Quenching: internal properties and environment

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

Abstract

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 satellite overquenching problem is caused by the too-rapid stripping of the satellites’ hot gas halos, which leads to rapid strangulation of star formation.

1 Introduction

Galaxies may be broadly divided into two categories: those that are forming stars fairly rapidly relative to their past averaged star formation rate (SFR), and those that show little recent star formation relative to their past average. It is well known that, at least at low redshift (), the former type tend to have blue colours and to be morphologically disk dominated, while the latter tend to have red colours and to be morphologically early type or spheroid dominated. Galaxies exhibit colour bimodalities throughout a wide range of cosmic history (Strateva et al., 2001; Bell et al., 2004; Baldry et al., 2004; Balogh et al., 2004; Blanton et al., 2005b). One of the fundamental questions in galaxy formation is: what are the main physical forces that regulate and in some cases quench star formation? Are these processes more closely correlated with internal galaxy properties such as mass or luminosity, or large scale environment (sometimes referred to as “Nature or Nurture”)?

There have been many studies on the impact of environment on galaxy properties. For example, Davis & Geller (1976) and many others found that early-type galaxies are more strongly clustered than the late-types, and Dressler (1980) systematically demonstrated that the fraction of elliptical and S0 galaxies is higher in denser environments. Similarly, it is well known that galaxies in dense environments tend to be red and to have depressed star formation rates (Hashimoto et al., 1998; Lewis et al., 2002; Gomez et al., 2003; Tanaka et al., 2004; Balogh et al., 2004; Kauffmann et al., 2004; Christlein & Zabludoff, 2005; Poggianti et al., 2006). There are several physical processes associated with environment that may play a role in galaxy transformation. Major (near equal-mass) mergers can transform spiral galaxies into ellipticals (Toomre & Toomre 1972; cf. Barnes 2002), and may also quench future star formation by ejecting the ISM from the galaxy via starburst, AGN, or shock-driven winds (Cox et al., 2004; Springel, Di Matteo, & Hernquist, 2005; Murray, Quataert, & Thompson, 2005). In rich clusters, where the probability of merging is suppressed because of the large relative velocities of galaxies, galaxy “harrassment” (rapid encounters or fly-bys) may cause a less dramatic form of transformation by heating disks, perhaps causing the formation of a bar and growth of a spheroidal component (Moore, Lake, & Katz, 1998). Also, cold gas can be stripped out of the galaxy both by tidal forces due to the background dark matter dominated potential of the cluster, and due to ram pressure stripping by the intracluster medium (Gunn & Gott, 1972; Abadi, Moore, & Bower, 1999; Quilis, Moore, & Bower, 2000; Chung et al., 2007). Similarly, the hot halo that provides future fuel for cooling and star formation may be efficiently stripped in dense environments, thus quenching further star formation by “starvation” or “strangulation” (Larson, Tinsley, & Caldwell, 1980; Balogh & Morris, 2000; Bekki, Couch, & Shioya, 2002).

However, studies by van den Bosch et al. (2008a) and Tanaka et al. (2004) suggest that processes specific to clusters (e.g. ram-pressure stripping) are not the main mechanisms for quenching star-formation activity. Similar results were also found at higher redshift (e.g., Cooper et al., 2006). Moreover, both the morphological and spectrophotometric characteristics of galaxies are also known to be strongly correlated with their internal properties, such as luminosity, mass, and internal velocity (Roberts & Haynes, 1994; Kauffmann et al., 2003). More massive or luminous galaxies are more likely to be spheroid dominated, to be red, and to have old stellar populations and little recent star formation. Indeed, Kauffmann et al. (2003) showed that galaxies appear to make a transition in all of these properties above a critical stellar mass of .

Again, there are various physical processes that one might expect to imprint this kind of dependence on internal properties. Supernova feedback has long been invoked as a mechanism that could heat and drive gas out of galaxies (Larson, 1974; Dekel & Silk, 1986), and is expected to be more effective in low-mass galaxies. There is also mounting observational evidence that AGN are associated with the quenching of star formation (Schawinski et al., 2006, 2007b; Salim et al., 2007). AGN feedback is expected to have more impact on massive galaxies, which host larger mass black holes (e.g. Silk & Rees, 1998).

The emerging picture is that AGN seem to have two modes of fueling and also to couple to their surroundings in different ways. “Bright mode” AGN are associated with high (near Eddington) fueling rates, and observationally with classical X-ray or optically bright quasars. The radiation emitted by these objects can couple with the cold gas in the galaxy, perhaps driving powerful winds that can drive the gas out of the galaxy and quench star formation (Murray, Quataert, & Thompson, 2005; Di Matteo, Springel, & Hernquist, 2005; Monaco & Fontanot, 2005).

In contrast, many massive galaxies seem to contain AGN which are accreting at a small fraction of their Eddington rate, and which typically do not show classical quasar-like signatures such as bright X-ray radiation or broad emission lines. However, these objects are associated with the efficient production of radio jets, which may be able to couple to and heat the hot gas in the galaxy’s halo (e.g. McNamara & Nulsen, 2007). These objects are often referred to as “radio mode” AGN (Croton et al., 2006). This process is expected to be a function both of internal properties and environment: the bigger the black hole, the more energy can be tapped (and black hole mass is of course correlated with galaxy mass), and empirically it is known that the fraction of radio-detected galaxies increases strongly with stellar mass (Best et al., 2005) and halo mass (Pasquali et al., 2008). But as well, the radio jets must have a “working surface” and therefore can only be effective in environments that can support a quasi-hydrostatic hot gas halo, such as groups and clusters. Galaxies in smaller mass halos () likely accrete most of their gas in a “cold flow”, and never form a hot halo (Birnboim & Dekel, 2003; Dekel & Birnboim, 2006; Kereš et al., 2005).

A great deal of recent progress has been made towards developing a comprehensive theory of galaxy formation. The semi-analytic approach, although it has its limitations, is a powerful and flexible tool for exploring detailed predictions based on this theor (e.g., White & Frenk, 1991; Kauffmann, White, & Guiderdoni, 1993; Kauffmann et al., 1999; Somerville & Primack, 1999; Cole et al., 2000; Somerville, Primack, & Faber, 2001; Springel et al., 2001; Benson et al., 2003; Hatton et al., 2003; Khochfar & Burkert, 2003, 2005; Kang et al., 2005). Several groups have now implemented one or both modes of black hole growth and AGN feedback into their semi-analytic models (e.g., Croton et al., 2006; Bower et al., 2006; Monaco, Fontanot, & Taffoni, 2007; Somerville et al., 2008b). There seems to be consensus that including these new processes leads to greatly improved agreement with key observations such as galaxy luminosity or mass functions, and the galaxy colour-magnitude distribution or stellar mass vs. specific star formation distribution. However, this necessitates including several new recipes and parameters associated with the poorly understood physics of black hole growth and AGN feedback. Each model contains somewhat different parameterizations and treatments of these processes, yet they all produce similar results for global quantities such as the galaxy luminosity function and colour-magnitude distribution, no doubt in part because these observations were “targets” that the modellers were trying to reproduce. One goal of our work here is to determine whether breaking down the fraction of quenched galaxies in the dual space of internal galaxy properties and environment can discriminate between these different treatments of AGN feedback.

