Numerical Parameters

# Young stars and dust in AFGL437: NICMOS/HST polarimetric imaging of an outflow source Casey A. Meakin, Dean C. Hines, and Roger I. Thompson Steward Observatory, University of Arizona, Tucson, AZ 85721 ###### Abstract We present near infrared broad band and polarimetric images of the compact star forming cluster AFGL437 obtained with the NICMOS instrument aboard HST. Our high resolution images reveal a well collimated bipolar reflection nebulosity in the cluster and allow us to identify WK34 as the illuminating source. The scattered light in the bipolar nebulosity centered on this source is very highly polarized (up to 79%). Such high levels of polarization implies a distribution of dust grains lacking large grains, contrary to the usual dust models of dark clouds. We discuss the geometry of the dust distribution giving rise to the bipolar reflection nebulosity and make mass estimates for the underlying scattering material. We find that the most likely inclination of the bipolar nebulosity, south lobe inclined towards Earth, is consistent with the inclination of the large scale CO molecular outflow associated with the cluster, strengthening the identification of WK34 as the source powering it. stars: formation, ISM: jets and outflows, infrared: ISM ## 1 Introduction Polarimetric images of star forming regions have revealed nebulosities with very high degrees of linear polarization which can only be accounted for by light scattering from small dust particles at nearly right angles (e.g., Werner, Capps & Dinerstein 1983). Many of these reflection nebulosities are associated with young optically invisible protostars, and in some cases even near-infrared invisible protostars. The polarization signatures associated with these reflection nebulae offer valuable clues about the spatial distribution of scattering material and the relative location of the illuminating source(s), sometimes betraying the location of previously undetected and highly obscured objects (e.g., Weintraub & Kastner 1996a). Polarization data can also be used to constrain the composition and size distribution of the dust grains responsible for scattering (e.g., Pendleton, Tielens & Werner 1990; Kim, Martin & Hendry 1994, KMH).

AFGL437 is a well studied compact cluster (\(\sim\)0.2 pc across) of young stars and reflection nebulosity 2\(\pm\)0.5 kpc from the sun (Arquilla & Goldsmith 1984, and references therein). The youth of this cluster is inferred from the presence of B stars and associated HII regions detected using optical spectroscopy (Cohen & Kuhi 1977). Three high luminosity members were found in an infrared survey (Wynn-Williams et al. 1981), two of which are counterparts to the optical reflection nebulosity studied by Cohen & Kuhi. Other signs of active star formation include radio CO observations (Gomez et al. 1992) of a broad, large scale (\(\sim\) 1 pc) bipolar molecular outflow coincident with the infrared cluster, and observations of water masers associated with cluster members (Torelles et al., 1992). Several dozen deeply embedded, lower luminosity members of the cluster were discovered through sensitive observations in the J, H and K bands by Weintraub & Kastner (1996b; hereafter WK1996). WK1996 also presented \(\sim 1^{\prime\prime}\) resolution ground based polarimetric images of the cluster in the J, H and K bands which revealed polarization levels up to \(\sim\) 50% in the nebulosity adjacent to one of the three high luminosity members, AFGL437N. The polarization pseudo-vectors of the most highly polarized region showed a centrosymmetric pattern centered on a before unseen intensity peak called WK34 by the authors. Follow up 3.8\(\mu m\) images of the cluster with \(\sim 1^{\prime\prime}\) resolution revealed a nebulosity centered on WK34 which is extended along the molecular CO outflow axis (Weintraub et al. 1996c). We have performed follow up 1 to 2\(\mu m\) polarimetric and broad band imaging of the reflection nebulosity associated with AFGL437 using HST/NICMOS. Our observations reveal a very narrow bipolar nebula in the field with polarization levels as high as 79\(\pm\)3% at 2 \(\mu\)m. Following a presentation of the data we discuss the physical implications of the observations and constraints placed upon the underlying mass distribution. This is followed by a summary of results and concluding remarks. ## 2 NICMOS Observations NICMOS polarimetric and broad band images of the central region of the AFGL437 IR cluster were obtained with 5 observations between Dec 30, 1997 and Feb 15, 1998 utilizing both the NIC1 and NIC2 cameras. The log of observations, the cameras used for each filter and the measured PSF FWHM and rms noise levels are presented in Table 1. The 1\(\mu\)m and 2\(\mu\)m polarimetry was obtained with the NIC1 and NIC2 cameras, respectively. Images of a blank patch of sky were observed through the F222M filter and the 2\(\mu\)m polarizers for background subtraction. The plate scales are \(\sim\)0.043''for camera 1 and \(\sim\)0.076''for camera 2. The resulting field of view at 1\(\mu m\) is 11.1''\(\times\)10.9''and the field of view for all other wavelengths is 19.5''\(\times\)19.3''.

Our raw MULTIACCUM image data was calibrated using custom IDL procedures to perform dark subtraction, cosmic ray removal, linearity correction and flat fielding (Thompson et al. 1999). The field was imaged in a 7-position spiral-dither pattern with a \(0.27^{\prime\prime}\) offset to sample over bad pixels and to average over sub pixel sensitivity. The most contemporaneous dark frames and flat fields maintained by the NICMOS Instrument Definition Team (IDT) team were used for the reduction. The photometric conversion from ADU s\({}^{-1}\) pix\({}^{-1}\) to Jy pix\({}^{-1}\) are given in Table 1 (M.Rieke 2000, private communication). The images were rectified to correct for the rectangular pixels projected onto the sky by the NICMOS detector array (Thompson et al. 1998). The rectification step is essential for producing unskewed polarization position angles across the field of view (Weintraub et al. 2000a; Hines, Schmidt & Schneider 2000, hereafter HSS2000). ### Polarimetry Our polarimetric data was reduced using the HSL algorithm as described in HSS2000. The error analysis for NICMOS polarimetry is expounded in great detail in HSS2000 as well as Sparks & Axon (1999, hereafter SA1999). These errors are discussed in the presentation of the data in the following two sections. The foreground linear polarization expected at near infrared wavelengths due to grain alignment in the intervening interstellar medium is observed to be very low (\(\leq\) 4%) for line of sight extinction through dark clouds with \(A_{V}\leq 20\) (Goodman et al. 1995; see also Weintraub, et al. 2000b for a discussion). Therefore any foreground polarization in our data is expected to contribute (or cancel) only a small fraction of that which we have observed. #### 2.1.1 2\(\mu m\) Polarimetry We present the polarimetric imaging results in Figures 1 and 2. In Figure 1 we present gray scale images of the fractional polarization and the polarized flux (fractional polarization times total intensity). In Figure 2 we present the polarization pseudo-vectors overlaid on a gray scale image of the \(2\mu m\) total intensity image measured through the polarizers (see image captions for details). The measured polarization levels in the field are remarkably high and reach a maximum value of 79% and 75% in the north and south lobes, respectively, of the bipolar nebulosity which is located near the center of the field. The polarization levels along the bipolar nebula in the field is shown in Figure 3 (the location of the slice is indicated in Figure 6 by the line _AB_ which is discussed below). The polarization properties have been calculated after rebinning the raw data into 2x2 pixel bins.

The errors in the measured polarization levels and the polarization angle are functions of both the intrinsic polarization levels, \(P\), and the signal to noise (S/N) of the individual polarizer images. Signal to noise levels are \(>10\) throughout most of the field and \(>100\) in the regions of the bright bipolar nebulosity. From the error analysis in SA1999 and HSS2000 we find for \(S/N\sim 10\) and \(P>50\%\) an uncertainty in \(P\) of \(\sigma_{P}\sim 15\%\) and a dispersion in the position angle, \(\sigma_{\theta}\sim 10^{o}\). For a \(S/N>100\) and \(P>50\%\) with no flat field problems, \(\sigma_{P}<1.4\%\) and \(\sigma_{\theta}<0.5^{o}\). Flat field residuals add an error and a conservative estimate will be a factor of two increase with \(\sigma_{P}\sim 3\%\) and \(\sigma_{\theta}\sim 1^{o}\). The high degrees of polarization observed in our NICMOS images are not commonly measured from the ground and are made possible by the high spatial resolution afforded by NICMOS/HST. With a native NIC2 camera resolution of 0.076''/pixel for our 2\(\mu\)m observations and a measured FWHM of 0.175'', the effective resolution after binning the data into 2x2 pixel bins is \(\sim\)0.35''(see Table 1). Ground based observations of the AFGL437 field were made by WK1996 and the highest value of linear polarization that they measured was \(\sim 50\%\) consistent with the lower spatial resolution (\(\sim 1^{\prime\prime}\)) of their images. Similar ground-vs-HST/NICMOS "beam-depolarizing" effects were seen in observations of the Egg Nebula (Sahai et al. 1998). The imaged field consists of many point sources and extended emission. The bright point source near the center of the field is AFGL437N and near the top of the image is AFGL437W (see Figure 2). The source between the lobes of the bipolar nebulosity is WK34. The nebulosity in the field is composed of a few main components. Centered on WK34 is an elongated narrow bipolar nebulosity extending in the N-S direction. The northern end of this bipolar structure veers slightly towards the east. The southern end of this bipolar nebulosity is seen to end in an east-west "ridge" of higher surface brightness emission just north of AFGL437S. Small patches of nebulosity also surround AFGL437N, S and W. In Figure 1 we see that the the bipolar nebulosity contains the most highly polarized emission. The bipolar nebulosity is also the most prominent object in the polarized flux image (where polarized flux is the total intensity image multiplied by the image of fractional polarization). Most of the polarization pseudo-vectors, shown in Figure 2, form a centrosymmetric pattern around the center of the bipolar nebula. These pseudo-vectors deviate from centrosymmetry and align in an E-W direction within a few arcseconds of the nebular waist. The polarization levels also drop to nearly zero a few arcseconds to the east and west of the nebular center. Less pronounced centrosymmetric patterns are apparent around AFGL437N and, to a lesser degree, AFGL437S, which lies just to the south of the observed field. The polarization levels in these regions, \(P<20\%\), are much lower than surrounding WK34. The polariza

tion pseudo-vectors align along the "ridge" of high surface brightness in the image at the intersection of the centrosymmetric pattern around WK34 and AFGL437S. The "ridge" may result from an interaction between these two sources (see also section 2.2). #### 2.1.2 1 \(\mu m\) Polarimetry Our 1 micron polarimetric images suffer from a low signal to noise (S/N of a few) resulting in large uncertainties in polarization and position angle. Therefore, we restrict our attention in this data set to the polarization and photometry in a circular 0.5\({}^{\prime\prime}\) radius aperture centered on the northern lobe (the location of the aperture is shown in Figure 6). For comparison we repeat this aperture measurement on the 2 micron data. The S/N in the aperture is above 100. At 1 \(\mu m\) we measure \(P=45\pm 3\%\) with \(\theta_{p}=24\pm 1^{o}\) and at 2\(\mu m\) we measure \(P=65\pm 3\%\) and \(\theta_{p}=28\pm 1^{o}\). The aperture polarimetric and photometric data are summarized in Table 2. The southern lobe is contaminated by a point source which is most evident in the ratio images in the bottom row of Figure 7, particularly the F160W/F110W ratio image. This point source contributes a large fraction of the \(1\mu m\) flux in the region so we ignore the polarization properties of the south lobe. ### Broad Band Images In Figure 4 we present gray scale images of the intensity measured though the F110W, F160W and F222M filters as well as the flux ratio images for the filter combinations F222M/F110W, F222M/F160W and F160W/F110W. In Figure 5 we present a three color composite image of the camera 2 data. The point sources and reflection nebulosity display a large range of flux ratios. The nebulosity near the bright sources AFGL437N, S and W is relatively blue within the field and has an F222M/F110W flux ratio of \(\sim\)10. Cohen and Kuhi (1977) found that the optical spectra of the extended emission in a \(4^{\prime\prime}\times 2.7^{\prime\prime}\) aperture centered on AFGL437N and S is consistent with slightly reddened (AV~6.5) B5 stars. We detect several faint, very red point sources in our field that were not detected in the WK1996 data of the same region. The nebulosity associated with WK34 is extremely red with an F222M/F110W intensity ratio as high as \(\sim\)100 indicating either a high degree of extinction towards this nebulosity or an illuminator with an intrinsically very red spectral energy distribution. Details of the WK34 reflection nebulosity are presented in Figure 7 with axes labeled in AU assuming a distance of 2 kpc. Figure 6 indicates the region and orientation of this closeup view relative

to the whole field. The data in Figure 7 has been rotated such that the principle axis of the bipolar nebulosity lies vertically. We fit this axis to the inner \(10^{\prime\prime}\) of the nebulosity where the axial symmetry is highest. We constrained the axis to go through WK34 and the intensity peaks in the north and south lobes. The position angle we fit is 100\({}^{o}\) east through north. We over plot this axis on the F222M intensity image in Figure 6 as line _AB_ and its perpendicular as line _CD_. An abrupt change in color is seen across an east-west "ridge" of brighter emission in the southern end of the field (see the F160W image in Figure 4 at the offset position \(\sim\)(5.0,5.0) and compare with the color composite image in Figure 5). The nebulosity north of the "ridge" is a relatively red feature in the field, consistent with it being illuminated by WK34, while just south the nebulosity is much bluer consistent with the B5 spectrum of AFGL437S. Patchy and filamentary dark features, possibly dust patches, are also apparent in the intensity and flux ratio images. ## 3 Discussion The most striking feature in the observed field is the bipolar reflection nebulosity extending in the N-S direction near the center of the field. It dominates the polarization and the polarized flux images (Figures 1 & 2). In this section we discuss this prominent bipolar nebula and the source near its center, WK34. Complementary contour plots of the region centered on the WK34 source (Figure 7) are presented in Figure 8. In the following subsections we discuss the nature of the illuminating source and the underlying mass distribution which gives rise to the reflection nebulosity. ### The Illuminating Source The polarization levels measured in the bipolar lobes are the highest in the entire field with values in the north and south lobes of 79\(\pm\)3% and 75\(\pm\)3%, respectively. The centrosymmetric polarization pseudo-vectors which surround the center of this nebulosity together with the very high percentage polarization suggests that this nebulosity is being illuminated by a single source at its center and that much of the illuminators light is singly scattered at near right angles into our line of sight and have traversed optically thin paths. The geometry of single scattering allows us to calculate the position of the illuminating source in the bipolar nebulosity by centroiding the normals to the polarization pseudo vectors. This works because an unpolarized photon scattering from a small particle (such as a dust

grain) acquires linear partial polarization in a direction perpendicular to the scattering plane (the plane containing the paths of the incident and scattered photons). We carried out a procedure to locate the illuminating source described in Weintraub et al. (2000a). We used only those pixels with \(P>50\%\) and a \(S/N>50\) for our centroiding calculation. The position that we find for the illuminating source using this method is within 2 pixels (\(<0.15^{\prime\prime}\)) of the centroid of the unresolved PSF at the equator of the bipolar object, i.e., WK34. This result strongly supports the original suggestion by WK1996 that this source is indeed illuminating the nebulosity. Furthermore, since we see an unresolved point source at this location it is very likely that we are imaging the source directly. ### The Nature of WK34 The point like source at the waist of the bipolar nebula, WK34, is seen in all of our broad band images. In both the F222M and F160W images we see the characteristic NICMOS PSF superposed on a patch of nebulosity (Figure 7). The PSF is more difficult to discern in the F110W image but an intensity peak is clearly apparent and its centroid is within a fraction of a pixel of the centroid of the PSF in the F160W and F222M images. Photometry was performed in each filter by subtracting a scaled field star PSF from the same image. The dominant source of uncertainty in this photometry arises from the difficulty in gauging a good subtraction due to the patchy distribution of background nebulosity. The WK34 photometry with conservative error estimates is summarized in Table 3. The emission from the WK34 source, presumably a young stellar object still in the outflow epoch, is likely to arise from multiple components including a photosphere, an accretion disk, as well as heated ambient material from which the star formed. Light scattering by ambient material in the vicinity of the star is also thought likely to affect the near infrared spectrum. Model spectral energy distributions of low mass young stellar objects including these components of emission have been calculated by Adams, Lada & Shu (1987). The WK34 photometry is compatible with these models which suggests that it is a low mass, low luminosity protostar. Observations at longer wavelengths are needed for a robust measure of the bolometric luminosity of this source. Nevertheless, there is additional evidence that the WK34 source is a low luminosity protostar including: (i) that the bulk of the cluster luminosity (L=10\({}^{4}\)L\({}_{\odot}\) at 2 kpc; Parmar et al. 1987) can be accounted for by the three early B ZAMS stars present in the cluster and, (ii) that the WK34 source lacks an HII region (determined by contemporaneous \(P\alpha\) NICMOS observations to be presented in another paper) indicating the lack of a hard ionizing continuum usually associated with high luminosity sources

