RC3-SDSS Galaxy Morphology and Environment

The Relation Between Galaxy Morphology and Environment in the Local Universe: An RC3-SDSS Picture

David J. Wilman11affiliation: Max-Planck-Insitut für extraterrestrische Physik, Giessenbachstrasse, 85748 Garching, Germany , Peter Erwin11affiliation: Max-Planck-Insitut für extraterrestrische Physik, Giessenbachstrasse, 85748 Garching, Germany 22affiliation: Universitäts-Sternwarte München, Scheinerstrasse 1, 81679 München, Germany
Abstract

We present results of an analysis of the local () morphology-environment relation for 911 bright () galaxies, based on matching classical RC3 morphologies with the SDSS-based group catalog of Yang et al., which includes halo mass estimates. This allows us to study how the relative fractions of spirals, lenticulars, and ellipticals depend on halo mass over a range of , from isolated single-galaxy halos to massive groups and low-mass clusters. We pay particular attention to how morphology relates to central vs. satellite status (where “central” galaxies are the most massive within their halo). The fraction of galaxies which are elliptical is a strong function of stellar mass; it is also a strong function of halo mass, but only for central galaxies. We interpret this as evidence for a scenario where elliptical galaxies are always formed, probably via mergers, as central galaxies within their halos, with satellite ellipticals being previously central galaxies accreted onto a larger halo. The overall fraction of galaxies which are S0 increases strongly with halo mass, from % to %. Here, too, we find striking differences between the central and satellite populations. % of central galaxies with stellar masses are S0 regardless of halo mass, but satellite S0 galaxies are only found in massive () halos, where they are % of the satellite population. This suggests two channels for forming S0 galaxies: one which operates for central galaxies, and another which transforms lower mass () accreted spirals into satellite S0 galaxies in massive halos. Analysis of finer morphological structure (bars and rings in disk galaxies) shows some trends with stellar mass, but none with halo mass; this is consistent with other recent studies which indicate that bars are not strongly influenced by galaxy environment. Radio sources in high-mass central galaxies are common, similarly so for elliptical and S0 galaxies, with a frequency that increases with the halo mass. Emission-line AGN (mostly LINERs) are more common in S0s, but show no strong trends with environment.

Subject headings:
galaxies: active — galaxies: elliptical and lenticular,cD — galaxies: spiral — galaxies: clusters: general — galaxies: groups: general — galaxies: evolution

1. Introduction

Galaxies come in many different shapes and sizes, but primarily consist of two dynamically stable components, bulges and disks, with additional contributions from quasi-stable features such as bars and rings. Hubble (1926) devised what has become known as the “tuning fork” classification to describe this morphological schema: elliptical galaxies ( pure bulge); spiral galaxies (disks containing spiral features, both barred and unbarred, with a sequence Sa–Sc111de Vaucouleurs & de Vaucouleurs (1964) extended this sequence further to Sd and Sm of decreasing bulge component and increasing spiral arm opening angle); and lenticular “S0” galaxies (defined by the presence of a disk with no discernable spiral arms).

The abundance of these galaxy types is now known to correlate strongly with environment: elliptical galaxies live preferentially in regions of very high local density (Dressler, 1980), inhabiting the cores of clusters and groups rather than their outskirts (Melnick & Sargent, 1977; Whitmore & Gilmore, 1991; Wilman et al., 2009). However, the total luminosity-limited fraction of ellipticals is similar in a wide range of environments (Desai et al., 2007; Wilman et al., 2009; Just et al., 2010) and has evolved very weakly since (Dressler et al., 1997; Fasano et al., 2000; Smith et al., 2005; Postman et al., 2005).

Lenticular galaxies, on the other hand, are globally no more abundant in clusters than they are in groups (Wilman et al., 2009), with a much weaker dependence on local density than ellipticals (Dressler, 1980; Dressler et al., 1997; Postman et al., 2005; Poggianti et al., 2008). A lower fraction at fixed luminosity is found only in the lower density field (Wilman et al., 2009). The global fraction of lenticular galaxies has grown by a factor in groups and clusters since (Dressler et al., 1997; Fasano et al., 2000; Wilman et al., 2009), potentially more rapidly in groups and low mass clusters than in high-mass clusters (Poggianti et al., 2009; Just et al., 2010). Since lenticulars and ellipticals make up the bulk of the low redshift passive population (e.g. Bundy et al., 2010), this means that the majority of galaxies which have ceased forming stars since have retained their disks as lenticulars. Beyond (up to ), there is no evidence for further evolution in the elliptical or S0 fraction in the high-mass clusters sampled to date (Smith et al., 2005; Postman et al., 2005).

To build a global picture of galaxy evolution, it is important to understand how the evolution of galaxies and their environment is intertwined, and which physical processes drive the suppression of star formation and the morphological transformations which are required to explain these observations.

It is attractive to explain morphological evolution in the context of bulge growth through galaxy mergers (Springel et al., 2005; Hopkins et al., 2010), which take place in the center of halos as a natural consequence of hierarchical clustering and dynamical friction (e.g. De Lucia & Blaizot, 2007; De Lucia et al., 2011). Elliptical galaxies almost certainly form through a mixture of major and minor mergers. However, the role of mergers in the formation of bulges in galaxies with disks is less clear. Cooling flows should form at the center of halos, and will reform a disk around the merger remnant so long as the gas is not too efficiently reheated. SPH simulations suggest that during mergers of galaxies with high gas fractions, much of the gas retains its angular momentum and reforms a disk, and that some component of the stellar disk can survive in all but 1:1 mergers (Hopkins et al., 2009). Meanwhile, secular processes might contribute of the galaxy mass in a “pseudobulge” (Kormendy & Kennicutt, 2004), or potentially a larger fraction at high redshift where disks are less dynamically stable (Genzel et al., 2008). That S0 galaxies exhibit more significant bulges on average than spiral galaxies (e.g. Dressler, 1980; Wilman et al., 2009; Laurikainen et al., 2010) is consistent with a merger origin. Nonetheless, there is currently no more than circumstantial evidence that bulge growth and the suppression of star formation in most S0s are causally linked.

Our observational picture still misses one vital and surprisingly straightforward ingredient: a full picture of how galaxy morphology depends upon environment at low redshift. Early studies of environment focussed almost exclusively on galaxy clusters, for which good statistics and strong trends are to be found even without high spectroscopic completeness. The more recent emphasis has been on extending these trends to high redshift with high resolution Hubble Space Telescope (HST) imaging. Modern local surveys such as the Sloan Digital Sky Survey (SDSS) are so large that much effort has been invested in the automated classification of morphological properties, such as the simple SDSS “concentration” index, and multi-component decomposition with different levels of sophistication (resolution dependent, e.g. Allen et al., 2006; Gadotti, 2009). An interesting alternative solution is the “Galaxy Zoo”, providing visual classifications for the whole SDSS, by employing an enthusiastic public to classify galaxies (Lintott et al., 2011).

The disadvantage of all these approaches is that new classification schemes tend to be relatively simplistic, with unknown systematics, and produce data which is difficult to assess on the basis of our existing understanding of the Hubble scheme. Standard Hubble type classifications within SDSS are available only for subsamples (e.g. Fukugita et al., 2007), although these are becoming larger (Nair & Abraham, 2010a).

In this paper we have taken the simple step of taking a sample of galaxies from the Third Reference Catalog of Bright Galaxies (RC3, de Vaucouleurs et al., 1991) which is matched to the SDSS Data Release 4 (DR4) to provide classical morphological information for a large sample of galaxies for which the selection function and environment can be properly characterized. For our purposes this provides an ideal sample to study environmental trends for galaxies with detailed and well understood classifications.

In section 2 we describe the sample, discussing the selection function of RC3 galaxies and the group catalog which we use to describe galaxy environment. Section 3 presents our results, including Hubble type fraction as a function of stellar and halo mass, a dichotomy between central and satellite galaxies, the nature of activity in the SDSS fiber spectra of galaxies with different morphological types and environments, and the dependence (or lack thereof) of morphological components (bars, rings etc) on environment. This is further discussed in the context of a hierarchically evolving Universe in section 4, and in section 5 we present our conclusions.

To compute distances, absolute magnitudes, and stellar masses, we assume a CDM cosmology with , , and equal to , , and 71 km s Mpc, respectively. Halo masses are presented in , to retain the native units of Yang et al. (2007).222 in our adopted cosmology.

2. Sample

2.1. The RC3 Catalog

The RC3 catalog (Third Reference Catalog of Bright Galaxies)333http://heasarc.nasa.gov/W3Browse/all/rc3.html provides information for a large sample of nearby galaxies (de Vaucouleurs et al., 1991). It “attempts to be reasonably complete for galaxies having apparent diameters larger than 1 arcmin at the D25 isophotal level and total B-band magnitudes brighter than about 15.5, with a redshift not in excess of 15,000 km/s”. Some smaller, fainter, and more distant galaxies are also included. The most important aspect from our point of view is that detailed morphological classifications (Hubble types) from photographic plates are provided.

Inspection of SDSS imaging for a subsample of RC3 galaxies confirms the majority of classifications. However, a significant minority of galaxies appear to be falsely classified, usually in the sense that some galaxies appearing to be early-type spirals or ellipticals are instead classified S0. We describe our reclassification process in section 2.4.

2.2. The SDSS Catalog

The SDSS DR4 (Sloan Digital Sky Survey Data Release 4, Adelman-McCarthy et al., 2006) provides photometry and spectroscopy for 565,715 galaxies across a total of 4783 square degrees. In the main sample, this is highly complete down to a limiting magnitude of 17.77 in -band dereddened Petrosian magnitudes, and limiting surface brightness of mag arcsec. Low level incompleteness exists mainly in the highest density regions due to the inability to assign fibers to targets with separations .

The SDSS spectroscopic sample is incomplete at the bright end due to fiber magnitude limits, applied to avoid saturation and excessive cross-talk in the spectrographs. Our catalog is based on the DR4 version of the New York University Value Added Galaxy Catalog (NYU-VAGC Blanton et al., 2005)), which includes objects with bright fiber magnitudes and is photometrically recalibrated across the sky. If we restrict ourselves to the SDSS area with DR4 spectroscopic coverage, we measure redshift completenesses of % for , % for , and % for (i.e., the fraction of galaxies in the NYU-VAGC which actually have SDSS spectroscopy). Strauss et al. (2002) studied the incompleteness of SDSS galaxy spectroscopy using local catalogs and found typical incompleteness of % for bright () galaxies. Significantly, this incompleteness was due to overlaps with saturated stars. What this indicates is that the bright-galaxy incompleteness is both low and, crucially, not related to galaxy type. Therefore this incompleteness is not important for our analysis.