The large and homegeneous databases provided by modern surveys, such as SDSS and GALEX, finally allow a statistically significant investigation of different sub-populations of galaxies. However, an obvious question that arises in any study of galaxy environment is exactly how to measure and characterize environment in observational samples. Clearly, it is desirable to span as broad a range of environments as possible, from isolated field galaxies to groups to rich clusters. The majority of the studies in the literature have parameterised environment in terms of the number of galaxies, either within a fixed metric aperture, or by the distance of the th-nearest galaxy, where is typically in the range 3–10. Although these indicators are straightforward to measure, they are not straightforward to interpret in physical terms or to compare with theoretical models (see discussions in Kauffmann et al. 2004 and Weinmann et al. 2006a). An alternate approach is to use a galaxy group catalogue, in which galaxies in an observational catalog are not only grouped together into putatively gravitationally bound structures, but also the total mass of their associated dark matter halo is estimated (Yang et al. 2007). Thus, the relationship between galaxy properties and dark matter halo properties can be studied directly. Another advantage of this method is that galaxies can be separated into “central” and “satellite” populations. Most of the environment-related tranformation mechanisms described above (such as stripping) are expected to work only on satellite galaxies, so this offers a way to separate out the effects of different physical processes.

Here we make use of a large galaxy group catalogue constructed from the SDSS using the halo-based galaxy group finder developed by Yang et al. (2005). These catalogues have already been used for several studies regarding the environment dependence of galaxy properties. Weinmann et al. (2006a), using the version based on the SDSS DR2, studied the correlations between colours, specific star formation rate and halo mass. Splitting the galaxy population into early and late types, based on their colours and specific star formation rates, they found that, at a fixed luminosity, the late (early) type fraction of galaxies increases (decreases) with decreasing halo mass. Using the much larger galaxy group catalogue of Yang et al. (2007; hereafter Y07), based on the SDSS DR4, van den Bosch et al. (2008a) showed that, on average, satellite galaxies are redder and more concentrated than central galaxies of the same stellar mass. They also found that the colour and concentration differences of central-satellite pairs matched in stellar mass are completely independent of the mass of the host halo of the satellite galaxy. This indicates that satellite-specific transformation mechanisms are equally efficient in host haloes of all masses and rules against satellite transformation mechanisms that are thought to operate only in very massive haloes. Further support for this was provided by van den Bosch et al. (2008b) and Pasquali et al. (2008), who showed that, at fixed stellar mass, the average colours and concentrations, as well as the occurrence of star formation and AGN activity, reveal only a very weak dependence on halo mass (but see Weinmann et al. 2008).

Weinmann et al. (2006b) compared the fractions of red and blue galaxies in the SDSS group catalogue of Weinmann et al. (2006a) with the semi-analytic model of galaxy formation of Croton et al. (2006). Although this model accurately fits the global statistics of the galaxy population, the model predicts a red fraction of satellites that is much higher than observed (see also Baldry et al., 2006; Coil et al., 2008).

In this paper we extend the study of Weinmann et al. (2006b) using the much larger galaxy group catalogue of Y07 and a larger suite of semi-analytic models. Another new aspect of our work here is that we augment the SDSS-based galaxy properties in the group catalogue with information derived from the GALEX-SDSS matched sample of Salim et al. (2007; hereafter S07). The S07 analysis provides complementary quantities such as stellar masses and star formation rates based on the two GALEX UV bands plus five-band SDSS photometry. The UV provides a much more sensitive probe of the recent star formation history of a galaxy than optical colours alone, which reflect the highly degenerate effects of stellar populations, metallicity, and dust extinction (Yi et al., 2005; Kaviraj et al., 2007). In addition, the UV can provide reliable measures of SFR for galaxies with weak or undetected emission lines.

The goal of this paper is to investigate the dependence of the fraction of quenched galaxies on galaxy properties and DM halo mass in both the observational group catalogue and in several different semi-analytic galaxy formation models. Another new aspect of our study with respect to previous comparisons (e.g. Weinmann et al., 2006b) is that we compare with the results from three independently developed semi-analytic codes, and for one of the codes, we examine three different variants with different physical ingredients. In this way, we investigate how these empirical results can constrain the input physics in these kinds of models. An outline of the rest of our paper is as follows: in §2, we describe the empirical data sets and the group catalogues used in our study; in §3 we describe the theoretical models; in §4 we present the results of our comparisons between the empirical data and the models; we discuss our results and conclude in §5.

2 The Data Sample

2.1 The SDSS Group Catalog

We make use of the Galaxy Group Catalog of Yang et al. (2007; Y07). The catalogue was constructed by applying the halo-based group finder of Yang et al. (2005) to the New York University Value-Added Galaxy Catalog (NYU-VAGC, Blanton et al. 2005a), which is based on the Sloan Digital Sky Survey (SDSS) Data Release 4 (DR4; Adelman-McCarthy et al. 2006). From the Main Galaxy Sample, Y07 selected galaxies with extinction-corrected -band apparent magnitude brighter than , within a redshift range , and with a redshift completeness . They augmented this sample with 7091 galaxies with with redshifts from alternate sources. The resulting sample (Sample II of Y07) has a mean redshift of and a total sky coverage of 4,514 deg, and contains 369,447 galaxies. In this paper, we refer to this as “the SDSS sample”.

All absolute magnitudes are k and evolution (e) corrected to the rest-frame, as described by Blanton et al. (2003). Stellar masses are computed using the relation between rest-frame optical colour and mass-to-light ratio of Bell et al. (2003), as specified in Y07, assuming a Kroupa IMF. Our sample is not volume limited, and we therefore attempt to correct for the resulting Malmquist bias by weighting each galaxy by a standard correction (Schmidt, 1968).

The group finder first identifies a potential group centre by the friends-of-friends algorithm (Davis et al., 1985), and then computes the characteristic luminosity of each tentative group. The characteristic group luminosity is defined as the (incompleteness corrected; see Y07) combined luminosity of all group members with . The characteristic group stellar mass is similarly the incompleteness-corrected total stellar mass contributed by galaxies with . Then, the velocity dispersion and the virial radius of the dark matter halo (DMH) associated with each tentative group are estimated iteratively, assuming a constant mass-to-light ratio as an initial guess. These two estimates can be used for determining the spherical Navarro, Frenk, & White (1997) (NFW)-type dark matter profile. Assuming a Gaussian probability distribution along the redshift direction and a projected spherical NFW dark matter profile for the perpendicular plane, group members are updated until there is no change in their memberships.

Lastly, a DMH mass is assigned to each group, assuming a one-to-one correlation between the characteristic stellar mass for each group and the halo mass derived from a theoretical mass function (e.g. Warren et al., 2005). We use the halo mass estimated from stellar mass, as luminosity-based halo mass estimates may be biased differently for groups with blue vs. red galaxies (Y07). Y07 find that they can assign group masses down to a lower limit of , although the completeness of the group catalogue begins to drop below unity for halo masses less than . The central galaxy in each group is identified as the galaxy with the largest stellar mass.

There are 204,813 groups in the resulting group catalogue. Note that we call all clusters “groups” regardless of their richness or density, including groups that contain only a single member. For a more detailed description of the group finder, and the results of extensive tests of its completeness, contamination, and purity, we refer interested readers to Yang et al. (2007).

Model box size (Mpc/h) Characteristics
S08 AGN-FB (fiducial) 120 Bright mode AGN-driven winds + Radio mode AGN heating
S08 no AGN-FB 120 Control model without AGN feedback
S08 HQ 120 cooling quenched according to the halo mass
dL06 120 Radio mode AGN heating
morgana 144 Bright mode AGN-driven winds + Radio mode AGN heating
Table 1: Model descriptions

2.2 Galex

The GALEX data provide near-UV (NUV, effective wavelength 2271Å) and far-UV (FUV, 1528Å) band information (Martin et al., 2005). Of 741 sq. deg. of GALEX unique imaging, 645 sq. deg. overlaps with the SDSS DR4 spectroscopic area. We make use of the GALEX-SDSS matched sample constructed by Salim et al. (2007; S07). S07 first define a SDSS parent sample in the GALEX overlap region of objects spectroscopically classified as galaxies, and having optical magnitude and redshift . This sample contains 49,346 galaxies. For each of the galaxies in the SDSS parent sample, S07 searched within a 4 arcsec radius (corresponding to 7 kpc at 0.1) for a match in the GALEX source catalog.