. ### The Underlying Mass Distribution Many optical and near-infrared reflection nebulae associated with low mass protostars have been successfully modeled as rotationally flattened protostellar envelopes with variously shaped evacuated cavities and an accretion disk (e.g. Whitney & Hartmann, 1993; Kenyon et al. 1993; Wood et al. 2001). Associated model SEDs have been made for a wide range of wavelengths providing a theoretical underpinning to the multiwavelength studies of YSOs (Adams, Lada & Shu, 1987). We find, however, that similar models fail to reproduce the reflection nebula associated with WK34. The most striking features which distinguish the bipolar nebula in our field are: (1) The appearance of very distinct, well separated lobes forming the bipolar nebula. (2) The distance between the intensity maximum in each lobe is separated by a large distance (\(\sim\) 5000 AU, for a cluster distance of 2 kpc) relative to the overall nebular size. (3) The nebular lobes are much longer than they are broad. Each of these characteristics requires a rotationally flattened envelope model with parameters outside a reasonable range, indicating the inadequacy of this model to explain our observations. For example, modeling the nebula with a rotating collapsing cloud model such as that described by Tereby, Shu & Cassen (1984) requires a centrifugal radius much larger than \(\sim\)2000 AU to explain the large separation between lobes, but then fails to produce the observed narrowness of the lobes. After an exhaustive study of parameter space with a single scattering radiative transfer code we find that no reasonable combination of rotating envelope, evacuated cavities and accretion disk can explain the observations adequately. The small effects of multiple scattering are likely to exacerbate the modeling by contributing extra illumination at the nebular waist. An alternative to the evacuated cavity model is one in which the bipolar reflection nebula is due to a large amount of outflow material ejected by the central source along the nebular axis. The observed bipolarity of such an _outflow nebula_ can then be further accentuated by the presence of an obscuring torus of material surrounding the central illuminating source, perhaps the remnant of the infalling parent envelope (see schematic diagram in Figure 9). This geometry is consistent with the pattern of polarization vectors which deviate from centrosymmetry near the waist of the bipolar nebulosity where they align along the equator of the nebula (see Figure 2). This type of polarization signature has been called a "polarization disk" and has been shown to be a phenomena of multiple scatterings in the presence of an optically thick equatorial disk (Bastien & Menard, 1988; Whitney & Hartmann, 1993). This polarization signature arises on the observer side of an optically thick disk being illuminated from the bipolar lobes: we are seeing photons scattered _over_ an optically thick disk into our line of sight. The location of the "null points", or regions of low polarization on either side of the "polarization disk", give us a rough estimate of the size of the optically thick disk. From Figure 2 we estimate a disk radius of \(\sim\)1000 AU. This pattern is common in

the bipolar nebulosity associated with both YSOs as well as protoplanetary nebulae such as the Egg Nebula (Sahai et al. 1998) and OH231.8+4.2. The latter object, also known as the Rotten Egg Nebula because of its sulfur content, is one of the few other astronomical objects with measured infrared polarization levels as high as those presented here (Ageorges & Walsh 2000; Meakin et al. 2003). The high levels of observed polarization constrain the size of dust particles responsible for scattering. The grain model proposed to explain the extinction in molecular clouds by KMH is only capable of polarizing 2\(\mu\)m light to a maximum of \(\sim\)70% (Weintraub, Goodman, & Akeson, 2000b). This is due to a component of large particles in the grain size distribution of this model. It is likely that the particles in the reflection nebula observed here are composed mainly of particles much smaller than the observed wavelength. The existence of small particles in the outflow lobes may be related to the outflow mechanism. Dust grains may be selectively accelerated into the outflow material based on size, or they may be processed by shocks or photodisentegration processes which occur during the star formation process. #### 3.3.1 Physical Parameter Estimates The relationship between the scattering optical depth through the lobe and the density is \(\tau_{los}=\bar{\rho_{d}}\Delta S\kappa_{s}\) where \(\bar{\rho_{d}}\) is the average lobe dust density, \(\Delta S\) is the line of sight extent of the nebula, and \(\kappa_{s}\) is the scattering opacity. If we assume that the nebula is optically thin, \(\tau_{los}<1\), we have: \[\bar{\rho}_{d}<\frac{1}{\Delta S\kappa_{s}}.\] (1) From Figure 8 we estimate a total lobe thickness \(\Delta S\approx 2000\) AU, assuming that the nebula is roughly cylindrical and that the 2\(\mu\)m intensity image traces its extent. The mass scattering opacity for a spherical dust grain with radius \(a\) is, \[\kappa_{s}=\omega Q_{ext}\frac{\pi a^{2}}{\rho_{i}4\pi a^{3}/3}=\omega Q_{ext} \frac{3}{4a\rho_{i}},\] (2) where \(\rho_{i}\) is the density of the material composing the dust, \(Q_{ext}\) is the extinction efficiency (proportionality between geometric cross section and extinction cross section), and \(\omega\) is the dust albedo (ratio between scattering and extinction cross section). Both \(Q_{ext}\) and \(\omega\) depend on the optical constants of the dust material and the ratio of the particle size to the wavelength. For the "astronomical silicates" and the graphite materials described by Draine & Lee (1984) and for particle sizes ranging between 0.1 and 1 \(\mu\)m, at near infrared wavelengths the product \(\omega Q_{ext}\) varies from close to zero to a few. We therefore expect a

scattering mass opacity to be of order \(\kappa_{s}\sim 1/\rho_{i}a\sim 10^{6}\)cm\({}^{2}\) g\({}^{-1}\) for material density (in g cm\({}^{-3}\)) and particle size (in microns) both of order unity. The average mass density of dust grains in the nebula for a line of sight through the nebular lobes where \(\tau\sim 1\) will then be of order \(\bar{\rho}_{d}\sim 10^{-13}\) g cm\({}^{-3}\). In the optically thin scattering limit, the intensity variation along the line of sight is proportional to the line of sight scattering optical depth and the flux from the central illuminating source which is \(F^{*}\propto L^{*}r^{-2}\), modulo any internal extinction between the source and the scattering location. The scattered light intensity variation with distance from the central source is then expected to vary as, \[I\sim\bar{\rho}_{d}\Delta Sr^{-2},\] (3) where \(r\) is the distance between the central source and scattering location. The intensity variation along the nebular axis is plotted in Figure 10 on a log-linear and log-log plot. The intensity is seen to drop off with distance from the central source with a roughly power law dependence, \(I\propto r^{\beta}\) with \(\beta\approx\)-3.0 for \(r>1\arcsec\). Assuming that the lobe depth, \(\Delta S\), is roughly constant in the scattering lobe then the inferred average line of sight dust density decreases inversely with distance from the central source, \(\bar{\rho}_{d}\approx\bar{\rho}_{d,0}(r/r_{0})^{-1}\). Integrating this distribution the _dust mass_ in the scattering lobe is, \[M_{l}=\frac{\pi\Delta S^{2}r_{0}}{4}\bar{\rho}_{d}(r_{0})\ln(r_{1}/r_{0})\sim 1 0^{27}\hbox{g},\] (4) where the integration is taken between \(r_{0}\sim 1\arcsec\) and \(r_{1}\sim 3\arcsec\), a lobe width of \(\Delta S\sim 2000\)AU is used, and \(\bar{\rho}_{d,0}=\bar{\rho}_{d}(r_{0})\) is taken as our previous order of magniture estimate, \(\rho_{d}\sim 10^{-13}\) g cm\({}^{-3}\). Inferring the total mass in the lobes requires knowledge of the gas to dust mass ratio, which may be much larger than the canonical value of \(\sim\)100 in the diffuse ISM due to grain destruction processes that may be occurring in the outflow. A great deal more information can be garnered from the infrared data presented in this paper by comparing it to observations at other wavelengths. For instance, high resolution CO observations of the nebula can provide a more robust map of the underlying mass distribution as well as the velocity structure. The velocity of the material can be used to test the hypothesis that we are seeing an outflow nebula, as opposed to an illuminated evacuated cavity. The combination of a molecular map and near infrared scattered light images at comparable resolution should be able to provide strong constraints on the nature of the dust particles in the outflow by providing more robust estimates of mass opacities. Dust properties may be varying strongly with location in the nebula due to the interaction of

the outflow with the ambient cloud material through shocks and photodissociation processes. These processes play an important role in the life cycle of dust in the universe, and may be potentially useful probes of the outflow mechanism operating in YSOs. #### 3.3.2 Nebular Inclination We conclude this section with a comment on the nebular inclination, noting that asymmetries in the morphology between the north and south lobes can be used as a constraint. It is a general feature of bipolar reflection nebula with mass distributions that have equatorial density enhancements that for small inclinations (out of the plane of the sky) the lobe tilted towards the observer has (1) a higher surface brightness, (2) is broader, and (3) peaks closer to the central illuminating source. These features arise from the relative amounts of obscuration caused by the equatorial material in projection against the illuminated lobes. All three of these features can be clearly seen in the contour plots presented in Figure 8 and the intensity profile in Figure 10 indicating that it is the _south lobe that is tilted towards the Earth_. ### Interaction with Environment Although the beam size in the \({}^{12}\)CO J=(2-1) maps of Gomez et al (1992) is comparable to the size of the entire NICMOS field of view, interesting correlations in morphology exist between these two data sets. A finger of high intensity emission is discernible in the CO maps which is aligned with the WK34 bipolar nebulosity. This finger of CO emission sweeps off towards the east, as though an extension of the similarly shaped infrared nebulosity seen in our images. The observed near infrared reflection nebulosity traces the polar axis of a fairly well collimated outflow emanating from WK34 on scales of \(\sim 1000\) AU. The ambient gas in the region may be redirecting the northern part of this outflow towards the east. This might explain why the geometric center of the large scale molecular outflow does not lie directly over the infrared cluster. The connection between the bipolar nebulosity and the larger scale outflow is further reinforced by the fact that the inclination of WK34 implied by the morphology of the infrared nebulosity (S lobe tilted toward Earth) is consistent with the orientation of the large scale molecular outflow (S lobe is blue shifted). ## 4