2.3. A Matched RC3-SDSS Catalog

We use the NYU-VAGC match to RC3 galaxies from Blanton et al. (2005). Although the matching radius was 45″ to compensate for the variable RC3 astrometrical accuracy, all matches are within 15″ (figure 7 of Blanton et al., 2005). Most of the galaxies under consideration are themselves larger than 15″ in size, and thus the incidence of false matches is low. There may be few occasions in which a false match is made for interacting or neighbouring galaxies, but this is unlikely to greatly influence our overall statistics.

Our full matched RC3-SDSS catalog contains 1340 galaxies, mostly in the range (median ), with a tail of bright galaxies extending to .

2.4. Morphological Reclassification

Subsequent examination of individual galaxies suggested that some of the RC3 classifications were in error (e.g., a “spiral” galaxy that was clearly an elliptical, or an “S0” that had strong spiral arms). To address this, we carried out a reclassification analysis for the sample. Two student interns independently examined all galaxies in our sample with assigned halo masses, identifying 406 cases with potentially incorrect general classification (i.e. E, S0 or spiral). We then examined each of these objects in detail, reclassifying them if necessary.444For reclassification, both color JPEG and background-subtracted -band FITS images were examined. In cases where a lenticular was reclassified as a spiral or vice-versa, we carried over any original disk-structure notations (bars and rings) from the original RC3 classification. 165 of the 406 flagged galaxies ended up with new classifications, including 6 of 23 ellipticals, 80 of 129 S0s and 65 of 230 spirals (a few galaxies have irregular or merger types). One galaxy (UGC5677) was clearly matched to the wrong SDSS object, due to especially poor RC3 astrometry; we assigned it zero weight in order to remove it from the sample. Finally, we also classified a total of 55 galaxies with (our primary magnitude limit; see Section 2.5) which had no classifications in the RC3.

The most striking aspect of this analysis was the high fraction of reclassified lenticulars: a total of 40% of the original (RC3) lenticulars ended up with different Hubble types (16 as ellipticals, 34 as spirals, and 9 as peculiar/merger-remnant systems). A similar high proportion of reclassified RC3 lenticulars can be seen in Figure 1 of Fukugita et al. (2007) and Figure 14 of Nair & Abraham (2010a). This led to a general reduction in the overall fraction of S0s and smaller increases in the elliptical and spiral fractions. The reclassification process actually strengthened the trends described in section 3.

2.5. SDSS Photometry and the RC3 Selection Function

Our goal is to examine the morphological composition of galaxies using the corrected RC3 classifications. This requires a detailed understanding of the inherently non-uniform RC3 selection, using the full SDSS catalog as the nominally complete “parent sample”.

Our photometry is based on the model magnitudes in the NYU-VAGC catalog, which we have corrected for galactic extinction (Schlegel et al., 1998). For large galaxies (, where is the radius containing half the -band Petrosian flux), the SDSS background can be oversubtracted, due to the outer part of the galaxy being treated as part of the sky; this effect is approximately color independent (Blanton et al., 2011). To account for this, we applied the photometric correction published by Blanton et al., as a function of the measured half-light radius (their Table 1, correction to v5.4 sky). This correction is generally consistent with those published by West et al. (2010) and Hyde & Bernardi (2009). A comparison with the latter correction for ellipticals – Figure 14 of Blanton et al. (2011) – suggests that these corrections might depend upon morphology. However, the differences are only significant () for galaxies with . Since only one of the galaxies in our sample is this large, we do not consider morphology-dependent corrections to be something to worry about.

As noted above, the main selection functions applying to the RC3 catalog are limits on (photographic) blue magnitude and isophotal diameter. To determine how the magnitude limit affected the selection, we generated an equivalent magnitude for all SDSS galaxies, using the SDSS and magnitudes555http://www.sdss.org/dr7/algorithms/sdssUBVRITransform.html #Lupton2005:

(1)

To evaluate the effects of the diameter limit, we used the SDSS measurement (the radius containing 90% of the Petrosian flux in r-band).

How well do our SDSS-derived magnitudes match the (largely photographic) magnitudes used as limits for RC3? Measurements of the RC3 total -band magnitude, , are available for a sub-sample of 150 SDSS-RC3 galaxies. For these objects we compare to derived from the SDSS photometry. We find that the RC3 and SDSS magnitudes are comparable in 144/150 cases, with significant scatter due to the large RC3 photometric errors. The other 6 objects have significantly underestimated fluxes from SDSS, with measured -band magnitudes of (corresponding to ). Five of these are clearly cases where deblending-related problems have affected the SDSS measurements. The sixth is an RC3 object (NGC842) mis-matched to the wrong SDSS galaxy due to a error in its RC3 cataloged position. We remove these objects by only considering galaxies with and , although the “true” magnitudes might be brighter than this limit. Assuming that this analysis is representative, we estimate that % of objects are lost due to poor SDSS photometry, and a % occurance of RC3-SDSS mismatches.

The first two panels of Figure 1 illustrates how SDSS-RC3 galaxies and the (almost complete) SDSS parent sample populate the magnitude-size parameter space. Not surprisingly, fainter or smaller galaxies are less likely to be found in the RC3 catalog. The third panel shows the ratio by number of RC3 to parent-sample objects as a function of these two parameters. To correct for the RC3 selection biases, we weight SDSS-RC3 galaxies by the inverse of this selection function: , computed in bins of 0.5 mag in magnitude and 5″ in . Some of the fainter, smaller objects have weights of up to 41. A threshold brighter than would remove these objects, but significantly worsen the overall statistics. We examine the robustness of our results by applying three different limits – , 15.5, and 15.0 – and checking that each result is consistent with each of the three limits applied.

We would like to compute fractions of the complete population down to a given luminosity limit. However, more luminous galaxies are visible to larger distances, and thus over larger cosmological volumes (this is the well-known Malmquist bias). To correct for this, we compute weights for our galaxies. In practice, is the volume within which a given galaxy is visible, and is the volume of the survey, defined to be the maximum value of (minimum ). To ensure we are insensitive to large weights, we have carefully examined our results both with and without these weights applied, and as a function of luminosity. Robust results are achieved with a luminosity limit of .

Figure 1.— 2D histograms used to determine the RC3 selection function, using a limit. The left and middle panels show counts of RC3 galaxies and SDSS parent sample galaxies binned by (the radius containing 90% of the -band Petrosian flux) and -band magnitude; horizontal color bars indicate the scales in galaxies per bin. The right panel shows the ratio of the left and middle panels, which is the basis of the RC3 selection function. The horizontal color bar indicates the ratio (from 0.0 to 1.0); white bins indicate no data (i.e., no galaxies in either sample are found in those bins).

2.6. The Group Catalog

For a full picture of how galaxy morphologies depend upon environment, we use the group catalog of Yang et al. (2007, Y07) constructed from SDSS DR4, and applied to galaxies in the range . The Y07 catalog is constructed iteratively using an algorithm which is an amalgam of friends-of-friends linking of galaxies to form groups and abundance matching to assign masses to those groups. Group halo masses are assigned based upon the rank order in terms of the group total stellar mass or luminosity of all galaxies brighter than an evolution and k-corrected -band absolute magnitude of . We use the stellar-mass-based halo masses, for which halos are complete down to ; this corresponds to a single red galaxy of stellar mass just making the cut in luminosity. This method provides halo masses for single as well as grouped galaxies.

We use Sample II as described by Y07, which contains a total of 369,447 galaxies including those with redshifts from sources other than SDSS and assumed redshifts for fiber collision galaxies as described. Galaxies and groups with incomplete local information are removed from the catalog, which means galaxies with completeness in the local “tiling sector” (Blanton et al., 2005) of C  (missing of neighbours) and groups on the edge of the survey with completeness ( of group members with C ). Isolated galaxies with stellar masses are not assigned halo masses, since they will live in halos below the halo mass limit. The vast majority of such galaxies are fainter than our cut.

Figure 2 examines how halo mass estimates for groups with members correlate with line-of-sight velocity dispersion (top) and number of confirmed members (bottom). is computed using the “Gapper” algorithm, appropriate for groups with a small number of members (Beers et al., 1990). The overplotted median - relations (using a running bin of 50 galaxies – or 5 galaxies for the most massive 25 groups) shows that a typical group halo mass of corresponds to a measured velocity dispersion of and –18 (median ). These masses are less than a simple prediction derived from the virial relation with (blue solid line), or the equivalent relation used by Y07, (magenta solid line). However, this is expected; application of the group-finder algorithm to mock catalogs predicts this discrepancy which results from the trimming of high peculiar velocity members at the tails of the velocity histogram (Y07). Thus corresponds to a true velocity dispersion of , and galaxies with large peculiar velocities will typically be assigned their own halo.

Figure 2.— Y07-calibrated group halo mass versus group rest-frame velocity dispersion (top) and number of group members (below) for groups with at least 3 members. The red line indicates the median of the distribution as a function of halo mass, computed over a running bin of 50 galaxies (5 for the 25 highest mass groups, dotted line). The blue solid line in the top plot is the result of a simple virial prediction, and the magenta dashed line is the simple fitting function used by Y07.

Y07 also classify galaxies as either central or satellite. In reality, a “central” galaxy is just the most massive galaxy in any given halo (i.e. equivalent to the Brightest Group Galaxy, BGG), regardless of its actual physical location within the group, and all other galaxies in the group are “satellites”. Skibba et al. (2011) show that a high fraction of so-called “central” galaxies are not in fact located at the center of the group in terms of either projected position or velocity: going from % for to % for . This must be a consequence of the dynamical state of many of these systems which will be caught in the midst of a major halo merger, or at a time before relaxation of the descendent halo. Nonetheless, there are good theoretical and observational reasons to treat the most massive galaxy differently from the other galaxies: it should have the deepest potential well of any galaxy in the halo, especially if it does sit at the center of the global potential (when one exists after relaxation). This means halo gas can cool more easily onto this galaxy than it can onto any of the others. Observationally, these two types of galaxy have been shown to behave quite differently on average: central galaxies are more likely than satellites to be forming stars and/or hosting radio AGN at fixed stellar and halo mass (Weinmann et al., 2006; von der Linden et al., 2007; Best et al., 2007; von der Linden et al., 2010). Therefore, we use these classifications to examine the dependence of galaxy morphology on whether the galaxy is a central or satellite galaxy as well as on the underlying halo mass.

