arXiv subjects

Xiaohu Yang

Publications and source records attributed to Xiaohu Yang.

At least 271 records · Page 15Linked to original sources

arXiv2009

The spin and orientation of dark matter halos within cosmic filaments

Clusters, filaments, sheets and voids are the building blocks of the cosmic web. In this study, we present and compare two distinct algorithms for finding cosmic filaments and sheets, a task which is far less well established than the identification of dark matter halos or voids. One method is based on the smoothed dark matter density field, the other uses the halo distributions directly. We apply both techniques to one high resolution N-body simulation and reconstruct the filamentary/sheet like network of the dark matter density field. We focus on investigating the properties of the dark matter halos inside these structures, in particular on the directions of their spins and the orientation of their shapes with respect to the directions of the filaments and sheets. We find that both the spin and the major axes of filament-halos with masses <= 10^{13} M_sun/h are preferentially aligned with the direction of the filaments. The spins and major axes of halos in sheets tend to lie parallel to the sheets. There is an opposite mass dependence of the alignment strengths for the spin (negative) and major (positive) axes, i.e. with increasing halo mass the major axis tends to be more strongly aligned with the direction of the filament whereas the alignment between halo spin and filament becomes weaker with increasing halo mass. The alignment strengths as a function of distance to the most massive node halo indicate that there is a transit large scale environment impact: from the 2-D collapse phase of the filament to the 3-D collapse phase of the cluster/node halo at small separation. Overall, the two algorithms for filament/sheet identification investigated here agree well with each other. The method based on halos alone can be easily adapted for use with observational data sets.

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arXiv2009

Alignments of Group Galaxies with Neighboring Groups

Using a sample of galaxy groups found in the Sloan Digital Sky Survey Data Release 4, we measure the following four types of alignment signals: (1) the alignment between the distributions of the satellites of each group relative to the direction of the nearest neighbor group (NNG); (2) the alignment between the major axis direction of the central galaxy of the host group (HG) and the direction of the NNG; (3) the alignment between the major axes of the central galaxies of the HG and the NNG; and (4) the alignment between the major axes of the satellites of the HG and the direction of the NNG. We find strong signal of alignment between the satellite distribution and the orientation of central galaxy relative to the direction of the NNG, even when the NNG is located beyond $3r_{\rm vir}$ of the host group. The major axis of the central galaxy of the HG is aligned with the direction of the NNG. The alignment signals are more prominent for groups that are more massive and with early type central galaxies. We also find that there is a preference for the two major axis of the central galaxies of the HG and NNG to be parallel for the system with both early central galaxies, however not for the systems with both late type central galaxies. For the orientation of satellite galaxies, we do not find any significant alignment signals relative to the direction of the NNG. From these four types of alignment measurements, we conclude that the large scale environment traced by the nearby group affects primarily the shape of the host dark matter halo, and hence also affects the distribution of satellite galaxies and the orientation of central galaxies. (Shortened version)

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arXiv2009

The nature of red dwarf galaxies

Using dark matter halos traced by galaxy groups selected from the Sloan Digital Sky Survey Data Release 4, we find that about 1/4 of the faint galaxies ($\rmag >-17.05$, hereafter dwarfs) that are the central galaxies in their own halo are not blue and star forming, as expected in standard models of galaxy formation, but are red. In contrast, this fraction is about 1/2 for dwarf satellite galaxies. Many red dwarf galaxies are physically associated with more massive halos. In total, about $\sim 45$% of red dwarf galaxies reside in massive halos as satellites, while another $\sim 25$% have a spatial distribution that is much more concentrated towards their nearest massive haloes than other dwarf galaxies. We use mock catalogs to show that the reddest population of non-satellite dwarf galaxies are distributed within about 3 times the virial radii of their nearest massive halos. We suggest that this population of dwarf galaxies are hosted by low-mass halos that have passed through their massive neighbors, and that the same environmental effects that cause satellite galaxies to become red are also responsible for the red colors of this population of galaxies. We do not find any significant radial dependence of the population of dwarf galaxies with the highest concentrations, suggesting that the mechanisms operating on these galaxies affect color more than structure. However, over 30% of dwarf galaxies are red and isolated and their origin remains unknown.