Weintra

Steward Observatory, University of Arizona, Tucson, AZ 85721 ###### Abstract We present near infrared broad band and polarimetric images of the compact star forming cluster AFGL437 obtained with the NICMOS instrument aboard HST. Our high resolution images reveal a well collimated bipolar reflection nebulosity in the cluster and allow us to identify WK34 as the illuminating source. The scattered light in the bipolar nebulosity centered on this source is very highly polarized (up to 79%). Such high levels of polarization implies a distribution of dust grains lacking large grains, contrary to the usual dust models of dark clouds. We discuss the geometry of the dust distribution giving rise to the bipolar reflection nebulosity and make mass estimates for the underlying scattering material. We find that the most likely inclination of the bipolar nebulosity, south lobe inclined towards Earth, is consistent with the inclination of the large scale CO molecular outflow associated with the cluster, strengthening the identification of WK34 as the source powering it. stars: formation, ISM: jets and outflows, infrared: ISM ## 1 Introduction Polarimetric images of star forming regions have revealed nebulosities with very high degrees of linear polarization which can only be accounted for by light scattering from small dust particles at nearly right angles (e.g., Werner, Capps & Dinerstein 1983). Many of these reflection nebulosities are associated with young optically invisible protostars, and in some cases even near-infrared invisible protostars. The polarization signatures associated with these reflection nebulae offer valuable clues about the spatial distribution of scattering material and the relative location of the illuminating source(s), sometimes betraying the location of previously undetected and highly obscured objects (e.g., Weintraub & Kastner 1996a). Polarization data can also be used to constrain the composition and size distribution of the dust grains responsible for scattering (e.g., Pendleton, Tielens & Werner 1990; Kim, Martin & Hendry 1994, KMH). AFGL437 is a well studied compact cluster (\(\sim\)0.2 pc across) of young stars and reflection nebulosity 2\(\pm\)0.5 kpc from the sun (Arquilla & Goldsmith 1984, and references therein). The youth of this cluster is inferred from the presence of B stars and associated HII regions detected using optical spectroscopy (Cohen & Kuhi 1977). Three high luminosity members were found in an infrared survey (Wynn-Williams et al. 1981), two of which are counterparts to the optical reflection nebulosity studied by Cohen & Kuhi. Other signs of active star formation include radio CO observations (Gomez et al. 1992) of a broad, large scale (\(\sim\) 1 pc) bipolar molecular outflow coincident with the infrared cluster, and observations of water masers associated with cluster members (Torelles et al., 1992). Several dozen deeply embedded, lower luminosity members of the cluster were discovered through sensitive observations in the J, H and K bands by Weintraub & Kastner (1996b; hereafter WK1996). WK1996 also presented \(\sim 1^{\prime\prime}\) resolution ground based polarimetric images of the cluster in the J, H and K bands which revealed polarization levels up to \(\sim\) 50% in the nebulosity adjacent to one of the three high luminosity members, AFGL437N. The polarization pseudo-vectors of the most highly polarized region showed a centrosymmetric pattern centered on a before unseen intensity peak called WK34 by the authors. Follow up 3.8\(\mu m\) images of the cluster with \(\sim 1^{\prime\prime}\) resolution revealed a nebulosity centered on WK34 which is extended along the molecular CO outflow axis (Weintraub et al. 1996c). We have performed follow up 1 to 2\(\mu m\) polarimetric and broad band imaging of the reflection nebulosity associated with AFGL437 using HST/NICMOS. Our observations reveal a very narrow bipolar nebula in the field with polarization levels as high as 79\(\pm\)3% at 2 \(\mu\)m. Following a presentation of the data we discuss the physical implications of the observations and constraints placed upon the underlying mass distribution. This is followed by a summary of results and concluding remarks. ## 2 NICMOS Observations NICMOS polarimetric and broad band images of the central region of the AFGL437 IR cluster were obtained with 5 observations between Dec 30, 1997 and Feb 15, 1998 utilizing both the NIC1 and NIC2 cameras. The log of observations, the cameras used for each filter and the measured PSF FWHM and rms noise levels are presented in Table 1. The 1\(\mu\)m and 2\(\mu\)m polarimetry was obtained with the NIC1 and NIC2 cameras, respectively. Images of a blank patch of sky were observed through the F222M filter and the 2\(\mu\)m polarizers for background subtraction. The plate scales are \(\sim\)0.043''for camera 1 and \(\sim\)0.076''for camera 2. The resulting field of view at 1\(\mu m\) is 11.1''\(\times\)10.9''and the field of view for all other wavelengths is 19.5''\(\times\)19.3''. Our raw MULTIACCUM image data was calibrated using custom IDL procedures to perform dark subtraction, cosmic ray removal, linearity correction and flat fielding (Thompson et al. 1999). The field was imaged in a 7-position spiral-dither pattern with a \(0.27^{\prime\prime}\) offset to sample over bad pixels and to average over sub pixel sensitivity. The most contemporaneous dark frames and flat fields maintained by the NICMOS Instrument Definition Team (IDT) team were used for the reduction. The photometric conversion from ADU s\({}^{-1}\) pix\({}^{-1}\) to Jy pix\({}^{-1}\) are given in Table 1 (M.Rieke 2000, private communication). The images were rectified to correct for the rectangular pixels projected onto the sky by the NICMOS detector array (Thompson et al. 1998). The rectification step is essential for producing unskewed polarization position angles across the field of view (Weintraub et al. 2000a; Hines, Schmidt & Schneider 2000, hereafter HSS2000). ### Polarimetry Our polarimetric data was reduced using the HSL algorithm as described in HSS2000. The error analysis for NICMOS polarimetry is expounded in great detail in HSS2000 as well as Sparks & Axon (1999, hereafter SA1999). These errors are discussed in the presentation of the data in the following two sections. The foreground linear polarization expected at near infrared wavelengths due to grain alignment in the intervening interstellar medium is observed to be very low (\(\leq\) 4%) for line of sight extinction through dark clouds with \(A_{V}\leq 20\) (Goodman et al. 1995; see also Weintraub, et al. 2000b for a discussion). Therefore any foreground polarization in our data is expected to contribute (or cancel) only a small fraction of that which we have observed. #### 2.1.1 2\(\mu m\) Polarimetry We present the polarimetric imaging results in Figures 1 and 2. In Figure 1 we present gray scale images of the fractional polarization and the polarized flux (fractional polarization times total intensity). In Figure 2 we present the polarization pseudo-vectors overlaid on a gray scale image of the \(2\mu m\) total intensity image measured through the polarizers (see image captions for details). The measured polarization levels in the field are remarkably high and reach a maximum value of 79% and 75% in the north and south lobes, respectively, of the bipolar nebulosity which is located near the center of the field. The polarization levels along the bipolar nebula in the field is shown in Figure 3 (the location of the slice is indicated in Figure 6 by the line _AB_ which is discussed below). The polarization properties have been calculated after rebinning the raw data into 2x2 pixel bins. The errors in the measured polarization levels and the polarization angle are functions of both the intrinsic polarization levels, \(P\), and the signal to noise (S/N) of the individual polarizer images. Signal to noise levels are \(>10\) throughout most of the field and \(>100\) in the regions of the bright bipolar nebulosity. From the error analysis in SA1999 and HSS2000 we find for \(S/N\sim 10\) and \(P>50\%\) an uncertainty in \(P\) of \(\sigma_{P}\sim 15\%\) and a dispersion in the position angle, \(\sigma_{\theta}\sim 10^{o}\). For a \(S/N>100\) and \(P>50\%\) with no flat field problems, \(\sigma_{P}<1.4\%\) and \(\sigma_{\theta}<0.5^{o}\). Flat field residuals add an error and a conservative estimate will be a factor of two increase with \(\sigma_{P}\sim 3\%\) and \(\sigma_{\theta}\sim 1^{o}\). The high degrees of polarization observed in our NICMOS images are not commonly measured from the ground and are made possible by the high spatial resolution afforded by NICMOS/HST. With a native NIC2 camera resolution of 0.076''/pixel for our 2\(\mu\)m observations and a measured FWHM of 0.175'', the effective resolution after binning the data into 2x2 pixel bins is \(\sim\)0.35''(see Table 1). Ground based observations of the AFGL437 field were made by WK1996 and the highest value of linear polarization that they measured was \(\sim 50\%\) consistent with the lower spatial resolution (\(\sim 1^{\prime\prime}\)) of their images. Similar ground-vs-HST/NICMOS "beam-depolarizing" effects were seen in observations of the Egg Nebula (Sahai et al. 1998). The imaged field consists of many point sources and extended emission. The bright point source near the center of the field is AFGL437N and near the top of the image is AFGL437W (see Figure 2). The source between the lobes of the bipolar nebulosity is WK34. The nebulosity in the field is composed of a few main components. Centered on WK34 is an elongated narrow bipolar nebulosity extending in the N-S direction. The northern end of this bipolar structure veers slightly towards the east. The southern end of this bipolar nebulosity is seen to end in an east-west "ridge" of higher surface brightness emission just north of AFGL437S. Small patches of nebulosity also surround AFGL437N, S and W. In Figure 1 we see that the the bipolar nebulosity contains the most highly polarized emission. The bipolar nebulosity is also the most prominent object in the polarized flux image (where polarized flux is the total intensity image multiplied by the image of fractional polarization). Most of the polarization pseudo-vectors, shown in Figure 2, form a centrosymmetric pattern around the center of the bipolar nebula. These pseudo-vectors deviate from centrosymmetry and align in an E-W direction within a few arcseconds of the nebular waist. The polarization levels also drop to nearly zero a few arcseconds to the east and west of the nebular center. Less pronounced centrosymmetric patterns are apparent around AFGL437N and, to a lesser degree, AFGL437S, which lies just to the south of the observed field. The polarization levels in these regions, \(P<20\%\), are much lower than surrounding WK34. The polarization pseudo-vectors align along the "ridge" of high surface brightness in the image at the intersection of the centrosymmetric pattern around WK34 and AFGL437S. The "ridge" may result from an interaction between these two sources (see also section 2.2). #### 2.1.2 1 \(\mu m\) Polarimetry Our 1 micron polarimetric images suffer from a low signal to noise (S/N of a few) resulting in large uncertainties in polarization and position angle. Therefore, we restrict our attention in this data set to the polarization and photometry in a circular 0.5\({}^{\prime\prime}\) radius aperture centered on the northern lobe (the location of the aperture is shown in Figure 6). For comparison we repeat this aperture measurement on the 2 micron data. The S/N in the aperture is above 100. At 1 \(\mu m\) we measure \(P=45\pm 3\%\) with \(\theta_{p}=24\pm 1^{o}\) and at 2\(\mu m\) we measure \(P=65\pm 3\%\) and \(\theta_{p}=28\pm 1^{o}\). The aperture polarimetric and photometric data are summarized in Table 2. The southern lobe is contaminated by a point source which is most evident in the ratio images in the bottom row of Figure 7, particularly the F160W/F110W ratio image. This point source contributes a large fraction of the \(1\mu m\) flux in the region so we ignore the polarization properties of the south lobe. ### Broad Band Images In Figure 4 we present gray scale images of the intensity measured though the F110W, F160W and F222M filters as well as the flux ratio images for the filter combinations F222M/F110W, F222M/F160W and F160W/F110W. In Figure 5 we present a three color composite image of the camera 2 data. The point sources and reflection nebulosity display a large range of flux ratios. The nebulosity near the bright sources AFGL437N, S and W is relatively blue within the field and has an F222M/F110W flux ratio of \(\sim\)10. Cohen and Kuhi (1977) found that the optical spectra of the extended emission in a \(4^{\prime\prime}\times 2.7^{\prime\prime}\) aperture centered on AFGL437N and S is consistent with slightly reddened (AV~6.5) B5 stars. We detect several faint, very red point sources in our field that were not detected in the WK1996 data of the same region. The nebulosity associated with WK34 is extremely red with an F222M/F110W intensity ratio as high as \(\sim\)100 indicating either a high degree of extinction towards this nebulosity or an illuminator with an intrinsically very red spectral energy distribution. Details of the WK34 reflection nebulosity are presented in Figure 7 with axes labeled in AU assuming a distance of 2 kpc. Figure 6 indicates the region and orientation of this closeup view relative to the whole field. The data in Figure 7 has been rotated such that the principle axis of the bipolar nebulosity lies vertically. We fit this axis to the inner \(10^{\prime\prime}\) of the nebulosity where the axial symmetry is highest. We constrained the axis to go through WK34 and the intensity peaks in the north and south lobes. The position angle we fit is 100\({}^{o}\) east through north. We over plot this axis on the F222M intensity image in Figure 6 as line _AB_ and its perpendicular as line _CD_. An abrupt change in color is seen across an east-west "ridge" of brighter emission in the southern end of the field (see the F160W image in Figure 4 at the offset position \(\sim\)(5.0,5.0) and compare with the color composite image in Figure 5). The nebulosity north of the "ridge" is a relatively red feature in the field, consistent with it being illuminated by WK34, while just south the nebulosity is much bluer consistent with the B5 spectrum of AFGL437S. Patchy and filamentary dark features, possibly dust patches, are also apparent in the intensity and flux ratio images. ## 3 Discussion The most striking feature in the observed field is the bipolar reflection nebulosity extending in the N-S direction near the center of the field. It dominates the polarization and the polarized flux images (Figures 1 & 2). In this section we discuss this prominent bipolar nebula and the source near its center, WK34. Complementary contour plots of the region centered on the WK34 source (Figure 7) are presented in Figure 8. In the following subsections we discuss the nature of the illuminating source and the underlying mass distribution which gives rise to the reflection nebulosity. ### The Illuminating Source The polarization levels measured in the bipolar lobes are the highest in the entire field with values in the north and south lobes of 79\(\pm\)3% and 75\(\pm\)3%, respectively. The centrosymmetric polarization pseudo-vectors which surround the center of this nebulosity together with the very high percentage polarization suggests that this nebulosity is being illuminated by a single source at its center and that much of the illuminators light is singly scattered at near right angles into our line of sight and have traversed optically thin paths. The geometry of single scattering allows us to calculate the position of the illuminating source in the bipolar nebulosity by centroiding the normals to the polarization pseudo vectors. This works because an unpolarized photon scattering from a small particle (such as a dust grain) acquires linear partial polarization in a direction perpendicular to the scattering plane (the plane containing the paths of the incident and scattered photons). We carried out a procedure to locate the illuminating source described in Weintraub et al. (2000a). We used only those pixels with \(P>50\%\) and a \(S/N>50\) for our centroiding calculation. The position that we find for the illuminating source using this method is within 2 pixels (\(<0.15^{\prime\prime}\)) of the centroid of the unresolved PSF at the equator of the bipolar object, i.e., WK34. This result strongly supports the original suggestion by WK1996 that this source is indeed illuminating the nebulosity. Furthermore, since we see an unresolved point source at this location it is very likely that we are imaging the source directly. ### The Nature of WK34 The point like source at the waist of the bipolar nebula, WK34, is seen in all of our broad band images. In both the F222M and F160W images we see the characteristic NICMOS PSF superposed on a patch of nebulosity (Figure 7). The PSF is more difficult to discern in the F110W image but an intensity peak is clearly apparent and its centroid is within a fraction of a pixel of the centroid of the PSF in the F160W and F222M images. Photometry was performed in each filter by subtracting a scaled field star PSF from the same image. The dominant source of uncertainty in this photometry arises from the difficulty in gauging a good subtraction due to the patchy distribution of background nebulosity. The WK34 photometry with conservative error estimates is summarized in Table 3. The emission from the WK34 source, presumably a young stellar object still in the outflow epoch, is likely to arise from multiple components including a photosphere, an accretion disk, as well as heated ambient material from which the star formed. Light scattering by ambient material in the vicinity of the star is also thought likely to affect the near infrared spectrum. Model spectral energy distributions of low mass young stellar objects including these components of emission have been calculated by Adams, Lada & Shu (1987). The WK34 photometry is compatible with these models which suggests that it is a low mass, low luminosity protostar. Observations at longer wavelengths are needed for a robust measure of the bolometric luminosity of this source. Nevertheless, there is additional evidence that the WK34 source is a low luminosity protostar including: (i) that the bulk of the cluster luminosity (L=10\({}^{4}\)L\({}_{\odot}\) at 2 kpc; Parmar et al. 1987) can be accounted for by the three early B ZAMS stars present in the cluster and, (ii) that the WK34 source lacks an HII region (determined by contemporaneous \(P\alpha\) NICMOS observations to be presented in another paper) indicating the lack of a hard ionizing continuum usually associated with high luminosity sources. ### The Underlying Mass Distribution Many optical and near-infrared reflection nebulae associated with low mass protostars have been successfully modeled as rotationally flattened protostellar envelopes with variously shaped evacuated cavities and an accretion disk (e.g. Whitney & Hartmann, 1993; Kenyon et al. 1993; Wood et al. 2001). Associated model SEDs have been made for a wide range of wavelengths providing a theoretical underpinning to the multiwavelength studies of YSOs (Adams, Lada & Shu, 1987). We find, however, that similar models fail to reproduce the reflection nebula associated with WK34. The most striking features which distinguish the bipolar nebula in our field are: (1) The appearance of very distinct, well separated lobes forming the bipolar nebula. (2) The distance between the intensity maximum in each lobe is separated by a large distance (\(\sim\) 5000 AU, for a cluster distance of 2 kpc) relative to the overall nebular size. (3) The nebular lobes are much longer than they are broad. Each of these characteristics requires a rotationally flattened envelope model with parameters outside a reasonable range, indicating the inadequacy of this model to explain our observations. For example, modeling the nebula with a rotating collapsing cloud model such as that described by Tereby, Shu & Cassen (1984) requires a centrifugal radius much larger than \(\sim\)2000 AU to explain the large separation between lobes, but then fails to produce the observed narrowness of the lobes. After an exhaustive study of parameter space with a single scattering radiative transfer code we find that no reasonable combination of rotating envelope, evacuated cavities and accretion disk can explain the observations adequately. The small effects of multiple scattering are likely to exacerbate the modeling by contributing extra illumination at the nebular waist. An alternative to the evacuated cavity model is one in which the bipolar reflection nebula is due to a large amount of outflow material ejected by the central source along the nebular axis. The observed bipolarity of such an _outflow nebula_ can then be further accentuated by the presence of an obscuring torus of material surrounding the central illuminating source, perhaps the remnant of the infalling parent envelope (see schematic diagram in Figure 9). This geometry is consistent with the pattern of polarization vectors which deviate from centrosymmetry near the waist of the bipolar nebulosity where they align along the equator of the nebula (see Figure 2). This type of polarization signature has been called a "polarization disk" and has been shown to be a phenomena of multiple scatterings in the presence of an optically thick equatorial disk (Bastien & Menard, 1988; Whitney & Hartmann, 1993). This polarization signature arises on the observer side of an optically thick disk being illuminated from the bipolar lobes: we are seeing photons scattered _over_ an optically thick disk into our line of sight. The location of the "null points", or regions of low polarization on either side of the "polarization disk", give us a rough estimate of the size of the optically thick disk. From Figure 2 we estimate a disk radius of \(\sim\)1000 AU. This pattern is common in the bipolar nebulosity associated with both YSOs as well as protoplanetary nebulae such as the Egg Nebula (Sahai et al. 1998) and OH231.8+4.2. The latter object, also known as the Rotten Egg Nebula because of its sulfur content, is one of the few other astronomical objects with measured infrared polarization levels as high as those presented here (Ageorges & Walsh 2000; Meakin et al. 2003). The high levels of observed polarization constrain the size of dust particles responsible for scattering. The grain model proposed to explain the extinction in molecular clouds by KMH is only capable of polarizing 2\(\mu\)m light to a maximum of \(\sim\)70% (Weintraub, Goodman, & Akeson, 2000b). This is due to a component of large particles in the grain size distribution of this model. It is likely that the particles in the reflection nebula observed here are composed mainly of particles much smaller than the observed wavelength. The existence of small particles in the outflow lobes may be related to the outflow mechanism. Dust grains may be selectively accelerated into the outflow material based on size, or they may be processed by shocks or photodisentegration processes which occur during the star formation process. #### 3.3.1 Physical Parameter Estimates The relationship between the scattering optical depth through the lobe and the density is \(\tau_{los}=\bar{\rho_{d}}\Delta S\kappa_{s}\) where \(\bar{\rho_{d}}\) is the average lobe dust density, \(\Delta S\) is the line of sight extent of the nebula, and \(\kappa_{s}\) is the scattering opacity. If we assume that the nebula is optically thin, \(\tau_{los}<1\), we have: \[\bar{\rho}_{d}<\frac{1}{\Delta S\kappa_{s}}.\] (1) From Figure 8 we estimate a total lobe thickness \(\Delta S\approx 2000\) AU, assuming that the nebula is roughly cylindrical and that the 2\(\mu\)m intensity image traces its extent. The mass scattering opacity for a spherical dust grain with radius \(a\) is, \[\kappa_{s}=\omega Q_{ext}\frac{\pi a^{2}}{\rho_{i}4\pi a^{3}/3}=\omega Q_{ext} \frac{3}{4a\rho_{i}},\] (2) where \(\rho_{i}\) is the density of the material composing the dust, \(Q_{ext}\) is the extinction efficiency (proportionality between geometric cross section and extinction cross section), and \(\omega\) is the dust albedo (ratio between scattering and extinction cross section). Both \(Q_{ext}\) and \(\omega\) depend on the optical constants of the dust material and the ratio of the particle size to the wavelength. For the "astronomical silicates" and the graphite materials described by Draine & Lee (1984) and for particle sizes ranging between 0.1 and 1 \(\mu\)m, at near infrared wavelengths the product \(\omega Q_{ext}\) varies from close to zero to a few. We therefore expect a scattering mass opacity to be of order \(\kappa_{s}\sim 1/\rho_{i}a\sim 10^{6}\)cm\({}^{2}\) g\({}^{-1}\) for material density (in g cm\({}^{-3}\)) and particle size (in microns) both of order unity. The average mass density of dust grains in the nebula for a line of sight through the nebular lobes where \(\tau\sim 1\) will then be of order \(\bar{\rho}_{d}\sim 10^{-13}\) g cm\({}^{-3}\). In the optically thin scattering limit, the intensity variation along the line of sight is proportional to the line of sight scattering optical depth and the flux from the central illuminating source which is \(F^{*}\propto L^{*}r^{-2}\), modulo any internal extinction between the source and the scattering location. The scattered light intensity variation with distance from the central source is then expected to vary as, \[I\sim\bar{\rho}_{d}\Delta Sr^{-2},\] (3) where \(r\) is the distance between the central source and scattering location. The intensity variation along the nebular axis is plotted in Figure 10 on a log-linear and log-log plot. The intensity is seen to drop off with distance from the central source with a roughly power law dependence, \(I\propto r^{\beta}\) with \(\beta\approx\)-3.0 for \(r>1\arcsec\). Assuming that the lobe depth, \(\Delta S\), is roughly constant in the scattering lobe then the inferred average line of sight dust density decreases inversely with distance from the central source, \(\bar{\rho}_{d}\approx\bar{\rho}_{d,0}(r/r_{0})^{-1}\). Integrating this distribution the _dust mass_ in the scattering lobe is, \[M_{l}=\frac{\pi\Delta S^{2}r_{0}}{4}\bar{\rho}_{d}(r_{0})\ln(r_{1}/r_{0})\sim 1 0^{27}\hbox{g},\] (4) where the integration is taken between \(r_{0}\sim 1\arcsec\) and \(r_{1}\sim 3\arcsec\), a lobe width of \(\Delta S\sim 2000\)AU is used, and \(\bar{\rho}_{d,0}=\bar{\rho}_{d}(r_{0})\) is taken as our previous order of magniture estimate, \(\rho_{d}\sim 10^{-13}\) g cm\({}^{-3}\). Inferring the total mass in the lobes requires knowledge of the gas to dust mass ratio, which may be much larger than the canonical value of \(\sim\)100 in the diffuse ISM due to grain destruction processes that may be occurring in the outflow. A great deal more information can be garnered from the infrared data presented in this paper by comparing it to observations at other wavelengths. For instance, high resolution CO observations of the nebula can provide a more robust map of the underlying mass distribution as well as the velocity structure. The velocity of the material can be used to test the hypothesis that we are seeing an outflow nebula, as opposed to an illuminated evacuated cavity. The combination of a molecular map and near infrared scattered light images at comparable resolution should be able to provide strong constraints on the nature of the dust particles in the outflow by providing more robust estimates of mass opacities. Dust properties may be varying strongly with location in the nebula due to the interaction of the outflow with the ambient cloud material through shocks and photodissociation processes. These processes play an important role in the life cycle of dust in the universe, and may be potentially useful probes of the outflow mechanism operating in YSOs. #### 3.3.2 Nebular Inclination We conclude this section with a comment on the nebular inclination, noting that asymmetries in the morphology between the north and south lobes can be used as a constraint. It is a general feature of bipolar reflection nebula with mass distributions that have equatorial density enhancements that for small inclinations (out of the plane of the sky) the lobe tilted towards the observer has (1) a higher surface brightness, (2) is broader, and (3) peaks closer to the central illuminating source. These features arise from the relative amounts of obscuration caused by the equatorial material in projection against the illuminated lobes. All three of these features can be clearly seen in the contour plots presented in Figure 8 and the intensity profile in Figure 10 indicating that it is the _south lobe that is tilted towards the Earth_. ### Interaction with Environment Although the beam size in the \({}^{12}\)CO J=(2-1) maps of Gomez et al (1992) is comparable to the size of the entire NICMOS field of view, interesting correlations in morphology exist between these two data sets. A finger of high intensity emission is discernible in the CO maps which is aligned with the WK34 bipolar nebulosity. This finger of CO emission sweeps off towards the east, as though an extension of the similarly shaped infrared nebulosity seen in our images. The observed near infrared reflection nebulosity traces the polar axis of a fairly well collimated outflow emanating from WK34 on scales of \(\sim 1000\) AU. The ambient gas in the region may be redirecting the northern part of this outflow towards the east. This might explain why the geometric center of the large scale molecular outflow does not lie directly over the infrared cluster. The connection between the bipolar nebulosity and the larger scale outflow is further reinforced by the fact that the inclination of WK34 implied by the morphology of the infrared nebulosity (S lobe tilted toward Earth) is consistent with the orientation of the large scale molecular outflow (S lobe is blue shifted). ## 4 Summary & Conclusions We have presented high resolution polarimetric and broad band images of the infrared cluster in AFGL437 which reveals a well collimated bipolar nebula. Our polarization measurements show that this nebula is being illuminated by predominantly one source, WK34. Photometry for this source is consistent with it being a _low luminosity protostar_. We note the following additional results. (1) A dust model that contains too many large (\(>1\mu\)m) dust particles, such as the KMH dust model which is successful in describing molecular cloud extinction, is inconsistent with the levels of polarization that we observe in the reflection nebulosity observed here. This indicates that the population of dust grains is composed mainly of smaller particles. (2) The equator of the observed bipolar nebula coincides with a "polarization disk" similar to that seen in other protostars and protoplanetary nebulae. This feature arises from the presence of an optically thick, nearly edge of torus of material. (3) The observed bipolar nebula resides near the center of a much larger scale bipolar CO outflow. We find that the inclination and alignment of the smaller scale, near-infrared bipolar nebula is similar to the cluster scale CO outflow. (4) The bipolar morphology, high aspect ratio (length to width), and high degrees of linear polarization of the near infrared nebulosity that we have observed cannot be reproduced with a collapsing envelope and evacuated cavity model which has been successful in explaining the near infrared nebulae associated with many other embedded YSOs. From these points we are led to a picture of AFGL437 in which a low luminosity protostar is the source of a well collimated axisymmetric bipolar outflow of gas and dust that is being illuminated by the central source. The lobes contain a low density population of small grains that scatter (thus polarizing) light from the central star. The small dust grains in the outflow which differ from those typical of molecular clouds are likely a result of processes occurring near the protostar. ## References * (1) Adams, F., Lada, C.J., Shu, F. 1987, ApJ, 312, 788 * (2) Ageorges, N., & Walsh, J. 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# Blazars and the emerging AGN/black hole X-ray binary paradigm Philip Uttley ###### Abstract We briefly review the emerging paradigm which links the radio-quiet and radio-loud classes of AGN to the different accretion states observed in stellar mass black hole X-ray binary systems (BHXRBs), and discuss the relevance of the AGN/BHXRB connection to blazar variability. X-ray Astrophysics Laboratory, NASA Goddard Spaceflight Center, Greenbelt, MD 20771 ## 1 Introduction In recent years, a new paradigm has emerged which seeks to link AGN behaviour with that of the stellar mass black hole X-ray binary systems. There are currently two main approaches to this endeavour. One is to compare the temporal variability of AGN and BHXRBs. This approach has already yielded very interesting results, proving that characteristic time-scales scale roughly linearly with black hole mass, and linking the temporal variability of several Seyfert galaxies to that of the BHXRB Cyg X-1 in its high/soft state (e.g. M\({}^{c}\)Hardy et al. 2004 and these proceedings). The other approach is based on the presence of jets in AGN and BHXRBs, and the relation of the associated radio emission to the X-rays (Merloni, Heinz & di Matteo, 2003; Falcke, Kording & Markoff, 2004). Also, the relationship of the jet (its presence or absence, and the presence of jet ejections) to the 'state' of BHXRB systems has led to efforts to describe the radio-loud/radio-quiet dichotomy in AGN in terms of analogous states to those seen in BHXRBs (e.g. Meier 2001; Falcke, Kording & Markoff 2004). ## 2 BHXRB Accretion States The range of BHXRB behaviour is very diverse, but the following broad picture has emerged, primarily from studies of X-ray transients which move through the full range of states during a single outburst (see McClintock & Remillard 2005; Fender 2005 for reviews). The _low/hard state_ appears to correspond generally to low accretion rates (less than a few per cent of Eddington), with relatively low luminosities and X-ray spectra dominated by a hard (photon index \(\Gamma<2\)) power-law continuum, with little or no obvious disk blackbody emission (which can be seen in the X-ray band in BHXRBs, due to their low black hole masses and hence high disk temperatures). Interestingly, all low/hard state BHXRBs show the presence of radio jets, which become stronger relative to the X-ray emission as the source drops to even lower accretion rates, with the power output possibly becoming jet-dominated at some point (Fender, 2005).