Of the 1340 galaxies in our SDSS-RC3 sample, 1194 have ; the sample size shrinks to 1064 when our cut is also applied. Within this subsample, there are 911 galaxies which have halo masses assigned by Y07, with 729 of these being central galaxies and 182 being satellites. It is important to note that our SDSS-RC3 sample does not include the richest, most massive galaxy clusters: the maximum halo mass is , while the maximum velocity dispersion is .

2.7. Stellar Masses

To examine how the galaxy population varies with stellar mass, we calculated stellar masses for each galaxy using the color-based mass-to-light () ratios of Zibetti et al. (2009, hereafter Z09), using SDSS colors and -band absolute magnitudes (including the necessary k-corrections). We prefer this approach over using the stellar masses of Yang et al. (2007), which are based on the ratios of Bell et al. (2003), because the Zibetti et al.  ratios include the effects of dust reddening and extinction, along with a spread of possible star-formation histories.

We also investigated using the stellar mass derivations of Gallazzi et al. (2005, hereafter G05)666These stellar masses, as well as H linewidth measurements, were taken from the MPA public webpage http://www.mpa-garching.mpg.de/SDSS/DR4/, which take advantage of SDSS spectroscopy for each galaxy. The G05 masses were estimated by fitting five spectral absorption features to estimate a -band ratio, applied to the -band luminosity. The drawback of this approach, from our perspective, is that the SDSS fiber spectra sample a relatively small, central region of the galaxies: since RC3 galaxies usually have diameters , the 3-arcsec SDSS fiber aperture captures only the inner region of the galaxy. For spiral galaxies, this can mean that the spectroscopic reflects the bulge or nuclear region, rather than the galaxy as a whole. In addition, spectroscopy-based stellar masses are not available for some galaxies (142 of the 1340 galaxies in our full RC3-SDSS matched sample).

In the rest of this paper, we mainly concentrate on the Z09-based stellar masses, but we tested all trends with stellar mass against the G05 and Y07 masses as well, and note when these provided different results.

2.8. Systematics and Limits in Stellar and Halo Masses

Figure 3 illustrates how galaxies of different morphological type populate the - plane. (The -band luminosity is computed applying both distance modulii in our chosen cosmology and k-corrections based on the kcorrect code of Blanton & Roweis 2007.) Spiral galaxies tend to have lower -band stellar light ratios, although the highest ratio galaxies are also spirals (with dust-obscured -band light). Ellipticals and S0s populate a fairly tight relation, indicating that there is little difference between a luminosity-based cut and a mass-based cut for E versus S0 classifications. At our selected luminosity cut of , an early-type galaxy has a typical stellar mass of . Cutting in mass instead of luminosity would reduce the unweighted total spiral fraction by less than .

Figure 3.— Stellar mass () versus -band luminosity () for all galaxies in our sample. Elliptical, S0, and spiral galaxies are indicated by red circles, green triangles, and blue stars, respectively. The vertical dashed line marks our luminosity cutoff.

Figure 3 also shows that spiral galaxies with can have masses down to . Because the halo mass estimates are ultimately based on galaxy stellar masses, these different stellar-mass limits have implications for our ability to find different galaxy types as a function of halo mass and galaxy status (central versus satellite). The simplest case is for central galaxies. If we consider isolated galaxies (where the galaxy is automatically the central galaxy of its halo), then a stellar-mass limit of implies a halo mass limit of for central E/S0 galaxies. The lower mass limit for spiral galaxies means that they can be found as central galaxies for halos with lower masses, down to the Y07 completeness limit (). This means that for halos masses , we should expect to find few or no central E/S0 galaxies, solely due to our luminosity cut.

A similar, albeit more complicated, effect applies to satellite galaxies. The minimum halo mass for a satellite galaxy can be estimated assuming that it is the second most massive galaxy in a two-galaxy group, with the central galaxy only marginally more massive. In this case, a satellite galaxy will have a halo mass , and we should expect to undercount E/S0 satellite galaxies in less massive halos. A spiral satellite with , on the other hand, could reside in a halo with total stellar mass content corresponding to halos of low mass (potentially down to the Y07 completeness limit).

The fact that our cut largely excludes E and S0 galaxies with stellar masses , while still including a large number of spiral galaxies with smaller stellar masses, means that direct comparisons of E, S0, and spiral galaxies will be biased for stellar masses . Consequently, when we consider fractions of different morphological types as a function of stellar or halo mass (e.g., in Sections 3.2 and 3.4), we limit ourselves to . This limit does not apply when we consider fraction within a given morphological class – e.g., the fraction of ellipticals with optical AGN spectra, or fractions of spirals with outer rings.

3. Results

In this section we look at how various galaxy classifications – broad Hubble types (elliptical, lenticular, spiral), spectroscopic properties, and morphological substructure (bars and rings) – depend on global galaxy properties and on group properties.

3.1. Uncertainties and Significance Testing

We use fractions to discuss the morphological composition of the local galaxy population. Fractions are by definition relative quantities and as such allow comparisons between different types, doing away with the need to renormalize to the total galaxy population in a given bin. However, the reader should keep in mind that focusing on fractions does have its own problems. For example, the total galaxy population in a given bin of stellar or halo mass, or luminosity, is not necessarily conserved with time. Since we consider multiple morphological types (e.g., elliptical versus S0 versus spiral), the fraction of a given type can change due to transformations between other types, and not just because the total number density of the first type is increasing or decreasing (e.g., if the S0 number density stays constant but spirals merge to form ellipticals, then the total number of E+Sp galaxies decreases and the S0 fraction will increase).

Our plots show fractions for each specified type within various bins. The error bars in these plots are 68% confidence limits from the Wilson (1927) binomial confidence interval, which is a more accurate way of estimating binomial uncertainties than the commonly used Gaussian approximation, especially as the frequencies approach 0 or 1; see Brown et al. (2001) for a comprehensive discussion of binomial uncertainties.

In the case of weighted counts, there is less guidance on the proper way to compute uncertainties. We estimate the uncertainties by first rescaling all (weighted) counts so that the total counts are equal to the original (unweighted) total counts in a given bin, and then computing the Wilson confidence limits using the rescaled counts.

We estimate the significance of apparent trends in these plots via a logistic regression analysis. In logistic regression, the probability of a binomial property (e.g., galaxy is S0 or not, galaxy is barred or not) as a function of some independent variable is modeled using the following function:

(2)

where is the probability for a galaxy having the particular property. The coefficient corresponds approximately to an intercept value, while is analogous to a slope and measures how strong the trend is. Note that the function always has values between 0 and 1 (appropriate for a probability), and is either monotonically increasing or decreasing.

In principle, we could fit straight lines to the binned frequencies and use the null probability for a nonzero slope as an estimate of a trend’s significance, but the logistic approach has two key advantages. First, a linear fit will yield (meaningless) frequency values above 1 or below 0 at some point, while the logistic curve is bounded between 0 and 1. Second and perhaps more importantly, linear fits to frequencies will be biased by the specific binning scheme used (number and spacing of bins), and by the assumption of Gaussian errors – an assumption that is not necessarily true for frequencies, especially for frequencies close to 0 or 1. Logistic regression uses all data points individually, making binning and error assumptions irrelevant.

The specific logistic regression code we use is from the Survey package777http://faculty.washington.edu/tlumley/survey/, implemented in the R statistical language888http://www.r-project.org/; this package allows for individual data points to have weights. The fitting process yields null-hypothesis probabilities for the intercept and slope (i.e., the probability that a logistic model with a value of 0 for the given coefficient could explain the data); we use the null-hypothesis probability for () as an estimate of an apparent trend’s significance. We also quote the best-fit value of and its uncertainty; positive values mean the frequency increases with the independent variable, while negative values indicate a trend of decreasing frequency. We caution the reader that this is not a universal indicator for a trend: trends more complicated than monotonic, smooth increase or decrease in probability could be poorly fit by the logistic model. Nonetheless, we feel this is superior to the commonly used approach of least squares linear fitting of binned data, for the reasons given above. A two-sample test such as the Kolmogorov-Smirnov test is also not advisable, both because it is calibrated only for unweighted data and because it measures the maximum, local difference between two samples (e.g. ellipticals and non-ellipticals) rather than the significance of a global trend.

3.2. Morphological Fractions Versus Luminosity and Stellar Mass

Figure 4.— Fractions of elliptical (red circles), lenticular (green triangles), and spiral (blue stars) galaxies as a function of B-band luminosity, with selection weights applied. Binomial errors are computed using the Wilson (1927) method.

Figure 4 shows how the fractions of elliptical, lenticular, and spiral type galaxies depends upon B-band luminosity within the full SDSS-RC3 sample. Selection weights are applied to galaxies; when plotting against luminosity, it is not necessary to apply weights.

The overall elliptical fraction is low, but clearly increases with luminosity (; note that this indicates a frequency that decreases as becomes more positive). The observed fraction of S0 galaxies decreases with luminosity (), whilst the fraction of spiral galaxies show little, if any dependence on luminosity down to (). From a theoretical standpoint, this is perhaps surprising, indicating that the overall probability that spiral arms have faded (likely associated with the suppression of star formation in a disk galaxy) is not a strong function of its luminosity.

Figure 5.— Fractions of each morphological type (elliptical, lenticular (S0), and spiral) for galaxies as a function of stellar mass, weighted using selection and weights.

We examine the stellar mass dependence of morphological fractions in the top panel of Figure 5, cut at and weighted to account for both selection and volume (). We also restrict our plots, and our logistic regression analysis, to galaxies with , because selection effects can lead to artificial suppression of elliptical and S0 populations relative to spirals below this mass limit (Section 2.8). The fraction of ellipticals does increase significantly with increasing stellar mass (). Overall, the S0 fraction appears to decrease as stellar mass increases, although this is not formally significant (). The fraction of spiral galaxies is essentially constant at % over this mass range (), similar to what was seen for trends with .

3.3. Morphological Fractions Versus Halo Mass

Figure 6.— As for Figure 5, but now showing morphological fractions as a function of halo mass (top), group velocity dispersion (middle), and number of group members (bottom); only galaxies with are considered. Dashed lines indicate logistic fits to the (unbinned) data.