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arXiv2009

Modeling Galaxy-Galaxy Weak Lensing with SDSS Groups

We use galaxy groups selected from the Sloan Digital Sky Survey (SDSS) together with mass models for individual groups to study the galaxy-galaxy lensing signals expected from galaxies of different luminosities and morphological types. We compare our model predictions with the observational results obtained from the SDSS by Mandelbaum et al. (2006) for the same samples of galaxies. The observational results are well reproduced in a $Λ$CDM model based on the WMAP 3-year data, but a $Λ$CDM model with higher $σ_8$, such as the one based on the WMAP 1-year data,significantly over-predicts the galaxy-galaxy lensing signal. We model, separately, the contributions to the galaxy-galaxy lensing signals from different galaxies: central versus satellite, early-type versus late-type, and galaxies in halos of different masses. We also examine how the predicted galaxy-galaxy lensing signal depends on the shape, density profile, and the location of the central galaxy with respect to its host halo.

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arXiv2009

Galaxy Groups in the SDSS DR4: III. the luminosity and stellar mass functions

Using a large galaxy group catalogue constructed from the Sloan Digital Sky Survey Data Release 4 (SDSS DR4) with an adaptive halo-based group finder, we investigate the luminosity and stellar mass functions for different populations of galaxies (central versus satellite; red versus blue; and galaxies in groups of different masses) and for groups themselves. The conditional stellar mass function (CSMF), which describes the stellar distribution of galaxies in halos of a given mass for central and satellite galaxies can be well modeled with a log-normal distribution and a modified Schechter form, respectively. On average, there are about 3 times as many central galaxies as satellites. Among the satellite population, there are in general more red galaxies than blue ones. For the central population, the luminosity function is dominated by red galaxies at the massive end, and by blue galaxies at the low mass end. At the very low-mass end ($M_\ast \la 10^9 h^{-2}\Msun$), however, there is a marked increase in the number of red centrals. We speculate that these galaxies are located close to large halos so that their star formation is truncated by the large-scale environments. The stellar-mass function of galaxy groups is well described by a double power law, with a characteristic stellar mass at $\sim 4\times 10^{10}h^{-2}\Msun$. Finally, we use the observed stellar mass function of central galaxies to constrain the stellar mass - halo mass relation for low mass halos, and obtain $M_{\ast, c}\propto M_h^{4.9}$ for $M_h \ll 10^{11} \msunh$.

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arXiv2009

Structural Properties of Central Galaxies in Groups and Clusters

Using a representative sample of 911 central galaxies (CENs) from the SDSS DR4 group catalogue, we study how the structure of the most massive members in groups and clusters depend on (1) galaxy stellar mass (Mstar), (2) dark matter halo mass of the host group (Mhalo), and (3) their halo-centric position. We establish and thoroughly test a GALFIT-based pipeline to fit 2D Sersic models to SDSS data. We find that the fitting results are most sensitive to the background sky level determination and strongly recommend using the SDSS global value. We find that uncertainties in the background translate into a strong covariance between the total magnitude, half-light size (r50), and Sersic index (n), especially for bright/massive galaxies. We find that n depends strongly on Mstar for CENs, but only weakly or not at all on Mhalo. Less (more) massive CENs tend to be disk (spheroid)-like over the full Mhalo range. Likewise, there is a clear r50-Mstar relation for CENs, with separate slopes for disks and spheroids. When comparing CENs with satellite galaxies (SATs), we find that low mass (<10e10.75 Msun/h^2) SATs have larger median n than CENs of similar Mstar. Low mass, late-type SATs have moderately smaller r50 than late-type CENs of the same Mstar. However, we find no size differences between spheroid-like CENs and SATs, and no structural differences between CENs and SATs matched in both mass and colour. The similarity of massive SATs and CENs shows that this distinction has no significant impact on the structure of spheroids. We conclude that Mstar is the most fundamental property determining the basic structure of a galaxy. The lack of a clear n-Mhalo relation rules out a distinct group mass for producing spheroids, and the responsible morphological transformation processes must occur at the centres of groups spanning a wide range of masses. (abridged)

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arXiv2009

The Correlation of Star Formation Quenching with Internal Galaxy Properties and Environment