Using a large library of model SEDs based on the Bruzual & Charlot (2003) population synthesis code, S07 then performed Bayesian SED fitting to the 7-band photometry () to obtain estimates of dust extinction, stellar mass, and star formation rate (SFR). These parameters were built from probability distribution functions, thus taking into account parameter degeneracies. The typical error in the specific SFR (obtained from the width of the SED fitting probability distribution) is 0.2 dex (star-forming galaxies) to 0.7 dex (passive galaxies).

Of the full S07 sample, we use 32,787 galaxies that are associated with SDSS galaxies in our group catalog, and exclude a small number of objects with very poor fits (see discussion in §4.3 in S07). The redshift range for this final sample is with mean redshift 0.104, and the redshift distribution is very similar to that of the parent SDSS sample.

3 Theoretical Models

We adopt a semi-analytic approach to model galaxy formation within the CDM picture. We make use of a total of 5 sets of models based on different prescriptions for our comparison with the empirical data. Three of the models are constructed using the latest version of the Somerville code (Somerville & Primack 1999; Somerville, Primack, & Faber 2001; Somerville et al. 2008b, hereafter S08). The others are the Millennium models (Croton et al., 2006; De Lucia et al., 2006) and the MORGANA models (Monaco, Fontanot, & Taffoni, 2007; Fontanot et al., 2006, 2007).

We describe the basic scheme in the Somerville code. We use an N-body simulation box to obtain the masses and positions of the “root” dark matter halos, and compute the merger history for each halo using the method of Somerville & Kolatt (1999). Within each dark matter halo, gas cools via atomic cooling (White & Frenk, 1991; Somerville & Primack, 1999) and forms a rotationally supported disk. The radial sizes of disks are computed using the model described in Somerville et al. (2008a), which accounts for the initial Navarro-Frenk-White profiles of the DM halos and the “adiabatic contraction” due to the self-gravity of the infalling baryons. Cold gas is turned into stars in the galactic disk following the Schmidt-Kennicutt law (Kennicutt, 1989, 1998), and gas with surface density lower than a critical threshold density (e.g. Martin & Kennicutt, 2001) does not form stars. Massive stars explode as supernovae and reheat the cold gas. We trace chemical evolution using a simple “effective yield” parameter. Each generation of stars produces a fixed “yield” of metals, which are deposited in the cold gas. This gas may then be ejected and mixed with the hot component by supernova or AGN driven winds.

When a satellite is subsumed into a larger dark matter halo, it is assumed that it immediately loses its hot gas halo, and thus does not receive any new supply of cold gas. The orbital decay and eventual merging, due to dynamical friction, of satellite galaxies within dark matter halos is tracked using a modified version of the Chandrasekhar (1943) formula (Boylan-Kolchin, Ma, & Quataert, 2008). Mass loss and tidal destruction are also accounted for, using a simplified version of the approach presented in Taylor & Babul (2004) and Zentner & Bullock (2003). Galaxy mergers trigger bursts of star formation, the efficiency and timescales of which are modelled using results from hydrodynamic simulations of galaxy-galaxy mergers.

The code also tracks the growth of black holes and the energy they produce. Every top level DM halo is seeded with a black hole of . Mergers trigger the “bright mode” black hole growth that is associated with luminous quasars. Following every merger with mass ratio greater than 1:10, the black hole grows at its Eddington rate until it reaches a critical mass. The critical mass is that at which the energy radiated by the black hole is sufficient to halt further accretion, i.e., the black hole growth is self-regulated (Hopkins et al., 2007). Soon after reaching the critical mass, the black hole enters a “blowout” phase, resulting in a decline in the accretion rate. The associated radiation can also drive winds that remove cold gas from the galaxy (see S08 for details).

The S08 models also incorporate “radio mode” feedback associated with low-efficiency accretion. The accretion rate is computed using the isothermal Bondi flow model of Nulsen & Fabian (2000). In the presence of a quasi-hydrostatic shock-heated gas halo, the energy from this accretion is assumed to drive radio jets that can heat the gas and partially or completely offset the cooling flow.

The resulting star formation and enrichment histories are convolved with the stellar population models of Bruzual & Charlot (2003) to compute magnitudes and colours. We have adopted a Chabrier IMF. The impact of dust extinction is modelled using an analytic model, as in De Lucia & Blaizot (2007).

The S08 fiducial model includes all of these mechanisms. We also consider a “no AGN feedback model”, which does not include either the bright mode or radio mode AGN feedback mechanisms, and the “Halo Quenching” model, in which cooling is shut off when a halo grows more massive than (see Table 1 for a summary of all models). The halo quenching model is included as an illustration of a quenching mechanism that has a simple dependence on halo mass only. A similar model has been considered by Cattaneo et al. (2006). It is based on the ideas proposed by Birnboim & Dekel (2003) and Dekel & Birnboim (2006), who suggest that whenever a halo grows above this critical quenching mass, the gas is shock-heated to near the virial temperature, and can be easily kept hot either by an AGN or by other processes such as heating by gas clumps or orbiting satellites (Dekel & Birnboim, 2008; Khochfar & Ostriker, 2008).

Figure 1: The distribution of -band absolute magnitude vs. colour. Gray shading and green contours show the conditional probability P(). The orange line shows the demarcation line for the “red” and “blue” galaxy populations used in this study.
Figure 2: Galaxy stellar mass vs. specific star formation rate. Gray shading and pink contours show the conditional probability P(). The purple line shows the demarcation line between “passive” and “active” galaxies used in this study.

We also consider two additional models from other groups in this study. The de Lucia et al. (2006, hereafter dL06) models contain similar ingredients to the S08 models, with the following differences. They are based on merger trees extracted from the Millennium N-body simulations (Springel et al., 2005). Unlike in the models of S08, they do not include the effects of adiabatic contraction and an NFW halo profile in their estimates of galaxy sizes, which leads to a different evolution in the star formation rates and gas fractions in their models. They use somewhat different (though similar in spirit) recipes for star formation and supernova feedback, and they use a different approach for modelling black hole growth (though, like S08, they assume that “bright mode” black hole growth is triggered by mergers). They do not include “bright mode” AGN feedback (AGN-driven winds), and their treatment of the radio mode feedback is again similar in spirit but different in detail from S08. Magnitudes and colours (including dust extinction) are computed in a similar manner to S08, and use a Chabrier IMF. We obtained the dL06 catalogs from the public Millennium database (http://www.g-vo.org/Millennium).

We also consider the predictions of the semi-analytic model morgana (Monaco, Fontanot, & Taffoni, 2007; Fontanot et al., 2006, 2007). morgana follows a scheme similar to S08 and dL06, but it includes a different treatment for the thermal processes acting on baryonic gas. More details on the updated version we use in this paper are presented in Lo Faro et al. (2008, in prep). The model is based on merger trees obtained using the pinocchio method (Monaco, Theuns, & Taffoni, 2002), similar to those predicted by N-body simulations. Gas cooling and infall follow the prescription described and tested in Viola et al. (2008), while star formation and stellar feedback are then modeled as in Monaco (2004). When two DM halos merge, dynamical friction, tidal stripping and tidal shocks on the satellite galaxies are followed using the Taffoni et al. (2003) formulation. Similarly to S08, when a satellite DM halo merges into a larger one, all of its hot gas is shock heated according to the new halo potential and gets removed from the satellite (thus implying that the corresponding satellite galaxy does not receive any further cold gas supply). Disc sizes are computed using the model of Mo, Mao & White (1998), and bulge sizes are computed assuming that kinetic energy is conserved in mergers.