We present the fraction of galaxies with and as a function of group/halo properties in Figure 6. The top panel presents the trends as a function of halo mass. This shows a strong dependence of morphological type on halo mass. The elliptical fraction is practically zero below (but this is most likely due to the selection effect discussed in section 2.8), then rises to a roughly constant level of –10% for more massive halos. The lenticular fraction increases dramatically from % in the very lowest halo masses to % at the high-mass end (the dashed green line shows the logistic fit, which has . The fraction of spiral galaxies naturally compensates for these trends with halo mass, decreasing from % to % going from the lowest mass to the highest mass halos ( for the logistic fit shown by the dashed blue line). Significant trends for S0s and spirals are also found with group velocity dispersion and number of members as the independent variable (logistic fits, shown in the center and lower panels).

The most dramatic outlying point in Figure 6 is the highest bin of (bottom panel), in which the spiral fraction jumps to almost . This bin is populated by a single group, the Abell 2199 supercluster (see e.g. Rines et al., 2002), which has apparently been merged by the Yang et al. (2007) group-finder algorithm into a single, overmassive group with 433 members. Most of the 18 RC3 galaxies belonging to this system lie outside the collapsed regions of the supercluster (including Abell 2197 and Abell 2199). Their spiral morphologies are therefore not surprising.

3.4. Comparing Central and Satellite Galaxies

Figure 7.— As for Figure 5, but now showing morphological fractions versus (left) and (right) separately for central galaxies (top) and satellite galaxies (below); only galaxies with are considered.

Figure 7 splits the galaxy population into central and satellite galaxies, which (at least theoretically) should be subject to different physical processes. The morphological fractions are plotted against both the stellar mass of individual galaxies (, left panels) and halo mass (, right panels). Once again, we restrict the plots and logistic-regression analyses to galaxies with (see Section 3.2).

The dependence of galaxy morphology on galaxy stellar mass shows some interesting differences when we consider central and satellite galaxies separately. The roughly constant fraction of spirals as a function of stellar mass for all galaxies (Figure 5) is replicated by the central galaxies; but for satellites we evidence of a trend where the frequency of spirals increases with mass, at least up to . For S0s, the apparent differences are even stronger: central S0s are a roughly constant fraction at all masses , while satellite S0s show a steep drop in frequency as stellar mass increases (however, this trend is not formally signficant: ). Clear trends are harder to discern for ellipticals; in general, they resemble the elliptical trend for all galaxies (Figure 5), with frequency increasing weakly but significantly with stellar mass ( for central ellipticals).

When we turn to the question of how the morphological fractions of central and satellite galaxies depend on halo mass, we see some striking differences. This is not actually true for spiral galaxies, which decline in frequency as halo mass increases for both central and satellite galaxies, just as we saw for galaxies in general (Figure 6). But when we look at elliptical galaxies, we see a clear dichotomy: the elliptical fraction for satellite galaxies is roughly constant (), while the fraction for central galaxies is a steeply increasing function of halo mass ().

S0 galaxies also show a dichotomy: the fraction of central galaxies which are S0 is roughly constant (the apparent decrease for is likely a result of the selection effect discussed in Section 2.8, above), but the fraction of satellite galaxies which are S0 jumps from % to % in higher-mass halos! This appears to be a highly significant difference; the logistic-regression value of probably understates the significance because an abrupt transition like that seen here is not well modeled by the logistic curve (it would, of course, not be well modeled by a simple linear fit to the binned fractions, either).

One clear implication from this analysis is the importance of group halo mass for determining galaxy morphology. For central galaxies, halo mass is clearly more important than galaxy mass. The frequency of central spirals is high and essentially constant over the stellar mass range . But when we look at variations in halo mass, we can see central spirals being replaced by central ellipticals as the halo mass grows; only the central S0 frequency seems to be independent of halo mass.

Halo mass also has a strong effect on satellite galaxies, although in a somewhat different fashion. As halo mass grows, the fraction of satellites which are spirals falls, just as happens for central galaxies. But satellite spirals in higher-mass halos are clearly being replaced by lenticular galaxies, which become the dominant type of satellites for .

3.5. Co-evolution of Morphology, Star Formation and AGN Activity

Physical processes which transform spiral galaxies into elliptical or lenticular galaxies should describe the destruction of a galaxy’s disk in the case of ellipticals, the enhancement of the bulge component for both ellipticals and bulge-dominated lenticulars, and the dissolution of spiral arms (lenticulars). Such processes should lead to the observed correlations between morphology and environment. In addition, these processes may be responsible for circumnuclear starbursts and AGN, along with the removal of gas and the general suppression of star formation.

We use the spectroscopic information from the SDSS survey to characterize the ongoing star formation and nuclear activity in our sample. H emission-line flux correlates strongly with the star formation rate, and is strongly bimodal for galaxies with and without significant star formation or nuclear activity (Balogh et al., 2004). SDSS spectral fibers sample only the central (diameter) of each galaxy, corresponding to 0.61–2.35 kpc at –0.04. This undersamples the galaxy as a whole, and will miss much of the ongoing star formation and H emission at large radii.

We use the Brinchmann et al. (2004, hereafter B04) calibration of H equivalent width, which corrects the emission flux for underlying stellar absorption. We find a bimodality in this quantity, with a low emission peak at Å (emission is negative), which we presume should be at Å (no emission for a truly passive galaxy). We define a galaxy as “passive core” if the H equivalent width is within of this peak (where in this case is the error in equivalent width, as estimated by B04, scaled up by a factor 2.473 calibrated to repeat measurements of the same galaxy)999http://www.mpa-garching.mpg.de/SDSS/DR4/raw_data.html . The typical value of 2.5 is Å for these galaxies.

Figure 8.— The fraction of disk galaxies with a passive core (SDSS fiber spectra lacking significant H emission, see text) versus Hubble type (top) and, restricted to S0/a–Sb types, versus log axis ratio (bottom). A high fraction of S0s have passive cores, as do some S0/a–Sb type spirals (but very few later types). Most passive-core spiral galaxies are close to face-on (low axis ratios).

The upper panel of Figure 8 shows the fraction of disk galaxies with a passive core as a function of Hubble type. Passive-core galaxies are, unsurprisingly, most common amongst S0 galaxies, and the fraction decreases going from the RC3 type S through S0 to S, going from E-like to spiral-like S0s. Among spirals, Sa galaxies are much more likely to have passive cores than later Hubble types ( Sa, Sab, Sb, going to zero for later types). The anomalously low S0/a passive-core fraction is difficult to explain, and we avoid interpreting this for now.

The lower panel of Figure 8 shows the fraction of S0/a–Sb galaxies with a passive core as a function of the RC3 value r25. This is the logarithmic axial ratio , where and are the semi-major and semi-minor axes measured out to a surface brightness of 25 mag arcsec in the -band. Low values of r25 imply near circular isophotes. The core of an early-type spiral is much more likely to be passive for a face-on inclination (low axis ratio), for which there will be no fiber contribution from the outer disk. In such early-type, face-on spirals the SDSS fiber spectrum can be dominated by bulge light. These correlations therefore suggest that star formation in the disk can be either truncated or heavily obscured in the inner regions, so that no significant H emission is detected in the fiber. Since we find a very low passive fraction in highly inclined, early-type spirals (where the outer disk is likely to be projected into the SDSS fiber aperture), we infer that the outer disks of early-type spirals are typically still forming stars, and that most passive-core spirals are passive only in the inner regions. This is consistent with visual inspection of color JPEG images of these galaxies: in many cases the inner bulge+bar region appears red, with blue outer spiral features, often separated by a ring.

The resulting picture of an inner truncation for star formation is a necessary simplification, given the limitations of our data. For comparison, longslit spectroscopy of four spiral galaxies lacking emission in the SDSS fiber revealed emission in the outer regions of two – and strong Balmer line absorption indicated recent star formation in the other two (Ishigaki et al., 2007).

Figure 9.— The “BPT” (Baldwin et al, 1981) emission-line ratio diagnostic diagram, showing the full parent sample (small points, all galaxies with S/N(all lines) ) overplotted with galaxies from our morphologically classified sample (galaxies with S/N(all lines) ), including elliptical (red circles), S0 (green triangles), S0/a-Sb (cyan stars), and Sc-Sm (blue stars) galaxies. Symbols with black dots at the centre contain a “radio-AGN” source (see text for formal definition). Most elliptical and S0 galaxies, and many early-type spirals, have AGN-like line ratios (lying to the right of the Kauffmann et al. (2003) and Kewley et al. (2001) lines), indicating hard ionization fields inconsistent with starbursts, but with [O iii]/H ratios typically lower than than 3, suggestive of LINERs rather than Seyfert galaxies. Recall that the parent sample goes to higher redshift, which means that SDSS fibers sample light out to larger physical radii.

Star formation is not the only possible source of H emission, of course. H emission traces ionized gas – and therefore requires both gas and ionizing radiation. The nature of that ionizing radiation can be explored via emission-line ratios, tracing the relative importance of different ionization levels and subsequent transitions. In Figure 9 we use the [N ii]H vs [O iii]/H diagnostic line-ratio diagram, commonly used to separate normal star forming galaxies from harder radiation fields typical of Seyfert and LINER (low-ionization nuclear emission-line region) type galaxies (Baldwin et al., 1981, the “BPT” diagram). The small points in the background trace the parent sample, demonstrating the overall distribution of galaxy line-ratios (where S/N(all lines) ). Overplotted are galaxies in the RC3-SDSS sample with S/N(all lines) , keyed by morphology (see caption). Anything to the right of the Kewley et al. (2001) dashed line cannot be explained by normal starburst models, whilst the Kauffmann et al. (2003) dashed line demarcates the boundary of normal star forming galaxies (to the left). It should be noted that RC3-SDSS galaxies are at lower redshifts than the typical parent sample galaxy, and so fiber spectra will be more dominated by nuclear emission. Nonetheless, it is interesting that almost all E/S0 galaxies with emission are classified as LINERs ([O iii]H implies a softer-than-Seyfert ionization field). Some S0s extend to the region between the two dashed lines (composite/transition systems, Kauffmann et al., 2003), whilst S0/a–Sb (and some later-type) spirals extend from the bottom (high metallicity) end of the star forming locus, up through the composite and LINER region to the Seyfert regime (with LINERs again the dominant population). As we sample only the central , the ionization source may well be related to accretion onto a super-massive black hole (SMBH).