We investigate the correlation of star formation quenching with internal galaxy properties and large scale environment (halo mass) in empirical data and theoretical models. We make use of the halo-based Group Catalog of Yang and collaborators, which is based on the Sloan Digital Sky Survey. Data from the Galaxy Evolution Explorer (GALEX) are also used to extract the recent star formation rate. In order to investigate the environmental effects, we examine the properties of "central" and "satellite" galaxies separately. For central galaxies, we are unable to conclude whether star formation quenching is primarily connected with halo mass or stellar mass, because these two quantities are themselves strongly correlated. For satellite galaxies, a nearly equally strong dependence on halo mass and stellar mass is seen. We make the same comparison for five different semi-analytic models based on three independently developed codes. We find that the models with AGN feedback reproduce reasonably well the dependence of the fraction of central red and passive galaxies on halo mass and stellar mass. However, for satellite galaxies, the same models badly overproduce the fraction of red/passive galaxies and do not reproduce the empirical trends with stellar mass or halo mass. This {\em satellite overquenching problem} is caused by the too-rapid stripping of the satellites' hot gas halos, which leads to rapid strangulation of star formation.

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arXiv2008

Environmental Effects on Satellite Galaxies: The Link Between Concentration, Size and Colour Profile

Using the SDSS DR4 group catalogue of Yang et al. (2007), we investigate sizes, concentrations, colour gradients and surface brightness profiles of central and satellite galaxies. We compare central and satellite galaxies at fixed stellar mass, in order to disentangle environmental from stellar mass dependencies. Early and late type galaxies are defined according to concentration. We find that at fixed stellar mass, late type satellite galaxies have smaller radii and larger concentrations than late type central galaxies. No such differences are found for early-type galaxies. We have also constructed surface brightness and colour profiles for the central and satellite galaxies in our sample. We find that late-type satellite galaxies have a lower surface brightness and redder colours than late-type central galaxies. We show that all observed differences between satellite and central galaxies can be explained by a simple fading model, in which the star formation in the disk decreases over timescales of 2-3 Gyr after a galaxy becomes a satellite. Processes that induce strong morphological changes (e.g. harassment) and processes that strip the galaxy of its entire ISM need not to be invoked in order to explain the environmental dependencies we find.

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arXiv2008

The subhalo - satellite connection and the fate of disrupted satellite galaxies

In the standard paradigm, satellite galaxies are believed to be associated with the population of dark matter subhalos. In this paper, we use the conditional stellar mass functions of {\it satellite galaxies} obtained from a large galaxy group catalogue together with models of the subhalo mass functions to explore the fraction and fate of stripped stars from satellites in galaxy groups and clusters of different masses. The majority of the stripped stars in massive halos are predicted to end up as intra-cluster stars, and the predicted amounts of the intra-cluster component as a function of the velocity dispersion of galaxy system match well the observational results obtained by Gonzalez et al. (2007). The fraction of the mass in the stripped stars to that remain bound in the central and satellite galaxies is the highest ($\sim 40%$ of the total stellar mass) in halos with masses $M_h\sim 10^{14}\msunh$. If all these stars end up in the intra-cluster component (Max), or maximum of them are accreted into the central galaxy (Min), then we can predict that a maximum $\sim 19%$ and a minimum $\sim 5%$ of the total stars in the whole universe are in terms of the diffused intra-cluster component. In the former case, in massive halos with $M_h \sim 10^{15} \msunh$, the stellar mass of the intra-cluster component is roughly 6 times as large as that of the central galaxy. This factor decreases to $\sim 2$, 1 and 0.1 in halos with $M_h \sim 10^{14}$, $10^{13}$, and $10^{12} \msunh$, respectively. The total amount of stars stripped from satellite galaxies is insufficient to build up the central galaxies in halos with masses $\la 10^{12.5}\msunh$, and so the quenching of star formation must occur in halos with higher masses. Abridged.

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arXiv2008

Galaxy Groups in the SDSS DR4: I. The Catalogue and Basic Properties

We use a modified version of the halo-based group finder developed by Yang et al. to select galaxy groups from the Sloan Digital Sky Survey (SDSS DR4). In the first step, a combination of two methods is used to identify the centers of potential groups and to estimate their characteristic luminosity. Using an iterative approach, the adaptive group finder then uses the average mass-to-light ratios of groups, obtained from the previous iteration, to assign a tentative mass to each group. This mass is then used to estimate the size and velocity dispersion of the underlying halo that hosts the group, which in turn is used to determine group membership in redshift space. Finally, each individual group is assigned two different halo masses: one based on its characteristic luminosity, and the other based on its characteristic stellar mass. Applying the group finder to the SDSS DR4, we obtain 301237 groups in a broad dynamic range, including systems of isolated galaxies. We use detailed mock galaxy catalogues constructed for the SDSS DR4 to test the performance of our group finder in terms of completeness of true members, contamination by interlopers, and accuracy of the assigned masses. This paper is the first in a series and focuses on the selection procedure, tests of the reliability of the group finder, and the basic properties of the group catalogue (e.g. the mass-to-light ratios, the halo mass to stellar mass ratios, etc.). The group catalogues including the membership of the groups are available at http://gax.shao.ac.cn/data/Group.html and http://www.astro.umass.edu/~xhyang/Group.html