A key ingredient in morgana is the inclusion of a self-consistent model for the accretion of gas onto supermassive black holes and the resulting AGN feedback modes (following Umemura 2001 and Granato et al. 2004, see Fontanot et al. 2006 for more details). This modeling assumes that the loss of angular momentum is the main regulator of black hole accretion. This is triggered by the presence of gas in the bulge component, and the almost complete loss of angular momentum of accreted gas is related to star formation activity. Following Granato et al. (2004), star formation creates a reservoir of low angular momentum gas which is then accreted at a rate regulated by the viscous accretion time scale or by the Eddington limit. The nature of feedback from the AGN depends on the accretion rate in Eddington units: whenever this is higher than 0.01 (“bright mode”), the AGN can trigger a massive galactic-scale wind (see Monaco & Fontanot, 2005) which leads to the complete removal of the ISM from the galaxy, while at lower accretion rates (“radio mode”) the energy is ejected through jets that feed back on the hot halo gas with an efficiency that scales with , where is the halo circular velocity. As a consequence, BH accretion requires some star formation to be triggered, and feedback follows the onset of cooling only after some time. The ejected energy heats the hot halo gas component and quenches the cooling flow. Galaxy SEDs, magnitudes and colours are obtained using the GRASIL spectro-photometric code with radiative transfer for computing the effect of dust (Silva et al., 1998).

In Table 1, we present a brief description of each model.

4 Results

In this section, we investigate the joint dependence of star formation quenching on stellar mass and halo mass, in order to try to contrain the physical mechanisms that are responsible for quenching. We make use of two indicators of quenched star formation: red optical colours, and low specific star formation rates (). Red optical colours are frequently used to isolate “quenched” galaxies; however, a red optical colour can arise from a degenerate combination of an old stellar population, a high metallicity, or strong dust extinction. SSFR based on UV-optical data are a more sensitive probe of recent star formation.

In order to mimic the selection effects of the flux-limited observational sample, we first assign redshifts to all the model galaxies by placing an “observer” in a corner of the simulation box. We apply the same flux limit used in the observational catalogs to the models by selecting only galaxies with apparent -band magnitude . We then apply the weighting factor, just as we do with the galaxies in the observational sample. Then, we exclude all halos that do not contain any galaxy brighter than , as these halos would not be included in the group catalog.

We apply these selection criteria for all of the model-data comparisons shown in the main text, unless otherwise noted. We also present our main results for the models without these selection criteria in the Appendix.

4.1 Global Distribution Functions: colour and SSFR

In Fig. 1, we present the global colour-magnitude relations (CMRs) at for the observations and theoretical models, along with the dividing line between the observed red sequence and the blue cloud (sometimes called the “green valley”). In this figure, we show the results for the whole SDSS sample, regardless of inclusion in the group catalog, and similarly we have not applied the observational selection criteria to the theoretical models. The magnitudes and colours are shown in the rest-frame system defined by Blanton et al. (2003). For the dL06 models, we used the observed frame magnitudes at , converted to absolute magnitudes. For the morgana galaxies, we compute the absolute magnitudes from the corresponding synthetic spectra. For the S08 models, when we computed standard frame colours and magnitudes, we produced a good match to the observed colour-magnitude relation expressed in the frame. However, when we computed the system colours as described in Blanton & Roweis (2007), we found it necessary to apply a shift of 0.05 magnitudes to the colour to match the location of the observed system red sequence. This is indicative of small differences in the shape of the SED’s in the semi-analytic models from the synthetic SED’s used by Blanton et al. (2003) for computing the k-corrections. It should also be noted that details in the population synthesis prescriptions, such as chemical enrichment and dust extinction, may also cause noticeable differences in colours (see Appendix for the effect of dust). Therefore, reproducing the CMR quantitatively in semi-analytic models is quite challenging.

The observations clearly show the familiar red sequence and blue cloud, and these features are reproduced reasonably well in all of the theoretical models, except the S08 no-AGN-feedback model. As has been pointed out before (e.g., Croton et al., 2006; Cattaneo et al., 2006), semi-analytic models without some kind of suppression of cooling in massive halos, e.g. by AGN feedback, predict that massive galaxies are still accreting plenty of cold gas at the present day, and therefore are star-forming and blue, in conflict with observations. We do see subtle differences in the structure of the CM distribution for the different models, for example, the S08-halo-quenching model produces very few low-luminosity red galaxies, and the dL06 model produces a very strong bimodality. Also, we notice that the red sequence in the halo-quenching model is slightly bluer compared with the S08 fiducial model. This is because the central galaxies in the halo-quenching model stop forming stars once their halo becomes more massive as . In general, this happens at an earlier epoch than the “radio mode” feedback is able to quench star formation. Because chemical evolution is also halted when star formation is quenched, the massive galaxies in the halo-quenching model do not become as enriched as do the galaxies in the fiducial model (see S08). We could have adjusted for this by increasing the chemical yield, but we chose to leave all the free parameters fixed in both models to allow a direct comparison.

The behavior of morgana is somewhat different from that of the other models. A clear red sequence is present at intermediate and faint magnitudes, but it fades away at bright magnitudes, in contrast to the observations. Luminous galaxies tend to be blue. We interpret this result as an inefficient quenching of star formation through “radio-mode” feedback in morgana. In fact, as explained in §. 3, in this model the AGN heating switches on only after some cooled gas has already started forming stars in the host galaxy. Obviously the residual activity is stronger for longer time delays between the onset of cooling flows and the accretion onto the central black hole. On the other hand, the blue cloud seems depleted. As shown in Fontanot et al. (2008, in prep), the depletion of the blue cloud is connected in part to the “satellite overquenching problem”, discussed further in §5, caused by the too-efficient strangulation of satellite galaxies. However, we shall see later that morgana also produces too few low mass blue central galaxies. This is likely due to strong supernova feedback.

Figure 3: The fraction of red galaxies (; left) and passive galaxies (; right) as a function of galaxy stellar mass. The empirical data are shown by a black solid line, and coloured lines show the results of the theoretical models, as indicated on the plot. We show the dependence for all galaxies (top), and for central (middle), and satellite (bottom) galaxies seperately. Each point contains at least 10 galaxies. Most of the SAMs reproduce the trend for central galaxies reasonably well, but predict a much larger fraction of small-mass red/passive satellite galaxies than are observed. The error bars indicate Poisson errors.
Figure 4: The red fraction (left) and passive fraction (right) as a function of halo mass, for different stellar mass bins, as indicated by different colours and symbol sizes (see plot legend). In each plot, results are shown for the observed SDSS or GALEX+SDSS group catalog (top left) and the five models as indicated on the plot. We present the results for central (top set of panels) and satellite (bottom set of panels) galaxies seperately. Each point contains at least 5 galaxies. The SAMs reproduce the main trends reasonably well for central galaxies, but satellite galaxies do not show the correct trend of with stellar mass.
Figure 5: The red fraction (left) and passive fraction (right) as a function of stellar mass, for different halo mass bins, as indicated by different colours and symbol sizes (see plot legend). The rest of the plot details are as in Fig. 4.

Given the strongly bimodal colour distribution exhibited by both the empirical data and most of the models, it is natural to define a dividing line between the two populations, and to investigate the fraction of galaxies in the red population, , as representing quenched objects. We adopt the same demarcation line between red and blue galaxies as Weinmann et al. (2006a, hereafter W06a):

(1)

as shown in Fig. 1.