At higher accretion rates (few per cent Eddington or greater), the sources can transition to a _high/soft state_ where the emission is dominated by blackbody emission from the accretion disk, with only a very weak, steep (\(\Gamma>2\)) power-law component present. The high/soft state is very interesting from the point of view of understanding BHXRB jets, because they become much weaker or may even disappear completely during this state, with the radio emission becoming undetectable (\(>30\) times fainter than the low/hard state) Bridging the power-law dominated and disk dominated states described above is the _intermediate state_ or _very high state_. The different names reflect the fact that the transition between a power-law-dominated and disk-dominated state can in fact be observed at either relatively low (few per cent Eddington) or rather high (tens of per cent Eddington) accretion rates, but the behavior is similar in either case and both types of transition state are now commonly thought of as being the same thing, which we will refer to as the intermediate state. As the name suggests, the intermediate state shows a spectrum intermediate between the low/hard and high/soft states, with relatively strong disk and strong steep (\(\Gamma>2\)) power-law contributions. The fraction of luminosity contributed by each component varies, so the state is in some sense loosely defined and can be quite unstable, flipping between more power-law dominated and disk dominated spectra on relatively short time-scales. The jet behaviour is also very interesting, with powerful relativistic ejections occuring as the disk component gets stronger (possibly connected to the quenching or disappearance of the jet in the high/soft state) although a persistent jet can exist in the more power-law dominated types of intermediate state. ## 3 Black hole Grand Unification Figure 1: Black hole ‘Grand Unification’. The different classes of AGN are grouped in terms of the accretion state they may occupy (see Meier 2001; Falcke, Körding & Markoff 2004 for a similar delineation).

The existence of the same states in AGN would be highly interesting, not only from a spectral and variability point of view, but also in terms of understanding the radio-loud/radio-quiet dichotomy, because it is clear from BHXRB studies that states with and without jets can occur in the same source. Therefore, it is possible that the presence of powerful jets in AGN may be related to the accretion state, and not necessarily to the black hole spin or AGN environment. The types of state seen in BHXRBs seem to be related to the interplay of the disk and power-law emission (perhaps the latter from a corona), and the presence and/or strength of the jet seems to be correlated with the presence of the power-law component. With this simple picture, we can construct a picture of 'Black Hole Grand Unification', shown in Fig. 1, where the distinction between radio-loud and radio-quiet AGN is governed by whether the source occupies the strong-jet, strong-corona states (low/hard and parts of the unstable intermediate state) or the weak-jet, disk-dominated states (high/soft and disk-dominated parts of the intermediate state). Note that we have classified low-luminosity AGN as low/hard state sources, as previously suggested by (Ho, 2005) in line with their low accretion rate and their unusual spectral energy distributions (SEDs), which do not show 'big blue bumps' (suggesting that the disk is truncated), and relatively strong radio emission (suggesting relatively strong jets). The dividing line between the distinctive high/soft and low/hard states and the intermediate state is murky. In BHXRBs these states can be distinguished from the intermediate state by their relative stability and X-ray colours (since the relative contributions of disk and power-law emission can be assessed in this way), but in AGN we cannot cleanly see most of the disk emission, which occurs in the FUV/EUV, so it is hard to judge whether a source SED is disk or power-law dominated. Changes from power-law to disk dominated and back again can take hours to weeks in BHXRBs, corresponding to thousands to millions of years for a \(10^{8}\) M\({}_{\odot}\) black hole, so for any given AGN we can only realistically observe a 'snapshot' of it in a single state. These limitations would make it difficult to distinguish between high/soft and intermediate states with strong disk emission, hence we might expect Seyferts and radio-quiet quasars to occupy either state. The intermediate and high/soft states are not tightly tied to accretion rate, but are observed above a few per cent Eddington, whereas only the low/hard state is seen at lower accretion rates (Maccarone, 2003). Thus it may be possible to distinguish low/hard and power-law dominated intermediate states in the radio-loud sources, in terms of the luminosity and power of the source. In general, one might expect FR II radio galaxies to correspond to the more powerful, higher accretion rate intermediate states, while FR I sources correspond to the low/hard state, but more massive black holes may possess sufficiently powerful jets that they correspond to FR II sources in the low/hard state also. ## 4 Implications for Blazars Following the standard paradigm for unifying blazars with non-beamed radio-loud AGN, we can roughly map the BL Lac sources on to the low/hard state,

and more powerful flat spectrum and steep spectrum radio quasars on to the intermediate state. The lack of significant optical permitted line emission, which distinguishes BL Lac objects and maps them on to FR I radio galaxies in the standard unification paradigm may be related to the lack of any significant disk emission which can drive the optical line emission (see Ho 2005). Interestingly, the timing behaviour of the different BHXRB states may shed light on variability behaviour of blazars, and offer a tantalising glimpse of what _GLAST_ might reveal in sufficiently long blazar light curves. In BHXRBs, strong quasi-periodic oscillations (QPOs), typically at around 1-10 Hz, are often observed in the intermediate state, especially the power-law dominated part, i.e. when a strong jet is present. If the variations are produced in an accretion flow which is coupled to the jet, similar behaviour might be seen in the blazars which occupy this state, but on time-scales of years (assuming linear scaling of QPO time-scales with black hole mass). In fact, periodic (or possibly quasi-periodic) continuum variations on time-scales of years have been claimed in a number of blazars, most notably OJ 287 (e.g. Valtaoja et al. 2000). These candidate periodicities 1 are often interpreted as being due to precession of the jet caused by a binary black hole system, but it is interesting that they occur on similar relative time-scales to the strong QPOs observed in the possibly analogous BHXRBs in the intermediate state, where the QPOs are probably intrinsic to the accretion flow and are not attributed to binary motion. When _GLAST_ is launched, it will provide high quality gamma-ray light curves for many blazars, which, if the mission is flown for sufficient duration, may be sufficient to detect periodicities in the lower-mass blazars and test the remarkable AGN/BHXRB connection still further. Footnote 1: The sampling and number of cycles observed may not yet be sufficient to show that the variations are strictly or quasi-periodic and not simply due to red noise (e.g. see discussion in Vaughan & Uttley 2005). ## References * Falcke, Kording & Markoff (2004) Falcke, H., Kording, E. & Markoff, S. 2004, A&A, 414, 895 * Fender (2005) Fender, R. 2005, to appear in W. H. G. Lewin, M. van der Klis eds., Compact Stellar X-ray Sources, Cambridge University Press, Cambridge (astro-ph/0303339) * Ho (2005) Ho, L. C. 2005, to appear in 'From X-ray Binaries to Quasars: Black Hole Accretion on All Mass Scales', ed. T. J. Maccarone, R. P. Fender, and L. C. Ho, Dordrecht: Kluwer (astro-ph/0504643) * Maccarone (2003) Maccarone, T. 2003, A&A, 409, 697 * McClintock & Remillard (2005) McClintock, J. E. & Remillard, R. A. 2005, to appear in W. H. G. Lewin, M. van der Klis eds., Compact Stellar X-ray Sources, Cambridge University Press, Cambridge (astro-ph/0306213) * M\({}^{\rm c}\)Hardy et al. (2004) M\({}^{\rm c}\)Hardy, I. M., Papadakis, I. E., Uttley, P., Page, M. J. & Mason, K. O., 2004, MNRAS, 348, 783 * Meier (2001) Meier, D. 2001, ApJ, 548, L9 * Merloni, Heinz & di Matteo (2003) Merloni, A., Heinz, S. & di Matteo, T. 2003, MNRAS, 345, 1057 * Valtaoja et al. (2000) Valtaoja, E., et al. 2001, ApJ, 531, 744 * Vaughan & Uttley (2005) Vaughan, S., & Uttley, P., 2005, proceedings of 35th COSPAR (astro-ph/0506456)

# A Morphological Study of Gamma-Ray Burst Host Galaxies C. Wainwright1 , E. Berger2 3 4 , B. E. Penprase1 Footnote 1: http://archive.stsci.edu/hst/ Footnote 2: Residual afterglow and/or supernova emission is detected in GRBs 970228, 991216, 030329, and 041006. Footnote 3: The length scale of the exponential disk defined above is related to the effective radius as \(r_{s}=r_{e}/1.68\), while \(\Sigma_{0}=5.36\Sigma_{e}\). Footnote 4: http://www.stsci.edu/software/tinytim/tinytim.html Footnote 1: http://archive.stsci.edu/hst/ ###### Abstract We present a comprehensive study of the morphological properties of 42 \(\gamma\)-ray burst (GRB) host galaxies imaged with the _Hubble Space Telescope_ in the optical band. The purpose of this study is to understand the relation of GRBs to their macro-environments, and to compare the GRB-selected galaxies to other high redshift samples. We perform both qualitative and quantitative analyses by categorizing the galaxies according to their visual properties, and by examining their surface brightness profiles. We find that all of the galaxies have approximately exponential profiles, indicative of galactic disks, and have a median scale length of about 1.7 kpc. Inspection of the visual morphologies reveals a high fraction of merging and interacting systems, with \(\sim 30\%\) showing clear signs of interaction, and an additional \(30\%\) exhibiting irregular and asymmetric structure which may be the result of recent mergers; these fractions are independent of redshift and galaxy luminosity. On the other hand, the three GRB host galaxies for which submillimeter and radio emission has been detected are isolated and compact, unlike the luminous submillimeter-selected galaxies. The fraction of mergers appears to be elevated compared to other high redshift samples, particularly for the low luminosities of GRB hosts (\(M_{B}\sim-16\) to \(-21\) mag). This suggests that merging and interacting galaxies undergoing a burst of star formation may be an efficient site for the production of GRB progenitors. Finally, we show that GRB hosts clearly follow the size-luminosity relation present in other galaxy samples, but thanks to absorption redshifts they help extend this relation to lower luminosities. gamma-rays:bursts -- galaxies:evolution -- galaxies:formation -- galaxies:structure

## 1 Introduction For nearly a century astronomers have attempted to classify galaxies by their apparent shape and to draw conclusions about the process of galaxy formation and evolution from these morphologies. The basic Hubble classification (Hubble 1926) and its variants (e.g., Hubble 1936; Sandage 1961) divide galaxies into three broad categories: elliptical, disk, and irregular. This morphological classification correlates with, among other physical properties, the star formation activity of the galaxies. Studies of local galaxy samples, as well as the currently-favored cold dark matter (\(\Lambda{\rm CDM}\)) model, also suggest that interactions and mergers play an important role in the build up of galactic and stellar mass, through both the accretion of material and an increase in the star formation rate. Thus, the morphological properties of galaxies as a function of cosmic time provide direct insight into the physical processes governing galaxy evolution. In this manner, analysis of deep fields obtained primarily with the _Hubble Space Telescope_ (HST) suggest that the locally-defined Hubble sequence may begin to break down at \(z\sim 1\)(van den Bergh 2002) with the emergence of a sizable fraction of faint, irregular, and interacting systems (e.g., Driver et al. 1995; Ellis 1997). While these observations, along with observations of local galaxies (e.g.,Arp 1966), suggest that mergers play a significant role in the formation of galaxies, three important limitations prevent a conclusive connection between morphology and galaxy formation at higher redshift. First and foremost, studies of galaxy morphologies rely on flux-limited samples, which may contain a large fraction of atypical objects; e.g., ultra-luminous submillimeter galaxies Chapman et al. (2003), or \(R<25\) mag optically-selected galaxies Conselice et al. (2003). Second, it is not clear how to relate the various samples (e.g., Lyman break galaxies, submillimeter-selected galaxies, near-IR selected galaxies) to the low redshift population or to each other. This is partly because of the different selection techniques and the differences in observed properties and space densities. Finally, at faint fluxes (\(R\gtrsim 25\) mag), where irregular galaxies may dominate the population, the distance scale relies on photometric redshifts, whose accuracy is difficult to assess. In this context, it is interesting to investigate the morphological properties of \(\gamma\)-ray burst (GRB) host galaxies. We now have conclusive evidence that GRBs mark the death of massive stars Stanek et al. (2003) and therefore pinpoint star-forming galaxies at all redshifts (Hogg & Fruchter 1999; Bloom et al. 2002; Christensen et al. 2004). This allows a uniform selection over a wide range of redshift and luminosity. In addition, absorption spectroscopy of the bright afterglows allows us to measure redshifts of arbitrarily faint galaxies. Thus, the current GRB host sample spans \(z\sim 0.1-4.5\) and \(M_{B}\approx-16\) to \(-21\) mag (i.e., \(0.01L_{*}\) to \(L_{*}\)).