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arXiv2008

Satellite Kinematics II: The Halo Mass-Luminosity Relation of Central Galaxies in SDSS

The kinematics of satellite galaxies reflect the masses of the extended dark matter haloes in which they orbit, and thus shed light on the mass-luminosity relation (MLR) of their corresponding central galaxies. In this paper we select a large sample of centrals and satellites from the Sloan Digital Sky Survey (SDSS) and measure the kinematics (velocity dispersions) of the satellite galaxies as a function of the $r$-band luminosity of the central galaxies. Using the analytical framework presented in Paper I, we use these data to infer {\it both} the mean and the scatter of the MLR of central galaxies, carefully taking account of selection effects and biases introduced by the stacking procedure. As expected, brighter centrals on average reside in more massive haloes. In addition, we find that the scatter in halo masses for centrals of a given luminosity, $σ_{\log M}$, also increases with increasing luminosity. As we demonstrate, this is consistent with $σ_{\log L}$, which reflects the scatter in the conditional probability function $P(L_c|M)$, being independent of halo mass. Our analysis of the satellite kinematics yields $σ_{\log L}=0.16\pm0.04$, in excellent agreement with constraints from clustering and group catalogues, and with predictions from a semi-analytical model of galaxy formation. We thus conclude that the amount of stochasticity in galaxy formation, which is characterized by $σ_{\log L}$, is well constrained, is independent of halo mass, and is in good agreement with current models of galaxy formation.

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arXiv2008

Galaxy Clustering & Galaxy-Galaxy Lensing: A Promising Union to Constrain Cosmological Parameters

Galaxy clustering and galaxy-galaxy lensing probe the connection between galaxies and their dark matter haloes in complementary ways. On one hand, the halo occupation statistics inferred from the observed clustering properties of galaxies are degenerate with the adopted cosmology. Consequently, different cosmologies imply different mass-to-light ratios for dark matter haloes. On the other hand, galaxy-galaxy lensing yields direct constraints on the actual mass-to-light ratios and it can be used to break this degeneracy, and thus to constrain cosmological parameters. In this paper we establish the link between galaxy luminosity and dark matter halo mass using the conditional luminosity function (CLF). We constrain the CLF parameters using the galaxy luminosity function and the luminosity dependence of the correlation lengths of galaxies. The resulting CLF models are used to predict the galaxy-galaxy lensing signal. For a cosmology with $(Ω_{\rm m},σ_8)=(0.238,0.734)$, the model accurately fits the galaxy-galaxy lensing data obtained from the SDSS. For a comparison cosmology with $(Ω_{\rm m},σ_8)=(0.3,0.9)$, however, we can accurately fit the luminosity function and clustering properties of the galaxy population, but the model predicts mass-to-light ratios that are too high, resulting in a strong overprediction of the galaxy-galaxy lensing signal. We conclude that the combination of galaxy clustering and galaxy-galaxy lensing is a powerful probe of the galaxy-dark matter connection, with the potential to yield tight constraints on cosmological parameters. Since this method mainly probes the mass distribution on non-linear scales, it is complementary to constraints obtained from the galaxy power-spectrum, which mainly probes the large-scale (linear) matter distribution.