We can also define the specific star formation rate (SSFR), as the present star formation rate divided by the stellar mass of the galaxy (), and plot a similar diagram in terms of SSFR and mass. In Fig. 2, we show the conditional probability distribution for SSFR as a function of stellar mass, as derived from the GALEX+SDSS observations, and for the models. The star formation rate is averaged over the past 100 Myr. Note that the number of galaxies in the sample is roughly 8 times smaller than the sample shown in the colour-magnitude distribution plot, because the field coverage of GALEX survey used in the Salim et al. study is not as wide as that of the SDSS. In a similar manner, we define a cut in SSFR to separate “active” star forming galaxies from “passive” ones. We define a galaxy as “passive” if the following condition is met:

(2)

Note here that our criterion is based on galaxy stellar mass in order to make a more direct comparison with the theoretical models. It is also worth noting that our criterion roughly corresponds to at and at . Below 0.1, SFR obtained from multiband photometry may not be robust due to the degeneracy of burst time and the mass fraction of a young population (e.g. Kaviraj et al., 2007).

Our demarcation is comparable to that of W06a when their criterion, which is based on the -band magnitude, is lowered by 0.6 dex. However, SFR estimates from emission lines, which were used by W06a, trace only very recent star formation, whereas the UV used here traces star formation over a longer timescale ( 1 Gyr). Therefore our “passive” sample is not directly comparable to that of W06a, though the results are qualitatively similar. The amount of UV flux in the passive galaxies is very small and can still be consistent with the amount of UV flux that can be produced by old stars such as low-mass horizontal-branch stars (see Yi et al. 2005 for details). In this regard it is justifiable to call them “passive”.

In Fig. 2, we see a well-defined “star-forming sequence” that produces the blue sequence in the traditional CM diagram, but the “quenched” population that produces the tight red sequence is quite spread out in SSFR. This is simply a reflection of the relative insensitivity of optical colours to small amounts of recent star formation. The precise values of SSFR at low levels of star formation cannot be estimated very accurately from the data, and therefore one should not take too seriously the position of the quenched galaxies in the SSFR vs.  plot. Again, the models with AGN feedback (or halo quenching) qualitatively reproduce the empirical distribution reasonably well, but show some interesting differences. The dL06 model has a strongly-bimodal distribution of SSFR, with most galaxies living either on the star-forming sequence or being completely quenched. In contrast, the S08 model has a larger population of “semi-quenched” galaxies at intermediate values of SSFR. The morgana model produces an even broader distribution of SSFR, with many quenched low-mass galaxies.

4.2 Dependence of Star Formation Quenching on Stellar Mass

Fig. 3 shows the dependence of  and  on galaxy stellar mass. We show  and  vs. stellar mass for all galaxies (upper panels), and for central and satellite galaxies separately (middle and lower panels, respectively). Although we do not specifically use the information from the group catalog in the uppermost panel, in all panels we use only the SDSS galaxies that are included in the group catalog, and apply the group catalog-like selection criteria to the theoretical models, as described at the beginning of this section.

In the empirical data,  shows a strong dependence on galaxy mass for both centrals and satellites, in the well-known sense that low-mass galaxies are largely blue, whereas massive galaxies are more likely to be red. It appears that  is a steeper function of stellar mass for central galaxies than for satellites. In general, the red galaxy fraction is higher for satellites for a fixed galaxy mass. Similarly, van den Bosch et al. (2008a, b) found that satellite galaxies have redder mean colours than centrals at a fixed stellar mass. The trends appear qualitatively very similar when we consider  as a function of stellar mass.

The S08 fiducial model, S08 halo-quenching model, and dL06 model all reproduce the trends in  and  with stellar mass quite well for central galaxies. Note the similarity of the predictions of the S08 fiducial and halo-quenching model. The S08 no AGN feedback model, as we have already seen, predicts the presence of too many massive blue central galaxies. morgana reproduces the sense of the trend of the red fraction with stellar mass, but slightly overproduces red galaxies at low stellar masses, and significantly overproduces blue galaxies at high stellar masses.

All of the models badly overproduce the number of low mass red satellites, and predict too weak a trend of  with stellar mass for these objects. The dL06 models predict a nearly flat run of  with stellar mass for satellites, with values that are much too high (close to unity) compared with the empirical values. At the highest satellite masses, there is too high a fraction of blue galaxies in the morgana model and the S08 no-AGN-feedback model. We can see by comparing the S08 no-AGN-feedback model with the fiducial model that AGN feedback does not affect galaxy colours below stellar masses of ; therefore the excess of low-mass red satellites is not connected with AGN feedback.

The conclusions we would draw from the comparison with  are qualitatively similar, though quantitatively somewhat different. For example, the dL06 model shows a better quantitative match to the  data than to  for central galaxies. The S08 fiducial and halo-quenching models produced almost indistinguishable results for (), but significantly different results for (). This is due to the age-metallicity degeneracy — as we discussed in §4.1, massive galaxies in the halo-quenching model are more metal poor than in the fiducial model. Therefore, although they are older (as seen in the  diagram), their optical colours are similar. Similarly, the large difference between  and  for the S08 no AGN-feedback model is due to dust extinction: in this model, massive galaxies are actively star forming, and therefore extremely dusty (see Appendix for more discussion of the effects of dust extinction).

The somewhat lower fraction of red/passive satellite galaxies in the S08 models is due to the inclusion of tidal destruction, which is not included in the dL06 or morgana models. In the S08 model, satellites that orbit within their host halo for a long time can eventually become tidally destroyed, and their stars are added to a “Diffuse Stellar Halo” (see S08). Naturally, in the absence of tidal destruction, these satellites exhaust all of their gas and become very red. However, we see here that although the inclusion of tidal destruction helps reduce the excess of low-mass red satellites in the models, a significant discrepancy still remains.

One might then wonder whether increasing the efficiency of tidal destruction could completely solve the satellite ’over-quenching’ problem that we see here. We do not believe that this is a viable solution, for several reasons. First, the tidal disruption model used by S08 was tuned to match the sub-structure mass function for very high-resolution N-body simulations. S08 also showed that their models correctly reproduce the total number of low-mass galaxies (i.e. the faint end slope of the stellar mass function), although the model overproduces low-mass bulge-dominated (red/passive) galaxies and underproduces low-mass disc-dominated (blue/active) galaxies. Significantly increasing the efficiency of tidal destruction would be in conflict with the N-body results and would also produce an overall deficit of low-mass galaxies. Put another way, tidal destruction can remove low-mass red satellites but cannot increase the number of low-mass blue satellites.

4.3 Dependence on Stellar Mass and Halo Mass

In this section we explore the dependence of  and  on DM halo mass and stellar mass. In Fig. 4 we show  and  as a function of halo mass, for different bins in stellar mass. We show the results for  and  for central galaxies (top row), and for satellite galaxies (bottom row). In Fig. 5, we show a similar plot, but this time with the galaxy stellar mass plotted on the x-axis, and different bins in halo mass shown by the different colors.

In the empirical data, we see that for massive central galaxies, there is no significant dependence of  on halo mass (environment) for fixed stellar mass. For intermediate mass galaxies (), the dependence on halo mass appears to be stronger, but there is a limited region of overlap in galaxies with different stellar masses that occupy halos of the same mass. This is because there is a fairly tight correlation between halo mass and stellar mass. Similar results are again obtained for .

The S08 fiducial and dL06 models, both of which include AGN feedback, do reasonably well at reproducing the overall trends for central galaxies, as does the S08 halo-quenching model. We see a hint of a dependence on stellar mass in intermediate mass halos () in the S08 models, while in the dL06 model, the dependence seems to be almost solely on halo mass. However, interestingly, we see almost the same stellar mass dependence in the S08 fiducial and halo-quenching models, while we know that the quenching mechanism is a pure function of halo mass in the halo-quenching model. The S08 no-AGN feedback model shows the correct trend with stellar mass at fixed halo mass (more massive galaxies have higher ), but the opposite trend with halo mass (more massive halos have lower ). Interestingly, morgana shows similar trends to the S08 no-AGN-feedback model: this implies that the current implementation of AGN feedback in this model is insufficient to fully cure the “star formation quenching” problem.