Here we present a comprehensive analysis of all optical HST observations of GRB host galaxies. The purpose of this study is twofold: First, to obtain information on the large-scale environments in which GRBs occur, as a clue to the formation of the progenitors. Second, to survey a set of high redshift galaxies which are physically related by their star formation activity, but which alleviate some of the selection effects of other samples. We summarize the HST observations in SS2, provide a qualitative (SS3) and quantitative (SS4) analysis of the host morphologies, and compare the results to other high redshift galaxy samples (SS5). We show that despite an overall diversity in the sizes and luminosities of GRB hosts, they invariably have roughly exponential profiles, with a large fraction undergoing mergers and interactions. ## 2 _Hubble Space Telescope_ Data We retrieved data from the HST archive1 for all available GRBs after "on-the-fly" pre-processing. These include \(29\) GRBs observed with the Space Telescope Imaging Spectrograph (STIS), \(8\) GRBs observed with the Wide-Field Planetary Camera 2 (WFPC2), and \(10\) GRBs observed with the Advanced Camera for Surveys (ACS). Details of the observations are summarized in Table 1. For each GRB we used the latest available images to reduce contamination from the afterglow and/or supernova emission2. Footnote 1: http://archive.stsci.edu/hst/ Footnote 2: Residual afterglow and/or supernova emission is detected in GRBs 970228, 991216, 030329, and 041006. We processed and combined individual exposures using the IRAF tasks drizzle (STIS, WFPC2) and multidrizzle (ACS) in the stsdas package (Fruchter & Hook 2002). In all cases we used pixfrac\(=0.8\), with pixscale\(=0.5\) for the STIS images, pixscale\(=0.7\) for the WFPC2 images, and pixscale\(=1.0\) for the ACS images. The resulting images have pixel scales of 0.025, 0.07, and 0.05 arcsec pix\({}^{-1}\), respectively. In Figures 1 and 2 we show grayscale and color images of the individual host galaxies. All images are flux-calibrated in the AB system according to the zero-points listed in the instrument handbooks (see also Sirianni et al. 2005), and are corrected for Galactic extinction (Schlegel et al. 1998). For GRB 011121 we used the extinction value determined by Price et al. (2002) from observations of the afterglow.

## 3 Morphological Classification To classify the morphological properties of the GRB host galaxies, we created eight different qualitative morphological categories. Each category is independent of the others and galaxies may fit into more than one category. In this manner we are able to place a large number of galaxies into individual categories and account for multiple features. The categories are: concentrated elliptical or circular structure, or blob-like (BL); conspicuous disk structure (D); highly asymmetric or irregular structure (AS); galactic structure containing knots (KN); galaxies with off-center peaks (OC); galaxies with tidal tails (TT); galaxies that are either undergoing mergers or are closely interacting (MI); and galaxies which are too faint for morphological analysis (TF). The classification has been carried out independently by C.W. and E.B., and the results are summarized in Tables 1 and 2. Of the 45 host galaxies observed with HST, three are not detected in our images, and an additional four are too faint to accurately categorize. These galaxies either occur at unknown redshifts, or \(z>1.5\). While these galaxies cannot be classified morphologically, they do indicate that a non-negligible fraction of GRBs (and hence of the formation of massive stars) occurs in very low luminosity and/or low surface brightness systems. In fact, given the measured redshifts and the magnitude limits for these galaxies we find that they typically have an absolute rest-frame \(B\)-band magnitude of \(M_{B}\gtrsim-17.5\) mag, somewhat fainter than the Large Magellanic Cloud. For the remaining 38 galaxies with morphological classification we combine the basic categories into two general groups: regular and irregular/interacting. Regular galaxies are those that are categorized exclusively as either blob- or disk-like. The primary difference between these two categories is that the blob-like galaxies have much higher luminosity concentrations, while the disk-like galaxies have symmetric extended features. In SS4 below we show that both the BL and D galaxies have surface brightness distributions that are well-described by exponential profiles and are therefore disk galaxies. The regular galaxies comprise about \(30\%\) of the total sample. The irregular category includes galaxies that are asymmetric or show signs of a merger or interaction. The latter includes multiple bright galaxies (e.g., the hosts of GRB 020405 and XRF 020903), or galaxies with filamentary structures (interpreted as tidal tails) extending towards nearby galaxies with which they are interacting (e.g., the host of GRB 000926). These tails are not symmetric about the center of the light distribution. A similar morphology is evident in the OC category, for which the extended low surface brightness emission is not likely to be part of an ordered disk structure. The majority of these galaxies do not have visible galactic neighbors. If they are the results of galactic mergers

then they are most likely in the late stages of the merging process, or alternatively signal an interaction with a lower mass galaxy. In this context the environment of GRB 991208 may be of particular interest. A faint galaxy \(\sim 7\) kpc from the host galaxy exhibits a tidal tail morphology suggesting that the host is interacting with a low mass companion. It is also interesting to note that the host of GRB 991208, with \(M_{B}\approx-18.2\) mag, is similar in brightness to the LMC, suggesting that mergers between dwarfs play an important role in the assembly of more massive galaxies; an illustrative local example is NGC 1487 which is an interacting system of two dwarf galaxies (Johansson & Bergvall 1990). The asymmetric galaxies exhibit clumpiness or concavities in their light distribution which may be interpreted as the result of an interaction. However, this morphology may also be interpreted as clumpiness in the distribution of the star formation activity, particularly in the case of higher redshift hosts for which we sample the rest-frame UV light. We note that the latter explanation may be partially supported by the lack of obvious nearby companions, although as in the case of the OC galaxies, these systems may be in the late stages of merging. The same argument holds for galaxies exhibiting knots, which could be the remnant bright cores of merging galaxies or signs of patchy star formation activity. A relevant example is the host of GRB 990705. This galaxy exhibits pronounced spiral structure with bright knots of star formation. At lower surface brightness (or higher redshift) the spiral arms may not be detected and the system might appear to have a knot morphology. For the galaxies with morphological classification, the ratio of irregular and merging or interacting systems to regular systems is about \(2:1\). This ratio does not change significantly as a function of redshift. Dividing the sample into \(z<1\) (low-\(z\)) and \(z>1\) (high-\(z\)) bins, we find that at low-\(z\) regular galaxies account for about \(36\%\) of the sample while \(64\%\) are irregular. For the high-\(z\) sample the fractions are \(31\%\) and \(56\%\), respectively, with the remainder being too faint. The only two categories with possible evolution between the low- and high-\(z\) samples are the tidal tails and disks. Tidal tails occur in about \(7\%\) of the low-\(z\) population, but appear in \(25\%\) of the high-\(z\) population, while disk galaxies make up \(36\%\) of the low-\(z\) population and only \(6\%\) of the high-\(z\) population. The latter trend may be attributed to surface brightness dimming, but the increase in the frequency of tidal features with redshift may be real since surface brightness dimming would tend to have the opposite effect. We finally note that some ambiguity exists amongst our broad classifications. For example, the host of GRB 990123 may be interpreted as a merger/interaction with strong tidal tails, where the burst itself occurred in the disrupted galaxy. Alternatively, this galaxy may be classified as a disk galaxy with a bright spiral arm accentuated by bright knots, which are presumably star forming HII regions. In this case, the burst was located in one of these

bright knots. Still, such cases comprise a relatively small fraction of the overall sample. ## 4 Surface Brightness Observations of local galaxies suggest that the surface brightness profiles of disk galaxies are roughly exponential, while those of elliptical galaxies and galaxy bulges tend to follow an \(r^{1/4}\) de Vaucouleurs law (de Vaucouleurs 1948). In this section we determine the surface brightness profiles and sizes of the GRB host galaxies and investigate their distributions as an additional input into their morphological classification. We determine the radial surface brightness distributions in two ways. First, for galaxies with a relatively simple apparent morphology we construct radial surface brightness plots using the IRAF task phot, with a range of apertures chosen to span the full extent of each host galaxy while maintaining \(S/N\gtrsim 5\) in each bin. A comparison of circular apertures to elliptical isophotes (using the IRAF task ellipse) indicates that the difference is typically within the uncertainty in individual apertures. The resulting surface brightness profiles are shown in Figures 3 and 4. For the host galaxies observed with WFPC2 and ACS in multiple filters we also plot the radial color profiles (Figure 5). None of the well-resolved host galaxies with high signal-to-noise detections exhibit a clear \(r^{1/4}\) profile, confirming their nature as disk and irregular galaxies. With the exception of the host galaxy of GRB 991208 all the galaxies are well-resolved relative to the instrumental point spread function as measured from stars in the field (Figures 3 and 4). We thus fit the surface brightness profiles of all systems with an exponential disk: \(\Sigma(r)=\Sigma_{0}{\rm exp}(-r/r_{s})\), leaving the central surface brightness (\(\Sigma_{0}\)) and the scale length (\(r_{s}\)) as free parameters. We find that the scale length distribution peaks at \(r_{s}\approx 0.09\arcsec\), with a tail extending to \(\sim 0.35\arcsec\). For the host galaxies observed in multiple filters we find that about \(60\%\) exhibit a color gradient as a function of radius (Figure 5), becoming redder at large radii. The single exception to this trend is the host galaxy of GRB 011121, which is somewhat bluer at larger radii. Since blue light traces recent star formation, the observed trend suggests that the star formation activity in GRB host galaxies is more concentrated than the overall light distribution. The trend observed for GRB 011121 may suggest that substantial star formation is taking place across the whole disk of the galaxy. While color information is not available for the host of GRB 990705, it too has fairly distributed star formation activity as shown by its spiral arm structure and bright knots. Our second approach in studying the surface brightness profiles is to use the GALFIT software (Peng et al. 2002). This allows us to fit all but the most irregularly shaped galaxy

(GRB 020405). In this case we use the generalized Sersic function (Sersic 1968) \[\Sigma(r)=\Sigma_{e}{\rm exp}[-\kappa((r/r_{e})^{1/n}-1)],\] (1) where \(n\) is the concentration parameter (\(n=1\) is equivalent to an exponential disk, while \(n=4\) is the de Vaucouleurs profile), \(\kappa\) is a constant that is coupled to the value of \(n\), \(r_{e}\) is the effective radius, and \(\Sigma_{e}\) is the surface brightness3 at \(r=r_{e}\). We generated point spread functions for the individual instruments and filters using the Tiny Tim software package4, assuming a power law spectrum \(F_{\nu}\propto\nu^{-1}\), which is roughly appropriate for the observed color distribution of GRB host galaxies (Berger et al. 2003). In all cases we find adequate fits to the host galaxies, with \(\chi^{2}_{r}\approx 0.5-2\) per degree of freedom. We note that some sources, particularly at low signal-to-noise, can be adequately fit with a range of \(n\sim 1-4\). For sources with complex morphology (e.g., XRF 020903) or contaminating point sources (e.g., GRB 011121) we use multiple components to account for substructure. The resulting values of \(n\) and \(r_{e}\) are listed in Table 1. Footnote 3: The length scale of the exponential disk defined above is related to the effective radius as \(r_{s}=r_{e}/1.68\), while \(\Sigma_{0}=5.36\Sigma_{e}\). Footnote 4: http://www.stsci.edu/software/tinytim/tinytim.html In Figure 6 we plot the distribution of \(r_{e}\) and \(n\) for the hosts with an accurate value of \(n\). For hosts without a known redshift we take advantage of the flat evolution of the angular diameter distance with redshift, and assume a value of \(8\) kpc arcsec\({}^{-1}\) appropriate for \(z\sim 1-3\). The distribution of \(n\) is strongly peaked around a value of \(\sim 1\), indicating that GRB hosts are well described as exponential disks. As noted in other studies (e.g., Ravindranath et al. 2004), \(n\lesssim 2\) is an efficient criterion for disk-dominated galaxies. The distribution of \(r_{e}\) ranges from about 0.3 to 10 kpc, with a peak at \(r_{e}\approx 1.7\) kpc. As shown in Figure 7 we do not find any correlation between \(r_{e}\) and \(n\) or redshift, although we note that there is a larger dispersion in \(r_{e}\) for \(z\lesssim 1\). This may be a result of surface brightness dimming which would tend to make higher redshift objects appear more compact. A comparison to the morphological analysis of galaxies in the FIRES data (Trujillo et al. 2004, 2005) suggests that the distributions of \(n\) values are similar, with the exception that the latter exhibit a tail at \(n\gtrsim 3\) (ellipticals) which may not present in the GRB sample. The distribution of effective radii, however, peaks at a large value compared to the GRB sample. To provide a direct comparison we corrected the values given in Trujillo et al. (2004) and Trujillo et al. (2005) for ellipticity and for the systematic over-estimate of about \(15\%\) compared to GALFIT results (see Figure 4 of Trujillo et al. 2004). The median effective radius of the FIRES galaxies is about a factor of two higher than that of the GRB sample.

The underlying reason for the smaller sizes of GRB host galaxies is revealed in the correlation between the effective radius and the rest-frame absolute \(B\)-band magnitude, \(M_{B}\) (Figure 7). The slope of the correlation for GRB hosts is remarkably similar to the relation found by Freeman (1970) for local exponential disks, but with a surface brightness that is about \(1-1.5\) mag arcsec\({}^{-2}\) higher. This is similar to the results found from the FIRES data, with the exception that the FIRES galaxies are brighter (and hence larger). ## 5 Discussion The sample of 42 GRB host galaxies imaged with HST yields several interesting trends. The host morphologies and surface brightness profiles indicate that GRB hosts are well described as exponential disks with sizes ranging from \(\sim 0.5-5\) kpc. In addition, GRB hosts exhibit a large fraction of interactions or mergers, particularly when compared to galaxies of similar luminosity from other surveys (Conselice et al. 2003). With the exception of GRB 990705, the GRB hosts lack distinctive spiral structure despite having predominantly disk dominated surface brightness profiles. As shown in SS4 the bulk of the galaxies have exponential surface brightness profiles. There are a few minor exceptions in low signal-to-noise filters, as well as in the case of GRB 021004, for which we find an adequate fit with an \(r^{1/4}\) profile using GALFIT; a fit with \(n=1\) is equally adequate. Except for GRB 990705, and possibly GRB 990123, none of the GRB host galaxies exhibit clear signs of spiral structure. This includes in particular the several hosts at \(z<0.5\), for which such structures should be easily detected. Conselice et al. (2004) show that spiral and bar structures should be visible at redshifts as high as \(z\sim 2.3\). The lack of ordered spiral structure in GRB hosts may point to a violent merger history which suppresses the emergence of spiral arms. The observed size-luminosity correlation presented in Figure 7 is in good agreement with that observed in other galaxy samples (e.g., Trujillo et al. 2005). However, the GRB sample extends this relation to lower luminosities due to the availability of absorption redshifts which are not subject to the brightness limit for spectroscopy imposed on flux-limited surveys. Three of the galaxies in our sample, GRBs 980703, 000418, and 010222, exhibit high luminosity at submillimeter and/or radio wavelengths (Berger et al. 2001; Frail et al. 2002; Berger et al. 2003). Contrary to the trend observed in submillimeter-selected galaxies (Chapman et al. 2003; Conselice et al. 2003), all three are highly symmetric and show no clear signs of interaction. Each was categorized as a blob-like galaxy, while GRB 980703 was additionally categorized as off-center. However, it has the most modest deviation of any of the

# Detection of neutral hydrogen in early-type dwarf galaxies of the Sculptor Group Antoine Bouchard Research School of Astronomy & Astrophysics, Mount Stromlo Observatory, Cotter Road, Weston Creek, ACT 2611 Australia and Australia Telescope National Facility, PO Box 76, Epping, NSW 1710, Australia bouchard@mso.anu.edu.au Helmut Jerjen, Gary S. Da Costa Research School of Astronomy & Astrophysics, Mount Stromlo Observatory, Cotter Road, Weston Creek, ACT 2611 Australia jerjen@mso.anu.edu.au, gdc@mso.anu.edu.au Jurgen Ott Australia Telescope National Facility, PO Box 76, Epping, NSW 1710, Australia Juergen.Ott@atnf.csiro.au ###### Abstract We present our results of deep 21 cm neutral hydrogen (Hi) line observations of five early and mixed-type dwarf galaxies in the nearby Sculptor group using the ATNF 64m Parkes1 Radio Telescope. Four of these objects, ESO294-G010, ESO410-G005, ESO540-G030, and ESO540-G032, were detected in Hi with neutral hydrogen masses in the range of \(2-9\times 10^{5}\) M\({}_{\odot}\) (\(M_{\rm HI}/L_{\rm B}\) = 0.08, 0.13, 0.16, and 0.18 \(M_{\odot}/L_{\odot}\), respectively). These Hi masses are consistent with the gas mass expected from stellar outflows over a large period of time. Higher spatial resolution Hi data from the Australia Telescope Compact Array1 interferometer

were further analysed to measure more accurate positions and the distribution of the Hi gas. In the cases of dwarfs ESO294-G010 and ESO540-G030, we find significant offsets of 290 pc and 460 pc, respectively, between the position of the Hi peak flux and the center of the stellar component. These offsets are likely to have internal cause such as the winds from star-forming regions. The fifth object, the spatially isolated dwarf elliptical Scl-dE1, remains undetected at our \(3\sigma\) limit of 22.5 mJy km s\({}^{-1}\) and thus must contain less than \(10^{5}\) M\({}_{\odot}\) of neutral hydrogen. This leaves Scl-dE1 as the only Sculptor group galaxy known where no interstellar medium has been found to date. The object joins a list of similar systems including the Local Group dwarfs Tucana and Cetus that do not fit into the global picture of the morphology-density relation where gas-rich dwarf irregulars are in relative isolation and gas-deficient dwarf ellipticals are satellites of more luminous galaxies. Footnote 1: footnotemark: Footnote 1: footnotemark: galaxies: dwarfs -- galaxies: ISM -- galaxies: group: Sculptor -- galaxies: evolution ## 1 Introduction Dwarf galaxies are at the center of a long debated galaxy evolution puzzle. Detailed studies of Local Group dwarfs have found increasing evidence that the specific morphological type of any particular dwarf is strongly correlated with the density of its local environment (i.e. the morphology-density realtion Einasto et al., 1974; van den Bergh, 1994): late-type dwarfs (mainly the dwarf irregulars, dIrr) tend to be further away from more massive and more luminous stellar systems than dwarf elliptical galaxies (dEs, including dwarf S0s, dS0, and dwarf spheroidals, dSph). These two main dwarf types differ in many other ways. In general, early-types, with their smooth ellipsoidal stellar distribution, lack an interstellar medium (ISM), possess low angular momentum (although see Geha et al., 2003, for a discussion on the luminous dEs), and have low current star formation rates (e.g. Mateo, 1998). In contrast, the late-types exhibit an irregular optical appearance that is dominated by Hii regions and ongoing star formation, large neutral hydrogen mass to luminosity ratios (e.g. Koribalski et al., 2004), and higher angular momentum. Morphologically, there is no clear boundary between the two main dwarf types, dIrr and dE. Instead, there exist mixed-type dwarfs (dIrr/dE, e.g. Phoenix) which exhibit properties inherent to both categories. Furthermore, detailed stellar population studies of Local Group dwarfs have revealed that dEs do not have simple single-burst, old stellar populations like globular clusters, but instead show a large variety of star formation histories (e.g. Grebel