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arXiv2008

The Rise and Fall of Galaxy Activity in Dark Matter Haloes

We use a SDSS galaxy group catalogue to study the dependence of galaxy activity on stellar mass, halo mass, and group hierarchy (centrals vs. satellites). We split our galaxy sample in star-forming galaxies, galaxies with optical AGN activity and radio sources. We find a smooth transition in halo mass as the activity of central galaxies changes from star formation to optical AGN activity to radio emission. Star-forming centrals preferentially reside in haloes with M<10^{12} Msun, central galaxies with optical-AGN activity typically inhabit haloes with M \sim 10^{13} Msun, and centrals emitting in the radio mainly reside in haloes more massive than 10^{14} Msun. Although this seems to suggest that the environment (halo mass) determines the type of activity of its central galaxy, we find a similar trend with stellar mass: central star formers typically have stellar masses below 10^{10} Msun, while optical-AGN hosts and central radio sources have characteristic stellar masses of 10^{10.8} Msun and 10^{11.6} Msun, respectively. Since more massive haloes typically host more massive centrals, it is unclear whether the activity of a central galaxy is causally connected to its stellar mass or to its halo mass. In general, satellite galaxies have their activity suppressed wrt central galaxies of the same stellar mass. At fixed stellar mass, we find that the activity of satellite galaxies depends only weakly on halo mass. In fact, for satellite galaxies the dependence of galaxy activity on halo mass is more than four times weaker than the dependence on stellar mass. As we discuss, all these results are consistent with a picture in which low mass haloes accrete cold gas, while massive haloes have coronae of hot gas that promote radio activity of their central galaxies. [Abridged]

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arXiv2008

An ideal mass assignment scheme for measuring the Power Spectrum with FFTs

In measuring the power spectrum of the distribution of large numbers of dark matter particles in simulations, or galaxies in observations, one has to use Fast Fourier Transforms (FFT) for calculational efficiency. However, because of the required mass assignment onto grid points in this method, the measured power spectrum $\la |δ^f(k)|^2\ra$ obtained with an FFT is not the true power spectrum $P(k)$ but instead one that is convolved with a window function $|W(\vec k)|^2$ in Fourier space. In a recent paper, Jing (2005) proposed an elegant algorithm to deconvolve the sampling effects of the window function and to extract the true power spectrum, and tests using N-body simulations show that this algorithm works very well for the three most commonly used mass assignment functions, i.e., the Nearest Grid Point (NGP), the Cloud In Cell (CIC) and the Triangular Shaped Cloud (TSC) methods. In this paper, rather than trying to deconvolve the sampling effects of the window function, we propose to select a particular function in performing the mass assignment that can minimize these effects. An ideal window function should fulfill the following criteria: (i) compact top-hat like support in Fourier space to minimize the sampling effects; (ii) compact support in real space to allow a fast and computationally feasible mass assignment onto grids. We find that the scale functions of Daubechies wavelet transformations are good candidates for such a purpose. Our tests using data from the Millennium Simulation show that the true power spectrum of dark matter can be accurately measured at a level better than 2% up to $k=0.7k_N$, without applying any deconvolution processes. The new scheme is especially valuable for measurements of higher order statistics, e.g. the bi-spectrum,........

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arXiv2008

The clustering of SDSS galaxy groups: mass and color dependence

We use a sample of galaxy groups selected from the SDSS DR 4 with an adaptive halo-based group finder to probe how the clustering strength of groups depends on their masses and colors. In particular, we determine the relative biases of groups of different masses, as well as that of groups with the same mass but with different colors. In agreement with previous studies, we find that more massive groups are more strongly clustered, and the inferred mass dependence of the halo bias is in good agreement with predictions for the $Λ$CDM cosmology. Regarding the color dependence, we find that groups with red centrals are more strongly clustered than groups of the same mass but with blue centrals. Similar results are obtained when the color of a group is defined to be the total color of its member galaxies. The color dependence is more prominent in less massive groups and becomes insignificant in groups with masses $\gta 10^{14}\msunh$. We construct a mock galaxy redshift survey constructed from the large Millenium simulation that is populated with galaxies according to the semi-analytical model of Croton et al. Applying our group finder to this mock survey, and analyzing the mock data in exactly the same way as the true data, we are able to accurately recover the intrinsic mass and color dependencies of the halo bias in the model. This suggests that our group finding algorithm and our method of assigning group masses do not induce spurious mass and/or color dependencies in the group-galaxy correlation function. The semi-analytical model reveals the same color dependence of the halo bias as we find in our group catalogue. In halos with $M\sim 10^{12}\msunh$, though, the strength of the color dependence is much stronger in the model than in the data.