Considering , we see somewhat different behavior. The S08 no AGN-feedback model produces no quenched galaxies at all in terms of . The S08 and dL06 models appear surprisingly similar, both showing almost a pure halo mass dependence (no significant dependence on stellar mass). On the other hand, morgana predicts a significant dependence of  on stellar mass, while showing overall low values of .

Observed satellite galaxies show an  dependence that is very similar to that of centrals for massive galaxies (). For intermediate and low mass satellites,  shows some dependence on both galaxy stellar mass and halo mass, but does not show the very sharp drop over intermediate halo masses () seen in the central population. In the semi-analytic models, we see that  for the satellites does not have a strong enough dependence on  at fixed halo mass.

The stellar mass dependence of  for satellites in the empirical sample is not as clear as it was in terms of . This may be in part due to the smaller size of the GALEX-SDSS matched sample used to obtain . The S08 models now all show a clear inverted trend:  is higher for lower mass galaxies (the opposite of the empirical trend). For the dL06 model, nearly all satellites are passive regardless of their stellar mass or halo mass. In morgana, satellite properties are a weak function of stellar mass, and the values of  are overall too high.

Based on Fig. 4 alone, we might be tempted to conclude that quenching is primarily a function of halo mass. However, Fig. 5 shows that quenching could equally well be considered to be primarily a function of stellar mass. We conclude that, especially for central galaxies, the degeneracy between stellar mass and halo mass is too strong to reach a firm conclusion on this point.

Figure 6: The fraction of “red” galaxies (; left) and passive galaxies (; right) for central (top set of plots) and satellite (bottom set of plots) galaxies in the (, ) plane. The fraction of red/passive galaxies in a given pixel in (, ) is indicated by the colour, where red colours indicate a higher red/passive fraction, as shown in the scale. To guide the eye, we draw a solid (dotted) line showing the approximate upper envelope of the central (satellite) galaxy mass distribution for the observational group catalog, and repeat this same line on every panel. Central and satellite galaxies in the observational group catalogs show noticably different joint dependencies on stellar mass and halo mass. The models with AGN feedback qualitatively reproduce the trends for central galaxies, but do not reproduce the empirical trends for satellites.

In Fig. 6, we present the  and  distributions in the plane. We pixelise the plane, compute  and  in each pixel, and indicate its value by the colour of the pixel. For example, a red colour indicates that galaxies are mostly red or passive within the pixel, while a blue colour indicates that most of the galaxies are blue/active. These diagrams reveal a number of interesting features. Considering the diagram for central galaxies in the empirical sample, we see that above a critical halo mass (), nearly all galaxies are red and passive. For intermediate halo masses , the structures show a complex dependence on both halo mass and stellar mass. In particular we note that above a “critical” stellar mass of , the majority of galaxies are red and passive, regardless of their halo mass (though such massive galaxies are not found in halos less massive than ). Comparing with the models that showed good qualitative behavior in terms of the binned quantities (S08 fiducial, S08 halo-quenching, and dL06), we can see that the distribution of the patterns in space are quite different from the observations — in general, the structures show stronger vertical divisions, indicating a stronger dependence on halo mass than on galaxy mass. It is interesting to note that these three models look much more similar to one another than any of the models does to the empirical data. It is also interesting that in terms of , the S08 fiducial and S08 halo-quenching models look very similar to one another, but they look extremely different in the  diagram. This again illustrates that optical colours are not an ideal probe of star formation quenching.

The observed satellites show an interesting striation, which is nearly horizontal at the highest and lowest stellar masses, but somewhat diagonal for intermediate masses. It appears that the majority of satellite galaxies are red/passive if they are more massive than a few times (just as for the central population), and are predominantly blue/active if they are less massive than , regardless of their halo mass. For intermediate halo masses, it seems that unlike for central galaxies, the critical mass that marks the transition between mostly blue and mostly red galaxies is a function of halo mass, and is lower for higher halo masses. This suggests that the star formation activity in the most massive satellites is regulated by the same processes that shape centrals, while lower mass satellites are influenced by environmental processes such as tidal forces or ram pressure stripping.

All the models fail quite miserably to reproduce the satellite properties. In addition to simply predicting too high a fraction of red satellites, none of the models shows the diagonal pattern of contours in the  or  diagrams. The few pixels with high blue fractions in the models lie at high stellar mass for their halo mass, which is the opposite from what is seen in the empirical data. These are simply galaxies that were forming stars as centrals and have become satellites very recently.

Readers are referred to the Appendix for a discussion of the impact on our results of the modelling of dust extinction, our imposed selection criteria, and possible biases in the procedure for assigning halo masses in the SDSS group catalog.

4.4 Connection with Morphology, Black Hole Formation and AGN Feedback

Figure 7: The fraction of early-type galaxies () for centrals (left) and satellites (right) in the SDSS group catalog. Early type galaxies are defined as having a concentration index () greater than 2.6.

These results naturally beg the question: which physical process(es) are responsible for imprinting this dependence of star formation quenching on galaxy and halo mass? Although this is a complex question that we will not be able to fully address in this paper, we attempt to at least identify some promising hypotheses that can be pursued futher in the future.

As already discussed by many authors (e.g. Kauffmann et al., 2003), we are suspicous that the correlation of star formation quenching with stellar mass may in fact be linked to the tendency of the increasing bulge fraction also with stellar mass and perhaps halo mass. Although we have only rough morphological information for SDSS, we make use of a standard cut in concentration index () to coarsely divide our sample into early and late type galaxies (early types have ; Strateva et al. 2001; Shimasaku et al. 2001). Such classification using the concentration index is subject to contamination at roughly the 20% level (Strateva et al., 2001). We then plot in the (,) plane as before1, and show the results in Fig. 7. We see a strikingly similar pattern to the one seen when we plotted  and  in this way in Fig. 6, indicating a very strong correlation between red, passive, and early type galaxies.

We test the connection of black hole mass with star formation quenching by plotting the ratio of black hole mass to the total stellar mass of the galaxy () in the same (,) plane, which we do in Fig. 8 (for central galaxies only). Note that all three semi-analytic model codes reproduce the empirical relation between bulge mass and black hole mass reasonably well within the observational errors. In the S08, dL06, and morgana models, we see that the galaxies that have the highest stellar mass to halo mass ratios have the lowest black hole mass to stellar mass ratios. This is a reflection of the spread in halo merger histories at fixed halo mass. In halos in which a massive black hole is formed relatively early, the cooling flow is also shut off at an earlier time, halting further galaxy growth except by mergers. Conversely, halos with relatively small black holes for their mass will be able to continue to cool, and the central galaxies will continue to form stars and remain blue. This is seen to be the case in the “blue ridge” in Fig. 6 (see panels h, k, and l). Note that neither the strong trend in nor the “blue ridge” is seen in the S08 “halo quenching” model, in which quenching is regulated purely by the halo mass.

In all three models with AGN feedback, there is also a trend with halo mass in the sense that larger mass halos have larger black hole-to-stellar mass ratios. This is due to the dual modes of black hole growth in the models. In the “bright mode”, the growth of the stellar bulge and the black hole are linked. Most of the black hole growth in the models occurs via this bright mode of black hole feeding. However, at late times, large mass halos can develop a hot hydrostatic halo which is assumed to fuel the “radio mode” of black hole growth. In these halos, the black hole can grow without any associated star formation, leading to an increase in . This is supported by the fact that we do not see such a trend in the halo quenching model, which only contains black hole growth via the bright mode.

We attempt to investigate whether this trend exists in the empirical data, using the SDSS velocity dispersion as a proxy for black hole mass. We compute from the relation using the empirical relation of Gebhardt et al. (2000). We assign a scatter to the black hole mass at a given by choosing a uniform random deviate over the 1 range quoted by Gebhardt et al. (2000) (we obtain indistinguishable results when a Gaussian random deviate is used). Interestingly, we see no evidence of a trend in with halo mass.