2001; Hensler et al. 2004). The morphology-density relation and the continuous range in stellar/gas properties across dwarf galaxy families naturally suggests that evolution from one main morphological class to the other might be an ongoing process that is still observable in the local Universe. Environmentally driven physical processes such as ram pressure stripping (Einasto et al., 1974) and/or tidal effects (Moore et al., 1996), or internal processes like stellar winds and supernovae explosions combined with the shallow gravitational potential of the galaxy could be responsible for a fast morphological transformation. In such a scenario, the mixed type dwarfs are thought to be in the transition phase from dIrr to a dE stage. While theoretically supported by numerical simulations (Mayer et al., 2001), Grebel et al. (2003) argued against this evolutionary scenario with two major objections: firstly, the fading of a dIrr to the typical luminosity of a dE would produce an object with too low metallicity than what is observed and, secondly, the removal of the ISM from a dIrr would not produce a non-rotating dE (see also Read & Gilmore, 2005). However, one should note that the absence of angular momentum is no longer considered as a defining element of the dE class since rotation was measured in some of the bright dEs (e.g. van Zee et al., 2004; De Rijcke et al., 2004, 2003; Pedraz et al., 2002; Simien & Prugniel, 2002). The limitation of the morphological classification is that it merely describes the stellar distribution of a galaxy and conveys little physical information on the objects. This classification scheme gives, at best, an imprecise view of the stellar population (i.e. it can not distinguish between a 1 Gyr and 15 Gyr old population) and conveys no information on the total mass, internal kinematics, or chemical composition. Yet, studies of Local Group dEs helped to establish empirical relations between morphology and physical parameters such as the morphology-density relation, but have failed to establish a direct quantitative correlation based on solid physical principles. Consequently, it is difficult to understand the relation between individual galaxy types and their respective evolutionary state. In fact, the properties of dwarf galaxies in the Local Group paint a rather complex picture. For example, the spatially isolated, mixed morphology galaxy LGS3 is dominated by an old stellar population but has had sustained star formation for most of its life (Aparicio et al. 1997; Miller et al. 2001). It also contains \(\sim\)6\(\times\)10\({}^{5}\) M\({}_{\odot}\) of Hi centered on the optical component of the galaxy (Young & Lo, 1997). The slightly less isolated Phoenix dwarf, also of mixed morphology, has a \(\sim 10^{5}\) M\({}_{\odot}\) Hi cloud that is offset by 650 pc (a third of the tidal radii, Martinez-Delgado et al. 1999) from the optical center (St-Germain et al., 1999) while also having a predominantly old stellar population but sustained, long term star formation (Holtzman et al., 2000). The similarly isolated Tucana dwarf has had no extended star formation (e.g. Da Costa, 1998) and contains no Hi within its optical boundaries. There is, however, a hydrogen cloud projected on the sky near the galaxy, which might be related (see Oosterloo et al., 1996). Further, the

Local Group dSph Sculptor apparently possesses two Hi clouds distributed symmetrically on either side of the optical center (Knapp et al. 1978; Carignan et al. 1998; Bouchard et al. 2003). The central regions (within \(\sim 1.7\) core radii or 230 pc) are, however, gas free and the galaxy itself contains only very old stars (\(>\) 10 Gyr) with no evidence of any ongoing star formation (Hurley-Keller et al. 1999; Monkiewicz et al. 1999). Due to this rather complex picture drawn from Local Group dwarfs, one needs to study a larger sample of galaxies -- therefore beyond the Local Group -- to establish a quantitative measure of the environmental influence on a dwarf system and to put it into a relation with the fundamental properties of the galaxies (e.g. stellar population, etc.). Such a relation needs to take into account the quantity of ISM and its distribution. Conselice et al. (2003, and references therein) previously reported that \(\sim 15\%\) of early-type dwarfs in the dense Virgo cluster have \(M_{\rm HI}\gtrsim 10^{7}M_{\odot}\). These galaxies are potentially newly accreted members or on orbits that never lead them in the cluster's center. In addition, they have Hi properties similar to Local Group transition and late-type dwarfs; the Local Group early-type dwarfs have much lower Hi content. It is argued that the Virgo cluster acts as an "evolutionary change engine" and that these Hi rich dEs were dIrrs that have recently made the transition by means of ram pressure or Kelvin-Helmholtz instabilities (i.e. the morphology-density relation at work). Alternatively, Buyle et al. (2005) suggests that an enhanced star formation rate due to ram pressure and gravitational interactions, will accelerate the gas depletion in such systems. Both these studies have targeted relatively bright dEs (\(L_{\rm B}\gtrsim 10^{7}L_{\odot}\)) in a dense environment, somewhat different to the situation of Local Group dEs. In order to assess the overall validity of the morphology-density relation and the relative importance of the environment in dwarf galaxy evolution, we must now study a regime of low mass galaxies in a low density environment. Under such conditions, the environmental impact on galaxy evolution should be minimized while the shallow potential well of the low mass dEs will help to amplify the effect of internal mechanisms (e.g. stellar winds, supernova explosions). The Sculptor group (Fig. 1), with its sparse galaxy distribution, provides an ideal laboratory to study galaxies in such an environment without having to hunt down truly isolated objects. Due to its proximity to the Local Group (1.5 to 4 Mpc, Jerjen et al. 1998; Karachentsev et al. 2003), detailed studies of stellar populations (Karachentsev et al., 2000; Skillman et al., 2003b; Olsen et al., 2004), ISM contents (Cote et al., 1997; de Blok et al., 2002), and chemical compositions (Skillman et al., 2003a) of Sculptor galaxies are available. There are six early-type dwarf galaxies known in the Sculptor group and prior to this study five have not been detected in Hi. The sixth, NGC 59, is a dS0 galaxy for which Cote et al. (1997) reported detections in both Hi (5.4\(\times 10^{6}\) M\({}_{\odot}\)) and H\(\alpha\). The five other galaxies

are: the dS0/dIrr ESO294-G010, the two dE/dIrr ESO540-G030 and ESO540-G032, the dSph ESO410-G005, and the dE Scl-dE1. For all but Scl-dE1, stellar photometry based on Hubble Space Telescope data reveals statistical evidence for the presence of blue stars in the central regions of these galaxies (Karachentsev et al., 2000; Jerjen & Rejkuba, 2001; Karachentsev et al., 2002, 2003) although the possibility that such stars result from photometric errors in the crowded central fields cannot be excluded at this time. In addition to these possibly young stars, Jerjen et al. (1998) have identified a small Hii region in ESO294-G010. This paper presents the results of a deep Hi study of these five early-type Sculptor group dwarfs and addresses the central question as to whether the light distribution of a galaxy (i.e. morphology) is sufficient to predict ISM content. The paper is organised as follows: the observations are described in section 2, section 3 describes the Hi properties of our sample galaxies, and section 4 provides a discussion of the Sculptor group. The main conclusions can be found in section 5. ## 2 Observations ### Sample properties We have observed the five lowest luminosity objects of the Sculptor group. They are also the only five objects of the group where no Hi detection were previously reported. General properties of these five dwarfs are described in detail in Jerjen et al. (1998, 2000). In Table 1, we list some of their physical parameters. The first two columns provide the coordinates. The distances \(D\) in Mpc have previously been measured using the tip of the red giant branch technique (Karachentsev et al., 2000, 2002, 2003). The apparent \(B\)-magnitudes \(m_{\rm B}\) and extinction are given in Jerjen et al. (2000). This allowed us to calculate the luminosities, \(L_{\rm B}\) (we adopted a value of M\({}_{\odot,B}\) = 5.5, Bessell et al. 1998), and absolute magnitudes, M\({}_{B}\). For ESO294-G010, the optical, spectroscopic velocity (Jerjen et al., 1998) is also listed in Table 1. ### Hi observations In 2004 October, the 64 m ATNF Parkes Radio Telescope was employed to obtain deep, high spectral resolution Hi spectra toward the five Sculptor dwarf galaxies. We used the Multibeam instrument in MX (beam-switching) mode along with the narrowband correlator in the MB7_8_1024 configuration provide 8 MHz bandwidth divided into 1024 channels. The observations were done at a central frequency of 1418 MHz, resulting in an Hi velocity

coverage from \(-300\) to \(1300\) km s\({}^{-1}\) with channel widths of 1.6 km s\({}^{-1}\) and a beam size of 14.1\({}^{\prime}\). This configuration enabled us to observe with seven beams simultaneously, keeping one beam on-source with the six others on adjacent sky, alternating the on source beam every two minutes. The integration times for the target galaxies were: 294 min for ESO294-G010, 210 min for ESO410-G005, 336 min for ESO540-G030, and 224 min for ESO540-G032. These resulted in clear detections in Hi. The RMS values are listed in Table 2. In the case of Scl-dE1, 434 min of on-source integration yielded a spectral RMS of 1.2 mJy but no detection. The obtained spectra were reduced using the LIVEDATA data reduction pipeline. The median of the Tukey smoothed bandpasses -- to remove the effect of radio frequency interference -- was used for calibration. The gridding was performed using GRIDZILLA, using the median of weighted values as estimator. Both LIVEDATA and GRIDZILLA are available in the AIPS++ software package. To remove residual baseline ripples, caused by a well known 5.8 MHz standing wave between the focus cabin and the vertex of the Parkes telescope, the MBSPECT robust fitting algorithm from the MIRIAD software package was used to fit (over the complete spectral region) and remove 7\({}^{th}\) or 8\({}^{th}\) order polynomials. The spectra of the five galaxies are shown in Fig. 2. Various moments (total flux, \(\int S_{v}\,\textrm{d}v\), flux weighted mean velocity, \(v_{\rm HI}\), and flux weighted velocity dispersion, \(\sigma_{\rm HI}\)) are listed Table 2. The errors listed were calculated using a Monte-Carlo approach where normally distributed noise (the RMS was used as the dispersion) was added to the spectra. Data from the Australia Telescope Compact Array (ATCA) archive are available for three of these objects: ESO294-G010, ESO540-G030, and ESO540-G032 (project C705). These data were obtained in 1998 December in the 750D array and the FULL_8_512 correlator configuration, corresponding to 8 MHz bandwidth divided in 512 channels. The source PKS1934-638 was used as flux calibrator and PKS0023-263 and PKS0022-423 were used for phase calibration. Taking advantage of our Parkes observations, we identified the channels in the ATCA data that contain the 21 cm line emission from the galaxies. Without the prior knowledge of the Hi velocity range provided by the Parkes dataset, it would have been impossible to detect the faint Hi signals near the target galaxies. Using the MIRIAD data reduction package, the data were gridded using 'natural' weighting to a channel spacing of 4 km s\({}^{-1}\) and pixel size of 10\({}^{\prime\prime}\). The images were deconvolved using the CLEAN algorithm and RESTORed to beam sizes of \(69^{\prime\prime}\times 52^{\prime\prime}\) for ESO294-G010, \(250^{\prime\prime}\times 35^{\prime\prime}\) for ESO540-G030, and \(157^{\prime\prime}\times 39^{\prime\prime}\) for ESO540-G032. To maximize the signal to noise ratio, we generated integrated intensity maps using only those channels where the flux rose above 1\(\sigma\) in the equivalent Parkes spectra channel. The results are shown in Fig. 3

which also shows optical images from the Digitized Sky Survey. ## 3 Results and discussion ### Hi association Galaxies in the Sculptor group have heliocentric velocities ranging from \(100<v<500\) km s\({}^{-1}\)(Cote et al., 1997). It was also previously established, by direct distance measurements (Jerjen et al., 1998; Karachentsev et al., 2000; Jerjen & Rejkuba, 2001; Karachentsev et al., 2003), that the galaxies we observed are genuine members of the Sculptor group. Since our Hi detections fall inside the velocity range mentioned above (our clouds have velocities between 100 km s\({}^{-1}\) and 250 km s\({}^{-1}\), Fig. 2) the assumption that they are related to the targeted galaxies is reasonable. However, we have no information on the distances to these Hi clouds and the possibility of foreground 21 cm emission with overlapping velocities cannot be excluded a priori. Because of the low velocity range and the projected position of the Sculptor group on the sky, there are two potential contamination sources: High Velocity Clouds (velocities between \(-300\) km s\({}^{-1}\) and \(250\) km s\({}^{-1}\)) and the Magellanic Stream (between 0 km s\({}^{-1}\) and 150 km s\({}^{-1}\), Putman et al. 2003; Bruns et al. 2005). High Velocity Clouds (HVCs) are Galactic Hi clouds with velocities that do not fit simple Galactic rotation models. We consider that HVC contamination is not a source of confusion for the observed positions due to the following reasons. First, there are no catalogued HVCs (Putman et al., 2002) within 30\({}^{\prime}\) of any of our targets and that, in addition, there are no HVCs with velocities consistent with those of our Hi detections within one degree. Second, the majority of Compact HVCs have sizes of the order of 30\({}^{\prime}\)(Braun & Burton, 2000; Bruns et al., 2001; Burton et al., 2001; de Heij et al., 2002) although the most compact HVC found to date has an extent of 4\({}^{\prime}\).4 (Bruns & Westmeier, 2004), twice the size of the present detections. We, however, recognise that the Hi maps of Fig. 3 come from aperture synthesis observations, so that it is likely some Hi flux remains undetected on the larger scales inaccessible with the array configuration employed (a problem that Bruns & Westmeier 2004 managed to avoid). By calculating the total Hi flux for the clouds from the ATCA data and comparing these with the Parkes data, we estimate that the ATCA observations recover \(\sim 40\)% of the flux for ESO294-G010, \(\sim 30\)% for ESO540-G030, and \(\sim 80\)% for ESO540-G032. The clouds should therefore be slightly larger than what is seen in Fig. 3, but, nevertheless, they remain significantly smaller than even the most extreme compact HVC.

The Magellanic Stream remains a problem because of its large radial velocity scatter near the Sculptor group (Bruns et al., 2005). Further analysis would be necessary if one wishes to disentangle the origins and establish the physical location of each single cloud in that direction. Nevertheless, there is generally a good agreement between the position of the Sculptor dwarfs and the Hi detections (Fig. 3). In the following, we will assume that the detected Hi clouds are indeed associated with the Sculptor group galaxies. ### Hi properties For each object, the RMS of the spectra, the total flux, the flux weighted mean velocity and velocity dispersion of the Hi are quoted in Table 2. We also estimated the Hi masses \(M_{\rm HI}\), expressed in solar units, M\({}_{\odot}\), using the standard equation: \[M_{\rm HI}=2.356\times 10^{5}~{}D^{2}~{}\int S_{v}\,\textrm{d}v\] (1) where \(D\) is the distance in Mpc (in Table 1), and \(S_{v}\) is the Hi flux density in Jansky. The integration was computed up to where the signal fell below the 1\(\sigma\) noise level on either side of the emission peak. The derived total Hi masses for ESO294-G010, ESO410-G005, ESO540-G030 and ESO540-G032 are \(M_{\rm HI}\) = (3.0\(\pm\)0.3)\(\times\)10\({}^{5}\) M\({}_{\odot}\) (the peak flux is 8\(\sigma\) above noise level), \(M_{\rm HI}\) = (7.3\(\pm\)1.5)\(\times\)10\({}^{5}\) M\({}_{\odot}\) (12\(\sigma\)), \(M_{\rm HI}\) = (8.9\(\pm\)1.9)\(\times\)10\({}^{5}\) M\({}_{\odot}\) (7\(\sigma\)) and \(M_{\rm HI}\) = (9.5\(\pm\)1.6)\(\times\)10\({}^{5}\) M\({}_{\odot}\) (9\(\sigma\)) respectively. The undetected galaxy, Scl-dE1, has an upper limit MHI<1.0x10\({}^{5}\) M\({}_{\odot}\) (3\(\sigma\) limit for an assumed 10 km s\({}^{-1}\) velocity dispersion at 4.21 Mpc). This is comparable to Tucana which has no Hi detected within its optical boundary (\(M_{\rm HI}\)/\(L_{\rm B}\)\(<\) 0.03 \(M_{\odot}/L_{\odot}\), Oosterloo et al., 1996). The Hi masses for the other four galaxies are comparable to that of similar Local Group mixed and early type dwarfs where Hi has been detected: Sculptor dSph has 2.3\(\times 10^{5}\) M\({}_{\odot}\)(\(M_{\rm HI}\)/\(L_{\rm B}\) = 0.2 \(M_{\odot}/L_{\odot}\), Bouchard et al., 2003), LGS3 has 4.2\(\times 10^{5}\) M\({}_{\odot}\)(\(M_{\rm HI}\)/\(L_{\rm B}\) = 0.3 \(M_{\odot}/L_{\odot}\), Young & Lo, 1997), Phoenix has 1.9\(\times 10^{5}\) M\({}_{\odot}\)(\(M_{\rm HI}\)/\(L_{\rm B}\) = 0.2 \(M_{\odot}/L_{\odot}\), St-Germain et al., 1999), and Antlia exhibits 6.8\(\times 10^{5}\) M\({}_{\odot}\)(\(M_{\rm HI}\)/\(L_{\rm B}\) = 0.4 \(M_{\odot}/L_{\odot}\), Barnes et al., 2001). Buyle et al. (2005) argued that the low values of \(M_{\rm HI}\)/\(L_{\rm B}\) typically found in dEs may be a direct result from a near complete gas depletion due to enhanced star formation efficiency. They were using the results of an analytical chemical evolution model (Pagel & Tautvaisiene, 1998) and stellar mass-to-light ratios (\(M_{\star}\)/\(L_{\rm B}\)) from a simple stellar population model (SSP Vazdekis et al., 1996). In this approach all the gas that has been ejected from stars (stellar winds, supernova explosions, planetary nebulae, etc.) is effectively expelled from the galaxy, but leaving part of the metals to enrich the chemical composition of subsequent gas inflow