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arXiv2008

Satellite Ecology: The Dearth of Environment Dependence

Using the Sloan Digital Sky Survey (SDSS) galaxy group catalogue of Yang et al. (2007), we study the average colour and average concentration of satellite galaxies as function of (i) their stellar mass, (ii) their group mass, and (iii) their group-centric radius. We find that the colours and concentrations of satellite galaxies are (almost) completely determined by their stellar mass. In particular, at fixed stellar mass, the average colours and concentrations of satellite galaxies are independent of either halo mass or halo-centric radius. We find clear evidence for mass segregation of satellite galaxies in haloes of all masses, and argue that this explains why satellites at smaller halo-centric radii are somewhat redder and somewhat more concentrated. In addition, the weak colour and concentration dependence of satellite galaxies on halo mass is simply a reflection of the fact that more massive haloes host, on average, more massive satellites. Combining these results with the fact that satellite galaxies are, on average, redder and somewhat more concentrated than central galaxies of the same stellar mass, the following picture emerges: galaxies become redder and somewhat more concentrated once they fall into a bigger halo (i.e., once they become a satellite galaxy). This is a clear manifestation of environment dependence. However, there is no indication that the magnitude of the transformation (or its timescale) depends on environment; a galaxy undergoes a transition when it becomes a satellite, but it does not matter whether it becomes a satellite of a small (Milky Way sized) halo, or of a massive cluster. We discuss the implication of this `dearth' of environment dependence for the physical processes responsible for transforming satellite galaxies.

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arXiv2008

Probing the Intrinsic Shape and Alignment of Dark Matter Haloes using SDSS Galaxy Groups

We study the three-dimensional and projected shapes of galaxy groups in the Sloan Digital Sky Survey Data Release 4, and examine the alignment between the orientation of the central galaxy and the spatial distribution of satellite galaxies. The projected ellipticity of a group is measured using the moments of the discrete distribution of its member galaxies. We infer the three-dimensional and projected axis ratios of their dark matter haloes by comparing the measured ellipticity distributions with those obtained from Monte Carlo simulations of projected, triaxial dark matter haloes with different axis ratios. We find that the halo shape has a strong dependence on the halo mass. While the haloes of low-mass groups are nearly spherical, those of massive groups tend to be prolate. For groups containing at least four members, the statistical distribution of their measured ellipticities does not have a strong dependence on the colors of their central galaxies. Our analysis further shows that the average three-dimensional axis ratio for haloes with $12<{\rm log}[M/(h^{-1}M_{\odot})]\leq15$ is about $1:0.46:0.46$, resulting in a projected axis ratio of $\sim 0.77$. Our results for the alignment between the orientation of the central galaxy of a group and the distribution of their satellite galaxies are in broad agreement with those obtained by Yang et al. The distribution of satellite galaxies preferentially aligns with the major axis of the central galaxy, with a clear dependence on both halo mass and galaxy colors. (abridged)

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arXiv2007

Galaxy Groups in the SDSS DR4: II. halo occupation statistics

We investigate various halo occupation statistics using a large galaxy group catalogue constructed from the SDSS DR4 with an adaptive halo-based group finder. The conditional luminosity function (CLF) is measured separately for all, red and blue galaxies, as well as in terms of central and satellite galaxies. The CLFs for central and satellite galaxies can be well modelled with a log-normal distribution and a modified Schechter form, respectively. About 85% of the central galaxies and about 80% of the satellite galaxies in halos with masses $M_h\ga 10^{14}\msunh$ are red galaxies. These numbers decrease to 50% and 40%, respectively, in halos with $M_h \sim 10^{12}\msunh$. For halos of a given mass, the distribution of the luminosities of central galaxies, $L_c$, has a dispersion of about 0.15 dex. The mean luminosity (stellar mass) of the central galaxies scales with halo mass as $L_c\propto M_h^{0.17}$ ($M_{*,c}\propto M_h^{0.22}$) for halos with masses $M\gg 10^{12.5}\msunh$, and both relations are significantly steeper for less massive halos. We also measure the luminosity (stellar mass) gap between the first and second brightest (most massive) member galaxies, $\log L_1 - \log L_2$ ($\log M_{*,1}-\log M_{*,2}$). These gap statistics, especially in halos with $M_h \la 10^{14.0}\msunh$, indicate that the luminosities of central galaxies are clearly distinct from those of their satellites. The fraction of fossil groups, defined as those groups with $\log L_1 - \log L_2\ge 0.8$, ranges from $\sim 2.5%$ for groups with $M_h\sim 10^{14}\msunh$ to 18-60% for groups with $M_h\sim 10^{13}\msunh$. Finally, we measure the fraction of satellites, which changes from $\sim 5.0%$ for galaxies with $\rmag\sim -22.0$ to $\sim40%$ for galaxies with $\rmag\sim -17.0$. (abridged)

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