We classify galaxies with emission lines into two basic categories. Anything with broad emission lines or lying to the right of the Kewley et al. (2001) line is termed “AGN”. All other emission line galaxies are called “star-forming”. Whilst these are commonly used definitions, we note that LINER-like ionization may also result from older stellar populations, shocks or interaction with hot, X-ray emitting gas (see e.g. Sarzi et al., 2010; Capetti & Baldi, 2011) and not solely from accretion onto a SMBH.

To understand the possible role of AGN feedback for the suppression of star formation, it is also useful to examine the radio properties of these galaxies. Models of galaxy formation invoke radio-mode AGN feedback, which suppresses cooling onto galaxies living at the centers of massive halos by coupling the kinetic energy of a radio jet to the cooling gas (e.g. Bower et al., 2006; Croton et al., 2006). To examine the role of radio-mode feedback, we cross-correlated our sample with the VLA (Very Large Array) FIRST (Faint Images of the Radio Sky at Twenty-Centimeters) survey (Becker et al., 1994). This 1.4GHz survey has a nominal detection threshold of 1 mJy, with a 90% confidence positional error circle of radius 1″ (0.5″ at the 3 mJy level). We first identified “nuclear” sources by requiring a match between SDSS and FIRST positions within 2″; this yielded 261 FIRST sources with fluxes mJy matched to the SDSS-RC3 sample.

Continuum radio emission at 1.4GHz originates via synchrotron emission, either in supernovae remnants (e.g. Condon & Yin, 1990; Condon, 1992; Weiler et al., 2002) – which correlates with star formation – or in interactions between jets and the ambient medium (e.g. Burbidge, 1956; Guthmann et al., 2002; Kaiser, 2006). We are primarily concerned with early-type galaxies, most of which are not forming stars. However, to ensure that we are dealing with nuclear radio sources which are unlikely to be due to star formation, we restricted ourselves to those galaxies whose radio emission was significantly stronger than what one would predict from the optically determined star formation rate; we refer to these as “radio-AGN” sources. Specifically, we used the fiber-based B04 star-formation rates (which are insensitive to aperture corrections and well matched to the average compact nuclear radio source), and then estimated the expected star-formation-based radio luminosity using the relation of Hopkins et al. (2001):

(3)

converted to a Kroupa (2001) IMF for consistency with B04. Since Hopkins et al. found approximately an order of magnitude scatter in their relation, we impose a conservative limit of in order to identify bona-fide radio-AGN sources. As an example, a source at the detection limit of the FIRST survey (flux of 1 mJy) at the high-redshift end of our sample () could be explained by a central SFR of , but would only be counted as a radio-AGN if the measured SFR was .

The resulting 140 galaxies in the SDSS-RC3 sample for which we found radio-AGN sources are indicated in Figure 9 by the black dots inside the galaxy symbols. Most elliptical and S0 galaxies with radio-AGN sources in our sample are LINERs, which suggests an active SMBH is indeed present.

Figures 10 to 13 show the fractions of elliptical (red circles) and S0 (green diamonds) galaxies which belong to each spectroscopic class (passive-core, star-forming, AGN), or with radio-AGN sources, divided into central (solid symbol) and satellite (open symbol) categories. This fraction is plotted both against stellar mass (left panels) and halo mass (right panels). These figures illustrate how the nuclear spectroscopic and radio properties of galaxies depend upon their morphology, mass and environment. In contrast to the plots in Section 3.2 and 3.4, we extend the stellar-mass plots here down to , because the bias towards spirals at low stellar masses (Section 2.8 and Figure 3) is no longer relevant.

Figure 10.— Fractions of elliptical (red circles) and S0 (green diamonds) galaxies with passive cores, separately for central galaxies (filled symbols) and satellite galaxies (open symbols), using selection and weights. This is presented in bins of stellar mass (left panel) and halo mass (right panel). Ellipticals, and low mass satellite S0s of high-mass halos, have predominantly passive cores.
Figure 11.— As Figure 10, but for star-forming galaxies. Only the central S0s of low mass halos (and few ellipticals or satellite S0s) have core spectra which put them in the star forming category.
Figure 12.— As Figure 10, but for emission-line AGN. Early-type AGN (typically LINERs) live mainly in S0s rather than ellipticals, and in high-mass galaxies. There is no obvious dependence on environment ( or central/satellite status).
Figure 13.— As Figure 10, but for radio-AGN sources (nuclear radio sources too bright to be explained by star formation). These live primarily in the central, massive galaxies of massive halos (elliptical and S0) or in massive satellite ellipticals.

Figure 10 shows that the cores of elliptical galaxies (both central and satellite) are much more freqently passive than S0s ( for central Es compared to % for central S0s, for satellite Es compared to for satellite S0s). The fraction of passive-core S0s is highest for low mass satellites, which all live in massive halos (section 3.4).

Figure 11 shows that the only significant population of early-type galaxies with core spectra indicating star formation are central S0s with low stellar masses in low-mass halos ( versus and versus ). Selection effects are relevant, such that low mass star-forming S0s only make it into our B-selected sample because they are bright in that band. However, this population extends into bins of stellar mass above our threshold , suggesting a physical truncation of star formation (and/or the presence of harder, AGN-like ionization) in central S0 galaxies of halos . There are no notable trends for star-forming cores in elliptical galaxies.

Figure 12 shows that emission-line AGN (mostly LINERs, Figure 9) are found much more frequently in S0s than in ellipticals (combined central plus satellite populations: % for ellipticals and % for S0s), and their frequency increases with stellar mass (notably for S0s, although this is not formally significant: ). However there is no measurable dependence on environment for AGN fraction, either in terms of halo mass or central versus satellite status.

Figure 13 further explores the AGN theme in terms of radio emission. The fraction of galaxies with radio-AGN sources increases with both galaxy mass and halo mass. For central ellipticals, we find for radio-AGN fraction versus galaxy mass and versus halo mass. The right-hand panel of the figure shows that for a given halo mass, central galaxies are more likely to host radio-AGN sources than satellite galaxies; the least likely hosts are satellite S0s.

3.6. Dependence on Environment and Hubble Type of Bar and Ring Fractions

Roughly two-thirds of local spiral galaxies – and a smaller fraction of S0 galaxies – are barred (e.g., Eskridge et al., 2000; Menéndez-Delmestre et al., 2007). Although -body simulations have long shown that bars can form spontaneously in isolated disks, simulations have also shown that bar formation can be triggered by tidal interactions (e.g., Noguchi, 1987; Salo, 1991; Noguchi, 1996; Berentzen et al., 2004). It is therefore plausible that local environment might influence the frequency (and possibly the size or strength) of bars in disk galaxies. Similarly, although outer rings are well understood as being primarily due to the interaction of a bar’s Outer Lindblad Resonance with gas in the disk (e.g., Buta & Combes, 1996), the fact that they are features of the outer disk means they are in principle more vulnerable to interactions than other, more central structures. Thus, we might expect that local environment could also influence the frequency of outer rings.

To estimate the bar fraction, we consider both strong (RC3 class SB) and weak (RC3 class SAB) bars in disk galaxies (S0s and spirals considered separately). We also restrict the sample to relatively face-on galaxies: those with RC3 axis ratios (). The latter restriction excludes highly inclined galaxies, where optical bar detection becomes difficult or impossible. We warn the reader in advance that we are probably underestimating the true bar fraction, since some bars will have been missed due to dust obscuration (see, e.g., Eskridge et al., 2000) and weaker and smaller bars will have been difficult to identify due to resolution effects. Our analysis should thus be seen as investigating the possible effects of group environment on large, strong bars, rather than on all possible bars.

We do find some evidence for trends in bar fraction with galaxy mass. Figure 14 suggest that the spiral bar fraction increases with galaxy stellar mass, although the significance of this depends on which set of stellar masses we use (e.g., using G05 masses, but only 0.058 with our preferred Z09-based masses, and 0.047 for the Y07 masses). A similar trend trend may exist for central S0s ( using Z09-based masses, with similar values for the other mass estimates). Such a trend would be consistent with the findings of Nair & Abraham (2010b) for a similar mass range.

We find no evidence for trends in bar fraction versus halo properties, either as a whole or when considering central and satellite galaxies separately (Figure 14, right panel). This is consistent with other recent studies of bar fraction with environment. For example, Marinova et al. (2009) found no difference in bar fraction (determined using optical HST images) across a range of local environments in the Abell 901/2 Supercluster, and Aguerri et al. (2009) found no evidence for a dependence of bar fraction (determined from SDSS images) with local environment; both of these studies used local projected surface density of galaxies as the “environment”. Li et al. (2009) also found no difference in the clustering properties of barred versus unbarred galaxies.

For outer rings and pseudorings, we restrict ourselves to S0–Sbc galaxies, which is where almost all such rings are found (Buta & Combes, 1996). We also consider rings and pseudorings separately, in part because previous work by Elmegreen et al. (1992) suggested there might be divergent trends for the two subtypes. There is no clear evidence for any trend of outer ring or pseudoring frequency with halo mass. The right-hand panel of Figure 15 appears to suggest a decreasing frequency with higher halo mass, at least for central galaxies, but this is not statistically significant, even if we lump outer rings and pseudorings together ( for central galaxies, for all galaxies). What does seem to be present is a decrease in outer ring or pseudoring frequency with increasing galaxy stellar mass, at least for central galaxies (left panel of Figure 15). These trends are relatively shallow, but statistically significant (e.g., for central galaxies, lumping both outer rings and pseudorings together). Since outer rings are usually associated with bars (e.g., Buta & Combes, 1996), and since the frequency of bars apparently increases with stellar mass as noted above, the lack of outer rings in more massive galaxies is highly significant.

The (tentative) absence of environmental trends for outer rings appears to contradict what Elmegreen et al. (1992) found: they argued that outer rings decreased in frequency for denser environments, while the frequency of pseudorings increased. One difference is that their main analysis was restricted to strongly barred S0 + S0/a galaxies only, and it is not clear how to compare their “field”, “pseudo-field” (possible group members), “group”, and “binary” classifications with our group halo properties. For example, a “binary galaxy” system could be low-halo-mass group with two significant members, or a subset of a larger group with a higher halo mass. It is also worth noting that the high outer-ring fraction reported by Elmegreen et al. for field galaxies is based on very small sample sizes (3 field galaxies, 4 pseudo-field galaxies).