and star formation. The resulting state is a metal-enhanced (unless the metals also escape) but inevitably gas deficient galaxy. Using the SSP model from Anders & Fritze-v. Alvensleben (2003) at a metallicity (Z) of 0.02 Z\({}_{\odot}\) and by assuming a constant star formation rate of 0.01 \(M_{\odot}\) per yr over the entire lifetime of the galaxy, we calculated that the ISM return from normal stellar evolution should give a mass-to-light ratio of the order of \(M_{\rm ISM}\)/\(L_{\rm B}\) = 0.25 \(M_{\odot}/L_{\odot}\) after 10 Gyr. Our objects have \(M_{\rm HI}\)/\(L_{\rm B}\) between 0.08 \(M_{\odot}/L_{\odot}\) and 0.19 \(M_{\odot}/L_{\odot}\), consistent with this simple case of passive, undisturbed evolution. Most of the expelled gas should therefore be retained in the galactic potential well and cooled to the form of Hi. This, however, implies that the pristine gas used to form stars in the galaxy, has not build-up any reservoirs and is instantly used up by star formation. We must therefore conclude that the Hi content in our galaxies is consistent with both the enhanced efficiency of star formation and gas buildup from stellar evolution. In the case of Scl-dE1, like many Local Group early-type dwarfs (as noted by Grebel et al., 2003) and even Galactic globular clusters, some factors may have prevented the cooling process and/or the accumulation of Hi in the system. Fig. 4 shows the relation between Hi mass and absolute magnitude for galaxies from the HIPASS Bright Galaxy Catalog (Koribalski et al., 2004), from the Centaurus A and Sculptor Group (Cote et al., 1997) and from the Local Group (Mateo, 1998, and references therein). Our results agree with that of Warren et al. (2004), who noted that dwarf galaxies have a larger spread in \(M_{\rm HI}\)/\(L_{\rm B}\) than brighter galaxies. There is indeed evidence that the spread is one order a magnitude larger in the dwarf regime compared to more luminous galaxies. ### Hi distribution The Hi maps in Fig. 3 show, in two out of three cases, an apparent offset between the Hi gas and stellar components of the galaxies. Because of the low signal to noise ratio in our aperture synthesis images we adopted a conservative error on the accurate position of the Hi emission peak of a third of the beam size. These offsets are \(\sim\)35\({}^{\prime\prime}\) (290 pc projected distance or \(\sim 0.9\) times its Holmberg radius, \(R_{\rm Ho}\), Jerjen et al. 2000) for ESO294-G010 -- greater than the \(\sim 20^{\prime\prime}\) accuracy -- and \(\sim\)30\({}^{\prime\prime}\) (460 pc or \(\sim 0.85\,R_{\rm Ho}\)) for ESO540-G030 -- greater than the \(\sim 10^{\prime\prime}\) accuracy. In the third case, ESO540-G032, the apparent offset is smaller than the uncertainty of the Hi position and thus consistent with being centered. An offset between the Hi and optical was previously detected in the Local Group galaxy Phoenix. Not only is the Hi in Phoenix found 5\({}^{\prime}\) or 650 pc from the optical center of the galaxy (St-Germain et al., 1999) but Gallart et al. (2001) also found that the gas is kine

matically separated from the optical by 29 km s\({}^{-1}\). These authors have also conducted semi-analytical and numerical analyses to demonstrate that the Hi offset is either the consequence of the environmental conditions, i.e. ram pressure by the intergalactic medium Phoenix travels through or the result of an internal process i.e. several supernova explosions in the dwarf. The authors favored the former explanation -- without discarding the latter -- because it produced a smooth, anisotropic structure similar to that observed. In the low density environment represented by the Sculptor Group, most galaxies can be considered as essentially isolated objects, and, in that respect, should be under similar conditions as Phoenix (which lies at 450 kpc from the Milky Way). More precisely, the closest neighbour to both ESO540-G030 and ESO540-G032 is the faint IB(s)m galaxy DDO6, at a relative 3-dimensional distance of 180 kpc and 100 kpc, respectively, while the brighter spiral NGC247 is around 700 kpc behind the pair. The closest neighbour of ESO294-G010 is the spiral NGC55 at a 3-dimensional distance of 160 kpc (radial distances from Karachentsev et al., 2004). Although these distances are significantly smaller than that of Phoenix to the Milky Way, the larger counterparts are of much lower mass. We can therefore draw similar conclusions as Gallart et al. (2001) to explain the Hi and optical geometry of the systems. The possibility of tidal stripping seems unlikely in this case as the gas would not be concentrated on one side of the optical but stretched on both sides. Furthermore, with the large distances separating the dwarfs to their neighbours, the tidal forces should be minimal. It is worth noting that, in the case of ESO294-G010, Jerjen et al. (1998) reported the existence of an Hii region \(\sim 18^{\prime\prime}\) south of its optical center while the Hi is on the north side. This is the opposite situation as was observed in Phoenix were the Hi emission is on the same side as the galaxy's youngest stars (Martinez-Delgado et al., 1999). This might suggest that in ESO294-G010, the supernova explosion/stellar wind scenario might play a bigger role than in the case of Phoenix. Detailed stellar population studies of these Sculptor dwarfs are needed to explore the various possibilities. The only Sculptor galaxy where no Hi is detected to date, Scl-dE1, is also one of the only two dEs of the group. Yet, contrary to the prediction of the morphology-density relation, this object is located far from any other group members. Its closest more massive neighbour, the starburst spiral NGC253, is spatially separated by \(\sim 480\) kpc (5.4\({}^{\circ}\) projected angular separation or \(\sim 400\) kpc tangential distance, and 270 kpc radial distance). We note that the spiral galaxy NGC45 is the closest in projection but its distance of 5.9 Mpc (Tully 1988) places it 2 Mpc, to the far end of the group. This situation of Scl-dE1 is reminiscent of the case of the isolated Local Group early-type dwarf Tucana (880 kpc away from the Milky Way) since both objects also have predominantly old stellar populations, or the Cetus dwarf (755 kpc from the Milky Way) which has some young stars (McConnachie et al., 2005) but no

Hi. Apart from the possibility of Scl-dE1, Tucana, and Cetus being on highly eccentric orbits that would lead these galaxies much closer to their neighbouring galaxies at perigalacticon, there is only a weak case for an environmentally driven gas removal process or ionisation and thus strong internal mechanisms (e.g. Supernovae driven winds or radiative feedback, see Dekel & Woo 2003) must be responsible for the properties of these objects. ## 4 On the Sculptor group and the morphology-density relation The Sculptor group is known to be a loose aggregation of several luminous galaxies with satellites and late-type dwarfs populating the space between rather than a virialized system (Jerjen et al., 1998). Fig. 1 shows the large extent of the galaxy distribution on the sky of \(\sim 25^{\circ}\) or over 1 Mpc across, at an assumed mean distance of 2.5 Mpc. Group members exhibit even a wider dispersion in their line of sight distances (Jerjen et al., 1998; Karachentsev et al., 2003). Cote et al. (1997) initially derived a dynamical crossing time of 3.2\(\times 10^{9}\) years assuming a virialized system and using projected distances to the tentative group center. Because of the "cigar-like distribution" (Jerjen et al., 1998) of the group the assumption of an isotropic system does not stand and this value can only be a lower limit whereas the true value must be closer to a Hubble time. This makes the Sculptor group a prototypical low density environment where interaction between galaxies are expected to be minimal and external gas stripping largely ineffective. Indeed, all but one galaxy of the Sculptor group have substantial amounts of Hi which is either primordial or the result from stellar feedback. In all cases, the environment of these galaxies has not managed to either remove that gas or ionise it. This can be viewed as a confirmation of the overall validity of the morphology-density relation in a low density environment. There is, however, one caveat: contrary to the standard view of the morphology-density relation and the environmentally driven late-type to early-type evolution scenario, the low mass end of the galaxy spectrum in the loosely-bound Sculptor group is not solely populated by late-type dwarfs. In fact, our results support the Grebel et al. (2003) contention that: _"Transition-type dwarfs are dSphs that kept their interstellar medium and therefore should replace dSphs in isolated locations where stripping is ineffective."_ This is further reinforced by the fact that our five target galaxies are of very low \(M_{\rm HI}/L_{\rm B}\) (see Table 2 and Fig. 4). In line with the morphology-density relation and because of the presence of both Hi gas and a centrally concentrated population of young blue stars (Karachentsev et al., 2000) in ESO410-G005, we propose a reclassification of ESO410-G005 (initially labelled dSph, Karachentsev et al. 2000) to dSph/dIrr. We believe that this reclassification would better

reflect the nature of this low mass dwarf. Similarly, since NGC59 contains both Hi (Cote et al., 1997) and Hii regions (Skillman et al., 2003b), it is not a genuine early-type dwarf and should be classified as dS0 pec. These changes give weight to the empirical relation between morphology and ISM content in the Sculptor group, i.e. a slightly irregular morphology caused by the presence of young stars seem to indeed indicate an underlying presence of ISM. Consequently, the Sculptor group has only one single early-type dwarf system: Scl-dE1, without Hi or any young stars (Karachentsev et al., 2003). This, however, highlights a second caveat in the morphology-density relation for low density environments. While the relation describes well the general trend of gas-rich dwarf irregular galaxies being relatively isolated stellar systems and early-type dwarfs the satellites of more luminous galaxies, it provides no explanation for the existence of an isolated gas deficient early-type dwarf galaxy like Scl-dE1. This object joins a list of similar systems including Tucana and Cetus that do not fit the global picture. Clearly these systems hold important clues to what extent internal gas expulsion mechanisms (supernova explosions or stellar winds) govern the passive evolution of dwarf galaxies in the field. ## 5 Conclusions In this paper we have presented the results of Hi observations toward the five lowest luminosity dwarf galaxies of the Scultor group. The main results are: 1. 1.All but one galaxy of the Sculptor group have substantial amounts of Hi (\(M_{\rm HI}\,>\,3\times 10^{5}\) M\({}_{\odot}\)). Four new Hi detections have been made with \(3\times 10^{5}\,\)M\({}_{\odot}\)\(<\,M_{\rm HI}\,<\,10^{6}\,\)M\({}_{\odot}\). The only undetected galaxy, Scl-dE1, must have \(M_{\rm HI}\,<\,10^{5}\) M\({}_{\odot}\). All Sculptor galaxies except Scl-dE1 have \(M_{\rm HI}\)/\(L_{\rm B}\,>\,0.08\)\(M_{\odot}/L_{\odot}\). 2. 2.The Hi masses for ESO294-G010, ESO410-G005, ESO540-G030, and ESO540-G032 are all consistent with passive, undisturbed evolution where all the gas from stellar winds has condensed in the form of Hi. 3. 3.ESO410-G005, formerly classified as a dSph galaxy, better fits the dSph/dIrr category while NGC59 is a dS0 pec. There is only one genuine early-type dwarf galaxy in the Sculptor group: Scl-dE1. 4. 4.At least two of the mixed-morphology galaxies, ESO294-G010 and ESO540-G030, have a significant offset between their optical and Hi components. These offsets are likely to be caused by winds from star forming regions. 5.

5.The morphology-density relation seems to be valid for low-density environments where mixed-type galaxies, and not late-types, replace the early-type systems when in isolation. 6. 6.Scl-dE1 joins Tucana and Cetus as an isolated low mass gas-deficient early-type dwarf. These objects require internal mechanisms to explain their evolutionary states. We would like to thank Sylvie Beaulieu, Lister Staveley-Smith and Barbel Koribalski for insightful discussions, as well as the anonymous referee for diligent and valuable comments. This research has been supported by the Australian Research Council through Discovery Project Grant DP0343156. The Digitized Sky Surveys were produced at the Space Telescope Science Institute under U.S. Government grant NAG W-2166.

# C i non-LTE spectral line formation in late-type stars 1-2 D. Fabbian\({}^{1}\) M. Asplund\({}^{1}\) M. Carlsson\({}^{2}\) D. Kiselman\({}^{3}\) \({}^{1}\)RSAA, The Australian National University, Mt. Stromlo Observatory, Cotter Rd., Weston ACT 2611, Australia email: damian@mso.anu.edu.au \({}^{2}\)Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029, Blindern, N-0315 Oslo, Norway \({}^{3}\)The Institute for Solar Physics of the Royal Swedish Academy of Sciences, AlbaNova University Centre, 106 91 Stockholm, Sweden (2005; ?? and in revised form ??) ###### Abstract We present non-Local Thermodynamic Equilibrium (non-LTE) calculations for neutral carbon spectral line formation, carried out for a grid of model atmospheres covering the range of late-type stars. The results of our detailed calculations suggest that the carbon non-LTE corrections in these stars are higher than usually adopted, remaining substantial even at low metallicity. For the most metal-poor stars in the sample of Akerman et al. (2004), the non-LTE abundance corrections are of the order of \(-0.35...-0.45\) dex (when neglecting H collisions). Applying our results to those observations, the apparent [C/O] upturn seen in their LTE analysis is no longer present, thus revealing no need to invoke contributions from Pop. III stars to the carbon nucleosynthesis. keywords: Line: formation, radiative transfer - stars: abundances, atmospheres, late type - galaxy: abundances + Footnote †: editors: V. Hill, P. François & F. Primas, eds. + Footnote †: editors: V. Hill, P. François & F. Primas, eds. + Footnote †: editors: V. Hill, P. François & F. Primas, eds. The lack of detailed investigations on the non-LTE formation of spectral lines for a variety of chemical elements is unfortunately a major obstacle in pushing current stellar abundance studies to the 0.1 dex precision limit or less. It is fundamental to have a clear understanding of the trends with for example metallicity, for various elements, as a way to shed light on the chemical evolution of our Galaxy and of the Universe in general. We have carried out non-LTE spectral line formation calculations for C i using the code _Multi_ (Carlsson 1986). A grid of MARCS model atmospheres with stellar parameters in the range \(4500\leq\)T\({}_{eff}\)\(\leq 7000\), \(2.0\leq\)\(\log\) g\(\leq 5.0\) and \(-3\leq\)[Fe/H]\(\leq 0\) has been employed. The carbon atomic model used in this study contains 217 energy levels and 650 radiative transitions (f-values and photo-ionization cross-sections from the OP database TOPbase, Cunto et al. 1993) and collisions with electrons and hydrogen are also included. The magnitude of the non-LTE effects affecting the formation of carbon spectral lines in these late-type stars and their trend with effective temperature, gravity, metallicity and carbon content have been investigated: spectral lines were found to be generally stronger in non-LTE across our parameter grid. Thus, with respect to the LTE approximation, we obtain negative abundance corrections, which become particularly severe at high temperature (6000-7000 K) and low gravity (2.0-3.0), where they can reach \(\sim-1.0\) dex and more, while for the most metal-poor halo turn-off stars \(\Delta\log\,\epsilon_{\rm C}\simeq-0.35...-0.45\). The driving non-LTE effects are found to be the source function dropping below the local Planck function (at solar metallicity), while increased line opacity is responsible for the non-LTE line strengthening at low metallicity. The most pronounced corrections are seen at [Fe/H]\(=-1\) dex, where these two effects work in the same sense. However, corrections are shown to be generally large across the whole grid