However, this result is not strongly conclusive, because it is not known whether the relationship between and depends on halo mass. However, these results are suggestive that there may be too much black hole growth via the “radio mode” in the models, perhaps indicating that other heating processes not associated with black hole growth may also be important in quenching cooling flows.

We caution, as well, that although it is tempting to try to interpret the “fine features” in these diagrams, the assignment of halo masses in the current SDSS group catalogs is not very precise (see the Appendix), and therefore only broad statistical trends should be taken seriously. It is possible that in the future, if more precise estimates of individual halo masses become available for large samples, for example from gravitational lensing or X-rays, we may be able to investigate these predicted trends in more detail.

Figure 8: Average black hole mass to galaxy stellar mass ratio for central galaxies, shown by the colour coding, as a function of  and , for four of the theoretical models. For the S08 and dL06 models, note the similarity of the structures seen here to those seen in the plot of  in Fig. 6. This suggests that for intermediate halo masses,  is closely related to in the models. We also show for the SDSS group catalogs, where , based on the SDSS measured velocity dispersion and the observed relation, is used as a proxy for the average black hole mass. Interestingly, the strong dependence of on halo mass is not visible.

5 Discussion and Conclusions

In this paper, we set out to investigate the significance of internal galaxy properties vs. environment in shaping the star formation history of galaxies, and to attempt to understand some of the physical processes that might be at work. We made use of the observational Group Catalog constructed from SDSS DR4 and the NYU-VAGC (Yang et al., 2007). The Group Catalog provides an estimate of the halo mass for each group, which can be directly compared with semi-analytic models. These halo mass estimates should provide a more unbiased probe of global environment than measures based on local galaxy density (e.g. distance to the -th nearest neighbor) 2.

We have also used a sub-sample of SDSS with GALEX coverage to estimate star formation rates (Salim et al., 2007), which should be a more direct probe of the physics of star formation quenching than optical colours. Besides, we make use of semi-analytic models from several independent groups (S08, dL06, morgana), and containing different sets of recipes representing physical processes.

We first investigated the global distribution of colour vs. magnitude and SSFR vs. stellar mass in the five models we considered, compared with the empirical data. Although the different models showed some differences in the details of their predictions for these quantities, the models with some kind of quenching (either due to AGN feedback or according to a critical halo mass) have similar qualitative features and on the whole are a reasonable match to the empirical data — not surprisingly, as these observational quantities have been a target for theoretical models for some time. We therefore found that it was sensible to identify active or quenched galaxies according either to a colour-magnitude criterion (the usual “green valley”), or a similar SSFR- criterion.

Next we investigated the stellar mass dependence of the quenched fraction, based on optical colours (), or on SSFR determined from SDSS+GALEX photometry (). Here we largely confirmed and reproduced results shown previously by other authors (though our results in terms of SSFR from GALEX are new), namely that the fraction of red/passive galaxies increases with stellar mass for both central and satellite galaxies, and that the models with AGN feedback or halo mass-based quenching reproduce this trend reasonably well for central galaxies, but fail badly for satellites. All of the models produce too high a fraction of red satellites and too flat a dependence of quenching on stellar mass, which we term the satellite over-quenching problem.

We then investigated the joint dependence of quenched fraction ( and ) on galaxy mass and halo mass. First we investigated  and  as a function of halo mass, in different stellar mass bins. A difficulty with this approach was that, especially for central galaxies, there is quite a limited range of stellar masses in halos of a given mass. Our analysis showed that, for central galaxies in the observational group catalogs, the fraction of quenched galaxies shows a strong dependence on halo mass at fixed stellar mass, but also shows a strong dependence on stellar mass at fixed halo mass. We were not able to determine which quantity is the primary driver of quenching. The S08 fiducial and dL06 models reproduced these trends fairly well. For observed satellite galaxies, there was a much stronger dependence on stellar mass visible in the  diagram (based on optical colours), and a weaker trend in the  diagram (based on UV-derived SSFR). Once again, all models failed to reproduce the satellite properties, and even showed an inverted trend in  with respect to the empirical data.

We also found it interesting to look at the pattern of  and  in terms of the two dimensional (-) plane. This analysis revealed that the contours of  and  for central galaxies can be interpreted either as a horizontal run or as a vertical run, again due to the halo mass – central galaxy mass degeneracy. The models showed quite a different pattern in this space, and tended to show stronger vertical boundaries, indicating a stronger dependence on halo mass. For both the empirical data and the models, these diagrams demonstrate the complexity of the interplay between halo mass and stellar mass, and are a promising tool for posing stringent tests on physical recipes in galaxy formation models. However, we caution that the estimates of halo mass in the SDSS group catalogs are statistical in nature, and this may introduce distortions into these distributions (see Appendix).

We attempted to probe the physical origin of these results by exploring additional correlations, such as the fraction of morphologically early type (spheroid dominated) galaxies in the observed sample, . We found a strikingly similar pattern for  in the (,) plane as we did for  and , suggesting that these quantities are tightly linked in some way. One natural possibility is that the bulge mass is correlated with the mass of a supermassive black hole, and that the black hole mass in turn controls the quenching of star formation. Intriguingly, we found that in the models with black hole-regulated AGN heating (S08 fiducial and dL06), the galaxies that were most likely to be blue, actively star forming, and disk dominated, were expected to be those with the smallest black hole for their mass. In addition, we saw a trend with halo mass, in the sense that central galaxies in larger mass halos are able to grow black holes more efficiently (the ratio of black hole mass to stellar mass is larger). These trends were much weaker or absent in models in which the black hole is not involved in regulating cooling (such as the “halo quenching” model). We do not have direct estimates of black hole masses for large samples of galaxies, but we used the measured SDSS velocity dispersion and the observed relation to obtain estimates of a black hole mass proxy, . We do not see a strong trend in for the SDSS group catalog, indicating either that this method for estimating the empirical black hole masses is too crude, or that the dependence of black hole mass on halo mass in the models is too strong.

Although the model predictions for the distribution of  and  in the (, ) plane do not match the observational results in detail, we conclude that the observational data are consistent with the basic qualitative picture presented by the models in which cooling is regulated by AGN feedback at least for central galaxies. In these models, the suppression of cooling and the quenching of star formation depend on two factors: the presence of a quasi-hydrostatic hot halo (strongly correlated with halo mass), and the mass of the supermassive black hole (strongly correlated with galaxy mass). This picture is also strongly supported by the recent work of Pasquali et al. (2008), which directly explored the dependence of “radio mode” and “bright mode” AGN activity on halo mass and stellar mass in these same SDSS group catalogs. The empirical data do not seem to support models in which the process that suppresses cooling is solely a function of halo mass (e.g., Dekel & Birnboim, 2008; Khochfar & Ostriker, 2008), although it will be important to explore the explicit predictions of alternate heating mechanisms (such as heating by clumps or infalling satellites) in detail.

The morgana model suffers from the largest disagreement with the observations. The treatment of the triggering of “radio mode” accretion in morgana is significantly different than in the other two models, requiring that star formation is inevitably associated with the triggering of radio mode accretion. Although the radio mode feedback mechanism adopted in morgana is largely able to solve the “overcooling problem” in terms of reproducing the galaxy stellar mass or luminosity function, this star formation makes many massive galaxies too blue. Our analysis places tight constraints on the links between star formation and AGN activity at late times, and highlights our current lack of understanding of the details of the processes that regulate both kinds of activity.