Figure 14.— Fractions of strong + weak bars in () S0 (green triangles) and spiral galaxies (blue stars) as a function of the galaxies’ stellar and halo masses, with selection and weights applied. Filled symbols indicate central galaxies and hollow symbols indicate satellite galaxies. In this plot, we consider only galaxies with isophotal axis ratios (i.e., relatively face-on).
Figure 15.— As for Figure 14, but now showing fractions of S0–Sbc galaxies which contain either outer rings (black circles) or outer pseudorings (green squares) as a function of the galaxies’ stellar and halo masses. Filled symbols indicate central galaxies and hollow symbols indicate satellite galaxies.
Figure 16.— As for Figure 14, but now showing fractions of spiral galaxies which contain inner rings (RC3 “r” classification, black circles) or inner pseudorings (“rs”, green circles) as a function of the galaxies’ stellar and halo masses. In this plot, we consider only galaxies with isophotal axis ratios (i.e., relatively face-on). Filled symbols indicate central galaxies and hollow symbols indicate satellite galaxies.
Figure 17.— As for Figure 16, but now showing fractions of galaxies with inner spirals (RC3 “s” classification).

The RC3 catalog also provides classifications for inner ring/spiral structure in spirals, specifying whether the main disk (outside the bar, if present) is purely spiral (s), contains an inner ring (r), or has an intermediate broken-ring or pseudoring appearance (rs); see, e.g., Figure 1 of Buta et al. (1994). We have looked for possible correlations of r/rs/s frequency with environment in our sample, but find no evidence for any clear trends with halo mass, dispersion, or number of group members (Figures 16 and 17). We note that the lack of any trend for the inner-ring fraction is possibly in conflict with Madore (1980), who found that galaxies with inner rings had fewer close companions (galaxies at projected distances kpc) than inner-spiral or inner-pseudoring galaxies. However, Madore pointed out that the number of close companions, so defined, seemed independent of whether or not a given galaxy was in a group.

We do find that the frequency of inner rings increases with galaxy luminosity and mass ( for , with similar slopes and similarly small values of for G05 and Y07 stellar masses). Given that inner rings are more common in early-type spirals (de Vaucouleurs & Buta, 1980), this trend could be a side effect of the tendency of early type spirals to be more massive than late-type spirals; it could also be due to the apparent increase in bar fraction with stellar mass noted above, since inner rings are usually due to bar-related resonances (Buta & Combes, 1996). Figure 17 does suggest a corresponding decrease in inner-spiral fraction with galaxy mass, though this is not statistically significant ().

4. Discussion

4.1. Where and How Are Elliptical Galaxies Formed?

Figure 5 shows that the global fraction of elliptical galaxies increases with stellar mass, while Figure 6 shows no such trend with halo mass, velocity dispersion or number of group members. This could naively be interpreted as evidence for a purely mass-dependent formation of ellipticals, independent of environment. However, Figure 7 shows that a strong trend with halo mass does exist when only central galaxies (the most massive ones in their group) are considered. No such trend is seen for satellites; the fraction of ellipticals for satellites correlates only with stellar mass. The similar stellar mass dependences of central and satellite ellipticals, and the relatively infrequent occurance of satellite ellipticals, argues for a common parent population for both types.

Simulations show that disks are largely destroyed by major mergers, leading to the formation of elliptical galaxies (e.g. Barnes, 1988). These events preferentially occur at the centers of halos: dynamical friction brings satellite galaxies to the bottom of the potential well where they merge with the central galaxy. Cosmological simulations show that mergers between the subhalos hosting satellite galaxies are rare (Angulo et al., 2009). The highest mass halos have the richest halo merger history, and the central galaxies of these halos are the most massive galaxies in the Universe (the most extreme examples being cD galaxies in clusters), with the most extensive merger histories of any galaxy (e.g. De Lucia & Blaizot, 2007).

If all ellipticals are formed as (or transformed into) ellipticals while they are still central galaxies within their own halos, then the observed correlations are perfectly consistent with our understanding of how ellipticals form via mergers (De Lucia et al., 2011). The more massive a halo, the more likely its central galaxy is to have undergone multiple major mergers, and thus the more likely it is to be an elliptical; such galaxies will naturally also tend to be more massive. Satellite ellipticals are galaxies which formed as ellipticals at the center of their progenitor halos – thus partaking in the general trends just outlined – and were subsequently accreted as ellipticals onto their current halos. Correlations with stellar mass will therefore persist for satellite ellipticals, whilst their previous (central-galaxy) correlation with halo mass is lost.

In this scenario, most properties of elliptical galaxies (in addition to mass and morphology) are determined by their formation as central galaxies, and subsequently frozen at the time of their accretion onto larger halos as satellites. Thus, aside from possible differences in mean stellar age, satellite and central ellipticals should follow the same general scaling relations. Studies have found that the well-known elliptical-galaxy scaling relations are indeed largely independent of environment, These include the slope of the fundamental plane (e.g., de la Rosa et al., 2001; Reda et al., 2005; Bernardi et al., 2006; but see also D’Onofrio et al., 2008; La Barbera et al., 2010), the color-magnitude and Kormendy relations (e.g., Hogg et al., 2004; Reda et al., 2005), and luminosity-size relations (Nair et al., 2010). Guo et al. (2009) and Weinmann et al. (2009) studied galaxies using the Y07 group catalog, specifically contrasting mass-matched central and satellite galaxies, and found no size or structural differences for “early-type” galaxies. Note that many of these studies lumped elliptical and S0 galaxies together, so there is in principle the possibility of confusion if ellipticals and S0s have trends that happen to cancel out when they are combined.

While there is evidence for age differences between ellipticals in different environments (e.g., Thomas et al., 2005; Bernardi et al., 2006; Saglia et al., 2010), this is still consistent with the overall picture. Ellipticals in high density environments are more likely to be satellite galaxies within massive halos, with properties frozen at the time of the accretion.

The picture outlined above implicitly assumes that once an elliptical has formed at the center of its halo, it is able to remain an elliptical. In the case of ellipticals created by “wet” (gas-rich) mergers, the problem is how to prevent significant residual gas from continuing to form stars; quasar-mode feedback is a promising solution (e.g., Granato et al., 2004; Springel et al., 2005; Hopkins et al., 2006). A more general, long-term problem is that posed by the presence of hot gas in the halo. Since the center of a halo is the natural destination for halo gas that is able to cool, some mechanism must exist for suppressing such cooling – otherwise, cool gas would accumulate in the center of the halo and potentially form a new stellar disk. (Note that satellite ellipticals do not suffer from this problem, since they do not sit at the centers of halos.)

This cool, low entropy gas has been observed in some massive clusters – but it is not ubiquitous; clusters with no cooling flows are in the majority (e.g. Nesci, 1991; Cavagnolo et al., 2009). The existence of cooling gas appears to be a requirement for central cluster galaxy to host either star formation (e.g. Donahue et al., 2010; Hicks et al., 2010) or radio AGN (e.g. Sun, 2009). It has been proposed that energy from a radio jet can offset cooling in a cluster and that this suppresses the growth of the central galaxy. Cavities containing low-density, hot gas have been observed spatially coincident to the radio lobes, and the total energy required to create such cavities is typically enough to balance cooling (e.g. McNamara et al., 2000; Fabian et al., 2000; Dunn & Fabian, 2006; Cavagnolo et al., 2010).

If radio-mode AGN feedback is also applicable for galaxies in lower-mass halos, then it could prevent significant cooling onto galaxies, suppressing their growth and allowing models of galaxy formation to match the high-mass exponential cutoff seen in the galaxy mass function (Bower et al., 2006; Croton et al., 2006). Cavities have been observed in the hot gas component of galaxy groups (Dong et al., 2010) and even individual elliptical galaxies (Baldi et al., 2009). The high fraction of radio sources we find for central ellipticals and S0s in halos with masses of (Figure 13; see also Best et al., 2007; Pasquali et al., 2009)) is potentially further support for the possibility that radio-mode feedback operates in halos of these masses. It is also possible that other forms of AGN feedback can suppress star formation in lower-mass halos; for example, Schawinski et al. (2009) have found evidence that low-luminosity AGN activity is associated with the disappearance of central molecular gas in S0 and elliptical galaxies.

More detailed models will be necessary to determine whether the fractions of central galaxies with elliptical as opposed to disk morphology, and their dependence on halo mass, can be quantitatively explained in the context of the expected merger history and suppression of disk re-formation (Wilman et al., in prep).

4.2. Where Are S0s Formed?

As with ellipticals, the dependence on halo mass of the S0 fraction is very different for satellite and central galaxies. The remarkable change in satellite S0 frequency, which jumps from % in lower-mass halos to % for halos with masses , suggests that spiral arms are often suppressed in a disk galaxy once it is accreted onto a halo, if the halo is more massive than .

In fact, we can argue that the majority of all present-day satellite S0 galaxies became S0s after they were accreted into halos more massive than . Since halos with do not have satellite S0s, any pre-existing S0s which formed in less massive progenitor halos and then fell into massive halos () must have originally been central galaxies. Assuming that these progenitor halos had a distribution of central morphological types similar to what we see today (if anything, they probably had lower S0 fractions in the past), then the mean central S0 fraction for the accreting progenitor halos would be %. The fraction of S0s in massive halos which are post-processed is therefore:

(4)

where is the fraction of massive-halo satellite galaxies which are post-processed S0s, and is the fraction of massive-halo satellites which are S0s. The present-day S0 satellite fraction ( %) thus requires that almost three quarters of these galaxies (i.e., % of satellite galaxies, or % of satellite S0s) fell into their present-day halos as spirals, becoming S0s during or after the accretion process.

We can go one step further, and apply equation 4 as a function of galaxy stellar mass. We limit this exercise to the stellar mass range for two reasons: first, as previously noted, S0s are lost due to selection effects below ; second, there are no satellite S0s in our sample with masses (see Figure 7). For simplicity, we assume that there is no significant stellar-mass change during or after the accretion process. The upper panel of figure 18 shows how and depend on stellar mass. We also show the equivalent fractions for spiral galaxies: i.e., and . What is striking about this plot is the apparent stellar-mass trend. For , the satellite S0 fraction is clearly too high to be explained by the pre-processed S0 population alone, requiring substantial conversion of accreted spirals into post-processed S0s. At the high-mass end, on the other hand, most or all of the satellite S0s can be explained as pre-processed S0s, with little or no conversion of spirals required. This is consistent with the fact that the satellite spiral fraction in the highest-mass bin is basically the same as the central spiral fraction, suggesting that all of the highest-mass spirals have remained spirals after accretion. This can be compared with van den Bosch et al. (2008, esp. their Figure 8), who apply a similar argument to suggest that the high fraction of massive, galaxies which have red colors is largely due to their pre-processing as central galaxies.