. In particular, to better constrain the evolution of the C/O ratio, we have focussed our attention on the non-LTE processes affecting the lines still visible in the metal-poor regime. The influence of changing the efficiency of H collisions (which probably remain the major source of uncertainty in our study and in similar ones), has also been investigated in the present work, showing little sensitivity of the overall resulting non-LTE abundance corrections for the metal-poor halo stars of interest, where they become less dramatic but still remain important (of the order of \(\Delta\log\,\epsilon_{\rm C}\simeq-0.25...-0.35\)) when setting efficient hydrogen collisions. Very recently, statistical equilibrium calculations for carbon across a grid of stellar parameters similar to the one adopted here, have been carried out by Takeda & Honda (2005). These authors find similar significantly large non-LTE corrections. A detailed comparison with their results is of interest and, together with full details of our study, will be shortly available in a subsequent paper (Fabbian et al. 2005). These findings have important consequences on studies of Galactic chemical evolution, in particular on the derivation of carbon abundance at low metallicity. Figure 1 shows results of Akerman et al. (2004), where those authors have assumed that the carbon non-LTE corrections are of the same order as those calculated for oxygen. An apparent upturn in the [C/O] ratio at low metallicity is then visible when an LTE analysis is performed. However, after applying the here calculated non-LTE corrections, such a trend is no longer present, which suggests it is probably due to errors intrinsic in the use of the LTE approximation. Instead, an almost flat "plateau" is recovered, with [C/O]\(\sim-0.7\) at [O/H]\(=-1\) and remaining approximately constant down to [O/H]\(\sim-2.5\). Thus, there is apparently no need to invoke C production in Pop. III stars, as advocated by Akerman et al. (2004) and Spite et al. (2005). More high-quality spectroscopic data for these metal-poor turn-off stars is highly desirable to better constrain the trends at low metallicity. ## References * [Akerman et al. (2004)] Akerman, C.J., Carigi, L., Nissen, P.E., Pettini, M. & Asplund, M. 2004, _A&A_ 414, 931 * [Carlsson (1986)] Carlsson, M. 1986, _'A Computer Program for Solving Multi-Level Non-LTE Radiative Transfer Problems in Moving or Static Atmospheres'_, in _Uppsala Astronomical Report No. 33_ * [Cunto, W., Mendoza, C., Ochsenbein, F., Zeippen, C. J. (1993)] Cunto, W., Mendoza, C., Ochsenbein, F., Zeippen, C. J. 1993, _A&A_ 275, L5 * [Fabbian et al. (2005)] Fabbian, D., Asplund, M., Carlsson, M., Kiselman, D. 2005, _to be submitted to A&A_ * [Gustafsson et al. (1999)] Gustafsson, B., Karlsson, T., Olsson, E., Edvardsson, B. & Ryde, N. 1999, _A&A_ 342, 426 * [] Takeda, Y. & Honda, S. 2005, PASJ 57, 65 Figure 1: Trend of the [C/O] ratio vs. oxygen abundance, in Milky Way halo and disk stars, in logarithmic abundances relative to solar. The empty symbols represent literature data (see Akerman et al. 2004). Filled symbols represent the abundance values we obtain with oxygen non–LTE corrections as adopted by those authors, but accounting for our larger non–LTE corrections for carbon. Both carbon and oxygen abundance corrections used in this plot are calculated neglecting inelastic collisions with hydrogen

leading to an rms of about 0.3 mK (2.8 mJy)4. We estimate the flux density scale to be accurate to about 30%. Footnote 4: The conversion between antenna temperature and flux density scale at 256 GHz for the 30m is 9.5 Jy/K. The final spectrum of the [CII] emission line in J1148+5251 is shown in Fig. 1. The \(\rm C^{+}\) fine-structure line is detected with a confidence 8 \(\sigma\). The velocity integrated flux is \(\rm 0.44\pm 0.05~{}K\,km\,s^{-1}\) (in antenna temperature, \(\rm T_{mb}=1.91~{}T_{A}\)), or \(\rm 4.1\pm 0.5\,Jy\,km\,s^{-1}\), and the line center corresponds within the uncertainties to the center of the CO line emission (Table 1 and Fig. 1). Bolatto et al. (2004) used the James Clerk Maxwell Telescope to detect the C\({}^{+}\) line in J1148+5251, but could only place an upper limit to its line strength. To compare their limits with our result we note that the peak intensity of our line (12 mJy) is three times lower than the rms (32 mJy) in their final spectrum smoothed to a resolution of 10 MHz (or \(\rm 12\,km\,s^{-1}\)). The [CII] velocity integrated flux reported in this paper is twice larger than the 1\(\sigma\) limit estimated by Bolatto et al. for the intensity of any putative line in the JCMT spectrum. ## 3 Discussion The emission of \(\rm C^{+}\) in J1148+5251 is an extreme example of what is seen in local infrared galaxies. The \(\rm L_{[CII]}/L_{FIR}\) ratio in J1148+5251 is \(2\times 10^{-4}\), about an order of magnitude smaller than in local starburst galaxies. This is illustrated in Fig. 2, where we plot the \(\rm L_{[CII]}/L_{FIR}\) ratio in nearby star-forming galaxies as a function of their far-infrared luminosity, together with the current upper limits for high-redshift sources and the value obtained for J1148+5251. A decrease of the \(\rm L_{[CII]}/L_{FIR}\) ratio with increasing \(\rm L_{FIR}\) beyond \(\rm 10^{11.5}\,L_{\odot}\) is clearly apparent in Fig. 2. The \(\rm L_{[CII]}/L_{FIR}\) ratio for J1148+5251 is consistent with this general trend. Note also that our sensitive detection is consistent with the upper limits inferred for other high-z QSOs in Fig. 2. The detection of strong [CII] emission suggests that the interstellar medium was already significantly enriched with metals at \(z=6.4\), i.e. when the universe was as young as 870 Myr. However, the chemical evolutionary models predict that the enrichment of carbon relative to the \(\alpha\) elements is delayed (since carbon is mostly produced by intermediate/low mass stars), and in particular the C/O ratio should be about 1/6 in the young stages of massive elliptical galaxies, while the absolute abundance of O should be similar to the local value, at least at an age of about 1 Gyr (Pipino & Matteucci, 2004). To achieve a better physical understanding of this source, and in particular to investigate whether the C-poor scenario is consistent with the data or not, we have compared all available observational data for the host galaxy of the quasar (i.e. [CII], FIR and CO transitions) with PDR models. The relevant observational data are summarized in the second column of Tab.2. We used the PDR model of Kaufman et al. (1999), modified for the conditions appropriate for J1148+5251. In particular, we lowered the carbon-to-oxygen abundance as discussed above. We did not include detailed models for the evolution of dust (Morgan & Edmunds, 2003), nor the possible contribution of dust from SNe (Maiolino et al., 2004), we simply scaled the the abundance of dust grains and PAHs proportionally to the carbon abundance. The model requires high densities and high UV radiation fields to reproduce the data. However, a PDR model which fits observations of typical star forming regions fails to reproduce the strength of the high-J CO transitions observed by Bertoldi et al. (2003b). It is possible to increase the

Yu.N.Parijskij, N.N.Bursov et al. RATAN-600 NEW ZENITH FIELD SURVEY AND CMB PROBLEMS 1020044 (40)110 RATAN-600 NEW ZENITH FIELD SURVEY AND CMB PROBLEMS Yu. N. Parijskij1, N. N. Bursov1, A. B. Berlin1, A. A. Balanovskij1, V. B. Khaikin 1, E. K. Majorova1, M. G. Mingaliev1, N. A. Nizhelskij1, O. M. Pylypenko2, P. A. Tsibulev1, O. V. Verkhodanov1, G. V. Zhekanis1, Yu. K. Zverev1 Special Astrophysical Observatory of RAS, 369167 Karachaj-Cherkesia, Nizhnij Arkhiz _"Saturn", 252148 Ukraine, Kiev, pr50 Richya Zhowtnya, 2B_ We present new RATAN-600 data on the synchrotron Galaxy radiation at the PLANCK Mission and WMAP frequencies at high Galactic latitudes upto \(\ell=3000\). The difference between the standard synchrotron template (\(\ell<50\)) of the WMAP group and RATAN-600 data was detected with the strong synchrotron "longitude quadrant asymmetry". It may change the WMAP estimates of \(z_{reheating}\) from low \(\ell\) polarization data. The polarized synchrotron noise for very deep observations (\(\ll 1\,\mu\)K) at the PLANCK HFI was not detected at \(\ell>200\) scales. "Sakharov Oscillations" in the E-mode (\(500<\ell<2000\)) should be well visible even at \(\sim\)10GHz. The polarized noise from relic gravitational waves (\(\ell\sim 80\)) may be confused with B-mode of synchrotron Galaxy polarized noise at the frequencies below 100 GHz, but there are no problems at HFIband. 1 par@sao.ru ## 1 Introduction The synchrotron and cosmology synchrotron noise from the Galaxy is one of the background screens between the early Universe and the observer. But for polarization experiments this screen may be the most dangerous due to possible high and frequency- dependant E- and B-modes of polarization (up to 70%). It is not easy to extrapolate available nice maps of the Galaxy synchrotron emission from decemeter low resolution data to PLANCK frequency and to the scales important for Cosmology. The first problem- unknown variations of spectral index with frequency and space, the second- correction for Faraday effect. The first broad review of the problem was done by M.Tegmark (Tegmark et al., 1999), with estimation of the range of possible effects in the Cosmology important part on the frequency- scale plane. The so cold "Pessimistic", "Middle", and "Optimistic" variants were suggested. Just after this paper we began to accumulate data on the Galaxy background with RATAN-600 multi-frequency receivers array (\(\sim\)30 channels in the 0.6GHz - 30 GHz band in I, L, R, U, Q Stocks parameters and with different resolution from few arc seconds to few arc minutes. Some preliminary results have been already published (Parijskij, 2000, 2003, Parijskij and Berlin, 2002; Parijskij and Bursov, 2002; Parijskij and Novikov, 2004). They were connected with spinning dust problem and new limit was found for this screen, much below Tegmark "Pessimistic" case at least at \(\ell=1000\), most important for CMB E-mode of polarization. New limit was also found for magnetic dust polarization, suggested by Princeton group recently. "Faraday" Galaxy noise was checked at LFI band. This noise can destroy the purity of the theoretical \(<B>=0\) requirements for Thomson scattering. Several recent experiments demonstrated, that synchrotron Galaxy noise has to be studied deeper, than before by several reasons (Naselsky et al., 2003) 1. The unexpectedly high Thomson scattering between the recombination epoch and observer, deduced from very strong polarization at low \(\ell\). It contradicts Ly-breaks results and requires new population of z\(\gg\)6 objects for early ionization of the Universe. Several alternative interpretations appeared in literature, and Galaxy polarization is in this list. 2. Strong interest in the processes of z=1000 recombination increases the importance of the polarization measurements of "Sakharov Oscillations" and many groups are waiting for much better information on the Galaxy polarization data. 3.The fundamental check ("experiment cruces") of the Inflation scenario- discovery of relic grav. waves. B-mode polarization at \(\ell\sim 100\) was suggested as the direct indication of the existence of the primordial grav. waves, (Zaldarriaga, 1995) predicted by I.Novikov in 60-ties. The reality of this experiment depends on the power of Synchrotron noise (which has \(<B>=<E>\), contrary to scalar Thomson effect, with \(<B>=0\)) at \(50<l<1004\) band. 4. The primordial magnetic field may be traced through polarization measurements by Faraday effect at z=1000 and by detection of the large (larger than

# Polarization of Quasars: Electronic Scattering in the Broad Absorption Line Region Hui-Yuan Wang, Ting-Gui Wang and Jun-Xian Wang whywang@mail.ustc.edu.cn Center for Astrophysics,University of Science and Technology of China, Hefei, 230026, China ###### Abstract It is widely accepted that the broad absoption line region (BALR) exists in most (if not all) quasars with a small covering factor. Recent works showed that the BALR is optically thick to soft and even medium energy X-rays, with a typical hydrogen column density of a few 10\({}^{23}\) to \(>\) 10\({}^{24}\) cm\({}^{-2}\). The electronic scattering in the thick absorber might contribute significantly to the observed continuum polarization for both BAL QSOs and non-BAL QSOs. In this paper, we present a detailed study of the electronic scattering in the BALR by assuming an equatorial and axisymmetric outflow model. Monte-Carlo simulations are performed to correct the effect of and radiation transfer and attenuation. Assuming an average covering factor of 0.2 of the BALR, which is consistent with observations, we find the electronic scattering in the BALR with a column density of \(\sim\) 4 \(\times\) 10\({}^{23}\) cm\({}^{-2}\) can successfully produce the observed average cotinuum polarization for both BAL QSOs and non-BAL QSOs. The observed distribution of the continuum polarization of radio quiet quasars (for both BAL QSOs and non-BAL QSOs) is helpful to study the dispersal distribution of the BALR. We find that, to match the observations, the maximum continuum polarization produced by the BALR (while viewed edge-on) peaks at \(P\) = 0.34%, which is much smaller than the average continuum polarization of BAL QSOs (\(P\) = 0.93%). The discrepancy can be explained by a selection bias, that the BAL with larger covering factor, and thus producing larger continuum polarization, is more likely to be detected. A larger sample of radio quiet quasars with accurate measurement of the continuum polarization will help give better constraints to the distribution of the BALR properties. polarization-scattering-quasars: absorption lines ## 1

Introduction About 10-20 % optically selected QSOs exhibit broad absorption troughs in resonant lines up to 0.1c blueward of the corresponding emission lines (Hewett & Foltz 2003, Reichard et al. 2003). Usually the Broad Absorption Lines (BAL) are detected only in high ionization ones, such as CIV, NV, SiIV and OVI, named high ionized BAL (HiBAL), but 10% of BAL QSOs show also low ionization lines (LiBAL), such as MgII, AlIII and even FeII. The blue shift of the absorption lines suggests that they are formed in a partially ionized wind, outflowing from the quasar. The observed flux ratios of the emission to absorption line imply that the covering factor of the BAL Region (BALR) be \(<\) 20% (Hamann, Korista & Morris 1993). Futhermore, the properties of UV/X-ray continuum and emission lines of BAL QSOs and non-BAL QSOs are also found to be similar (Weymann et al. 1991; Reichard et al. 2003; Green et al. 2001). These facts lead to a general picture that BALR covers only a small fraction of sky and may be present in every quasar (Weymann et al. 1991). We note there are evidences suggesting that LiBAL QSOs are in a special evolution phase of quasars rather than merely viewed on a special inclination (Voit, Weymann & Korista 1993; Canalizo & Stockton 2001; c.f., Willott, Rawlings,& Grimes 2003; Lewis, Chapman, & Kuncic 2003). The evidence for non-spherical BALR is also supported by the discovery that BAL QSOs are usually more polarized than non-BAL QSOs (Ogle et al. 1999). BAL QSO is the only high polarization population among the radio quiet QSOs (e.g., Stockman, Moore & Angel 1984). Stockman et al. found 9 of 30 BAL QSOs show high polarization (\(P>1.5\%\)) in the optical continuum. The result was confirmed later by Schmidt & Hines (1999), who found the average polarization degree of BAL QSOs is 2.4 times that of the optically selected quasars. Consistently, Hutsem\(\grave{e}\)kers & Lamy (2001) obtained average polarization degrees of \(\sim\) 0.43\(\%\), 0.93\(\%\) and 1.46\(\%\) for non-BAL QSOs, HiBAL QSOs and LiBAL QSOs respectively. This result is similar to that of Schmidt & Hines (1999): 0.4\(\%\) and 1.0\(\%\) for non-BAL and BAL QSOs. It is also evident that the polarization distribution of non-BAL QSOs drops sharply toward high polarization (see also Berriman et al. 1990). BAL QSOs are notorious X-ray weak following the work of Green & Mathur (1996; see also Brinkmann et al. 1999). Now we have strong evidences that the weakness in X-rays is not intrinsic but due to strong X-ray absorption, with the hydrogen column density of a few 10\({}^{23}\) to \(>\) 10\({}^{24}\) cm\({}^{-2}\) (Wang et al. 1999; Gallagher et al. 2000; Mathur et al. 2000). The X-ray absorber might be responsible for the recently detected blueshifted X-ray BALs, suggesting they are outflowing at even higher velocities and highly ionized (Chartas et al. 2002; 2003). The electronic scattering in the thick X-ray absorber may contribute significantly to the observed continuum polarization for both BAL QSOs and non-BAL QOSs, if BALR exists in every quasar. In this paper, we perform detailed calculations and Monte Carlo simulations

to study the polarization produced by electronic scattering in the BALR. By comparing the expected polarizations with the observed ones, we give strong contraints to the BALR model. ## 2 Models and the Monte-Carlo method There are many dynamic models for the BAL outflow, depending on the flow type (hydrodynamic or hydromagnetic flow) and the accelerating mechanisms (radiation, gas pressure or magnetic field). In most models, the flow is accelerated through the resonant line scattering, which is supported by the line-locking phenomena. A general difficulty of such models, however, is to prevent the flow from being fully ionized while its average density drops rapidly with increasing radius. One solution proposed by Murry & Chiang (1995, hereafter MC95) is that the flow is shielded from the intense soft X-ray radiation by highly ionized medium in the inner region with a typical column density of a few \(10^{23}\) cm\({}^{-2}\) to 10\({}^{24}\) cm\({}^{-2}\). This shielding gas can also account for the observed heavy X-ray absorption. This model is in qualitative agreement with more recent hydrodynamic calculation of the radiative accelerated wind from an accretion disk (Proga, Stone & Kallman. 2001). The second solution is the two-phase flow, in which a dense, low ionization, cold clouds are embeded in a highly ionized, hot and tenuous medium. The cold clouds with a small filling factor, accelerated by the line and continuum radiation pressure to high velocities, is responsible for the BAL features. An implement to the second scheme is the massive hydromagnetic and radiative driven wind model. In the model, the massive high-ionized continuous outflow is driven centrifugally, and accelerated radiatively by the central continuum source (Everett 2002; Konigl & Kartje 1994; de Kool & Begelman 1995). The total column density of the hot medium is also very large (with N=H1022 cm~-21026 cm\({}^{-2}\) ). In fact such a medium itself can also be considered as the shielding gas. A third scheme is the dusty wind due to the mass loss of stars in the nucleus; both the dust absorption and the line scattering contribute to the accelerating force of the gas (Voit et al. 1993; Scoville & Norman 1995). Following MC95, we assume an equatorial and axisymmetric outflow, with a half open angle \(\theta_{0}\) (see Fig. 1). In this paper, we focus on the continuum polarization produced by the electronic scattering in the outflow, and leave the study of the resonant scattering, which can produce obvious polarization around the broad absorption trough, in a future paper (Wang et al. in prep). The shielding gas is the major source of the electronic scattering and X-ray photo-electronic absorption. Since both the scattering and X-ray absorption are insensitive to the density profile of the shielding gas, we assume a constant electron density in this region. We consider a range of column densities (\(10^{23}\) to \(>10^{24}\) cm\({}^{-2}\)) for this region, consistent with that obtained from the X-ray observations.