For satellite galaxies, the empirical diagrams suggested that quenching depends on both stellar mass and halo mass, such that the “critical stellar mass” that divides active from passive (blue from red) galaxies decreases with increasing halo mass. None of the models was successful in predicting this trend. Including tidal destruction of satellites, as was done in the S08 models, improves the agreement with the data because satellites that have been orbiting for a long time within the host halo (which tend to be red and passive) are destroyed. However, it seems that tidal destruction cannot provide a full solution to the problem.

The problems with over-quenching of satellites in semi-analytic models have been demonstrated before (e.g. Weinmann et al., 2006b) and are likely due to the assumption applied in nearly all SAMs that the hot gas halo, which is the source of new cooling gas, is stripped off instantly when a galaxy becomes a satellite in a larger halo (sometimes called “strangulation”). Therefore satellites fairly quickly consume their remaining cold gas reservoirs and become red and passive (e.g. Crowl & Kenney, 2006). However, recent hydrodynamic simulations have found that the hot gas halos of satellites are not stripped instantly (Kawata & Mulchaey, 2008; McCarthy et al., 2008). Recently, several authors (Kang & van den Bosch, 2008; Font et al., 2008) have proposed improved recipes for the treatment of cooling onto satellites, which produce better results for the predictions of satellite colours. Clearly, our analysis should be repeated with one of these improved treatments implemented in our models. However, it is probably also important to properly treat the effects of ram pressure stripping on both the satellites’ hot halo and the cold gas in the galaxy (Lanzoni et al., 2005; Quilis, Moore, & Bower, 2000; Okamoto & Nagashima, 2003). This will clearly be an important area for improvements to the modelling and further investigations.

Acknowledgments

The empirical data derived from the Sloan Digital Sky Survey and the Galaxy Evolution Explorer (GALEX) observations played a critical role in this project. We warmly thank G. de Lucia and G. Lemson for help with the Millennium Catalogs and database server, and Sadegh Khochfar and Marc Sarzi for numerous insightful discussions. We are also grateful to the referee for several important clarifications. SKY acknowledges support from the Basic Research Program of the Korea Science and Engineering Foundation (R01-2006-000-10716-0). TK is grateful for the hospitality of the Max-Planck-Institut für Astronomie in Heidelberg during his visit. FF and PM thank Laura Silva for help in the use of GRASIL. Some of the calculations were carried out at the PIA cluster of the Max-Planck-Institut für Astronomie at the Rechenzentrum Garching.

Figure 9: The fraction of ”red” () (left panels) and ”passive” galaxies () (right panels) in models without dust corrections. The colour scale is as in Fig. 6. We present the results for central galaxies (left) and satellite (right) galaxies seperately. We see that the details of the  distribution are quite sensitive to the dust correction, whereas is not noticably affected by the dust correction. We also note that the dust-free  results appear more similar to the  results, which presumably probe the physical properties of galaxies more directly.
Figure 10: The fraction of “red” galaxies () (left panels) and of “passive” galaxies () (right panels) without selection criteria. The colour scale is as in Fig. 6. We present the results for central galaxies (left) and satellite (right) galaxies seperately. It can be inferred that our main results do not depend on our selection criteria.

Appendix : The effect of dust, selection criteria, and group catalog halo mass estimates

All of our models include a treatment of dust extinction, which affects both the colours and magnitudes of the model galaxies. In addition, as mentioned in §4, for our main analysis we have applied selection criteria to the models to mimic those that we believe to be present in the SDSS group catalog. We include only galaxies with apparent -band magnitude brighter than 17.77 mags, and we also excluded halos which do not contain any galaxy member brighter than . In this Appendix we provide the results for the 2-d distributions of  and  for the theoretical models without dust extinction and without selection criteria applied. In addition, we test for possible biases that may arise from the approach used to assign halo masses to the groups in the SDSS group catalogs by applying this method to the model mock catalogs.

In Fig. 9 we show  and  without any ’dust corrections applied to the models. Since we do not have magnitude information without dust corrections for the dL06 models, only the S08 fiducial and morgana models are shown. Interestingly, the results now look much more similar to the results seen before for . In particular, the blue ridge which was visible in the  diagrams corresponded to a red ridge in the  diagram (Fig. 6). The blue ridge is now visible in  as well, indicating that these galaxies are actually actively star forming, and were predicted to be red only because of dust extinction. In the case of , the dust correction only affects the galaxy selection and causes a negligible change in the diagrams. The treatment of dust extinction is one of the most uncertain aspects of the modelling, and this highlights the advantage of using intrinsic physical quantities extracted from the observations.

Fig. 10 shows the model predictions with no selection effects applied. Comparing this with Fig. 6, we see that the results appear unchanged above a halo mass and a stellar mass . This is reassuring in the context of our present analysis. However, we can also see that there is interesting predicted behavior at lower halo and galaxy masses than we can currently probe, and also interesting differences between the models at these masses. This suggests that it would be extremely useful to obtain similar data that are complete to fainter levels, so that we could probe lower mass galaxies and lower mass halos.

Figure 11: The true halo mass in the fiducial semi-analytic model of S08, compared with the halo mass estimate based on the total stellar mass in the halo, using a procedure similar to that of Y07 for the SDSS-based group catalog. The colour-scale indicates the stellar mass of the central galaxy in each halo, as shown by the key on the figure. Although the mean halo mass is reproduced fairly well, there is quite a large scatter in the true halo mass at a given estimated halo mass.

Finally, we investigate the procedure used to assign halo masses to the groups that are identified in the SDSS group catalog. For the results presented here, stellar masses for several models are obtained from Bell et al. (2003) like Y07, and halo masses are assigned based on the “characteristic” stellar mass of the group, where the characteristic stellar mass is defined as the total stellar mass contributed by galaxies with . Halo masses are then assigned by matching the rank-ordered list of group characteristic stellar masses with a rank-ordered list of dark matter halo masses from a theoretical estimate of the DM halo mass function, assuming a monotonic mapping between the characteristic stellar mass and DM halo mass (see §2.1 and Y07). We apply this procedure to the halos in the mock catalog produced with the S08 fiducial semi-analytic model, and show the comparison between the true and estimated halo mass in Fig. 11. We see that although the mean halo mass is estimated fairly accurately, there is a large scatter in true halo mass at a given value of the estimated halo mass.

Figure 12: The fraction of “red” galaxies () as a function of halo mass and stellar mass, where halo masses have been assigned in the semi-analytic models using an approach similar to that used in the SDSS group catalogs. The colour scale is as in Fig. 6. We present the results for central galaxies (left) and satellite (right) galaxies seperately. We see that the procedure used to assign halo masses in the SDSS group catalogs reduces the scatter in  at fixed halo mass, and washes out many of the detailed features of the 2d distribution that are visible in the raw model predictions.

In Fig. 12, we show again the distribution of  with halo mass and stellar mass, now using the Y07-like halo mass estimates for the semi-analytic models instead of the true halo masses. We see that the procedure artificially reduces the scatter in  at fixed halo mass. This can be attributed to two effects. First, the halo mass estimates in the Y07 group catalogue are based on the total stellar mass in the halo, which strongly correlates with the stellar mass of the central galaxy. In addition, the Y07 group catalogue includes corrections for various incompleteness effects in the SDSS (the factor C in Eqs. 3–4 in Y07), which creates scatter that is not visible in the mock catalogues. It should also be noted that the halo-mass estimating algorithm of Y07 washes out many of the detailed features that are visible in the model predictions. Hence we should not make too much of the detailed features in the empirical - diagrams but should focus on the mean trends instead.

Footnotes

  1. Because of the difficulty of mapping the morphological information available in the models to the observable concentration index, we do not show the model predictions. The qualitative trends in the models are similar.
  2. But note that some groups have started measuring galaxy number densities using search ellipsoids large enough to be representative of massive cluster halos (e.g., Schawinski et al., 2007a; Yoon et al., 2008)

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