The lower panel of figure 18 makes some of this more explicit. Here we show our estimate for the fraction of pre-processed S0s, assumed to be equal to the fraction of central S0s in the top panel. We also estimate the fraction of post-processed S0s using equation 4; as hinted in the top panel, the fraction of satellite S0s which are post-processed increases to lower masses. Finally, we also plot the fraction of “missing” satellite spirals, which is the fraction of central spirals minus the fraction of satellite spirals in halos. This quantity represents the fraction of accreted spirals which are no longer present as spirals; these are assumed to have transformed into S0s or else merged with other galaxies. In each mass bin, the fractions of post-processed S0s and missing spirals are equal within the errors, strongly suggesting that the missing spirals have indeed been converted into (post-processed) S0s.

Figure 18.— Top: Observed fractions of S0 and spiral galaxies as a function of stellar mass for central galaxies (solid points and lines) and for the satellites of massive () halos (open points and dashed lines). Bottom: Estimated fractions for the satellite population of massive halos, divided into “pre-processed” S0 galaxies (pre-existing S0 galaxies accreted by the halo) and “post-processed” S0 galaxies (accreted as spiral galaxies and subsequently transformed). These fractions assume that the morphological fractions of galaxies at the time of accretion matches the currently observed central-galaxy fractions (top panel). We also show the fraction of “missing satellite spirals”—these are galaxies accreted as spirals which are no longer present as spirals (i.e., they are presumably either transformed into S0’s or merged to form ellipticals).

4.3. How Are S0s Formed?

The persistence and visibility of spiral arms clearly correlates with the presence of gas and star formation: spiral galaxy disks are forming stars, while S0 disks are typically passive (e.g., Figure 8). The absence of spiral arms in S0 galaxies can be explained by the combination of increased random motions of disk stars with age, which erases existing spiral patterns, and lack of young stars in regular, “cold” orbits, which would otherwise maintain or reform spiral patterns (see e.g. section 6.1 of Sellwood, 2011, and references therein).

Star forming galaxies at z typically have enough atomic and molecular gas to maintain star formation for only another Gyr on average at present rates (for the statistics of local galaxies see Saintonge et al., 2011). Ongoing disk star formation for times of order the Hubble time thus requires the availability of additional gas, accreted from the surroundings. This gas is usually assumed to be shock-heated upon accretion onto halos, resulting in a “hot atmosphere” which subsequently (in the absence of further heating) cools onto the galaxy (White & Frenk, 1991).

The transformation of spiral galaxies into S0s therefore requires that star formation is suppressed, both by the exhaustion or removal of existing disk gas and by the prevention of further gas accretion from the environment. Our results suggest a difference between the transformation of post-processed satellite galaxies in halos on the one hand, and that of central galaxies in halos down to our limiting halo mass of independent of halo mass – on the other hand. We therefore expect different mechanisms to be responsible for S0 formation in these two regimes.

Finally, whatever mechanisms are operating, they also need to explain the observed structural differences between spirals and S0s. S0s have traditionally been characterized as having extremely high ratios (e.g., Dressler, 1980); for example, the compilation of Simien & de Vaucouleurs (1986) has a mean for S0s. More recent studies which account for variable bulge profiles (i.e., Sérsic instead of de Vaucouleurs profiles) and the effects of additional components such as bars have resulted in lower values for S0s – but the large study using 2D decompositions of disk galaxies by Laurikainen et al. (2010) still finds that the mean (and maximum) values for S0s are higher than those of spirals (though there is considerable overlap, and some S0s have ); see Figure 4 of that paper. Christlein & Zabludoff (2004) constructed separate luminosity functions for disks and for bulges as a function of . For intermediate, galaxies (assumed to be typical for S0s), they found that while the characteristic luminosity of bulges strongly increases with , the characteristic luminosity of disks is almost constant. Simple toy models are then used to show that this is inconsistent with changes in resulting from pure disk fading – but that a model in which evolves through the growth of bulges is consistent with data. We also note that Burstein et al. (2005) presented evidence indicating the -band luminosities of local S0s were, on the whole, too high for all of them to be explained by fading of gas-stripped spirals.

4.3.1 Satellite S0s

We have presented evidence that the majority of S0s in halos were likely accreted as spiral galaxies, and have since been post-processed, leading to their current S0 morphology. We have also shown that lower mass S0s () are more likely to have experienced post-processing, whilst the fraction of higher mass S0s is more consistent with an accreted field population (pre-processed into S0s as central galaxies). Thus, post-processing is more relevant for lower mass disk galaxies, while higher-mass accreted spirals are more likely to persist as spirals in the group environment. This puts potential limits on the post-processing mechanism(s); in this section, we focus on those which remove gas from the galaxy, since that is an essential prerequisite for preventing further star formation and the persistence of spiral structure in the disk.

A promising way of removing gas from spiral galaxies in massive groups and clusters is to remove it via interactions with the gas of the hot intra-group or intra-cluster medium (IGM/ICM). The physical nature of this interaction can – very broadly – take three forms: ram-pressure stripping (Gunn & Gott, 1972), viscous stripping (Nulsen, 1982), and thermal evaporation (Cowie & Songaila, 1977). Ram-pressure refers to the pressure exerted due to the galaxy’s motion relative to the IGM/ICM and acts very quickly in regions of very dense, hot gas such as the cores of massive clusters (see e.g. Moran et al., 2007); ram-pressure stripping can potentially be strong enough to remove tightly-bound cold gas in the galaxy disk. Viscous stripping refers to the slower removal of low density gas via turbulence at the interface between the galaxy and IGM/ICM. Both of these mechanisms depend primarily on the IGM/ICM density and the galaxy velocity. Evaporation instead removes gas via thermally induced collisions, and depends on the temperature of the IGM/ICM; it can also act on central galaxies, and so is not exclusive to satellite galaxies.

There is direct observational evidence for ram-pressure stripping of cold gas from disk galaxies in the Virgo Cluster (see e.g. Gavazzi et al., 2008; Chung et al., 2009, and references therein) and also in the Coma Cluster (e.g., Vollmer et al., 2001). However, Virgo and Coma are relatively massive systems (clusters with ), supporting dense ICMs and rapid galaxy motions, both of which lead to stronger galaxy-ICM interactions. Even here, stripping of disk gas in most cases seems to be partial, acting only on the outer parts of the disk and leaving a more tightly bound core gas component, which can continue forming stars. This is also seen in simulations (e.g. Kapferer et al., 2009). The main problem is that it is not clear whether stripping of tightly bound cold gas can ever operate effectively in lower-mass clusters and groups (e.g., ). Moran et al. (2007) studied passive spirals and S0s in two clusters at and concluded that ram-pressure stripping was significant only in the more massive cluster, with its much denser ICM.

A more widely applicable process is “strangulation” (Larson et al., 1980), which refers to the ram-pressure removal of just the hot gas halo of a galaxy. Since the halo gas is much thinner, hotter, and much less strongly bound than the cold disk gas, it is vulnerable to removal by lower velocities and lower ICM/IGM densities, making it a plausible mechanism for lower-mass clusters and groups. Simulations of strangulation find that, as for ram-pressure stripping of the cold gas, the central, most strongly bound hot gas component can survive the stripping process (McCarthy et al., 2008; Kawata & Mulchaey, 2008; Bekki, 2009). This is not necessarily a problem, however. Partial stripping of the hot gas causes star formation to be suppressed over longer timescales than if all of the hot gas and most or all of the cold gas were stripped (e.g., in the standard ram-pressure-stripping scenario). With little or no cooling of hot gas onto a satellite galaxy, the remaining cold disk gas will be exhausted in Gyr.

Alternatively, a gravitational mechanism might be responsible for the post-processing of group galaxies. Galaxies with an extended history of minor mergers are likely to form a high remnant with S0 morphology (e.g. Bournaud et al., 2007). However, if galaxies follow dark matter, the probability of satellite-satellite mergers is low (Angulo et al., 2009) and so we expect this to be more important in the case of central S0s (see below). A more promising, slow-acting mechanism is the cumulative effect of low-velocity tidal interactions with the other group galaxies (Bekki & Couch, 2011). This is distinct from the frequent, high-velocity encounters in more massive clusters, often referred to as “harassment” (e.g. Moore et al., 1998; Gnedin, 2003). The simulations of Bekki & Couch (2011) show that repeated interactions can drive tidal stripping and compression of the gas, leading to its more rapid exhaustion than in an isolated case; this process also produces bulge growth via central star formation – albeit by only %. Tidal interactions also enhance the random motions of stars, which thickens the disk and helps suppress spiral arms. This mechanism acts preferentially on lower mass galaxies (which are more easily perturbed) and on galaxies in lower mass groups (). Encouragingly, this is consistent with our population of post-processed S0s (predominantly lower panel of Figure 18).

4.3.2 Central S0s

In most cases, the central galaxy of a halo lives at the bottom of the global potential well, and has little or no velocity offset with respect to the hot gas (see Skibba et al., 2011, for more detail and caveats). Therefore, stripping cannot operate under these conditions, and we must look for other mechanisms to suppress star formation in central S0s.

The centers of halos are where galaxy mergers predominate. Since mergers where one or more galaxy is gas-rich can induce starbursts that rapidly consume the gas (plus potential quasar-mode feedback), this is a potential route for forming S0s. Minor mergers, in particular, should be more common than major mergers and have the additional utility of tending to add mass to the bulge without completely destroying the disk (Bekki, 1998; Eliche-Moral et al., 2006; Bournaud et al., 2005, 2007); this would help increase the ratio of central S0s. Of course, major mergers — and multiple minor mergers (e.g., Bournaud et al., 2007) — are more likely to produce an elliptical remnant. Since higher-mass halos, with their richer merger history, are probably more likely to have had major mergers for their central galaxies (e.g., Wang & Kauffmann, 2008), we would expect the central galaxies of higher-mass halos to be ellipticals more often, which is indeed the trend we see for our sample (Figure 7).

This suggests that the existence of S0 galaxies with -band luminosities brighter than any spiral galaxy, as pointed out by Burstein et al. (2005), does not mean S0s cannot form through disk fading of spirals. Instead, it suggests that the most massive S0s are a mixture of S0s which are still the central galaxies within their groups and formerly central (pre-processed) S0s which were accreted into massive groups and clusters. Less massive S0s are then more likely to be post-processed spirals.

We are still left with the problem — similar to that we faced with explaining the lack of recent star-formation activity in central ellipticals — of how to prevent cooling halo gas from accreting onto central S0s and triggering new star formation. In principle, the same AGN-feedback mechanisms invoked for central ellipticals (see Section 4.1) could apply. We do in fact find relatively high radio-AGN frequencies in central S0’s, especially in more massive halos (Figure 13). A possible problem is the lower masses of central black holes in S0s, which could make feedback less efficient. (Since SMBH mass scales with bulge mass rather than total galaxy mass — e.g., Kormendy & Gebhardt 2001, Kormendy et al. 2011 — S0s will tend to have smaller SMBHs than ellipticals of the same stellar mass.) However, recent simulations by Gaspari et al. (2011) suggest that relatively weak feedback may be all that is needed to keep cooling flows from developing in groups. We also see high fractions of optical AGN in central S0s as well (Figure 12), which could be helpful given the evidence that low-luminosity AGN may be associated with the disappearance of central molecular gas even in galaxies having stellar masses of a few (Schawinski et al., 2009).

4.4. Evolution of the S0 Fraction

Comparisons with samples at different redshifts require care – especially where different selection limits, environmental definitions, and classification methods are employed. The top panel of Figure 18 indicates that the S0 fraction is sensitive to the mass or luminosity threshold imposed – a problem that is accentuated when comparing samples from different redshifts and with different photometry.

Since most high-redshift studies where the S0 fractions are computed are for massive clusters, and thus not good direct comparisons with our sample, we compare our local S0 fractions with the group and field sample presented by Wilman et al. (2009). In Figure 5 of that paper, morphological fractions are computed with a luminosity cut of , for comparison with cluster fractions from the literature.101010Selection and systematics are discussed in Section 4.2 of that paper.. Assuming passive evolution, the luminosities of ellipticals and S0s will decrease between and now; thus, we need to adjust our local luminosity cutoff accordingly. Based on the updated calculations of van Dokkum & Franx (2001)111111Available at http://www.astro.yale.edu/dokkum/evocalc/, we estimate mag fading in for E and S0 galaxies, and therefore adopt a local luminosity limit of for comparison purposes.121212We compute plus the correction for oversubtracted background – see Section 2.5. Note that star-forming spiral galaxies are not expected to fade as much as elliptical or S0 galaxies; some may even increase in luminosity. Consequently, the local sample may have an excess of spirals relative to the higher-redshift sample, since some spirals with at now have .

The Wilman et al. (2009) statistics are based on two overall classifications of environment: “groups” and “field”. Their groups do not have halo mass estimates, but they do have velocity dispersions. Since almost all the Wilman et al. groups have dispersion , we divide our local sample into equivalent subsets, with “groups” defined as halos having dispersions (this amounts to 90 groups containing a total of 185 classified galaxies) and the “field” defined as all other halos.

The S0 fraction for the field shows no evolution over this redshift range: % at versus % at . But in groups we do see some evidence for evolution: the fraction rises from % at to % locally. This parallels at least qualitatively the increase in S0 fraction observed for clusters over the same redshift range (e.g., Dressler et al., 1997; Fasano et al., 2000; Poggianti et al., 2009). Quantitatively, it also seems to agree with the evolution in S0 fraction observed by Just et al. (2010) for the lower-mass clusters in their sample (those with velocity dispersion ).

4.5. Differences in AGN/LINER Fraction Between Ellipticals and S0s

Figure 12 shows that the fraction of emission-line AGN (mostly LINERS) is similar for central and satellite galaxies, and does not depend significantly on halo mass. It does increase with stellar mass, and is much higher in S0s than in elliptical galaxies of the same mass (except at the very highest-mass end).

The mass of central supermassive black holes is known to increase with galaxy (more properly, bulge) mass (e.g., Magorrian et al., 1998; Marconi & Hunt, 2003; Häring & Rix, 2004). The increasing fraction of emission-line AGN with galaxy mass could thus potentially result from more powerful ionizing sources due to higher black hole masses. However, the mass of an elliptical galaxy is larger than the bulge mass of an S0 of equivalent stellar mass. The implication of a tight bulge mass–black hole mass relation is that an elliptical galaxy should also have a more massive black hole. In fact, however, we generally see a higher fraction of both optical AGN and radio-AGN in S0 galaxies, (Figures 12 and 13).

One possible solution might be that some S0s have retained a small amount of tightly bound gas in their cores, which can then be ionized by accretion onto the black hole. The absence in radio-bright elliptical galaxies of H-emitting ionized gas suggests this gas is truly absent – either because it is too hot or because it has been expelled. Gas is heated to X-ray emitting temperatures during simulations of major mergers (e.g., Cox et al., 2006) – but the inclusion of hot gas in suites of merger simulations is still preliminary (see, e.g., Moster et al., 2011), and the results are highly sensitive to the balance of heating and cooling.

5. Conclusions

We have created a catalog of 1064 nearby (median ), bright ( and ) galaxies, which combines RC3 morphological classifications and the NYU-VAGC version of the SDSS DR4 photometric and spectroscopic data; magnitudes have been corrected to account for the undersubtracted background, and stellar masses were determined using color-based mass-to-light ratios calibrated by Zibetti et al. (2009) and applied to the -band absolute magnitudes. The main morphological classifications (elliptical vs. S0 vs. spiral) were checked by visual examination of SDSS images; a total of 165 galaxies ended up being re-classified, and 55 more were classified for the first time.

To this dataset we added halo masses and central vs. satellite status (where “central” = most massive galaxy in its group) from the group catalog of Yang et al. (2007, Y07), which resulted in a total of 911 galaxies with halo mass assignments; 729 of these are central galaxies and 182 are satellites. The main advantage of the Y07 catalog is that it spans the full range of halo masses down to . This allows us to describe the dependence of morphological fractions on halo mass at for the first time, from smaller clusters down to single-galaxy halos. (We also determined total number of galaxies per group and group velocity dispersions for the Y07 groups in our sample, in order to check the robustness of the halo-mass-based results.) Using the full SDSS DR4 catalog as a parent sample, we characterized the selection function of our catalog as a function of magnitude (synthesized using SDSS colors) and galaxy size (, the radius containing 90% of the Petrosian flux in r-band). Our sample is robust to a luminosity limit of , which corresponds to a stellar mass of for E and S0 galaxies. Galaxies are weighted to correct for the selection bias, and are also weighted by to correct for Malmquist bias. This allows us to examine the fraction of galaxies of various types as a function of stellar and halo mass. We use a weighted logistic regression method to allow us to assess the statistical significance of apparent trends. This method has the advantages of modeling a binomial property without binning of data, and it allows for individual data points to have weights.

We find that the global fraction of elliptical galaxies increases with galaxy luminosity and with stellar mass, but not with halo mass. The fraction of S0s declines to high stellar mass, but increases with halo mass, group velocity dispersion and number of neighbours. These results are consistent with previous work at higher redshift which found the S0 fraction to increase in groups relative to the field population, whilst the elliptical fraction remains roughly constant (Wilman et al., 2009).

The fraction of central galaxies with elliptical morphology increases with stellar and halo mass, consistent with their formation in mergers. In contrast, the fraction of satellite ellipticals is globally low at all halo masses, but increases with stellar mass. We interpret this as evidence that satellite ellipticals were formed as the central galaxies of progenitor halos, which were subsequently accreted onto their present halo.

Limited to , a modest fraction of central galaxies are S0s (%, with little dependence on stellar or halo mass). The remaining S0s are satellites of massive halos only – we find that the fraction of satellites with S0 morphology rises from % in halos with to % above this threshold. Presuming S0s to be spirals in which star formation has been suppressed (leading in turn to the suppression of spiral arms), we interpret our result as a strong indication that there are two populations of S0s, in which star formation has been suppressed in different ways.

Central S0s may be formed via suppression of star formation during minor mergers and/or by feedback from AGN, with similarities to the elliptical population. Satellite S0s which became S0s while they were still central galaxies within their progenitor halos constitute a pre-processed population which can account for up to of the satellite S0s, including all of those with .

However, the higher fraction of S0s in higher-mass halos implies that many satellite S0s were accreted as spiral galaxies. These accreted spirals were then post-processed, becoming satellite S0s, and are the dominant source of satellite S0s in the range . Altogether, we estimate that % of our satellite S0s were accreted as spirals.

Central S0 and elliptical galaxies frequently host radio sources, consistent with radio-mode heating of the surrounding hot gas. This heating may offset cooling onto these galaxies, and thus suppress star formation. However, S0s host ionized gas components – mostly LINERs – much more frequently than elliptical galaxies of the same mass.

We find no strong dependence of structural subcomponents – bars, inner rings/spirals, outer rings – on environment, in contrast to some earlier studies (e.g. Elmegreen et al., 1992), though we do find evidence that the frequency of both bars and inner rings increases, and the frequency of outer rings decreases, with galaxy mass.

By comparing our results with the study of Wilman et al. (2009), we find tentative evidence that the fraction of bright S0s in intermediate-mass groups (those with velocity dispersions ) has increased in the last Gyr, rising from % at to %. This is at least qualitatively consistent with increases in the fraction of S0s in clusters reported by other studies.

We would particularly like to thank our student interns, Mareike Berger and Daniel Gunzl, for helping check the existing morphological classifications of the galaxies, and Niv Drory for helping set up the initial database system. We thank the referee for some very helpful suggestions and comments which contributed significantly to the improvement of this paper. We also benefitted from helpful conversations with, and comments from, Gabriella de Lucia, Fabio Fontanot, John Mulchaey, Stefano Zibetti, Roberto Saglia, Preethi Nair, Simone Weinmann, Andrea Biviano, and Dimitri Gadotti. P.E. was supported by DFG Priority Program 1177 (“Witnesses of Cosmic History: Formation and evolution of black holes, galaxies and their environment”). Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Korean Scientist Group, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington. This research also made use of the Lyon-Meudon Extragalactic Database (LEDA; http: //leda.univ-lyon1.fr) and the NASA/IPAC Extragalactic Database (NED); the latter is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

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